%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX171^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:38 AM UTC 2026
% Result : Theorem 47.53s 7.11s
% Output : Refutation 47.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX171^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:11:29 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.24/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.40 % (2685728)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.69/0.40 % (2685739)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.69/0.40 % (2685739)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.69/0.40 % (2685739)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3187593021:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.69/0.40 % (2685735)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2147420776:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.69/0.40 % (2685733)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3125675139:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.69/0.40 % (2685734)lrs+10_16_si=on:nwc=1.5:random_seed=2332190367:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.69/0.40 % (2685737)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2464046372:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.69/0.40 % (2685736)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3636795238:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.69/0.40 % (2685738)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3194163459:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.69/0.40 % (2685735)Instruction limit reached!
% 0.69/0.40 % (2685735)------------------------------
% 0.69/0.40 % (2685735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.40 % (2685735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.40 % (2685735)CaDiCaL version: 2.1.3
% 0.69/0.40 % (2685735)Termination reason: Instruction limit
% 0.69/0.40 % (2685735)Termination phase: shuffling
% 0.69/0.40 % (2685735)Time elapsed: 0.002 s
% 0.69/0.40 % (2685735)Peak memory usage: 10 MB
% 0.69/0.40 % (2685735)Instructions burned: 3 (million)
% 0.69/0.40 % (2685734)Instruction limit reached!
% 0.69/0.40 % (2685734)------------------------------
% 0.69/0.40 % (2685734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.40 % (2685734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.40 % (2685734)CaDiCaL version: 2.1.3
% 0.69/0.40 % (2685734)Termination reason: Instruction limit
% 0.69/0.40 % (2685734)Termination phase: shuffling
% 0.69/0.40 % (2685734)Time elapsed: 0.008 s
% 0.69/0.40 % (2685734)Peak memory usage: 10 MB
% 0.69/0.40 % (2685734)Instructions burned: 19 (million)
% 0.69/0.40 % (2685737)Instruction limit reached!
% 0.69/0.40 % (2685737)------------------------------
% 0.69/0.40 % (2685737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.40 % (2685737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.40 % (2685737)CaDiCaL version: 2.1.3
% 0.69/0.40 % (2685737)Termination reason: Instruction limit
% 0.69/0.40 % (2685737)Termination phase: Property scanning
% 0.69/0.40 % (2685737)Time elapsed: 0.011 s
% 0.69/0.40 % (2685737)Peak memory usage: 10 MB
% 0.69/0.40 % (2685737)Instructions burned: 25 (million)
% 0.69/0.40 % (2685747)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=42556066:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.40 % (2685747)Instruction limit reached!
% 0.69/0.40 % (2685747)------------------------------
% 0.69/0.40 % (2685747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.40 % (2685747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.40 % (2685747)CaDiCaL version: 2.1.3
% 0.69/0.40 % (2685747)Termination reason: Instruction limit
% 0.69/0.40 % (2685747)Termination phase: shuffling
% 0.69/0.40 % (2685747)Time elapsed: 0.003 s
% 0.69/0.40 % (2685747)Peak memory usage: 9 MB
% 0.69/0.40 % (2685747)Instructions burned: 6 (million)
% 0.69/0.40 % (2685749)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.44 % (2685739)Instruction limit reached!
% 0.69/0.44 % (2685739)------------------------------
% 0.69/0.44 % (2685739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685739)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685739)Termination reason: Instruction limit
% 0.69/0.44 % (2685739)Termination phase: Property scanning
% 0.69/0.44 % (2685739)Time elapsed: 0.037 s
% 0.69/0.44 % (2685739)Peak memory usage: 13 MB
% 0.69/0.44 % (2685739)Instructions burned: 161 (million)
% 0.69/0.44 % (2685749)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2486184775:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.69/0.44 % (2685738)Instruction limit reached!
% 0.69/0.44 % (2685738)------------------------------
% 0.69/0.44 % (2685738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685738)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685738)Termination reason: Instruction limit
% 0.69/0.44 % (2685738)Termination phase: Preprocessing 3
% 0.69/0.44 % (2685738)Time elapsed: 0.034 s
% 0.69/0.44 % (2685738)Peak memory usage: 12 MB
% 0.69/0.44 % (2685738)Instructions burned: 77 (million)
% 0.69/0.44 % (2685749)Instruction limit reached!
% 0.69/0.44 % (2685749)------------------------------
% 0.69/0.44 % (2685749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685749)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685749)Termination reason: Instruction limit
% 0.69/0.44 % (2685749)Termination phase: shuffling
% 0.69/0.44 % (2685749)Time elapsed: 0.004 s
% 0.69/0.44 % (2685749)Peak memory usage: 10 MB
% 0.69/0.44 % (2685749)Instructions burned: 9 (million)
% 0.69/0.44 % (2685753)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.69/0.44 % (2685753)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.44 % (2685748)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=615635451:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.69/0.44 % (2685733)Instruction limit reached!
% 0.69/0.44 % (2685733)------------------------------
% 0.69/0.44 % (2685733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685733)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685733)Termination reason: Instruction limit
% 0.69/0.44 % (2685733)Termination phase: Preprocessing 3
% 0.69/0.44 % (2685733)Time elapsed: 0.040 s
% 0.69/0.44 % (2685733)Peak memory usage: 12 MB
% 0.69/0.44 % (2685733)Instructions burned: 88 (million)
% 0.69/0.44 % (2685753)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=503757514:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.69/0.44 % (2685751)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2864093372:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.69/0.44 % (2685748)Instruction limit reached!
% 0.69/0.44 % (2685748)------------------------------
% 0.69/0.44 % (2685748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685748)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685748)Termination reason: Instruction limit
% 0.69/0.44 % (2685748)Termination phase: shuffling
% 0.69/0.44 % (2685748)Time elapsed: 0.007 s
% 0.69/0.44 % (2685748)Peak memory usage: 9 MB
% 0.69/0.44 % (2685748)Instructions burned: 6 (million)
% 0.69/0.44 % (2685753)Instruction limit reached!
% 0.69/0.44 % (2685753)------------------------------
% 0.69/0.44 % (2685753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.44 % (2685753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.44 % (2685753)CaDiCaL version: 2.1.3
% 0.69/0.44 % (2685753)Termination reason: Instruction limit
% 0.69/0.47 % (2685753)Termination phase: shuffling
% 0.69/0.47 % (2685753)Time elapsed: 0.007 s
% 0.69/0.47 % (2685753)Peak memory usage: 10 MB
% 0.69/0.47 % (2685753)Instructions burned: 31 (million)
% 0.69/0.47 % (2685751)Instruction limit reached!
% 0.69/0.47 % (2685751)------------------------------
% 0.69/0.47 % (2685751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.47 % (2685751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.47 % (2685751)CaDiCaL version: 2.1.3
% 0.69/0.47 % (2685751)Termination reason: Instruction limit
% 0.69/0.47 % (2685751)Termination phase: shuffling
% 0.69/0.47 % (2685751)Time elapsed: 0.006 s
% 0.69/0.47 % (2685751)Peak memory usage: 10 MB
% 0.69/0.47 % (2685751)Instructions burned: 13 (million)
% 0.69/0.47 % (2685755)lrs+10_1_si=on:cs=on:random_seed=2254517280:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.69/0.47 % (2685757)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.69/0.47 % (2685754)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=665916892:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.69/0.47 % (2685761)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4048799882:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.69/0.47 % (2685755)Instruction limit reached!
% 0.69/0.47 % (2685755)------------------------------
% 0.69/0.47 % (2685755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.47 % (2685755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.47 % (2685755)CaDiCaL version: 2.1.3
% 0.69/0.47 % (2685755)Termination reason: Instruction limit
% 0.69/0.47 % (2685755)Termination phase: shuffling
% 0.69/0.47 % (2685755)Time elapsed: 0.004 s
% 0.69/0.47 % (2685755)Peak memory usage: 10 MB
% 0.69/0.47 % (2685755)Instructions burned: 9 (million)
% 0.69/0.47 % (2685757)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3310238653:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.47 % (2685757)Instruction limit reached!
% 0.69/0.47 % (2685757)------------------------------
% 0.69/0.47 % (2685757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.47 % (2685757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.47 % (2685757)CaDiCaL version: 2.1.3
% 0.69/0.47 % (2685757)Termination reason: Instruction limit
% 0.69/0.47 % (2685757)Termination phase: shuffling
% 0.69/0.47 % (2685757)Time elapsed: 0.003 s
% 0.69/0.47 % (2685757)Peak memory usage: 10 MB
% 0.69/0.47 % (2685757)Instructions burned: 7 (million)
% 0.69/0.47 % (2685760)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2251333365:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.69/0.47 % (2685762)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=970426884:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.69/0.47 % (2685767)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1235303759:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.69/0.47 % (2685762)Instruction limit reached!
% 0.69/0.47 % (2685762)------------------------------
% 0.69/0.47 % (2685762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.47 % (2685762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.47 % (2685762)CaDiCaL version: 2.1.3
% 0.69/0.47 % (2685762)Termination reason: Instruction limit
% 0.69/0.47 % (2685762)Termination phase: Property scanning
% 0.69/0.47 % (2685762)Time elapsed: 0.011 s
% 0.69/0.47 % (2685762)Peak memory usage: 10 MB
% 0.69/0.47 % (2685762)Instructions burned: 27 (million)
% 0.69/0.47 % (2685768)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3601354573:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.69/0.47 % (2685760)Instruction limit reached!
% 0.69/0.47 % (2685760)------------------------------
% 0.69/0.47 % (2685760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.47 % (2685760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685760)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685760)Termination reason: Instruction limit
% 1.52/0.53 % (2685760)Termination phase: Preprocessing 3
% 1.52/0.53 % (2685760)Time elapsed: 0.017 s
% 1.52/0.53 % (2685760)Peak memory usage: 11 MB
% 1.52/0.53 % (2685760)Instructions burned: 39 (million)
% 1.52/0.53 % (2685767)Instruction limit reached!
% 1.52/0.53 % (2685767)------------------------------
% 1.52/0.53 % (2685767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685767)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685767)Termination reason: Instruction limit
% 1.52/0.53 % (2685767)Termination phase: shuffling
% 1.52/0.53 % (2685767)Time elapsed: 0.006 s
% 1.52/0.53 % (2685767)Peak memory usage: 10 MB
% 1.52/0.53 % (2685767)Instructions burned: 14 (million)
% 1.52/0.53 % (2685772)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1254834135:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.52/0.53 % (2685775)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1271439727:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.52/0.53 % (2685774)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3608560326:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.52/0.53 % (2685774)Instruction limit reached!
% 1.52/0.53 % (2685774)------------------------------
% 1.52/0.53 % (2685774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685774)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685774)Termination reason: Instruction limit
% 1.52/0.53 % (2685774)Termination phase: shuffling
% 1.52/0.53 % (2685774)Time elapsed: 0.002 s
% 1.52/0.53 % (2685774)Peak memory usage: 9 MB
% 1.52/0.53 % (2685774)Instructions burned: 4 (million)
% 1.52/0.53 % (2685772)Instruction limit reached!
% 1.52/0.53 % (2685772)------------------------------
% 1.52/0.53 % (2685772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685772)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685772)Termination reason: Instruction limit
% 1.52/0.53 % (2685772)Termination phase: shuffling
% 1.52/0.53 % (2685772)Time elapsed: 0.007 s
% 1.52/0.53 % (2685772)Peak memory usage: 10 MB
% 1.52/0.53 % (2685772)Instructions burned: 16 (million)
% 1.52/0.53 % (2685775)Instruction limit reached!
% 1.52/0.53 % (2685775)------------------------------
% 1.52/0.53 % (2685775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685775)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685775)Termination reason: Instruction limit
% 1.52/0.53 % (2685775)Termination phase: shuffling
% 1.52/0.53 % (2685775)Time elapsed: 0.012 s
% 1.52/0.53 % (2685775)Peak memory usage: 10 MB
% 1.52/0.53 % (2685775)Instructions burned: 27 (million)
% 1.52/0.53 % (2685761)Instruction limit reached!
% 1.52/0.53 % (2685761)------------------------------
% 1.52/0.53 % (2685761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.53 % (2685761)CaDiCaL version: 2.1.3
% 1.52/0.53 % (2685761)Termination reason: Instruction limit
% 1.52/0.53 % (2685761)Termination phase: Saturation
% 1.52/0.53 % (2685761)Time elapsed: 0.059 s
% 1.52/0.53 % (2685761)Peak memory usage: 15 MB
% 1.52/0.53 % (2685761)Instructions burned: 252 (million)
% 1.52/0.53 % (2685779)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=312202825:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.52/0.53 % (2685780)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1028198390:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.52/0.53 % (2685782)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.52/0.53 % (2685754)Instruction limit reached!
% 1.52/0.53 % (2685754)------------------------------
% 1.52/0.53 % (2685754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.53 % (2685754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.61 % (2685754)CaDiCaL version: 2.1.3
% 2.19/0.61 % (2685754)Termination reason: Instruction limit
% 2.19/0.61 % (2685754)Termination phase: Saturation
% 2.19/0.61 % (2685754)Time elapsed: 0.069 s
% 2.19/0.61 % (2685754)Peak memory usage: 12 MB
% 2.19/0.61 % (2685754)Instructions burned: 87 (million)
% 2.19/0.61 % (2685782)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=2874038705:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.19/0.61 % (2685781)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.19/0.61 % (2685781)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.19/0.61 % (2685782)Instruction limit reached!
% 2.19/0.61 % (2685782)------------------------------
% 2.19/0.61 % (2685782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.61 % (2685782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.61 % (2685782)CaDiCaL version: 2.1.3
% 2.19/0.61 % (2685782)Termination reason: Instruction limit
% 2.19/0.61 % (2685782)Termination phase: shuffling
% 2.19/0.61 % (2685782)Time elapsed: 0.002 s
% 2.19/0.61 % (2685782)Peak memory usage: 10 MB
% 2.19/0.61 % (2685782)Instructions burned: 10 (million)
% 2.19/0.61 % (2685781)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3966226955:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.19/0.61 % (2685779)Instruction limit reached!
% 2.19/0.61 % (2685779)------------------------------
% 2.19/0.61 % (2685779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.61 % (2685779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.61 % (2685779)CaDiCaL version: 2.1.3
% 2.19/0.61 % (2685779)Termination reason: Instruction limit
% 2.19/0.61 % (2685779)Termination phase: shuffling
% 2.19/0.61 % (2685779)Time elapsed: 0.011 s
% 2.19/0.61 % (2685779)Peak memory usage: 10 MB
% 2.19/0.61 % (2685779)Instructions burned: 25 (million)
% 2.19/0.61 % (2685787)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=239763723:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.19/0.61 % (2685781)Instruction limit reached!
% 2.19/0.61 % (2685781)------------------------------
% 2.19/0.61 % (2685781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.61 % (2685781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.61 % (2685781)CaDiCaL version: 2.1.3
% 2.19/0.61 % (2685781)Termination reason: Instruction limit
% 2.19/0.61 % (2685781)Termination phase: shuffling
% 2.19/0.61 % (2685781)Time elapsed: 0.007 s
% 2.19/0.61 % (2685781)Peak memory usage: 10 MB
% 2.19/0.61 % (2685781)Instructions burned: 15 (million)
% 2.19/0.61 % (2685787)Instruction limit reached!
% 2.19/0.61 % (2685787)------------------------------
% 2.19/0.61 % (2685787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.61 % (2685787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.61 % (2685787)CaDiCaL version: 2.1.3
% 2.19/0.61 % (2685787)Termination reason: Instruction limit
% 2.19/0.61 % (2685787)Termination phase: shuffling
% 2.19/0.61 % (2685787)Time elapsed: 0.002 s
% 2.19/0.61 % (2685787)Peak memory usage: 9 MB
% 2.19/0.61 % (2685787)Instructions burned: 7 (million)
% 2.19/0.61 % (2685786)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1983495543:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.19/0.61 % (2685792)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3461028350:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.19/0.61 % (2685789)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1079919509:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.19/0.61 % (2685791)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=189641341:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.44/0.68 % (2685786)Instruction limit reached!
% 2.44/0.68 % (2685786)------------------------------
% 2.44/0.68 % (2685786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685786)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685786)Termination reason: Instruction limit
% 2.44/0.68 % (2685786)Termination phase: Property scanning
% 2.44/0.68 % (2685786)Time elapsed: 0.014 s
% 2.44/0.68 % (2685786)Peak memory usage: 10 MB
% 2.44/0.68 % (2685786)Instructions burned: 32 (million)
% 2.44/0.68 % (2685789)Instruction limit reached!
% 2.44/0.68 % (2685789)------------------------------
% 2.44/0.68 % (2685789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685789)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685789)Termination reason: Instruction limit
% 2.44/0.68 % (2685789)Termination phase: shuffling
% 2.44/0.68 % (2685789)Time elapsed: 0.011 s
% 2.44/0.68 % (2685789)Peak memory usage: 10 MB
% 2.44/0.68 % (2685789)Instructions burned: 23 (million)
% 2.44/0.68 % (2685791)Instruction limit reached!
% 2.44/0.68 % (2685791)------------------------------
% 2.44/0.68 % (2685791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685791)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685791)Termination reason: Instruction limit
% 2.44/0.68 % (2685791)Termination phase: shuffling
% 2.44/0.68 % (2685791)Time elapsed: 0.009 s
% 2.44/0.68 % (2685791)Peak memory usage: 10 MB
% 2.44/0.68 % (2685791)Instructions burned: 20 (million)
% 2.44/0.68 % (2685780)Instruction limit reached!
% 2.44/0.68 % (2685780)------------------------------
% 2.44/0.68 % (2685780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685780)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685780)Termination reason: Instruction limit
% 2.44/0.68 % (2685780)Termination phase: Preprocessing 3
% 2.44/0.68 % (2685780)Time elapsed: 0.047 s
% 2.44/0.68 % (2685780)Peak memory usage: 11 MB
% 2.44/0.68 % (2685780)Instructions burned: 62 (million)
% 2.44/0.68 % (2685797)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=428661521:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.44/0.68 % (2685799)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=850009297:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.44/0.68 % (2685800)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.44/0.68 % (2685800)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=290355228:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.44/0.68 % (2685800)Instruction limit reached!
% 2.44/0.68 % (2685800)------------------------------
% 2.44/0.68 % (2685800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685800)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685800)Termination reason: Instruction limit
% 2.44/0.68 % (2685800)Termination phase: shuffling
% 2.44/0.68 % (2685800)Time elapsed: 0.004 s
% 2.44/0.68 % (2685800)Peak memory usage: 9 MB
% 2.44/0.68 % (2685800)Instructions burned: 9 (million)
% 2.44/0.68 % (2685798)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1638375063:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.44/0.68 % (2685799)Instruction limit reached!
% 2.44/0.68 % (2685799)------------------------------
% 2.44/0.68 % (2685799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.68 % (2685799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.68 % (2685799)CaDiCaL version: 2.1.3
% 2.44/0.68 % (2685799)Termination reason: Instruction limit
% 2.44/0.68 % (2685799)Termination phase: Preprocessing 2
% 2.44/0.68 % (2685799)Time elapsed: 0.018 s
% 2.44/0.68 % (2685799)Peak memory usage: 11 MB
% 2.44/0.68 % (2685799)Instructions burned: 42 (million)
% 2.44/0.68 % (2685804)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4080318907:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.65/0.75 % (2685806)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=1625829325:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.65/0.75 % (2685768)Instruction limit reached!
% 2.65/0.75 % (2685768)------------------------------
% 2.65/0.75 % (2685768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (2685768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (2685768)CaDiCaL version: 2.1.3
% 2.65/0.75 % (2685768)Termination reason: Instruction limit
% 2.65/0.75 % (2685768)Termination phase: Saturation
% 2.65/0.75 % (2685768)Time elapsed: 0.142 s
% 2.65/0.75 % (2685768)Peak memory usage: 15 MB
% 2.65/0.75 % (2685768)Instructions burned: 328 (million)
% 2.65/0.75 % (2685809)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.65/0.75 % (2685797)Instruction limit reached!
% 2.65/0.75 % (2685797)------------------------------
% 2.65/0.75 % (2685797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (2685797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (2685797)CaDiCaL version: 2.1.3
% 2.65/0.75 % (2685797)Termination reason: Instruction limit
% 2.65/0.75 % (2685797)Termination phase: Twee Goal Transformation
% 2.65/0.75 % (2685797)Time elapsed: 0.062 s
% 2.65/0.75 % (2685797)Peak memory usage: 13 MB
% 2.65/0.75 % (2685797)Instructions burned: 143 (million)
% 2.65/0.75 % (2685809)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3932195907:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.65/0.75 % (2685809)Instruction limit reached!
% 2.65/0.75 % (2685809)------------------------------
% 2.65/0.75 % (2685809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (2685809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (2685809)CaDiCaL version: 2.1.3
% 2.65/0.75 % (2685809)Termination reason: Instruction limit
% 2.65/0.75 % (2685809)Termination phase: shuffling
% 2.65/0.75 % (2685809)Time elapsed: 0.003 s
% 2.65/0.75 % (2685809)Peak memory usage: 9 MB
% 2.65/0.75 % (2685809)Instructions burned: 7 (million)
% 2.65/0.75 % (2685810)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=811485435:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.65/0.75 % (2685812)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2860948727:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.65/0.75 % (2685810)Instruction limit reached!
% 2.65/0.75 % (2685810)------------------------------
% 2.65/0.75 % (2685810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (2685810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (2685810)CaDiCaL version: 2.1.3
% 2.65/0.75 % (2685810)Termination reason: Instruction limit
% 2.65/0.75 % (2685810)Termination phase: shuffling
% 2.65/0.75 % (2685810)Time elapsed: 0.011 s
% 2.65/0.75 % (2685810)Peak memory usage: 10 MB
% 2.65/0.75 % (2685810)Instructions burned: 24 (million)
% 2.65/0.75 % (2685812)Instruction limit reached!
% 2.65/0.75 % (2685812)------------------------------
% 2.65/0.75 % (2685812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.75 % (2685812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.75 % (2685812)CaDiCaL version: 2.1.3
% 2.65/0.75 % (2685812)Termination reason: Instruction limit
% 2.65/0.75 % (2685812)Termination phase: shuffling
% 2.65/0.75 % (2685812)Time elapsed: 0.009 s
% 2.65/0.75 % (2685812)Peak memory usage: 10 MB
% 2.65/0.75 % (2685812)Instructions burned: 20 (million)
% 2.65/0.75 % (2685815)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1563647414:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.65/0.75 % (2685804)Instruction limit reached!
% 2.65/0.75 % (2685804)------------------------------
% 2.65/0.75 % (2685804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/0.81 % (2685804)CaDiCaL version: 2.1.3
% 3.33/0.81 % (2685804)Termination reason: Instruction limit
% 3.33/0.81 % (2685804)Termination phase: Saturation
% 3.33/0.81 % (2685804)Time elapsed: 0.080 s
% 3.33/0.81 % (2685804)Peak memory usage: 14 MB
% 3.33/0.81 % (2685804)Instructions burned: 181 (million)
% 3.33/0.81 % (2685816)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=932899846:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.33/0.81 % (2685806)Instruction limit reached!
% 3.33/0.81 % (2685806)------------------------------
% 3.33/0.81 % (2685806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/0.81 % (2685806)CaDiCaL version: 2.1.3
% 3.33/0.81 % (2685806)Termination reason: Instruction limit
% 3.33/0.81 % (2685806)Termination phase: Property scanning
% 3.33/0.81 % (2685806)Time elapsed: 0.076 s
% 3.33/0.81 % (2685806)Peak memory usage: 13 MB
% 3.33/0.81 % (2685806)Instructions burned: 179 (million)
% 3.33/0.81 % (2685818)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3208539475:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.33/0.81 % (2685820)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3105187764:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.33/0.81 % (2685736)Instruction limit reached!
% 3.33/0.81 % (2685736)------------------------------
% 3.33/0.81 % (2685736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/0.81 % (2685736)CaDiCaL version: 2.1.3
% 3.33/0.81 % (2685736)Termination reason: Instruction limit
% 3.33/0.81 % (2685736)Termination phase: Saturation
% 3.33/0.81 % (2685736)Time elapsed: 0.337 s
% 3.33/0.81 % (2685736)Peak memory usage: 18 MB
% 3.33/0.81 % (2685736)Instructions burned: 635 (million)
% 3.33/0.81 % (2685818)Instruction limit reached!
% 3.33/0.81 % (2685818)------------------------------
% 3.33/0.81 % (2685818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/0.81 % (2685818)CaDiCaL version: 2.1.3
% 3.33/0.81 % (2685818)Termination reason: Instruction limit
% 3.33/0.81 % (2685818)Termination phase: SInE selection
% 3.33/0.81 % (2685818)Time elapsed: 0.020 s
% 3.33/0.81 % (2685818)Peak memory usage: 10 MB
% 3.33/0.81 % (2685818)Instructions burned: 46 (million)
% 3.33/0.81 % (2685798)Instruction limit reached!
% 3.33/0.81 % (2685798)------------------------------
% 3.33/0.81 % (2685798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/0.81 % (2685798)CaDiCaL version: 2.1.3
% 3.33/0.81 % (2685798)Termination reason: Instruction limit
% 3.33/0.81 % (2685798)Termination phase: Property scanning
% 3.33/0.81 % (2685798)Time elapsed: 0.145 s
% 3.33/0.81 % (2685798)Peak memory usage: 13 MB
% 3.33/0.81 % (2685798)Instructions burned: 194 (million)
% 3.33/0.81 % (2685824)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.33/0.81 % (2685823)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1754905226:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.33/0.81 % (2685824)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=352703105:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.33/0.81 % (2685825)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3924660899:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.33/0.81 % (2685823)Instruction limit reached!
% 3.33/0.81 % (2685823)------------------------------
% 3.33/0.81 % (2685823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.33/0.81 % (2685823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685823)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685823)Termination reason: Instruction limit
% 3.85/0.91 % (2685823)Termination phase: shuffling
% 3.85/0.91 % (2685823)Time elapsed: 0.009 s
% 3.85/0.91 % (2685823)Peak memory usage: 10 MB
% 3.85/0.91 % (2685823)Instructions burned: 21 (million)
% 3.85/0.91 % (2685825)Instruction limit reached!
% 3.85/0.91 % (2685825)------------------------------
% 3.85/0.91 % (2685825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685825)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685825)Termination reason: Instruction limit
% 3.85/0.91 % (2685825)Termination phase: shuffling
% 3.85/0.91 % (2685825)Time elapsed: 0.007 s
% 3.85/0.91 % (2685825)Peak memory usage: 10 MB
% 3.85/0.91 % (2685825)Instructions burned: 15 (million)
% 3.85/0.91 % (2685829)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3128501893:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 3.85/0.91 % (2685830)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=3796405584:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 3.85/0.91 % (2685829)Instruction limit reached!
% 3.85/0.91 % (2685829)------------------------------
% 3.85/0.91 % (2685829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685829)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685829)Termination reason: Instruction limit
% 3.85/0.91 % (2685829)Termination phase: SInE selection
% 3.85/0.91 % (2685829)Time elapsed: 0.028 s
% 3.85/0.91 % (2685829)Peak memory usage: 11 MB
% 3.85/0.91 % (2685829)Instructions burned: 67 (million)
% 3.85/0.91 % (2685830)Instruction limit reached!
% 3.85/0.91 % (2685830)------------------------------
% 3.85/0.91 % (2685830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685830)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685830)Termination reason: Instruction limit
% 3.85/0.91 % (2685830)Termination phase: Preprocessing 3
% 3.85/0.91 % (2685830)Time elapsed: 0.022 s
% 3.85/0.91 % (2685830)Peak memory usage: 11 MB
% 3.85/0.91 % (2685830)Instructions burned: 51 (million)
% 3.85/0.91 % (2685792)Instruction limit reached!
% 3.85/0.91 % (2685792)------------------------------
% 3.85/0.91 % (2685792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685792)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685792)Termination reason: Instruction limit
% 3.85/0.91 % (2685792)Termination phase: Saturation
% 3.85/0.91 % (2685792)Time elapsed: 0.269 s
% 3.85/0.91 % (2685792)Peak memory usage: 14 MB
% 3.85/0.91 % (2685792)Instructions burned: 1241 (million)
% 3.85/0.91 % (2685835)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2239880185:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.85/0.91 % (2685834)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3643815429:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.85/0.91 % (2685833)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2436007021:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.85/0.91 % (2685835)Instruction limit reached!
% 3.85/0.91 % (2685835)------------------------------
% 3.85/0.91 % (2685835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/0.91 % (2685835)CaDiCaL version: 2.1.3
% 3.85/0.91 % (2685835)Termination reason: Instruction limit
% 3.85/0.91 % (2685835)Termination phase: Property scanning
% 3.85/0.91 % (2685835)Time elapsed: 0.008 s
% 3.85/0.91 % (2685835)Peak memory usage: 10 MB
% 3.85/0.91 % (2685835)Instructions burned: 36 (million)
% 3.85/0.91 % (2685824)Instruction limit reached!
% 3.85/0.91 % (2685824)------------------------------
% 3.85/0.91 % (2685824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.85/0.91 % (2685824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685824)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685824)Termination reason: Instruction limit
% 5.35/1.06 % (2685824)Termination phase: Saturation
% 5.35/1.06 % (2685824)Time elapsed: 0.086 s
% 5.35/1.06 % (2685824)Peak memory usage: 13 MB
% 5.35/1.06 % (2685824)Instructions burned: 202 (million)
% 5.35/1.06 % (2685820)Refutation not found, incomplete strategy
% 5.35/1.06 % (2685820)------------------------------
% 5.35/1.06 % (2685820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.06 % (2685820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685820)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685820)Termination reason: Refutation not found, incomplete strategy
% 5.35/1.06 % (2685820)Time elapsed: 0.124 s
% 5.35/1.06 % (2685820)Peak memory usage: 16 MB
% 5.35/1.06 % (2685820)Instructions burned: 273 (million)
% 5.35/1.06 % (2685820)------------------------------
% 5.35/1.06 % (2685820)------------------------------
% 5.35/1.06 % (2685833)Instruction limit reached!
% 5.35/1.06 % (2685833)------------------------------
% 5.35/1.06 % (2685833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.06 % (2685833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685833)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685833)Termination reason: Instruction limit
% 5.35/1.06 % (2685833)Termination phase: shuffling
% 5.35/1.06 % (2685833)Time elapsed: 0.014 s
% 5.35/1.06 % (2685833)Peak memory usage: 10 MB
% 5.35/1.06 % (2685833)Instructions burned: 31 (million)
% 5.35/1.06 % (2685839)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3847256145:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.35/1.06 % (2685840)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.35/1.06 % (2685840)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3406114199:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.35/1.06 % (2685841)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=224444140:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.35/1.06 % (2685842)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3809402199:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 5.35/1.06 % (2685839)Instruction limit reached!
% 5.35/1.06 % (2685839)------------------------------
% 5.35/1.06 % (2685839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.06 % (2685839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685839)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685839)Termination reason: Instruction limit
% 5.35/1.06 % (2685839)Termination phase: Preprocessing 3
% 5.35/1.06 % (2685839)Time elapsed: 0.015 s
% 5.35/1.06 % (2685839)Peak memory usage: 12 MB
% 5.35/1.06 % (2685839)Instructions burned: 67 (million)
% 5.35/1.06 % (2685815)Instruction limit reached!
% 5.35/1.06 % (2685815)------------------------------
% 5.35/1.06 % (2685815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.06 % (2685815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685815)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685815)Termination reason: Instruction limit
% 5.35/1.06 % (2685815)Termination phase: Saturation
% 5.35/1.06 % (2685815)Time elapsed: 0.180 s
% 5.35/1.06 % (2685815)Peak memory usage: 16 MB
% 5.35/1.06 % (2685815)Instructions burned: 317 (million)
% 5.35/1.06 % (2685847)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2811713991:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.35/1.06 % (2685848)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3727166667:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 5.35/1.06 % (2685834)Instruction limit reached!
% 5.35/1.06 % (2685834)------------------------------
% 5.35/1.06 % (2685834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.35/1.06 % (2685834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/1.06 % (2685834)CaDiCaL version: 2.1.3
% 5.35/1.06 % (2685834)Termination reason: Instruction limit
% 5.35/1.06 % (2685834)Termination phase: Function definition elimination
% 5.35/1.06 % (2685834)Time elapsed: 0.060 s
% 5.35/1.06 % (2685834)Peak memory usage: 13 MB
% 5.35/1.06 % (2685834)Instructions burned: 139 (million)
% 5.90/1.15 % (2685842)Instruction limit reached!
% 5.90/1.15 % (2685842)------------------------------
% 5.90/1.15 % (2685842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685842)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685842)Termination reason: Instruction limit
% 5.90/1.15 % (2685842)Termination phase: Property scanning
% 5.90/1.15 % (2685842)Time elapsed: 0.043 s
% 5.90/1.15 % (2685842)Peak memory usage: 13 MB
% 5.90/1.15 % (2685842)Instructions burned: 96 (million)
% 5.90/1.15 % (2685851)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2370645:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.90/1.15 % (2685852)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=416807930:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.90/1.15 % (2685840)Instruction limit reached!
% 5.90/1.15 % (2685840)------------------------------
% 5.90/1.15 % (2685840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685840)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685840)Termination reason: Instruction limit
% 5.90/1.15 % (2685840)Termination phase: Saturation
% 5.90/1.15 % (2685840)Time elapsed: 0.075 s
% 5.90/1.15 % (2685840)Peak memory usage: 12 MB
% 5.90/1.15 % (2685840)Instructions burned: 182 (million)
% 5.90/1.15 % (2685855)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1907193352:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.90/1.15 % (2685841)Instruction limit reached!
% 5.90/1.15 % (2685841)------------------------------
% 5.90/1.15 % (2685841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685841)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685841)Termination reason: Instruction limit
% 5.90/1.15 % (2685841)Termination phase: Saturation
% 5.90/1.15 % (2685841)Time elapsed: 0.105 s
% 5.90/1.15 % (2685841)Peak memory usage: 15 MB
% 5.90/1.15 % (2685841)Instructions burned: 247 (million)
% 5.90/1.15 % (2685855)Instruction limit reached!
% 5.90/1.15 % (2685855)------------------------------
% 5.90/1.15 % (2685855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685855)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685855)Termination reason: Instruction limit
% 5.90/1.15 % (2685855)Termination phase: Property scanning
% 5.90/1.15 % (2685855)Time elapsed: 0.019 s
% 5.90/1.15 % (2685855)Peak memory usage: 10 MB
% 5.90/1.15 % (2685855)Instructions burned: 44 (million)
% 5.90/1.15 % (2685847)Instruction limit reached!
% 5.90/1.15 % (2685847)------------------------------
% 5.90/1.15 % (2685847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685847)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685847)Termination reason: Instruction limit
% 5.90/1.15 % (2685847)Termination phase: Saturation
% 5.90/1.15 % (2685847)Time elapsed: 0.099 s
% 5.90/1.15 % (2685847)Peak memory usage: 15 MB
% 5.90/1.15 % (2685847)Instructions burned: 431 (million)
% 5.90/1.15 % (2685852)Instruction limit reached!
% 5.90/1.15 % (2685852)------------------------------
% 5.90/1.15 % (2685852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.90/1.15 % (2685859)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2156787903:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 5.90/1.15 % (2685852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.15 % (2685852)CaDiCaL version: 2.1.3
% 5.90/1.15 % (2685852)Termination reason: Instruction limit
% 5.90/1.15 % (2685852)Termination phase: Saturation
% 5.90/1.15 % (2685852)Time elapsed: 0.058 s
% 5.90/1.15 % (2685852)Peak memory usage: 13 MB
% 5.90/1.15 % (2685852)Instructions burned: 131 (million)
% 5.90/1.15 % (2685857)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1629120879:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 5.90/1.15 % (2685858)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=717363239:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.18/1.26 % (2685861)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3673666417:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 6.18/1.26 % (2685859)Instruction limit reached!
% 6.18/1.26 % (2685859)------------------------------
% 6.18/1.26 % (2685859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.18/1.26 % (2685859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.26 % (2685859)CaDiCaL version: 2.1.3
% 6.18/1.26 % (2685859)Termination reason: Instruction limit
% 6.18/1.26 % (2685859)Termination phase: Property scanning
% 6.18/1.26 % (2685859)Time elapsed: 0.023 s
% 6.18/1.26 % (2685859)Peak memory usage: 13 MB
% 6.18/1.26 % (2685859)Instructions burned: 100 (million)
% 6.18/1.26 % (2685865)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1101088232:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 6.18/1.26 % (2685861)Instruction limit reached!
% 6.18/1.26 % (2685861)------------------------------
% 6.18/1.26 % (2685861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.18/1.26 % (2685861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.26 % (2685861)CaDiCaL version: 2.1.3
% 6.18/1.26 % (2685861)Termination reason: Instruction limit
% 6.18/1.26 % (2685861)Termination phase: Property scanning
% 6.18/1.26 % (2685861)Time elapsed: 0.027 s
% 6.18/1.26 % (2685861)Peak memory usage: 11 MB
% 6.18/1.26 % (2685861)Instructions burned: 65 (million)
% 6.18/1.26 % (2685865)Instruction limit reached!
% 6.18/1.26 % (2685865)------------------------------
% 6.18/1.26 % (2685865)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.18/1.26 % (2685865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.26 % (2685865)CaDiCaL version: 2.1.3
% 6.18/1.26 % (2685865)Termination reason: Instruction limit
% 6.18/1.26 % (2685865)Termination phase: Saturation
% 6.18/1.26 % (2685865)Time elapsed: 0.023 s
% 6.18/1.26 % (2685865)Peak memory usage: 12 MB
% 6.18/1.26 % (2685865)Instructions burned: 108 (million)
% 6.18/1.26 % (2685867)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=4241499230:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 6.18/1.26 % (2685868)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=598251242:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 6.18/1.26 % (2685816)Instruction limit reached!
% 6.18/1.26 % (2685816)------------------------------
% 6.18/1.26 % (2685816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.18/1.26 % (2685816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.26 % (2685816)CaDiCaL version: 2.1.3
% 6.18/1.26 % (2685816)Termination reason: Instruction limit
% 6.18/1.26 % (2685816)Termination phase: Saturation
% 6.18/1.26 % (2685816)Time elapsed: 0.413 s
% 6.18/1.26 % (2685816)Peak memory usage: 19 MB
% 6.18/1.26 % (2685816)Instructions burned: 854 (million)
% 6.18/1.26 % (2685871)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2942368816:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.18/1.26 % (2685868)Instruction limit reached!
% 6.18/1.26 % (2685868)------------------------------
% 6.18/1.26 % (2685868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.18/1.26 % (2685868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.18/1.26 % (2685868)CaDiCaL version: 2.1.3
% 6.18/1.26 % (2685868)Termination reason: Instruction limit
% 6.18/1.26 % (2685868)Termination phase: Saturation
% 6.18/1.26 % (2685868)Time elapsed: 0.093 s
% 6.18/1.26 % (2685868)Peak memory usage: 16 MB
% 6.18/1.26 % (2685868)Instructions burned: 375 (million)
% 6.18/1.26 % (2685851)Instruction limit reached!
% 6.18/1.26 % (2685851)------------------------------
% 6.18/1.26 % (2685851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.40 % (2685851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.40 % (2685851)CaDiCaL version: 2.1.3
% 7.13/1.40 % (2685851)Termination reason: Instruction limit
% 7.13/1.40 % (2685851)Termination phase: Saturation
% 7.13/1.40 % (2685851)Time elapsed: 0.237 s
% 7.13/1.40 % (2685851)Peak memory usage: 18 MB
% 7.13/1.40 % (2685851)Instructions burned: 516 (million)
% 7.13/1.40 % (2685857)Refutation not found, incomplete strategy
% 7.13/1.40 % (2685857)------------------------------
% 7.13/1.40 % (2685857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.40 % (2685857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.40 % (2685857)CaDiCaL version: 2.1.3
% 7.13/1.40 % (2685857)Termination reason: Refutation not found, incomplete strategy
% 7.13/1.40 % (2685857)Time elapsed: 0.170 s
% 7.13/1.40 % (2685857)Peak memory usage: 17 MB
% 7.13/1.40 % (2685857)Instructions burned: 356 (million)
% 7.13/1.40 % (2685857)------------------------------
% 7.13/1.40 % (2685857)------------------------------
% 7.13/1.40 % (2685873)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=562036582:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 7.13/1.40 % (2685874)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=1352008764:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 7.13/1.40 % (2685873)Instruction limit reached!
% 7.13/1.40 % (2685873)------------------------------
% 7.13/1.40 % (2685873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.13/1.40 % (2685873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.13/1.40 % (2685873)CaDiCaL version: 2.1.3
% 7.13/1.40 % (2685873)Termination reason: Instruction limit
% 7.13/1.40 % (2685873)Termination phase: Property scanning
% 7.13/1.40 % (2685873)Time elapsed: 0.008 s
% 7.13/1.40 % (2685873)Peak memory usage: 10 MB
% 7.13/1.40 % (2685873)Instructions burned: 37 (million)
% 7.13/1.40 % (2685876)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3070232778:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2991 on theBenchmark for (2991ds/66Mi)
% 7.39/1.40 % (2685878)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2838701917:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 7.39/1.40 % (2685874)Instruction limit reached!
% 7.39/1.40 % (2685874)------------------------------
% 7.39/1.40 % (2685874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.40 % (2685874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.40 % (2685874)CaDiCaL version: 2.1.3
% 7.39/1.40 % (2685874)Termination reason: Instruction limit
% 7.39/1.40 % (2685874)Termination phase: Preprocessing 3
% 7.39/1.40 % (2685874)Time elapsed: 0.041 s
% 7.39/1.40 % (2685874)Peak memory usage: 13 MB
% 7.39/1.40 % (2685874)Instructions burned: 92 (million)
% 7.39/1.40 % (2685876)Instruction limit reached!
% 7.39/1.40 % (2685876)------------------------------
% 7.39/1.40 % (2685876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.40 % (2685876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.40 % (2685876)CaDiCaL version: 2.1.3
% 7.39/1.40 % (2685876)Termination reason: Instruction limit
% 7.39/1.40 % (2685876)Termination phase: Saturation
% 7.39/1.40 % (2685876)Time elapsed: 0.033 s
% 7.39/1.40 % (2685876)Peak memory usage: 12 MB
% 7.39/1.40 % (2685876)Instructions burned: 67 (million)
% 7.39/1.40 % (2685878)Instruction limit reached!
% 7.39/1.40 % (2685878)------------------------------
% 7.39/1.40 % (2685878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.39/1.40 % (2685878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.39/1.40 % (2685878)CaDiCaL version: 2.1.3
% 7.39/1.40 % (2685878)Termination reason: Instruction limit
% 7.39/1.40 % (2685878)Termination phase: shuffling
% 7.39/1.40 % (2685878)Time elapsed: 0.019 s
% 7.39/1.40 % (2685878)Peak memory usage: 10 MB
% 7.39/1.40 % (2685878)Instructions burned: 23 (million)
% 7.39/1.40 % (2685881)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=3410417716:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 7.39/1.40 % (2685882)lrs+10_1_sil=128000:si=on:urr=on:random_seed=740889465:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 8.02/1.51 % (2685883)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 8.02/1.51 % (2685882)Instruction limit reached!
% 8.02/1.51 % (2685882)------------------------------
% 8.02/1.51 % (2685882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.02/1.51 % (2685882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.51 % (2685882)CaDiCaL version: 2.1.3
% 8.02/1.51 % (2685882)Termination reason: Instruction limit
% 8.02/1.51 % (2685882)Termination phase: Property scanning
% 8.02/1.51 % (2685882)Time elapsed: 0.007 s
% 8.02/1.51 % (2685882)Peak memory usage: 10 MB
% 8.02/1.51 % (2685882)Instructions burned: 31 (million)
% 8.02/1.51 % (2685883)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=361557576:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 8.02/1.51 % (2685886)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=2903200999:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 8.02/1.51 % (2685858)Instruction limit reached!
% 8.02/1.51 % (2685858)------------------------------
% 8.02/1.51 % (2685858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.02/1.51 % (2685858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.51 % (2685858)CaDiCaL version: 2.1.3
% 8.02/1.51 % (2685858)Termination reason: Instruction limit
% 8.02/1.51 % (2685858)Termination phase: Saturation
% 8.02/1.51 % (2685858)Time elapsed: 0.264 s
% 8.02/1.51 % (2685858)Peak memory usage: 17 MB
% 8.02/1.51 % (2685858)Instructions burned: 452 (million)
% 8.02/1.51 % (2685889)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=418935893:i=227:sd=1:bd=all:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/227Mi)
% 8.02/1.51 % (2685883)Instruction limit reached!
% 8.02/1.51 % (2685883)------------------------------
% 8.02/1.51 % (2685883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.02/1.51 % (2685883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.51 % (2685883)CaDiCaL version: 2.1.3
% 8.02/1.51 % (2685883)Termination reason: Instruction limit
% 8.02/1.51 % (2685883)Termination phase: Saturation
% 8.02/1.51 % (2685883)Time elapsed: 0.057 s
% 8.02/1.51 % (2685883)Peak memory usage: 12 MB
% 8.02/1.51 % (2685883)Instructions burned: 138 (million)
% 8.02/1.51 % (2685848)Instruction limit reached!
% 8.02/1.51 % (2685848)------------------------------
% 8.02/1.51 % (2685848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.02/1.51 % (2685848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.51 % (2685848)CaDiCaL version: 2.1.3
% 8.02/1.51 % (2685848)Termination reason: Instruction limit
% 8.02/1.51 % (2685848)Termination phase: Saturation
% 8.02/1.51 % (2685848)Time elapsed: 0.422 s
% 8.02/1.51 % (2685848)Peak memory usage: 20 MB
% 8.02/1.51 % (2685848)Instructions burned: 874 (million)
% 8.02/1.51 % (2685891)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 8.02/1.51 % (2685891)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2908664604:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 8.02/1.51 % (2685892)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3632540689:i=116:ep=RSTC:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/116Mi)
% 8.02/1.51 % (2685886)Instruction limit reached!
% 8.02/1.51 % (2685886)------------------------------
% 8.02/1.51 % (2685886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.02/1.51 % (2685886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/1.51 % (2685886)CaDiCaL version: 2.1.3
% 8.02/1.51 % (2685886)Termination reason: Instruction limit
% 8.02/1.51 % (2685886)Termination phase: Saturation
% 8.02/1.51 % (2685886)Time elapsed: 0.081 s
% 8.02/1.51 % (2685886)Peak memory usage: 16 MB
% 8.02/1.51 % (2685886)Instructions burned: 344 (million)
% 8.02/1.51 % (2685895)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=801749021:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 8.68/1.65 % (2685881)Instruction limit reached!
% 8.68/1.65 % (2685881)------------------------------
% 8.68/1.65 % (2685881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685881)CaDiCaL version: 2.1.3
% 8.68/1.65 % (2685881)Termination reason: Instruction limit
% 8.68/1.65 % (2685881)Termination phase: Saturation
% 8.68/1.65 % (2685881)Time elapsed: 0.143 s
% 8.68/1.65 % (2685881)Peak memory usage: 18 MB
% 8.68/1.65 % (2685881)Instructions burned: 338 (million)
% 8.68/1.65 % (2685889)Instruction limit reached!
% 8.68/1.65 % (2685889)------------------------------
% 8.68/1.65 % (2685889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685889)CaDiCaL version: 2.1.3
% 8.68/1.65 % (2685889)Termination reason: Instruction limit
% 8.68/1.65 % (2685889)Termination phase: Saturation
% 8.68/1.65 % (2685889)Time elapsed: 0.102 s
% 8.68/1.65 % (2685889)Peak memory usage: 14 MB
% 8.68/1.65 % (2685889)Instructions burned: 227 (million)
% 8.68/1.65 % (2685871)Instruction limit reached!
% 8.68/1.65 % (2685871)------------------------------
% 8.68/1.65 % (2685871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685871)CaDiCaL version: 2.1.3
% 8.68/1.65 % (2685871)Termination reason: Instruction limit
% 8.68/1.65 % (2685871)Termination phase: Saturation
% 8.68/1.65 % (2685871)Time elapsed: 0.249 s
% 8.68/1.65 % (2685871)Peak memory usage: 17 MB
% 8.68/1.65 % (2685871)Instructions burned: 496 (million)
% 8.68/1.65 % (2685892)Instruction limit reached!
% 8.68/1.65 % (2685892)------------------------------
% 8.68/1.65 % (2685892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685892)CaDiCaL version: 2.1.3
% 8.68/1.65 % (2685892)Termination reason: Instruction limit
% 8.68/1.65 % (2685892)Termination phase: Property scanning
% 8.68/1.65 % (2685892)Time elapsed: 0.051 s
% 8.68/1.65 % (2685892)Peak memory usage: 13 MB
% 8.68/1.65 % (2685892)Instructions burned: 117 (million)
% 8.68/1.65 % (2685897)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1069050137:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.68/1.65 % (2685900)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.68/1.65 % (2685898)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2658332360:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2989 on theBenchmark for (2989ds/9840Mi)
% 8.68/1.65 % (2685899)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=3226981369:i=421:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/421Mi)
% 8.68/1.65 % (2685900)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=1478819074:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.68/1.65 % (2685891)Instruction limit reached!
% 8.68/1.65 % (2685891)------------------------------
% 8.68/1.65 % (2685891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685891)CaDiCaL version: 2.1.3
% 8.68/1.65 % (2685891)Termination reason: Instruction limit
% 8.68/1.65 % (2685891)Termination phase: Saturation
% 8.68/1.65 % (2685891)Time elapsed: 0.148 s
% 8.68/1.65 % (2685891)Peak memory usage: 15 MB
% 8.68/1.65 % (2685891)Instructions burned: 374 (million)
% 8.68/1.65 % (2685895)Instruction limit reached!
% 8.68/1.65 % (2685895)------------------------------
% 8.68/1.65 % (2685895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.68/1.65 % (2685895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/1.65 % (2685895)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685895)Termination reason: Instruction limit
% 9.83/1.82 % (2685895)Termination phase: Saturation
% 9.83/1.82 % (2685895)Time elapsed: 0.138 s
% 9.83/1.82 % (2685895)Peak memory usage: 18 MB
% 9.83/1.82 % (2685895)Instructions burned: 576 (million)
% 9.83/1.82 % (2685905)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1692469320:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/31Mi)
% 9.83/1.82 % (2685906)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 9.83/1.82 % (2685906)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 9.83/1.82 % (2685906)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=663077933:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2988 on theBenchmark for (2988ds/1440Mi)
% 9.83/1.82 % (2685897)Instruction limit reached!
% 9.83/1.82 % (2685897)------------------------------
% 9.83/1.82 % (2685897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.83/1.82 % (2685897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/1.82 % (2685897)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685897)Termination reason: Instruction limit
% 9.83/1.82 % (2685897)Termination phase: Saturation
% 9.83/1.82 % (2685897)Time elapsed: 0.109 s
% 9.83/1.82 % (2685897)Peak memory usage: 12 MB
% 9.83/1.82 % (2685897)Instructions burned: 270 (million)
% 9.83/1.82 % (2685905)Instruction limit reached!
% 9.83/1.82 % (2685905)------------------------------
% 9.83/1.82 % (2685905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.83/1.82 % (2685905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/1.82 % (2685905)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685905)Termination reason: Instruction limit
% 9.83/1.82 % (2685905)Termination phase: Property scanning
% 9.83/1.82 % (2685905)Time elapsed: 0.018 s
% 9.83/1.82 % (2685905)Peak memory usage: 10 MB
% 9.83/1.82 % (2685905)Instructions burned: 42 (million)
% 9.83/1.82 % (2685900)Instruction limit reached!
% 9.83/1.82 % (2685900)------------------------------
% 9.83/1.82 % (2685900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.83/1.82 % (2685900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/1.82 % (2685900)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685900)Termination reason: Instruction limit
% 9.83/1.82 % (2685900)Termination phase: Saturation
% 9.83/1.82 % (2685900)Time elapsed: 0.118 s
% 9.83/1.82 % (2685900)Peak memory usage: 15 MB
% 9.83/1.82 % (2685900)Instructions burned: 270 (million)
% 9.83/1.82 % (2685909)dis+10_2_sil=128000:si=on:random_seed=549216767:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2988 on theBenchmark for (2988ds/339Mi)
% 9.83/1.82 % (2685910)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1579055888:i=111:add=on:fgj=on:rtra=on:fdi=1024_2988 on theBenchmark for (2988ds/111Mi)
% 9.83/1.82 % (2685912)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3408174604:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/122Mi)
% 9.83/1.82 % (2685910)Instruction limit reached!
% 9.83/1.82 % (2685910)------------------------------
% 9.83/1.82 % (2685910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.83/1.82 % (2685910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/1.82 % (2685910)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685910)Termination reason: Instruction limit
% 9.83/1.82 % (2685910)Termination phase: Property scanning
% 9.83/1.82 % (2685910)Time elapsed: 0.049 s
% 9.83/1.82 % (2685910)Peak memory usage: 12 MB
% 9.83/1.82 % (2685910)Instructions burned: 111 (million)
% 9.83/1.82 % (2685912)Instruction limit reached!
% 9.83/1.82 % (2685912)------------------------------
% 9.83/1.82 % (2685912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.83/1.82 % (2685912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.83/1.82 % (2685912)CaDiCaL version: 2.1.3
% 9.83/1.82 % (2685912)Termination reason: Instruction limit
% 9.83/1.82 % (2685912)Termination phase: Property scanning
% 9.83/1.82 % (2685912)Time elapsed: 0.054 s
% 10.19/1.98 % (2685912)Peak memory usage: 13 MB
% 10.19/1.98 % (2685912)Instructions burned: 123 (million)
% 10.19/1.98 % (2685915)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=1693914460:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/136Mi)
% 10.19/1.98 % (2685899)Instruction limit reached!
% 10.19/1.98 % (2685899)------------------------------
% 10.19/1.98 % (2685899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.98 % (2685899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.98 % (2685899)CaDiCaL version: 2.1.3
% 10.19/1.98 % (2685899)Termination reason: Instruction limit
% 10.19/1.98 % (2685899)Termination phase: Saturation
% 10.19/1.98 % (2685899)Time elapsed: 0.197 s
% 10.19/1.98 % (2685899)Peak memory usage: 16 MB
% 10.19/1.98 % (2685899)Instructions burned: 422 (million)
% 10.19/1.98 % (2685917)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=140021039:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2987 on theBenchmark for (2987ds/232Mi)
% 10.19/1.98 % (2685918)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=2468116196:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2987 on theBenchmark for (2987ds/1254Mi)
% 10.19/1.98 % (2685915)Instruction limit reached!
% 10.19/1.98 % (2685915)------------------------------
% 10.19/1.98 % (2685915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.98 % (2685915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.98 % (2685915)CaDiCaL version: 2.1.3
% 10.19/1.98 % (2685915)Termination reason: Instruction limit
% 10.19/1.98 % (2685915)Termination phase: Property scanning
% 10.19/1.98 % (2685915)Time elapsed: 0.062 s
% 10.19/1.98 % (2685915)Peak memory usage: 16 MB
% 10.19/1.98 % (2685915)Instructions burned: 137 (million)
% 10.19/1.98 % (2685921)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 10.19/1.98 % (2685909)Instruction limit reached!
% 10.19/1.98 % (2685909)------------------------------
% 10.19/1.98 % (2685909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.98 % (2685909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.98 % (2685909)CaDiCaL version: 2.1.3
% 10.19/1.98 % (2685909)Termination reason: Instruction limit
% 10.19/1.98 % (2685909)Termination phase: Saturation
% 10.19/1.98 % (2685909)Time elapsed: 0.153 s
% 10.19/1.98 % (2685909)Peak memory usage: 14 MB
% 10.19/1.98 % (2685909)Instructions burned: 340 (million)
% 10.19/1.98 % (2685921)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=2390960231:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2986 on theBenchmark for (2986ds/281Mi)
% 10.19/1.98 % (2685922)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=325590949:i=619:add=on:rtra=on_2986 on theBenchmark for (2986ds/619Mi)
% 10.19/1.98 % (2685917)Instruction limit reached!
% 10.19/1.98 % (2685917)------------------------------
% 10.19/1.98 % (2685917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.98 % (2685917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.98 % (2685917)CaDiCaL version: 2.1.3
% 10.19/1.98 % (2685917)Termination reason: Instruction limit
% 10.19/1.98 % (2685917)Termination phase: Saturation
% 10.19/1.98 % (2685917)Time elapsed: 0.101 s
% 10.19/1.98 % (2685917)Peak memory usage: 14 MB
% 10.19/1.98 % (2685917)Instructions burned: 233 (million)
% 10.19/1.98 % (2685918)Refutation not found, incomplete strategy
% 10.19/1.98 % (2685918)------------------------------
% 10.19/1.98 % (2685918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 10.19/1.98 % (2685918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.19/1.98 % (2685918)CaDiCaL version: 2.1.3
% 10.19/1.98 % (2685918)Termination reason: Refutation not found, incomplete strategy
% 10.19/1.98 % (2685918)Time elapsed: 0.101 s
% 10.19/1.98 % (2685918)Peak memory usage: 15 MB
% 10.19/1.98 % (2685918)Instructions burned: 227 (million)
% 10.19/1.98 % (2685918)------------------------------
% 10.19/1.98 % (2685918)------------------------------
% 10.19/1.98 % (2685925)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1567976484:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/865Mi)
% 13.41/2.29 % (2685926)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3983481846:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/212Mi)
% 13.41/2.29 % (2685921)Instruction limit reached!
% 13.41/2.29 % (2685921)------------------------------
% 13.41/2.29 % (2685921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685921)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685921)Termination reason: Instruction limit
% 13.41/2.29 % (2685921)Termination phase: Saturation
% 13.41/2.29 % (2685921)Time elapsed: 0.115 s
% 13.41/2.29 % (2685921)Peak memory usage: 12 MB
% 13.41/2.29 % (2685921)Instructions burned: 281 (million)
% 13.41/2.29 % (2685929)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=1301755831:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/130Mi)
% 13.41/2.29 % (2685926)Instruction limit reached!
% 13.41/2.29 % (2685926)------------------------------
% 13.41/2.29 % (2685926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685926)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685926)Termination reason: Instruction limit
% 13.41/2.29 % (2685926)Termination phase: Saturation
% 13.41/2.29 % (2685926)Time elapsed: 0.090 s
% 13.41/2.29 % (2685926)Peak memory usage: 14 MB
% 13.41/2.29 % (2685926)Instructions burned: 213 (million)
% 13.41/2.29 % (2685906)Instruction limit reached!
% 13.41/2.29 % (2685906)------------------------------
% 13.41/2.29 % (2685906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685906)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685906)Termination reason: Instruction limit
% 13.41/2.29 % (2685906)Termination phase: Saturation
% 13.41/2.29 % (2685906)Time elapsed: 0.354 s
% 13.41/2.29 % (2685906)Peak memory usage: 21 MB
% 13.41/2.29 % (2685906)Instructions burned: 1441 (million)
% 13.41/2.29 % (2685931)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=190058115:st=1.5:i=346:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/346Mi)
% 13.41/2.29 % (2685932)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=619778821:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2985 on theBenchmark for (2985ds/152Mi)
% 13.41/2.29 % (2685929)Instruction limit reached!
% 13.41/2.29 % (2685929)------------------------------
% 13.41/2.29 % (2685929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685929)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685929)Termination reason: Instruction limit
% 13.41/2.29 % (2685929)Termination phase: Property scanning
% 13.41/2.29 % (2685929)Time elapsed: 0.057 s
% 13.41/2.29 % (2685929)Peak memory usage: 13 MB
% 13.41/2.29 % (2685929)Instructions burned: 131 (million)
% 13.41/2.29 % (2685935)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=722469284:i=75:ep=R:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/75Mi)
% 13.41/2.29 % (2685932)Instruction limit reached!
% 13.41/2.29 % (2685932)------------------------------
% 13.41/2.29 % (2685932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685932)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685932)Termination reason: Instruction limit
% 13.41/2.29 % (2685932)Termination phase: Inequality splitting
% 13.41/2.29 % (2685932)Time elapsed: 0.035 s
% 13.41/2.29 % (2685932)Peak memory usage: 13 MB
% 13.41/2.29 % (2685932)Instructions burned: 155 (million)
% 13.41/2.29 % (2685931)Refutation not found, incomplete strategy
% 13.41/2.29 % (2685931)------------------------------
% 13.41/2.29 % (2685931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.41/2.29 % (2685931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.41/2.29 % (2685931)CaDiCaL version: 2.1.3
% 13.41/2.29 % (2685931)Termination reason: Refutation not found, incomplete strategy
% 13.41/2.29 % (2685931)Time elapsed: 0.048 s
% 13.41/2.29 % (2685931)Peak memory usage: 13 MB
% 13.41/2.29 % (2685931)Instructions burned: 94 (million)
% 13.41/2.29 % (2685931)------------------------------
% 15.82/2.68 % (2685931)------------------------------
% 15.82/2.68 % (2685937)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=1415046095:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/387Mi)
% 15.82/2.68 % (2685938)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3338491666:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2984 on theBenchmark for (2984ds/148Mi)
% 15.82/2.68 % (2685935)Instruction limit reached!
% 15.82/2.68 % (2685935)------------------------------
% 15.82/2.68 % (2685935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.82/2.68 % (2685935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.82/2.68 % (2685935)CaDiCaL version: 2.1.3
% 15.82/2.68 % (2685935)Termination reason: Instruction limit
% 15.82/2.68 % (2685935)Termination phase: Property scanning
% 15.82/2.68 % (2685935)Time elapsed: 0.032 s
% 15.82/2.68 % (2685935)Peak memory usage: 11 MB
% 15.82/2.68 % (2685935)Instructions burned: 77 (million)
% 15.82/2.68 % (2685941)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=2685476761:i=161:piset=and:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/161Mi)
% 15.82/2.68 % (2685938)Instruction limit reached!
% 15.82/2.68 % (2685938)------------------------------
% 15.82/2.68 % (2685938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.82/2.68 % (2685938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.82/2.68 % (2685938)CaDiCaL version: 2.1.3
% 15.82/2.68 % (2685938)Termination reason: Instruction limit
% 15.82/2.68 % (2685938)Termination phase: Saturation
% 15.82/2.68 % (2685938)Time elapsed: 0.062 s
% 15.82/2.68 % (2685938)Peak memory usage: 12 MB
% 15.82/2.68 % (2685938)Instructions burned: 148 (million)
% 15.82/2.68 % (2685922)Instruction limit reached!
% 15.82/2.68 % (2685922)------------------------------
% 15.82/2.68 % (2685922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.82/2.68 % (2685922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.82/2.68 % (2685922)CaDiCaL version: 2.1.3
% 15.82/2.68 % (2685922)Termination reason: Instruction limit
% 15.82/2.68 % (2685922)Termination phase: Saturation
% 15.82/2.68 % (2685922)Time elapsed: 0.307 s
% 15.82/2.68 % (2685922)Peak memory usage: 18 MB
% 15.82/2.68 % (2685922)Instructions burned: 620 (million)
% 15.82/2.68 % (2685943)lrs+10_1_sil=128000:si=on:random_seed=154736664:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/888Mi)
% 15.82/2.68 % (2685937)Instruction limit reached!
% 15.82/2.68 % (2685937)------------------------------
% 15.82/2.68 % (2685937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.82/2.68 % (2685937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.82/2.68 % (2685937)CaDiCaL version: 2.1.3
% 15.82/2.68 % (2685937)Termination reason: Instruction limit
% 15.82/2.68 % (2685937)Termination phase: Saturation
% 15.82/2.68 % (2685937)Time elapsed: 0.103 s
% 15.82/2.68 % (2685937)Peak memory usage: 12 MB
% 15.82/2.68 % (2685937)Instructions burned: 389 (million)
% 15.82/2.68 % (2685941)Instruction limit reached!
% 15.82/2.68 % (2685941)------------------------------
% 15.82/2.68 % (2685941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.82/2.68 % (2685941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.82/2.68 % (2685941)CaDiCaL version: 2.1.3
% 15.82/2.68 % (2685941)Termination reason: Instruction limit
% 15.82/2.68 % (2685941)Termination phase: Property scanning
% 15.82/2.68 % (2685941)Time elapsed: 0.069 s
% 15.82/2.68 % (2685941)Peak memory usage: 13 MB
% 15.82/2.68 % (2685941)Instructions burned: 161 (million)
% 15.82/2.68 % (2685944)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=2211475589:i=136:add=on:ins=4:rtra=on:sup=off_2983 on theBenchmark for (2983ds/136Mi)
% 15.82/2.68 % (2685946)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1061932623:i=88:s2at=3:nm=2:rtra=on:rawr=on_2983 on theBenchmark for (2983ds/88Mi)
% 15.82/2.68 % (2685947)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3020077559:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2983 on theBenchmark for (2983ds/93Mi)
% 15.82/2.68 % (2685946)Instruction limit reached!
% 17.72/2.99 % (2685946)------------------------------
% 17.72/2.99 % (2685946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685946)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685946)Termination reason: Instruction limit
% 17.72/2.99 % (2685946)Termination phase: Property scanning
% 17.72/2.99 % (2685946)Time elapsed: 0.037 s
% 17.72/2.99 % (2685946)Peak memory usage: 11 MB
% 17.72/2.99 % (2685946)Instructions burned: 90 (million)
% 17.72/2.99 % (2685947)Instruction limit reached!
% 17.72/2.99 % (2685947)------------------------------
% 17.72/2.99 % (2685947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685947)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685947)Termination reason: Instruction limit
% 17.72/2.99 % (2685947)Termination phase: Saturation
% 17.72/2.99 % (2685947)Time elapsed: 0.039 s
% 17.72/2.99 % (2685947)Peak memory usage: 12 MB
% 17.72/2.99 % (2685947)Instructions burned: 95 (million)
% 17.72/2.99 % (2685944)Instruction limit reached!
% 17.72/2.99 % (2685944)------------------------------
% 17.72/2.99 % (2685944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685944)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685944)Termination reason: Instruction limit
% 17.72/2.99 % (2685944)Termination phase: Property scanning
% 17.72/2.99 % (2685944)Time elapsed: 0.059 s
% 17.72/2.99 % (2685944)Peak memory usage: 12 MB
% 17.72/2.99 % (2685944)Instructions burned: 136 (million)
% 17.72/2.99 % (2685952)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1914008039:s2a=on:i=240:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/240Mi)
% 17.72/2.99 % (2685951)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1755343562:i=2186:rtra=on:ixr=off_2982 on theBenchmark for (2982ds/2186Mi)
% 17.72/2.99 % (2685953)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=991158962:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2982 on theBenchmark for (2982ds/805Mi)
% 17.72/2.99 % (2685952)Instruction limit reached!
% 17.72/2.99 % (2685952)------------------------------
% 17.72/2.99 % (2685952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685952)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685952)Termination reason: Instruction limit
% 17.72/2.99 % (2685952)Termination phase: Saturation
% 17.72/2.99 % (2685952)Time elapsed: 0.103 s
% 17.72/2.99 % (2685952)Peak memory usage: 14 MB
% 17.72/2.99 % (2685952)Instructions burned: 241 (million)
% 17.72/2.99 % (2685957)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 17.72/2.99 % (2685957)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=2776589902:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2981 on theBenchmark for (2981ds/391Mi)
% 17.72/2.99 % (2685925)Instruction limit reached!
% 17.72/2.99 % (2685925)------------------------------
% 17.72/2.99 % (2685925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685925)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685925)Termination reason: Instruction limit
% 17.72/2.99 % (2685925)Termination phase: Saturation
% 17.72/2.99 % (2685925)Time elapsed: 0.497 s
% 17.72/2.99 % (2685925)Peak memory usage: 20 MB
% 17.72/2.99 % (2685925)Instructions burned: 866 (million)
% 17.72/2.99 % (2685959)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=4195808291:i=355:av=off:fsr=off:rtra=on:ixr=off_2981 on theBenchmark for (2981ds/355Mi)
% 17.72/2.99 % (2685957)Instruction limit reached!
% 17.72/2.99 % (2685957)------------------------------
% 17.72/2.99 % (2685957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.72/2.99 % (2685957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.72/2.99 % (2685957)CaDiCaL version: 2.1.3
% 17.72/2.99 % (2685957)Termination reason: Instruction limit
% 17.72/2.99 % (2685957)Termination phase: Saturation
% 17.72/2.99 % (2685957)Time elapsed: 0.159 s
% 19.87/3.17 % (2685957)Peak memory usage: 13 MB
% 19.87/3.17 % (2685957)Instructions burned: 393 (million)
% 19.87/3.17 % (2685962)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=2999221938:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2979 on theBenchmark for (2979ds/314Mi)
% 19.87/3.17 % (2685959)Instruction limit reached!
% 19.87/3.17 % (2685959)------------------------------
% 19.87/3.17 % (2685959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.87/3.17 % (2685959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.87/3.17 % (2685959)CaDiCaL version: 2.1.3
% 19.87/3.17 % (2685959)Termination reason: Instruction limit
% 19.87/3.17 % (2685959)Termination phase: Saturation
% 19.87/3.17 % (2685959)Time elapsed: 0.237 s
% 19.87/3.17 % (2685959)Peak memory usage: 15 MB
% 19.87/3.17 % (2685959)Instructions burned: 356 (million)
% 19.87/3.17 % (2685943)Instruction limit reached!
% 19.87/3.17 % (2685943)------------------------------
% 19.87/3.17 % (2685943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.87/3.17 % (2685943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.87/3.17 % (2685943)CaDiCaL version: 2.1.3
% 19.87/3.17 % (2685943)Termination reason: Instruction limit
% 19.87/3.17 % (2685943)Termination phase: Saturation
% 19.87/3.17 % (2685943)Time elapsed: 0.488 s
% 19.87/3.17 % (2685943)Peak memory usage: 19 MB
% 19.87/3.17 % (2685943)Instructions burned: 889 (million)
% 19.87/3.17 % (2685953)Instruction limit reached!
% 19.87/3.17 % (2685953)------------------------------
% 19.87/3.17 % (2685953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.87/3.17 % (2685953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.87/3.17 % (2685953)CaDiCaL version: 2.1.3
% 19.87/3.17 % (2685953)Termination reason: Instruction limit
% 19.87/3.17 % (2685953)Termination phase: Saturation
% 19.87/3.17 % (2685953)Time elapsed: 0.399 s
% 19.87/3.17 % (2685953)Peak memory usage: 18 MB
% 19.87/3.17 % (2685953)Instructions burned: 806 (million)
% 19.87/3.17 % (2685966)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1088379238:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=2470:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2978 on theBenchmark for (2978ds/2470Mi)
% 19.87/3.17 % (2685967)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=3999671917:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2978 on theBenchmark for (2978ds/673Mi)
% 19.87/3.17 % (2685965)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=919864873:s2a=on:i=251:fsr=off:rtra=on_2978 on theBenchmark for (2978ds/251Mi)
% 19.87/3.17 % (2685962)Refutation not found, incomplete strategy
% 19.87/3.17 % (2685962)------------------------------
% 19.87/3.17 % (2685962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.87/3.17 % (2685962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.87/3.17 % (2685962)CaDiCaL version: 2.1.3
% 19.87/3.17 % (2685962)Termination reason: Refutation not found, incomplete strategy
% 19.87/3.17 % (2685962)Time elapsed: 0.238 s
% 19.87/3.17 % (2685962)Peak memory usage: 15 MB
% 19.87/3.17 % (2685962)Instructions burned: 289 (million)
% 19.87/3.17 % (2685962)------------------------------
% 19.87/3.17 % (2685962)------------------------------
% 19.87/3.17 % (2685971)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=3029597441:i=116:ep=RSTC:rtra=on:ntd=on_2977 on theBenchmark for (2977ds/116Mi)
% 19.87/3.17 % (2685965)Instruction limit reached!
% 19.87/3.17 % (2685965)------------------------------
% 19.87/3.17 % (2685965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.87/3.17 % (2685965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.87/3.17 % (2685965)CaDiCaL version: 2.1.3
% 19.87/3.17 % (2685965)Termination reason: Instruction limit
% 19.87/3.17 % (2685965)Termination phase: Saturation
% 19.87/3.17 % (2685965)Time elapsed: 0.202 s
% 19.87/3.17 % (2685965)Peak memory usage: 14 MB
% 19.87/3.17 % (2685965)Instructions burned: 251 (million)
% 19.87/3.17 % (2685973)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2556526147:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2976 on theBenchmark for (2976ds/270Mi)
% 21.68/3.56 % (2685971)Instruction limit reached!
% 21.68/3.56 % (2685971)------------------------------
% 21.68/3.56 % (2685971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.68/3.56 % (2685971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.68/3.56 % (2685971)CaDiCaL version: 2.1.3
% 21.68/3.56 % (2685971)Termination reason: Instruction limit
% 21.68/3.56 % (2685971)Termination phase: Property scanning
% 21.68/3.56 % (2685971)Time elapsed: 0.105 s
% 21.68/3.56 % (2685971)Peak memory usage: 12 MB
% 21.68/3.56 % (2685971)Instructions burned: 116 (million)
% 21.68/3.56 % (2685975)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1989342746:hsq=on:hsqr=16,1:s2a=on:i=30:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2975 on theBenchmark for (2975ds/30Mi)
% 21.68/3.56 % (2685975)Instruction limit reached!
% 21.68/3.56 % (2685975)------------------------------
% 21.68/3.56 % (2685975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.68/3.56 % (2685975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.68/3.56 % (2685975)CaDiCaL version: 2.1.3
% 21.68/3.56 % (2685975)Termination reason: Instruction limit
% 21.68/3.56 % (2685975)Termination phase: shuffling
% 21.68/3.56 % (2685975)Time elapsed: 0.013 s
% 21.68/3.56 % (2685975)Peak memory usage: 10 MB
% 21.68/3.56 % (2685975)Instructions burned: 30 (million)
% 21.68/3.56 % (2685977)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 21.68/3.56 % (2685977)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=719304937:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2975 on theBenchmark for (2975ds/39Mi)
% 21.68/3.56 % (2685977)Instruction limit reached!
% 21.68/3.56 % (2685977)------------------------------
% 21.68/3.56 % (2685977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.68/3.56 % (2685977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.68/3.56 % (2685977)CaDiCaL version: 2.1.3
% 21.68/3.56 % (2685977)Termination reason: Instruction limit
% 21.68/3.56 % (2685977)Termination phase: Property scanning
% 21.68/3.56 % (2685977)Time elapsed: 0.017 s
% 21.68/3.56 % (2685977)Peak memory usage: 10 MB
% 21.68/3.56 % (2685977)Instructions burned: 40 (million)
% 21.68/3.56 % (2685979)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=966131366:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2974 on theBenchmark for (2974ds/365Mi)
% 21.68/3.56 % (2685967)Instruction limit reached!
% 21.68/3.56 % (2685967)------------------------------
% 21.68/3.56 % (2685967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.68/3.56 % (2685967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.68/3.56 % (2685967)CaDiCaL version: 2.1.3
% 21.68/3.56 % (2685967)Termination reason: Instruction limit
% 21.68/3.56 % (2685967)Termination phase: Saturation
% 21.68/3.56 % (2685967)Time elapsed: 0.409 s
% 21.68/3.56 % (2685967)Peak memory usage: 17 MB
% 21.68/3.56 % (2685967)Instructions burned: 673 (million)
% 21.68/3.56 % (2685973)Instruction limit reached!
% 21.68/3.56 % (2685973)------------------------------
% 21.68/3.56 % (2685973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.68/3.56 % (2685973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.68/3.56 % (2685973)CaDiCaL version: 2.1.3
% 21.68/3.56 % (2685973)Termination reason: Instruction limit
% 21.68/3.56 % (2685973)Termination phase: Saturation
% 21.68/3.56 % (2685973)Time elapsed: 0.198 s
% 21.68/3.56 % (2685973)Peak memory usage: 12 MB
% 21.68/3.56 % (2685973)Instructions burned: 270 (million)
% 21.68/3.56 % (2685981)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2049324226:i=158:av=off:rtra=on_2974 on theBenchmark for (2974ds/158Mi)
% 21.68/3.56 % (2685982)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 21.68/3.56 % (2685982)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2238805434:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2973 on theBenchmark for (2973ds/252Mi)
% 21.68/3.56 % (2685981)Instruction limit reached!
% 21.68/3.56 % (2685981)------------------------------
% 21.68/3.56 % (2685981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685981)CaDiCaL version: 2.1.3
% 22.44/3.65 % (2685981)Termination reason: Instruction limit
% 22.44/3.65 % (2685981)Termination phase: Saturation
% 22.44/3.65 % (2685981)Time elapsed: 0.095 s
% 22.44/3.65 % (2685981)Peak memory usage: 14 MB
% 22.44/3.65 % (2685981)Instructions burned: 160 (million)
% 22.44/3.65 % (2685989)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=3647284514:i=213:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/213Mi)
% 22.44/3.65 % (2685989)Refutation not found, incomplete strategy
% 22.44/3.65 % (2685989)------------------------------
% 22.44/3.65 % (2685989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685989)CaDiCaL version: 2.1.3
% 22.44/3.65 % (2685989)Termination reason: Refutation not found, incomplete strategy
% 22.44/3.65 % (2685989)Time elapsed: 0.019 s
% 22.44/3.65 % (2685989)Peak memory usage: 13 MB
% 22.44/3.65 % (2685989)Instructions burned: 41 (million)
% 22.44/3.65 % (2685989)------------------------------
% 22.44/3.65 % (2685989)------------------------------
% 22.44/3.65 % (2685991)dis+1010_28_sil=128000:tgt=full:plsq=on:plsqc=1:cnfonf=off:si=on:plsqr=128,1:uwa=off:slsqc=2:sac=on:slsq=on:random_seed=715138000:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2972 on theBenchmark for (2972ds/160Mi)
% 22.44/3.65 % (2685979)Instruction limit reached!
% 22.44/3.65 % (2685979)------------------------------
% 22.44/3.65 % (2685979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685979)CaDiCaL version: 2.1.3
% 22.44/3.65 % (2685979)Termination reason: Instruction limit
% 22.44/3.65 % (2685979)Termination phase: Saturation
% 22.44/3.65 % (2685979)Time elapsed: 0.277 s
% 22.44/3.65 % (2685979)Peak memory usage: 16 MB
% 22.44/3.65 % (2685979)Instructions burned: 365 (million)
% 22.44/3.65 % (2685951)Instruction limit reached!
% 22.44/3.65 % (2685951)------------------------------
% 22.44/3.65 % (2685951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685951)CaDiCaL version: 2.1.3
% 22.44/3.65 % (2685951)Termination reason: Instruction limit
% 22.44/3.65 % (2685951)Termination phase: Saturation
% 22.44/3.65 % (2685951)Time elapsed: 1.095 s
% 22.44/3.65 % (2685951)Peak memory usage: 15 MB
% 22.44/3.65 % (2685951)Instructions burned: 2186 (million)
% 22.44/3.65 % (2685982)Instruction limit reached!
% 22.44/3.65 % (2685982)------------------------------
% 22.44/3.65 % (2685982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685982)CaDiCaL version: 2.1.3
% 22.44/3.65 % (2685982)Termination reason: Instruction limit
% 22.44/3.65 % (2685982)Termination phase: Saturation
% 22.44/3.65 % (2685982)Time elapsed: 0.201 s
% 22.44/3.65 % (2685982)Peak memory usage: 15 MB
% 22.44/3.65 % (2685982)Instructions burned: 252 (million)
% 22.44/3.65 % (2685995)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=1516272425:s2a=on:i=386:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/386Mi)
% 22.44/3.65 % (2685994)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 22.44/3.65 % (2685993)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=2545365552:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/763Mi)
% 22.44/3.65 % (2685994)ott+1010_40_sil=128000:tgt=full:plsq=on:plsqc=5:si=on:sos=all:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2086646502:i=237:hsql=off:fgj=on:piset=all_but_not_eq:bd=preordered:av=off:rtra=on:ss=axioms:sgt=4:rawr=on_2971 on theBenchmark for (2971ds/237Mi)
% 22.44/3.65 % (2685991)Instruction limit reached!
% 22.44/3.65 % (2685991)------------------------------
% 22.44/3.65 % (2685991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.44/3.65 % (2685991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.44/3.65 % (2685991)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2685991)Termination reason: Instruction limit
% 23.41/3.76 % (2685991)Termination phase: Function definition elimination
% 23.41/3.76 % (2685991)Time elapsed: 0.115 s
% 23.41/3.76 % (2685991)Peak memory usage: 13 MB
% 23.41/3.76 % (2685991)Instructions burned: 162 (million)
% 23.41/3.76 % (2686000)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=1941633659:i=300:piset=and:nm=32:rtra=on_2971 on theBenchmark for (2971ds/300Mi)
% 23.41/3.76 % (2685995)Instruction limit reached!
% 23.41/3.76 % (2685995)------------------------------
% 23.41/3.76 % (2685995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2685995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.41/3.76 % (2685995)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2685995)Termination reason: Instruction limit
% 23.41/3.76 % (2685995)Termination phase: Saturation
% 23.41/3.76 % (2685995)Time elapsed: 0.162 s
% 23.41/3.76 % (2685995)Peak memory usage: 12 MB
% 23.41/3.76 % (2685995)Instructions burned: 386 (million)
% 23.41/3.76 % (2686000)Instruction limit reached!
% 23.41/3.76 % (2686000)------------------------------
% 23.41/3.76 % (2686000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2686000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.41/3.76 % (2686000)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2686000)Termination reason: Instruction limit
% 23.41/3.76 % (2686000)Termination phase: Property scanning
% 23.41/3.76 % (2686000)Time elapsed: 0.127 s
% 23.41/3.76 % (2686000)Peak memory usage: 13 MB
% 23.41/3.76 % (2686000)Instructions burned: 301 (million)
% 23.41/3.76 % (2686002)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=205013939:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2969 on theBenchmark for (2969ds/567Mi)
% 23.41/3.76 % (2686003)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=2222257830:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2969 on theBenchmark for (2969ds/379Mi)
% 23.41/3.76 % (2685994)Instruction limit reached!
% 23.41/3.76 % (2685994)------------------------------
% 23.41/3.76 % (2685994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2685994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.41/3.76 % (2685994)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2685994)Termination reason: Instruction limit
% 23.41/3.76 % (2685994)Termination phase: Saturation
% 23.41/3.76 % (2685994)Time elapsed: 0.197 s
% 23.41/3.76 % (2685994)Peak memory usage: 14 MB
% 23.41/3.76 % (2685994)Instructions burned: 237 (million)
% 23.41/3.76 % (2686006)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3972188597:s2a=on:i=429:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2969 on theBenchmark for (2969ds/429Mi)
% 23.41/3.76 % (2686006)Instruction limit reached!
% 23.41/3.76 % (2686006)------------------------------
% 23.41/3.76 % (2686006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2686006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.41/3.76 % (2686006)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2686006)Termination reason: Instruction limit
% 23.41/3.76 % (2686006)Termination phase: Saturation
% 23.41/3.76 % (2686006)Time elapsed: 0.106 s
% 23.41/3.76 % (2686006)Peak memory usage: 17 MB
% 23.41/3.76 % (2686006)Instructions burned: 431 (million)
% 23.41/3.76 % (2686008)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=330917953:i=478:bd=all:rtra=on_2967 on theBenchmark for (2967ds/478Mi)
% 23.41/3.76 % (2686003)Instruction limit reached!
% 23.41/3.76 % (2686003)------------------------------
% 23.41/3.76 % (2686003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2686003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.41/3.76 % (2686003)CaDiCaL version: 2.1.3
% 23.41/3.76 % (2686003)Termination reason: Instruction limit
% 23.41/3.76 % (2686003)Termination phase: Saturation
% 23.41/3.76 % (2686003)Time elapsed: 0.171 s
% 23.41/3.76 % (2686003)Peak memory usage: 16 MB
% 23.41/3.76 % (2686003)Instructions burned: 380 (million)
% 23.41/3.76 % (2686010)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=993979742:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2967 on theBenchmark for (2967ds/445Mi)
% 23.41/3.76 % (2686002)Instruction limit reached!
% 23.41/3.76 % (2686002)------------------------------
% 23.41/3.76 % (2686002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.41/3.76 % (2686002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2686002)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2686002)Termination reason: Instruction limit
% 24.69/4.03 % (2686002)Termination phase: Saturation
% 24.69/4.03 % (2686002)Time elapsed: 0.228 s
% 24.69/4.03 % (2686002)Peak memory usage: 12 MB
% 24.69/4.03 % (2686002)Instructions burned: 567 (million)
% 24.69/4.03 % (2686012)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=503404632:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2967 on theBenchmark for (2967ds/71Mi)
% 24.69/4.03 % (2686012)Instruction limit reached!
% 24.69/4.03 % (2686012)------------------------------
% 24.69/4.03 % (2686012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.69/4.03 % (2686012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2686012)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2686012)Termination reason: Instruction limit
% 24.69/4.03 % (2686012)Termination phase: Property scanning
% 24.69/4.03 % (2686012)Time elapsed: 0.029 s
% 24.69/4.03 % (2686012)Peak memory usage: 11 MB
% 24.69/4.03 % (2686012)Instructions burned: 72 (million)
% 24.69/4.03 % (2685993)Instruction limit reached!
% 24.69/4.03 % (2685993)------------------------------
% 24.69/4.03 % (2685993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.69/4.03 % (2685993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2685993)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2685993)Termination reason: Instruction limit
% 24.69/4.03 % (2685993)Termination phase: Saturation
% 24.69/4.03 % (2685993)Time elapsed: 0.451 s
% 24.69/4.03 % (2685993)Peak memory usage: 17 MB
% 24.69/4.03 % (2685993)Instructions burned: 764 (million)
% 24.69/4.03 % (2686008)Instruction limit reached!
% 24.69/4.03 % (2686008)------------------------------
% 24.69/4.03 % (2686008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.69/4.03 % (2686008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2686008)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2686008)Termination reason: Instruction limit
% 24.69/4.03 % (2686008)Termination phase: Saturation
% 24.69/4.03 % (2686008)Time elapsed: 0.122 s
% 24.69/4.03 % (2686008)Peak memory usage: 18 MB
% 24.69/4.03 % (2686008)Instructions burned: 481 (million)
% 24.69/4.03 % (2686014)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1484466079:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2966 on theBenchmark for (2966ds/302Mi)
% 24.69/4.03 % (2686016)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 24.69/4.03 % (2686016)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 24.69/4.03 % (2686015)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=3100189123:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2966 on theBenchmark for (2966ds/4980Mi)
% 24.69/4.03 % (2686016)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1584762646:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2966 on theBenchmark for (2966ds/100Mi)
% 24.69/4.03 % (2685966)Instruction limit reached!
% 24.69/4.03 % (2685966)------------------------------
% 24.69/4.03 % (2685966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.69/4.03 % (2685966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2685966)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2685966)Termination reason: Instruction limit
% 24.69/4.03 % (2685966)Termination phase: Saturation
% 24.69/4.03 % (2685966)Time elapsed: 1.217 s
% 24.69/4.03 % (2685966)Peak memory usage: 18 MB
% 24.69/4.03 % (2685966)Instructions burned: 2470 (million)
% 24.69/4.03 % (2686015)Refutation not found, incomplete strategy
% 24.69/4.03 % (2686015)------------------------------
% 24.69/4.03 % (2686015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.69/4.03 % (2686015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.69/4.03 % (2686015)CaDiCaL version: 2.1.3
% 24.69/4.03 % (2686015)Termination reason: Refutation not found, incomplete strategy
% 24.69/4.03 % (2686015)Time elapsed: 0.018 s
% 24.69/4.03 % (2686015)Peak memory usage: 12 MB
% 24.69/4.03 % (2686015)Instructions burned: 42 (million)
% 24.69/4.03 % (2686015)------------------------------
% 24.69/4.03 % (2686015)------------------------------
% 26.69/4.19 % (2686016)Instruction limit reached!
% 26.69/4.19 % (2686016)------------------------------
% 26.69/4.19 % (2686016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.69/4.19 % (2686016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.69/4.19 % (2686016)CaDiCaL version: 2.1.3
% 26.69/4.19 % (2686016)Termination reason: Instruction limit
% 26.69/4.19 % (2686016)Termination phase: Twee Goal Transformation
% 26.69/4.19 % (2686016)Time elapsed: 0.022 s
% 26.69/4.19 % (2686016)Peak memory usage: 11 MB
% 26.69/4.19 % (2686016)Instructions burned: 104 (million)
% 26.69/4.19 % (2686022)lrs+2_64_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_first:bsr=unit_only:cbe=off:uwa=interpreted_only:nwc=0.5:slsqc=5:sac=on:slsq=on:random_seed=3030626823:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2966 on theBenchmark for (2966ds/493Mi)
% 26.69/4.19 % (2686020)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3533605507:i=76:piset=equals:rtra=on:ntd=on_2966 on theBenchmark for (2966ds/76Mi)
% 26.69/4.19 % (2686021)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=2767587200:i=289:rtra=on_2966 on theBenchmark for (2966ds/289Mi)
% 26.69/4.19 % (2686020)Instruction limit reached!
% 26.69/4.19 % (2686020)------------------------------
% 26.69/4.19 % (2686020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.69/4.19 % (2686020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.69/4.19 % (2686020)CaDiCaL version: 2.1.3
% 26.69/4.19 % (2686020)Termination reason: Instruction limit
% 26.69/4.19 % (2686020)Termination phase: Property scanning
% 26.69/4.19 % (2686020)Time elapsed: 0.032 s
% 26.69/4.19 % (2686020)Peak memory usage: 11 MB
% 26.69/4.19 % (2686020)Instructions burned: 77 (million)
% 26.69/4.19 % (2686026)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1945234180:cond=on:i=34:hud=10:nm=10:rtra=on_2965 on theBenchmark for (2965ds/34Mi)
% 26.69/4.19 % (2686010)Instruction limit reached!
% 26.69/4.19 % (2686010)------------------------------
% 26.69/4.19 % (2686010)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.69/4.19 % (2686010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.69/4.19 % (2686010)CaDiCaL version: 2.1.3
% 26.69/4.19 % (2686010)Termination reason: Instruction limit
% 26.69/4.19 % (2686010)Termination phase: Saturation
% 26.69/4.19 % (2686010)Time elapsed: 0.202 s
% 26.69/4.19 % (2686010)Peak memory usage: 16 MB
% 26.69/4.19 % (2686010)Instructions burned: 445 (million)
% 26.69/4.19 % (2686026)Instruction limit reached!
% 26.69/4.19 % (2686026)------------------------------
% 26.69/4.19 % (2686026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.69/4.19 % (2686026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.69/4.19 % (2686026)CaDiCaL version: 2.1.3
% 26.69/4.19 % (2686026)Termination reason: Instruction limit
% 26.69/4.19 % (2686026)Termination phase: Property scanning
% 26.69/4.19 % (2686026)Time elapsed: 0.015 s
% 26.69/4.19 % (2686026)Peak memory usage: 10 MB
% 26.69/4.19 % (2686026)Instructions burned: 34 (million)
% 26.69/4.19 % (2686028)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 26.69/4.19 % (2686028)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=2382859480:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2965 on theBenchmark for (2965ds/372Mi)
% 26.69/4.19 % (2686029)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=3936560876:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2965 on theBenchmark for (2965ds/670Mi)
% 26.69/4.19 % (2686014)Instruction limit reached!
% 26.69/4.19 % (2686014)------------------------------
% 26.69/4.19 % (2686014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 26.69/4.19 % (2686014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 26.69/4.19 % (2686014)CaDiCaL version: 2.1.3
% 26.69/4.19 % (2686014)Termination reason: Instruction limit
% 26.69/4.19 % (2686014)Termination phase: Saturation
% 26.69/4.19 % (2686014)Time elapsed: 0.133 s
% 26.69/4.19 % (2686014)Peak memory usage: 14 MB
% 26.69/4.19 % (2686014)Instructions burned: 302 (million)
% 27.54/4.55 % (2686032)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1994064564:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2965 on theBenchmark for (2965ds/647Mi)
% 27.54/4.55 % (2686022)Instruction limit reached!
% 27.54/4.55 % (2686022)------------------------------
% 27.54/4.55 % (2686022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.54/4.55 % (2686022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.54/4.55 % (2686022)CaDiCaL version: 2.1.3
% 27.54/4.55 % (2686022)Termination reason: Instruction limit
% 27.54/4.55 % (2686022)Termination phase: Saturation
% 27.54/4.55 % (2686022)Time elapsed: 0.140 s
% 27.54/4.55 % (2686022)Peak memory usage: 15 MB
% 27.54/4.55 % (2686022)Instructions burned: 493 (million)
% 27.54/4.55 % (2686034)dis+10_128_sil=128000:tgt=full:plsq=on:plsqc=3:cnfonf=off:si=on:sp=arity:spb=goal_then_units:uwa=one_side_interpreted:nwc=1.5:random_seed=3155799287:i=857:add=off:kws=frequency:rtra=on:ntd=on_2964 on theBenchmark for (2964ds/857Mi)
% 27.54/4.55 % (2686021)Instruction limit reached!
% 27.54/4.55 % (2686021)------------------------------
% 27.54/4.55 % (2686021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.54/4.55 % (2686021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.54/4.55 % (2686021)CaDiCaL version: 2.1.3
% 27.54/4.55 % (2686021)Termination reason: Instruction limit
% 27.54/4.55 % (2686021)Termination phase: Saturation
% 27.54/4.55 % (2686021)Time elapsed: 0.180 s
% 27.54/4.55 % (2686021)Peak memory usage: 15 MB
% 27.54/4.55 % (2686021)Instructions burned: 290 (million)
% 27.54/4.55 % (2686036)dis+1010_4_anc=all_dependent:to=lpo:sil=128000:fde=unused:cnfonf=conj_eager:si=on:sp=reverse_frequency:lma=off:spb=intro:cbe=off:uwa=off:random_seed=2619221825:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2964 on theBenchmark for (2964ds/693Mi)
% 27.54/4.55 % (2686028)Instruction limit reached!
% 27.54/4.55 % (2686028)------------------------------
% 27.54/4.55 % (2686028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.54/4.55 % (2686028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.54/4.55 % (2686028)CaDiCaL version: 2.1.3
% 27.54/4.55 % (2686028)Termination reason: Instruction limit
% 27.54/4.55 % (2686028)Termination phase: Saturation
% 27.54/4.55 % (2686028)Time elapsed: 0.161 s
% 27.54/4.55 % (2686028)Peak memory usage: 16 MB
% 27.54/4.55 % (2686028)Instructions burned: 372 (million)
% 27.54/4.55 % (2685867)Instruction limit reached!
% 27.54/4.55 % (2685867)------------------------------
% 27.54/4.55 % (2685867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.54/4.55 % (2685867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.54/4.55 % (2685867)CaDiCaL version: 2.1.3
% 27.54/4.55 % (2685867)Termination reason: Instruction limit
% 27.54/4.55 % (2685867)Termination phase: Saturation
% 27.54/4.55 % (2685867)Time elapsed: 2.961 s
% 27.54/4.55 % (2685867)Peak memory usage: 37 MB
% 27.54/4.55 % (2685867)Instructions burned: 5757 (million)
% 27.54/4.55 % (2686038)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=2952092647:i=285:hud=10:bd=all:rtra=on:ss=axioms_2963 on theBenchmark for (2963ds/285Mi)
% 27.54/4.55 % (2686040)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 27.54/4.55 % (2686040)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=762371518:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2963 on theBenchmark for (2963ds/52Mi)
% 27.54/4.56 % (2686040)Instruction limit reached!
% 27.54/4.56 % (2686040)------------------------------
% 27.54/4.56 % (2686040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.54/4.56 % (2686040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.54/4.56 % (2686040)CaDiCaL version: 2.1.3
% 27.54/4.56 % (2686040)Termination reason: Instruction limit
% 27.54/4.56 % (2686040)Termination phase: Preprocessing 3
% 27.54/4.56 % (2686040)Time elapsed: 0.023 s
% 27.54/4.56 % (2686040)Peak memory usage: 11 MB
% 27.54/4.56 % (2686040)Instructions burned: 53 (million)
% 27.54/4.56 % (2686042)dis+10_1_si=on:random_seed=2155847203:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2962 on theBenchmark for (2962ds/407Mi)
% 27.54/4.56 % (2686034)Instruction limit reached!
% 27.54/4.56 % (2686034)------------------------------
% 27.54/4.56 % (2686034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686034)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686034)Termination reason: Instruction limit
% 29.06/4.79 % (2686034)Termination phase: Saturation
% 29.06/4.79 % (2686034)Time elapsed: 0.218 s
% 29.06/4.79 % (2686034)Peak memory usage: 18 MB
% 29.06/4.79 % (2686034)Instructions burned: 858 (million)
% 29.06/4.79 % (2686044)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1843536076:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2962 on theBenchmark for (2962ds/2240Mi)
% 29.06/4.79 % (2686038)Instruction limit reached!
% 29.06/4.79 % (2686038)------------------------------
% 29.06/4.79 % (2686038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686038)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686038)Termination reason: Instruction limit
% 29.06/4.79 % (2686038)Termination phase: Saturation
% 29.06/4.79 % (2686038)Time elapsed: 0.125 s
% 29.06/4.79 % (2686038)Peak memory usage: 15 MB
% 29.06/4.79 % (2686038)Instructions burned: 287 (million)
% 29.06/4.79 % (2686029)Instruction limit reached!
% 29.06/4.79 % (2686029)------------------------------
% 29.06/4.79 % (2686029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686029)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686029)Termination reason: Instruction limit
% 29.06/4.79 % (2686029)Termination phase: Saturation
% 29.06/4.79 % (2686029)Time elapsed: 0.314 s
% 29.06/4.79 % (2686029)Peak memory usage: 18 MB
% 29.06/4.79 % (2686029)Instructions burned: 670 (million)
% 29.06/4.79 % (2686046)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=4092227748:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2962 on theBenchmark for (2962ds/336Mi)
% 29.06/4.79 % (2686032)Instruction limit reached!
% 29.06/4.79 % (2686032)------------------------------
% 29.06/4.79 % (2686032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686032)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686032)Termination reason: Instruction limit
% 29.06/4.79 % (2686032)Termination phase: Saturation
% 29.06/4.79 % (2686032)Time elapsed: 0.312 s
% 29.06/4.79 % (2686032)Peak memory usage: 18 MB
% 29.06/4.79 % (2686032)Instructions burned: 647 (million)
% 29.06/4.79 % (2686047)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=617208074:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2961 on theBenchmark for (2961ds/1142Mi)
% 29.06/4.79 % (2686049)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1697483002:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2961 on theBenchmark for (2961ds/376Mi)
% 29.06/4.79 % (2686036)Instruction limit reached!
% 29.06/4.79 % (2686036)------------------------------
% 29.06/4.79 % (2686036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686036)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686036)Termination reason: Instruction limit
% 29.06/4.79 % (2686036)Termination phase: Saturation
% 29.06/4.79 % (2686036)Time elapsed: 0.282 s
% 29.06/4.79 % (2686036)Peak memory usage: 13 MB
% 29.06/4.79 % (2686036)Instructions burned: 693 (million)
% 29.06/4.79 % (2686042)Instruction limit reached!
% 29.06/4.79 % (2686042)------------------------------
% 29.06/4.79 % (2686042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.06/4.79 % (2686042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.06/4.79 % (2686042)CaDiCaL version: 2.1.3
% 29.06/4.79 % (2686042)Termination reason: Instruction limit
% 29.06/4.79 % (2686042)Termination phase: Saturation
% 29.06/4.79 % (2686042)Time elapsed: 0.176 s
% 29.06/4.79 % (2686042)Peak memory usage: 16 MB
% 29.06/4.79 % (2686042)Instructions burned: 407 (million)
% 29.06/4.79 % (2686053)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 29.06/4.79 % (2686052)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=1140802714:i=766:bd=all:rtra=on_2961 on theBenchmark for (2961ds/766Mi)
% 29.06/4.79 % (2686053)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=2810238418:st=3:uwa_fpi=on:i=959:fgj=on:piset=pi_sigma:hud=5:nm=16:rtra=on:fe=abstraction:ss=axioms:ixr=off:ntd=on_2960 on theBenchmark for (2960ds/959Mi)
% 31.35/4.91 % (2686046)Instruction limit reached!
% 31.35/4.91 % (2686046)------------------------------
% 31.35/4.91 % (2686046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/4.91 % (2686046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/4.91 % (2686046)CaDiCaL version: 2.1.3
% 31.35/4.91 % (2686046)Termination reason: Instruction limit
% 31.35/4.91 % (2686046)Termination phase: Saturation
% 31.35/4.91 % (2686046)Time elapsed: 0.167 s
% 31.35/4.91 % (2686046)Peak memory usage: 16 MB
% 31.35/4.91 % (2686046)Instructions burned: 337 (million)
% 31.35/4.91 % (2686056)dis+1010_1024_sil=128000:plsq=on:plsqc=1:e2e=on:si=on:lma=off:plsqr=64,1:uwa=interpreted_only:fd=off:random_seed=670131718:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2960 on theBenchmark for (2960ds/6359Mi)
% 31.35/4.91 % (2686049)Instruction limit reached!
% 31.35/4.91 % (2686049)------------------------------
% 31.35/4.91 % (2686049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/4.91 % (2686049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/4.91 % (2686049)CaDiCaL version: 2.1.3
% 31.35/4.91 % (2686049)Termination reason: Instruction limit
% 31.35/4.91 % (2686049)Termination phase: Saturation
% 31.35/4.91 % (2686049)Time elapsed: 0.164 s
% 31.35/4.91 % (2686049)Peak memory usage: 16 MB
% 31.35/4.91 % (2686049)Instructions burned: 376 (million)
% 31.35/4.91 % (2686058)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3064209909:st=4:i=35:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2959 on theBenchmark for (2959ds/35Mi)
% 31.35/4.91 % (2686058)Instruction limit reached!
% 31.35/4.91 % (2686058)------------------------------
% 31.35/4.91 % (2686058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/4.91 % (2686058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/4.91 % (2686058)CaDiCaL version: 2.1.3
% 31.35/4.91 % (2686058)Termination reason: Instruction limit
% 31.35/4.91 % (2686058)Termination phase: SInE selection
% 31.35/4.91 % (2686058)Time elapsed: 0.016 s
% 31.35/4.91 % (2686058)Peak memory usage: 10 MB
% 31.35/4.91 % (2686058)Instructions burned: 37 (million)
% 31.35/4.91 % (2686060)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=3887524106:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2959 on theBenchmark for (2959ds/53Mi)
% 31.35/4.91 % (2686060)Instruction limit reached!
% 31.35/4.91 % (2686060)------------------------------
% 31.35/4.91 % (2686060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/4.91 % (2686060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/4.91 % (2686060)CaDiCaL version: 2.1.3
% 31.35/4.91 % (2686060)Termination reason: Instruction limit
% 31.35/4.91 % (2686060)Termination phase: Property scanning
% 31.35/4.91 % (2686060)Time elapsed: 0.022 s
% 31.35/4.91 % (2686060)Peak memory usage: 10 MB
% 31.35/4.91 % (2686060)Instructions burned: 53 (million)
% 31.35/4.91 % (2686062)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=3834265643:s2a=on:i=876:s2at=6:nm=2:rtra=on_2959 on theBenchmark for (2959ds/876Mi)
% 31.35/4.91 % (2686047)Refutation not found, incomplete strategy
% 31.35/4.91 % (2686047)------------------------------
% 31.35/4.91 % (2686047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/4.91 % (2686047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/4.91 % (2686047)CaDiCaL version: 2.1.3
% 31.35/4.91 % (2686047)Termination reason: Refutation not found, incomplete strategy
% 31.35/4.91 % (2686047)Time elapsed: 0.399 s
% 31.35/4.91 % (2686047)Peak memory usage: 19 MB
% 31.35/4.91 % (2686047)Instructions burned: 768 (million)
% 31.35/4.91 % (2686047)------------------------------
% 31.35/4.91 % (2686047)------------------------------
% 31.35/4.91 % (2686064)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=798915424:i=57:ep=R:rtra=on:ntd=on_2957 on theBenchmark for (2957ds/57Mi)
% 31.35/4.91 % (2686064)Instruction limit reached!
% 31.35/4.91 % (2686064)------------------------------
% 31.35/4.91 % (2686064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686064)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686064)Termination reason: Instruction limit
% 31.35/5.03 % (2686064)Termination phase: Property scanning
% 31.35/5.03 % (2686064)Time elapsed: 0.024 s
% 31.35/5.03 % (2686064)Peak memory usage: 11 MB
% 31.35/5.03 % (2686064)Instructions burned: 58 (million)
% 31.35/5.03 % (2686052)Instruction limit reached!
% 31.35/5.03 % (2686052)------------------------------
% 31.35/5.03 % (2686052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686052)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686052)Termination reason: Instruction limit
% 31.35/5.03 % (2686052)Termination phase: Saturation
% 31.35/5.03 % (2686052)Time elapsed: 0.369 s
% 31.35/5.03 % (2686052)Peak memory usage: 20 MB
% 31.35/5.03 % (2686052)Instructions burned: 766 (million)
% 31.35/5.03 % (2686066)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 31.35/5.03 % (2686066)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=2644791781:i=306:bd=all:rtra=on_2957 on theBenchmark for (2957ds/306Mi)
% 31.35/5.03 % (2686067)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=3715649204:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2957 on theBenchmark for (2957ds/262Mi)
% 31.35/5.03 % (2686053)Instruction limit reached!
% 31.35/5.03 % (2686053)------------------------------
% 31.35/5.03 % (2686053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686053)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686053)Termination reason: Instruction limit
% 31.35/5.03 % (2686053)Termination phase: Saturation
% 31.35/5.03 % (2686053)Time elapsed: 0.422 s
% 31.35/5.03 % (2686053)Peak memory usage: 20 MB
% 31.35/5.03 % (2686053)Instructions burned: 960 (million)
% 31.35/5.03 % (2686070)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 31.35/5.03 % (2686070)ott+1002_16_sil=128000:si=on:random_seed=3525901358:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2956 on theBenchmark for (2956ds/409Mi)
% 31.35/5.03 % (2686067)Instruction limit reached!
% 31.35/5.03 % (2686067)------------------------------
% 31.35/5.03 % (2686067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686067)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686067)Termination reason: Instruction limit
% 31.35/5.03 % (2686067)Termination phase: Saturation
% 31.35/5.03 % (2686067)Time elapsed: 0.128 s
% 31.35/5.03 % (2686067)Peak memory usage: 15 MB
% 31.35/5.03 % (2686067)Instructions burned: 262 (million)
% 31.35/5.03 % (2686066)Instruction limit reached!
% 31.35/5.03 % (2686066)------------------------------
% 31.35/5.03 % (2686066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686066)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686066)Termination reason: Instruction limit
% 31.35/5.03 % (2686066)Termination phase: Saturation
% 31.35/5.03 % (2686066)Time elapsed: 0.147 s
% 31.35/5.03 % (2686066)Peak memory usage: 16 MB
% 31.35/5.03 % (2686066)Instructions burned: 306 (million)
% 31.35/5.03 % (2686072)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=1735361129:s2a=on:i=381:rtra=on_2955 on theBenchmark for (2955ds/381Mi)
% 31.35/5.03 % (2686073)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=59591264:cond=on:i=324:rtra=on:ntd=on_2955 on theBenchmark for (2955ds/324Mi)
% 31.35/5.03 % (2686044)Instruction limit reached!
% 31.35/5.03 % (2686044)------------------------------
% 31.35/5.03 % (2686044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.35/5.03 % (2686044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.35/5.03 % (2686044)CaDiCaL version: 2.1.3
% 31.35/5.03 % (2686044)Termination reason: Instruction limit
% 31.35/5.03 % (2686044)Termination phase: Saturation
% 31.35/5.03 % (2686044)Time elapsed: 0.730 s
% 31.35/5.03 % (2686044)Peak memory usage: 22 MB
% 31.35/5.03 % (2686044)Instructions burned: 2242 (million)
% 31.35/5.03 % (2686076)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=4065807731:i=240:kws=inv_precedence:rtra=on_2954 on theBenchmark for (2954ds/240Mi)
% 34.07/5.22 % (2686062)Instruction limit reached!
% 34.07/5.22 % (2686062)------------------------------
% 34.07/5.22 % (2686062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686062)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686062)Termination reason: Instruction limit
% 34.07/5.22 % (2686062)Termination phase: Saturation
% 34.07/5.22 % (2686062)Time elapsed: 0.439 s
% 34.07/5.22 % (2686062)Peak memory usage: 17 MB
% 34.07/5.22 % (2686062)Instructions burned: 878 (million)
% 34.07/5.22 % (2686070)Instruction limit reached!
% 34.07/5.22 % (2686070)------------------------------
% 34.07/5.22 % (2686070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686070)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686070)Termination reason: Instruction limit
% 34.07/5.22 % (2686070)Termination phase: Saturation
% 34.07/5.22 % (2686070)Time elapsed: 0.182 s
% 34.07/5.22 % (2686070)Peak memory usage: 16 MB
% 34.07/5.22 % (2686070)Instructions burned: 410 (million)
% 34.07/5.22 % (2686078)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 34.07/5.22 % (2686078)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2117466938:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2954 on theBenchmark for (2954ds/124Mi)
% 34.07/5.22 % (2686079)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=3549812998:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2954 on theBenchmark for (2954ds/223Mi)
% 34.07/5.22 % (2686076)Instruction limit reached!
% 34.07/5.22 % (2686076)------------------------------
% 34.07/5.22 % (2686076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686076)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686076)Termination reason: Instruction limit
% 34.07/5.22 % (2686076)Termination phase: Saturation
% 34.07/5.22 % (2686076)Time elapsed: 0.062 s
% 34.07/5.22 % (2686076)Peak memory usage: 16 MB
% 34.07/5.22 % (2686076)Instructions burned: 243 (million)
% 34.07/5.22 % (2686082)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1452479039:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2954 on theBenchmark for (2954ds/282Mi)
% 34.07/5.22 % (2686073)Instruction limit reached!
% 34.07/5.22 % (2686073)------------------------------
% 34.07/5.22 % (2686073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686073)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686073)Termination reason: Instruction limit
% 34.07/5.22 % (2686073)Termination phase: Saturation
% 34.07/5.22 % (2686073)Time elapsed: 0.147 s
% 34.07/5.22 % (2686073)Peak memory usage: 16 MB
% 34.07/5.22 % (2686073)Instructions burned: 325 (million)
% 34.07/5.22 % (2686078)Instruction limit reached!
% 34.07/5.22 % (2686078)------------------------------
% 34.07/5.22 % (2686078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686078)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686078)Termination reason: Instruction limit
% 34.07/5.22 % (2686078)Termination phase: Property scanning
% 34.07/5.22 % (2686078)Time elapsed: 0.054 s
% 34.07/5.22 % (2686078)Peak memory usage: 12 MB
% 34.07/5.22 % (2686078)Instructions burned: 125 (million)
% 34.07/5.22 % (2686072)Instruction limit reached!
% 34.07/5.22 % (2686072)------------------------------
% 34.07/5.22 % (2686072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.07/5.22 % (2686072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.07/5.22 % (2686072)CaDiCaL version: 2.1.3
% 34.07/5.22 % (2686072)Termination reason: Instruction limit
% 34.07/5.22 % (2686072)Termination phase: Saturation
% 34.07/5.22 % (2686072)Time elapsed: 0.171 s
% 34.07/5.22 % (2686072)Peak memory usage: 17 MB
% 34.07/5.22 % (2686072)Instructions burned: 383 (million)
% 34.07/5.22 % (2686084)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=1754734650:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2953 on theBenchmark for (2953ds/464Mi)
% 36.36/5.63 % (2686085)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2987615953:i=88:s2at=3:nm=2:rtra=on:rawr=on_2953 on theBenchmark for (2953ds/88Mi)
% 36.36/5.63 % (2686086)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=3971799302:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2953 on theBenchmark for (2953ds/280Mi)
% 36.36/5.63 % (2686082)Instruction limit reached!
% 36.36/5.63 % (2686082)------------------------------
% 36.36/5.63 % (2686082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.63 % (2686082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.63 % (2686082)CaDiCaL version: 2.1.3
% 36.36/5.63 % (2686082)Termination reason: Instruction limit
% 36.36/5.63 % (2686082)Termination phase: Saturation
% 36.36/5.63 % (2686082)Time elapsed: 0.066 s
% 36.36/5.63 % (2686082)Peak memory usage: 15 MB
% 36.36/5.63 % (2686082)Instructions burned: 283 (million)
% 36.36/5.63 % (2686079)Instruction limit reached!
% 36.36/5.63 % (2686079)------------------------------
% 36.36/5.63 % (2686079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.63 % (2686079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.63 % (2686079)CaDiCaL version: 2.1.3
% 36.36/5.63 % (2686079)Termination reason: Instruction limit
% 36.36/5.63 % (2686079)Termination phase: Saturation
% 36.36/5.63 % (2686079)Time elapsed: 0.095 s
% 36.36/5.63 % (2686079)Peak memory usage: 14 MB
% 36.36/5.63 % (2686079)Instructions burned: 223 (million)
% 36.36/5.63 % (2686090)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 36.36/5.63 % (2686090)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3348730115:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2953 on theBenchmark for (2953ds/4386Mi)
% 36.36/5.63 % (2686085)Instruction limit reached!
% 36.36/5.63 % (2686085)------------------------------
% 36.36/5.63 % (2686085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.63 % (2686085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.63 % (2686085)CaDiCaL version: 2.1.3
% 36.36/5.63 % (2686085)Termination reason: Instruction limit
% 36.36/5.63 % (2686085)Termination phase: Property scanning
% 36.36/5.63 % (2686085)Time elapsed: 0.037 s
% 36.36/5.63 % (2686085)Peak memory usage: 11 MB
% 36.36/5.63 % (2686085)Instructions burned: 89 (million)
% 36.36/5.63 % (2686091)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 36.36/5.63 % (2686091)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 36.36/5.63 % (2686091)ott+21_3:13_sil=128000:cnfonf=off:sas=cadical:si=on:sp=arity:lma=off:lsd=10:uwa=one_side_interpreted:mep=off:chr=on:random_seed=951270866:hsq=on:st=2:i=483:sd=1:hsql=off:rtra=on:fe=abstraction:fdi=32:ss=axioms:sgt=20:ntd=on_2953 on theBenchmark for (2953ds/483Mi)
% 36.36/5.63 % (2686093)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1491860588:i=73:rtra=on_2953 on theBenchmark for (2953ds/73Mi)
% 36.36/5.63 % (2686093)Instruction limit reached!
% 36.36/5.63 % (2686093)------------------------------
% 36.36/5.63 % (2686093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.63 % (2686093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.63 % (2686093)CaDiCaL version: 2.1.3
% 36.36/5.63 % (2686093)Termination reason: Instruction limit
% 36.36/5.63 % (2686093)Termination phase: Preprocessing 3
% 36.36/5.63 % (2686093)Time elapsed: 0.032 s
% 36.36/5.63 % (2686093)Peak memory usage: 12 MB
% 36.36/5.63 % (2686093)Instructions burned: 74 (million)
% 36.36/5.63 % (2686096)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2386328374:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2952 on theBenchmark for (2952ds/176Mi)
% 36.36/5.63 % (2686086)Instruction limit reached!
% 36.36/5.63 % (2686086)------------------------------
% 36.36/5.63 % (2686086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.36/5.63 % (2686086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.36/5.63 % (2686086)CaDiCaL version: 2.1.3
% 37.79/5.82 % (2686086)Termination reason: Instruction limit
% 37.79/5.82 % (2686086)Termination phase: Saturation
% 37.79/5.82 % (2686086)Time elapsed: 0.115 s
% 37.79/5.82 % (2686086)Peak memory usage: 13 MB
% 37.79/5.82 % (2686086)Instructions burned: 281 (million)
% 37.79/5.82 % (2686098)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 37.79/5.82 % (2686098)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=3031631899:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2952 on theBenchmark for (2952ds/39Mi)
% 37.79/5.82 % (2686098)Instruction limit reached!
% 37.79/5.82 % (2686098)------------------------------
% 37.79/5.82 % (2686098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.79/5.82 % (2686098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.79/5.82 % (2686098)CaDiCaL version: 2.1.3
% 37.79/5.82 % (2686098)Termination reason: Instruction limit
% 37.79/5.82 % (2686098)Termination phase: Property scanning
% 37.79/5.82 % (2686098)Time elapsed: 0.017 s
% 37.79/5.82 % (2686098)Peak memory usage: 10 MB
% 37.79/5.82 % (2686098)Instructions burned: 40 (million)
% 37.79/5.82 % (2686096)Instruction limit reached!
% 37.79/5.82 % (2686096)------------------------------
% 37.79/5.82 % (2686096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.79/5.82 % (2686096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.79/5.82 % (2686096)CaDiCaL version: 2.1.3
% 37.79/5.82 % (2686096)Termination reason: Instruction limit
% 37.79/5.82 % (2686096)Termination phase: Saturation
% 37.79/5.82 % (2686096)Time elapsed: 0.072 s
% 37.79/5.82 % (2686096)Peak memory usage: 12 MB
% 37.79/5.82 % (2686096)Instructions burned: 177 (million)
% 37.79/5.82 % (2686100)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4083753577:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2951 on theBenchmark for (2951ds/708Mi)
% 37.79/5.82 % (2686101)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 37.79/5.82 % (2686084)Instruction limit reached!
% 37.79/5.82 % (2686084)------------------------------
% 37.79/5.83 % (2686084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.79/5.83 % (2686084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.79/5.83 % (2686084)CaDiCaL version: 2.1.3
% 37.79/5.83 % (2686084)Termination reason: Instruction limit
% 37.79/5.83 % (2686084)Termination phase: Saturation
% 37.79/5.83 % (2686084)Time elapsed: 0.198 s
% 37.79/5.83 % (2686084)Peak memory usage: 16 MB
% 37.79/5.83 % (2686084)Instructions burned: 465 (million)
% 37.79/5.83 % (2686101)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=982148397:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2951 on theBenchmark for (2951ds/252Mi)
% 37.79/5.83 % (2686103)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=1777006598:i=823:fsr=off:rtra=on_2951 on theBenchmark for (2951ds/823Mi)
% 37.79/5.83 % (2686091)Instruction limit reached!
% 37.79/5.83 % (2686091)------------------------------
% 37.79/5.83 % (2686091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.79/5.83 % (2686091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.79/5.83 % (2686091)CaDiCaL version: 2.1.3
% 37.79/5.83 % (2686091)Termination reason: Instruction limit
% 37.79/5.83 % (2686091)Termination phase: Saturation
% 37.79/5.83 % (2686091)Time elapsed: 0.220 s
% 37.79/5.83 % (2686091)Peak memory usage: 17 MB
% 37.79/5.83 % (2686091)Instructions burned: 483 (million)
% 37.79/5.83 % (2686106)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 37.79/5.83 % (2686106)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=51035496:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2950 on theBenchmark for (2950ds/16202Mi)
% 37.79/5.83 % (2686101)Instruction limit reached!
% 37.79/5.83 % (2686101)------------------------------
% 37.79/5.83 % (2686101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 37.79/5.83 % (2686101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 37.79/5.83 % (2686101)CaDiCaL version: 2.1.3
% 37.79/5.83 % (2686101)Termination reason: Instruction limit
% 41.34/6.29 % (2686101)Termination phase: Saturation
% 41.34/6.29 % (2686101)Time elapsed: 0.110 s
% 41.34/6.29 % (2686101)Peak memory usage: 15 MB
% 41.34/6.29 % (2686101)Instructions burned: 253 (million)
% 41.34/6.29 % (2686108)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=1798966779:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2950 on theBenchmark for (2950ds/300Mi)
% 41.34/6.29 % (2686108)Instruction limit reached!
% 41.34/6.29 % (2686108)------------------------------
% 41.34/6.29 % (2686108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.34/6.29 % (2686108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.34/6.29 % (2686108)CaDiCaL version: 2.1.3
% 41.34/6.29 % (2686108)Termination reason: Instruction limit
% 41.34/6.29 % (2686108)Termination phase: Saturation
% 41.34/6.29 % (2686108)Time elapsed: 0.121 s
% 41.34/6.29 % (2686108)Peak memory usage: 12 MB
% 41.34/6.29 % (2686108)Instructions burned: 301 (million)
% 41.34/6.29 % (2686110)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 41.34/6.29 % (2686110)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 41.34/6.29 % (2686110)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=1412155466:i=177:add=on:bd=preordered:rtra=on:rawr=on_2949 on theBenchmark for (2949ds/177Mi)
% 41.34/6.29 % (2686100)Instruction limit reached!
% 41.34/6.29 % (2686100)------------------------------
% 41.34/6.29 % (2686100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.34/6.29 % (2686100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.34/6.29 % (2686100)CaDiCaL version: 2.1.3
% 41.34/6.29 % (2686100)Termination reason: Instruction limit
% 41.34/6.29 % (2686100)Termination phase: Saturation
% 41.34/6.29 % (2686100)Time elapsed: 0.319 s
% 41.34/6.29 % (2686100)Peak memory usage: 18 MB
% 41.34/6.29 % (2686100)Instructions burned: 709 (million)
% 41.34/6.29 % (2686112)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=1652675039:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2948 on theBenchmark for (2948ds/715Mi)
% 41.34/6.29 % (2686110)Instruction limit reached!
% 41.34/6.29 % (2686110)------------------------------
% 41.34/6.29 % (2686110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.34/6.29 % (2686110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.34/6.29 % (2686110)CaDiCaL version: 2.1.3
% 41.34/6.29 % (2686110)Termination reason: Instruction limit
% 41.34/6.29 % (2686110)Termination phase: Property scanning
% 41.34/6.29 % (2686110)Time elapsed: 0.076 s
% 41.34/6.29 % (2686110)Peak memory usage: 13 MB
% 41.34/6.29 % (2686110)Instructions burned: 179 (million)
% 41.34/6.29 % (2686103)Instruction limit reached!
% 41.34/6.29 % (2686103)------------------------------
% 41.34/6.29 % (2686103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 41.34/6.29 % (2686103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 41.34/6.29 % (2686103)CaDiCaL version: 2.1.3
% 41.34/6.29 % (2686103)Termination reason: Instruction limit
% 41.34/6.29 % (2686103)Termination phase: Saturation
% 41.34/6.29 % (2686103)Time elapsed: 0.332 s
% 41.34/6.29 % (2686103)Peak memory usage: 14 MB
% 41.34/6.29 % (2686103)Instructions burned: 824 (million)
% 41.34/6.29 % (2686114)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 41.34/6.29 % (2686114)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 41.34/6.29 % (2686115)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3639991840:s2a=on:i=606:s2at=5:add=on:sd=2:ep=R:bd=preordered:rtra=on:ss=included:sgt=40_2948 on theBenchmark for (2948ds/606Mi)
% 41.34/6.29 % (2686114)dis+11_1_sil=128000:plsqc=3:cnfonf=lazy_gen:si=on:sp=const_max:lma=off:plsqr=19,3:lcm=predicate:uwa=off:fd=preordered:nwc=1:random_seed=78818720:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2948 on theBenchmark for (2948ds/230Mi)
% 41.34/6.29 % (2686114)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 41.34/6.29 % (2686114)Instruction limit reached!
% 41.34/6.29 % (2686114)------------------------------
% 41.34/6.29 % (2686114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686114)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686114)Termination reason: Instruction limit
% 42.98/6.59 % (2686114)Termination phase: Saturation
% 42.98/6.59 % (2686114)Time elapsed: 0.149 s
% 42.98/6.59 % (2686114)Peak memory usage: 16 MB
% 42.98/6.59 % (2686114)Instructions burned: 231 (million)
% 42.98/6.59 % (2686118)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 42.98/6.59 % (2686118)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=3000660477:lrd=on:i=841:nm=0:rtra=on_2946 on theBenchmark for (2946ds/841Mi)
% 42.98/6.59 % (2686112)Instruction limit reached!
% 42.98/6.59 % (2686112)------------------------------
% 42.98/6.59 % (2686112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686112)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686112)Termination reason: Instruction limit
% 42.98/6.59 % (2686112)Termination phase: Saturation
% 42.98/6.59 % (2686112)Time elapsed: 0.309 s
% 42.98/6.59 % (2686112)Peak memory usage: 19 MB
% 42.98/6.59 % (2686112)Instructions burned: 717 (million)
% 42.98/6.59 % (2686120)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2951061601:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2945 on theBenchmark for (2945ds/445Mi)
% 42.98/6.59 % (2686115)Instruction limit reached!
% 42.98/6.59 % (2686115)------------------------------
% 42.98/6.59 % (2686115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686115)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686115)Termination reason: Instruction limit
% 42.98/6.59 % (2686115)Termination phase: Saturation
% 42.98/6.59 % (2686115)Time elapsed: 0.295 s
% 42.98/6.59 % (2686115)Peak memory usage: 17 MB
% 42.98/6.59 % (2686115)Instructions burned: 608 (million)
% 42.98/6.59 % (2686090)Instruction limit reached!
% 42.98/6.59 % (2686090)------------------------------
% 42.98/6.59 % (2686090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686090)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686090)Termination reason: Instruction limit
% 42.98/6.59 % (2686090)Termination phase: Saturation
% 42.98/6.59 % (2686090)Time elapsed: 0.841 s
% 42.98/6.59 % (2686090)Peak memory usage: 18 MB
% 42.98/6.59 % (2686090)Instructions burned: 4389 (million)
% 42.98/6.59 % (2686123)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 42.98/6.59 % (2686123)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 42.98/6.59 % (2686123)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2380102291:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2944 on theBenchmark for (2944ds/100Mi)
% 42.98/6.59 % (2686122)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=1376530460:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2944 on theBenchmark for (2944ds/71Mi)
% 42.98/6.59 % (2686123)Instruction limit reached!
% 42.98/6.59 % (2686123)------------------------------
% 42.98/6.59 % (2686123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686123)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686123)Termination reason: Instruction limit
% 42.98/6.59 % (2686123)Termination phase: Saturation
% 42.98/6.59 % (2686123)Time elapsed: 0.022 s
% 42.98/6.59 % (2686123)Peak memory usage: 11 MB
% 42.98/6.59 % (2686123)Instructions burned: 105 (million)
% 42.98/6.59 % (2686122)Instruction limit reached!
% 42.98/6.59 % (2686122)------------------------------
% 42.98/6.59 % (2686122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.98/6.59 % (2686122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.98/6.59 % (2686122)CaDiCaL version: 2.1.3
% 42.98/6.59 % (2686122)Termination reason: Instruction limit
% 42.98/6.59 % (2686122)Termination phase: Property scanning
% 47.53/7.11 % (2686126)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 47.53/7.11 % (2686122)Time elapsed: 0.031 s
% 47.53/7.11 % (2686122)Peak memory usage: 11 MB
% 47.53/7.11 % (2686122)Instructions burned: 76 (million)
% 47.53/7.11 % (2686126)lrs+2_128_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=const_max:sos=on:plsqr=32,1:spb=goal:uwa=interpreted_only:slsqc=3:random_seed=1973143528:i=1352:add=on:aac=none:rtra=on_2944 on theBenchmark for (2944ds/1352Mi)
% 47.53/7.11 % (2686127)lrs-1002_4:1_sfv=off:to=lpo:plsq=on:prc=on:e2e=on:si=on:hsqlw=5:ser=on:spb=goal:acc=on:uwa=off:foolp=on:s2agt=16:slsqc=1:slsq=on:random_seed=1610866311:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2944 on theBenchmark for (2944ds/646Mi)
% 47.53/7.11 % (2686120)Instruction limit reached!
% 47.53/7.11 % (2686120)------------------------------
% 47.53/7.11 % (2686120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686120)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686120)Termination reason: Instruction limit
% 47.53/7.11 % (2686120)Termination phase: Saturation
% 47.53/7.11 % (2686120)Time elapsed: 0.201 s
% 47.53/7.11 % (2686120)Peak memory usage: 16 MB
% 47.53/7.11 % (2686120)Instructions burned: 446 (million)
% 47.53/7.11 % (2686130)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=1282283610:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2943 on theBenchmark for (2943ds/1924Mi)
% 47.53/7.11 % (2686118)Instruction limit reached!
% 47.53/7.11 % (2686118)------------------------------
% 47.53/7.11 % (2686118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686118)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686118)Termination reason: Instruction limit
% 47.53/7.11 % (2686118)Termination phase: Property scanning
% 47.53/7.11 % (2686118)Time elapsed: 0.332 s
% 47.53/7.11 % (2686118)Peak memory usage: 16 MB
% 47.53/7.11 % (2686118)Instructions burned: 843 (million)
% 47.53/7.11 % (2686132)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=900737860:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2942 on theBenchmark for (2942ds/984Mi)
% 47.53/7.11 % (2686126)Instruction limit reached!
% 47.53/7.11 % (2686126)------------------------------
% 47.53/7.11 % (2686126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686126)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686126)Termination reason: Instruction limit
% 47.53/7.11 % (2686126)Termination phase: Saturation
% 47.53/7.11 % (2686126)Time elapsed: 0.299 s
% 47.53/7.11 % (2686126)Peak memory usage: 23 MB
% 47.53/7.11 % (2686126)Instructions burned: 1358 (million)
% 47.53/7.11 % (2686127)Instruction limit reached!
% 47.53/7.11 % (2686127)------------------------------
% 47.53/7.11 % (2686127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686127)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686127)Termination reason: Instruction limit
% 47.53/7.11 % (2686127)Termination phase: Saturation
% 47.53/7.11 % (2686127)Time elapsed: 0.293 s
% 47.53/7.11 % (2686127)Peak memory usage: 17 MB
% 47.53/7.11 % (2686127)Instructions burned: 647 (million)
% 47.53/7.11 % (2686134)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=4197408603:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2941 on theBenchmark for (2941ds/592Mi)
% 47.53/7.11 % (2686136)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=2626268101:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2941 on theBenchmark for (2941ds/872Mi)
% 47.53/7.11 % (2686134)Instruction limit reached!
% 47.53/7.11 % (2686134)------------------------------
% 47.53/7.11 % (2686134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686134)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686134)Termination reason: Instruction limit
% 47.53/7.11 % (2686134)Termination phase: Saturation
% 47.53/7.11 % (2686134)Time elapsed: 0.147 s
% 47.53/7.11 % (2686134)Peak memory usage: 18 MB
% 47.53/7.11 % (2686134)Instructions burned: 596 (million)
% 47.53/7.11 % (2686138)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 47.53/7.11 % (2686138)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1885135450:i=999:add=on:rtra=on_2939 on theBenchmark for (2939ds/999Mi)
% 47.53/7.11 % (2686132)Instruction limit reached!
% 47.53/7.11 % (2686132)------------------------------
% 47.53/7.11 % (2686132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686132)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686132)Termination reason: Instruction limit
% 47.53/7.11 % (2686132)Termination phase: Saturation
% 47.53/7.11 % (2686132)Time elapsed: 0.440 s
% 47.53/7.11 % (2686132)Peak memory usage: 21 MB
% 47.53/7.11 % (2686132)Instructions burned: 986 (million)
% 47.53/7.11 % (2686140)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 47.53/7.11 % (2686140)dis+1010_1_to=lpo:irw=on:plsq=on:drc=ordering:plsqc=4:cnfonf=lazy_simp:si=on:sp=reverse_frequency:sos=on:plsqr=32,1:cbe=off:uwa=off:rp=on:lwlo=on:random_seed=3811675369:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2938 on theBenchmark for (2938ds/244Mi)
% 47.53/7.11 % (2686138)Instruction limit reached!
% 47.53/7.11 % (2686138)------------------------------
% 47.53/7.11 % (2686138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686138)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686138)Termination reason: Instruction limit
% 47.53/7.11 % (2686138)Termination phase: Saturation
% 47.53/7.11 % (2686138)Time elapsed: 0.245 s
% 47.53/7.11 % (2686138)Peak memory usage: 16 MB
% 47.53/7.11 % (2686138)Instructions burned: 1001 (million)
% 47.53/7.11 % (2686142)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=3750114003:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2937 on theBenchmark for (2937ds/113Mi)
% 47.53/7.11 % (2686136)Instruction limit reached!
% 47.53/7.11 % (2686136)------------------------------
% 47.53/7.11 % (2686136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686136)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686136)Termination reason: Instruction limit
% 47.53/7.11 % (2686136)Termination phase: Saturation
% 47.53/7.11 % (2686136)Time elapsed: 0.411 s
% 47.53/7.11 % (2686136)Peak memory usage: 19 MB
% 47.53/7.11 % (2686136)Instructions burned: 874 (million)
% 47.53/7.11 % (2686140)Instruction limit reached!
% 47.53/7.11 % (2686140)------------------------------
% 47.53/7.11 % (2686140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686140)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686140)Termination reason: Instruction limit
% 47.53/7.11 % (2686140)Termination phase: Saturation
% 47.53/7.11 % (2686140)Time elapsed: 0.103 s
% 47.53/7.11 % (2686140)Peak memory usage: 15 MB
% 47.53/7.11 % (2686140)Instructions burned: 244 (million)
% 47.53/7.11 % (2686142)Instruction limit reached!
% 47.53/7.11 % (2686142)------------------------------
% 47.53/7.11 % (2686142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686142)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686142)Termination reason: Instruction limit
% 47.53/7.11 % (2686142)Termination phase: Property scanning
% 47.53/7.11 % (2686142)Time elapsed: 0.027 s
% 47.53/7.11 % (2686142)Peak memory usage: 12 MB
% 47.53/7.11 % (2686142)Instructions burned: 116 (million)
% 47.53/7.11 % (2686144)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=579092668:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2936 on theBenchmark for (2936ds/7795Mi)
% 47.53/7.11 % (2686145)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4161319595:st=2:i=5026:sd=1:rtra=on:ss=axioms_2936 on theBenchmark for (2936ds/5026Mi)
% 47.53/7.11 % (2686146)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 47.53/7.11 % (2686146)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=3640904630:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2936 on theBenchmark for (2936ds/763Mi)
% 47.53/7.11 % (2685898)Instruction limit reached!
% 47.53/7.11 % (2685898)------------------------------
% 47.53/7.11 % (2685898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2685898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2685898)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2685898)Termination reason: Instruction limit
% 47.53/7.11 % (2685898)Termination phase: Saturation
% 47.53/7.11 % (2685898)Time elapsed: 5.362 s
% 47.53/7.11 % (2685898)Peak memory usage: 49 MB
% 47.53/7.11 % (2685898)Instructions burned: 9840 (million)
% 47.53/7.11 % (2686150)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2982766025:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2935 on theBenchmark for (2935ds/1144Mi)
% 47.53/7.11 % (2686146)Instruction limit reached!
% 47.53/7.11 % (2686146)------------------------------
% 47.53/7.11 % (2686146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686146)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686146)Termination reason: Instruction limit
% 47.53/7.11 % (2686146)Termination phase: Saturation
% 47.53/7.11 % (2686146)Time elapsed: 0.176 s
% 47.53/7.11 % (2686146)Peak memory usage: 15 MB
% 47.53/7.11 % (2686146)Instructions burned: 767 (million)
% 47.53/7.11 % (2686152)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 47.53/7.11 % (2686152)dis+1002_50_to=kbo:sil=128000:tgt=ground:plsq=on:plsqc=1:si=on:sp=occurrence:plsqr=64,1:nwc=3:flr=on:chr=on:random_seed=1907939551:hsqr=23,10:uwa_fpi=on:i=52:kws=frequency:hud=15:fsr=off:rtra=on:amm=off:ntd=on:rawr=on_2934 on theBenchmark for (2934ds/52Mi)
% 47.53/7.11 % (2686152)Instruction limit reached!
% 47.53/7.11 % (2686152)------------------------------
% 47.53/7.11 % (2686152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686152)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686152)Termination reason: Instruction limit
% 47.53/7.11 % (2686152)Termination phase: Preprocessing 3
% 47.53/7.11 % (2686152)Time elapsed: 0.013 s
% 47.53/7.11 % (2686152)Peak memory usage: 11 MB
% 47.53/7.11 % (2686152)Instructions burned: 55 (million)
% 47.53/7.11 % (2686154)dis+1010_1_sil=128000:si=on:etr=on:uwa=off:random_seed=2584137516:i=1724:fsr=off:rtra=on:fe=abstraction_2934 on theBenchmark for (2934ds/1724Mi)
% 47.53/7.11 % (2686130)Instruction limit reached!
% 47.53/7.11 % (2686130)------------------------------
% 47.53/7.11 % (2686130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686130)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686130)Termination reason: Instruction limit
% 47.53/7.11 % (2686130)Termination phase: Saturation
% 47.53/7.11 % (2686130)Time elapsed: 0.879 s
% 47.53/7.11 % (2686130)Peak memory usage: 23 MB
% 47.53/7.11 % (2686130)Instructions burned: 1926 (million)
% 47.53/7.11 % (2686156)dis-1004_128_to=kbo:sil=128000:tgt=full:si=on:fdtod=off:sp=const_frequency:spb=goal:uwa=off:slsqc=3:slsq=on:random_seed=1863735737:i=439:add=on:slsql=off:rtra=on:ntd=on_2934 on theBenchmark for (2934ds/439Mi)
% 47.53/7.11 % (2686150) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2685728-2686150"...
% 47.53/7.11 % (2686156)Instruction limit reached!
% 47.53/7.11 % (2686156)------------------------------
% 47.53/7.11 % (2686156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.11 % (2686156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.11 % (2686156)CaDiCaL version: 2.1.3
% 47.53/7.11 % (2686156)Termination reason: Instruction limit
% 47.53/7.11 % (2686156)Termination phase: Saturation
% 47.53/7.11 % (2686156)Time elapsed: 0.195 s
% 47.53/7.11 % (2686156)Peak memory usage: 16 MB
% 47.53/7.11 % (2686156)Instructions burned: 440 (million)
% 47.53/7.11 % (2686150)...printing done.
% 47.53/7.11 % (2686158)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1621719012:i=6395:sd=1:rtra=on:ss=axioms_2931 on theBenchmark for (2931ds/6395Mi)
% 47.53/7.11 % (2686150)Refutation found. Thanks to Tanya!
% 47.53/7.11 % SZS status Theorem for theBenchmark
% 47.53/7.11 % SZS output start Proof for theBenchmark
% 47.53/7.11 thf(type_def_5, type, term: $tType).
% 47.53/7.11 thf(type_def_6, type, subst: $tType).
% 47.53/7.11 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 47.53/7.11 thf(type_def_8, type, d_term: $tType).
% 47.53/7.11 thf(type_def_9, type, d_subst: $tType).
% 47.53/7.11 thf(func_def_0, type, one: term).
% 47.53/7.11 thf(func_def_1, type, ap: (term > term > term)).
% 47.53/7.11 thf(func_def_2, type, lam: (term > term)).
% 47.53/7.11 thf(func_def_3, type, sub: (term > subst > term)).
% 47.53/7.11 thf(func_def_4, type, id: subst).
% 47.53/7.11 thf(func_def_5, type, sh: subst).
% 47.53/7.11 thf(func_def_6, type, push: (term > subst > subst)).
% 47.53/7.11 thf(func_def_7, type, comp: (subst > subst > subst)).
% 47.53/7.11 thf(func_def_8, type, var: (term > $o)).
% 47.53/7.11 thf(func_def_9, type, pushprop_lem1v2: $o).
% 47.53/7.11 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 47.53/7.11 thf(func_def_11, type, axmap: $o).
% 47.53/7.11 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 47.53/7.11 thf(func_def_13, type, shinj: $o).
% 47.53/7.11 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 47.53/7.11 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 47.53/7.11 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 47.53/7.11 thf(func_def_17, type, induction2lem: $o).
% 47.53/7.11 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 47.53/7.11 thf(func_def_19, type, axvarshift: $o).
% 47.53/7.11 thf(func_def_20, type, hoasapinj2: $o).
% 47.53/7.11 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 47.53/7.11 thf(func_def_22, type, hoasapinj1: $o).
% 47.53/7.11 thf(func_def_23, type, ulamvar1: $o).
% 47.53/7.11 thf(func_def_24, type, induction2lem_lthm: $o).
% 47.53/7.11 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 47.53/7.11 thf(func_def_26, type, apnotvar: $o).
% 47.53/7.11 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 47.53/7.11 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 47.53/7.11 thf(func_def_29, type, hoasinduction_lthm: $o).
% 47.53/7.11 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 47.53/7.11 thf(func_def_31, type, hoaslaminj: $o).
% 47.53/7.11 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 47.53/7.11 thf(func_def_33, type, induction2lem_gthm: $o).
% 47.53/7.11 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 47.53/7.11 thf(func_def_35, type, hoasinduction_lem3: $o).
% 47.53/7.11 thf(func_def_36, type, hoasinduction_lem2: $o).
% 47.53/7.11 thf(func_def_37, type, termmset_lthm: $o).
% 47.53/7.11 thf(func_def_38, type, hoasinduction_lem1: $o).
% 47.53/7.11 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 47.53/7.11 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 47.53/7.11 thf(func_def_41, type, hoasapnotvar: $o).
% 47.53/7.11 thf(func_def_42, type, hoasinduction_lem0: $o).
% 47.53/7.11 thf(func_def_43, type, hoasinduction: $o).
% 47.53/7.11 thf(func_def_44, type, hoasinduction_gthm: $o).
% 47.53/7.11 thf(func_def_45, type, axapp: $o).
% 47.53/7.11 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 47.53/7.11 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 47.53/7.11 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 47.53/7.11 thf(func_def_49, type, ulamvarind: $o).
% 47.53/7.11 thf(func_def_50, type, induction: $o).
% 47.53/7.11 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 47.53/7.11 thf(func_def_52, type, termmset_gthm: $o).
% 47.53/7.11 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 47.53/7.11 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 47.53/7.11 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 47.53/7.11 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 47.53/7.11 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 47.53/7.11 thf(func_def_58, type, pushprop_lem2v2: $o).
% 47.53/7.11 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 47.53/7.11 thf(func_def_60, type, axclos: $o).
% 47.53/7.11 thf(func_def_61, type, axassoc: $o).
% 47.53/7.11 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 47.53/7.11 thf(func_def_63, type, pushprop_lthm: $o).
% 47.53/7.11 thf(func_def_64, type, apinj2: $o).
% 47.53/7.11 thf(func_def_65, type, apinj1: $o).
% 47.53/7.11 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 47.53/7.11 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 47.53/7.11 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 47.53/7.11 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 47.53/7.11 thf(func_def_70, type, axvarcons: $o).
% 47.53/7.11 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 47.53/7.11 thf(func_def_72, type, axscons: $o).
% 47.53/7.11 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 47.53/7.11 thf(func_def_74, type, axidr: $o).
% 47.53/7.11 thf(func_def_75, type, pushprop_lem1: $o).
% 47.53/7.11 thf(func_def_76, type, laminj: $o).
% 47.53/7.11 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 47.53/7.11 thf(func_def_78, type, pushprop_lem0: $o).
% 47.53/7.11 thf(func_def_79, type, pushprop_gthm: $o).
% 47.53/7.11 thf(func_def_80, type, axabs: $o).
% 47.53/7.11 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 47.53/7.11 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 47.53/7.11 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 47.53/7.11 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 47.53/7.11 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 47.53/7.11 thf(func_def_86, type, lamnotap: $o).
% 47.53/7.11 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 47.53/7.11 thf(func_def_88, type, hoaslamnotvar: $o).
% 47.53/7.11 thf(func_def_89, type, axidl: $o).
% 47.53/7.11 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 47.53/7.11 thf(func_def_91, type, induction2_lthm: $o).
% 47.53/7.11 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 47.53/7.11 thf(func_def_93, type, substmonoid_lthm: $o).
% 47.53/7.11 thf(func_def_94, type, pushprop: $o).
% 47.53/7.11 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 47.53/7.11 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 47.53/7.11 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 47.53/7.11 thf(func_def_98, type, substmonoid: $o).
% 47.53/7.11 thf(func_def_99, type, lamnotvar: $o).
% 47.53/7.11 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 47.53/7.11 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 47.53/7.11 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 47.53/7.11 thf(func_def_103, type, induction2_gthm: $o).
% 47.53/7.11 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 47.53/7.11 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_106, type, hoaslamnotap: $o).
% 47.53/7.11 thf(func_def_107, type, substmonoid_gthm: $o).
% 47.53/7.11 thf(func_def_108, type, ulamvarsh: $o).
% 47.53/7.11 thf(func_def_109, type, induction2: $o).
% 47.53/7.11 thf(func_def_110, type, pushprop_lem3v2: $o).
% 47.53/7.11 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 47.53/7.11 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 47.53/7.11 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 47.53/7.11 thf(func_def_114, type, axshiftcons: $o).
% 47.53/7.11 thf(func_def_115, type, termmset: $o).
% 47.53/7.11 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 47.53/7.11 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 47.53/7.11 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 47.53/7.11 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 47.53/7.11 thf(func_def_120, type, axvarid: $o).
% 47.53/7.11 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 47.53/7.11 thf(func_def_122, type, d2term: (d_term > term)).
% 47.53/7.11 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 47.53/7.11 thf(func_def_124, type, d_one: d_term).
% 47.53/7.11 thf(func_def_125, type, d_id: d_subst).
% 47.53/7.11 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)).
% 47.53/7.11 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 47.53/7.11 thf(func_def_131, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 47.53/7.11 thf(func_def_132, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 47.53/7.11 thf(func_def_133, type, db2: !>[X0: $tType]:(X0)).
% 47.53/7.11 thf(func_def_134, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 47.53/7.11 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 47.53/7.11 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 47.53/7.11 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_138, type, sP1: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_139, type, sP2: $o).
% 47.53/7.11 thf(func_def_140, type, sP3: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_141, type, sP4: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_142, type, sP5: $o).
% 47.53/7.11 thf(func_def_143, type, sP6: $o).
% 47.53/7.11 thf(func_def_144, type, sP7: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_145, type, sP8: $o).
% 47.53/7.11 thf(func_def_146, type, sP9: $o).
% 47.53/7.11 thf(func_def_147, type, sP10: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_149, type, sP12: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_150, type, sP13: $o).
% 47.53/7.11 thf(func_def_151, type, sP14: $o).
% 47.53/7.11 thf(func_def_152, type, sP15: $o).
% 47.53/7.11 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_154, type, sP17: $o).
% 47.53/7.11 thf(func_def_155, type, sP18: $o).
% 47.53/7.11 thf(func_def_156, type, sP19: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_157, type, sP20: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_158, type, sP21: $o).
% 47.53/7.11 thf(func_def_159, type, sP22: $o).
% 47.53/7.11 thf(func_def_160, type, sP23: $o).
% 47.53/7.11 thf(func_def_161, type, sP24: $o).
% 47.53/7.11 thf(func_def_162, type, sP25: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_163, type, sP26: $o).
% 47.53/7.11 thf(func_def_164, type, sP27: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_165, type, sP28: $o).
% 47.53/7.11 thf(func_def_166, type, sP29: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_167, type, sP30: $o).
% 47.53/7.11 thf(func_def_168, type, sP31: $o).
% 47.53/7.11 thf(func_def_169, type, sP32: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_170, type, sP33: $o).
% 47.53/7.11 thf(func_def_171, type, sP34: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_172, type, sP35: $o).
% 47.53/7.11 thf(func_def_173, type, sP36: $o).
% 47.53/7.11 thf(func_def_174, type, sP37: $o).
% 47.53/7.11 thf(func_def_175, type, sP38: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_176, type, sP39: $o).
% 47.53/7.11 thf(func_def_177, type, sP40: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_178, type, sP41: $o).
% 47.53/7.11 thf(func_def_179, type, sP42: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_180, type, sP43: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_181, type, sP44: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_182, type, sP45: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_183, type, sP46: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_184, type, sP47: $o).
% 47.53/7.11 thf(func_def_185, type, sP48: $o).
% 47.53/7.11 thf(func_def_186, type, sP49: $o).
% 47.53/7.11 thf(func_def_187, type, sP50: $o).
% 47.53/7.11 thf(func_def_188, type, sP51: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_189, type, sP52: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_190, type, sP53: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_191, type, sP54: $o).
% 47.53/7.11 thf(func_def_192, type, sP55: $o).
% 47.53/7.11 thf(func_def_193, type, sP56: ((subst > term > subst > $o) > $o)).
% 47.53/7.11 thf(func_def_194, type, sP57: ((term > $o) > $o)).
% 47.53/7.11 thf(func_def_195, type, sP58: $o).
% 47.53/7.11 thf(func_def_196, type, sP59: $o).
% 47.53/7.11 thf(func_def_197, type, sP60: $o).
% 47.53/7.11 thf(func_def_198, type, sP61: $o).
% 47.53/7.11 thf(func_def_199, type, sK62: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_200, type, sK63: term).
% 47.53/7.11 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_202, type, sK65: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_203, type, sK66: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_204, type, sK67: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_205, type, sK68: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_206, type, sK69: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_207, type, sK70: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_209, type, sK72: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_210, type, sK73: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_211, type, sK74: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_212, type, sK75: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_213, type, sK76: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_214, type, sK77: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_215, type, sK78: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_216, type, sK79: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_217, type, sK80: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_218, type, sK81: (term > $o)).
% 47.53/7.11 thf(func_def_219, type, sK82: term).
% 47.53/7.11 thf(func_def_220, type, sK83: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_221, type, sK84: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_222, type, sK85: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_223, type, sK86: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_224, type, sK87: (term > subst > term > term)).
% 47.53/7.11 thf(func_def_225, type, sK88: (term > (term > $o) > term)).
% 47.53/7.11 thf(func_def_226, type, sK89: ((term > $o) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_227, type, sK90: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_228, type, sK91: term).
% 47.53/7.11 thf(func_def_229, type, sK92: term).
% 47.53/7.11 thf(func_def_230, type, sK93: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_231, type, sK94: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_232, type, sK95: term).
% 47.53/7.11 thf(func_def_233, type, sK96: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_234, type, sK97: ((subst > term > subst > $o) > term > $o)).
% 47.53/7.11 thf(func_def_235, type, sK98: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_236, type, sK99: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_237, type, sK100: term).
% 47.53/7.11 thf(func_def_238, type, sK101: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_239, type, sK102: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_240, type, sK103: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_241, type, sK104: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_242, type, sK105: term).
% 47.53/7.11 thf(func_def_243, type, sK106: (term > $o)).
% 47.53/7.11 thf(func_def_244, type, sK107: (term > term)).
% 47.53/7.11 thf(func_def_245, type, sK108: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_246, type, sK109: ((term > $o) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_247, type, sK110: ((term > $o) > term > term)).
% 47.53/7.11 thf(func_def_248, type, sK111: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_249, type, sK112: term).
% 47.53/7.11 thf(func_def_250, type, sK113: (term > $o)).
% 47.53/7.11 thf(func_def_251, type, sK114: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_252, type, sK115: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_253, type, sK116: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_254, type, sK117: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_255, type, sK118: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_256, type, sK119: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_257, type, sK120: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_258, type, sK121: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_259, type, sK122: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_260, type, sK123: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_261, type, sK124: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_262, type, sK125: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_263, type, sK126: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_264, type, sK127: term).
% 47.53/7.11 thf(func_def_265, type, sK128: (term > $o)).
% 47.53/7.11 thf(func_def_266, type, sK129: term).
% 47.53/7.11 thf(func_def_267, type, sK130: subst).
% 47.53/7.11 thf(func_def_268, type, sK131: subst).
% 47.53/7.11 thf(func_def_269, type, sK132: subst).
% 47.53/7.11 thf(func_def_270, type, sK133: term).
% 47.53/7.11 thf(func_def_271, type, sK134: subst).
% 47.53/7.11 thf(func_def_272, type, sK135: (term > $o)).
% 47.53/7.11 thf(func_def_273, type, sK136: term).
% 47.53/7.11 thf(func_def_274, type, sK137: (term > term)).
% 47.53/7.11 thf(func_def_275, type, sK138: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_276, type, sK139: ((term > $o) > subst > term)).
% 47.53/7.11 thf(func_def_277, type, sK140: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_278, type, sK141: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_279, type, sK142: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_280, type, sK143: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_281, type, sK144: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_282, type, sK145: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_283, type, sK146: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_284, type, sK147: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_285, type, sK148: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_286, type, sK149: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_287, type, sK150: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_288, type, sK151: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_289, type, sK152: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_290, type, sK153: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_291, type, sK154: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_292, type, sK155: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_293, type, sK156: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_294, type, sK157: term).
% 47.53/7.11 thf(func_def_295, type, sK158: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_296, type, sK159: term).
% 47.53/7.11 thf(func_def_297, type, sK160: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_298, type, sK161: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_299, type, sK162: (term > $o)).
% 47.53/7.11 thf(func_def_300, type, sK163: term).
% 47.53/7.11 thf(func_def_301, type, sK164: (term > term)).
% 47.53/7.11 thf(func_def_302, type, sK165: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_303, type, sK166: term).
% 47.53/7.11 thf(func_def_304, type, sK167: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_305, type, sK168: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_306, type, sK169: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_308, type, sK171: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_309, type, sK172: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_310, type, sK173: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_311, type, sK174: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_312, type, sK175: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_313, type, sK176: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_314, type, sK177: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_315, type, sK178: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_318, type, sK181: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_319, type, sK182: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_320, type, sK183: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_321, type, sK184: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_322, type, sK185: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_323, type, sK186: term).
% 47.53/7.11 thf(func_def_324, type, sK187: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_325, type, sK188: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_326, type, sK189: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_327, type, sK190: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_328, type, sK191: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_329, type, sK192: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_330, type, sK193: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_331, type, sK194: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_332, type, sK195: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_333, type, sK196: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_334, type, sK197: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_335, type, sK198: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_336, type, sK199: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_337, type, sK200: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_338, type, sK201: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_339, type, sK202: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_340, type, sK203: subst).
% 47.53/7.11 thf(func_def_341, type, sK204: (term > $o)).
% 47.53/7.11 thf(func_def_342, type, sK205: term).
% 47.53/7.11 thf(func_def_343, type, sK206: (term > term)).
% 47.53/7.11 thf(func_def_344, type, sK207: ((term > $o) > subst > term)).
% 47.53/7.11 thf(func_def_345, type, sK208: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_346, type, sK209: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_347, type, sK210: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_348, type, sK211: term).
% 47.53/7.11 thf(func_def_349, type, sK212: (term > $o)).
% 47.53/7.11 thf(func_def_350, type, sK213: (term > term)).
% 47.53/7.11 thf(func_def_351, type, sK214: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_352, type, sK215: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_353, type, sK216: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_354, type, sK217: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_355, type, sK218: term).
% 47.53/7.11 thf(func_def_356, type, sK219: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_357, type, sK220: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_358, type, sK221: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_359, type, sK222: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_360, type, sK223: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_361, type, sK224: term).
% 47.53/7.11 thf(func_def_362, type, sK225: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_363, type, sK226: ((subst > term > subst > $o) > term > term)).
% 47.53/7.11 thf(func_def_364, type, sK227: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_365, type, sK228: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_366, type, sK229: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_367, type, sK230: term).
% 47.53/7.11 thf(func_def_368, type, sK231: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_369, type, sK232: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_370, type, sK233: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_371, type, sK234: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_372, type, sK235: (term > $o)).
% 47.53/7.11 thf(func_def_373, type, sK236: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_374, type, sK237: term).
% 47.53/7.11 thf(func_def_375, type, sK238: term).
% 47.53/7.11 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > (term > $o) > term)).
% 47.53/7.11 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_379, type, sK242: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_380, type, sK243: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_381, type, sK244: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_382, type, sK245: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_383, type, sK246: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_384, type, sK247: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_385, type, sK248: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_386, type, sK249: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_387, type, sK250: term).
% 47.53/7.11 thf(func_def_388, type, sK251: (term > $o)).
% 47.53/7.11 thf(func_def_389, type, sK252: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_390, type, sK253: ((subst > term > subst > $o) > (term > $o) > term)).
% 47.53/7.11 thf(func_def_391, type, sK254: ((term > $o) > term > term)).
% 47.53/7.11 thf(func_def_392, type, sK255: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_393, type, sK256: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_394, type, sK257: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_395, type, sK258: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_396, type, sK259: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_398, type, sK261: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_399, type, sK262: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_400, type, sK263: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_401, type, sK264: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_402, type, sK265: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_403, type, sK266: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_404, type, sK267: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_405, type, sK268: term).
% 47.53/7.11 thf(func_def_406, type, sK269: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_407, type, sK270: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_408, type, sK271: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_409, type, sK272: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_410, type, sK273: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > term > term)).
% 47.53/7.11 thf(func_def_413, type, sK276: term).
% 47.53/7.11 thf(func_def_414, type, sK277: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_415, type, sK278: ((subst > term > subst > $o) > term > term)).
% 47.53/7.11 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_417, type, sK280: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_418, type, sK281: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_419, type, sK282: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_420, type, sK283: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_421, type, sK284: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_422, type, sK285: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_423, type, sK286: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_424, type, sK287: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_425, type, sK288: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_426, type, sK289: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_427, type, sK290: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_428, type, sK291: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_429, type, sK292: term).
% 47.53/7.11 thf(func_def_430, type, sK293: (term > $o)).
% 47.53/7.11 thf(func_def_431, type, sK294: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_432, type, sK295: term).
% 47.53/7.11 thf(func_def_433, type, sK296: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_434, type, sK297: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_435, type, sK298: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_436, type, sK299: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_437, type, sK300: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_438, type, sK301: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_439, type, sK302: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_440, type, sK303: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_441, type, sK304: ((subst > term > subst > $o) > (term > $o) > term)).
% 47.53/7.11 thf(func_def_442, type, sK305: ((term > $o) > term > term)).
% 47.53/7.11 thf(func_def_443, type, sK306: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_444, type, sK307: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_445, type, sK308: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_446, type, sK309: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_447, type, sK310: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_448, type, sK311: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_449, type, sK312: term).
% 47.53/7.11 thf(func_def_450, type, sK313: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_451, type, sK314: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_452, type, sK315: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_453, type, sK316: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_454, type, sK317: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_455, type, sK318: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_456, type, sK319: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_457, type, sK320: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_458, type, sK321: term).
% 47.53/7.11 thf(func_def_459, type, sK322: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_460, type, sK323: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_461, type, sK324: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_462, type, sK325: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_463, type, sK326: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_464, type, sK327: ((subst > term > subst > $o) > term > term)).
% 47.53/7.11 thf(func_def_465, type, sK328: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_466, type, sK329: subst).
% 47.53/7.11 thf(func_def_467, type, sK330: term).
% 47.53/7.11 thf(func_def_468, type, sK331: (subst > term > term)).
% 47.53/7.11 thf(func_def_469, type, sK332: (subst > term > term)).
% 47.53/7.11 thf(func_def_470, type, sK333: term).
% 47.53/7.11 thf(func_def_471, type, sK334: subst).
% 47.53/7.11 thf(func_def_472, type, sK335: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_473, type, sK336: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_474, type, sK337: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_475, type, sK338: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_476, type, sK339: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_477, type, sK340: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_478, type, sK341: term).
% 47.53/7.11 thf(func_def_479, type, sK342: term).
% 47.53/7.11 thf(func_def_480, type, sK343: term).
% 47.53/7.11 thf(func_def_481, type, sK344: subst).
% 47.53/7.11 thf(func_def_482, type, sK345: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_483, type, sK346: term).
% 47.53/7.11 thf(func_def_484, type, sK347: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_485, type, sK348: (term > (subst > term > term) > term)).
% 47.53/7.11 thf(func_def_486, type, sK349: (term > (subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_487, type, sK350: (term > (subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_488, type, sK351: (term > (subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_489, type, sK352: (term > (subst > term > term) > term)).
% 47.53/7.11 thf(func_def_490, type, sK353: (term > (subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_491, type, sK354: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_492, type, sK355: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_493, type, sK356: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_494, type, sK357: term).
% 47.53/7.11 thf(func_def_495, type, sK358: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_496, type, sK359: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_497, type, sK360: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_498, type, sK361: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_499, type, sK362: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_500, type, sK363: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_501, type, sK364: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_502, type, sK365: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_503, type, sK366: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_504, type, sK367: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_505, type, sK368: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_506, type, sK369: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_507, type, sK370: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_508, type, sK371: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_509, type, sK372: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_510, type, sK373: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_511, type, sK374: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_512, type, sK375: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_513, type, sK376: term).
% 47.53/7.11 thf(func_def_514, type, sK377: term).
% 47.53/7.11 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_516, type, sK379: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_517, type, sK380: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_518, type, sK381: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_519, type, sK382: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_520, type, sK383: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_521, type, sK384: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_522, type, sK385: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_523, type, sK386: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_524, type, sK387: (term > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_525, type, sK388: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_526, type, sK389: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_527, type, sK390: term).
% 47.53/7.11 thf(func_def_528, type, sK391: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_529, type, sK392: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_530, type, sK393: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_531, type, sK394: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_532, type, sK395: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_533, type, sK396: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_534, type, sK397: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_535, type, sK398: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_536, type, sK399: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_537, type, sK400: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_538, type, sK401: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_539, type, sK402: ((subst > term > subst > $o) > term > $o)).
% 47.53/7.11 thf(func_def_540, type, sK403: term).
% 47.53/7.11 thf(func_def_541, type, sK404: (term > $o)).
% 47.53/7.11 thf(func_def_542, type, sK405: term).
% 47.53/7.11 thf(func_def_543, type, sK406: (term > term)).
% 47.53/7.11 thf(func_def_544, type, sK407: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_545, type, sK408: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_546, type, sK409: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_547, type, sK410: ((subst > term > subst > $o) > (term > $o) > term)).
% 47.53/7.11 thf(func_def_548, type, sK411: (term > (term > $o) > term)).
% 47.53/7.11 thf(func_def_549, type, sK412: (term > $o)).
% 47.53/7.11 thf(func_def_550, type, sK413: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_551, type, sK414: term).
% 47.53/7.11 thf(func_def_552, type, sK415: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_553, type, sK416: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_554, type, sK417: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_555, type, sK418: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_556, type, sK419: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_557, type, sK420: term).
% 47.53/7.11 thf(func_def_558, type, sK421: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_559, type, sK422: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_560, type, sK423: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_562, type, sK425: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_563, type, sK426: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_564, type, sK427: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_565, type, sK428: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_567, type, sK430: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_568, type, sK431: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_569, type, sK432: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_571, type, sK434: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_572, type, sK435: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_573, type, sK436: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_574, type, sK437: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_575, type, sK438: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_576, type, sK439: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_577, type, sK440: (term > $o)).
% 47.53/7.11 thf(func_def_578, type, sK441: term).
% 47.53/7.11 thf(func_def_579, type, sK442: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_580, type, sK443: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_581, type, sK444: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_582, type, sK445: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_583, type, sK446: ((term > $o) > (subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_584, type, sK447: ((subst > term > subst > $o) > subst > term > term)).
% 47.53/7.11 thf(func_def_585, type, sK448: (term > (term > $o) > term)).
% 47.53/7.11 thf(func_def_586, type, sK449: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_587, type, sK450: term).
% 47.53/7.11 thf(func_def_588, type, sK451: term).
% 47.53/7.11 thf(func_def_589, type, sK452: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_590, type, sK453: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_591, type, sK454: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_592, type, sK455: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_593, type, sK456: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_594, type, sK457: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_595, type, sK458: ((subst > term > subst > $o) > subst)).
% 47.53/7.11 thf(func_def_596, type, sK459: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_597, type, sK460: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_598, type, sK461: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_599, type, sK462: ((term > $o) > subst > term)).
% 47.53/7.11 thf(func_def_600, type, sK463: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_601, type, sK464: subst).
% 47.53/7.11 thf(func_def_602, type, sK465: term).
% 47.53/7.11 thf(func_def_603, type, sK466: (term > $o)).
% 47.53/7.11 thf(func_def_604, type, sK467: (term > term)).
% 47.53/7.11 thf(func_def_605, type, sK468: term).
% 47.53/7.11 thf(func_def_606, type, sK469: (term > $o)).
% 47.53/7.11 thf(func_def_607, type, sK470: term).
% 47.53/7.11 thf(func_def_608, type, sK471: (term > term)).
% 47.53/7.11 thf(func_def_609, type, sK472: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_610, type, sK473: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_611, type, sK474: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_612, type, sK475: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_613, type, sK476: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_614, type, sK477: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_615, type, sK478: subst).
% 47.53/7.11 thf(func_def_616, type, sK479: term).
% 47.53/7.11 thf(func_def_617, type, sK480: term).
% 47.53/7.11 thf(func_def_618, type, sK481: subst).
% 47.53/7.11 thf(func_def_619, type, sK482: term).
% 47.53/7.11 thf(func_def_620, type, sK483: subst).
% 47.53/7.11 thf(func_def_621, type, sK484: (term > $o)).
% 47.53/7.11 thf(func_def_622, type, sK485: (term > $o)).
% 47.53/7.11 thf(func_def_623, type, sK486: term).
% 47.53/7.11 thf(func_def_624, type, sK487: term).
% 47.53/7.11 thf(func_def_625, type, sK488: (term > $o)).
% 47.53/7.11 thf(func_def_626, type, sK489: (term > $o)).
% 47.53/7.11 thf(func_def_627, type, sK490: term).
% 47.53/7.11 thf(func_def_628, type, sK491: subst).
% 47.53/7.11 thf(func_def_629, type, sK492: term).
% 47.53/7.11 thf(func_def_630, type, sK493: term).
% 47.53/7.11 thf(func_def_631, type, sK494: term).
% 47.53/7.11 thf(func_def_632, type, sK495: term).
% 47.53/7.11 thf(func_def_633, type, sK496: term).
% 47.53/7.11 thf(func_def_634, type, sK497: term).
% 47.53/7.11 thf(func_def_635, type, sK498: term).
% 47.53/7.11 thf(func_def_636, type, sK499: subst).
% 47.53/7.11 thf(func_def_637, type, sK500: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_638, type, sK501: term).
% 47.53/7.11 thf(func_def_639, type, sK502: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_640, type, sK503: ((subst > term > subst > $o) > term)).
% 47.53/7.11 thf(func_def_641, type, sK504: term).
% 47.53/7.11 thf(func_def_642, type, sK505: term).
% 47.53/7.11 thf(func_def_643, type, sK506: subst).
% 47.53/7.11 thf(func_def_644, type, sK507: term).
% 47.53/7.11 thf(func_def_645, type, sK508: term).
% 47.53/7.11 thf(func_def_646, type, sK509: (subst > term > term)).
% 47.53/7.11 thf(func_def_647, type, sK510: term).
% 47.53/7.11 thf(func_def_648, type, sK511: subst).
% 47.53/7.11 thf(func_def_649, type, sK512: (subst > term > term)).
% 47.53/7.11 thf(func_def_650, type, sK513: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_651, type, sK514: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_652, type, sK515: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_653, type, sK516: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_654, type, sK517: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_655, type, sK518: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_656, type, sK519: term).
% 47.53/7.11 thf(func_def_657, type, sK520: term).
% 47.53/7.11 thf(func_def_658, type, sK521: term).
% 47.53/7.11 thf(func_def_659, type, sK522: term).
% 47.53/7.11 thf(func_def_660, type, sK523: term).
% 47.53/7.11 thf(func_def_661, type, sK524: term).
% 47.53/7.11 thf(func_def_662, type, sK525: term).
% 47.53/7.11 thf(func_def_663, type, sK526: term).
% 47.53/7.11 thf(func_def_664, type, sK527: term).
% 47.53/7.11 thf(func_def_665, type, sK528: term).
% 47.53/7.11 thf(func_def_666, type, sK529: term).
% 47.53/7.11 thf(func_def_667, type, sK530: term).
% 47.53/7.11 thf(func_def_668, type, sK531: term).
% 47.53/7.11 thf(func_def_669, type, sK532: term).
% 47.53/7.11 thf(func_def_670, type, sK533: (term > subst > term > term)).
% 47.53/7.11 thf(func_def_671, type, sK534: term).
% 47.53/7.11 thf(func_def_672, type, sK535: term).
% 47.53/7.11 thf(func_def_673, type, sK536: term).
% 47.53/7.11 thf(func_def_674, type, sK537: term).
% 47.53/7.11 thf(func_def_675, type, sK538: term).
% 47.53/7.11 thf(func_def_676, type, sK539: term).
% 47.53/7.11 thf(func_def_677, type, sK540: term).
% 47.53/7.11 thf(func_def_678, type, sK541: term).
% 47.53/7.11 thf(func_def_679, type, sK542: term).
% 47.53/7.11 thf(func_def_680, type, sK543: subst).
% 47.53/7.11 thf(func_def_681, type, sK544: term).
% 47.53/7.11 thf(func_def_682, type, sK545: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_683, type, sK546: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_684, type, sK547: (term > subst > term > term)).
% 47.53/7.11 thf(func_def_685, type, sK548: term).
% 47.53/7.11 thf(func_def_686, type, sK549: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_687, type, sK550: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_688, type, sK551: ((subst > term > subst > $o) > term > $o)).
% 47.53/7.11 thf(func_def_689, type, sK552: subst).
% 47.53/7.11 thf(func_def_690, type, sK553: term).
% 47.53/7.11 thf(func_def_691, type, sK554: (term > $o)).
% 47.53/7.11 thf(func_def_692, type, sK555: (term > $o)).
% 47.53/7.11 thf(func_def_693, type, sK556: term).
% 47.53/7.11 thf(func_def_694, type, sK557: subst).
% 47.53/7.11 thf(func_def_695, type, sK558: ((term > $o) > (term > $o) > term > subst > term)).
% 47.53/7.11 thf(func_def_696, type, sK559: ((term > $o) > term > subst > term > $o)).
% 47.53/7.11 thf(func_def_697, type, sK560: subst).
% 47.53/7.11 thf(func_def_698, type, sK561: term).
% 47.53/7.11 thf(func_def_699, type, sK562: (term > $o)).
% 47.53/7.11 thf(func_def_700, type, sK563: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_701, type, sK564: subst).
% 47.53/7.11 thf(func_def_702, type, sK565: subst).
% 47.53/7.11 thf(func_def_703, type, sK566: subst).
% 47.53/7.11 thf(func_def_704, type, sK567: term).
% 47.53/7.11 thf(func_def_705, type, sK568: subst).
% 47.53/7.11 thf(func_def_706, type, sK569: (term > $o)).
% 47.53/7.11 thf(func_def_707, type, sK570: term).
% 47.53/7.11 thf(func_def_708, type, sK571: subst).
% 47.53/7.11 thf(func_def_709, type, sK572: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_710, type, sK573: (subst > term > (term > $o) > term > $o)).
% 47.53/7.11 thf(func_def_711, type, sK574: (subst > d_subst)).
% 47.53/7.11 thf(func_def_712, type, sK575: term).
% 47.53/7.11 thf(func_def_713, type, sK576: (term > $o)).
% 47.53/7.11 thf(func_def_714, type, sK577: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_715, type, sK578: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_716, type, sK579: term).
% 47.53/7.11 thf(func_def_717, type, sK580: term).
% 47.53/7.11 thf(func_def_718, type, sK581: term).
% 47.53/7.11 thf(func_def_719, type, sK582: term).
% 47.53/7.11 thf(func_def_720, type, sK583: subst).
% 47.53/7.11 thf(func_def_721, type, sK584: subst).
% 47.53/7.11 thf(func_def_722, type, sK585: subst).
% 47.53/7.11 thf(func_def_723, type, sK586: subst).
% 47.53/7.11 thf(func_def_724, type, sK587: (term > d_term)).
% 47.53/7.11 thf(func_def_725, type, sK588: ((subst > term > subst > $o) > term > $o)).
% 47.53/7.11 thf(func_def_726, type, sK589: (subst > term > subst > $o)).
% 47.53/7.11 thf(func_def_727, type, sK590: ((term > $o) > term)).
% 47.53/7.11 thf(func_def_728, type, sK591: (term > $o)).
% 47.53/7.11 thf(func_def_729, type, sK592: subst).
% 47.53/7.11 thf(func_def_730, type, sK593: (term > $o)).
% 47.53/7.11 thf(func_def_731, type, sK594: term).
% 47.53/7.11 thf(func_def_732, type, sK595: (term > (term > $o) > subst > (term > $o) > term)).
% 47.53/7.11 thf(func_def_733, type, sK596: term).
% 47.53/7.11 thf(func_def_734, type, sK597: (term > subst > term > term)).
% 47.53/7.11 thf(func_def_735, type, sK598: term).
% 47.53/7.11 thf(func_def_736, type, sK599: term).
% 47.53/7.11 thf(func_def_737, type, sK600: term).
% 47.53/7.11 thf(func_def_738, type, sK601: term).
% 47.53/7.11 thf(func_def_739, type, sK602: (subst > term > term)).
% 47.53/7.11 thf(func_def_740, type, sK603: term).
% 47.53/7.11 thf(func_def_741, type, sK604: term).
% 47.53/7.11 thf(func_def_742, type, sK605: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_743, type, sK606: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_744, type, sK607: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_745, type, sK608: term).
% 47.53/7.11 thf(func_def_746, type, sK609: ((subst > term > term) > term)).
% 47.53/7.11 thf(func_def_747, type, sK610: ((subst > term > term) > subst)).
% 47.53/7.11 thf(func_def_748, type, sK611: (term > subst > term > term)).
% 47.53/7.11 thf(f1,axiom,(
% 47.53/7.11 (sh = ((d2subst @ d_id))) & (! [X20 : term,X15 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & hoasinduction_lem1 & ! [X5 : d_subst] : (X5 = d_id) & (! [X18 : (subst > term > term),X46 : term,X47 : term] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & axclos & ~lamnotap & ~(var @ (d2term @ d_one)) & substmonoid_gthm & (! [X15 : term,X19 : term,X20 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id))))) & (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X28 @ id) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))))) & (one = ((d2term @ d_one))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))) & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))) & ! [X1 : d_term] : (X1 = d_one) & hoasapinj1_gthm & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))))) <=> hoasinduction_lem3v2a_lthm) & induction2lem_gthm & axassoc & pushprop_lem0_gthm & (! [X13 : term,X19 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (! [X18 : (subst > term > term),X33 : term,X31 : (subst > term > term),X32 : subst] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslaminj) & ((! [X22 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id)) => (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) <=> hoasinduction_lthm) & hoasapnotvar_gthm & hoaslamnotvar & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))))) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X15 : term,X14 : subst,X26 : (term > $o),X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)))) <=> pushprop_lem1_lthm) & hoasapnotvar & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & hoasinduction_lem2_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction <=> ! [X10 : (term > $o),X21 : term] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X21))) & (! [X17 : subst,X16 : term,X10 : (term > $o)] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) <=> induction2lem) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & (pushprop_lem1 <=> ! [X10 : (term > $o),X14 : subst,X13 : term,X15 : term,X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & pushprop_lem1_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_lem2_gthm & axabs & pushprop_lthm_orig & (hoasinduction_lem3v2 <=> ! [X48 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & hoasinduction_lem3a_gthm & hoasinduction_gthm & (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem1_lthm & (pushprop_lem0 <=> ! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotap_lthm & hoaslamnotap_gthm & (! [X15 : term,X13 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & hoasinduction_lem3b_gthm & axmap & hoasinduction_lem1v2 & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoasinduction_lem2v2_gthm & hoaslaminj_gthm & apnotvar & induction2_gthm & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & (hoasapinj2 <=> ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) & pushprop_lem3v2 & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & (pushprop_lem0_lthm <=> ! [X13 : term,X10 : (term > $o),X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & pushprop_lem2v2_lthm & (hoasinduction_lem3v2a <=> ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))))) & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_gthm & (axshiftcons <=> ! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X18 : (subst > term > term),X32 : subst,X33 : term,X31 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))))) <=> hoaslaminj_lthm) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X13 : term,X14 : subst,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & axvarshift & hoaslamnotvar_lthm & (id = ((d2subst @ d_id))) & hoasinduction_lem1v2_gthm & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & lamnotvar & pushprop_lem2v2_gthm & ulamvarsh & ~ulamvar1 & pushprop & (! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) <=> hoasinduction_lem2) & (! [X13 : term,X11 : (term > $o),X10 : (term > $o),X14 : subst] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarind & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) => ! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)))))))) & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X35 : term,X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X41 : subst,X40 : term,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & pushprop_lem1v2_gthm & hoasinduction_lem1_gthm & pushprop_gthm & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & pushprop_lthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoasinduction_lem3v2_gthm & (induction2 <=> ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))) & (laminj <=> ! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & axapp & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & pushprop_lem3v2_lthm & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X44 : term,X45 : term] : (~(X11 @ X44) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj2_gthm & (hoasapinj2_lthm <=> (! [X15 : term,X20 : term,X13 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & termmset_gthm & hoasapnotvar_lthm & hoasinduction_lem3_gthm & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))))))),
% 47.53/7.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 47.53/7.11 thf(f2,conjecture,(
% 47.53/7.11 (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X3 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X2 : term,X4 : subst,X3 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => (! [X6 : (subst > term > term)] : (! [X3 : subst,X1 : subst,X2 : term] : (((sub @ (X6 @ X1 @ X2) @ X3)) = ((X6 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X6 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X6 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)),
% 47.53/7.11 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction)).
% 47.53/7.11 thf(f3,negated_conjecture,(
% 47.53/7.11 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X4 : subst,X3 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X2 : term,X4 : subst,X3 : subst] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => (! [X2 : term,X5 : term] : ((X0 @ id @ X2 @ id) => ((X0 @ id @ X5 @ id) => (X0 @ id @ (hoasap @ id @ X2 @ id @ X5) @ id))) => (! [X6 : (subst > term > term)] : (! [X3 : subst,X1 : subst,X2 : term] : (((sub @ (X6 @ X1 @ X2) @ X3)) = ((X6 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => (! [X2 : term] : ((X0 @ id @ X2 @ id) => (X0 @ id @ (X6 @ id @ X2) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X6 @ X1 @ X2)))) @ id))) => ! [X2 : term] : (X0 @ id @ X2 @ id)))))) = hoasinduction)),
% 47.53/7.11 inference(negated_conjecture,[status(cth)],[f2])).
% 47.53/7.11 thf(f4,plain,(
% 47.53/7.11 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X1 @ X4 @ (comp @ X2 @ X3)) => (X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) => (! [X5 : subst,X6 : term,X7 : subst,X8 : subst] : ((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8) => (X0 @ X5 @ X6 @ (comp @ X7 @ X8))) => (! [X9 : term] : ((hoasvar @ id @ X9 @ id) => (X0 @ id @ X9 @ id)) => (! [X10 : term,X11 : term] : ((X0 @ id @ X10 @ id) => ((X0 @ id @ X11 @ id) => (X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id))) => (! [X12 : (subst > term > term)] : (! [X13 : subst,X14 : subst,X15 : term] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) => (! [X16 : term] : ((X0 @ id @ X16 @ id) => (X0 @ id @ (X12 @ id @ X16) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X17 : subst, X18 : term] : ((X12 @ X17 @ X18)))) @ id))) => ! [X19 : term] : (X0 @ id @ X19 @ id)))))) = hoasinduction)),
% 47.53/7.11 inference(rectify,[],[f3])).
% 47.53/7.11 thf(f5,plain,(
% 47.53/7.11 ~(! [X0 : (subst > term > subst > $o)] : (! [X2 : subst,X3 : subst,X4 : term,X1 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) => (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) = $true)) => (! [X6 : term,X5 : subst,X8 : subst,X7 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) => (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) = $true)) => (! [X9 : term] : ((((hoasvar @ id @ X9 @ id)) = $true) => ($true = ((X0 @ id @ X9 @ id)))) => (! [X11 : term,X10 : term] : ((((X0 @ id @ X10 @ id)) = $true) => (($true = ((X0 @ id @ X11 @ id))) => (((X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id)) = $true))) => (! [X12 : (subst > term > term)] : (! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) => (! [X16 : term] : ((((X0 @ id @ X16 @ id)) = $true) => (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X19 : term] : (((X0 @ id @ X19 @ id)) = $true)))))) <=> (hoasinduction = $true))),
% 47.53/7.11 inference(fool_elimination,[],[f4])).
% 47.53/7.11 thf(f6,plain,(
% 47.53/7.11 (sh = ((d2subst @ d_id))) & (! [X0 : term,X1 : term,X2 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> apinj2) & hoasinduction_lem1 & ! [X4 : d_subst] : (d_id = X4) & (! [X5 : (subst > term > term),X6 : term,X7 : term] : (~ ! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7)))) <=> hoaslamnotap) & axclos & ~lamnotap & ~(var @ (d2term @ d_one)) & substmonoid_gthm & (! [X11 : term,X12 : term,X13 : term,X14 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> apinj1) & (hoasinduction_lem3_lthm <=> (! [X15 : term] : (((sub @ X15 @ id)) = X15) => (! [X16 : (subst > term > subst > $o),X17 : term] : ((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X19 : term] : ((X16 @ id @ (X18 @ id @ X19) @ id) | ~(X16 @ id @ X19 @ id)) | (X16 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X20 : subst,X21 : subst,X22 : term] : (((sub @ (X18 @ X20 @ X22) @ X21)) = ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) | ~ ! [X23 : term] : ((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id) | ~(X16 @ id @ X23 @ id))) => ! [X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X26 : (subst > term > term)] : (~ ! [X27 : subst,X28 : subst,X29 : term] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) | ~ ! [X30 : term] : ((X24 @ id @ (X26 @ id @ X30) @ id) | ~(X24 @ id @ X30 @ id)) | (X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31) | ~(X24 @ X33 @ X32 @ (comp @ X34 @ X31))) | ~ ! [X35 : term] : ((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id) | ~(X24 @ id @ X35 @ id)) | ~ ! [X36 : subst,X37 : subst,X38 : subst,X39 : term] : ((X24 @ X36 @ X39 @ (comp @ X37 @ X38)) | ~(X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) | (X24 @ id @ (lam @ X25) @ id))))) & (hoasinduction_lthm_3 <=> (! [X40 : (subst > term > subst > $o)] : ~ ! [X41 : (term > $o)] : ~ ! [X42 : term] : (((X40 @ id @ X42 @ id)) = ((X41 @ X42))) => (! [X43 : term,X44 : (term > $o)] : (~ ! [X45 : term] : (~(var @ X45) | (X44 @ X45)) | (X44 @ X43) | ~ ! [X46 : term] : (~ ! [X47 : term] : (~(X44 @ X47) | (X44 @ (sub @ X46 @ (push @ X47 @ id)))) | (X44 @ (lam @ X46))) | ~ ! [X48 : term,X49 : term] : ((X44 @ (ap @ X48 @ X49)) | ~(X44 @ X48) | ~(X44 @ X49))) => (! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : (term > $o),X53 : term] : (~ ! [X54 : term] : (~(X52 @ X54) | (X52 @ (sub @ X53 @ (push @ X54 @ id)))) | ~ ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) | (X52 @ (lam @ X53)) | ~ ! [X56 : (subst > term > term)] : ((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id) | ~ ! [X57 : term,X58 : subst,X59 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) = ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ~ ! [X60 : term] : (~(X51 @ id @ X60 @ id) | (X51 @ id @ (X56 @ id @ X60) @ id)))) => ! [X61 : (subst > term > subst > $o),X62 : term] : (~ ! [X63 : (subst > term > term)] : (~ ! [X64 : term] : ((X61 @ id @ (X63 @ id @ X64) @ id) | ~(X61 @ id @ X64 @ id)) | (X61 @ id @ (lam @ (X63 @ sh @ one)) @ id) | ~ ! [X65 : subst,X66 : subst,X67 : term] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66))))) | (X61 @ id @ X62 @ id) | ~ ! [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (~(X61 @ X68 @ X71 @ (comp @ X69 @ X70)) | (X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) | ~ ! [X72 : term] : ((X61 @ id @ X72 @ id) | ~(var @ (sub @ X72 @ id))) | ~ ! [X73 : term,X74 : term] : ((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id) | ~(X61 @ id @ X73 @ id) | ~(X61 @ id @ X74 @ id)) | ~ ! [X75 : subst,X76 : subst,X77 : subst,X78 : term] : (~(X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75) | (X61 @ X77 @ X78 @ (comp @ X76 @ X75))))))))) & (one = ((d2term @ d_one))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ! [X79 : d_subst,X80 : d_subst] : ((((d2subst @ X79)) = ((d2subst @ X80))) => (X79 = X80)) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (axscons <=> ! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81)) & (! [X82 : (subst > term > subst > $o),X83 : term] : (~ ! [X84 : term,X85 : term] : ((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id) | ~(X82 @ id @ X84 @ id) | ~(X82 @ id @ X85 @ id)) | (X82 @ id @ X83 @ id) | ~ ! [X86 : (subst > term > term)] : ((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id) | ~ ! [X87 : term] : ((X82 @ id @ (X86 @ id @ X87) @ id) | ~(X82 @ id @ X87 @ id)) | ~ ! [X88 : term,X89 : subst,X90 : subst] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90)))))) <=> hoasinduction_no_psi_cond) & (hoasinduction_lem3a_lthm <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => (! [X92 : (subst > term > subst > $o),X93 : term] : (~ ! [X94 : term] : (~(X92 @ id @ X94 @ id) | (X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) | (X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id) | ~ ! [X95 : (subst > term > term)] : (~ ! [X96 : subst,X97 : term,X98 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) = ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ~ ! [X99 : term] : (~(X92 @ id @ X99 @ id) | (X92 @ id @ (X95 @ id @ X99) @ id)) | (X92 @ id @ (lam @ (X95 @ sh @ one)) @ id))) => ! [X100 : (subst > term > subst > $o),X101 : term] : ((X100 @ id @ (lam @ X101) @ id) | ~ ! [X102 : term] : ((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id) | ~(X100 @ id @ X102 @ id)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X104 : subst,X105 : term,X106 : subst] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106))) | ~ ! [X107 : term] : (~(X100 @ id @ X107 @ id) | (X100 @ id @ (X103 @ id @ X107) @ id)) | (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)))))) & (hoasinduction_lem3a <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (~ ! [X110 : term] : ((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id) | ~(X108 @ id @ X110 @ id)) | (X108 @ id @ (lam @ X109) @ id) | ~ ! [X111 : (subst > term > term)] : (~ ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113))) | ~ ! [X115 : term] : (~(X108 @ id @ X115 @ id) | (X108 @ id @ (X111 @ id @ X115) @ id)) | (X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)))) & ! [X116 : d_term] : (d_one = X116) & hoasapinj1_gthm & ((! [X117 : term] : ~ ! [X118 : (subst > term > term)] : ~ ! [X119 : term,X120 : subst] : (((sub @ X117 @ (push @ X119 @ X120))) = ((X118 @ X120 @ X119))) => (! [X121 : term] : (((sub @ X121 @ id)) = X121) => ! [X122 : term,X123 : (term > $o),X124 : (subst > term > subst > $o)] : (~ ! [X125 : term] : (((X124 @ id @ X125 @ id)) = ((X123 @ X125))) | ~ ! [X126 : term] : (~(X123 @ X126) | (X123 @ (sub @ X122 @ (push @ X126 @ id)))) | (X123 @ (lam @ X122)) | ~ ! [X127 : (subst > term > term)] : (~ ! [X128 : subst,X129 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))) | (X124 @ id @ (lam @ (X127 @ sh @ one)) @ id) | ~ ! [X131 : term] : (~(X124 @ id @ X131 @ id) | (X124 @ id @ (X127 @ id @ X131) @ id)))))) <=> hoasinduction_lem3v2a_lthm) & induction2lem_gthm & axassoc & pushprop_lem0_gthm & (! [X132 : term,X133 : term,X134 : term,X135 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133)))) <=> hoasapinj1) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (! [X138 : (subst > term > term),X139 : term,X140 : (subst > term > term),X141 : subst] : ((((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))) | (((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ~ ! [X142 : term,X143 : subst,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) | ~ ! [X145 : subst,X146 : subst,X147 : term] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145))))) <=> hoaslaminj) & ((! [X148 : term,X149 : (term > $o)] : (~ ! [X150 : term,X151 : term] : (~(X149 @ X151) | ~(X149 @ X150) | (X149 @ (ap @ X151 @ X150))) | ~ ! [X152 : term] : (~ ! [X153 : term] : ((X149 @ (sub @ X152 @ (push @ X153 @ id))) | ~(X149 @ X153)) | (X149 @ (lam @ X152))) | (X149 @ X148) | ~ ! [X154 : term] : ((X149 @ X154) | ~(var @ X154))) => (! [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : (~ ! [X158 : subst,X159 : subst,X160 : term,X161 : subst] : (~(X156 @ X159 @ X160 @ (comp @ X161 @ X158)) | (X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) | (X156 @ id @ (ap @ X157 @ X155) @ id) | ~ ! [X162 : term,X163 : term] : (~(X156 @ id @ X162 @ id) | (X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id) | ~(X156 @ id @ X163 @ id)) | ~ ! [X164 : subst,X165 : subst,X166 : term,X167 : subst] : (~(X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165) | (X156 @ X167 @ X166 @ (comp @ X164 @ X165))) | ~(X156 @ id @ X157 @ id) | ~(X156 @ id @ X155 @ id)) => (! [X168 : term,X169 : (subst > term > subst > $o)] : (~ ! [X170 : subst,X171 : term,X172 : subst,X173 : subst] : (~(X169 @ X170 @ X171 @ (comp @ X172 @ X173)) | (X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) | ~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : ((X169 @ X174 @ X176 @ (comp @ X175 @ X177)) | ~(X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) | ~ ! [X178 : term] : (~(X169 @ id @ X178 @ id) | (X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) | (X169 @ id @ (lam @ X168) @ id) | ~ ! [X179 : (subst > term > term)] : (~ ! [X180 : term] : ((X169 @ id @ (X179 @ id @ X180) @ id) | ~(X169 @ id @ X180 @ id)) | ~ ! [X181 : subst,X182 : subst,X183 : term] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) = ((sub @ (X179 @ X182 @ X183) @ X181))) | (X169 @ id @ (lam @ (X179 @ sh @ one)) @ id))) => ! [X184 : term,X185 : (subst > term > subst > $o)] : (~ ! [X186 : subst,X187 : subst,X188 : term,X189 : subst] : (~(X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189) | (X185 @ X186 @ X188 @ (comp @ X187 @ X189))) | (X185 @ id @ X184 @ id) | ~ ! [X190 : term,X191 : term] : (~(X185 @ id @ X190 @ id) | ~(X185 @ id @ X191 @ id) | (X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) | ~ ! [X192 : subst,X193 : term,X194 : subst,X195 : subst] : (~(X185 @ X192 @ X193 @ (comp @ X194 @ X195)) | (X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) | ~ ! [X196 : term] : ((X185 @ id @ X196 @ id) | ~(var @ (sub @ X196 @ id))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~(X185 @ id @ X198 @ id) | (X185 @ id @ (X197 @ id @ X198) @ id)) | (X185 @ id @ (lam @ (X197 @ sh @ one)) @ id) | ~ ! [X199 : subst,X200 : term,X201 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))))) <=> hoasinduction_lthm) & hoasapnotvar_gthm & hoaslamnotvar & (hoasinduction_lem3v2_lthm <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X206 : subst,X207 : subst,X208 : term,X209 : subst] : ((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207) | ~(X203 @ X206 @ X208 @ (comp @ X209 @ X207))) | ~ ! [X210 : term] : (((X205 @ X210)) = ((X203 @ id @ X210 @ id))) | (X205 @ (lam @ X204)) | ~ ! [X211 : term] : ((X205 @ (sub @ X204 @ (push @ X211 @ id))) | ~(X205 @ X211)) | ~ ! [X212 : subst,X213 : term,X214 : subst,X215 : subst] : (~(X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212) | (X203 @ X214 @ X213 @ (comp @ X215 @ X212))) | ~ ! [X216 : (subst > term > term)] : ((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id) | ~ ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) | ~ ! [X220 : term] : ((X203 @ id @ (X216 @ id @ X220) @ id) | ~(X203 @ id @ X220 @ id)))))) & (hoasinduction_no_psi_cond_lthm <=> (! [X221 : (subst > term > subst > $o)] : ~ ! [X222 : (term > $o)] : ~ ! [X223 : term] : (((X221 @ id @ X223 @ id)) = ((X222 @ X223))) => (! [X224 : term,X225 : (term > $o)] : (~ ! [X226 : term,X227 : term] : ((X225 @ (ap @ X226 @ X227)) | ~(X225 @ X227) | ~(X225 @ X226)) | ~ ! [X228 : term] : ((X225 @ (lam @ X228)) | ~ ! [X229 : term] : ((X225 @ (sub @ X228 @ (push @ X229 @ id))) | ~(X225 @ X229))) | ~ ! [X230 : term] : ((X225 @ X230) | ~(var @ X230)) | (X225 @ X224)) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => (! [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : ((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id) | ~ ! [X236 : term,X237 : subst,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | ~ ! [X239 : term] : (~(X232 @ id @ X239 @ id) | (X232 @ id @ (X235 @ id @ X239) @ id))) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) | ~ ! [X241 : term] : (~(X234 @ X241) | (X234 @ (sub @ X233 @ (push @ X241 @ id)))) | (X234 @ (lam @ X233))) => ! [X242 : term,X243 : (subst > term > subst > $o)] : ((X243 @ id @ X242 @ id) | ~ ! [X244 : term,X245 : term] : (~(X243 @ id @ X244 @ id) | ~(X243 @ id @ X245 @ id) | (X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id)) | ~ ! [X246 : (subst > term > term)] : (~ ! [X247 : term] : (~(X243 @ id @ X247 @ id) | (X243 @ id @ (X246 @ id @ X247) @ id)) | ~ ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) | (X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)))))))) & ((! [X251 : term,X252 : subst] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X253 : subst,X254 : term] : (((comp @ sh @ (push @ X254 @ X253))) = X253) => ! [X255 : term,X256 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o)] : ((X258 @ (sub @ X255 @ (push @ X256 @ X257))) | ~(X259 @ X255)))) <=> pushprop_lem1_lthm) & hoasapnotvar & ((^[X260 : subst, X261 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & ((! [X262 : term] : (((sub @ X262 @ id)) = X262) => ! [X263 : term] : (((sub @ X263 @ id)) = X263)) <=> termmset_lthm) & hoasinduction_lem2_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction <=> ! [X264 : (term > $o),X265 : term] : (~ ! [X266 : term,X267 : term] : ((X264 @ (ap @ X267 @ X266)) | ~(X264 @ X266) | ~(X264 @ X267)) | ~ ! [X268 : term] : ((X264 @ (lam @ X268)) | ~(X264 @ X268)) | ~ ! [X269 : term] : ((X264 @ X269) | ~(var @ X269)) | (X264 @ X265))) & (! [X270 : subst,X271 : term,X272 : (term > $o)] : ((X272 @ (sub @ X271 @ X270)) | ~ ! [X273 : term] : (~ ! [X274 : term] : (~(X272 @ X274) | (X272 @ (sub @ X273 @ (push @ X274 @ id)))) | (X272 @ (lam @ X273))) | ~ ! [X275 : term] : (~(var @ X275) | (X272 @ (sub @ X275 @ X270))) | ~ ! [X276 : term,X277 : term] : (~(X272 @ X277) | ~(X272 @ X276) | (X272 @ (ap @ X276 @ X277)))) <=> induction2lem) & (hoasapinj1_lthm <=> (! [X278 : term] : (((sub @ X278 @ id)) = X278) => (! [X279 : term,X280 : term,X281 : term,X282 : term] : ((((ap @ X281 @ X280)) != ((ap @ X282 @ X279))) | (X281 = X282)) => ! [X283 : term,X284 : term,X285 : term,X286 : term] : ((((ap @ (sub @ X283 @ id) @ X284)) != ((ap @ (sub @ X286 @ id) @ X285))) | (X283 = X286))))) & (pushprop_lem1 <=> ! [X287 : (term > $o),X288 : subst,X289 : term,X290 : term,X291 : (term > $o)] : (~(X287 @ X289) | (X291 @ (sub @ X289 @ (push @ X290 @ X288))))) & pushprop_lem1_gthm & (! [X292 : term] : ~ ! [X293 : (subst > term > term)] : (((sub @ X292 @ (push @ one @ sh))) != ((X293 @ sh @ one))) <=> hoasinduction_lem3b) & hoasinduction_lem2_gthm & axabs & pushprop_lthm_orig & (hoasinduction_lem3v2 <=> ! [X294 : term,X295 : (subst > term > subst > $o),X296 : (term > $o)] : (~ ! [X297 : subst,X298 : subst,X299 : term,X300 : subst] : (~(X295 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300) @ X297) | (X295 @ X298 @ X299 @ (comp @ X300 @ X297))) | ~ ! [X301 : subst,X302 : subst,X303 : term,X304 : subst] : (~(X295 @ X302 @ X303 @ (comp @ X304 @ X301)) | (X295 @ (comp @ X302 @ X304) @ (sub @ X303 @ X304) @ X301)) | ~ ! [X305 : term] : (~(X296 @ X305) | (X296 @ (sub @ X294 @ (push @ X305 @ id)))) | (X296 @ (lam @ X294)) | ~ ! [X306 : (subst > term > term)] : (~ ! [X307 : term] : (~(X295 @ id @ X307 @ id) | (X295 @ id @ (X306 @ id @ X307) @ id)) | ~ ! [X308 : subst,X309 : term,X310 : subst] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) | (X295 @ id @ (lam @ (X306 @ sh @ one)) @ id)) | ~ ! [X311 : term] : (((X296 @ X311)) = ((X295 @ id @ X311 @ id))))) & hoasinduction_lem3a_gthm & hoasinduction_gthm & (! [X312 : term,X313 : (subst > term > subst > $o)] : ((X313 @ id @ (lam @ (sub @ X312 @ (push @ one @ sh))) @ id) | ~ ! [X314 : (subst > term > term)] : ((X313 @ id @ (lam @ (X314 @ sh @ one)) @ id) | ~ ! [X315 : term] : (~(X313 @ id @ X315 @ id) | (X313 @ id @ (X314 @ id @ X315) @ id)) | ~ ! [X316 : term,X317 : subst,X318 : subst] : (((sub @ (X314 @ X317 @ X316) @ X318)) = ((X314 @ (comp @ X317 @ X318) @ (sub @ X316 @ X318))))) | ~ ! [X319 : term] : (~(X313 @ id @ X319 @ id) | (X313 @ id @ (sub @ X312 @ (push @ X319 @ id)) @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem1_lthm & (pushprop_lem0 <=> ! [X320 : subst,X321 : (term > $o),X322 : term] : ~ ! [X323 : (term > $o)] : ~ ! [X324 : term] : (((X323 @ X324)) = ((X321 @ (sub @ X324 @ (push @ X322 @ X320)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotap_lthm & hoaslamnotap_gthm & (! [X325 : term,X326 : term] : ((((sub @ X326 @ sh)) != ((sub @ X325 @ sh))) | (X325 = X326)) <=> shinj) & hoasinduction_lem3b_gthm & axmap & hoasinduction_lem1v2 & (substmonoid <=> (! [X327 : subst] : (((comp @ X327 @ id)) = X327) & ! [X328 : subst] : (((comp @ id @ X328)) = X328))) & (axvarid <=> ! [X329 : term] : (((sub @ X329 @ id)) = X329)) & (termmset <=> ! [X330 : term] : (((sub @ X330 @ id)) = X330)) & hoasinduction_lem2v2_gthm & hoaslaminj_gthm & apnotvar & induction2_gthm & (! [X331 : subst] : (((comp @ X331 @ id)) = X331) <=> axidr) & (hoasapinj2 <=> ! [X332 : term,X333 : term,X334 : term,X335 : term] : ((((ap @ (sub @ X334 @ id) @ X333)) != ((ap @ (sub @ X335 @ id) @ X332))) | (X332 = X333))) & pushprop_lem3v2 & (hoasinduction_lem3b_lthm <=> ! [X336 : term] : ~ ! [X337 : (subst > term > term)] : (((X337 @ sh @ one)) != ((sub @ X336 @ (push @ one @ sh))))) & (! [X338 : term] : ~ ! [X339 : (subst > term > term)] : ~ ! [X340 : term,X341 : subst] : (((sub @ X338 @ (push @ X340 @ X341))) = ((X339 @ X341 @ X340))) <=> hoasinduction_lem3v2_f) & (pushprop_p_and_p_prime = (^[X342 : term, X343 : subst, X344 : (term > $o), X345 : (term > $o)] : (! [X346 : term] : (((X345 @ X346)) = ((X344 @ (sub @ X346 @ (push @ X342 @ X343)))))))) & ! [X347 : term] : ? [X348 : d_term] : (((d2term @ X348)) = X347) & (axidl <=> ! [X349 : subst] : (((comp @ id @ X349)) = X349)) & (pushprop_lem0_lthm <=> ! [X350 : term,X351 : (term > $o),X352 : subst] : ~ ! [X353 : (term > $o)] : ~ ! [X354 : term] : (((X353 @ X354)) = ((X351 @ (sub @ X354 @ (push @ X350 @ X352)))))) & pushprop_lem2v2_lthm & (hoasinduction_lem3v2a <=> ! [X355 : term,X356 : (subst > term > subst > $o),X357 : (term > $o)] : (~ ! [X358 : term] : (((X357 @ X358)) = ((X356 @ id @ X358 @ id))) | (X357 @ (lam @ X355)) | ~ ! [X359 : (subst > term > term)] : ((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id) | ~ ! [X360 : term] : ((X356 @ id @ (X359 @ id @ X360) @ id) | ~(X356 @ id @ X360 @ id)) | ~ ! [X361 : subst,X362 : subst,X363 : term] : (((X359 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361))) = ((sub @ (X359 @ X362 @ X363) @ X361)))) | ~ ! [X364 : term] : (~(X357 @ X364) | (X357 @ (sub @ X355 @ (push @ X364 @ id)))))) & ! [X365 : d_term,X366 : d_term] : ((((d2term @ X366)) = ((d2term @ X365))) => (X365 = X366)) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_gthm & (axshiftcons <=> ! [X367 : subst,X368 : term] : (((comp @ sh @ (push @ X368 @ X367))) = X367)) & (hoasinduction <=> ! [X369 : (subst > term > subst > $o),X370 : term] : (~ ! [X371 : term] : (~(var @ (sub @ X371 @ id)) | (X369 @ id @ X371 @ id)) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (~(X369 @ X373 @ X375 @ (comp @ X374 @ X372)) | (X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) | ~ ! [X376 : term,X377 : term] : ((X369 @ id @ (ap @ (sub @ X377 @ id) @ X376) @ id) | ~(X369 @ id @ X376 @ id) | ~(X369 @ id @ X377 @ id)) | ~ ! [X378 : (subst > term > term)] : ((X369 @ id @ (lam @ (X378 @ sh @ one)) @ id) | ~ ! [X379 : subst,X380 : subst,X381 : term] : (((sub @ (X378 @ X379 @ X381) @ X380)) = ((X378 @ (comp @ X379 @ X380) @ (sub @ X381 @ X380)))) | ~ ! [X382 : term] : ((X369 @ id @ (X378 @ id @ X382) @ id) | ~(X369 @ id @ X382 @ id))) | (X369 @ id @ X370 @ id) | ~ ! [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (~(X369 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383) @ X386) | (X369 @ X385 @ X384 @ (comp @ X383 @ X386))))) & ((! [X387 : term,X388 : subst] : (((sub @ one @ (push @ X387 @ X388))) = X387) => (! [X389 : subst,X390 : term] : (((comp @ sh @ (push @ X390 @ X389))) = X389) => (! [X391 : term,X392 : term] : ((X391 = X392) | (((lam @ X392)) != ((lam @ X391)))) => ! [X393 : (subst > term > term),X394 : subst,X395 : term,X396 : (subst > term > term)] : (~ ! [X397 : subst,X398 : term,X399 : subst] : (((X396 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399))) = ((sub @ (X396 @ X397 @ X398) @ X399))) | (((X396 @ X394 @ X395)) = ((X393 @ X394 @ X395))) | ~ ! [X400 : term,X401 : subst,X402 : subst] : (((X393 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401))) = ((sub @ (X393 @ X402 @ X400) @ X401))) | (((lam @ (X393 @ sh @ one))) != ((lam @ (X396 @ sh @ one)))))))) <=> hoaslaminj_lthm) & ((! [X403 : term,X404 : subst] : (((sub @ one @ (push @ X403 @ X404))) = X403) => ! [X405 : (term > $o),X406 : term,X407 : subst,X408 : (term > $o)] : (~ ! [X409 : term] : (((X408 @ X409)) = ((X405 @ (sub @ X409 @ (push @ X406 @ X407))))) | ~(X405 @ X406) | (X408 @ one))) <=> pushprop_lem1v2_lthm) & axvarshift & hoaslamnotvar_lthm & (id = ((d2subst @ d_id))) & hoasinduction_lem1v2_gthm & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : (subst > term > term)] : ((X411 @ id @ (lam @ (X412 @ sh @ one)) @ id) | ~ ! [X413 : term] : (~(X411 @ id @ X413 @ id) | (X411 @ id @ (X412 @ id @ X413) @ id)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((X412 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414))) = ((sub @ (X412 @ X416 @ X415) @ X414)))) | (X411 @ id @ (lam @ X410) @ id) | ~ ! [X417 : subst,X418 : term,X419 : subst,X420 : subst] : (~(X411 @ (comp @ X417 @ X419) @ (sub @ X418 @ X419) @ X420) | (X411 @ X417 @ X418 @ (comp @ X419 @ X420))) | ~ ! [X421 : subst,X422 : term,X423 : subst,X424 : subst] : ((X411 @ (comp @ X423 @ X421) @ (sub @ X422 @ X421) @ X424) | ~(X411 @ X423 @ X422 @ (comp @ X421 @ X424))) | ~ ! [X425 : term] : ((X411 @ id @ (sub @ X410 @ (push @ X425 @ id)) @ id) | ~(X411 @ id @ X425 @ id)))) & lamnotvar & pushprop_lem2v2_gthm & ulamvarsh & ~ulamvar1 & pushprop & (! [X426 : term,X427 : term,X428 : (subst > term > subst > $o)] : (~ ! [X429 : subst,X430 : subst,X431 : subst,X432 : term] : ((X428 @ (comp @ X430 @ X429) @ (sub @ X432 @ X429) @ X431) | ~(X428 @ X430 @ X432 @ (comp @ X429 @ X431))) | ~(X428 @ id @ X427 @ id) | ~ ! [X433 : subst,X434 : term,X435 : subst,X436 : subst] : ((X428 @ X435 @ X434 @ (comp @ X433 @ X436)) | ~(X428 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433) @ X436)) | (X428 @ id @ (ap @ X427 @ X426) @ id) | ~(X428 @ id @ X426 @ id) | ~ ! [X437 : term,X438 : term] : (~(X428 @ id @ X437 @ id) | ~(X428 @ id @ X438 @ id) | (X428 @ id @ (ap @ (sub @ X437 @ id) @ X438) @ id))) <=> hoasinduction_lem2) & (! [X439 : term,X440 : (term > $o),X441 : (term > $o),X442 : subst] : ((X440 @ one) | ~(X441 @ X439) | ~ ! [X443 : term] : (((X440 @ X443)) = ((X441 @ (sub @ X443 @ (push @ X439 @ X442)))))) <=> pushprop_lem1v2) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ulamvarind & (induction2lem_lthm <=> (! [X444 : subst,X445 : term] : (((sub @ one @ (push @ X445 @ X444))) = X445) => (! [X446 : term,X447 : subst] : (((comp @ sh @ (push @ X446 @ X447))) = X447) => (! [X448 : subst] : (((comp @ X448 @ id)) = X448) => (! [X449 : term,X450 : (term > $o)] : ((X450 @ X449) | ~ ! [X451 : term,X452 : term] : (~(X450 @ X451) | (X450 @ (ap @ X452 @ X451)) | ~(X450 @ X452)) | ~ ! [X453 : term] : ((X450 @ X453) | ~(var @ X453)) | ~ ! [X454 : term] : ((X450 @ (lam @ X454)) | ~(X450 @ X454))) => ! [X455 : term,X456 : (term > $o),X457 : subst] : (~ ! [X458 : term] : ((X456 @ (lam @ X458)) | ~ ! [X459 : term] : ((X456 @ (sub @ X458 @ (push @ X459 @ id))) | ~(X456 @ X459))) | (X456 @ (sub @ X455 @ X457)) | ~ ! [X460 : term] : ((X456 @ (sub @ X460 @ X457)) | ~(var @ X460)) | ~ ! [X461 : term,X462 : term] : (~(X456 @ X461) | (X456 @ (ap @ X461 @ X462)) | ~(X456 @ X462)))))))) & (hoasinduction_lem3aa_lthm <=> ! [X463 : (subst > term > subst > $o),X464 : term] : ((X463 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id) | ~ ! [X465 : term] : (~(X463 @ id @ X465 @ id) | (X463 @ id @ (sub @ X464 @ (push @ X465 @ id)) @ id)) | ~ ! [X466 : (subst > term > term)] : (~ ! [X467 : term] : ((X463 @ id @ (X466 @ id @ X467) @ id) | ~(X463 @ id @ X467 @ id)) | (X463 @ id @ (lam @ (X466 @ sh @ one)) @ id) | ~ ! [X468 : term,X469 : subst,X470 : subst] : (((sub @ (X466 @ X469 @ X468) @ X470)) = ((X466 @ (comp @ X469 @ X470) @ (sub @ X468 @ X470))))))) & (hoasinduction_lem3aaa <=> ! [X471 : term,X472 : (subst > term > subst > $o)] : ((X472 @ id @ (lam @ (sub @ X471 @ (push @ one @ sh))) @ id) | ~ ! [X473 : term,X474 : (subst > term > term)] : ((X472 @ id @ (lam @ (X474 @ sh @ one)) @ id) | ~ ! [X475 : term,X476 : subst,X477 : subst] : (((sub @ (sub @ X473 @ (push @ X475 @ X477)) @ X476)) = ((sub @ (X474 @ X477 @ X475) @ X476))) | ~ ! [X478 : term] : ((X472 @ id @ (X474 @ id @ X478) @ id) | ~(X472 @ id @ X478 @ id)) | ~ ! [X479 : subst,X480 : term,X481 : subst] : (((X474 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479))) = ((sub @ X473 @ (push @ (sub @ X480 @ X479) @ (comp @ X481 @ X479)))))) | ~ ! [X482 : term] : ((X472 @ id @ (sub @ X471 @ (push @ X482 @ id)) @ id) | ~(X472 @ id @ X482 @ id)))) & pushprop_lem1v2_gthm & hoasinduction_lem1_gthm & pushprop_gthm & (hoasinduction_p_and_p_prime = (^[X483 : (subst > term > subst > $o), X484 : (term > $o)] : (! [X485 : term] : (((X484 @ X485)) = ((X483 @ id @ X485 @ id)))))) & pushprop_lthm & ((! [X486 : subst] : (((comp @ id @ X486)) = X486) => (! [X487 : subst] : (((comp @ X487 @ id)) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) & ! [X489 : subst] : (((comp @ id @ X489)) = X489)))) <=> substmonoid_lthm) & (hoasinduction_lem0 <=> ! [X490 : (subst > term > subst > $o)] : ~ ! [X491 : (term > $o)] : ~ ! [X492 : term] : (((X490 @ id @ X492 @ id)) = ((X491 @ X492)))) & hoasinduction_lem3v2_gthm & (induction2 <=> ! [X493 : (term > $o),X494 : term] : (~ ! [X495 : term] : ((X493 @ (lam @ X495)) | ~ ! [X496 : term] : (~(X493 @ X496) | (X493 @ (sub @ X495 @ (push @ X496 @ id))))) | (X493 @ X494) | ~ ! [X497 : term,X498 : term] : (~(X493 @ X498) | ~(X493 @ X497) | (X493 @ (ap @ X497 @ X498))) | ~ ! [X499 : term] : (~(var @ X499) | (X493 @ X499)))) & (laminj <=> ! [X500 : term,X501 : term] : ((((lam @ X501)) != ((lam @ X500))) | (X500 = X501))) & axapp & (hoasinduction_lem0_lthm <=> ! [X502 : (subst > term > subst > $o)] : ~ ! [X503 : (term > $o)] : ~ ! [X504 : term] : (((X503 @ X504)) = ((X502 @ id @ X504 @ id)))) & pushprop_lem3v2_lthm & (hoasinduction_lem2v2 <=> ! [X505 : (subst > term > subst > $o),X506 : (term > $o),X507 : term,X508 : term] : (~(X506 @ X507) | ~ ! [X509 : term] : (((X505 @ id @ X509 @ id)) = ((X506 @ X509))) | ~ ! [X510 : term,X511 : term] : (~(X505 @ id @ X511 @ id) | ~(X505 @ id @ X510 @ id) | (X505 @ id @ (ap @ (sub @ X511 @ id) @ X510) @ id)) | ~(X506 @ X508) | (X506 @ (ap @ X507 @ X508)) | ~ ! [X512 : subst,X513 : term,X514 : subst,X515 : subst] : ((X505 @ (comp @ X515 @ X514) @ (sub @ X513 @ X514) @ X512) | ~(X505 @ X515 @ X513 @ (comp @ X514 @ X512))) | ~ ! [X516 : subst,X517 : subst,X518 : subst,X519 : term] : (~(X505 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517) @ X516) | (X505 @ X518 @ X519 @ (comp @ X517 @ X516))))) & (axvarcons <=> ! [X520 : term,X521 : subst] : (((sub @ one @ (push @ X520 @ X521))) = X520)) & (hoasinduction_lem3v2_f_lthm <=> ! [X522 : term] : ~ ! [X523 : (subst > term > term)] : ~ ! [X524 : subst,X525 : term] : (((X523 @ X524 @ X525)) = ((sub @ X522 @ (push @ X525 @ X524))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasapinj2_gthm & (hoasapinj2_lthm <=> (! [X526 : term,X527 : term,X528 : term,X529 : term] : ((((ap @ X528 @ X529)) != ((ap @ X526 @ X527))) | (X527 = X529)) => ! [X530 : term,X531 : term,X532 : term,X533 : term] : ((X530 = X531) | (((ap @ (sub @ X532 @ id) @ X531)) != ((ap @ (sub @ X533 @ id) @ X530)))))) & termmset_gthm & hoasapnotvar_lthm & hoasinduction_lem3_gthm & (induction2_lthm <=> (! [X534 : term] : (((sub @ X534 @ id)) = X534) => (! [X535 : subst,X536 : (term > $o),X537 : term] : (~ ! [X538 : term] : (~(var @ X538) | (X536 @ (sub @ X538 @ X535))) | ~ ! [X539 : term,X540 : term] : (~(X536 @ X540) | ~(X536 @ X539) | (X536 @ (ap @ X539 @ X540))) | ~ ! [X541 : term] : (~ ! [X542 : term] : (~(X536 @ X542) | (X536 @ (sub @ X541 @ (push @ X542 @ id)))) | (X536 @ (lam @ X541))) | (X536 @ (sub @ X537 @ X535))) => ! [X543 : term,X544 : (term > $o)] : ((X544 @ X543) | ~ ! [X545 : term] : ((X544 @ X545) | ~(var @ X545)) | ~ ! [X546 : term,X547 : term] : ((X544 @ (ap @ X546 @ X547)) | ~(X544 @ X547) | ~(X544 @ X546)) | ~ ! [X548 : term] : ((X544 @ (lam @ X548)) | ~ ! [X549 : term] : (~(X544 @ X549) | (X544 @ (sub @ X548 @ (push @ X549 @ id)))))))))),
% 47.53/7.11 inference(rectify,[],[f1])).
% 47.53/7.11 thf(f7,plain,(
% 47.53/7.11 (((d2subst @ d_id)) = sh) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & (hoasinduction_lem1 = $true) & ! [X4 : d_subst] : (d_id = X4) & (! [X7 : term,X6 : term,X5 : (subst > term > term)] : ((((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))) | ~ ! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8)))) <=> (hoaslamnotap = $true)) & (axclos = $true) & ~ (lamnotap = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (substmonoid_gthm = $true) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X15 : term] : (((sub @ X15 @ id)) = X15) => (! [X16 : (subst > term > subst > $o),X17 : term] : ((((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X18 : (subst > term > term)] : (~ ! [X19 : term] : ((((X16 @ id @ (X18 @ id @ X19) @ id)) = $true) | ~ (((X16 @ id @ X19 @ id)) = $true)) | (((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ~ ! [X21 : subst,X22 : term,X20 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) = ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) | ~ ! [X23 : term] : ((((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true) | ~ (((X16 @ id @ X23 @ id)) = $true))) => ! [X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X26 : (subst > term > term)] : (~ ! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) | ~ ! [X30 : term] : ((((X24 @ id @ (X26 @ id @ X30) @ id)) = $true) | ~ (((X24 @ id @ X30 @ id)) = $true)) | (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) = $true) | ~ (((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) = $true)) | ~ ! [X35 : term] : ((((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) = $true) | ~ (((X24 @ id @ X35 @ id)) = $true)) | ~ ! [X36 : subst,X37 : subst,X38 : subst,X39 : term] : ((((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) = $true) | ~ (((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) = $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X40 : (subst > term > subst > $o)] : ~ ! [X41 : (term > $o)] : ~ ! [X42 : term] : (((X40 @ id @ X42 @ id)) = ((X41 @ X42))) => (! [X43 : term,X44 : (term > $o)] : (~ ! [X45 : term] : (~ (((var @ X45)) = $true) | ($true = ((X44 @ X45)))) | (((X44 @ X43)) = $true) | ~ ! [X46 : term] : (~ ! [X47 : term] : (~ (((X44 @ X47)) = $true) | (((X44 @ (sub @ X46 @ (push @ X47 @ id)))) = $true)) | (((X44 @ (lam @ X46))) = $true)) | ~ ! [X48 : term,X49 : term] : ((((X44 @ (ap @ X48 @ X49))) = $true) | ~ (((X44 @ X48)) = $true) | ~ (((X44 @ X49)) = $true))) => (! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : (term > $o),X53 : term] : (~ ! [X54 : term] : (~ (((X52 @ X54)) = $true) | (((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true)) | ~ ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) | ($true = ((X52 @ (lam @ X53)))) | ~ ! [X56 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ~ ! [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) = ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ~ ! [X60 : term] : (~ (((X51 @ id @ X60 @ id)) = $true) | (((X51 @ id @ (X56 @ id @ X60) @ id)) = $true)))) => ! [X61 : (subst > term > subst > $o),X62 : term] : (~ ! [X63 : (subst > term > term)] : (~ ! [X64 : term] : ((((X61 @ id @ (X63 @ id @ X64) @ id)) = $true) | ~ (((X61 @ id @ X64 @ id)) = $true)) | (((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) = $true) | ~ ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66))))) | (((X61 @ id @ X62 @ id)) = $true) | ~ ! [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (~ (((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) = $true) | (((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) = $true)) | ~ ! [X72 : term] : ((((X61 @ id @ X72 @ id)) = $true) | ~ (((var @ (sub @ X72 @ id))) = $true)) | ~ ! [X73 : term,X74 : term] : ((((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) = $true) | ~ (((X61 @ id @ X73 @ id)) = $true) | ~ (((X61 @ id @ X74 @ id)) = $true)) | ~ ! [X75 : subst,X76 : subst,X77 : subst,X78 : term] : (~ (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) = $true) | (((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) = $true)))))))) & (one = ((d2term @ d_one))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ! [X80 : d_subst,X79 : d_subst] : ((((d2subst @ X79)) = ((d2subst @ X80))) => (X79 = X80)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & (! [X82 : (subst > term > subst > $o),X83 : term] : (~ ! [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) = $true) | ~ (((X82 @ id @ X84 @ id)) = $true) | ~ (((X82 @ id @ X85 @ id)) = $true)) | (((X82 @ id @ X83 @ id)) = $true) | ~ ! [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ~ ! [X87 : term] : ((((X82 @ id @ (X86 @ id @ X87) @ id)) = $true) | ~ (((X82 @ id @ X87 @ id)) = $true)) | ~ ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90)))))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => (! [X92 : (subst > term > subst > $o),X93 : term] : (~ ! [X94 : term] : (~ (((X92 @ id @ X94 @ id)) = $true) | (((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true)) | (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X95 : (subst > term > term)] : (~ ! [X98 : subst,X96 : subst,X97 : term] : (((sub @ (X95 @ X96 @ X97) @ X98)) = ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ~ ! [X99 : term] : (~ (((X92 @ id @ X99 @ id)) = $true) | (((X92 @ id @ (X95 @ id @ X99) @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true))) => ! [X100 : (subst > term > subst > $o),X101 : term] : ((((X100 @ id @ (lam @ X101) @ id)) = $true) | ~ ! [X102 : term] : ((((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) = $true) | ~ (((X100 @ id @ X102 @ id)) = $true)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106))) | ~ ! [X107 : term] : (~ (((X100 @ id @ X107 @ id)) = $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) | (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true)))))) & ((hoasinduction_lem3a = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (~ ! [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) = $true) | ~ (((X108 @ id @ X110 @ id)) = $true)) | ($true = ((X108 @ id @ (lam @ X109) @ id))) | ~ ! [X111 : (subst > term > term)] : (~ ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113))) | ~ ! [X115 : term] : (~ (((X108 @ id @ X115 @ id)) = $true) | (((X108 @ id @ (X111 @ id @ X115) @ id)) = $true)) | (((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) = $true)))) & ! [X116 : d_term] : (d_one = X116) & (hoasapinj1_gthm = $true) & ((! [X117 : term] : ~ ! [X118 : (subst > term > term)] : ~ ! [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) = ((X118 @ X120 @ X119))) => (! [X121 : term] : (((sub @ X121 @ id)) = X121) => ! [X122 : term,X123 : (term > $o),X124 : (subst > term > subst > $o)] : (~ ! [X125 : term] : (((X124 @ id @ X125 @ id)) = ((X123 @ X125))) | ~ ! [X126 : term] : (~ (((X123 @ X126)) = $true) | (((X123 @ (sub @ X122 @ (push @ X126 @ id)))) = $true)) | (((X123 @ (lam @ X122))) = $true) | ~ ! [X127 : (subst > term > term)] : (~ ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))) | (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ~ ! [X131 : term] : (~ ($true = ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (induction2lem_gthm = $true) & (axassoc = $true) & (pushprop_lem0_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & ((hoaslaminj = $true) <=> ! [X140 : (subst > term > term),X139 : term,X138 : (subst > term > term),X141 : subst] : (~ ! [X145 : subst,X146 : subst,X147 : term] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | (((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ~ ! [X144 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & ((! [X148 : term,X149 : (term > $o)] : (~ ! [X150 : term,X151 : term] : (~ (((X149 @ X151)) = $true) | ~ (((X149 @ X150)) = $true) | (((X149 @ (ap @ X151 @ X150))) = $true)) | ~ ! [X152 : term] : (~ ! [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) = $true) | ~ (((X149 @ X153)) = $true)) | (((X149 @ (lam @ X152))) = $true)) | (((X149 @ X148)) = $true) | ~ ! [X154 : term] : ((((X149 @ X154)) = $true) | ~ (((var @ X154)) = $true))) => (! [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : (~ ! [X158 : subst,X159 : subst,X160 : term,X161 : subst] : (~ (((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) = $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true)) | (((X156 @ id @ (ap @ X157 @ X155) @ id)) = $true) | ~ ! [X162 : term,X163 : term] : (~ (((X156 @ id @ X162 @ id)) = $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true) | ~ (((X156 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : subst,X166 : term,X167 : subst] : (~ (((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) = $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) | ~ (((X156 @ id @ X157 @ id)) = $true) | ~ (((X156 @ id @ X155 @ id)) = $true)) => (! [X168 : term,X169 : (subst > term > subst > $o)] : (~ ! [X170 : subst,X171 : term,X172 : subst,X173 : subst] : (~ (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) = $true) | (((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true)) | ~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : ((((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true) | ~ (((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) = $true)) | ~ ! [X178 : term] : (~ (((X169 @ id @ X178 @ id)) = $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) | (((X169 @ id @ (lam @ X168) @ id)) = $true) | ~ ! [X179 : (subst > term > term)] : (~ ! [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) = $true) | ~ (((X169 @ id @ X180 @ id)) = $true)) | ~ ! [X181 : subst,X183 : term,X182 : subst] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) = ((sub @ (X179 @ X182 @ X183) @ X181))) | (((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true))) => ! [X184 : term,X185 : (subst > term > subst > $o)] : (~ ! [X186 : subst,X187 : subst,X188 : term,X189 : subst] : (~ (((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) = $true) | (((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) = $true)) | (((X185 @ id @ X184 @ id)) = $true) | ~ ! [X190 : term,X191 : term] : (~ (((X185 @ id @ X190 @ id)) = $true) | ~ ($true = ((X185 @ id @ X191 @ id))) | (((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true)) | ~ ! [X192 : subst,X193 : term,X194 : subst,X195 : subst] : (~ (((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) = $true) | (((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) = $true)) | ~ ! [X196 : term] : ((((X185 @ id @ X196 @ id)) = $true) | ~ ($true = ((var @ (sub @ X196 @ id))))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~ (((X185 @ id @ X198 @ id)) = $true) | (((X185 @ id @ (X197 @ id @ X198) @ id)) = $true)) | (((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))))) <=> (hoasinduction_lthm = $true)) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X206 : subst,X207 : subst,X208 : term,X209 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) = $true) | ~ (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) = $true)) | ~ ! [X210 : term] : (((X205 @ X210)) = ((X203 @ id @ X210 @ id))) | (((X205 @ (lam @ X204))) = $true) | ~ ! [X211 : term] : ((((X205 @ (sub @ X204 @ (push @ X211 @ id)))) = $true) | ~ (((X205 @ X211)) = $true)) | ~ ! [X212 : subst,X213 : term,X214 : subst,X215 : subst] : (~ (((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) = $true) | (((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) = $true)) | ~ ! [X216 : (subst > term > term)] : ((((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ~ ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) | ~ ! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | ~ (((X203 @ id @ X220 @ id)) = $true)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X221 : (subst > term > subst > $o)] : ~ ! [X222 : (term > $o)] : ~ ! [X223 : term] : (((X221 @ id @ X223 @ id)) = ((X222 @ X223))) => (! [X224 : term,X225 : (term > $o)] : (~ ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | ~ ($true = ((X225 @ X227))) | ~ (((X225 @ X226)) = $true)) | ~ ! [X228 : term] : ((((X225 @ (lam @ X228))) = $true) | ~ ! [X229 : term] : ((((X225 @ (sub @ X228 @ (push @ X229 @ id)))) = $true) | ~ (((X225 @ X229)) = $true))) | ~ ! [X230 : term] : ((((X225 @ X230)) = $true) | ~ (((var @ X230)) = $true)) | (((X225 @ X224)) = $true)) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => (! [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : ((((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X237 : subst,X236 : term,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | ~ ! [X239 : term] : (~ (((X232 @ id @ X239 @ id)) = $true) | (((X232 @ id @ (X235 @ id @ X239) @ id)) = $true))) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) | ~ ! [X241 : term] : (~ (((X234 @ X241)) = $true) | (((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true)) | (((X234 @ (lam @ X233))) = $true)) => ! [X242 : term,X243 : (subst > term > subst > $o)] : ((((X243 @ id @ X242 @ id)) = $true) | ~ ! [X244 : term,X245 : term] : (~ (((X243 @ id @ X244 @ id)) = $true) | ~ (((X243 @ id @ X245 @ id)) = $true) | ($true = ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id)))) | ~ ! [X246 : (subst > term > term)] : (~ ! [X247 : term] : (~ (((X243 @ id @ X247 @ id)) = $true) | (((X243 @ id @ (X246 @ id @ X247) @ id)) = $true)) | ~ ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) | (((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) = $true)))))))) & ((! [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) = X253) => ! [X255 : term,X256 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o)] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | ~ (((X259 @ X255)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X262 : term] : (((sub @ X262 @ id)) = X262) => ! [X263 : term] : (((sub @ X263 @ id)) = X263)) <=> (termmset_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((induction = $true) <=> ! [X264 : (term > $o),X265 : term] : (~ ! [X266 : term,X267 : term] : ((((X264 @ (ap @ X267 @ X266))) = $true) | ~ (((X264 @ X266)) = $true) | ~ (((X264 @ X267)) = $true)) | ~ ! [X268 : term] : ((((X264 @ (lam @ X268))) = $true) | ~ (((X264 @ X268)) = $true)) | ~ ! [X269 : term] : ((((X264 @ X269)) = $true) | ~ (((var @ X269)) = $true)) | (((X264 @ X265)) = $true))) & (! [X270 : subst,X271 : term,X272 : (term > $o)] : ((((X272 @ (sub @ X271 @ X270))) = $true) | ~ ! [X273 : term] : (~ ! [X274 : term] : (~ (((X272 @ X274)) = $true) | (((X272 @ (sub @ X273 @ (push @ X274 @ id)))) = $true)) | (((X272 @ (lam @ X273))) = $true)) | ~ ! [X275 : term] : (~ (((var @ X275)) = $true) | (((X272 @ (sub @ X275 @ X270))) = $true)) | ~ ! [X276 : term,X277 : term] : (~ (((X272 @ X277)) = $true) | ~ ($true = ((X272 @ X276))) | (((X272 @ (ap @ X276 @ X277))) = $true))) <=> (induction2lem = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X278 : term] : (((sub @ X278 @ id)) = X278) => (! [X279 : term,X280 : term,X281 : term,X282 : term] : ((((ap @ X281 @ X280)) != ((ap @ X282 @ X279))) | (X281 = X282)) => ! [X283 : term,X284 : term,X285 : term,X286 : term] : ((((ap @ (sub @ X283 @ id) @ X284)) != ((ap @ (sub @ X286 @ id) @ X285))) | (X283 = X286))))) & ((pushprop_lem1 = $true) <=> ! [X287 : (term > $o),X288 : subst,X289 : term,X290 : term,X291 : (term > $o)] : (~ (((X287 @ X289)) = $true) | (((X291 @ (sub @ X289 @ (push @ X290 @ X288)))) = $true))) & (pushprop_lem1_gthm = $true) & (! [X292 : term] : ~ ! [X293 : (subst > term > term)] : (((sub @ X292 @ (push @ one @ sh))) != ((X293 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_lem2_gthm = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X294 : term,X295 : (subst > term > subst > $o),X296 : (term > $o)] : (~ ! [X297 : subst,X298 : subst,X299 : term,X300 : subst] : (~ (((X295 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300) @ X297)) = $true) | (((X295 @ X298 @ X299 @ (comp @ X300 @ X297))) = $true)) | ~ ! [X301 : subst,X302 : subst,X303 : term,X304 : subst] : (~ (((X295 @ X302 @ X303 @ (comp @ X304 @ X301))) = $true) | (((X295 @ (comp @ X302 @ X304) @ (sub @ X303 @ X304) @ X301)) = $true)) | ~ ! [X305 : term] : (~ (((X296 @ X305)) = $true) | (((X296 @ (sub @ X294 @ (push @ X305 @ id)))) = $true)) | (((X296 @ (lam @ X294))) = $true) | ~ ! [X306 : (subst > term > term)] : (~ ! [X307 : term] : (~ (((X295 @ id @ X307 @ id)) = $true) | (((X295 @ id @ (X306 @ id @ X307) @ id)) = $true)) | ~ ! [X308 : subst,X309 : term,X310 : subst] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) | (((X295 @ id @ (lam @ (X306 @ sh @ one)) @ id)) = $true)) | ~ ! [X311 : term] : (((X296 @ X311)) = ((X295 @ id @ X311 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_gthm = $true) & (! [X312 : term,X313 : (subst > term > subst > $o)] : ((((X313 @ id @ (lam @ (sub @ X312 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X314 : (subst > term > term)] : ((((X313 @ id @ (lam @ (X314 @ sh @ one)) @ id)) = $true) | ~ ! [X315 : term] : (~ (((X313 @ id @ X315 @ id)) = $true) | (((X313 @ id @ (X314 @ id @ X315) @ id)) = $true)) | ~ ! [X316 : term,X317 : subst,X318 : subst] : (((sub @ (X314 @ X317 @ X316) @ X318)) = ((X314 @ (comp @ X317 @ X318) @ (sub @ X316 @ X318))))) | ~ ! [X319 : term] : (~ (((X313 @ id @ X319 @ id)) = $true) | (((X313 @ id @ (sub @ X312 @ (push @ X319 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X320 : subst,X321 : (term > $o),X322 : term] : ~ ! [X323 : (term > $o)] : ~ ! [X324 : term] : (((X323 @ X324)) = ((X321 @ (sub @ X324 @ (push @ X322 @ X320)))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_lthm = $true) & (hoaslamnotap_gthm = $true) & (! [X325 : term,X326 : term] : ((((sub @ X326 @ sh)) != ((sub @ X325 @ sh))) | (X325 = X326)) <=> (shinj = $true)) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoasinduction_lem1v2 = $true) & ((substmonoid = $true) <=> (! [X327 : subst] : (((comp @ X327 @ id)) = X327) & ! [X328 : subst] : (((comp @ id @ X328)) = X328))) & ((axvarid = $true) <=> ! [X329 : term] : (((sub @ X329 @ id)) = X329)) & ((termmset = $true) <=> ! [X330 : term] : (((sub @ X330 @ id)) = X330)) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (apnotvar = $true) & (induction2_gthm = $true) & (! [X331 : subst] : (((comp @ X331 @ id)) = X331) <=> (axidr = $true)) & ((hoasapinj2 = $true) <=> ! [X332 : term,X333 : term,X334 : term,X335 : term] : ((((ap @ (sub @ X334 @ id) @ X333)) != ((ap @ (sub @ X335 @ id) @ X332))) | (X332 = X333))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X336 : term] : ~ ! [X337 : (subst > term > term)] : (((X337 @ sh @ one)) != ((sub @ X336 @ (push @ one @ sh))))) & (! [X338 : term] : ~ ! [X339 : (subst > term > term)] : ~ ! [X340 : term,X341 : subst] : (((sub @ X338 @ (push @ X340 @ X341))) = ((X339 @ X341 @ X340))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ! [X347 : term] : ? [X348 : d_term] : (((d2term @ X348)) = X347) & ((axidl = $true) <=> ! [X349 : subst] : (((comp @ id @ X349)) = X349)) & ((pushprop_lem0_lthm = $true) <=> ! [X350 : term,X351 : (term > $o),X352 : subst] : ~ ! [X353 : (term > $o)] : ~ ! [X354 : term] : (((X353 @ X354)) = ((X351 @ (sub @ X354 @ (push @ X350 @ X352)))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X355 : term,X356 : (subst > term > subst > $o),X357 : (term > $o)] : (~ ! [X358 : term] : (((X357 @ X358)) = ((X356 @ id @ X358 @ id))) | (((X357 @ (lam @ X355))) = $true) | ~ ! [X359 : (subst > term > term)] : ((((X356 @ id @ (lam @ (X359 @ sh @ one)) @ id)) = $true) | ~ ! [X360 : term] : ((((X356 @ id @ (X359 @ id @ X360) @ id)) = $true) | ~ (((X356 @ id @ X360 @ id)) = $true)) | ~ ! [X361 : subst,X362 : subst,X363 : term] : (((X359 @ (comp @ X362 @ X361) @ (sub @ X363 @ X361))) = ((sub @ (X359 @ X362 @ X363) @ X361)))) | ~ ! [X364 : term] : (~ (((X357 @ X364)) = $true) | (((X357 @ (sub @ X355 @ (push @ X364 @ id)))) = $true)))) & ! [X365 : d_term,X366 : d_term] : ((((d2term @ X366)) = ((d2term @ X365))) => (X365 = X366)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X367 : subst,X368 : term] : (((comp @ sh @ (push @ X368 @ X367))) = X367)) & ((hoasinduction = $true) <=> ! [X369 : (subst > term > subst > $o),X370 : term] : (~ ! [X371 : term] : (~ ($true = ((var @ (sub @ X371 @ id)))) | (((X369 @ id @ X371 @ id)) = $true)) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (~ (((X369 @ X373 @ X375 @ (comp @ X374 @ X372))) = $true) | (((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) = $true)) | ~ ! [X376 : term,X377 : term] : ((((X369 @ id @ (ap @ (sub @ X377 @ id) @ X376) @ id)) = $true) | ~ (((X369 @ id @ X376 @ id)) = $true) | ~ (((X369 @ id @ X377 @ id)) = $true)) | ~ ! [X378 : (subst > term > term)] : (($true = ((X369 @ id @ (lam @ (X378 @ sh @ one)) @ id))) | ~ ! [X379 : subst,X380 : subst,X381 : term] : (((sub @ (X378 @ X379 @ X381) @ X380)) = ((X378 @ (comp @ X379 @ X380) @ (sub @ X381 @ X380)))) | ~ ! [X382 : term] : ((((X369 @ id @ (X378 @ id @ X382) @ id)) = $true) | ~ (((X369 @ id @ X382 @ id)) = $true))) | (((X369 @ id @ X370 @ id)) = $true) | ~ ! [X383 : subst,X384 : term,X385 : subst,X386 : subst] : (~ ($true = ((X369 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383) @ X386))) | ($true = ((X369 @ X385 @ X384 @ (comp @ X383 @ X386))))))) & ((! [X387 : term,X388 : subst] : (((sub @ one @ (push @ X387 @ X388))) = X387) => (! [X389 : subst,X390 : term] : (((comp @ sh @ (push @ X390 @ X389))) = X389) => (! [X391 : term,X392 : term] : ((X391 = X392) | (((lam @ X392)) != ((lam @ X391)))) => ! [X393 : (subst > term > term),X394 : subst,X395 : term,X396 : (subst > term > term)] : (~ ! [X397 : subst,X398 : term,X399 : subst] : (((X396 @ (comp @ X397 @ X399) @ (sub @ X398 @ X399))) = ((sub @ (X396 @ X397 @ X398) @ X399))) | (((X396 @ X394 @ X395)) = ((X393 @ X394 @ X395))) | ~ ! [X400 : term,X401 : subst,X402 : subst] : (((X393 @ (comp @ X402 @ X401) @ (sub @ X400 @ X401))) = ((sub @ (X393 @ X402 @ X400) @ X401))) | (((lam @ (X393 @ sh @ one))) != ((lam @ (X396 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & ((! [X403 : term,X404 : subst] : (((sub @ one @ (push @ X403 @ X404))) = X403) => ! [X405 : (term > $o),X406 : term,X407 : subst,X408 : (term > $o)] : (~ ! [X409 : term] : (((X408 @ X409)) = ((X405 @ (sub @ X409 @ (push @ X406 @ X407))))) | ~ (((X405 @ X406)) = $true) | (((X408 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (axvarshift = $true) & (hoaslamnotvar_lthm = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X410 : term,X411 : (subst > term > subst > $o)] : (~ ! [X412 : (subst > term > term)] : ((((X411 @ id @ (lam @ (X412 @ sh @ one)) @ id)) = $true) | ~ ! [X413 : term] : (~ (((X411 @ id @ X413 @ id)) = $true) | (((X411 @ id @ (X412 @ id @ X413) @ id)) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst] : (((X412 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414))) = ((sub @ (X412 @ X416 @ X415) @ X414)))) | (((X411 @ id @ (lam @ X410) @ id)) = $true) | ~ ! [X417 : subst,X418 : term,X419 : subst,X420 : subst] : (~ (((X411 @ (comp @ X417 @ X419) @ (sub @ X418 @ X419) @ X420)) = $true) | (((X411 @ X417 @ X418 @ (comp @ X419 @ X420))) = $true)) | ~ ! [X421 : subst,X422 : term,X423 : subst,X424 : subst] : ((((X411 @ (comp @ X423 @ X421) @ (sub @ X422 @ X421) @ X424)) = $true) | ~ (((X411 @ X423 @ X422 @ (comp @ X421 @ X424))) = $true)) | ~ ! [X425 : term] : ((((X411 @ id @ (sub @ X410 @ (push @ X425 @ id)) @ id)) = $true) | ~ (((X411 @ id @ X425 @ id)) = $true)))) & (lamnotvar = $true) & (pushprop_lem2v2_gthm = $true) & (ulamvarsh = $true) & ~ (ulamvar1 = $true) & (pushprop = $true) & (! [X426 : term,X427 : term,X428 : (subst > term > subst > $o)] : (~ ! [X429 : subst,X430 : subst,X431 : subst,X432 : term] : ((((X428 @ (comp @ X430 @ X429) @ (sub @ X432 @ X429) @ X431)) = $true) | ~ (((X428 @ X430 @ X432 @ (comp @ X429 @ X431))) = $true)) | ~ (((X428 @ id @ X427 @ id)) = $true) | ~ ! [X433 : subst,X434 : term,X435 : subst,X436 : subst] : ((((X428 @ X435 @ X434 @ (comp @ X433 @ X436))) = $true) | ~ (((X428 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433) @ X436)) = $true)) | (((X428 @ id @ (ap @ X427 @ X426) @ id)) = $true) | ~ ($true = ((X428 @ id @ X426 @ id))) | ~ ! [X437 : term,X438 : term] : (~ (((X428 @ id @ X437 @ id)) = $true) | ~ (((X428 @ id @ X438 @ id)) = $true) | (((X428 @ id @ (ap @ (sub @ X437 @ id) @ X438) @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & (! [X439 : term,X440 : (term > $o),X441 : (term > $o),X442 : subst] : ((((X440 @ one)) = $true) | ~ (((X441 @ X439)) = $true) | ~ ! [X443 : term] : (((X440 @ X443)) = ((X441 @ (sub @ X443 @ (push @ X439 @ X442)))))) <=> (pushprop_lem1v2 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((induction2lem_lthm = $true) <=> (! [X444 : subst,X445 : term] : (((sub @ one @ (push @ X445 @ X444))) = X445) => (! [X446 : term,X447 : subst] : (((comp @ sh @ (push @ X446 @ X447))) = X447) => (! [X448 : subst] : (((comp @ X448 @ id)) = X448) => (! [X449 : term,X450 : (term > $o)] : ((((X450 @ X449)) = $true) | ~ ! [X451 : term,X452 : term] : (~ (((X450 @ X451)) = $true) | (((X450 @ (ap @ X452 @ X451))) = $true) | ~ (((X450 @ X452)) = $true)) | ~ ! [X453 : term] : ((((X450 @ X453)) = $true) | ~ (((var @ X453)) = $true)) | ~ ! [X454 : term] : ((((X450 @ (lam @ X454))) = $true) | ~ (((X450 @ X454)) = $true))) => ! [X455 : term,X456 : (term > $o),X457 : subst] : (~ ! [X458 : term] : ((((X456 @ (lam @ X458))) = $true) | ~ ! [X459 : term] : ((((X456 @ (sub @ X458 @ (push @ X459 @ id)))) = $true) | ~ (((X456 @ X459)) = $true))) | (((X456 @ (sub @ X455 @ X457))) = $true) | ~ ! [X460 : term] : ((((X456 @ (sub @ X460 @ X457))) = $true) | ~ ($true = ((var @ X460)))) | ~ ! [X461 : term,X462 : term] : (~ (((X456 @ X461)) = $true) | (((X456 @ (ap @ X461 @ X462))) = $true) | ~ (((X456 @ X462)) = $true)))))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X463 : (subst > term > subst > $o),X464 : term] : ((((X463 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X465 : term] : (~ (((X463 @ id @ X465 @ id)) = $true) | (((X463 @ id @ (sub @ X464 @ (push @ X465 @ id)) @ id)) = $true)) | ~ ! [X466 : (subst > term > term)] : (~ ! [X467 : term] : ((((X463 @ id @ (X466 @ id @ X467) @ id)) = $true) | ~ (((X463 @ id @ X467 @ id)) = $true)) | (((X463 @ id @ (lam @ (X466 @ sh @ one)) @ id)) = $true) | ~ ! [X468 : term,X469 : subst,X470 : subst] : (((sub @ (X466 @ X469 @ X468) @ X470)) = ((X466 @ (comp @ X469 @ X470) @ (sub @ X468 @ X470))))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X471 : term,X472 : (subst > term > subst > $o)] : ((((X472 @ id @ (lam @ (sub @ X471 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X473 : term,X474 : (subst > term > term)] : ((((X472 @ id @ (lam @ (X474 @ sh @ one)) @ id)) = $true) | ~ ! [X475 : term,X476 : subst,X477 : subst] : (((sub @ (sub @ X473 @ (push @ X475 @ X477)) @ X476)) = ((sub @ (X474 @ X477 @ X475) @ X476))) | ~ ! [X478 : term] : ((((X472 @ id @ (X474 @ id @ X478) @ id)) = $true) | ~ (((X472 @ id @ X478 @ id)) = $true)) | ~ ! [X479 : subst,X480 : term,X481 : subst] : (((X474 @ (comp @ X481 @ X479) @ (sub @ X480 @ X479))) = ((sub @ X473 @ (push @ (sub @ X480 @ X479) @ (comp @ X481 @ X479)))))) | ~ ! [X482 : term] : ((((X472 @ id @ (sub @ X471 @ (push @ X482 @ id)) @ id)) = $true) | ~ (((X472 @ id @ X482 @ id)) = $true)))) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lthm = $true) & ((! [X486 : subst] : (((comp @ id @ X486)) = X486) => (! [X487 : subst] : (((comp @ X487 @ id)) = X487) => (! [X488 : subst] : (((comp @ X488 @ id)) = X488) & ! [X489 : subst] : (((comp @ id @ X489)) = X489)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X490 : (subst > term > subst > $o)] : ~ ! [X491 : (term > $o)] : ~ ! [X492 : term] : (((X490 @ id @ X492 @ id)) = ((X491 @ X492)))) & (hoasinduction_lem3v2_gthm = $true) & ((induction2 = $true) <=> ! [X493 : (term > $o),X494 : term] : (~ ! [X495 : term] : ((((X493 @ (lam @ X495))) = $true) | ~ ! [X496 : term] : (~ (((X493 @ X496)) = $true) | ($true = ((X493 @ (sub @ X495 @ (push @ X496 @ id))))))) | (((X493 @ X494)) = $true) | ~ ! [X497 : term,X498 : term] : (~ (((X493 @ X498)) = $true) | ~ (((X493 @ X497)) = $true) | (((X493 @ (ap @ X497 @ X498))) = $true)) | ~ ! [X499 : term] : (~ (((var @ X499)) = $true) | ($true = ((X493 @ X499)))))) & ((laminj = $true) <=> ! [X500 : term,X501 : term] : ((((lam @ X501)) != ((lam @ X500))) | (X500 = X501))) & (axapp = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X502 : (subst > term > subst > $o)] : ~ ! [X503 : (term > $o)] : ~ ! [X504 : term] : (((X503 @ X504)) = ((X502 @ id @ X504 @ id)))) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X505 : (subst > term > subst > $o),X506 : (term > $o),X507 : term,X508 : term] : (~ ($true = ((X506 @ X507))) | ~ ! [X509 : term] : (((X505 @ id @ X509 @ id)) = ((X506 @ X509))) | ~ ! [X510 : term,X511 : term] : (~ (((X505 @ id @ X511 @ id)) = $true) | ~ (((X505 @ id @ X510 @ id)) = $true) | (((X505 @ id @ (ap @ (sub @ X511 @ id) @ X510) @ id)) = $true)) | ~ (((X506 @ X508)) = $true) | (((X506 @ (ap @ X507 @ X508))) = $true) | ~ ! [X512 : subst,X513 : term,X514 : subst,X515 : subst] : ((((X505 @ (comp @ X515 @ X514) @ (sub @ X513 @ X514) @ X512)) = $true) | ~ (((X505 @ X515 @ X513 @ (comp @ X514 @ X512))) = $true)) | ~ ! [X516 : subst,X517 : subst,X518 : subst,X519 : term] : (~ (((X505 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517) @ X516)) = $true) | (((X505 @ X518 @ X519 @ (comp @ X517 @ X516))) = $true)))) & ((axvarcons = $true) <=> ! [X520 : term,X521 : subst] : (((sub @ one @ (push @ X520 @ X521))) = X520)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X522 : term] : ~ ! [X523 : (subst > term > term)] : ~ ! [X524 : subst,X525 : term] : (((X523 @ X524 @ X525)) = ((sub @ X522 @ (push @ X525 @ X524))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X526 : term,X527 : term,X528 : term,X529 : term] : ((((ap @ X528 @ X529)) != ((ap @ X526 @ X527))) | (X527 = X529)) => ! [X530 : term,X531 : term,X532 : term,X533 : term] : ((X530 = X531) | (((ap @ (sub @ X532 @ id) @ X531)) != ((ap @ (sub @ X533 @ id) @ X530)))))) & (termmset_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((induction2_lthm = $true) <=> (! [X534 : term] : (((sub @ X534 @ id)) = X534) => (! [X535 : subst,X536 : (term > $o),X537 : term] : (~ ! [X538 : term] : (~ (((var @ X538)) = $true) | (((X536 @ (sub @ X538 @ X535))) = $true)) | ~ ! [X539 : term,X540 : term] : (~ (((X536 @ X540)) = $true) | ~ (((X536 @ X539)) = $true) | (((X536 @ (ap @ X539 @ X540))) = $true)) | ~ ! [X541 : term] : (~ ! [X542 : term] : (~ (((X536 @ X542)) = $true) | (((X536 @ (sub @ X541 @ (push @ X542 @ id)))) = $true)) | (((X536 @ (lam @ X541))) = $true)) | (((X536 @ (sub @ X537 @ X535))) = $true)) => ! [X543 : term,X544 : (term > $o)] : ((((X544 @ X543)) = $true) | ~ ! [X545 : term] : ((((X544 @ X545)) = $true) | ~ (((var @ X545)) = $true)) | ~ ! [X546 : term,X547 : term] : ((((X544 @ (ap @ X546 @ X547))) = $true) | ~ (((X544 @ X547)) = $true) | ~ (((X544 @ X546)) = $true)) | ~ ! [X548 : term] : ((((X544 @ (lam @ X548))) = $true) | ~ ! [X549 : term] : (~ (((X544 @ X549)) = $true) | (((X544 @ (sub @ X548 @ (push @ X549 @ id)))) = $true)))))))),
% 47.53/7.11 inference(fool_elimination,[],[f6])).
% 47.53/7.11 thf(f8,plain,(
% 47.53/7.11 ~(! [X0 : (subst > term > subst > $o)] : (! [X2 : subst,X3 : subst,X4 : term,X1 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) => (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) = $true)) => (! [X6 : term,X5 : subst,X8 : subst,X7 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) => (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) = $true)) => (! [X9 : term] : ((((hoasvar @ id @ X9 @ id)) = $true) => ($true = ((X0 @ id @ X9 @ id)))) => (! [X11 : term,X10 : term] : ((((X0 @ id @ X10 @ id)) = $true) => (($true = ((X0 @ id @ X11 @ id))) => (((X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id)) = $true))) => (! [X12 : (subst > term > term)] : (! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) => (! [X16 : term] : ((((X0 @ id @ X16 @ id)) = $true) => (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true))) => ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true)))))) <=> (hoasinduction = $true))),
% 47.53/7.11 inference(rectify,[],[f5])).
% 47.53/7.11 thf(f9,plain,(
% 47.53/7.11 (((d2subst @ d_id)) = sh) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & (hoasinduction_lem1 = $true) & ! [X4 : d_subst] : (d_id = X4) & (! [X7 : term,X6 : term,X5 : (subst > term > term)] : ((((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))) | ~ ! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8)))) <=> (hoaslamnotap = $true)) & (axclos = $true) & ~ (lamnotap = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (substmonoid_gthm = $true) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X15 : term] : (((sub @ X15 @ id)) = X15) => (! [X16 : (subst > term > subst > $o),X17 : term] : ((((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X18 : (subst > term > term)] : (~ ! [X19 : term] : ((((X16 @ id @ (X18 @ id @ X19) @ id)) = $true) | ~ (((X16 @ id @ X19 @ id)) = $true)) | (((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ~ ! [X21 : subst,X22 : term,X20 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) = ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) | ~ ! [X23 : term] : ((((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true) | ~ (((X16 @ id @ X23 @ id)) = $true))) => ! [X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X26 : (subst > term > term)] : (~ ! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) | ~ ! [X30 : term] : ((((X24 @ id @ (X26 @ id @ X30) @ id)) = $true) | ~ (((X24 @ id @ X30 @ id)) = $true)) | (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true)) | ~ ! [X31 : subst,X32 : term,X33 : subst,X34 : subst] : ((((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) = $true) | ~ (((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) = $true)) | ~ ! [X35 : term] : ((((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) = $true) | ~ (((X24 @ id @ X35 @ id)) = $true)) | ~ ! [X36 : subst,X37 : subst,X38 : subst,X39 : term] : ((((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) = $true) | ~ (((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) = $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X40 : (subst > term > subst > $o)] : ~ ! [X41 : (term > $o)] : ~ ! [X42 : term] : (((X40 @ id @ X42 @ id)) = ((X41 @ X42))) => (! [X43 : term,X44 : (term > $o)] : (~ ! [X45 : term] : (~ (((var @ X45)) = $true) | ($true = ((X44 @ X45)))) | (((X44 @ X43)) = $true) | ~ ! [X46 : term] : (~ ! [X47 : term] : (~ (((X44 @ X47)) = $true) | (((X44 @ (sub @ X46 @ (push @ X47 @ id)))) = $true)) | (((X44 @ (lam @ X46))) = $true)) | ~ ! [X48 : term,X49 : term] : ((((X44 @ (ap @ X48 @ X49))) = $true) | ~ (((X44 @ X48)) = $true) | ~ (((X44 @ X49)) = $true))) => (! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : (term > $o),X53 : term] : (~ ! [X54 : term] : (~ (((X52 @ X54)) = $true) | (((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true)) | ~ ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) | ($true = ((X52 @ (lam @ X53)))) | ~ ! [X56 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ~ ! [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) = ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ~ ! [X60 : term] : (~ (((X51 @ id @ X60 @ id)) = $true) | (((X51 @ id @ (X56 @ id @ X60) @ id)) = $true)))) => ! [X61 : (subst > term > subst > $o),X62 : term] : (~ ! [X63 : (subst > term > term)] : (~ ! [X64 : term] : ((((X61 @ id @ (X63 @ id @ X64) @ id)) = $true) | ~ (((X61 @ id @ X64 @ id)) = $true)) | (((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) = $true) | ~ ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66))))) | (((X61 @ id @ X62 @ id)) = $true) | ~ ! [X68 : subst,X69 : subst,X70 : subst,X71 : term] : (~ (((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) = $true) | (((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) = $true)) | ~ ! [X72 : term] : ((((X61 @ id @ X72 @ id)) = $true) | ~ (((var @ (sub @ X72 @ id))) = $true)) | ~ ! [X73 : term,X74 : term] : ((((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) = $true) | ~ (((X61 @ id @ X73 @ id)) = $true) | ~ (((X61 @ id @ X74 @ id)) = $true)) | ~ ! [X75 : subst,X76 : subst,X77 : subst,X78 : term] : (~ (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) = $true) | (((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) = $true)))))))) & (one = ((d2term @ d_one))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ! [X80 : d_subst,X79 : d_subst] : ((((d2subst @ X79)) = ((d2subst @ X80))) => (X79 = X80)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & (! [X82 : (subst > term > subst > $o),X83 : term] : (~ ! [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) = $true) | ~ (((X82 @ id @ X84 @ id)) = $true) | ~ (((X82 @ id @ X85 @ id)) = $true)) | (((X82 @ id @ X83 @ id)) = $true) | ~ ! [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ~ ! [X87 : term] : ((((X82 @ id @ (X86 @ id @ X87) @ id)) = $true) | ~ (((X82 @ id @ X87 @ id)) = $true)) | ~ ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90)))))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X91 : term] : (((sub @ X91 @ id)) = X91) => (! [X92 : (subst > term > subst > $o),X93 : term] : (~ ! [X94 : term] : (~ (((X92 @ id @ X94 @ id)) = $true) | (((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true)) | (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X95 : (subst > term > term)] : (~ ! [X98 : subst,X96 : subst,X97 : term] : (((sub @ (X95 @ X96 @ X97) @ X98)) = ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ~ ! [X99 : term] : (~ (((X92 @ id @ X99 @ id)) = $true) | (((X92 @ id @ (X95 @ id @ X99) @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true))) => ! [X100 : (subst > term > subst > $o),X101 : term] : ((((X100 @ id @ (lam @ X101) @ id)) = $true) | ~ ! [X102 : term] : ((((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) = $true) | ~ (((X100 @ id @ X102 @ id)) = $true)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106))) | ~ ! [X107 : term] : (~ (((X100 @ id @ X107 @ id)) = $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) | (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true)))))) & ((hoasinduction_lem3a = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (~ ! [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) = $true) | ~ (((X108 @ id @ X110 @ id)) = $true)) | ($true = ((X108 @ id @ (lam @ X109) @ id))) | ~ ! [X111 : (subst > term > term)] : (~ ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113))) | ~ ! [X115 : term] : (~ (((X108 @ id @ X115 @ id)) = $true) | (((X108 @ id @ (X111 @ id @ X115) @ id)) = $true)) | (((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) = $true)))) & ! [X116 : d_term] : (d_one = X116) & (hoasapinj1_gthm = $true) & ((! [X117 : term] : ~ ! [X118 : (subst > term > term)] : ~ ! [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) = ((X118 @ X120 @ X119))) => (! [X121 : term] : (((sub @ X121 @ id)) = X121) => ! [X122 : term,X123 : (term > $o),X124 : (subst > term > subst > $o)] : (~ ! [X125 : term] : (((X124 @ id @ X125 @ id)) = ((X123 @ X125))) | ~ ! [X126 : term] : (~ (((X123 @ X126)) = $true) | (((X123 @ (sub @ X122 @ (push @ X126 @ id)))) = $true)) | (((X123 @ (lam @ X122))) = $true) | ~ ! [X127 : (subst > term > term)] : (~ ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))) | (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ~ ! [X131 : term] : (~ ($true = ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (induction2lem_gthm = $true) & (axassoc = $true) & (pushprop_lem0_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & ((hoaslaminj = $true) <=> ! [X140 : (subst > term > term),X139 : term,X138 : (subst > term > term),X141 : subst] : (~ ! [X145 : subst,X146 : subst,X147 : term] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | (((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ~ ! [X144 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & ((! [X148 : term,X149 : (term > $o)] : (~ ! [X150 : term,X151 : term] : (~ (((X149 @ X151)) = $true) | ~ (((X149 @ X150)) = $true) | (((X149 @ (ap @ X151 @ X150))) = $true)) | ~ ! [X152 : term] : (~ ! [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) = $true) | ~ (((X149 @ X153)) = $true)) | (((X149 @ (lam @ X152))) = $true)) | (((X149 @ X148)) = $true) | ~ ! [X154 : term] : ((((X149 @ X154)) = $true) | ~ (((var @ X154)) = $true))) => (! [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : (~ ! [X158 : subst,X159 : subst,X160 : term,X161 : subst] : (~ (((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) = $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true)) | (((X156 @ id @ (ap @ X157 @ X155) @ id)) = $true) | ~ ! [X162 : term,X163 : term] : (~ (((X156 @ id @ X162 @ id)) = $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true) | ~ (((X156 @ id @ X163 @ id)) = $true)) | ~ ! [X164 : subst,X165 : subst,X166 : term,X167 : subst] : (~ (((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) = $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) | ~ (((X156 @ id @ X157 @ id)) = $true) | ~ (((X156 @ id @ X155 @ id)) = $true)) => (! [X168 : term,X169 : (subst > term > subst > $o)] : (~ ! [X170 : subst,X171 : term,X172 : subst,X173 : subst] : (~ (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) = $true) | (((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true)) | ~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : ((((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true) | ~ (((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) = $true)) | ~ ! [X178 : term] : (~ (((X169 @ id @ X178 @ id)) = $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) | (((X169 @ id @ (lam @ X168) @ id)) = $true) | ~ ! [X179 : (subst > term > term)] : (~ ! [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) = $true) | ~ (((X169 @ id @ X180 @ id)) = $true)) | ~ ! [X181 : subst,X183 : term,X182 : subst] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) = ((sub @ (X179 @ X182 @ X183) @ X181))) | (((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true))) => ! [X184 : term,X185 : (subst > term > subst > $o)] : (~ ! [X186 : subst,X187 : subst,X188 : term,X189 : subst] : (~ (((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) = $true) | (((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) = $true)) | (((X185 @ id @ X184 @ id)) = $true) | ~ ! [X190 : term,X191 : term] : (~ (((X185 @ id @ X190 @ id)) = $true) | ~ ($true = ((X185 @ id @ X191 @ id))) | (((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true)) | ~ ! [X192 : subst,X193 : term,X194 : subst,X195 : subst] : (~ (((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) = $true) | (((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) = $true)) | ~ ! [X196 : term] : ((((X185 @ id @ X196 @ id)) = $true) | ~ ($true = ((var @ (sub @ X196 @ id))))) | ~ ! [X197 : (subst > term > term)] : (~ ! [X198 : term] : (~ (((X185 @ id @ X198 @ id)) = $true) | (((X185 @ id @ (X197 @ id @ X198) @ id)) = $true)) | (((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))))))) <=> (hoasinduction_lthm = $true)) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X206 : subst,X207 : subst,X208 : term,X209 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) = $true) | ~ (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) = $true)) | ~ ! [X210 : term] : (((X205 @ X210)) = ((X203 @ id @ X210 @ id))) | (((X205 @ (lam @ X204))) = $true) | ~ ! [X211 : term] : ((((X205 @ (sub @ X204 @ (push @ X211 @ id)))) = $true) | ~ (((X205 @ X211)) = $true)) | ~ ! [X212 : subst,X213 : term,X214 : subst,X215 : subst] : (~ (((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) = $true) | (((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) = $true)) | ~ ! [X216 : (subst > term > term)] : ((((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ~ ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) | ~ ! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | ~ (((X203 @ id @ X220 @ id)) = $true)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X221 : (subst > term > subst > $o)] : ~ ! [X222 : (term > $o)] : ~ ! [X223 : term] : (((X221 @ id @ X223 @ id)) = ((X222 @ X223))) => (! [X224 : term,X225 : (term > $o)] : (~ ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | ~ ($true = ((X225 @ X227))) | ~ (((X225 @ X226)) = $true)) | ~ ! [X228 : term] : ((((X225 @ (lam @ X228))) = $true) | ~ ! [X229 : term] : ((((X225 @ (sub @ X228 @ (push @ X229 @ id)))) = $true) | ~ (((X225 @ X229)) = $true))) | ~ ! [X230 : term] : ((((X225 @ X230)) = $true) | ~ (((var @ X230)) = $true)) | (((X225 @ X224)) = $true)) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => (! [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : ((((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X237 : subst,X236 : term,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | ~ ! [X239 : term] : (~ (((X232 @ id @ X239 @ id)) = $true) | (((X232 @ id @ (X235 @ id @ X239) @ id)) = $true))) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) | ~ ! [X241 : term] : (~ (((X234 @ X241)) = $true) | (((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true)) | (((X234 @ (lam @ X233))) = $true)) => ! [X242 : term,X243 : (subst > term > subst > $o)] : ((((X243 @ id @ X242 @ id)) = $true) | ~ ! [X244 : term,X245 : term] : (~ (((X243 @ id @ X244 @ id)) = $true) | ~ (((X243 @ id @ X245 @ id)) = $true) | ($true = ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id)))) | ~ ! [X246 : (subst > term > term)] : (~ ! [X247 : term] : (~ (((X243 @ id @ X247 @ id)) = $true) | (((X243 @ id @ (X246 @ id @ X247) @ id)) = $true)) | ~ ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) | (((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) = $true)))))))) & ((! [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) = X253) => ! [X255 : term,X256 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o)] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | ~ (((X259 @ X255)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X260 : term] : (((sub @ X260 @ id)) = X260) => ! [X261 : term] : (((sub @ X261 @ id)) = X261)) <=> (termmset_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((induction = $true) <=> ! [X262 : (term > $o),X263 : term] : (~ ! [X264 : term,X265 : term] : ((((X262 @ (ap @ X265 @ X264))) = $true) | ~ (((X262 @ X264)) = $true) | ~ (((X262 @ X265)) = $true)) | ~ ! [X266 : term] : ((((X262 @ (lam @ X266))) = $true) | ~ (((X262 @ X266)) = $true)) | ~ ! [X267 : term] : ((((X262 @ X267)) = $true) | ~ (((var @ X267)) = $true)) | (((X262 @ X263)) = $true))) & (! [X268 : subst,X269 : term,X270 : (term > $o)] : ((((X270 @ (sub @ X269 @ X268))) = $true) | ~ ! [X271 : term] : (~ ! [X272 : term] : (~ (((X270 @ X272)) = $true) | (((X270 @ (sub @ X271 @ (push @ X272 @ id)))) = $true)) | ($true = ((X270 @ (lam @ X271))))) | ~ ! [X273 : term] : (~ (((var @ X273)) = $true) | (((X270 @ (sub @ X273 @ X268))) = $true)) | ~ ! [X274 : term,X275 : term] : (~ (((X270 @ X275)) = $true) | ~ (((X270 @ X274)) = $true) | (((X270 @ (ap @ X274 @ X275))) = $true))) <=> (induction2lem = $true)) & ((! [X276 : term] : (((sub @ X276 @ id)) = X276) => (! [X279 : term,X278 : term,X277 : term,X280 : term] : ((((ap @ X279 @ X278)) != ((ap @ X280 @ X277))) | (X279 = X280)) => ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282)))))) <=> (hoasapinj1_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X285 : (term > $o),X286 : subst,X287 : term,X288 : term,X289 : (term > $o)] : (~ (((X285 @ X287)) = $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true))) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X290 : term] : ~ ! [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) != ((X291 @ sh @ one)))) & (hoasinduction_lem2_gthm = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X292 : term,X293 : (subst > term > subst > $o),X294 : (term > $o)] : (~ ! [X295 : subst,X296 : subst,X297 : term,X298 : subst] : (~ (((X293 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298) @ X295)) = $true) | (((X293 @ X296 @ X297 @ (comp @ X298 @ X295))) = $true)) | ~ ! [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (~ (((X293 @ X300 @ X301 @ (comp @ X302 @ X299))) = $true) | (((X293 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302) @ X299)) = $true)) | ~ ! [X303 : term] : (~ (((X294 @ X303)) = $true) | (((X294 @ (sub @ X292 @ (push @ X303 @ id)))) = $true)) | (((X294 @ (lam @ X292))) = $true) | ~ ! [X304 : (subst > term > term)] : (~ ! [X305 : term] : (~ (((X293 @ id @ X305 @ id)) = $true) | (((X293 @ id @ (X304 @ id @ X305) @ id)) = $true)) | ~ ! [X307 : term,X308 : subst,X306 : subst] : (((sub @ (X304 @ X306 @ X307) @ X308)) = ((X304 @ (comp @ X306 @ X308) @ (sub @ X307 @ X308)))) | (((X293 @ id @ (lam @ (X304 @ sh @ one)) @ id)) = $true)) | ~ ! [X309 : term] : (((X294 @ X309)) = ((X293 @ id @ X309 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_gthm = $true) & (! [X310 : term,X311 : (subst > term > subst > $o)] : ((((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) = $true) | ~ ! [X313 : term] : (~ (((X311 @ id @ X313 @ id)) = $true) | (((X311 @ id @ (X312 @ id @ X313) @ id)) = $true)) | ~ ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316))))) | ~ ! [X317 : term] : (~ (((X311 @ id @ X317 @ id)) = $true) | (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem0 = $true) <=> ! [X320 : term,X318 : subst,X319 : (term > $o)] : ~ ! [X321 : (term > $o)] : ~ ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318)))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_lthm = $true) & (hoaslamnotap_gthm = $true) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) <=> (shinj = $true)) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (hoasinduction_lem1v2 = $true) & ((substmonoid = $true) <=> (! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))) & ((axvarid = $true) <=> ! [X327 : term] : (((sub @ X327 @ id)) = X327)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (hoasinduction_lem2v2_gthm = $true) & (hoaslaminj_gthm = $true) & (apnotvar = $true) & (induction2_gthm = $true) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) <=> (axidr = $true)) & ((hoasapinj2 = $true) <=> ! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331))))) & (pushprop_lem3v2 = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X334 : term] : ~ ! [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) != ((X335 @ sh @ one)))) & (! [X336 : term] : ~ ! [X337 : (subst > term > term)] : ~ ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) <=> (axidl = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X343 : term,X344 : (term > $o),X345 : subst] : ~ ! [X346 : (term > $o)] : ~ ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X348 : term,X349 : (subst > term > subst > $o),X350 : (term > $o)] : (~ ! [X351 : term] : (((X349 @ id @ X351 @ id)) = ((X350 @ X351))) | (((X350 @ (lam @ X348))) = $true) | ~ ! [X352 : (subst > term > term)] : ((((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) = $true) | ~ ! [X353 : term] : ((((X349 @ id @ (X352 @ id @ X353) @ id)) = $true) | ~ (((X349 @ id @ X353 @ id)) = $true)) | ~ ! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X352 @ X355 @ X356) @ X354)) = ((X352 @ (comp @ X355 @ X354) @ (sub @ X356 @ X354))))) | ~ ! [X357 : term] : (~ (((X350 @ X357)) = $true) | (((X350 @ (sub @ X348 @ (push @ X357 @ id)))) = $true)))) & ! [X359 : d_term,X358 : d_term] : ((((d2term @ X358)) = ((d2term @ X359))) => (X358 = X359)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360)) & ((hoasinduction = $true) <=> ! [X362 : (subst > term > subst > $o),X363 : term] : (~ ! [X364 : term] : (~ (((var @ (sub @ X364 @ id))) = $true) | (((X362 @ id @ X364 @ id)) = $true)) | ~ ! [X365 : subst,X366 : subst,X367 : subst,X368 : term] : (~ (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) = $true) | (((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) = $true)) | ~ ! [X369 : term,X370 : term] : ((((X362 @ id @ (ap @ (sub @ X370 @ id) @ X369) @ id)) = $true) | ~ ($true = ((X362 @ id @ X369 @ id))) | ~ (((X362 @ id @ X370 @ id)) = $true)) | ~ ! [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) = $true) | ~ ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373))) | ~ ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | ~ (((X362 @ id @ X375 @ id)) = $true))) | (((X362 @ id @ X363 @ id)) = $true) | ~ ! [X376 : subst,X377 : term,X378 : subst,X379 : subst] : (~ (((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) = $true) | (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) = $true)))) & ((hoaslaminj_lthm = $true) <=> (! [X381 : subst,X380 : term] : (((sub @ one @ (push @ X380 @ X381))) = X380) => (! [X382 : subst,X383 : term] : (((comp @ sh @ (push @ X383 @ X382))) = X382) => (! [X385 : term,X384 : term] : ((X384 = X385) | (((lam @ X385)) != ((lam @ X384)))) => ! [X389 : (subst > term > term),X386 : (subst > term > term),X387 : subst,X388 : term] : ((((lam @ (X386 @ sh @ one))) != ((lam @ (X389 @ sh @ one)))) | (((X389 @ X387 @ X388)) = ((X386 @ X387 @ X388))) | ~ ! [X394 : subst,X395 : subst,X393 : term] : (((sub @ (X386 @ X395 @ X393) @ X394)) = ((X386 @ (comp @ X395 @ X394) @ (sub @ X393 @ X394)))) | ~ ! [X391 : term,X390 : subst,X392 : subst] : (((X389 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392))) = ((sub @ (X389 @ X390 @ X391) @ X392)))))))) & ((! [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) = X396) => ! [X398 : (term > $o),X399 : term,X400 : subst,X401 : (term > $o)] : (~ ! [X402 : term] : (((X401 @ X402)) = ((X398 @ (sub @ X402 @ (push @ X399 @ X400))))) | ~ (((X398 @ X399)) = $true) | (((X401 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (axvarshift = $true) & (hoaslamnotvar_lthm = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X403 : term,X404 : (subst > term > subst > $o)] : (~ ! [X405 : (subst > term > term)] : ((((X404 @ id @ (lam @ (X405 @ sh @ one)) @ id)) = $true) | ~ ! [X406 : term] : (~ ($true = ((X404 @ id @ X406 @ id))) | (((X404 @ id @ (X405 @ id @ X406) @ id)) = $true)) | ~ ! [X408 : term,X407 : subst,X409 : subst] : (((sub @ (X405 @ X409 @ X408) @ X407)) = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407))))) | (((X404 @ id @ (lam @ X403) @ id)) = $true) | ~ ! [X410 : subst,X411 : term,X412 : subst,X413 : subst] : (~ (((X404 @ (comp @ X410 @ X412) @ (sub @ X411 @ X412) @ X413)) = $true) | (((X404 @ X410 @ X411 @ (comp @ X412 @ X413))) = $true)) | ~ ! [X414 : subst,X415 : term,X416 : subst,X417 : subst] : ((((X404 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414) @ X417)) = $true) | ~ (((X404 @ X416 @ X415 @ (comp @ X414 @ X417))) = $true)) | ~ ! [X418 : term] : ((((X404 @ id @ (sub @ X403 @ (push @ X418 @ id)) @ id)) = $true) | ~ (((X404 @ id @ X418 @ id)) = $true)))) & (lamnotvar = $true) & (pushprop_lem2v2_gthm = $true) & (ulamvarsh = $true) & ~ (ulamvar1 = $true) & (pushprop = $true) & (! [X419 : term,X420 : term,X421 : (subst > term > subst > $o)] : (~ ! [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((((X421 @ (comp @ X423 @ X422) @ (sub @ X425 @ X422) @ X424)) = $true) | ~ (((X421 @ X423 @ X425 @ (comp @ X422 @ X424))) = $true)) | ~ (((X421 @ id @ X420 @ id)) = $true) | ~ ! [X426 : subst,X427 : term,X428 : subst,X429 : subst] : ((((X421 @ X428 @ X427 @ (comp @ X426 @ X429))) = $true) | ~ (((X421 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426) @ X429)) = $true)) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | ~ (((X421 @ id @ X419 @ id)) = $true) | ~ ! [X430 : term,X431 : term] : (~ (((X421 @ id @ X430 @ id)) = $true) | ~ (((X421 @ id @ X431 @ id)) = $true) | (((X421 @ id @ (ap @ (sub @ X430 @ id) @ X431) @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & (! [X432 : term,X433 : (term > $o),X434 : (term > $o),X435 : subst] : ((((X433 @ one)) = $true) | ~ (((X434 @ X432)) = $true) | ~ ! [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) = ((X433 @ X436)))) <=> (pushprop_lem1v2 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((induction2lem_lthm = $true) <=> (! [X438 : term,X437 : subst] : (((sub @ one @ (push @ X438 @ X437))) = X438) => (! [X439 : term,X440 : subst] : (((comp @ sh @ (push @ X439 @ X440))) = X440) => (! [X441 : subst] : (((comp @ X441 @ id)) = X441) => (! [X442 : term,X443 : (term > $o)] : ((((X443 @ X442)) = $true) | ~ ! [X444 : term,X445 : term] : (~ (((X443 @ X444)) = $true) | (((X443 @ (ap @ X445 @ X444))) = $true) | ~ (((X443 @ X445)) = $true)) | ~ ! [X446 : term] : ((((X443 @ X446)) = $true) | ~ (((var @ X446)) = $true)) | ~ ! [X447 : term] : ((((X443 @ (lam @ X447))) = $true) | ~ (((X443 @ X447)) = $true))) => ! [X448 : term,X449 : (term > $o),X450 : subst] : (~ ! [X451 : term] : ((((X449 @ (lam @ X451))) = $true) | ~ ! [X452 : term] : ((((X449 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | ~ (((X449 @ X452)) = $true))) | (((X449 @ (sub @ X448 @ X450))) = $true) | ~ ! [X453 : term] : ((((X449 @ (sub @ X453 @ X450))) = $true) | ~ (((var @ X453)) = $true)) | ~ ! [X454 : term,X455 : term] : (~ (((X449 @ X454)) = $true) | (((X449 @ (ap @ X454 @ X455))) = $true) | ~ (((X449 @ X455)) = $true)))))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X456 : (subst > term > subst > $o),X457 : term] : ((((X456 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X458 : term] : (~ (((X456 @ id @ X458 @ id)) = $true) | (((X456 @ id @ (sub @ X457 @ (push @ X458 @ id)) @ id)) = $true)) | ~ ! [X459 : (subst > term > term)] : (~ ! [X460 : term] : ((((X456 @ id @ (X459 @ id @ X460) @ id)) = $true) | ~ ($true = ((X456 @ id @ X460 @ id)))) | (((X456 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true) | ~ ! [X463 : subst,X462 : subst,X461 : term] : (((sub @ (X459 @ X462 @ X461) @ X463)) = ((X459 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X466 : term,X467 : (subst > term > term)] : ((((X465 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true) | ~ ! [X470 : subst,X468 : term,X469 : subst] : (((sub @ (sub @ X466 @ (push @ X468 @ X470)) @ X469)) = ((sub @ (X467 @ X470 @ X468) @ X469))) | ~ ! [X471 : term] : ((((X465 @ id @ (X467 @ id @ X471) @ id)) = $true) | ~ (((X465 @ id @ X471 @ id)) = $true)) | ~ ! [X473 : term,X472 : subst,X474 : subst] : (((sub @ X466 @ (push @ (sub @ X473 @ X472) @ (comp @ X474 @ X472)))) = ((X467 @ (comp @ X474 @ X472) @ (sub @ X473 @ X472))))) | ~ ! [X475 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X475 @ id)) @ id)) = $true) | ~ (((X465 @ id @ X475 @ id)) = $true)))) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lthm = $true) & ((! [X476 : subst] : (((comp @ id @ X476)) = X476) => (! [X477 : subst] : (((comp @ X477 @ id)) = X477) => (! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)))) <=> (substmonoid_lthm = $true)) & (! [X480 : (subst > term > subst > $o)] : ~ ! [X481 : (term > $o)] : ~ ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) <=> (hoasinduction_lem0 = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((induction2 = $true) <=> ! [X483 : (term > $o),X484 : term] : (~ ! [X485 : term] : ((((X483 @ (lam @ X485))) = $true) | ~ ! [X486 : term] : (~ (((X483 @ X486)) = $true) | (((X483 @ (sub @ X485 @ (push @ X486 @ id)))) = $true))) | (((X483 @ X484)) = $true) | ~ ! [X487 : term,X488 : term] : (~ (((X483 @ X488)) = $true) | ~ (((X483 @ X487)) = $true) | (((X483 @ (ap @ X487 @ X488))) = $true)) | ~ ! [X489 : term] : (~ (((var @ X489)) = $true) | (((X483 @ X489)) = $true)))) & ((laminj = $true) <=> ! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491))) & (axapp = $true) & (! [X492 : (subst > term > subst > $o)] : ~ ! [X493 : (term > $o)] : ~ ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X495 : (subst > term > subst > $o),X496 : (term > $o),X497 : term,X498 : term] : (~ (((X496 @ X497)) = $true) | ~ ! [X499 : term] : (((X495 @ id @ X499 @ id)) = ((X496 @ X499))) | ~ ! [X500 : term,X501 : term] : (~ (((X495 @ id @ X501 @ id)) = $true) | ~ (((X495 @ id @ X500 @ id)) = $true) | (((X495 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) = $true)) | ~ (((X496 @ X498)) = $true) | (((X496 @ (ap @ X497 @ X498))) = $true) | ~ ! [X502 : subst,X503 : term,X504 : subst,X505 : subst] : ((((X495 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504) @ X502)) = $true) | ~ (((X495 @ X505 @ X503 @ (comp @ X504 @ X502))) = $true)) | ~ ! [X506 : subst,X507 : subst,X508 : subst,X509 : term] : (~ (((X495 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507) @ X506)) = $true) | (((X495 @ X508 @ X509 @ (comp @ X507 @ X506))) = $true)))) & ((axvarcons = $true) <=> ! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : ~ ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasapinj2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X516 : term,X519 : term,X518 : term,X517 : term] : ((X517 = X519) | (((ap @ X516 @ X517)) != ((ap @ X518 @ X519)))) => ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)))) & (termmset_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((induction2_lthm = $true) <=> (! [X524 : term] : (((sub @ X524 @ id)) = X524) => (! [X525 : subst,X526 : (term > $o),X527 : term] : (~ ! [X528 : term] : (~ (((var @ X528)) = $true) | (((X526 @ (sub @ X528 @ X525))) = $true)) | ~ ! [X529 : term,X530 : term] : (~ (((X526 @ X530)) = $true) | ~ (((X526 @ X529)) = $true) | (((X526 @ (ap @ X529 @ X530))) = $true)) | ~ ! [X531 : term] : (~ ! [X532 : term] : (~ (((X526 @ X532)) = $true) | (((X526 @ (sub @ X531 @ (push @ X532 @ id)))) = $true)) | (((X526 @ (lam @ X531))) = $true)) | (((X526 @ (sub @ X527 @ X525))) = $true)) => ! [X533 : term,X534 : (term > $o)] : ((((X534 @ X533)) = $true) | ~ ! [X535 : term] : ((((X534 @ X535)) = $true) | ~ (((var @ X535)) = $true)) | ~ ! [X536 : term,X537 : term] : ((((X534 @ (ap @ X536 @ X537))) = $true) | ~ (((X534 @ X537)) = $true) | ~ (((X534 @ X536)) = $true)) | ~ ! [X538 : term] : ((((X534 @ (lam @ X538))) = $true) | ~ ! [X539 : term] : (~ (((X534 @ X539)) = $true) | (((X534 @ (sub @ X538 @ (push @ X539 @ id)))) = $true)))))))),
% 47.53/7.11 inference(rectify,[],[f7])).
% 47.53/7.11 thf(f10,plain,(
% 47.53/7.11 (pushprop_lem2v2_gthm = $true) & (! [X480 : (subst > term > subst > $o)] : ~ ! [X481 : (term > $o)] : ~ ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X290 : term] : ~ ! [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) != ((X291 @ sh @ one)))) & ((! [X476 : subst] : (((comp @ id @ X476)) = X476) => (! [X477 : subst] : (((comp @ X477 @ id)) = X477) => (! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)))) <=> (substmonoid_lthm = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & ((substmonoid = $true) <=> (! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) = X251) => (! [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) = X253) => ! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true))))) & (lamnotap != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X221 : (subst > term > subst > $o)] : ~ ! [X222 : (term > $o)] : ~ ! [X223 : term] : (((X221 @ id @ X223 @ id)) = ((X222 @ X223))) => (! [X225 : (term > $o),X224 : term] : (~ ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | (((X225 @ X226)) != $true) | ($true != ((X225 @ X227)))) | ~ ! [X230 : term] : ((((var @ X230)) != $true) | (((X225 @ X230)) = $true)) | (((X225 @ X224)) = $true) | ~ ! [X228 : term] : (~ ! [X229 : term] : ((((X225 @ X229)) != $true) | (((X225 @ (sub @ X228 @ (push @ X229 @ id)))) = $true)) | (((X225 @ (lam @ X228))) = $true))) => (! [X231 : term] : (((sub @ X231 @ id)) = X231) => (! [X233 : term,X232 : (subst > term > subst > $o),X234 : (term > $o)] : (~ ! [X235 : (subst > term > term)] : (~ ! [X237 : subst,X236 : term,X238 : subst] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X235 @ X238 @ X236) @ X237))) | (((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X239 : term] : ((((X232 @ id @ X239 @ id)) != $true) | (((X232 @ id @ (X235 @ id @ X239) @ id)) = $true))) | ~ ! [X241 : term] : ((((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true) | (((X234 @ X241)) != $true)) | ~ ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) | (((X234 @ (lam @ X233))) = $true)) => ! [X243 : (subst > term > subst > $o),X242 : term] : (~ ! [X246 : (subst > term > term)] : ((((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) = $true) | ~ ! [X247 : term] : ((((X243 @ id @ (X246 @ id @ X247) @ id)) = $true) | (((X243 @ id @ X247 @ id)) != $true)) | ~ ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250))))) | (((X243 @ id @ X242 @ id)) = $true) | ~ ! [X245 : term,X244 : term] : ((((X243 @ id @ X245 @ id)) != $true) | ($true = ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id))) | (((X243 @ id @ X244 @ id)) != $true)))))))) & (termmset_gthm = $true) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) <=> (shinj = $true)) & (! [X269 : term,X270 : (term > $o),X268 : subst] : (~ ! [X271 : term] : (~ ! [X272 : term] : ((((X270 @ X272)) != $true) | (((X270 @ (sub @ X271 @ (push @ X272 @ id)))) = $true)) | ($true = ((X270 @ (lam @ X271))))) | ~ ! [X273 : term] : ((((var @ X273)) != $true) | (((X270 @ (sub @ X273 @ X268))) = $true)) | (((X270 @ (sub @ X269 @ X268))) = $true) | ~ ! [X275 : term,X274 : term] : ((((X270 @ X275)) != $true) | (((X270 @ (ap @ X274 @ X275))) = $true) | (((X270 @ X274)) != $true))) <=> (induction2lem = $true)) & ! [X80 : d_subst,X79 : d_subst] : ((((d2subst @ X79)) = ((d2subst @ X80))) => (X79 = X80)) & (hoasapnotvar = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X149 : (term > $o),X148 : term] : (~ ! [X154 : term] : ((((X149 @ X154)) = $true) | (((var @ X154)) != $true)) | (((X149 @ X148)) = $true) | ~ ! [X152 : term] : ((((X149 @ (lam @ X152))) = $true) | ~ ! [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) = $true) | (((X149 @ X153)) != $true))) | ~ ! [X150 : term,X151 : term] : ((((X149 @ X151)) != $true) | (((X149 @ X150)) != $true) | (((X149 @ (ap @ X151 @ X150))) = $true))) => (! [X157 : term,X156 : (subst > term > subst > $o),X155 : term] : (~ ! [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) != $true) | (((X156 @ id @ X163 @ id)) != $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)) | (((X156 @ id @ X155 @ id)) != $true) | (((X156 @ id @ (ap @ X157 @ X155) @ id)) = $true) | (((X156 @ id @ X157 @ id)) != $true) | ~ ! [X167 : subst,X166 : term,X165 : subst,X164 : subst] : ((((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) != $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) | ~ ! [X160 : term,X161 : subst,X159 : subst,X158 : subst] : ((((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) != $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true))) => (! [X168 : term,X169 : (subst > term > subst > $o)] : ((((X169 @ id @ (lam @ X168) @ id)) = $true) | ~ ! [X178 : term] : ((((X169 @ id @ X178 @ id)) != $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) | ~ ! [X177 : subst,X175 : subst,X176 : term,X174 : subst] : ((((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) != $true) | (((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true)) | ~ ! [X173 : subst,X172 : subst,X170 : subst,X171 : term] : ((((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true) | (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) != $true)) | ~ ! [X179 : (subst > term > term)] : ((((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ~ ! [X181 : subst,X183 : term,X182 : subst] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) = ((sub @ (X179 @ X182 @ X183) @ X181))) | ~ ! [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) = $true) | (((X169 @ id @ X180 @ id)) != $true)))) => ! [X184 : term,X185 : (subst > term > subst > $o)] : (~ ! [X196 : term] : (($true != ((var @ (sub @ X196 @ id)))) | (((X185 @ id @ X196 @ id)) = $true)) | ~ ! [X197 : (subst > term > term)] : ((((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) = $true) | ~ ! [X198 : term] : ((((X185 @ id @ (X197 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) | ~ ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199))))) | ~ ! [X188 : term,X189 : subst,X186 : subst,X187 : subst] : ((((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) = $true) | (((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) != $true)) | (((X185 @ id @ X184 @ id)) = $true) | ~ ! [X194 : subst,X195 : subst,X192 : subst,X193 : term] : ((((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) != $true) | (((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) = $true)) | ~ ! [X190 : term,X191 : term] : ((((X185 @ id @ X190 @ id)) != $true) | (((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) = $true) | ($true != ((X185 @ id @ X191 @ id))))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3a = $true) <=> ! [X109 : term,X108 : (subst > term > subst > $o)] : (~ ! [X110 : term] : ((((X108 @ id @ X110 @ id)) != $true) | (((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) = $true)) | ($true = ((X108 @ id @ (lam @ X109) @ id))) | ~ ! [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) = $true) | ~ ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113))) | ~ ! [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) = $true) | (((X108 @ id @ X115 @ id)) != $true))))) & ((hoaslaminj_lthm = $true) <=> (! [X381 : subst,X380 : term] : (((sub @ one @ (push @ X380 @ X381))) = X380) => (! [X382 : subst,X383 : term] : (((comp @ sh @ (push @ X383 @ X382))) = X382) => (! [X385 : term,X384 : term] : ((X384 = X385) | (((lam @ X385)) != ((lam @ X384)))) => ! [X389 : (subst > term > term),X386 : (subst > term > term),X387 : subst,X388 : term] : ((((lam @ (X386 @ sh @ one))) != ((lam @ (X389 @ sh @ one)))) | (((X389 @ X387 @ X388)) = ((X386 @ X387 @ X388))) | ~ ! [X394 : subst,X395 : subst,X393 : term] : (((sub @ (X386 @ X395 @ X393) @ X394)) = ((X386 @ (comp @ X395 @ X394) @ (sub @ X393 @ X394)))) | ~ ! [X391 : term,X390 : subst,X392 : subst] : (((X389 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392))) = ((sub @ (X389 @ X390 @ X391) @ X392)))))))) & ! [X4 : d_subst] : (d_id = X4) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (pushprop_lem3v2 = $true) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) <=> (axidr = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : ~ ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514))))) & (! [X263 : term,X262 : (term > $o)] : (~ ! [X266 : term] : ((((X262 @ (lam @ X266))) = $true) | (((X262 @ X266)) != $true)) | (((X262 @ X263)) = $true) | ~ ! [X267 : term] : ((((X262 @ X267)) = $true) | (((var @ X267)) != $true)) | ~ ! [X265 : term,X264 : term] : ((((X262 @ X264)) != $true) | (((X262 @ X265)) != $true) | (((X262 @ (ap @ X265 @ X264))) = $true))) <=> (induction = $true)) & ((! [X524 : term] : (((sub @ X524 @ id)) = X524) => (! [X525 : subst,X526 : (term > $o),X527 : term] : (~ ! [X529 : term,X530 : term] : ((((X526 @ X530)) != $true) | (((X526 @ X529)) != $true) | (((X526 @ (ap @ X529 @ X530))) = $true)) | ~ ! [X528 : term] : ((((X526 @ (sub @ X528 @ X525))) = $true) | (((var @ X528)) != $true)) | (((X526 @ (sub @ X527 @ X525))) = $true) | ~ ! [X531 : term] : (~ ! [X532 : term] : ((((X526 @ X532)) != $true) | (((X526 @ (sub @ X531 @ (push @ X532 @ id)))) = $true)) | (((X526 @ (lam @ X531))) = $true))) => ! [X534 : (term > $o),X533 : term] : (~ ! [X537 : term,X536 : term] : ((((X534 @ X537)) != $true) | (((X534 @ (ap @ X536 @ X537))) = $true) | (((X534 @ X536)) != $true)) | ~ ! [X535 : term] : ((((X534 @ X535)) = $true) | (((var @ X535)) != $true)) | ~ ! [X538 : term] : (~ ! [X539 : term] : ((((X534 @ X539)) != $true) | (((X534 @ (sub @ X538 @ (push @ X539 @ id)))) = $true)) | (((X534 @ (lam @ X538))) = $true)) | (((X534 @ X533)) = $true)))) <=> (induction2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((axvarcons = $true) <=> ! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510)) & (hoasapinj1_gthm = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X457 : term,X456 : (subst > term > subst > $o)] : (~ ! [X458 : term] : ((((X456 @ id @ X458 @ id)) != $true) | (((X456 @ id @ (sub @ X457 @ (push @ X458 @ id)) @ id)) = $true)) | (((X456 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X459 : (subst > term > term)] : (~ ! [X463 : subst,X462 : subst,X461 : term] : (((sub @ (X459 @ X462 @ X461) @ X463)) = ((X459 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463)))) | ~ ! [X460 : term] : ((((X456 @ id @ (X459 @ id @ X460) @ id)) = $true) | ($true != ((X456 @ id @ X460 @ id)))) | (((X456 @ id @ (lam @ (X459 @ sh @ one)) @ id)) = $true)))) & ((hoaslaminj = $true) <=> ! [X140 : (subst > term > term),X139 : term,X138 : (subst > term > term),X141 : subst] : (~ ! [X145 : subst,X146 : subst,X147 : term] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | (((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ~ ! [X144 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & (! [X293 : (subst > term > subst > $o),X292 : term,X294 : (term > $o)] : (~ ! [X309 : term] : (((X294 @ X309)) = ((X293 @ id @ X309 @ id))) | ~ ! [X304 : (subst > term > term)] : (~ ! [X307 : term,X308 : subst,X306 : subst] : (((sub @ (X304 @ X306 @ X307) @ X308)) = ((X304 @ (comp @ X306 @ X308) @ (sub @ X307 @ X308)))) | ~ ! [X305 : term] : ((((X293 @ id @ (X304 @ id @ X305) @ id)) = $true) | (((X293 @ id @ X305 @ id)) != $true)) | (((X293 @ id @ (lam @ (X304 @ sh @ one)) @ id)) = $true)) | (((X294 @ (lam @ X292))) = $true) | ~ ! [X303 : term] : ((((X294 @ X303)) != $true) | (((X294 @ (sub @ X292 @ (push @ X303 @ id)))) = $true)) | ~ ! [X301 : term,X302 : subst,X299 : subst,X300 : subst] : ((((X293 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302) @ X299)) = $true) | (((X293 @ X300 @ X301 @ (comp @ X302 @ X299))) != $true)) | ~ ! [X296 : subst,X298 : subst,X295 : subst,X297 : term] : ((((X293 @ X296 @ X297 @ (comp @ X298 @ X295))) = $true) | (((X293 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298) @ X295)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ! [X359 : d_term,X358 : d_term] : ((((d2term @ X358)) = ((d2term @ X359))) => (X358 = X359)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X260 : term] : (((sub @ X260 @ id)) = X260) => ! [X261 : term] : (((sub @ X261 @ id)) = X261)) <=> (termmset_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331))))) & (induction2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X334 : term] : ~ ! [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) != ((X335 @ sh @ one)))) & (pushprop_lem0_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X320 : term,X318 : subst,X319 : (term > $o)] : ~ ! [X321 : (term > $o)] : ~ ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318)))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X40 : (subst > term > subst > $o)] : ~ ! [X41 : (term > $o)] : ~ ! [X42 : term] : (((X40 @ id @ X42 @ id)) = ((X41 @ X42))) => (! [X44 : (term > $o),X43 : term] : (~ ! [X46 : term] : ((((X44 @ (lam @ X46))) = $true) | ~ ! [X47 : term] : ((((X44 @ (sub @ X46 @ (push @ X47 @ id)))) = $true) | (((X44 @ X47)) != $true))) | ~ ! [X49 : term,X48 : term] : ((((X44 @ X49)) != $true) | (((X44 @ (ap @ X48 @ X49))) = $true) | (((X44 @ X48)) != $true)) | ~ ! [X45 : term] : (($true = ((X44 @ X45))) | (((var @ X45)) != $true)) | (((X44 @ X43)) = $true)) => (! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X53 : term,X52 : (term > $o)] : (~ ! [X56 : (subst > term > term)] : (~ ! [X60 : term] : ((((X51 @ id @ X60 @ id)) != $true) | (((X51 @ id @ (X56 @ id @ X60) @ id)) = $true)) | (((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ~ ! [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) = ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58))))) | ($true = ((X52 @ (lam @ X53)))) | ~ ! [X54 : term] : ((((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true) | (((X52 @ X54)) != $true)) | ~ ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55)))) => ! [X62 : term,X61 : (subst > term > subst > $o)] : (~ ! [X63 : (subst > term > term)] : ((((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) = $true) | ~ ! [X64 : term] : ((((X61 @ id @ X64 @ id)) != $true) | (((X61 @ id @ (X63 @ id @ X64) @ id)) = $true)) | ~ ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66))))) | ~ ! [X71 : term,X68 : subst,X69 : subst,X70 : subst] : ((((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) != $true) | (((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) = $true)) | ~ ! [X78 : term,X75 : subst,X77 : subst,X76 : subst] : ((((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) = $true) | (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) != $true)) | ~ ! [X74 : term,X73 : term] : ((((X61 @ id @ X74 @ id)) != $true) | (((X61 @ id @ X73 @ id)) != $true) | (((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) = $true)) | (((X61 @ id @ X62 @ id)) = $true) | ~ ! [X72 : term] : ((((X61 @ id @ X72 @ id)) = $true) | (((var @ (sub @ X72 @ id))) != $true)))))))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1 = $true) <=> ! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true))) & (hoasinduction_lem3v2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X343 : term,X344 : (term > $o),X345 : subst] : ~ ! [X346 : (term > $o)] : ~ ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & (hoasinduction_lem1_gthm = $true) & (! [X496 : (term > $o),X498 : term,X497 : term,X495 : (subst > term > subst > $o)] : (~ ! [X508 : subst,X506 : subst,X509 : term,X507 : subst] : ((((X495 @ X508 @ X509 @ (comp @ X507 @ X506))) = $true) | (((X495 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507) @ X506)) != $true)) | (((X496 @ X497)) != $true) | ~ ! [X500 : term,X501 : term] : ((((X495 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) = $true) | (((X495 @ id @ X500 @ id)) != $true) | (((X495 @ id @ X501 @ id)) != $true)) | ~ ! [X503 : term,X504 : subst,X505 : subst,X502 : subst] : ((((X495 @ X505 @ X503 @ (comp @ X504 @ X502))) != $true) | (((X495 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504) @ X502)) = $true)) | (((X496 @ (ap @ X497 @ X498))) = $true) | (((X496 @ X498)) != $true) | ~ ! [X499 : term] : (((X495 @ id @ X499 @ id)) = ((X496 @ X499)))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X310 : term,X311 : (subst > term > subst > $o)] : ((((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X312 : (subst > term > term)] : (~ ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | (((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) = $true) | ~ ! [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) = $true) | (((X311 @ id @ X313 @ id)) != $true))) | ~ ! [X317 : term] : ((((X311 @ id @ X317 @ id)) != $true) | (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) = $true)))) & ((! [X91 : term] : (((sub @ X91 @ id)) = X91) => (! [X93 : term,X92 : (subst > term > subst > $o)] : (~ ! [X95 : (subst > term > term)] : (~ ! [X98 : subst,X96 : subst,X97 : term] : (((sub @ (X95 @ X96 @ X97) @ X98)) = ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true) | ~ ! [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) = $true) | (((X92 @ id @ X99 @ id)) != $true))) | ~ ! [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true)) | (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true)) => ! [X101 : term,X100 : (subst > term > subst > $o)] : ((((X100 @ id @ (lam @ X101) @ id)) = $true) | ~ ! [X102 : term] : ((((X100 @ id @ X102 @ id)) != $true) | (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) = $true)) | ~ ! [X103 : (subst > term > term)] : (~ ! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) | (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true) | ~ ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (ulamvarsh = $true) & (pushprop = $true) & (! [X464 : term,X465 : (subst > term > subst > $o)] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X467 : (subst > term > term),X466 : term] : ((((X465 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true) | ~ ! [X470 : subst,X468 : term,X469 : subst] : (((sub @ (sub @ X466 @ (push @ X468 @ X470)) @ X469)) = ((sub @ (X467 @ X470 @ X468) @ X469))) | ~ ! [X471 : term] : ((((X465 @ id @ (X467 @ id @ X471) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) | ~ ! [X473 : term,X472 : subst,X474 : subst] : (((sub @ X466 @ (push @ (sub @ X473 @ X472) @ (comp @ X474 @ X472)))) = ((X467 @ (comp @ X474 @ X472) @ (sub @ X473 @ X472))))) | ~ ! [X475 : term] : ((((X465 @ id @ X475 @ id)) != $true) | (((X465 @ id @ (sub @ X464 @ (push @ X475 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) <=> (axidl = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X516 : term,X519 : term,X518 : term,X517 : term] : ((X517 = X519) | (((ap @ X516 @ X517)) != ((ap @ X518 @ X519)))) => ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)))) & (pushprop_lem1_gthm = $true) & (pushprop_gthm = $true) & (axabs = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X83 : term,X82 : (subst > term > subst > $o)] : (~ ! [X85 : term,X84 : term] : ((((X82 @ id @ X85 @ id)) != $true) | (((X82 @ id @ X84 @ id)) != $true) | (((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) = $true)) | (((X82 @ id @ X83 @ id)) = $true) | ~ ! [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ~ ! [X87 : term] : ((((X82 @ id @ X87 @ id)) != $true) | (((X82 @ id @ (X86 @ id @ X87) @ id)) = $true)) | ~ ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90))))))) & (axapp = $true) & (hoaslamnotvar = $true) & ! [X116 : d_term] : (d_one = X116) & (! [X404 : (subst > term > subst > $o),X403 : term] : (~ ! [X416 : subst,X417 : subst,X414 : subst,X415 : term] : ((((X404 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414) @ X417)) = $true) | (((X404 @ X416 @ X415 @ (comp @ X414 @ X417))) != $true)) | (((X404 @ id @ (lam @ X403) @ id)) = $true) | ~ ! [X418 : term] : ((((X404 @ id @ (sub @ X403 @ (push @ X418 @ id)) @ id)) = $true) | (((X404 @ id @ X418 @ id)) != $true)) | ~ ! [X405 : (subst > term > term)] : (~ ! [X406 : term] : ((((X404 @ id @ (X405 @ id @ X406) @ id)) = $true) | ($true != ((X404 @ id @ X406 @ id)))) | (((X404 @ id @ (lam @ (X405 @ sh @ one)) @ id)) = $true) | ~ ! [X408 : term,X407 : subst,X409 : subst] : (((sub @ (X405 @ X409 @ X408) @ X407)) = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407))))) | ~ ! [X412 : subst,X410 : subst,X413 : subst,X411 : term] : ((((X404 @ (comp @ X410 @ X412) @ (sub @ X411 @ X412) @ X413)) != $true) | (((X404 @ X410 @ X411 @ (comp @ X412 @ X413))) = $true))) <=> (hoasinduction_lem3 = $true)) & ((laminj = $true) <=> ! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491))) & (hoasapinj2_gthm = $true) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & (ulamvarind = $true) & ((induction2 = $true) <=> ! [X484 : term,X483 : (term > $o)] : (~ ! [X487 : term,X488 : term] : ((((X483 @ X487)) != $true) | (((X483 @ (ap @ X487 @ X488))) = $true) | (((X483 @ X488)) != $true)) | ~ ! [X485 : term] : (~ ! [X486 : term] : ((((X483 @ X486)) != $true) | (((X483 @ (sub @ X485 @ (push @ X486 @ id)))) = $true)) | (((X483 @ (lam @ X485))) = $true)) | (((X483 @ X484)) = $true) | ~ ! [X489 : term] : ((((X483 @ X489)) = $true) | (((var @ X489)) != $true)))) & (pushprop_lem3v2_lthm = $true) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (! [X7 : term,X6 : term,X5 : (subst > term > term)] : ((((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))) | ~ ! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8)))) <=> (hoaslamnotap = $true)) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3_lthm = $true) <=> (! [X15 : term] : (((sub @ X15 @ id)) = X15) => (! [X17 : term,X16 : (subst > term > subst > $o)] : (~ ! [X23 : term] : ((((X16 @ id @ X23 @ id)) != $true) | (((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true)) | (((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X18 : (subst > term > term)] : (~ ! [X19 : term] : ((((X16 @ id @ X19 @ id)) != $true) | (((X16 @ id @ (X18 @ id @ X19) @ id)) = $true)) | (((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ~ ! [X21 : subst,X22 : term,X20 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) = ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21)))))) => ! [X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X35 : term] : ((((X24 @ id @ X35 @ id)) != $true) | (((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) = $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true) | ~ ! [X36 : subst,X37 : subst,X38 : subst,X39 : term] : ((((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) != $true) | (((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) = $true)) | ~ ! [X26 : (subst > term > term)] : (~ ! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) | (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) = $true) | ~ ! [X30 : term] : ((((X24 @ id @ X30 @ id)) != $true) | (((X24 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ~ ! [X33 : subst,X31 : subst,X32 : term,X34 : subst] : ((((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) = $true) | (((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) != $true)))))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) = X396) => ! [X400 : subst,X398 : (term > $o),X401 : (term > $o),X399 : term] : ((((X398 @ X399)) != $true) | (((X401 @ one)) = $true) | ~ ! [X402 : term] : (((X401 @ X402)) = ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & (axclos = $true) & (ulamvar1 != $true) & ((axvarid = $true) <=> ! [X327 : term] : (((sub @ X327 @ id)) = X327)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X216 : (subst > term > term)] : (~ ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) | (((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ~ ! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | (((X203 @ id @ X220 @ id)) != $true))) | ~ ! [X209 : subst,X208 : term,X207 : subst,X206 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) = $true) | (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) != $true)) | ~ ! [X211 : term] : ((((X205 @ (sub @ X204 @ (push @ X211 @ id)))) = $true) | (((X205 @ X211)) != $true)) | (((X205 @ (lam @ X204))) = $true) | ~ ! [X214 : subst,X215 : subst,X213 : term,X212 : subst] : ((((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) != $true) | (((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) = $true)) | ~ ! [X210 : term] : (((X205 @ X210)) = ((X203 @ id @ X210 @ id)))))) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & (! [X492 : (subst > term > subst > $o)] : ~ ! [X493 : (term > $o)] : ~ ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494))) <=> (hoasinduction_lem0_lthm = $true)) & ((! [X276 : term] : (((sub @ X276 @ id)) = X276) => (! [X279 : term,X278 : term,X277 : term,X280 : term] : ((((ap @ X279 @ X278)) != ((ap @ X280 @ X277))) | (X279 = X280)) => ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282)))))) <=> (hoasapinj1_lthm = $true)) & (! [X336 : term] : ~ ! [X337 : (subst > term > term)] : ~ ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339)))) <=> (hoasinduction_lem3v2_f = $true)) & (substmonoid_gthm = $true) & (! [X349 : (subst > term > subst > $o),X350 : (term > $o),X348 : term] : (~ ! [X351 : term] : (((X349 @ id @ X351 @ id)) = ((X350 @ X351))) | (((X350 @ (lam @ X348))) = $true) | ~ ! [X357 : term] : ((((X350 @ (sub @ X348 @ (push @ X357 @ id)))) = $true) | (((X350 @ X357)) != $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : term] : ((((X349 @ id @ X353 @ id)) != $true) | (((X349 @ id @ (X352 @ id @ X353) @ id)) = $true)) | ~ ! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X352 @ X355 @ X356) @ X354)) = ((X352 @ (comp @ X355 @ X354) @ (sub @ X356 @ X354)))) | (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem2_lthm = $true) & (lamnotvar = $true) & ((hoasinduction_lem2 = $true) <=> ! [X421 : (subst > term > subst > $o),X420 : term,X419 : term] : (~ ! [X431 : term,X430 : term] : ((((X421 @ id @ (ap @ (sub @ X430 @ id) @ X431) @ id)) = $true) | (((X421 @ id @ X430 @ id)) != $true) | (((X421 @ id @ X431 @ id)) != $true)) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | (((X421 @ id @ X420 @ id)) != $true) | ~ ! [X428 : subst,X429 : subst,X426 : subst,X427 : term] : ((((X421 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426) @ X429)) != $true) | (((X421 @ X428 @ X427 @ (comp @ X426 @ X429))) = $true)) | (((X421 @ id @ X419 @ id)) != $true) | ~ ! [X423 : subst,X422 : subst,X424 : subst,X425 : term] : ((((X421 @ (comp @ X423 @ X422) @ (sub @ X425 @ X422) @ X424)) = $true) | (((X421 @ X423 @ X425 @ (comp @ X422 @ X424))) != $true)))) & (hoasinduction_lem1 = $true) & (axassoc = $true) & ((induction2lem_lthm = $true) <=> (! [X438 : term,X437 : subst] : (((sub @ one @ (push @ X438 @ X437))) = X438) => (! [X439 : term,X440 : subst] : (((comp @ sh @ (push @ X439 @ X440))) = X440) => (! [X441 : subst] : (((comp @ X441 @ id)) = X441) => (! [X442 : term,X443 : (term > $o)] : (~ ! [X446 : term] : ((((X443 @ X446)) = $true) | (((var @ X446)) != $true)) | ~ ! [X444 : term,X445 : term] : ((((X443 @ X445)) != $true) | (((X443 @ X444)) != $true) | (((X443 @ (ap @ X445 @ X444))) = $true)) | (((X443 @ X442)) = $true) | ~ ! [X447 : term] : ((((X443 @ (lam @ X447))) = $true) | (((X443 @ X447)) != $true))) => ! [X449 : (term > $o),X448 : term,X450 : subst] : (~ ! [X451 : term] : ((((X449 @ (lam @ X451))) = $true) | ~ ! [X452 : term] : ((((X449 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X449 @ X452)) != $true))) | ~ ! [X453 : term] : ((((var @ X453)) != $true) | (((X449 @ (sub @ X453 @ X450))) = $true)) | ~ ! [X454 : term,X455 : term] : ((((X449 @ (ap @ X454 @ X455))) = $true) | (((X449 @ X455)) != $true) | (((X449 @ X454)) != $true)) | (((X449 @ (sub @ X448 @ X450))) = $true))))))) & (hoasinduction_lem1v2 = $true) & (! [X433 : (term > $o),X432 : term,X435 : subst,X434 : (term > $o)] : (~ ! [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) = ((X433 @ X436))) | (((X434 @ X432)) != $true) | (((X433 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & (one = ((d2term @ d_one))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axshiftcons = $true) <=> ! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem2v2 = $true) & (! [X362 : (subst > term > subst > $o),X363 : term] : (~ ! [X365 : subst,X368 : term,X367 : subst,X366 : subst] : ((((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) != $true) | (((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) = $true)) | ~ ! [X377 : term,X376 : subst,X378 : subst,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) != $true) | (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) = $true)) | (((X362 @ id @ X363 @ id)) = $true) | ~ ! [X370 : term,X369 : term] : ((((X362 @ id @ X370 @ id)) != $true) | (((X362 @ id @ (ap @ (sub @ X370 @ id) @ X369) @ id)) = $true) | ($true != ((X362 @ id @ X369 @ id)))) | ~ ! [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) = $true) | ~ ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373))) | ~ ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | (((X362 @ id @ X375 @ id)) != $true))) | ~ ! [X364 : term] : ((((X362 @ id @ X364 @ id)) = $true) | (((var @ (sub @ X364 @ id))) != $true))) <=> (hoasinduction = $true)) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X117 : term] : ~ ! [X118 : (subst > term > term)] : ~ ! [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) = ((X118 @ X120 @ X119))) => (! [X121 : term] : (((sub @ X121 @ id)) = X121) => ! [X122 : term,X124 : (subst > term > subst > $o),X123 : (term > $o)] : (~ ! [X126 : term] : ((((X123 @ (sub @ X122 @ (push @ X126 @ id)))) = $true) | (((X123 @ X126)) != $true)) | ~ ! [X127 : (subst > term > term)] : (~ ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))) | ~ ! [X131 : term] : (($true != ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))) | (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true)) | ~ ! [X125 : term] : (((X124 @ id @ X125 @ id)) = ((X123 @ X125))) | (((X123 @ (lam @ X122))) = $true)))))),
% 47.53/7.12 inference(flattening,[],[f9])).
% 47.53/7.12 thf(f11,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ? [X12 : (subst > term > term)] : (((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true) & ! [X16 : term] : ((((X0 @ id @ X16 @ id)) != $true) | (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true))) & ! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))))) | ? [X11 : term,X10 : term] : (((((X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id)) != $true) & ($true = ((X0 @ id @ X11 @ id)))) & (((X0 @ id @ X10 @ id)) = $true))) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true))) | ? [X7 : subst,X6 : term,X8 : subst,X5 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) & (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) != $true))) | ? [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) & (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) != $true))) <~> (hoasinduction = $true)),
% 47.53/7.12 inference(ennf_transformation,[],[f8])).
% 47.53/7.12 thf(f12,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (? [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) & (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) != $true)) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | ? [X10 : term,X11 : term] : ((((X0 @ id @ X10 @ id)) = $true) & (((X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id)) != $true) & ($true = ((X0 @ id @ X11 @ id)))) | ? [X7 : subst,X6 : term,X8 : subst,X5 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) & (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) != $true)) | ? [X12 : (subst > term > term)] : (! [X16 : term] : ((((X0 @ id @ X16 @ id)) != $true) | (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) & ! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true))) <~> (hoasinduction = $true)),
% 47.53/7.12 inference(flattening,[],[f11])).
% 47.53/7.12 thf(f13,plain,(
% 47.53/7.12 (pushprop_lem2v2_gthm = $true) & (! [X480 : (subst > term > subst > $o)] : ? [X481 : (term > $o)] : ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X290 : term] : ? [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) = ((X291 @ sh @ one)))) & ((((! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)) | ? [X477 : subst] : (((comp @ X477 @ id)) != X477)) | ? [X476 : subst] : (((comp @ id @ X476)) != X476)) <=> (substmonoid_lthm = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & ((substmonoid = $true) <=> (! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true)) | ? [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) != X253)) | ? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251))) & (lamnotap != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X242 : term,X243 : (subst > term > subst > $o)] : ((((X243 @ id @ X242 @ id)) = $true) | ? [X245 : term,X244 : term] : ((((X243 @ id @ X245 @ id)) = $true) & ($true != ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id))) & (((X243 @ id @ X244 @ id)) = $true)) | ? [X246 : (subst > term > term)] : (! [X247 : term] : ((((X243 @ id @ (X246 @ id @ X247) @ id)) = $true) | (((X243 @ id @ X247 @ id)) != $true)) & ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) & (((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) != $true))) | ? [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (! [X235 : (subst > term > term)] : (? [X237 : subst,X238 : subst,X236 : term] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) != ((sub @ (X235 @ X238 @ X236) @ X237))) | ? [X239 : term] : ((((X232 @ id @ (X235 @ id @ X239) @ id)) != $true) & (((X232 @ id @ X239 @ id)) = $true)) | (((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true)) & ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) & (((X234 @ (lam @ X233))) != $true) & ! [X241 : term] : ((((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true) | (((X234 @ X241)) != $true)))) | ? [X231 : term] : (((sub @ X231 @ id)) != X231)) | ? [X224 : term,X225 : (term > $o)] : (! [X230 : term] : ((((var @ X230)) != $true) | (((X225 @ X230)) = $true)) & ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | (((X225 @ X226)) != $true) | ($true != ((X225 @ X227)))) & ! [X228 : term] : (? [X229 : term] : ((((X225 @ X229)) = $true) & (((X225 @ (sub @ X228 @ (push @ X229 @ id)))) != $true)) | (((X225 @ (lam @ X228))) = $true)) & (((X225 @ X224)) != $true))) | ? [X221 : (subst > term > subst > $o)] : ! [X222 : (term > $o)] : ? [X223 : term] : (((X221 @ id @ X223 @ id)) != ((X222 @ X223))))) & (termmset_gthm = $true) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) <=> (shinj = $true)) & ((induction2lem = $true) <=> ! [X268 : subst,X270 : (term > $o),X269 : term] : (? [X273 : term] : ((((var @ X273)) = $true) & (((X270 @ (sub @ X273 @ X268))) != $true)) | ? [X271 : term] : (($true != ((X270 @ (lam @ X271)))) & ! [X272 : term] : ((((X270 @ X272)) != $true) | (((X270 @ (sub @ X271 @ (push @ X272 @ id)))) = $true))) | ? [X275 : term,X274 : term] : ((((X270 @ X275)) = $true) & (((X270 @ (ap @ X274 @ X275))) != $true) & (((X270 @ X274)) = $true)) | (((X270 @ (sub @ X269 @ X268))) = $true))) & ! [X80 : d_subst,X79 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (hoasapnotvar = $true) & (hoasapnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lthm = $true) <=> (((! [X185 : (subst > term > subst > $o),X184 : term] : (? [X196 : term] : (($true = ((var @ (sub @ X196 @ id)))) & (((X185 @ id @ X196 @ id)) != $true)) | ? [X190 : term,X191 : term] : ((((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true) & ($true = ((X185 @ id @ X191 @ id))) & (((X185 @ id @ X190 @ id)) = $true)) | ? [X188 : term,X186 : subst,X187 : subst,X189 : subst] : ((((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) = $true) & (((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) != $true)) | ? [X197 : (subst > term > term)] : (! [X198 : term] : ((((X185 @ id @ (X197 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199)))) & (((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true)) | (((X185 @ id @ X184 @ id)) = $true) | ? [X193 : term,X192 : subst,X194 : subst,X195 : subst] : ((((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) != $true) & (((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) = $true))) | ? [X169 : (subst > term > subst > $o),X168 : term] : (! [X177 : subst,X175 : subst,X176 : term,X174 : subst] : ((((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) != $true) | (((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true)) & (((X169 @ id @ (lam @ X168) @ id)) != $true) & ! [X173 : subst,X172 : subst,X170 : subst,X171 : term] : ((((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true) | (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) != $true)) & ! [X178 : term] : ((((X169 @ id @ X178 @ id)) != $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) & ! [X179 : (subst > term > term)] : ((((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X181 : subst,X182 : subst,X183 : term] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) != ((sub @ (X179 @ X182 @ X183) @ X181))) | ? [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) != $true) & (((X169 @ id @ X180 @ id)) = $true))))) | ? [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : ((((X156 @ id @ X157 @ id)) = $true) & ! [X160 : term,X161 : subst,X159 : subst,X158 : subst] : ((((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) != $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true)) & (((X156 @ id @ X155 @ id)) = $true) & (((X156 @ id @ (ap @ X157 @ X155) @ id)) != $true) & ! [X167 : subst,X166 : term,X165 : subst,X164 : subst] : ((((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) != $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) & ! [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) != $true) | (((X156 @ id @ X163 @ id)) != $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)))) | ? [X149 : (term > $o),X148 : term] : ((((X149 @ X148)) != $true) & ! [X150 : term,X151 : term] : ((((X149 @ X151)) != $true) | (((X149 @ X150)) != $true) | (((X149 @ (ap @ X151 @ X150))) = $true)) & ! [X154 : term] : ((((X149 @ X154)) = $true) | (((var @ X154)) != $true)) & ! [X152 : term] : ((((X149 @ (lam @ X152))) = $true) | ? [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) != $true) & (((X149 @ X153)) = $true)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3a = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (($true = ((X108 @ id @ (lam @ X109) @ id))) | ? [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) != $true) & ! [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) = $true) | (((X108 @ id @ X115 @ id)) != $true)) & ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113)))) | ? [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) != $true) & (((X108 @ id @ X110 @ id)) = $true)))) & ((hoaslaminj_lthm = $true) <=> (((! [X387 : subst,X388 : term,X389 : (subst > term > term),X386 : (subst > term > term)] : ((((lam @ (X386 @ sh @ one))) != ((lam @ (X389 @ sh @ one)))) | (((X389 @ X387 @ X388)) = ((X386 @ X387 @ X388))) | ? [X392 : subst,X391 : term,X390 : subst] : (((X389 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392))) != ((sub @ (X389 @ X390 @ X391) @ X392))) | ? [X393 : term,X395 : subst,X394 : subst] : (((sub @ (X386 @ X395 @ X393) @ X394)) != ((X386 @ (comp @ X395 @ X394) @ (sub @ X393 @ X394))))) | ? [X385 : term,X384 : term] : ((((lam @ X385)) = ((lam @ X384))) & (X384 != X385))) | ? [X383 : term,X382 : subst] : (((comp @ sh @ (push @ X383 @ X382))) != X382)) | ? [X380 : term,X381 : subst] : (((sub @ one @ (push @ X380 @ X381))) != X380))) & ! [X4 : d_subst] : (d_id = X4) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (pushprop_lem3v2 = $true) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) <=> (axidr = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X512 : term] : ? [X513 : (subst > term > term)] : ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514))))) & ((induction = $true) <=> ! [X263 : term,X262 : (term > $o)] : (? [X265 : term,X264 : term] : ((((X262 @ (ap @ X265 @ X264))) != $true) & (((X262 @ X265)) = $true) & (((X262 @ X264)) = $true)) | (((X262 @ X263)) = $true) | ? [X267 : term] : ((((X262 @ X267)) != $true) & (((var @ X267)) = $true)) | ? [X266 : term] : ((((X262 @ X266)) = $true) & (((X262 @ (lam @ X266))) != $true)))) & (((! [X534 : (term > $o),X533 : term] : ((((X534 @ X533)) = $true) | ? [X535 : term] : ((((var @ X535)) = $true) & (((X534 @ X535)) != $true)) | ? [X538 : term] : (! [X539 : term] : ((((X534 @ X539)) != $true) | (((X534 @ (sub @ X538 @ (push @ X539 @ id)))) = $true)) & (((X534 @ (lam @ X538))) != $true)) | ? [X537 : term,X536 : term] : ((((X534 @ X536)) = $true) & (((X534 @ (ap @ X536 @ X537))) != $true) & (((X534 @ X537)) = $true))) | ? [X525 : subst,X527 : term,X526 : (term > $o)] : (! [X528 : term] : ((((X526 @ (sub @ X528 @ X525))) = $true) | (((var @ X528)) != $true)) & ! [X529 : term,X530 : term] : ((((X526 @ X530)) != $true) | (((X526 @ X529)) != $true) | (((X526 @ (ap @ X529 @ X530))) = $true)) & (((X526 @ (sub @ X527 @ X525))) != $true) & ! [X531 : term] : (? [X532 : term] : ((((X526 @ (sub @ X531 @ (push @ X532 @ id)))) != $true) & (((X526 @ X532)) = $true)) | (((X526 @ (lam @ X531))) = $true)))) | ? [X524 : term] : (((sub @ X524 @ id)) != X524)) <=> (induction2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((axvarcons = $true) <=> ! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510)) & (hoasapinj1_gthm = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X457 : term,X456 : (subst > term > subst > $o)] : (? [X459 : (subst > term > term)] : (! [X463 : subst,X462 : subst,X461 : term] : (((sub @ (X459 @ X462 @ X461) @ X463)) = ((X459 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463)))) & (((X456 @ id @ (lam @ (X459 @ sh @ one)) @ id)) != $true) & ! [X460 : term] : ((((X456 @ id @ (X459 @ id @ X460) @ id)) = $true) | ($true != ((X456 @ id @ X460 @ id))))) | ? [X458 : term] : ((((X456 @ id @ X458 @ id)) = $true) & (((X456 @ id @ (sub @ X457 @ (push @ X458 @ id)) @ id)) != $true)) | (((X456 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id)) = $true))) & ((hoaslaminj = $true) <=> ! [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ? [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) != ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | ? [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) != ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & (! [X292 : term,X294 : (term > $o),X293 : (subst > term > subst > $o)] : (? [X304 : (subst > term > term)] : (! [X307 : term,X308 : subst,X306 : subst] : (((sub @ (X304 @ X306 @ X307) @ X308)) = ((X304 @ (comp @ X306 @ X308) @ (sub @ X307 @ X308)))) & ! [X305 : term] : ((((X293 @ id @ (X304 @ id @ X305) @ id)) = $true) | (((X293 @ id @ X305 @ id)) != $true)) & (((X293 @ id @ (lam @ (X304 @ sh @ one)) @ id)) != $true)) | ? [X309 : term] : (((X294 @ X309)) != ((X293 @ id @ X309 @ id))) | ? [X303 : term] : ((((X294 @ (sub @ X292 @ (push @ X303 @ id)))) != $true) & (((X294 @ X303)) = $true)) | ? [X302 : subst,X300 : subst,X299 : subst,X301 : term] : ((((X293 @ X300 @ X301 @ (comp @ X302 @ X299))) = $true) & (((X293 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302) @ X299)) != $true)) | ? [X298 : subst,X296 : subst,X295 : subst,X297 : term] : ((((X293 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298) @ X295)) = $true) & (((X293 @ X296 @ X297 @ (comp @ X298 @ X295))) != $true)) | (((X294 @ (lam @ X292))) = $true)) <=> (hoasinduction_lem3v2 = $true)) & ! [X358 : d_term,X359 : d_term] : ((X358 = X359) | (((d2term @ X358)) != ((d2term @ X359)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((termmset_lthm = $true) <=> (? [X260 : term] : (((sub @ X260 @ id)) != X260) | ! [X261 : term] : (((sub @ X261 @ id)) = X261))) & ((hoasapinj2 = $true) <=> ! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331))))) & (induction2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X334 : term] : ? [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) = ((X335 @ sh @ one)))) & (pushprop_lem0_gthm = $true) & (! [X318 : subst,X320 : term,X319 : (term > $o)] : ? [X321 : (term > $o)] : ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X61 : (subst > term > subst > $o),X62 : term] : (? [X72 : term] : ((((X61 @ id @ X72 @ id)) != $true) & (((var @ (sub @ X72 @ id))) = $true)) | ? [X69 : subst,X71 : term,X68 : subst,X70 : subst] : ((((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) != $true) & (((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) = $true)) | ? [X74 : term,X73 : term] : ((((X61 @ id @ X73 @ id)) = $true) & (((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) != $true) & (((X61 @ id @ X74 @ id)) = $true)) | ? [X78 : term,X76 : subst,X75 : subst,X77 : subst] : ((((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) != $true) & (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) = $true)) | (((X61 @ id @ X62 @ id)) = $true) | ? [X63 : (subst > term > term)] : (! [X64 : term] : ((((X61 @ id @ X64 @ id)) != $true) | (((X61 @ id @ (X63 @ id @ X64) @ id)) = $true)) & (((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) != $true) & ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66)))))) | ? [X52 : (term > $o),X51 : (subst > term > subst > $o),X53 : term] : (! [X56 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ? [X59 : subst,X57 : term,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) != ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ? [X60 : term] : ((((X51 @ id @ (X56 @ id @ X60) @ id)) != $true) & (((X51 @ id @ X60 @ id)) = $true))) & ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) & ! [X54 : term] : ((((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true) | (((X52 @ X54)) != $true)) & ($true != ((X52 @ (lam @ X53)))))) | ? [X50 : term] : (((sub @ X50 @ id)) != X50)) | ? [X44 : (term > $o),X43 : term] : (! [X49 : term,X48 : term] : ((((X44 @ X49)) != $true) | (((X44 @ (ap @ X48 @ X49))) = $true) | (((X44 @ X48)) != $true)) & (((X44 @ X43)) != $true) & ! [X45 : term] : (($true = ((X44 @ X45))) | (((var @ X45)) != $true)) & ! [X46 : term] : (? [X47 : term] : ((((X44 @ X47)) = $true) & (((X44 @ (sub @ X46 @ (push @ X47 @ id)))) != $true)) | (((X44 @ (lam @ X46))) = $true)))) | ? [X40 : (subst > term > subst > $o)] : ! [X41 : (term > $o)] : ? [X42 : term] : (((X40 @ id @ X42 @ id)) != ((X41 @ X42))))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1 = $true) <=> ! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true))) & (hoasinduction_lem3v2_gthm = $true) & (apnotvar = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X344 : (term > $o),X343 : term,X345 : subst] : ? [X346 : (term > $o)] : ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & (hoasinduction_lem1_gthm = $true) & (! [X496 : (term > $o),X495 : (subst > term > subst > $o),X498 : term,X497 : term] : (? [X499 : term] : (((X495 @ id @ X499 @ id)) != ((X496 @ X499))) | ? [X501 : term,X500 : term] : ((((X495 @ id @ X500 @ id)) = $true) & (((X495 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) != $true) & (((X495 @ id @ X501 @ id)) = $true)) | ? [X509 : term,X506 : subst,X507 : subst,X508 : subst] : ((((X495 @ X508 @ X509 @ (comp @ X507 @ X506))) != $true) & (((X495 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507) @ X506)) = $true)) | (((X496 @ (ap @ X497 @ X498))) = $true) | (((X496 @ X498)) != $true) | ? [X502 : subst,X503 : term,X505 : subst,X504 : subst] : ((((X495 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504) @ X502)) != $true) & (((X495 @ X505 @ X503 @ (comp @ X504 @ X502))) = $true)) | (((X496 @ X497)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X310 : term,X311 : (subst > term > subst > $o)] : (? [X317 : term] : ((((X311 @ id @ X317 @ id)) = $true) & (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) != $true)) | (((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ? [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) != $true) & ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) = $true) | (((X311 @ id @ X313 @ id)) != $true)))) <=> (hoasinduction_lem3aa = $true)) & (((! [X101 : term,X100 : (subst > term > subst > $o)] : (? [X103 : (subst > term > term)] : (! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) & (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) != $true) & ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106)))) | ? [X102 : term] : ((((X100 @ id @ X102 @ id)) = $true) & (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) != $true)) | (((X100 @ id @ (lam @ X101) @ id)) = $true)) | ? [X92 : (subst > term > subst > $o),X93 : term] : (! [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true)) & ! [X95 : (subst > term > term)] : (? [X98 : subst,X97 : term,X96 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) != ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ? [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) != $true) & (((X92 @ id @ X99 @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true)) & (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true))) | ? [X91 : term] : (((sub @ X91 @ id)) != X91)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (ulamvarsh = $true) & (pushprop = $true) & (! [X465 : (subst > term > subst > $o),X464 : term] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ? [X475 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X475 @ id)) @ id)) != $true) & (((X465 @ id @ X475 @ id)) = $true)) | ? [X467 : (subst > term > term),X466 : term] : (! [X471 : term] : ((((X465 @ id @ (X467 @ id @ X471) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X473 : term,X472 : subst,X474 : subst] : (((sub @ X466 @ (push @ (sub @ X473 @ X472) @ (comp @ X474 @ X472)))) = ((X467 @ (comp @ X474 @ X472) @ (sub @ X473 @ X472)))) & ! [X470 : subst,X468 : term,X469 : subst] : (((sub @ (sub @ X466 @ (push @ X468 @ X470)) @ X469)) = ((sub @ (X467 @ X470 @ X468) @ X469))) & (((X465 @ id @ (lam @ (X467 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) <=> (axidl = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 != X519) & (((ap @ X516 @ X517)) = ((ap @ X518 @ X519)))) | ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)))) & (pushprop_lem1_gthm = $true) & (pushprop_gthm = $true) & (axabs = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) | ? [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true) & (((X82 @ id @ X85 @ id)) = $true)) | ? [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : term] : ((((X82 @ id @ X87 @ id)) != $true) | (((X82 @ id @ (X86 @ id @ X87) @ id)) = $true)) & ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90))))))) & (axapp = $true) & (hoaslamnotvar = $true) & ! [X116 : d_term] : (d_one = X116) & (! [X403 : term,X404 : (subst > term > subst > $o)] : (? [X418 : term] : ((((X404 @ id @ X418 @ id)) = $true) & (((X404 @ id @ (sub @ X403 @ (push @ X418 @ id)) @ id)) != $true)) | ? [X405 : (subst > term > term)] : (! [X406 : term] : ((((X404 @ id @ (X405 @ id @ X406) @ id)) = $true) | ($true != ((X404 @ id @ X406 @ id)))) & ! [X408 : term,X407 : subst,X409 : subst] : (((sub @ (X405 @ X409 @ X408) @ X407)) = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407)))) & (((X404 @ id @ (lam @ (X405 @ sh @ one)) @ id)) != $true)) | ? [X414 : subst,X417 : subst,X415 : term,X416 : subst] : ((((X404 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414) @ X417)) != $true) & (((X404 @ X416 @ X415 @ (comp @ X414 @ X417))) = $true)) | (((X404 @ id @ (lam @ X403) @ id)) = $true) | ? [X411 : term,X410 : subst,X412 : subst,X413 : subst] : ((((X404 @ (comp @ X410 @ X412) @ (sub @ X411 @ X412) @ X413)) = $true) & (((X404 @ X410 @ X411 @ (comp @ X412 @ X413))) != $true))) <=> (hoasinduction_lem3 = $true)) & ((laminj = $true) <=> ! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491))) & (hoasapinj2_gthm = $true) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & (ulamvarind = $true) & (! [X484 : term,X483 : (term > $o)] : (? [X485 : term] : ((((X483 @ (lam @ X485))) != $true) & ! [X486 : term] : ((((X483 @ X486)) != $true) | (((X483 @ (sub @ X485 @ (push @ X486 @ id)))) = $true))) | ? [X487 : term,X488 : term] : ((((X483 @ X488)) = $true) & (((X483 @ (ap @ X487 @ X488))) != $true) & (((X483 @ X487)) = $true)) | ? [X489 : term] : ((((X483 @ X489)) != $true) & (((var @ X489)) = $true)) | (((X483 @ X484)) = $true)) <=> (induction2 = $true)) & (pushprop_lem3v2_lthm = $true) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & ((hoaslamnotap = $true) <=> ! [X5 : (subst > term > term),X6 : term,X7 : term] : (? [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))))) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X24 : (subst > term > subst > $o),X25 : term] : (? [X38 : subst,X39 : term,X37 : subst,X36 : subst] : ((((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) = $true) & (((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) != $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true) | ? [X26 : (subst > term > term)] : (! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) & (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) != $true) & ! [X30 : term] : ((((X24 @ id @ X30 @ id)) != $true) | (((X24 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X31 : subst,X34 : subst,X33 : subst,X32 : term] : ((((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) = $true) & (((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) != $true)) | ? [X35 : term] : ((((X24 @ id @ X35 @ id)) = $true) & (((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) != $true))) | ? [X16 : (subst > term > subst > $o),X17 : term] : (! [X23 : term] : ((((X16 @ id @ X23 @ id)) != $true) | (((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true)) & ! [X18 : (subst > term > term)] : ((((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : ((((X16 @ id @ X19 @ id)) = $true) & (((X16 @ id @ (X18 @ id @ X19) @ id)) != $true)) | ? [X20 : subst,X22 : term,X21 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) != ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) & (((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) != $true))) | ? [X15 : term] : (((sub @ X15 @ id)) != X15))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) != X396) | ! [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) = $true) | (((X398 @ X399)) != $true) | ? [X402 : term] : (((X401 @ X402)) != ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & (axclos = $true) & (ulamvar1 != $true) & ((axvarid = $true) <=> ! [X327 : term] : (((sub @ X327 @ id)) = X327)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X202 : term] : (((sub @ X202 @ id)) != X202) | ! [X204 : term,X205 : (term > $o),X203 : (subst > term > subst > $o)] : (? [X208 : term,X206 : subst,X207 : subst,X209 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) != $true) & (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) = $true)) | ? [X212 : subst,X215 : subst,X213 : term,X214 : subst] : ((((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) != $true) & (((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) = $true)) | ? [X210 : term] : (((X205 @ X210)) != ((X203 @ id @ X210 @ id))) | ? [X216 : (subst > term > term)] : (! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | (((X203 @ id @ X220 @ id)) != $true)) & ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) & (((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true)) | ? [X211 : term] : ((((X205 @ X211)) = $true) & (((X205 @ (sub @ X204 @ (push @ X211 @ id)))) != $true)) | (((X205 @ (lam @ X204))) = $true)))) & (hoaslamnotvar_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X492 : (subst > term > subst > $o)] : ? [X493 : (term > $o)] : ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494)))) & (((! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282)))) | ? [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) = ((ap @ X280 @ X277))) & (X279 != X280))) | ? [X276 : term] : (((sub @ X276 @ id)) != X276)) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X336 : term] : ? [X337 : (subst > term > term)] : ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339))))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X349 : (subst > term > subst > $o),X350 : (term > $o),X348 : term] : (? [X351 : term] : (((X349 @ id @ X351 @ id)) != ((X350 @ X351))) | ? [X352 : (subst > term > term)] : (! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X352 @ X355 @ X356) @ X354)) = ((X352 @ (comp @ X355 @ X354) @ (sub @ X356 @ X354)))) & ! [X353 : term] : ((((X349 @ id @ X353 @ id)) != $true) | (((X349 @ id @ (X352 @ id @ X353) @ id)) = $true)) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true)) | (((X350 @ (lam @ X348))) = $true) | ? [X357 : term] : ((((X350 @ (sub @ X348 @ (push @ X357 @ id)))) != $true) & (((X350 @ X357)) = $true)))) & (hoasinduction_lem2_lthm = $true) & (lamnotvar = $true) & (! [X421 : (subst > term > subst > $o),X420 : term,X419 : term] : (? [X429 : subst,X427 : term,X426 : subst,X428 : subst] : ((((X421 @ X428 @ X427 @ (comp @ X426 @ X429))) != $true) & (((X421 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426) @ X429)) = $true)) | (((X421 @ id @ X420 @ id)) != $true) | ? [X431 : term,X430 : term] : ((((X421 @ id @ X431 @ id)) = $true) & (((X421 @ id @ (ap @ (sub @ X430 @ id) @ X431) @ id)) != $true) & (((X421 @ id @ X430 @ id)) = $true)) | (((X421 @ id @ X419 @ id)) != $true) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | ? [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((((X421 @ X423 @ X425 @ (comp @ X422 @ X424))) = $true) & (((X421 @ (comp @ X423 @ X422) @ (sub @ X425 @ X422) @ X424)) != $true))) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem1 = $true) & (axassoc = $true) & ((induction2lem_lthm = $true) <=> ((((! [X450 : subst,X449 : (term > $o),X448 : term] : (? [X451 : term] : (! [X452 : term] : ((((X449 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X449 @ X452)) != $true)) & (((X449 @ (lam @ X451))) != $true)) | ? [X453 : term] : ((((X449 @ (sub @ X453 @ X450))) != $true) & (((var @ X453)) = $true)) | (((X449 @ (sub @ X448 @ X450))) = $true) | ? [X454 : term,X455 : term] : ((((X449 @ (ap @ X454 @ X455))) != $true) & (((X449 @ X455)) = $true) & (((X449 @ X454)) = $true))) | ? [X442 : term,X443 : (term > $o)] : ((((X443 @ X442)) != $true) & ! [X446 : term] : ((((X443 @ X446)) = $true) | (((var @ X446)) != $true)) & ! [X444 : term,X445 : term] : ((((X443 @ X445)) != $true) | (((X443 @ X444)) != $true) | (((X443 @ (ap @ X445 @ X444))) = $true)) & ! [X447 : term] : ((((X443 @ (lam @ X447))) = $true) | (((X443 @ X447)) != $true)))) | ? [X441 : subst] : (((comp @ X441 @ id)) != X441)) | ? [X440 : subst,X439 : term] : (((comp @ sh @ (push @ X439 @ X440))) != X440)) | ? [X438 : term,X437 : subst] : (((sub @ one @ (push @ X438 @ X437))) != X438))) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) = $true) | (((X434 @ X432)) != $true) | ? [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) != ((X433 @ X436))))) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & (one = ((d2term @ d_one))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axshiftcons = $true) <=> ! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem2v2 = $true) & ((hoasinduction = $true) <=> ! [X363 : term,X362 : (subst > term > subst > $o)] : (? [X364 : term] : ((((var @ (sub @ X364 @ id))) = $true) & (((X362 @ id @ X364 @ id)) != $true)) | ? [X365 : subst,X367 : subst,X366 : subst,X368 : term] : ((((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) != $true) & (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) = $true)) | ? [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) != $true) & ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | (((X362 @ id @ X375 @ id)) != $true)) & ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373)))) | ? [X369 : term,X370 : term] : ((((X362 @ id @ (ap @ (sub @ X370 @ id) @ X369) @ id)) != $true) & ($true = ((X362 @ id @ X369 @ id))) & (((X362 @ id @ X370 @ id)) = $true)) | ? [X376 : subst,X378 : subst,X377 : term,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) = $true) & (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) != $true)) | (((X362 @ id @ X363 @ id)) = $true))) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X124 : (subst > term > subst > $o),X123 : (term > $o),X122 : term] : (? [X126 : term] : ((((X123 @ (sub @ X122 @ (push @ X126 @ id)))) != $true) & (((X123 @ X126)) = $true)) | (((X123 @ (lam @ X122))) = $true) | ? [X125 : term] : (((X124 @ id @ X125 @ id)) != ((X123 @ X125))) | ? [X127 : (subst > term > term)] : (! [X131 : term] : (($true != ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))) & (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) != $true) & ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))))) | ? [X121 : term] : (((sub @ X121 @ id)) != X121)) | ? [X117 : term] : ! [X118 : (subst > term > term)] : ? [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) != ((X118 @ X120 @ X119)))))),
% 47.53/7.12 inference(ennf_transformation,[],[f10])).
% 47.53/7.12 thf(f14,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & ((? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ? [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) != X253) | ! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) <=> ! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((laminj = $true) <=> ! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491))) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & ((axshiftcons = $true) <=> ! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360)) & ((! [X124 : (subst > term > subst > $o),X123 : (term > $o),X122 : term] : (? [X126 : term] : ((((X123 @ (sub @ X122 @ (push @ X126 @ id)))) != $true) & (((X123 @ X126)) = $true)) | (((X123 @ (lam @ X122))) = $true) | ? [X125 : term] : (((X124 @ id @ X125 @ id)) != ((X123 @ X125))) | ? [X127 : (subst > term > term)] : (! [X131 : term] : (($true != ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))) & (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) != $true) & ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))))) | ? [X121 : term] : (((sub @ X121 @ id)) != X121) | ? [X117 : term] : ! [X118 : (subst > term > term)] : ? [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) != ((X118 @ X120 @ X119)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((? [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (! [X235 : (subst > term > term)] : (? [X237 : subst,X238 : subst,X236 : term] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) != ((sub @ (X235 @ X238 @ X236) @ X237))) | ? [X239 : term] : ((((X232 @ id @ (X235 @ id @ X239) @ id)) != $true) & (((X232 @ id @ X239 @ id)) = $true)) | (((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true)) & ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) & (((X234 @ (lam @ X233))) != $true) & ! [X241 : term] : ((((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true) | (((X234 @ X241)) != $true))) | ? [X224 : term,X225 : (term > $o)] : (! [X230 : term] : ((((var @ X230)) != $true) | (((X225 @ X230)) = $true)) & ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | (((X225 @ X226)) != $true) | ($true != ((X225 @ X227)))) & ! [X228 : term] : (? [X229 : term] : ((((X225 @ X229)) = $true) & (((X225 @ (sub @ X228 @ (push @ X229 @ id)))) != $true)) | (((X225 @ (lam @ X228))) = $true)) & (((X225 @ X224)) != $true)) | ! [X242 : term,X243 : (subst > term > subst > $o)] : ((((X243 @ id @ X242 @ id)) = $true) | ? [X245 : term,X244 : term] : ((((X243 @ id @ X245 @ id)) = $true) & ($true != ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id))) & (((X243 @ id @ X244 @ id)) = $true)) | ? [X246 : (subst > term > term)] : (! [X247 : term] : ((((X243 @ id @ (X246 @ id @ X247) @ id)) = $true) | (((X243 @ id @ X247 @ id)) != $true)) & ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) & (((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) != $true))) | ? [X231 : term] : (((sub @ X231 @ id)) != X231) | ? [X221 : (subst > term > subst > $o)] : ! [X222 : (term > $o)] : ? [X223 : term] : (((X221 @ id @ X223 @ id)) != ((X222 @ X223)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((? [X442 : term,X443 : (term > $o)] : ((((X443 @ X442)) != $true) & ! [X446 : term] : ((((X443 @ X446)) = $true) | (((var @ X446)) != $true)) & ! [X444 : term,X445 : term] : ((((X443 @ X445)) != $true) | (((X443 @ X444)) != $true) | (((X443 @ (ap @ X445 @ X444))) = $true)) & ! [X447 : term] : ((((X443 @ (lam @ X447))) = $true) | (((X443 @ X447)) != $true))) | ! [X450 : subst,X449 : (term > $o),X448 : term] : (? [X451 : term] : (! [X452 : term] : ((((X449 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X449 @ X452)) != $true)) & (((X449 @ (lam @ X451))) != $true)) | ? [X453 : term] : ((((X449 @ (sub @ X453 @ X450))) != $true) & (((var @ X453)) = $true)) | (((X449 @ (sub @ X448 @ X450))) = $true) | ? [X454 : term,X455 : term] : ((((X449 @ (ap @ X454 @ X455))) != $true) & (((X449 @ X455)) = $true) & (((X449 @ X454)) = $true))) | ? [X438 : term,X437 : subst] : (((sub @ one @ (push @ X438 @ X437))) != X438) | ? [X441 : subst] : (((comp @ X441 @ id)) != X441) | ? [X440 : subst,X439 : term] : (((comp @ sh @ (push @ X439 @ X440))) != X440)) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) | ? [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true) & (((X82 @ id @ X85 @ id)) = $true)) | ? [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : term] : ((((X82 @ id @ X87 @ id)) != $true) | (((X82 @ id @ (X86 @ id @ X87) @ id)) = $true)) & ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90))))))) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) <=> (shinj = $true)) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) <=> (axidr = $true)) & (axabs = $true) & ((hoasinduction_lthm = $true) <=> (? [X169 : (subst > term > subst > $o),X168 : term] : (! [X177 : subst,X175 : subst,X176 : term,X174 : subst] : ((((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) != $true) | (((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true)) & (((X169 @ id @ (lam @ X168) @ id)) != $true) & ! [X173 : subst,X172 : subst,X170 : subst,X171 : term] : ((((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true) | (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) != $true)) & ! [X178 : term] : ((((X169 @ id @ X178 @ id)) != $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) & ! [X179 : (subst > term > term)] : ((((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X181 : subst,X182 : subst,X183 : term] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) != ((sub @ (X179 @ X182 @ X183) @ X181))) | ? [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) != $true) & (((X169 @ id @ X180 @ id)) = $true)))) | ? [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : ((((X156 @ id @ X157 @ id)) = $true) & ! [X160 : term,X161 : subst,X159 : subst,X158 : subst] : ((((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) != $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true)) & (((X156 @ id @ X155 @ id)) = $true) & (((X156 @ id @ (ap @ X157 @ X155) @ id)) != $true) & ! [X167 : subst,X166 : term,X165 : subst,X164 : subst] : ((((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) != $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) & ! [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) != $true) | (((X156 @ id @ X163 @ id)) != $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true))) | ! [X185 : (subst > term > subst > $o),X184 : term] : (? [X196 : term] : (($true = ((var @ (sub @ X196 @ id)))) & (((X185 @ id @ X196 @ id)) != $true)) | ? [X190 : term,X191 : term] : ((((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true) & ($true = ((X185 @ id @ X191 @ id))) & (((X185 @ id @ X190 @ id)) = $true)) | ? [X188 : term,X186 : subst,X187 : subst,X189 : subst] : ((((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) = $true) & (((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) != $true)) | ? [X197 : (subst > term > term)] : (! [X198 : term] : ((((X185 @ id @ (X197 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199)))) & (((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true)) | (((X185 @ id @ X184 @ id)) = $true) | ? [X193 : term,X192 : subst,X194 : subst,X195 : subst] : ((((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) != $true) & (((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) = $true))) | ? [X149 : (term > $o),X148 : term] : ((((X149 @ X148)) != $true) & ! [X150 : term,X151 : term] : ((((X149 @ X151)) != $true) | (((X149 @ X150)) != $true) | (((X149 @ (ap @ X151 @ X150))) = $true)) & ! [X154 : term] : ((((X149 @ X154)) = $true) | (((var @ X154)) != $true)) & ! [X152 : term] : ((((X149 @ (lam @ X152))) = $true) | ? [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) != $true) & (((X149 @ X153)) = $true)))))) & ((induction2lem = $true) <=> ! [X268 : subst,X270 : (term > $o),X269 : term] : (? [X273 : term] : ((((var @ X273)) = $true) & (((X270 @ (sub @ X273 @ X268))) != $true)) | ? [X271 : term] : (($true != ((X270 @ (lam @ X271)))) & ! [X272 : term] : ((((X270 @ X272)) != $true) | (((X270 @ (sub @ X271 @ (push @ X272 @ id)))) = $true))) | ? [X275 : term,X274 : term] : ((((X270 @ X275)) = $true) & (((X270 @ (ap @ X274 @ X275))) != $true) & (((X270 @ X274)) = $true)) | (((X270 @ (sub @ X269 @ X268))) = $true))) & (ulamvarind = $true) & ((termmset_lthm = $true) <=> (? [X260 : term] : (((sub @ X260 @ id)) != X260) | ! [X261 : term] : (((sub @ X261 @ id)) = X261))) & ! [X116 : d_term] : (d_one = X116) & (! [X484 : term,X483 : (term > $o)] : (? [X485 : term] : ((((X483 @ (lam @ X485))) != $true) & ! [X486 : term] : ((((X483 @ X486)) != $true) | (((X483 @ (sub @ X485 @ (push @ X486 @ id)))) = $true))) | ? [X487 : term,X488 : term] : ((((X483 @ X488)) = $true) & (((X483 @ (ap @ X487 @ X488))) != $true) & (((X483 @ X487)) = $true)) | ? [X489 : term] : ((((X483 @ X489)) != $true) & (((var @ X489)) = $true)) | (((X483 @ X484)) = $true)) <=> (induction2 = $true)) & ((? [X92 : (subst > term > subst > $o),X93 : term] : (! [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true)) & ! [X95 : (subst > term > term)] : (? [X98 : subst,X97 : term,X96 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) != ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ? [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) != $true) & (((X92 @ id @ X99 @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true)) & (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true)) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | ! [X101 : term,X100 : (subst > term > subst > $o)] : (? [X103 : (subst > term > term)] : (! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) & (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) != $true) & ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106)))) | ? [X102 : term] : ((((X100 @ id @ X102 @ id)) = $true) & (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) != $true)) | (((X100 @ id @ (lam @ X101) @ id)) = $true))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X496 : (term > $o),X495 : (subst > term > subst > $o),X498 : term,X497 : term] : (? [X499 : term] : (((X495 @ id @ X499 @ id)) != ((X496 @ X499))) | ? [X501 : term,X500 : term] : ((((X495 @ id @ X500 @ id)) = $true) & (((X495 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) != $true) & (((X495 @ id @ X501 @ id)) = $true)) | ? [X509 : term,X506 : subst,X507 : subst,X508 : subst] : ((((X495 @ X508 @ X509 @ (comp @ X507 @ X506))) != $true) & (((X495 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507) @ X506)) = $true)) | (((X496 @ (ap @ X497 @ X498))) = $true) | (((X496 @ X498)) != $true) | ? [X502 : subst,X503 : term,X505 : subst,X504 : subst] : ((((X495 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504) @ X502)) != $true) & (((X495 @ X505 @ X503 @ (comp @ X504 @ X502))) = $true)) | (((X496 @ X497)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((hoaslaminj = $true) <=> ! [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ? [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) != ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | ? [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) != ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((? [X276 : term] : (((sub @ X276 @ id)) != X276) | ? [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) = ((ap @ X280 @ X277))) & (X279 != X280)) | ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282))))) <=> (hoasapinj1_lthm = $true)) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) <=> ! [X290 : term] : ? [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) = ((X291 @ sh @ one)))) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X358 : d_term,X359 : d_term] : ((X358 = X359) | (((d2term @ X358)) != ((d2term @ X359)))) & ((hoasapinj2_lthm = $true) <=> (? [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 != X519) & (((ap @ X516 @ X517)) = ((ap @ X518 @ X519)))) | ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)))) & ((axvarcons = $true) <=> ! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510)) & (pushprop_lem3v2 = $true) & (! [X292 : term,X294 : (term > $o),X293 : (subst > term > subst > $o)] : (? [X304 : (subst > term > term)] : (! [X307 : term,X308 : subst,X306 : subst] : (((sub @ (X304 @ X306 @ X307) @ X308)) = ((X304 @ (comp @ X306 @ X308) @ (sub @ X307 @ X308)))) & ! [X305 : term] : ((((X293 @ id @ (X304 @ id @ X305) @ id)) = $true) | (((X293 @ id @ X305 @ id)) != $true)) & (((X293 @ id @ (lam @ (X304 @ sh @ one)) @ id)) != $true)) | ? [X309 : term] : (((X294 @ X309)) != ((X293 @ id @ X309 @ id))) | ? [X303 : term] : ((((X294 @ (sub @ X292 @ (push @ X303 @ id)))) != $true) & (((X294 @ X303)) = $true)) | ? [X302 : subst,X300 : subst,X299 : subst,X301 : term] : ((((X293 @ X300 @ X301 @ (comp @ X302 @ X299))) = $true) & (((X293 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302) @ X299)) != $true)) | ? [X298 : subst,X296 : subst,X295 : subst,X297 : term] : ((((X293 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298) @ X295)) = $true) & (((X293 @ X296 @ X297 @ (comp @ X298 @ X295))) != $true)) | (((X294 @ (lam @ X292))) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X336 : term] : ? [X337 : (subst > term > term)] : ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axvarid = $true) <=> ! [X327 : term] : (((sub @ X327 @ id)) = X327)) & ! [X4 : d_subst] : (d_id = X4) & ((hoasinduction_lem0_lthm = $true) <=> ! [X492 : (subst > term > subst > $o)] : ? [X493 : (term > $o)] : ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494)))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) != X396) | ! [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) = $true) | (((X398 @ X399)) != $true) | ? [X402 : term] : (((X401 @ X402)) != ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & (apnotvar = $true) & (pushprop_gthm = $true) & (! [X318 : subst,X320 : term,X319 : (term > $o)] : ? [X321 : (term > $o)] : ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))) <=> (pushprop_lem0 = $true)) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) <=> (axidl = $true)) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & ((substmonoid = $true) <=> (! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X457 : term,X456 : (subst > term > subst > $o)] : (? [X459 : (subst > term > term)] : (! [X463 : subst,X462 : subst,X461 : term] : (((sub @ (X459 @ X462 @ X461) @ X463)) = ((X459 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463)))) & (((X456 @ id @ (lam @ (X459 @ sh @ one)) @ id)) != $true) & ! [X460 : term] : ((((X456 @ id @ (X459 @ id @ X460) @ id)) = $true) | ($true != ((X456 @ id @ X460 @ id))))) | ? [X458 : term] : ((((X456 @ id @ X458 @ id)) = $true) & (((X456 @ id @ (sub @ X457 @ (push @ X458 @ id)) @ id)) != $true)) | (((X456 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id)) = $true))) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & (! [X403 : term,X404 : (subst > term > subst > $o)] : (? [X418 : term] : ((((X404 @ id @ X418 @ id)) = $true) & (((X404 @ id @ (sub @ X403 @ (push @ X418 @ id)) @ id)) != $true)) | ? [X405 : (subst > term > term)] : (! [X406 : term] : ((((X404 @ id @ (X405 @ id @ X406) @ id)) = $true) | ($true != ((X404 @ id @ X406 @ id)))) & ! [X408 : term,X407 : subst,X409 : subst] : (((sub @ (X405 @ X409 @ X408) @ X407)) = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407)))) & (((X404 @ id @ (lam @ (X405 @ sh @ one)) @ id)) != $true)) | ? [X414 : subst,X417 : subst,X415 : term,X416 : subst] : ((((X404 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414) @ X417)) != $true) & (((X404 @ X416 @ X415 @ (comp @ X414 @ X417))) = $true)) | (((X404 @ id @ (lam @ X403) @ id)) = $true) | ? [X411 : term,X410 : subst,X412 : subst,X413 : subst] : ((((X404 @ (comp @ X410 @ X412) @ (sub @ X411 @ X412) @ X413)) = $true) & (((X404 @ X410 @ X411 @ (comp @ X412 @ X413))) != $true))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X344 : (term > $o),X343 : term,X345 : subst] : ? [X346 : (term > $o)] : ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X202 : term] : (((sub @ X202 @ id)) != X202) | ! [X204 : term,X205 : (term > $o),X203 : (subst > term > subst > $o)] : (? [X208 : term,X206 : subst,X207 : subst,X209 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) != $true) & (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) = $true)) | ? [X212 : subst,X215 : subst,X213 : term,X214 : subst] : ((((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) != $true) & (((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) = $true)) | ? [X210 : term] : (((X205 @ X210)) != ((X203 @ id @ X210 @ id))) | ? [X216 : (subst > term > term)] : (! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | (((X203 @ id @ X220 @ id)) != $true)) & ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) & (((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true)) | ? [X211 : term] : ((((X205 @ X211)) = $true) & (((X205 @ (sub @ X204 @ (push @ X211 @ id)))) != $true)) | (((X205 @ (lam @ X204))) = $true)))) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3a = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (($true = ((X108 @ id @ (lam @ X109) @ id))) | ? [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) != $true) & ! [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) = $true) | (((X108 @ id @ X115 @ id)) != $true)) & ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113)))) | ? [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) != $true) & (((X108 @ id @ X110 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & ((induction = $true) <=> ! [X263 : term,X262 : (term > $o)] : (? [X265 : term,X264 : term] : ((((X262 @ (ap @ X265 @ X264))) != $true) & (((X262 @ X265)) = $true) & (((X262 @ X264)) = $true)) | (((X262 @ X263)) = $true) | ? [X267 : term] : ((((X262 @ X267)) != $true) & (((var @ X267)) = $true)) | ? [X266 : term] : ((((X262 @ X266)) = $true) & (((X262 @ (lam @ X266))) != $true)))) & ((hoasapinj2 = $true) <=> ! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331))))) & ((substmonoid_lthm = $true) <=> ((! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)) | ? [X476 : subst] : (((comp @ id @ X476)) != X476) | ? [X477 : subst] : (((comp @ X477 @ id)) != X477))) & (! [X310 : term,X311 : (subst > term > subst > $o)] : (? [X317 : term] : ((((X311 @ id @ X317 @ id)) = $true) & (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) != $true)) | (((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ? [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) != $true) & ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) = $true) | (((X311 @ id @ X313 @ id)) != $true)))) <=> (hoasinduction_lem3aa = $true)) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & ((? [X380 : term,X381 : subst] : (((sub @ one @ (push @ X380 @ X381))) != X380) | ! [X387 : subst,X388 : term,X389 : (subst > term > term),X386 : (subst > term > term)] : ((((lam @ (X386 @ sh @ one))) != ((lam @ (X389 @ sh @ one)))) | (((X389 @ X387 @ X388)) = ((X386 @ X387 @ X388))) | ? [X392 : subst,X391 : term,X390 : subst] : (((X389 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392))) != ((sub @ (X389 @ X390 @ X391) @ X392))) | ? [X393 : term,X395 : subst,X394 : subst] : (((sub @ (X386 @ X395 @ X393) @ X394)) != ((X386 @ (comp @ X395 @ X394) @ (sub @ X393 @ X394))))) | ? [X385 : term,X384 : term] : ((((lam @ X385)) = ((lam @ X384))) & (X384 != X385)) | ? [X383 : term,X382 : subst] : (((comp @ sh @ (push @ X383 @ X382))) != X382)) <=> (hoaslaminj_lthm = $true)) & (! [X465 : (subst > term > subst > $o),X464 : term] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ? [X475 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X475 @ id)) @ id)) != $true) & (((X465 @ id @ X475 @ id)) = $true)) | ? [X467 : (subst > term > term),X466 : term] : (! [X471 : term] : ((((X465 @ id @ (X467 @ id @ X471) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X473 : term,X472 : subst,X474 : subst] : (((sub @ X466 @ (push @ (sub @ X473 @ X472) @ (comp @ X474 @ X472)))) = ((X467 @ (comp @ X474 @ X472) @ (sub @ X473 @ X472)))) & ! [X470 : subst,X468 : term,X469 : subst] : (((sub @ (sub @ X466 @ (push @ X468 @ X470)) @ X469)) = ((sub @ (X467 @ X470 @ X468) @ X469))) & (((X465 @ id @ (lam @ (X467 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3aaa = $true)) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X480 : (subst > term > subst > $o)] : ? [X481 : (term > $o)] : ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction = $true) <=> ! [X363 : term,X362 : (subst > term > subst > $o)] : (? [X364 : term] : ((((var @ (sub @ X364 @ id))) = $true) & (((X362 @ id @ X364 @ id)) != $true)) | ? [X365 : subst,X367 : subst,X366 : subst,X368 : term] : ((((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) != $true) & (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) = $true)) | ? [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) != $true) & ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | (((X362 @ id @ X375 @ id)) != $true)) & ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373)))) | ? [X369 : term,X370 : term] : ((((X362 @ id @ (ap @ (sub @ X370 @ id) @ X369) @ id)) != $true) & ($true = ((X362 @ id @ X369 @ id))) & (((X362 @ id @ X370 @ id)) = $true)) | ? [X376 : subst,X378 : subst,X377 : term,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) = $true) & (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) != $true)) | (((X362 @ id @ X363 @ id)) = $true))) & ((pushprop_lem1v2 = $true) <=> ! [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) = $true) | (((X434 @ X432)) != $true) | ? [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) != ((X433 @ X436))))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X16 : (subst > term > subst > $o),X17 : term] : (! [X23 : term] : ((((X16 @ id @ X23 @ id)) != $true) | (((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true)) & ! [X18 : (subst > term > term)] : ((((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : ((((X16 @ id @ X19 @ id)) = $true) & (((X16 @ id @ (X18 @ id @ X19) @ id)) != $true)) | ? [X20 : subst,X22 : term,X21 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) != ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) & (((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) != $true)) | ? [X15 : term] : (((sub @ X15 @ id)) != X15) | ! [X24 : (subst > term > subst > $o),X25 : term] : (? [X38 : subst,X39 : term,X37 : subst,X36 : subst] : ((((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) = $true) & (((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) != $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true) | ? [X26 : (subst > term > term)] : (! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) & (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) != $true) & ! [X30 : term] : ((((X24 @ id @ X30 @ id)) != $true) | (((X24 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X31 : subst,X34 : subst,X33 : subst,X32 : term] : ((((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) = $true) & (((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) != $true)) | ? [X35 : term] : ((((X24 @ id @ X35 @ id)) = $true) & (((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) != $true))))) & ((hoasinduction_lthm_3 = $true) <=> (? [X50 : term] : (((sub @ X50 @ id)) != X50) | ? [X44 : (term > $o),X43 : term] : (! [X49 : term,X48 : term] : ((((X44 @ X49)) != $true) | (((X44 @ (ap @ X48 @ X49))) = $true) | (((X44 @ X48)) != $true)) & (((X44 @ X43)) != $true) & ! [X45 : term] : (($true = ((X44 @ X45))) | (((var @ X45)) != $true)) & ! [X46 : term] : (? [X47 : term] : ((((X44 @ X47)) = $true) & (((X44 @ (sub @ X46 @ (push @ X47 @ id)))) != $true)) | (((X44 @ (lam @ X46))) = $true))) | ? [X52 : (term > $o),X51 : (subst > term > subst > $o),X53 : term] : (! [X56 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ? [X59 : subst,X57 : term,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) != ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ? [X60 : term] : ((((X51 @ id @ (X56 @ id @ X60) @ id)) != $true) & (((X51 @ id @ X60 @ id)) = $true))) & ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) & ! [X54 : term] : ((((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true) | (((X52 @ X54)) != $true)) & ($true != ((X52 @ (lam @ X53))))) | ! [X61 : (subst > term > subst > $o),X62 : term] : (? [X72 : term] : ((((X61 @ id @ X72 @ id)) != $true) & (((var @ (sub @ X72 @ id))) = $true)) | ? [X69 : subst,X71 : term,X68 : subst,X70 : subst] : ((((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) != $true) & (((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) = $true)) | ? [X74 : term,X73 : term] : ((((X61 @ id @ X73 @ id)) = $true) & (((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) != $true) & (((X61 @ id @ X74 @ id)) = $true)) | ? [X78 : term,X76 : subst,X75 : subst,X77 : subst] : ((((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) != $true) & (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) = $true)) | (((X61 @ id @ X62 @ id)) = $true) | ? [X63 : (subst > term > term)] : (! [X64 : term] : ((((X61 @ id @ X64 @ id)) != $true) | (((X61 @ id @ (X63 @ id @ X64) @ id)) = $true)) & (((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) != $true) & ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66)))))) | ? [X40 : (subst > term > subst > $o)] : ! [X41 : (term > $o)] : ? [X42 : term] : (((X40 @ id @ X42 @ id)) != ((X41 @ X42))))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X334 : term] : ? [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) = ((X335 @ sh @ one)))) & ((hoasinduction_lem3v2a = $true) <=> ! [X349 : (subst > term > subst > $o),X350 : (term > $o),X348 : term] : (? [X351 : term] : (((X349 @ id @ X351 @ id)) != ((X350 @ X351))) | ? [X352 : (subst > term > term)] : (! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X352 @ X355 @ X356) @ X354)) = ((X352 @ (comp @ X355 @ X354) @ (sub @ X356 @ X354)))) & ! [X353 : term] : ((((X349 @ id @ X353 @ id)) != $true) | (((X349 @ id @ (X352 @ id @ X353) @ id)) = $true)) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true)) | (((X350 @ (lam @ X348))) = $true) | ? [X357 : term] : ((((X350 @ (sub @ X348 @ (push @ X357 @ id)))) != $true) & (((X350 @ X357)) = $true)))) & ! [X80 : d_subst,X79 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & ((hoaslamnotap = $true) <=> ! [X5 : (subst > term > term),X6 : term,X7 : term] : (? [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & (! [X421 : (subst > term > subst > $o),X420 : term,X419 : term] : (? [X429 : subst,X427 : term,X426 : subst,X428 : subst] : ((((X421 @ X428 @ X427 @ (comp @ X426 @ X429))) != $true) & (((X421 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426) @ X429)) = $true)) | (((X421 @ id @ X420 @ id)) != $true) | ? [X431 : term,X430 : term] : ((((X421 @ id @ X431 @ id)) = $true) & (((X421 @ id @ (ap @ (sub @ X430 @ id) @ X431) @ id)) != $true) & (((X421 @ id @ X430 @ id)) = $true)) | (((X421 @ id @ X419 @ id)) != $true) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | ? [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((((X421 @ X423 @ X425 @ (comp @ X422 @ X424))) = $true) & (((X421 @ (comp @ X423 @ X422) @ (sub @ X425 @ X422) @ X424)) != $true))) <=> (hoasinduction_lem2 = $true)) & (axmap = $true) & ((induction2_lthm = $true) <=> (! [X534 : (term > $o),X533 : term] : ((((X534 @ X533)) = $true) | ? [X535 : term] : ((((var @ X535)) = $true) & (((X534 @ X535)) != $true)) | ? [X538 : term] : (! [X539 : term] : ((((X534 @ X539)) != $true) | (((X534 @ (sub @ X538 @ (push @ X539 @ id)))) = $true)) & (((X534 @ (lam @ X538))) != $true)) | ? [X537 : term,X536 : term] : ((((X534 @ X536)) = $true) & (((X534 @ (ap @ X536 @ X537))) != $true) & (((X534 @ X537)) = $true))) | ? [X525 : subst,X527 : term,X526 : (term > $o)] : (! [X528 : term] : ((((X526 @ (sub @ X528 @ X525))) = $true) | (((var @ X528)) != $true)) & ! [X529 : term,X530 : term] : ((((X526 @ X530)) != $true) | (((X526 @ X529)) != $true) | (((X526 @ (ap @ X529 @ X530))) = $true)) & (((X526 @ (sub @ X527 @ X525))) != $true) & ! [X531 : term] : (? [X532 : term] : ((((X526 @ (sub @ X531 @ (push @ X532 @ id)))) != $true) & (((X526 @ X532)) = $true)) | (((X526 @ (lam @ X531))) = $true))) | ? [X524 : term] : (((sub @ X524 @ id)) != X524))) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X512 : term] : ? [X513 : (subst > term > term)] : ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514))))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(flattening,[],[f13])).
% 47.53/7.12 thf(f15,definition,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : ((((sP0 @ X0)) = $true) <=> ? [X12 : (subst > term > term)] : (! [X16 : term] : ((((X0 @ id @ X16 @ id)) != $true) | (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) & ! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f16,definition,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : ((((sP1 @ X0)) = $true) <=> ? [X10 : term,X11 : term] : ((((X0 @ id @ X10 @ id)) = $true) & (((X0 @ id @ (hoasap @ id @ X10 @ id @ X11) @ id)) != $true) & ($true = ((X0 @ id @ X11 @ id)))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f17,definition,(
% 47.53/7.12 (sP2 = $true) <=> ! [X0 : (subst > term > subst > $o)] : (? [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) & (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) != $true)) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | (((sP1 @ X0)) = $true) | ? [X7 : subst,X6 : term,X8 : subst,X5 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) & (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) != $true)) | (((sP0 @ X0)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f18,plain,(
% 47.53/7.12 (sP2 = $true) <~> (hoasinduction = $true)),
% 47.53/7.12 inference(definition_folding,[],[f12,f17,f16,f15])).
% 47.53/7.12 thf(f19,definition,(
% 47.53/7.12 ! [X526 : (term > $o)] : ((((sP3 @ X526)) = $true) <=> ! [X529 : term,X530 : term] : ((((X526 @ X530)) != $true) | (((X526 @ X529)) != $true) | (((X526 @ (ap @ X529 @ X530))) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f20,definition,(
% 47.53/7.12 ! [X534 : (term > $o)] : ((((sP4 @ X534)) = $true) <=> ? [X537 : term,X536 : term] : ((((X534 @ X536)) = $true) & (((X534 @ (ap @ X536 @ X537))) != $true) & (((X534 @ X537)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f21,definition,(
% 47.53/7.12 ($true = sP5) <=> ! [X534 : (term > $o),X533 : term] : ((((X534 @ X533)) = $true) | ? [X535 : term] : ((((var @ X535)) = $true) & (((X534 @ X535)) != $true)) | ? [X538 : term] : (! [X539 : term] : ((((X534 @ X539)) != $true) | (((X534 @ (sub @ X538 @ (push @ X539 @ id)))) = $true)) & (((X534 @ (lam @ X538))) != $true)) | (((sP4 @ X534)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f22,definition,(
% 47.53/7.12 (sP6 = $true) <=> (($true = sP5) | ? [X525 : subst,X527 : term,X526 : (term > $o)] : (! [X528 : term] : ((((X526 @ (sub @ X528 @ X525))) = $true) | (((var @ X528)) != $true)) & (((sP3 @ X526)) = $true) & (((X526 @ (sub @ X527 @ X525))) != $true) & ! [X531 : term] : (? [X532 : term] : ((((X526 @ (sub @ X531 @ (push @ X532 @ id)))) != $true) & (((X526 @ X532)) = $true)) | (((X526 @ (lam @ X531))) = $true))) | ? [X524 : term] : (((sub @ X524 @ id)) != X524))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f23,definition,(
% 47.53/7.12 ! [X421 : (subst > term > subst > $o)] : ((((sP7 @ X421)) = $true) <=> ? [X431 : term,X430 : term] : ((((X421 @ id @ X431 @ id)) = $true) & (((X421 @ id @ (ap @ (sub @ X430 @ id) @ X431) @ id)) != $true) & (((X421 @ id @ X430 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f24,definition,(
% 47.53/7.12 (sP8 = $true) <=> ! [X421 : (subst > term > subst > $o),X420 : term,X419 : term] : (? [X429 : subst,X427 : term,X426 : subst,X428 : subst] : ((((X421 @ X428 @ X427 @ (comp @ X426 @ X429))) != $true) & (((X421 @ (comp @ X428 @ X426) @ (sub @ X427 @ X426) @ X429)) = $true)) | (((X421 @ id @ X420 @ id)) != $true) | (((sP7 @ X421)) = $true) | (((X421 @ id @ X419 @ id)) != $true) | (((X421 @ id @ (ap @ X420 @ X419) @ id)) = $true) | ? [X422 : subst,X423 : subst,X424 : subst,X425 : term] : ((((X421 @ X423 @ X425 @ (comp @ X422 @ X424))) = $true) & (((X421 @ (comp @ X423 @ X422) @ (sub @ X425 @ X422) @ X424)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f25,definition,(
% 47.53/7.12 (sP9 = $true) <=> ! [X349 : (subst > term > subst > $o),X350 : (term > $o),X348 : term] : (? [X351 : term] : (((X349 @ id @ X351 @ id)) != ((X350 @ X351))) | ? [X352 : (subst > term > term)] : (! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X352 @ X355 @ X356) @ X354)) = ((X352 @ (comp @ X355 @ X354) @ (sub @ X356 @ X354)))) & ! [X353 : term] : ((((X349 @ id @ X353 @ id)) != $true) | (((X349 @ id @ (X352 @ id @ X353) @ id)) = $true)) & (((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id)) != $true)) | (((X350 @ (lam @ X348))) = $true) | ? [X357 : term] : ((((X350 @ (sub @ X348 @ (push @ X357 @ id)))) != $true) & (((X350 @ X357)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f26,definition,(
% 47.53/7.12 ! [X61 : (subst > term > subst > $o)] : ((((sP10 @ X61)) = $true) <=> ? [X63 : (subst > term > term)] : (! [X64 : term] : ((((X61 @ id @ X64 @ id)) != $true) | (((X61 @ id @ (X63 @ id @ X64) @ id)) = $true)) & (((X61 @ id @ (lam @ (X63 @ sh @ one)) @ id)) != $true) & ! [X67 : term,X66 : subst,X65 : subst] : (((sub @ (X63 @ X65 @ X67) @ X66)) = ((X63 @ (comp @ X65 @ X66) @ (sub @ X67 @ X66))))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f27,definition,(
% 47.53/7.12 ! [X61 : (subst > term > subst > $o)] : ((((sP11 @ X61)) = $true) <=> ? [X74 : term,X73 : term] : ((((X61 @ id @ X73 @ id)) = $true) & (((X61 @ id @ (ap @ (sub @ X74 @ id) @ X73) @ id)) != $true) & (((X61 @ id @ X74 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f28,definition,(
% 47.53/7.12 ! [X44 : (term > $o)] : ((((sP12 @ X44)) = $true) <=> ! [X49 : term,X48 : term] : ((((X44 @ X49)) != $true) | (((X44 @ (ap @ X48 @ X49))) = $true) | (((X44 @ X48)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f29,definition,(
% 47.53/7.12 (sP13 = $true) <=> ! [X61 : (subst > term > subst > $o),X62 : term] : (? [X72 : term] : ((((X61 @ id @ X72 @ id)) != $true) & (((var @ (sub @ X72 @ id))) = $true)) | ? [X69 : subst,X71 : term,X68 : subst,X70 : subst] : ((((X61 @ (comp @ X68 @ X69) @ (sub @ X71 @ X69) @ X70)) != $true) & (((X61 @ X68 @ X71 @ (comp @ X69 @ X70))) = $true)) | (((sP11 @ X61)) = $true) | ? [X78 : term,X76 : subst,X75 : subst,X77 : subst] : ((((X61 @ X77 @ X78 @ (comp @ X76 @ X75))) != $true) & (((X61 @ (comp @ X77 @ X76) @ (sub @ X78 @ X76) @ X75)) = $true)) | (((X61 @ id @ X62 @ id)) = $true) | (((sP10 @ X61)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f30,definition,(
% 47.53/7.12 (sP14 = $true) <=> ? [X52 : (term > $o),X51 : (subst > term > subst > $o),X53 : term] : (! [X56 : (subst > term > term)] : ((((X51 @ id @ (lam @ (X56 @ sh @ one)) @ id)) = $true) | ? [X59 : subst,X57 : term,X58 : subst] : (((sub @ (X56 @ X59 @ X57) @ X58)) != ((X56 @ (comp @ X59 @ X58) @ (sub @ X57 @ X58)))) | ? [X60 : term] : ((((X51 @ id @ (X56 @ id @ X60) @ id)) != $true) & (((X51 @ id @ X60 @ id)) = $true))) & ! [X55 : term] : (((X51 @ id @ X55 @ id)) = ((X52 @ X55))) & ! [X54 : term] : ((((X52 @ (sub @ X53 @ (push @ X54 @ id)))) = $true) | (((X52 @ X54)) != $true)) & ($true != ((X52 @ (lam @ X53)))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f31,definition,(
% 47.53/7.12 (sP15 = $true) <=> (? [X50 : term] : (((sub @ X50 @ id)) != X50) | ? [X44 : (term > $o),X43 : term] : ((((sP12 @ X44)) = $true) & (((X44 @ X43)) != $true) & ! [X45 : term] : (($true = ((X44 @ X45))) | (((var @ X45)) != $true)) & ! [X46 : term] : (? [X47 : term] : ((((X44 @ X47)) = $true) & (((X44 @ (sub @ X46 @ (push @ X47 @ id)))) != $true)) | (((X44 @ (lam @ X46))) = $true))) | (sP14 = $true) | (sP13 = $true) | ? [X40 : (subst > term > subst > $o)] : ! [X41 : (term > $o)] : ? [X42 : term] : (((X40 @ id @ X42 @ id)) != ((X41 @ X42))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f32,definition,(
% 47.53/7.12 ! [X24 : (subst > term > subst > $o)] : ((((sP16 @ X24)) = $true) <=> ? [X26 : (subst > term > term)] : (! [X28 : subst,X29 : term,X27 : subst] : (((sub @ (X26 @ X27 @ X29) @ X28)) = ((X26 @ (comp @ X27 @ X28) @ (sub @ X29 @ X28)))) & (((X24 @ id @ (lam @ (X26 @ sh @ one)) @ id)) != $true) & ! [X30 : term] : ((((X24 @ id @ X30 @ id)) != $true) | (((X24 @ id @ (X26 @ id @ X30) @ id)) = $true))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f33,definition,(
% 47.53/7.12 (sP17 = $true) <=> ? [X16 : (subst > term > subst > $o),X17 : term] : (! [X23 : term] : ((((X16 @ id @ X23 @ id)) != $true) | (((X16 @ id @ (sub @ X17 @ (push @ X23 @ id)) @ id)) = $true)) & ! [X18 : (subst > term > term)] : ((((X16 @ id @ (lam @ (X18 @ sh @ one)) @ id)) = $true) | ? [X19 : term] : ((((X16 @ id @ X19 @ id)) = $true) & (((X16 @ id @ (X18 @ id @ X19) @ id)) != $true)) | ? [X20 : subst,X22 : term,X21 : subst] : (((sub @ (X18 @ X20 @ X22) @ X21)) != ((X18 @ (comp @ X20 @ X21) @ (sub @ X22 @ X21))))) & (((X16 @ id @ (lam @ (sub @ X17 @ (push @ one @ sh))) @ id)) != $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f34,definition,(
% 47.53/7.12 (sP18 = $true) <=> ((sP17 = $true) | ? [X15 : term] : (((sub @ X15 @ id)) != X15) | ! [X24 : (subst > term > subst > $o),X25 : term] : (? [X38 : subst,X39 : term,X37 : subst,X36 : subst] : ((((X24 @ (comp @ X36 @ X37) @ (sub @ X39 @ X37) @ X38)) = $true) & (((X24 @ X36 @ X39 @ (comp @ X37 @ X38))) != $true)) | (((X24 @ id @ (lam @ X25) @ id)) = $true) | (((sP16 @ X24)) = $true) | ? [X31 : subst,X34 : subst,X33 : subst,X32 : term] : ((((X24 @ X33 @ X32 @ (comp @ X34 @ X31))) = $true) & (((X24 @ (comp @ X33 @ X34) @ (sub @ X32 @ X34) @ X31)) != $true)) | ? [X35 : term] : ((((X24 @ id @ X35 @ id)) = $true) & (((X24 @ id @ (sub @ X25 @ (push @ X35 @ id)) @ id)) != $true))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f35,definition,(
% 47.53/7.12 ! [X362 : (subst > term > subst > $o)] : ((((sP19 @ X362)) = $true) <=> ? [X369 : term,X370 : term] : ((((X362 @ id @ (ap @ (sub @ X370 @ id) @ X369) @ id)) != $true) & ($true = ((X362 @ id @ X369 @ id))) & (((X362 @ id @ X370 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f36,definition,(
% 47.53/7.12 ! [X362 : (subst > term > subst > $o)] : ((((sP20 @ X362)) = $true) <=> ? [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) != $true) & ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | (((X362 @ id @ X375 @ id)) != $true)) & ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373)))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f37,definition,(
% 47.53/7.12 (sP21 = $true) <=> ! [X363 : term,X362 : (subst > term > subst > $o)] : (? [X364 : term] : ((((var @ (sub @ X364 @ id))) = $true) & (((X362 @ id @ X364 @ id)) != $true)) | ? [X365 : subst,X367 : subst,X366 : subst,X368 : term] : ((((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) != $true) & (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) = $true)) | (((sP20 @ X362)) = $true) | (((sP19 @ X362)) = $true) | ? [X376 : subst,X378 : subst,X377 : term,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) = $true) & (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) != $true)) | (((X362 @ id @ X363 @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f38,definition,(
% 47.53/7.12 (sP22 = $true) <=> ! [X465 : (subst > term > subst > $o),X464 : term] : ((((X465 @ id @ (lam @ (sub @ X464 @ (push @ one @ sh))) @ id)) = $true) | ? [X475 : term] : ((((X465 @ id @ (sub @ X464 @ (push @ X475 @ id)) @ id)) != $true) & (((X465 @ id @ X475 @ id)) = $true)) | ? [X467 : (subst > term > term),X466 : term] : (! [X471 : term] : ((((X465 @ id @ (X467 @ id @ X471) @ id)) = $true) | (((X465 @ id @ X471 @ id)) != $true)) & ! [X473 : term,X472 : subst,X474 : subst] : (((sub @ X466 @ (push @ (sub @ X473 @ X472) @ (comp @ X474 @ X472)))) = ((X467 @ (comp @ X474 @ X472) @ (sub @ X473 @ X472)))) & ! [X470 : subst,X468 : term,X469 : subst] : (((sub @ (sub @ X466 @ (push @ X468 @ X470)) @ X469)) = ((sub @ (X467 @ X470 @ X468) @ X469))) & (((X465 @ id @ (lam @ (X467 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f39,definition,(
% 47.53/7.12 (sP23 = $true) <=> (? [X380 : term,X381 : subst] : (((sub @ one @ (push @ X380 @ X381))) != X380) | ! [X387 : subst,X388 : term,X389 : (subst > term > term),X386 : (subst > term > term)] : ((((lam @ (X386 @ sh @ one))) != ((lam @ (X389 @ sh @ one)))) | (((X389 @ X387 @ X388)) = ((X386 @ X387 @ X388))) | ? [X392 : subst,X391 : term,X390 : subst] : (((X389 @ (comp @ X390 @ X392) @ (sub @ X391 @ X392))) != ((sub @ (X389 @ X390 @ X391) @ X392))) | ? [X393 : term,X395 : subst,X394 : subst] : (((sub @ (X386 @ X395 @ X393) @ X394)) != ((X386 @ (comp @ X395 @ X394) @ (sub @ X393 @ X394))))) | ? [X385 : term,X384 : term] : ((((lam @ X385)) = ((lam @ X384))) & (X384 != X385)) | ? [X383 : term,X382 : subst] : (((comp @ sh @ (push @ X383 @ X382))) != X382))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f40,definition,(
% 47.53/7.12 (sP24 = $true) <=> ! [X310 : term,X311 : (subst > term > subst > $o)] : (? [X317 : term] : ((((X311 @ id @ X317 @ id)) = $true) & (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) != $true)) | (((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ? [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) != $true) & ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) = $true) | (((X311 @ id @ X313 @ id)) != $true))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f41,definition,(
% 47.53/7.12 ! [X262 : (term > $o)] : ((((sP25 @ X262)) = $true) <=> ? [X265 : term,X264 : term] : ((((X262 @ (ap @ X265 @ X264))) != $true) & (((X262 @ X265)) = $true) & (((X262 @ X264)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f42,definition,(
% 47.53/7.12 (sP26 = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (($true = ((X108 @ id @ (lam @ X109) @ id))) | ? [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) != $true) & ! [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) = $true) | (((X108 @ id @ X115 @ id)) != $true)) & ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113)))) | ? [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) != $true) & (((X108 @ id @ X110 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f43,definition,(
% 47.53/7.12 ! [X203 : (subst > term > subst > $o)] : ((((sP27 @ X203)) = $true) <=> ? [X216 : (subst > term > term)] : (! [X220 : term] : ((((X203 @ id @ (X216 @ id @ X220) @ id)) = $true) | (((X203 @ id @ X220 @ id)) != $true)) & ! [X217 : term,X218 : subst,X219 : subst] : (((X216 @ (comp @ X219 @ X218) @ (sub @ X217 @ X218))) = ((sub @ (X216 @ X219 @ X217) @ X218))) & (((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f44,definition,(
% 47.53/7.12 (sP28 = $true) <=> (? [X202 : term] : (((sub @ X202 @ id)) != X202) | ! [X204 : term,X205 : (term > $o),X203 : (subst > term > subst > $o)] : (? [X208 : term,X206 : subst,X207 : subst,X209 : subst] : ((((X203 @ (comp @ X206 @ X209) @ (sub @ X208 @ X209) @ X207)) != $true) & (((X203 @ X206 @ X208 @ (comp @ X209 @ X207))) = $true)) | ? [X212 : subst,X215 : subst,X213 : term,X214 : subst] : ((((X203 @ X214 @ X213 @ (comp @ X215 @ X212))) != $true) & (((X203 @ (comp @ X214 @ X215) @ (sub @ X213 @ X215) @ X212)) = $true)) | ? [X210 : term] : (((X205 @ X210)) != ((X203 @ id @ X210 @ id))) | (((sP27 @ X203)) = $true) | ? [X211 : term] : ((((X205 @ X211)) = $true) & (((X205 @ (sub @ X204 @ (push @ X211 @ id)))) != $true)) | (((X205 @ (lam @ X204))) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f45,definition,(
% 47.53/7.12 ! [X404 : (subst > term > subst > $o)] : ((((sP29 @ X404)) = $true) <=> ? [X405 : (subst > term > term)] : (! [X406 : term] : ((((X404 @ id @ (X405 @ id @ X406) @ id)) = $true) | ($true != ((X404 @ id @ X406 @ id)))) & ! [X408 : term,X407 : subst,X409 : subst] : (((sub @ (X405 @ X409 @ X408) @ X407)) = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407)))) & (((X404 @ id @ (lam @ (X405 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f46,definition,(
% 47.53/7.12 (sP30 = $true) <=> ! [X403 : term,X404 : (subst > term > subst > $o)] : (? [X418 : term] : ((((X404 @ id @ X418 @ id)) = $true) & (((X404 @ id @ (sub @ X403 @ (push @ X418 @ id)) @ id)) != $true)) | (((sP29 @ X404)) = $true) | ? [X414 : subst,X417 : subst,X415 : term,X416 : subst] : ((((X404 @ (comp @ X416 @ X414) @ (sub @ X415 @ X414) @ X417)) != $true) & (((X404 @ X416 @ X415 @ (comp @ X414 @ X417))) = $true)) | (((X404 @ id @ (lam @ X403) @ id)) = $true) | ? [X411 : term,X410 : subst,X412 : subst,X413 : subst] : ((((X404 @ (comp @ X410 @ X412) @ (sub @ X411 @ X412) @ X413)) = $true) & (((X404 @ X410 @ X411 @ (comp @ X412 @ X413))) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f47,definition,(
% 47.53/7.12 (sP31 = $true) <=> ! [X457 : term,X456 : (subst > term > subst > $o)] : (? [X459 : (subst > term > term)] : (! [X463 : subst,X462 : subst,X461 : term] : (((sub @ (X459 @ X462 @ X461) @ X463)) = ((X459 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463)))) & (((X456 @ id @ (lam @ (X459 @ sh @ one)) @ id)) != $true) & ! [X460 : term] : ((((X456 @ id @ (X459 @ id @ X460) @ id)) = $true) | ($true != ((X456 @ id @ X460 @ id))))) | ? [X458 : term] : ((((X456 @ id @ X458 @ id)) = $true) & (((X456 @ id @ (sub @ X457 @ (push @ X458 @ id)) @ id)) != $true)) | (((X456 @ id @ (lam @ (sub @ X457 @ (push @ one @ sh))) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f48,definition,(
% 47.53/7.12 ! [X293 : (subst > term > subst > $o)] : (($true = ((sP32 @ X293))) <=> ? [X304 : (subst > term > term)] : (! [X307 : term,X308 : subst,X306 : subst] : (((sub @ (X304 @ X306 @ X307) @ X308)) = ((X304 @ (comp @ X306 @ X308) @ (sub @ X307 @ X308)))) & ! [X305 : term] : ((((X293 @ id @ (X304 @ id @ X305) @ id)) = $true) | (((X293 @ id @ X305 @ id)) != $true)) & (((X293 @ id @ (lam @ (X304 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f49,definition,(
% 47.53/7.12 (sP33 = $true) <=> ! [X292 : term,X294 : (term > $o),X293 : (subst > term > subst > $o)] : (($true = ((sP32 @ X293))) | ? [X309 : term] : (((X294 @ X309)) != ((X293 @ id @ X309 @ id))) | ? [X303 : term] : ((((X294 @ (sub @ X292 @ (push @ X303 @ id)))) != $true) & (((X294 @ X303)) = $true)) | ? [X302 : subst,X300 : subst,X299 : subst,X301 : term] : ((((X293 @ X300 @ X301 @ (comp @ X302 @ X299))) = $true) & (((X293 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302) @ X299)) != $true)) | ? [X298 : subst,X296 : subst,X295 : subst,X297 : term] : ((((X293 @ (comp @ X296 @ X298) @ (sub @ X297 @ X298) @ X295)) = $true) & (((X293 @ X296 @ X297 @ (comp @ X298 @ X295))) != $true)) | (((X294 @ (lam @ X292))) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f50,definition,(
% 47.53/7.12 ! [X495 : (subst > term > subst > $o)] : ((((sP34 @ X495)) = $true) <=> ? [X501 : term,X500 : term] : ((((X495 @ id @ X500 @ id)) = $true) & (((X495 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) != $true) & (((X495 @ id @ X501 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f51,definition,(
% 47.53/7.12 (sP35 = $true) <=> ! [X496 : (term > $o),X495 : (subst > term > subst > $o),X498 : term,X497 : term] : (? [X499 : term] : (((X495 @ id @ X499 @ id)) != ((X496 @ X499))) | (((sP34 @ X495)) = $true) | ? [X509 : term,X506 : subst,X507 : subst,X508 : subst] : ((((X495 @ X508 @ X509 @ (comp @ X507 @ X506))) != $true) & (((X495 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507) @ X506)) = $true)) | (((X496 @ (ap @ X497 @ X498))) = $true) | (((X496 @ X498)) != $true) | ? [X502 : subst,X503 : term,X505 : subst,X504 : subst] : ((((X495 @ (comp @ X505 @ X504) @ (sub @ X503 @ X504) @ X502)) != $true) & (((X495 @ X505 @ X503 @ (comp @ X504 @ X502))) = $true)) | (((X496 @ X497)) != $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f52,definition,(
% 47.53/7.12 (sP36 = $true) <=> ? [X92 : (subst > term > subst > $o),X93 : term] : (! [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true)) & ! [X95 : (subst > term > term)] : (? [X98 : subst,X97 : term,X96 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) != ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ? [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) != $true) & (((X92 @ id @ X99 @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true)) & (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f53,definition,(
% 47.53/7.12 (sP37 = $true) <=> ((sP36 = $true) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | ! [X101 : term,X100 : (subst > term > subst > $o)] : (? [X103 : (subst > term > term)] : (! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) & (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) != $true) & ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106)))) | ? [X102 : term] : ((((X100 @ id @ X102 @ id)) = $true) & (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) != $true)) | (((X100 @ id @ (lam @ X101) @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f54,definition,(
% 47.53/7.12 ! [X483 : (term > $o)] : ((((sP38 @ X483)) = $true) <=> ? [X487 : term,X488 : term] : ((((X483 @ X488)) = $true) & (((X483 @ (ap @ X487 @ X488))) != $true) & (((X483 @ X487)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f55,definition,(
% 47.53/7.12 (sP39 = $true) <=> ! [X484 : term,X483 : (term > $o)] : (? [X485 : term] : ((((X483 @ (lam @ X485))) != $true) & ! [X486 : term] : ((((X483 @ X486)) != $true) | (((X483 @ (sub @ X485 @ (push @ X486 @ id)))) = $true))) | (((sP38 @ X483)) = $true) | ? [X489 : term] : ((((X483 @ X489)) != $true) & (((var @ X489)) = $true)) | (((X483 @ X484)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f56,definition,(
% 47.53/7.12 ! [X270 : (term > $o)] : ((((sP40 @ X270)) = $true) <=> ? [X275 : term,X274 : term] : ((((X270 @ X275)) = $true) & (((X270 @ (ap @ X274 @ X275))) != $true) & (((X270 @ X274)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f57,definition,(
% 47.53/7.12 (sP41 = $true) <=> ! [X268 : subst,X270 : (term > $o),X269 : term] : (? [X273 : term] : ((((var @ X273)) = $true) & (((X270 @ (sub @ X273 @ X268))) != $true)) | ? [X271 : term] : (($true != ((X270 @ (lam @ X271)))) & ! [X272 : term] : ((((X270 @ X272)) != $true) | (((X270 @ (sub @ X271 @ (push @ X272 @ id)))) = $true))) | (((sP40 @ X270)) = $true) | (((X270 @ (sub @ X269 @ X268))) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f58,definition,(
% 47.53/7.12 ! [X149 : (term > $o)] : ((((sP42 @ X149)) = $true) <=> ! [X150 : term,X151 : term] : ((((X149 @ X151)) != $true) | (((X149 @ X150)) != $true) | (((X149 @ (ap @ X151 @ X150))) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f59,definition,(
% 47.53/7.12 ! [X185 : (subst > term > subst > $o)] : ((((sP43 @ X185)) = $true) <=> ? [X197 : (subst > term > term)] : (! [X198 : term] : ((((X185 @ id @ (X197 @ id @ X198) @ id)) = $true) | (((X185 @ id @ X198 @ id)) != $true)) & ! [X200 : term,X201 : subst,X199 : subst] : (((sub @ (X197 @ X201 @ X200) @ X199)) = ((X197 @ (comp @ X201 @ X199) @ (sub @ X200 @ X199)))) & (((X185 @ id @ (lam @ (X197 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f60,definition,(
% 47.53/7.12 ! [X185 : (subst > term > subst > $o)] : ((((sP44 @ X185)) = $true) <=> ? [X190 : term,X191 : term] : ((((X185 @ id @ (ap @ (sub @ X191 @ id) @ X190) @ id)) != $true) & ($true = ((X185 @ id @ X191 @ id))) & (((X185 @ id @ X190 @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f61,definition,(
% 47.53/7.12 ! [X156 : (subst > term > subst > $o)] : ((((sP45 @ X156)) = $true) <=> ! [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) != $true) | (((X156 @ id @ X163 @ id)) != $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f62,definition,(
% 47.53/7.12 ! [X169 : (subst > term > subst > $o)] : ((((sP46 @ X169)) = $true) <=> ! [X179 : (subst > term > term)] : ((((X169 @ id @ (lam @ (X179 @ sh @ one)) @ id)) = $true) | ? [X181 : subst,X182 : subst,X183 : term] : (((X179 @ (comp @ X182 @ X181) @ (sub @ X183 @ X181))) != ((sub @ (X179 @ X182 @ X183) @ X181))) | ? [X180 : term] : ((((X169 @ id @ (X179 @ id @ X180) @ id)) != $true) & (((X169 @ id @ X180 @ id)) = $true))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f63,definition,(
% 47.53/7.12 (sP47 = $true) <=> ? [X169 : (subst > term > subst > $o),X168 : term] : (! [X177 : subst,X175 : subst,X176 : term,X174 : subst] : ((((X169 @ (comp @ X174 @ X175) @ (sub @ X176 @ X175) @ X177)) != $true) | (((X169 @ X174 @ X176 @ (comp @ X175 @ X177))) = $true)) & (((X169 @ id @ (lam @ X168) @ id)) != $true) & ! [X173 : subst,X172 : subst,X170 : subst,X171 : term] : ((((X169 @ (comp @ X170 @ X172) @ (sub @ X171 @ X172) @ X173)) = $true) | (((X169 @ X170 @ X171 @ (comp @ X172 @ X173))) != $true)) & ! [X178 : term] : ((((X169 @ id @ X178 @ id)) != $true) | (((X169 @ id @ (sub @ X168 @ (push @ X178 @ id)) @ id)) = $true)) & (((sP46 @ X169)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f64,definition,(
% 47.53/7.12 (sP48 = $true) <=> ! [X185 : (subst > term > subst > $o),X184 : term] : (? [X196 : term] : (($true = ((var @ (sub @ X196 @ id)))) & (((X185 @ id @ X196 @ id)) != $true)) | (((sP44 @ X185)) = $true) | ? [X188 : term,X186 : subst,X187 : subst,X189 : subst] : ((((X185 @ (comp @ X186 @ X187) @ (sub @ X188 @ X187) @ X189)) = $true) & (((X185 @ X186 @ X188 @ (comp @ X187 @ X189))) != $true)) | (((sP43 @ X185)) = $true) | (((X185 @ id @ X184 @ id)) = $true) | ? [X193 : term,X192 : subst,X194 : subst,X195 : subst] : ((((X185 @ (comp @ X192 @ X194) @ (sub @ X193 @ X194) @ X195)) != $true) & (((X185 @ X192 @ X193 @ (comp @ X194 @ X195))) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f65,definition,(
% 47.53/7.12 (sP49 = $true) <=> ? [X149 : (term > $o),X148 : term] : ((((X149 @ X148)) != $true) & (((sP42 @ X149)) = $true) & ! [X154 : term] : ((((X149 @ X154)) = $true) | (((var @ X154)) != $true)) & ! [X152 : term] : ((((X149 @ (lam @ X152))) = $true) | ? [X153 : term] : ((((X149 @ (sub @ X152 @ (push @ X153 @ id)))) != $true) & (((X149 @ X153)) = $true))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f66,definition,(
% 47.53/7.12 (sP50 = $true) <=> ((sP47 = $true) | ? [X155 : term,X156 : (subst > term > subst > $o),X157 : term] : ((((X156 @ id @ X157 @ id)) = $true) & ! [X160 : term,X161 : subst,X159 : subst,X158 : subst] : ((((X156 @ X159 @ X160 @ (comp @ X161 @ X158))) != $true) | (((X156 @ (comp @ X159 @ X161) @ (sub @ X160 @ X161) @ X158)) = $true)) & (((X156 @ id @ X155 @ id)) = $true) & (((X156 @ id @ (ap @ X157 @ X155) @ id)) != $true) & ! [X167 : subst,X166 : term,X165 : subst,X164 : subst] : ((((X156 @ (comp @ X167 @ X164) @ (sub @ X166 @ X164) @ X165)) != $true) | (((X156 @ X167 @ X166 @ (comp @ X164 @ X165))) = $true)) & (((sP45 @ X156)) = $true)) | (sP48 = $true) | (sP49 = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f67,definition,(
% 47.53/7.12 ! [X82 : (subst > term > subst > $o)] : ((((sP51 @ X82)) = $true) <=> ? [X86 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X86 @ sh @ one)) @ id)) != $true) & ! [X87 : term] : ((((X82 @ id @ X87 @ id)) != $true) | (((X82 @ id @ (X86 @ id @ X87) @ id)) = $true)) & ! [X90 : subst,X89 : subst,X88 : term] : (((sub @ (X86 @ X89 @ X88) @ X90)) = ((X86 @ (comp @ X89 @ X90) @ (sub @ X88 @ X90))))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f68,definition,(
% 47.53/7.12 ! [X449 : (term > $o)] : ((((sP52 @ X449)) = $true) <=> ? [X454 : term,X455 : term] : ((((X449 @ (ap @ X454 @ X455))) != $true) & (((X449 @ X455)) = $true) & (((X449 @ X454)) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f69,definition,(
% 47.53/7.12 ! [X443 : (term > $o)] : ((((sP53 @ X443)) = $true) <=> ! [X444 : term,X445 : term] : ((((X443 @ X445)) != $true) | (((X443 @ X444)) != $true) | (((X443 @ (ap @ X445 @ X444))) = $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f70,definition,(
% 47.53/7.12 (sP54 = $true) <=> ! [X450 : subst,X449 : (term > $o),X448 : term] : (? [X451 : term] : (! [X452 : term] : ((((X449 @ (sub @ X451 @ (push @ X452 @ id)))) = $true) | (((X449 @ X452)) != $true)) & (((X449 @ (lam @ X451))) != $true)) | ? [X453 : term] : ((((X449 @ (sub @ X453 @ X450))) != $true) & (((var @ X453)) = $true)) | (((X449 @ (sub @ X448 @ X450))) = $true) | (((sP52 @ X449)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f71,definition,(
% 47.53/7.12 (sP55 = $true) <=> (? [X442 : term,X443 : (term > $o)] : ((((X443 @ X442)) != $true) & ! [X446 : term] : ((((X443 @ X446)) = $true) | (((var @ X446)) != $true)) & (((sP53 @ X443)) = $true) & ! [X447 : term] : ((((X443 @ (lam @ X447))) = $true) | (((X443 @ X447)) != $true))) | (sP54 = $true) | ? [X438 : term,X437 : subst] : (((sub @ one @ (push @ X438 @ X437))) != X438) | ? [X441 : subst] : (((comp @ X441 @ id)) != X441) | ? [X440 : subst,X439 : term] : (((comp @ sh @ (push @ X439 @ X440))) != X440))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f72,definition,(
% 47.53/7.12 ! [X243 : (subst > term > subst > $o)] : ((((sP56 @ X243)) = $true) <=> ? [X246 : (subst > term > term)] : (! [X247 : term] : ((((X243 @ id @ (X246 @ id @ X247) @ id)) = $true) | (((X243 @ id @ X247 @ id)) != $true)) & ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X246 @ X248 @ X249) @ X250)) = ((X246 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) & (((X243 @ id @ (lam @ (X246 @ sh @ one)) @ id)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f73,definition,(
% 47.53/7.12 ! [X225 : (term > $o)] : ((((sP57 @ X225)) = $true) <=> ! [X226 : term,X227 : term] : ((((X225 @ (ap @ X226 @ X227))) = $true) | (((X225 @ X226)) != $true) | ($true != ((X225 @ X227)))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f74,definition,(
% 47.53/7.12 (sP58 = $true) <=> ? [X232 : (subst > term > subst > $o),X233 : term,X234 : (term > $o)] : (! [X235 : (subst > term > term)] : (? [X237 : subst,X238 : subst,X236 : term] : (((X235 @ (comp @ X238 @ X237) @ (sub @ X236 @ X237))) != ((sub @ (X235 @ X238 @ X236) @ X237))) | ? [X239 : term] : ((((X232 @ id @ (X235 @ id @ X239) @ id)) != $true) & (((X232 @ id @ X239 @ id)) = $true)) | (((X232 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true)) & ! [X240 : term] : (((X234 @ X240)) = ((X232 @ id @ X240 @ id))) & (((X234 @ (lam @ X233))) != $true) & ! [X241 : term] : ((((X234 @ (sub @ X233 @ (push @ X241 @ id)))) = $true) | (((X234 @ X241)) != $true)))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f75,definition,(
% 47.53/7.12 (sP59 = $true) <=> ? [X224 : term,X225 : (term > $o)] : (! [X230 : term] : ((((var @ X230)) != $true) | (((X225 @ X230)) = $true)) & (((sP57 @ X225)) = $true) & ! [X228 : term] : (? [X229 : term] : ((((X225 @ X229)) = $true) & (((X225 @ (sub @ X228 @ (push @ X229 @ id)))) != $true)) | (((X225 @ (lam @ X228))) = $true)) & (((X225 @ X224)) != $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f76,definition,(
% 47.53/7.12 (sP60 = $true) <=> ((sP58 = $true) | (sP59 = $true) | ! [X242 : term,X243 : (subst > term > subst > $o)] : ((((X243 @ id @ X242 @ id)) = $true) | ? [X245 : term,X244 : term] : ((((X243 @ id @ X245 @ id)) = $true) & ($true != ((X243 @ id @ (ap @ (sub @ X244 @ id) @ X245) @ id))) & (((X243 @ id @ X244 @ id)) = $true)) | (((sP56 @ X243)) = $true)) | ? [X231 : term] : (((sub @ X231 @ id)) != X231) | ? [X221 : (subst > term > subst > $o)] : ! [X222 : (term > $o)] : ? [X223 : term] : (((X221 @ id @ X223 @ id)) != ((X222 @ X223))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f77,definition,(
% 47.53/7.12 (sP61 = $true) <=> (! [X124 : (subst > term > subst > $o),X123 : (term > $o),X122 : term] : (? [X126 : term] : ((((X123 @ (sub @ X122 @ (push @ X126 @ id)))) != $true) & (((X123 @ X126)) = $true)) | (((X123 @ (lam @ X122))) = $true) | ? [X125 : term] : (((X124 @ id @ X125 @ id)) != ((X123 @ X125))) | ? [X127 : (subst > term > term)] : (! [X131 : term] : (($true != ((X124 @ id @ X131 @ id))) | ($true = ((X124 @ id @ (X127 @ id @ X131) @ id)))) & (((X124 @ id @ (lam @ (X127 @ sh @ one)) @ id)) != $true) & ! [X129 : subst,X128 : subst,X130 : term] : (((sub @ (X127 @ X128 @ X130) @ X129)) = ((X127 @ (comp @ X128 @ X129) @ (sub @ X130 @ X129)))))) | ? [X121 : term] : (((sub @ X121 @ id)) != X121) | ? [X117 : term] : ! [X118 : (subst > term > term)] : ? [X120 : subst,X119 : term] : (((sub @ X117 @ (push @ X119 @ X120))) != ((X118 @ X120 @ X119))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 47.53/7.12 thf(f78,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & ((? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ? [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) != X253) | ! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) <=> ! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((laminj = $true) <=> ! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491))) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) <=> (apinj2 = $true)) & ((axshiftcons = $true) <=> ! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360)) & ((sP61 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((sP60 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((sP55 = $true) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) | ? [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true) & (((X82 @ id @ X85 @ id)) = $true)) | (((sP51 @ X82)) = $true))) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) <=> (shinj = $true)) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) <=> (axidr = $true)) & (axabs = $true) & ((hoasinduction_lthm = $true) <=> (sP50 = $true)) & ((induction2lem = $true) <=> (sP41 = $true)) & (ulamvarind = $true) & ((termmset_lthm = $true) <=> (? [X260 : term] : (((sub @ X260 @ id)) != X260) | ! [X261 : term] : (((sub @ X261 @ id)) = X261))) & ! [X116 : d_term] : (d_one = X116) & ((sP39 = $true) <=> (induction2 = $true)) & ((sP37 = $true) <=> (hoasinduction_lem3a_lthm = $true)) & ((sP35 = $true) <=> (hoasinduction_lem2v2 = $true)) & ((hoaslaminj = $true) <=> ! [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ? [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) != ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | ? [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) != ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139))))) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) <=> (apinj1 = $true)) & ((? [X276 : term] : (((sub @ X276 @ id)) != X276) | ? [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) = ((ap @ X280 @ X277))) & (X279 != X280)) | ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282))))) <=> (hoasapinj1_lthm = $true)) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) <=> ! [X290 : term] : ? [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) = ((X291 @ sh @ one)))) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X358 : d_term,X359 : d_term] : ((X358 = X359) | (((d2term @ X358)) != ((d2term @ X359)))) & ((hoasapinj2_lthm = $true) <=> (? [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 != X519) & (((ap @ X516 @ X517)) = ((ap @ X518 @ X519)))) | ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)))) & ((axvarcons = $true) <=> ! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510)) & (pushprop_lem3v2 = $true) & ((sP33 = $true) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X336 : term] : ? [X337 : (subst > term > term)] : ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axvarid = $true) <=> ! [X327 : term] : (((sub @ X327 @ id)) = X327)) & ! [X4 : d_subst] : (d_id = X4) & ((hoasinduction_lem0_lthm = $true) <=> ! [X492 : (subst > term > subst > $o)] : ? [X493 : (term > $o)] : ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494)))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) != X396) | ! [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) = $true) | (((X398 @ X399)) != $true) | ? [X402 : term] : (((X401 @ X402)) != ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & (apnotvar = $true) & (pushprop_gthm = $true) & (! [X318 : subst,X320 : term,X319 : (term > $o)] : ? [X321 : (term > $o)] : ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))) <=> (pushprop_lem0 = $true)) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) <=> (axidl = $true)) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & ((substmonoid = $true) <=> (! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP31 = $true)) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) <=> (axscons = $true)) & ((sP30 = $true) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X344 : (term > $o),X343 : term,X345 : subst] : ? [X346 : (term > $o)] : ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP28 = $true)) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3a = $true) <=> (sP26 = $true)) & (hoasapnotvar_lthm = $true) & ((induction = $true) <=> ! [X263 : term,X262 : (term > $o)] : ((((sP25 @ X262)) = $true) | (((X262 @ X263)) = $true) | ? [X267 : term] : ((((X262 @ X267)) != $true) & (((var @ X267)) = $true)) | ? [X266 : term] : ((((X262 @ X266)) = $true) & (((X262 @ (lam @ X266))) != $true)))) & ((hoasapinj2 = $true) <=> ! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331))))) & ((substmonoid_lthm = $true) <=> ((! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)) | ? [X476 : subst] : (((comp @ id @ X476)) != X476) | ? [X477 : subst] : (((comp @ X477 @ id)) != X477))) & ((sP24 = $true) <=> (hoasinduction_lem3aa = $true)) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & ((sP23 = $true) <=> (hoaslaminj_lthm = $true)) & ((sP22 = $true) <=> (hoasinduction_lem3aaa = $true)) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X480 : (subst > term > subst > $o)] : ? [X481 : (term > $o)] : ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction = $true) <=> (sP21 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) = $true) | (((X434 @ X432)) != $true) | ? [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) != ((X433 @ X436))))) & ((hoasinduction_lem3_lthm = $true) <=> (sP18 = $true)) & ((hoasinduction_lthm_3 = $true) <=> (sP15 = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X334 : term] : ? [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) = ((X335 @ sh @ one)))) & ((hoasinduction_lem3v2a = $true) <=> (sP9 = $true)) & ! [X80 : d_subst,X79 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj1 = $true) <=> ! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133))))) & ((hoaslamnotap = $true) <=> ! [X5 : (subst > term > term),X6 : term,X7 : term] : (? [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((sP8 = $true) <=> (hoasinduction_lem2 = $true)) & (axmap = $true) & ((induction2_lthm = $true) <=> (sP6 = $true)) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X512 : term] : ? [X513 : (subst > term > term)] : ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514))))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(definition_folding,[],[f14,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19])).
% 47.53/7.12 thf(f79,plain,(
% 47.53/7.12 ((sP2 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) != $true) | (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) = $true)) & ! [X9 : term] : (($true = ((X0 @ id @ X9 @ id))) | (((hoasvar @ id @ X9 @ id)) != $true)) & ? [X17 : term] : (((X0 @ id @ X17 @ id)) != $true) & (((sP1 @ X0)) != $true) & ! [X7 : subst,X6 : term,X8 : subst,X5 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) != $true) | (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) = $true)) & (((sP0 @ X0)) != $true))) & (! [X0 : (subst > term > subst > $o)] : (? [X4 : term,X1 : subst,X3 : subst,X2 : subst] : ((((X0 @ X1 @ X4 @ (comp @ X2 @ X3))) = $true) & (((X0 @ (comp @ X1 @ X2) @ (sub @ X4 @ X2) @ X3)) != $true)) | ? [X9 : term] : (($true != ((X0 @ id @ X9 @ id))) & (((hoasvar @ id @ X9 @ id)) = $true)) | ! [X17 : term] : (((X0 @ id @ X17 @ id)) = $true) | (((sP1 @ X0)) = $true) | ? [X7 : subst,X6 : term,X8 : subst,X5 : subst] : ((((X0 @ (comp @ X5 @ X7) @ (sub @ X6 @ X7) @ X8)) = $true) & (((X0 @ X5 @ X6 @ (comp @ X7 @ X8))) != $true)) | (((sP0 @ X0)) = $true)) | (sP2 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f17])).
% 47.53/7.12 thf(f80,plain,(
% 47.53/7.12 ((sP2 = $true) | ? [X0 : (subst > term > subst > $o)] : (! [X1 : term,X2 : subst,X3 : subst,X4 : subst] : ((((X0 @ X2 @ X1 @ (comp @ X4 @ X3))) != $true) | ($true = ((X0 @ (comp @ X2 @ X4) @ (sub @ X1 @ X4) @ X3)))) & ! [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) | (((hoasvar @ id @ X5 @ id)) != $true)) & ? [X6 : term] : (((X0 @ id @ X6 @ id)) != $true) & (((sP1 @ X0)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((X0 @ (comp @ X10 @ X7) @ (sub @ X8 @ X7) @ X9)) != $true) | (((X0 @ X10 @ X8 @ (comp @ X7 @ X9))) = $true)) & (((sP0 @ X0)) != $true))) & (! [X11 : (subst > term > subst > $o)] : (? [X12 : term,X13 : subst,X14 : subst,X15 : subst] : ((((X11 @ X13 @ X12 @ (comp @ X15 @ X14))) = $true) & (((X11 @ (comp @ X13 @ X15) @ (sub @ X12 @ X15) @ X14)) != $true)) | ? [X16 : term] : ((((X11 @ id @ X16 @ id)) != $true) & (((hoasvar @ id @ X16 @ id)) = $true)) | ! [X17 : term] : (((X11 @ id @ X17 @ id)) = $true) | (((sP1 @ X11)) = $true) | ? [X18 : subst,X19 : term,X20 : subst,X21 : subst] : ((((X11 @ (comp @ X21 @ X18) @ (sub @ X19 @ X18) @ X20)) = $true) & (((X11 @ X21 @ X19 @ (comp @ X18 @ X20))) != $true)) | (((sP0 @ X11)) = $true)) | (sP2 != $true))),
% 47.53/7.12 inference(rectify,[],[f79])).
% 47.53/7.12 thf(f81,plain,(
% 47.53/7.12 ((sP2 = $true) | (! [X1 : term,X2 : subst,X3 : subst,X4 : subst] : ((((sK62 @ X2 @ X1 @ (comp @ X4 @ X3))) != $true) | (((sK62 @ (comp @ X2 @ X4) @ (sub @ X1 @ X4) @ X3)) = $true)) & ! [X5 : term] : ((((sK62 @ id @ X5 @ id)) = $true) | (((hoasvar @ id @ X5 @ id)) != $true)) & (((sK62 @ id @ sK63 @ id)) != $true) & (((sP1 @ sK62)) != $true) & ! [X7 : subst,X8 : term,X9 : subst,X10 : subst] : ((((sK62 @ (comp @ X10 @ X7) @ (sub @ X8 @ X7) @ X9)) != $true) | (((sK62 @ X10 @ X8 @ (comp @ X7 @ X9))) = $true)) & (((sP0 @ sK62)) != $true))) & (! [X11 : (subst > term > subst > $o)] : (((((X11 @ (sK65 @ X11) @ (sK64 @ X11) @ (comp @ (sK67 @ X11) @ (sK66 @ X11)))) = $true) & (((X11 @ (comp @ (sK65 @ X11) @ (sK67 @ X11)) @ (sub @ (sK64 @ X11) @ (sK67 @ X11)) @ (sK66 @ X11))) != $true)) | (($true != ((X11 @ id @ (sK68 @ X11) @ id))) & (((hoasvar @ id @ (sK68 @ X11) @ id)) = $true)) | ! [X17 : term] : (((X11 @ id @ X17 @ id)) = $true) | (((sP1 @ X11)) = $true) | ((((X11 @ (comp @ (sK72 @ X11) @ (sK69 @ X11)) @ (sub @ (sK70 @ X11) @ (sK69 @ X11)) @ (sK71 @ X11))) = $true) & (((X11 @ (sK72 @ X11) @ (sK70 @ X11) @ (comp @ (sK69 @ X11) @ (sK71 @ X11)))) != $true)) | (((sP0 @ X11)) = $true)) | (sP2 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK62),skolemize(X6,sK63),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f80])).
% 47.53/7.12 thf(f85,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X12 : (subst > term > term)] : (? [X16 : term] : ((((X0 @ id @ X16 @ id)) = $true) & (((X0 @ id @ (X12 @ id @ X16) @ id)) != $true)) | ? [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) != ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) = $true))) & (? [X12 : (subst > term > term)] : (! [X16 : term] : ((((X0 @ id @ X16 @ id)) != $true) | (((X0 @ id @ (X12 @ id @ X16) @ id)) = $true)) & ! [X15 : term,X13 : subst,X14 : subst] : (((sub @ (X12 @ X14 @ X15) @ X13)) = ((X12 @ (comp @ X14 @ X13) @ (sub @ X15 @ X13)))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X12 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP0 @ X0)) != $true)))),
% 47.53/7.12 inference(nnf_transformation,[],[f15])).
% 47.53/7.12 thf(f86,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (? [X2 : term] : ((((X0 @ id @ X2 @ id)) = $true) & (((X0 @ id @ (X1 @ id @ X2) @ id)) != $true)) | ? [X3 : term,X4 : subst,X5 : subst] : (((sub @ (X1 @ X5 @ X3) @ X4)) != ((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4)))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true))) & (? [X6 : (subst > term > term)] : (! [X7 : term] : ((((X0 @ id @ X7 @ id)) != $true) | (((X0 @ id @ (X6 @ id @ X7) @ id)) = $true)) & ! [X8 : term,X9 : subst,X10 : subst] : (((X6 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9))) = ((sub @ (X6 @ X10 @ X8) @ X9))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X6 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP0 @ X0)) != $true)))),
% 47.53/7.12 inference(rectify,[],[f85])).
% 47.53/7.12 thf(f87,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP0 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (((((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true) & (((X0 @ id @ (X1 @ id @ (sK75 @ X1 @ X0)) @ id)) != $true)) | (((X1 @ (comp @ (sK78 @ X1) @ (sK77 @ X1)) @ (sub @ (sK76 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK78 @ X1) @ (sK76 @ X1)) @ (sK77 @ X1)))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true))) & ((! [X7 : term] : ((((X0 @ id @ X7 @ id)) != $true) | (((X0 @ id @ (sK79 @ X0 @ id @ X7) @ id)) = $true)) & ! [X8 : term,X9 : subst,X10 : subst] : (((sub @ (sK79 @ X0 @ X10 @ X8) @ X9)) = ((sK79 @ X0 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9)))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK79 @ X0 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP0 @ X0)) != $true)))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f86])).
% 47.53/7.12 thf(f88,plain,(
% 47.53/7.12 ((hoasinduction != $true) | (sP2 != $true)) & ((hoasinduction = $true) | (sP2 = $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f18])).
% 47.53/7.12 thf(f141,plain,(
% 47.53/7.12 ! [X156 : (subst > term > subst > $o)] : (((((sP45 @ X156)) = $true) | ? [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) = $true) & (((X156 @ id @ X163 @ id)) = $true) & (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) != $true))) & (! [X163 : term,X162 : term] : ((((X156 @ id @ X162 @ id)) != $true) | (((X156 @ id @ X163 @ id)) != $true) | (((X156 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)) = $true)) | (((sP45 @ X156)) != $true)))),
% 47.53/7.12 inference(nnf_transformation,[],[f61])).
% 47.53/7.12 thf(f142,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP45 @ X0)) = $true) | ? [X1 : term,X2 : term] : ((((X0 @ id @ X2 @ id)) = $true) & (((X0 @ id @ X1 @ id)) = $true) & (((X0 @ id @ (ap @ (sub @ X1 @ id) @ X2) @ id)) != $true))) & (! [X3 : term,X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ X3 @ id)) != $true) | (((X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) = $true)) | (((sP45 @ X0)) != $true)))),
% 47.53/7.12 inference(rectify,[],[f141])).
% 47.53/7.12 thf(f143,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP45 @ X0)) = $true) | ((((X0 @ id @ (sK193 @ X0) @ id)) = $true) & (((X0 @ id @ (sK192 @ X0) @ id)) = $true) & (((X0 @ id @ (ap @ (sub @ (sK192 @ X0) @ id) @ (sK193 @ X0)) @ id)) != $true))) & (! [X3 : term,X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ X3 @ id)) != $true) | (((X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) = $true)) | (((sP45 @ X0)) != $true)))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f142])).
% 47.53/7.12 thf(f165,plain,(
% 47.53/7.12 ((sP37 = $true) | ((sP36 != $true) & ! [X91 : term] : (((sub @ X91 @ id)) = X91) & ? [X101 : term,X100 : (subst > term > subst > $o)] : (! [X103 : (subst > term > term)] : (? [X107 : term] : ((((X100 @ id @ X107 @ id)) = $true) & (((X100 @ id @ (X103 @ id @ X107) @ id)) != $true)) | (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true) | ? [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) != ((sub @ (X103 @ X104 @ X105) @ X106)))) & ! [X102 : term] : ((((X100 @ id @ X102 @ id)) != $true) | (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) = $true)) & (((X100 @ id @ (lam @ X101) @ id)) != $true)))) & (((sP36 = $true) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | ! [X101 : term,X100 : (subst > term > subst > $o)] : (? [X103 : (subst > term > term)] : (! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) & (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) != $true) & ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106)))) | ? [X102 : term] : ((((X100 @ id @ X102 @ id)) = $true) & (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) != $true)) | (((X100 @ id @ (lam @ X101) @ id)) = $true))) | (sP37 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f53])).
% 47.53/7.12 thf(f166,plain,(
% 47.53/7.12 ((sP37 = $true) | ((sP36 != $true) & ! [X91 : term] : (((sub @ X91 @ id)) = X91) & ? [X101 : term,X100 : (subst > term > subst > $o)] : (! [X103 : (subst > term > term)] : (? [X107 : term] : ((((X100 @ id @ X107 @ id)) = $true) & (((X100 @ id @ (X103 @ id @ X107) @ id)) != $true)) | (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) = $true) | ? [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) != ((sub @ (X103 @ X104 @ X105) @ X106)))) & ! [X102 : term] : ((((X100 @ id @ X102 @ id)) != $true) | (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) = $true)) & (((X100 @ id @ (lam @ X101) @ id)) != $true)))) & ((sP36 = $true) | ? [X91 : term] : (((sub @ X91 @ id)) != X91) | ! [X101 : term,X100 : (subst > term > subst > $o)] : (? [X103 : (subst > term > term)] : (! [X107 : term] : ((((X100 @ id @ X107 @ id)) != $true) | (((X100 @ id @ (X103 @ id @ X107) @ id)) = $true)) & (((X100 @ id @ (lam @ (X103 @ sh @ one)) @ id)) != $true) & ! [X104 : subst,X106 : subst,X105 : term] : (((X103 @ (comp @ X104 @ X106) @ (sub @ X105 @ X106))) = ((sub @ (X103 @ X104 @ X105) @ X106)))) | ? [X102 : term] : ((((X100 @ id @ X102 @ id)) = $true) & (((X100 @ id @ (sub @ X101 @ (push @ X102 @ id)) @ id)) != $true)) | (((X100 @ id @ (lam @ X101) @ id)) = $true)) | (sP37 != $true))),
% 47.53/7.12 inference(flattening,[],[f165])).
% 47.53/7.12 thf(f167,plain,(
% 47.53/7.12 ((sP37 = $true) | ((sP36 != $true) & ! [X0 : term] : (((sub @ X0 @ id)) = X0) & ? [X1 : term,X2 : (subst > term > subst > $o)] : (! [X3 : (subst > term > term)] : (? [X4 : term] : ((((X2 @ id @ X4 @ id)) = $true) & (((X2 @ id @ (X3 @ id @ X4) @ id)) != $true)) | (((X2 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | ? [X5 : subst,X6 : subst,X7 : term] : (((X3 @ (comp @ X5 @ X6) @ (sub @ X7 @ X6))) != ((sub @ (X3 @ X5 @ X7) @ X6)))) & ! [X8 : term] : ((((X2 @ id @ X8 @ id)) != $true) | (((X2 @ id @ (sub @ X1 @ (push @ X8 @ id)) @ id)) = $true)) & (((X2 @ id @ (lam @ X1) @ id)) != $true)))) & ((sP36 = $true) | ? [X9 : term] : (((sub @ X9 @ id)) != X9) | ! [X10 : term,X11 : (subst > term > subst > $o)] : (? [X12 : (subst > term > term)] : (! [X13 : term] : ((((X11 @ id @ X13 @ id)) != $true) | ($true = ((X11 @ id @ (X12 @ id @ X13) @ id)))) & (((X11 @ id @ (lam @ (X12 @ sh @ one)) @ id)) != $true) & ! [X14 : subst,X15 : subst,X16 : term] : (((X12 @ (comp @ X14 @ X15) @ (sub @ X16 @ X15))) = ((sub @ (X12 @ X14 @ X16) @ X15)))) | ? [X17 : term] : ((((X11 @ id @ X17 @ id)) = $true) & (((X11 @ id @ (sub @ X10 @ (push @ X17 @ id)) @ id)) != $true)) | (((X11 @ id @ (lam @ X10) @ id)) = $true)) | (sP37 != $true))),
% 47.53/7.12 inference(rectify,[],[f166])).
% 47.53/7.12 thf(f168,plain,(
% 47.53/7.12 ((sP37 = $true) | ((sP36 != $true) & ! [X0 : term] : (((sub @ X0 @ id)) = X0) & (! [X3 : (subst > term > term)] : (((((sK219 @ id @ (sK220 @ X3) @ id)) = $true) & (((sK219 @ id @ (X3 @ id @ (sK220 @ X3)) @ id)) != $true)) | (((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sub @ (X3 @ (sK221 @ X3) @ (sK223 @ X3)) @ (sK222 @ X3))) != ((X3 @ (comp @ (sK221 @ X3) @ (sK222 @ X3)) @ (sub @ (sK223 @ X3) @ (sK222 @ X3)))))) & ! [X8 : term] : ((((sK219 @ id @ X8 @ id)) != $true) | (((sK219 @ id @ (sub @ sK218 @ (push @ X8 @ id)) @ id)) = $true)) & (((sK219 @ id @ (lam @ sK218) @ id)) != $true)))) & ((sP36 = $true) | (((sub @ sK224 @ id)) != sK224) | ! [X10 : term,X11 : (subst > term > subst > $o)] : ((! [X13 : term] : ((((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ (sK225 @ X11 @ id @ X13) @ id)) = $true)) & (((X11 @ id @ (lam @ (sK225 @ X11 @ sh @ one)) @ id)) != $true) & ! [X14 : subst,X15 : subst,X16 : term] : (((sK225 @ X11 @ (comp @ X14 @ X15) @ (sub @ X16 @ X15))) = ((sub @ (sK225 @ X11 @ X14 @ X16) @ X15)))) | ((((X11 @ id @ (sK226 @ X11 @ X10) @ id)) = $true) & (((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true)) | (((X11 @ id @ (lam @ X10) @ id)) = $true)) | (sP37 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK218,sK219,vAPP,vAPP,vAPP,vAPP,sK224,vAPP,vAPP]),skolemize(X1,sK218),skolemize(X2,sK219),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X9,sK224),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f167])).
% 47.53/7.12 thf(f169,plain,(
% 47.53/7.12 ((sP36 = $true) | ! [X92 : (subst > term > subst > $o),X93 : term] : (? [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) != $true) & (((X92 @ id @ X94 @ id)) = $true)) | ? [X95 : (subst > term > term)] : (! [X98 : subst,X97 : term,X96 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) = ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) & ! [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) = $true) | (((X92 @ id @ X99 @ id)) != $true)) & (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) != $true)) | (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) = $true))) & (? [X92 : (subst > term > subst > $o),X93 : term] : (! [X94 : term] : ((((X92 @ id @ (sub @ X93 @ (push @ X94 @ id)) @ id)) = $true) | (((X92 @ id @ X94 @ id)) != $true)) & ! [X95 : (subst > term > term)] : (? [X98 : subst,X97 : term,X96 : subst] : (((sub @ (X95 @ X96 @ X97) @ X98)) != ((X95 @ (comp @ X96 @ X98) @ (sub @ X97 @ X98)))) | ? [X99 : term] : ((((X92 @ id @ (X95 @ id @ X99) @ id)) != $true) & (((X92 @ id @ X99 @ id)) = $true)) | (((X92 @ id @ (lam @ (X95 @ sh @ one)) @ id)) = $true)) & (((X92 @ id @ (lam @ (sub @ X93 @ (push @ one @ sh))) @ id)) != $true)) | (sP36 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f52])).
% 47.53/7.12 thf(f170,plain,(
% 47.53/7.12 ((sP36 = $true) | ! [X0 : (subst > term > subst > $o),X1 : term] : (? [X2 : term] : ((((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)) != $true) & (((X0 @ id @ X2 @ id)) = $true)) | ? [X3 : (subst > term > term)] : (! [X4 : subst,X5 : term,X6 : subst] : (((sub @ (X3 @ X6 @ X5) @ X4)) = ((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4)))) & ! [X7 : term] : ((((X0 @ id @ (X3 @ id @ X7) @ id)) = $true) | (((X0 @ id @ X7 @ id)) != $true)) & (((X0 @ id @ (lam @ (X3 @ sh @ one)) @ id)) != $true)) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true))) & (? [X8 : (subst > term > subst > $o),X9 : term] : (! [X10 : term] : ((((X8 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)) = $true) | (((X8 @ id @ X10 @ id)) != $true)) & ! [X11 : (subst > term > term)] : (? [X12 : subst,X13 : term,X14 : subst] : (((X11 @ (comp @ X14 @ X12) @ (sub @ X13 @ X12))) != ((sub @ (X11 @ X14 @ X13) @ X12))) | ? [X15 : term] : ((((X8 @ id @ (X11 @ id @ X15) @ id)) != $true) & (((X8 @ id @ X15 @ id)) = $true)) | (((X8 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true)) & (((X8 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id)) != $true)) | (sP36 != $true))),
% 47.53/7.12 inference(rectify,[],[f169])).
% 47.53/7.12 thf(f171,plain,(
% 47.53/7.12 ((sP36 = $true) | ! [X0 : (subst > term > subst > $o),X1 : term] : ((($true != ((X0 @ id @ (sub @ X1 @ (push @ (sK227 @ X1 @ X0) @ id)) @ id))) & (((X0 @ id @ (sK227 @ X1 @ X0) @ id)) = $true)) | (! [X4 : subst,X5 : term,X6 : subst] : (((sK228 @ X0 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4))) = ((sub @ (sK228 @ X0 @ X6 @ X5) @ X4))) & ! [X7 : term] : ((((X0 @ id @ (sK228 @ X0 @ id @ X7) @ id)) = $true) | (((X0 @ id @ X7 @ id)) != $true)) & (((X0 @ id @ (lam @ (sK228 @ X0 @ sh @ one)) @ id)) != $true)) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true))) & ((! [X10 : term] : ((((sK229 @ id @ (sub @ sK230 @ (push @ X10 @ id)) @ id)) = $true) | (((sK229 @ id @ X10 @ id)) != $true)) & ! [X11 : (subst > term > term)] : ((((X11 @ (comp @ (sK233 @ X11) @ (sK231 @ X11)) @ (sub @ (sK232 @ X11) @ (sK231 @ X11)))) != ((sub @ (X11 @ (sK233 @ X11) @ (sK232 @ X11)) @ (sK231 @ X11)))) | ((((sK229 @ id @ (X11 @ id @ (sK234 @ X11)) @ id)) != $true) & (((sK229 @ id @ (sK234 @ X11) @ id)) = $true)) | (((sK229 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true)) & (((sK229 @ id @ (lam @ (sub @ sK230 @ (push @ one @ sh))) @ id)) != $true)) | (sP36 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK229,sK230,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X8,sK229),skolemize(X9,sK230),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f170])).
% 47.53/7.12 thf(f200,plain,(
% 47.53/7.12 ((sP26 = $true) | ? [X108 : (subst > term > subst > $o),X109 : term] : (($true != ((X108 @ id @ (lam @ X109) @ id))) & ! [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) = $true) | ? [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) != $true) & (((X108 @ id @ X115 @ id)) = $true)) | ? [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) != ((sub @ (X111 @ X112 @ X114) @ X113)))) & ! [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) = $true) | (((X108 @ id @ X110 @ id)) != $true)))) & (! [X108 : (subst > term > subst > $o),X109 : term] : (($true = ((X108 @ id @ (lam @ X109) @ id))) | ? [X111 : (subst > term > term)] : ((((X108 @ id @ (lam @ (X111 @ sh @ one)) @ id)) != $true) & ! [X115 : term] : ((((X108 @ id @ (X111 @ id @ X115) @ id)) = $true) | (((X108 @ id @ X115 @ id)) != $true)) & ! [X112 : subst,X113 : subst,X114 : term] : (((X111 @ (comp @ X112 @ X113) @ (sub @ X114 @ X113))) = ((sub @ (X111 @ X112 @ X114) @ X113)))) | ? [X110 : term] : ((((X108 @ id @ (sub @ X109 @ (push @ X110 @ id)) @ id)) != $true) & (((X108 @ id @ X110 @ id)) = $true))) | (sP26 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f42])).
% 47.53/7.12 thf(f201,plain,(
% 47.53/7.12 ((sP26 = $true) | ? [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ (lam @ X1) @ id)) != $true) & ! [X2 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | ? [X3 : term] : ((((X0 @ id @ (X2 @ id @ X3) @ id)) != $true) & (((X0 @ id @ X3 @ id)) = $true)) | ? [X4 : subst,X5 : subst,X6 : term] : (((X2 @ (comp @ X4 @ X5) @ (sub @ X6 @ X5))) != ((sub @ (X2 @ X4 @ X6) @ X5)))) & ! [X7 : term] : ((((X0 @ id @ (sub @ X1 @ (push @ X7 @ id)) @ id)) = $true) | (((X0 @ id @ X7 @ id)) != $true)))) & (! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ X9) @ id)) = $true) | ? [X10 : (subst > term > term)] : ((((X8 @ id @ (lam @ (X10 @ sh @ one)) @ id)) != $true) & ! [X11 : term] : ((((X8 @ id @ (X10 @ id @ X11) @ id)) = $true) | (((X8 @ id @ X11 @ id)) != $true)) & ! [X12 : subst,X13 : subst,X14 : term] : (((sub @ (X10 @ X12 @ X14) @ X13)) = ((X10 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))))) | ? [X15 : term] : ((((X8 @ id @ (sub @ X9 @ (push @ X15 @ id)) @ id)) != $true) & (((X8 @ id @ X15 @ id)) = $true))) | (sP26 != $true))),
% 47.53/7.12 inference(rectify,[],[f200])).
% 47.53/7.12 thf(f202,plain,(
% 47.53/7.12 ((sP26 = $true) | ((((sK311 @ id @ (lam @ sK312) @ id)) != $true) & ! [X2 : (subst > term > term)] : ((((sK311 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | ((((sK311 @ id @ (X2 @ id @ (sK313 @ X2)) @ id)) != $true) & (((sK311 @ id @ (sK313 @ X2) @ id)) = $true)) | (((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2)))))) & ! [X7 : term] : ((((sK311 @ id @ (sub @ sK312 @ (push @ X7 @ id)) @ id)) = $true) | (((sK311 @ id @ X7 @ id)) != $true)))) & (! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ X9) @ id)) = $true) | ((((X8 @ id @ (lam @ (sK317 @ X8 @ sh @ one)) @ id)) != $true) & ! [X11 : term] : ((((X8 @ id @ (sK317 @ X8 @ id @ X11) @ id)) = $true) | (((X8 @ id @ X11 @ id)) != $true)) & ! [X12 : subst,X13 : subst,X14 : term] : (((sub @ (sK317 @ X8 @ X12 @ X14) @ X13)) = ((sK317 @ X8 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))))) | ((((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true) & (((X8 @ id @ (sK318 @ X9 @ X8) @ id)) = $true))) | (sP26 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK311,sK312,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK311),skolemize(X1,sK312),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f201])).
% 47.53/7.12 thf(f206,plain,(
% 47.53/7.12 ((sP24 = $true) | ? [X310 : term,X311 : (subst > term > subst > $o)] : (! [X317 : term] : ((((X311 @ id @ X317 @ id)) != $true) | (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) = $true)) & (((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) != $true) & ! [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) = $true) | ? [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) != ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | ? [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) != $true) & (((X311 @ id @ X313 @ id)) = $true))))) & (! [X310 : term,X311 : (subst > term > subst > $o)] : (? [X317 : term] : ((((X311 @ id @ X317 @ id)) = $true) & (((X311 @ id @ (sub @ X310 @ (push @ X317 @ id)) @ id)) != $true)) | (((X311 @ id @ (lam @ (sub @ X310 @ (push @ one @ sh))) @ id)) = $true) | ? [X312 : (subst > term > term)] : ((((X311 @ id @ (lam @ (X312 @ sh @ one)) @ id)) != $true) & ! [X316 : subst,X314 : term,X315 : subst] : (((sub @ (X312 @ X315 @ X314) @ X316)) = ((X312 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X311 @ id @ (X312 @ id @ X313) @ id)) = $true) | (((X311 @ id @ X313 @ id)) != $true)))) | (sP24 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f40])).
% 47.53/7.12 thf(f207,plain,(
% 47.53/7.12 ((sP24 = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : (! [X2 : term] : ((((X1 @ id @ X2 @ id)) != $true) | (((X1 @ id @ (sub @ X0 @ (push @ X2 @ id)) @ id)) = $true)) & (((X1 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id)) != $true) & ! [X3 : (subst > term > term)] : ((((X1 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | ? [X4 : subst,X5 : term,X6 : subst] : (((sub @ (X3 @ X6 @ X5) @ X4)) != ((X3 @ (comp @ X6 @ X4) @ (sub @ X5 @ X4)))) | ? [X7 : term] : ((((X1 @ id @ (X3 @ id @ X7) @ id)) != $true) & (((X1 @ id @ X7 @ id)) = $true))))) & (! [X8 : term,X9 : (subst > term > subst > $o)] : (? [X10 : term] : ((((X9 @ id @ X10 @ id)) = $true) & (((X9 @ id @ (sub @ X8 @ (push @ X10 @ id)) @ id)) != $true)) | (((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | ? [X11 : (subst > term > term)] : ((((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id)) != $true) & ! [X12 : subst,X13 : term,X14 : subst] : (((X11 @ (comp @ X14 @ X12) @ (sub @ X13 @ X12))) = ((sub @ (X11 @ X14 @ X13) @ X12))) & ! [X15 : term] : ((((X9 @ id @ (X11 @ id @ X15) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true)))) | (sP24 != $true))),
% 47.53/7.12 inference(rectify,[],[f206])).
% 47.53/7.12 thf(f208,plain,(
% 47.53/7.12 ((sP24 = $true) | (! [X2 : term] : ((((sK322 @ id @ X2 @ id)) != $true) | (((sK322 @ id @ (sub @ sK321 @ (push @ X2 @ id)) @ id)) = $true)) & (((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id)) != $true) & ! [X3 : (subst > term > term)] : ((((sK322 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sub @ (X3 @ (sK325 @ X3) @ (sK324 @ X3)) @ (sK323 @ X3))) != ((X3 @ (comp @ (sK325 @ X3) @ (sK323 @ X3)) @ (sub @ (sK324 @ X3) @ (sK323 @ X3))))) | ((((sK322 @ id @ (X3 @ id @ (sK326 @ X3)) @ id)) != $true) & (((sK322 @ id @ (sK326 @ X3) @ id)) = $true))))) & (! [X8 : term,X9 : (subst > term > subst > $o)] : (((((X9 @ id @ (sK327 @ X9 @ X8) @ id)) = $true) & (((X9 @ id @ (sub @ X8 @ (push @ (sK327 @ X9 @ X8) @ id)) @ id)) != $true)) | (((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | ((((X9 @ id @ (lam @ (sK328 @ X9 @ sh @ one)) @ id)) != $true) & ! [X12 : subst,X13 : term,X14 : subst] : (((sK328 @ X9 @ (comp @ X14 @ X12) @ (sub @ X13 @ X12))) = ((sub @ (sK328 @ X9 @ X14 @ X13) @ X12))) & ! [X15 : term] : ((((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true)))) | (sP24 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK321,sK322,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK321),skolemize(X1,sK322),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f207])).
% 47.53/7.12 thf(f216,plain,(
% 47.53/7.12 ((sP21 = $true) | ? [X363 : term,X362 : (subst > term > subst > $o)] : (! [X364 : term] : ((((var @ (sub @ X364 @ id))) != $true) | (((X362 @ id @ X364 @ id)) = $true)) & ! [X365 : subst,X367 : subst,X366 : subst,X368 : term] : ((((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) = $true) | (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) != $true)) & (((sP20 @ X362)) != $true) & (((sP19 @ X362)) != $true) & ! [X376 : subst,X378 : subst,X377 : term,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) != $true) | (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) = $true)) & (((X362 @ id @ X363 @ id)) != $true))) & (! [X363 : term,X362 : (subst > term > subst > $o)] : (? [X364 : term] : ((((var @ (sub @ X364 @ id))) = $true) & (((X362 @ id @ X364 @ id)) != $true)) | ? [X365 : subst,X367 : subst,X366 : subst,X368 : term] : ((((X362 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367) @ X365)) != $true) & (((X362 @ X366 @ X368 @ (comp @ X367 @ X365))) = $true)) | (((sP20 @ X362)) = $true) | (((sP19 @ X362)) = $true) | ? [X376 : subst,X378 : subst,X377 : term,X379 : subst] : ((((X362 @ (comp @ X378 @ X376) @ (sub @ X377 @ X376) @ X379)) = $true) & (((X362 @ X378 @ X377 @ (comp @ X376 @ X379))) != $true)) | (((X362 @ id @ X363 @ id)) = $true)) | (sP21 != $true))),
% 47.53/7.12 inference(nnf_transformation,[],[f37])).
% 47.53/7.12 thf(f217,plain,(
% 47.53/7.12 ((sP21 = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : (! [X2 : term] : ((((var @ (sub @ X2 @ id))) != $true) | (((X1 @ id @ X2 @ id)) = $true)) & ! [X3 : subst,X4 : subst,X5 : subst,X6 : term] : ((((X1 @ (comp @ X5 @ X4) @ (sub @ X6 @ X4) @ X3)) = $true) | (((X1 @ X5 @ X6 @ (comp @ X4 @ X3))) != $true)) & (((sP20 @ X1)) != $true) & ($true != ((sP19 @ X1))) & ! [X7 : subst,X8 : subst,X9 : term,X10 : subst] : ((((X1 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7) @ X10)) != $true) | (((X1 @ X8 @ X9 @ (comp @ X7 @ X10))) = $true)) & ($true != ((X1 @ id @ X0 @ id))))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (? [X13 : term] : ((((var @ (sub @ X13 @ id))) = $true) & (((X12 @ id @ X13 @ id)) != $true)) | ? [X14 : subst,X15 : subst,X16 : subst,X17 : term] : ((((X12 @ (comp @ X16 @ X15) @ (sub @ X17 @ X15) @ X14)) != $true) & (((X12 @ X16 @ X17 @ (comp @ X15 @ X14))) = $true)) | (((sP20 @ X12)) = $true) | (((sP19 @ X12)) = $true) | ? [X18 : subst,X19 : subst,X20 : term,X21 : subst] : ((((X12 @ (comp @ X19 @ X18) @ (sub @ X20 @ X18) @ X21)) = $true) & (((X12 @ X19 @ X20 @ (comp @ X18 @ X21))) != $true)) | (((X12 @ id @ X11 @ id)) = $true)) | (sP21 != $true))),
% 47.53/7.12 inference(rectify,[],[f216])).
% 47.53/7.12 thf(f218,plain,(
% 47.53/7.12 ((sP21 = $true) | (! [X2 : term] : ((((var @ (sub @ X2 @ id))) != $true) | (((sK358 @ id @ X2 @ id)) = $true)) & ! [X3 : subst,X4 : subst,X5 : subst,X6 : term] : ((((sK358 @ (comp @ X5 @ X4) @ (sub @ X6 @ X4) @ X3)) = $true) | (((sK358 @ X5 @ X6 @ (comp @ X4 @ X3))) != $true)) & (((sP20 @ sK358)) != $true) & (((sP19 @ sK358)) != $true) & ! [X7 : subst,X8 : subst,X9 : term,X10 : subst] : ((((sK358 @ (comp @ X8 @ X7) @ (sub @ X9 @ X7) @ X10)) != $true) | (((sK358 @ X8 @ X9 @ (comp @ X7 @ X10))) = $true)) & (((sK358 @ id @ sK357 @ id)) != $true))) & (! [X11 : term,X12 : (subst > term > subst > $o)] : (((((var @ (sub @ (sK359 @ X12) @ id))) = $true) & (((X12 @ id @ (sK359 @ X12) @ id)) != $true)) | ((((X12 @ (comp @ (sK362 @ X12) @ (sK361 @ X12)) @ (sub @ (sK363 @ X12) @ (sK361 @ X12)) @ (sK360 @ X12))) != $true) & (((X12 @ (sK362 @ X12) @ (sK363 @ X12) @ (comp @ (sK361 @ X12) @ (sK360 @ X12)))) = $true)) | (((sP20 @ X12)) = $true) | (((sP19 @ X12)) = $true) | ((((X12 @ (comp @ (sK365 @ X12) @ (sK364 @ X12)) @ (sub @ (sK366 @ X12) @ (sK364 @ X12)) @ (sK367 @ X12))) = $true) & (((X12 @ (sK365 @ X12) @ (sK366 @ X12) @ (comp @ (sK364 @ X12) @ (sK367 @ X12)))) != $true)) | (((X12 @ id @ X11 @ id)) = $true)) | (sP21 != $true))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK357,sK358,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK357),skolemize(X1,sK358),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f217])).
% 47.53/7.12 thf(f219,plain,(
% 47.53/7.12 ! [X362 : (subst > term > subst > $o)] : (((((sP20 @ X362)) = $true) | ! [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) = $true) | ? [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) != $true) & (((X362 @ id @ X375 @ id)) = $true)) | ? [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X371 @ X372 @ X374) @ X373))))) & (? [X371 : (subst > term > term)] : ((((X362 @ id @ (lam @ (X371 @ sh @ one)) @ id)) != $true) & ! [X375 : term] : ((((X362 @ id @ (X371 @ id @ X375) @ id)) = $true) | (((X362 @ id @ X375 @ id)) != $true)) & ! [X374 : term,X373 : subst,X372 : subst] : (((X371 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X371 @ X372 @ X374) @ X373)))) | (((sP20 @ X362)) != $true)))),
% 47.53/7.12 inference(nnf_transformation,[],[f36])).
% 47.53/7.12 thf(f220,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP20 @ X0)) = $true) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ? [X2 : term] : ((((X0 @ id @ (X1 @ id @ X2) @ id)) != $true) & (((X0 @ id @ X2 @ id)) = $true)) | ? [X3 : term,X4 : subst,X5 : subst] : (((sub @ (X1 @ X5 @ X3) @ X4)) != ((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4)))))) & (? [X6 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true) & ! [X7 : term] : ((((X0 @ id @ (X6 @ id @ X7) @ id)) = $true) | (((X0 @ id @ X7 @ id)) != $true)) & ! [X8 : term,X9 : subst,X10 : subst] : (((X6 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9))) = ((sub @ (X6 @ X10 @ X8) @ X9)))) | (((sP20 @ X0)) != $true)))),
% 47.53/7.12 inference(rectify,[],[f219])).
% 47.53/7.12 thf(f221,plain,(
% 47.53/7.12 ! [X0 : (subst > term > subst > $o)] : (((((sP20 @ X0)) = $true) | ! [X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ((((X0 @ id @ (X1 @ id @ (sK368 @ X1 @ X0)) @ id)) != $true) & (((X0 @ id @ (sK368 @ X1 @ X0) @ id)) = $true)) | (((sub @ (X1 @ (sK371 @ X1) @ (sK369 @ X1)) @ (sK370 @ X1))) != ((X1 @ (comp @ (sK371 @ X1) @ (sK370 @ X1)) @ (sub @ (sK369 @ X1) @ (sK370 @ X1))))))) & (((((X0 @ id @ (lam @ (sK372 @ X0 @ sh @ one)) @ id)) != $true) & ! [X7 : term] : ((((X0 @ id @ (sK372 @ X0 @ id @ X7) @ id)) = $true) | (((X0 @ id @ X7 @ id)) != $true)) & ! [X8 : term,X9 : subst,X10 : subst] : (((sub @ (sK372 @ X0 @ X10 @ X8) @ X9)) = ((sK372 @ X0 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9))))) | (((sP20 @ X0)) != $true)))),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f220])).
% 47.53/7.12 thf(f276,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & (((? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ? [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) != X253) | ! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) = X251) & ! [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) = X253) & ? [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) != $true) & (((X259 @ X255)) = $true))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((pushprop_lem1 = $true) | ? [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) = $true) & (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) != $true))) & (! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true)) | (pushprop_lem1 != $true))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((laminj = $true) | ? [X490 : term,X491 : term] : ((((lam @ X491)) = ((lam @ X490))) & (X490 != X491))) & (! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491)) | (laminj != $true))) & ((! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 != X2) & (((ap @ X1 @ X0)) = ((ap @ X3 @ X2)))))) & (((axshiftcons = $true) | ? [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) != X360)) & (! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360) | (axshiftcons != $true))) & (((sP61 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP61 != $true))) & (((sP60 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP60 != $true))) & (((sP55 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP55 != $true))) & (((hoasinduction_no_psi_cond = $true) | ? [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) != $true) & ! [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) = $true) | (((X82 @ id @ X84 @ id)) != $true) | (((X82 @ id @ X85 @ id)) != $true)) & (((sP51 @ X82)) != $true))) & (! [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) | ? [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true) & (((X82 @ id @ X85 @ id)) = $true)) | (((sP51 @ X82)) = $true)) | (hoasinduction_no_psi_cond != $true))) & ((! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) | (shinj != $true)) & ((shinj = $true) | ? [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) = ((sub @ X323 @ sh))) & (X323 != X324)))) & ((! [X329 : subst] : (((comp @ X329 @ id)) = X329) | (axidr != $true)) & ((axidr = $true) | ? [X329 : subst] : (((comp @ X329 @ id)) != X329))) & (axabs = $true) & (((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true))) & (((induction2lem = $true) | (sP41 != $true)) & ((sP41 = $true) | (induction2lem != $true))) & (ulamvarind = $true) & (((termmset_lthm = $true) | (! [X260 : term] : (((sub @ X260 @ id)) = X260) & ? [X261 : term] : (((sub @ X261 @ id)) != X261))) & ((? [X260 : term] : (((sub @ X260 @ id)) != X260) | ! [X261 : term] : (((sub @ X261 @ id)) = X261)) | (termmset_lthm != $true))) & ! [X116 : d_term] : (d_one = X116) & (((sP39 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP39 != $true))) & (((sP37 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP37 != $true))) & (((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true))) & (((hoaslaminj = $true) | ? [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) = ((lam @ (X138 @ sh @ one)))) & ! [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) & ! [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) & (((X138 @ X141 @ X139)) != ((X140 @ X141 @ X139))))) & (! [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ? [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) != ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | ? [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) != ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139)))) | (hoaslaminj != $true))) & ((! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) = ((ap @ X14 @ X12))) & (X11 != X14)))) & (((? [X276 : term] : (((sub @ X276 @ id)) != X276) | ? [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) = ((ap @ X280 @ X277))) & (X279 != X280)) | ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282))))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X276 : term] : (((sub @ X276 @ id)) = X276) & ! [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) != ((ap @ X280 @ X277))) | (X279 = X280)) & ? [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 != X284) & (((ap @ (sub @ X284 @ id) @ X283)) = ((ap @ (sub @ X281 @ id) @ X282))))))) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & (((hoasinduction_lem3b = $true) | ? [X290 : term] : ! [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) != ((X291 @ sh @ one)))) & (! [X290 : term] : ? [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) = ((X291 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X358 : d_term,X359 : d_term] : ((X358 = X359) | (((d2term @ X358)) != ((d2term @ X359)))) & (((hoasapinj2_lthm = $true) | (! [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 = X519) | (((ap @ X516 @ X517)) != ((ap @ X518 @ X519)))) & ? [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) = ((ap @ (sub @ X522 @ id) @ X521))) & (X520 != X521)))) & ((? [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 != X519) & (((ap @ X516 @ X517)) = ((ap @ X518 @ X519)))) | ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521))) | (hoasapinj2_lthm != $true))) & (((axvarcons = $true) | ? [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) != X510)) & (! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510) | (axvarcons != $true))) & (pushprop_lem3v2 = $true) & (((sP33 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP33 != $true))) & (pushprop_lem2v2_lthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X336 : term] : ! [X337 : (subst > term > term)] : ? [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) != ((sub @ X336 @ (push @ X338 @ X339))))) & (! [X336 : term] : ? [X337 : (subst > term > term)] : ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339)))) | (hoasinduction_lem3v2_f != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((axvarid = $true) | ? [X327 : term] : (((sub @ X327 @ id)) != X327)) & (! [X327 : term] : (((sub @ X327 @ id)) = X327) | (axvarid != $true))) & ! [X4 : d_subst] : (d_id = X4) & (((hoasinduction_lem0_lthm = $true) | ? [X492 : (subst > term > subst > $o)] : ! [X493 : (term > $o)] : ? [X494 : term] : (((X492 @ id @ X494 @ id)) != ((X493 @ X494)))) & (! [X492 : (subst > term > subst > $o)] : ? [X493 : (term > $o)] : ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494))) | (hoasinduction_lem0_lthm != $true))) & (((pushprop_lem1v2_lthm = $true) | (! [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) = X396) & ? [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) != $true) & (((X398 @ X399)) = $true) & ! [X402 : term] : (((X401 @ X402)) = ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & ((? [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) != X396) | ! [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) = $true) | (((X398 @ X399)) != $true) | ? [X402 : term] : (((X401 @ X402)) != ((X398 @ (sub @ X402 @ (push @ X399 @ X400))))))) | (pushprop_lem1v2_lthm != $true))) & (apnotvar = $true) & (pushprop_gthm = $true) & ((! [X318 : subst,X320 : term,X319 : (term > $o)] : ? [X321 : (term > $o)] : ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X318 : subst,X320 : term,X319 : (term > $o)] : ! [X321 : (term > $o)] : ? [X322 : term] : (((X321 @ X322)) != ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))))) & ((! [X342 : subst] : (((comp @ id @ X342)) = X342) | (axidl != $true)) & ((axidl = $true) | ? [X342 : subst] : (((comp @ id @ X342)) != X342))) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & (((substmonoid = $true) | (? [X326 : subst] : (((comp @ id @ X326)) != X326) | ? [X325 : subst] : (((comp @ X325 @ id)) != X325))) & ((! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325)) | (substmonoid != $true))) & (((hoasinduction_lem3aa_lthm = $true) | (sP31 != $true)) & ((sP31 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & ((! [X328 : term] : (((sub @ X328 @ id)) = X328) | (termmset != $true)) & ((termmset = $true) | ? [X328 : term] : (((sub @ X328 @ id)) != X328))) & ((! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) | (axscons != $true)) & ((axscons = $true) | ? [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) != X81))) & (((sP30 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP30 != $true))) & (hoasinduction_lem2_lthm = $true) & (((pushprop_lem0_lthm = $true) | ? [X344 : (term > $o),X343 : term,X345 : subst] : ! [X346 : (term > $o)] : ? [X347 : term] : (((X346 @ X347)) != ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & (! [X344 : (term > $o),X343 : term,X345 : subst] : ? [X346 : (term > $o)] : ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345))))) | (pushprop_lem0_lthm != $true))) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & (((hoasinduction_lem3v2_lthm = $true) | (sP28 != $true)) & ((sP28 = $true) | (hoasinduction_lem3v2_lthm != $true))) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & (((hoasinduction_lem3a = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a != $true))) & (hoasapnotvar_lthm = $true) & (((induction = $true) | ? [X263 : term,X262 : (term > $o)] : ((((sP25 @ X262)) != $true) & (((X262 @ X263)) != $true) & ! [X267 : term] : ((((X262 @ X267)) = $true) | (((var @ X267)) != $true)) & ! [X266 : term] : ((((X262 @ X266)) != $true) | (((X262 @ (lam @ X266))) = $true)))) & (! [X263 : term,X262 : (term > $o)] : ((((sP25 @ X262)) = $true) | (((X262 @ X263)) = $true) | ? [X267 : term] : ((((X262 @ X267)) != $true) & (((var @ X267)) = $true)) | ? [X266 : term] : ((((X262 @ X266)) = $true) & (((X262 @ (lam @ X266))) != $true))) | (induction != $true))) & (((hoasapinj2 = $true) | ? [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 != X331) & (((ap @ (sub @ X333 @ id) @ X330)) = ((ap @ (sub @ X332 @ id) @ X331))))) & (! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331)))) | (hoasapinj2 != $true))) & (((substmonoid_lthm = $true) | ((? [X479 : subst] : (((comp @ id @ X479)) != X479) | ? [X478 : subst] : (((comp @ X478 @ id)) != X478)) & ! [X476 : subst] : (((comp @ id @ X476)) = X476) & ! [X477 : subst] : (((comp @ X477 @ id)) = X477))) & (((! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)) | ? [X476 : subst] : (((comp @ id @ X476)) != X476) | ? [X477 : subst] : (((comp @ X477 @ id)) != X477)) | (substmonoid_lthm != $true))) & (((sP24 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP24 != $true))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (((sP23 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP23 != $true))) & (((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true))) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & ((! [X480 : (subst > term > subst > $o)] : ? [X481 : (term > $o)] : ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X480 : (subst > term > subst > $o)] : ! [X481 : (term > $o)] : ? [X482 : term] : (((X481 @ X482)) != ((X480 @ id @ X482 @ id))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((hoasinduction = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction != $true))) & (((pushprop_lem1v2 = $true) | ? [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) != $true) & (((X434 @ X432)) = $true) & ! [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) = ((X433 @ X436))))) & (! [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) = $true) | (((X434 @ X432)) != $true) | ? [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) != ((X433 @ X436)))) | (pushprop_lem1v2 != $true))) & (((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true))) & (((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasinduction_lem3b_lthm = $true) | ? [X334 : term] : ! [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) != ((X335 @ sh @ one)))) & (! [X334 : term] : ? [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) = ((X335 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((hoasinduction_lem3v2a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3v2a != $true))) & ! [X80 : d_subst,X79 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((hoasapinj1 = $true) | ? [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 != X135) & (((ap @ (sub @ X135 @ id) @ X134)) = ((ap @ (sub @ X132 @ id) @ X133))))) & (! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133)))) | (hoasapinj1 != $true))) & (((hoaslamnotap = $true) | ? [X5 : (subst > term > term),X6 : term,X7 : term] : (! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8))) & (((lam @ (X5 @ sh @ one))) = ((ap @ (sub @ X6 @ id) @ X7))))) & (! [X5 : (subst > term > term),X6 : term,X7 : term] : (? [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7)))) | (hoaslamnotap != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & (((sP8 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP8 != $true))) & (axmap = $true) & (((induction2_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (induction2_lthm != $true))) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X512 : term] : ! [X513 : (subst > term > term)] : ? [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) != ((sub @ X512 @ (push @ X515 @ X514))))) & (! [X512 : term] : ? [X513 : (subst > term > term)] : ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514)))) | (hoasinduction_lem3v2_f_lthm != $true))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(nnf_transformation,[],[f78])).
% 47.53/7.12 thf(f277,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & (? [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) != X251) | ? [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) != X253) | ! [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) = $true) | (((X259 @ X255)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X252 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X252))) = X251) & ! [X254 : term,X253 : subst] : (((comp @ sh @ (push @ X254 @ X253))) = X253) & ? [X255 : term,X257 : subst,X258 : (term > $o),X259 : (term > $o),X256 : term] : ((((X258 @ (sub @ X255 @ (push @ X256 @ X257)))) != $true) & (((X259 @ X255)) = $true)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) | ? [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) = $true) & (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) != $true))) & (! [X287 : term,X285 : (term > $o),X289 : (term > $o),X288 : term,X286 : subst] : ((((X285 @ X287)) != $true) | (((X289 @ (sub @ X287 @ (push @ X288 @ X286)))) = $true)) | (pushprop_lem1 != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((laminj = $true) | ? [X490 : term,X491 : term] : ((((lam @ X491)) = ((lam @ X490))) & (X490 != X491))) & (! [X490 : term,X491 : term] : ((((lam @ X491)) != ((lam @ X490))) | (X490 = X491)) | (laminj != $true)) & (! [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 = X2) | (((ap @ X1 @ X0)) != ((ap @ X3 @ X2)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X2 : term,X0 : term,X1 : term,X3 : term] : ((X0 != X2) & (((ap @ X1 @ X0)) = ((ap @ X3 @ X2))))) & ((axshiftcons = $true) | ? [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) != X360)) & (! [X361 : term,X360 : subst] : (((comp @ sh @ (push @ X361 @ X360))) = X360) | (axshiftcons != $true)) & ((sP61 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP61 != $true)) & ((sP60 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP60 != $true)) & ((sP55 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP55 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) != $true) & ! [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) = $true) | (((X82 @ id @ X84 @ id)) != $true) | (((X82 @ id @ X85 @ id)) != $true)) & (((sP51 @ X82)) != $true))) & (! [X82 : (subst > term > subst > $o),X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) | ? [X84 : term,X85 : term] : ((((X82 @ id @ (ap @ (sub @ X84 @ id) @ X85) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true) & (((X82 @ id @ X85 @ id)) = $true)) | (((sP51 @ X82)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) != ((sub @ X323 @ sh))) | (X323 = X324)) | (shinj != $true)) & ((shinj = $true) | ? [X324 : term,X323 : term] : ((((sub @ X324 @ sh)) = ((sub @ X323 @ sh))) & (X323 != X324))) & (! [X329 : subst] : (((comp @ X329 @ id)) = X329) | (axidr != $true)) & ((axidr = $true) | ? [X329 : subst] : (((comp @ X329 @ id)) != X329)) & (axabs = $true) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((induction2lem = $true) | (sP41 != $true)) & ((sP41 = $true) | (induction2lem != $true)) & (ulamvarind = $true) & ((termmset_lthm = $true) | (! [X260 : term] : (((sub @ X260 @ id)) = X260) & ? [X261 : term] : (((sub @ X261 @ id)) != X261))) & (? [X260 : term] : (((sub @ X260 @ id)) != X260) | ! [X261 : term] : (((sub @ X261 @ id)) = X261) | (termmset_lthm != $true)) & ! [X116 : d_term] : (d_one = X116) & ((sP39 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP39 != $true)) & ((sP37 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP37 != $true)) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((hoaslaminj = $true) | ? [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) = ((lam @ (X138 @ sh @ one)))) & ! [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) = ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) & ! [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) = ((sub @ (X138 @ X143 @ X142) @ X144))) & (((X138 @ X141 @ X139)) != ((X140 @ X141 @ X139))))) & (! [X138 : (subst > term > term),X139 : term,X141 : subst,X140 : (subst > term > term)] : ((((lam @ (X140 @ sh @ one))) != ((lam @ (X138 @ sh @ one)))) | ? [X145 : subst,X147 : term,X146 : subst] : (((sub @ (X140 @ X146 @ X147) @ X145)) != ((X140 @ (comp @ X146 @ X145) @ (sub @ X147 @ X145)))) | ? [X143 : subst,X142 : term,X144 : subst] : (((X138 @ (comp @ X143 @ X144) @ (sub @ X142 @ X144))) != ((sub @ (X138 @ X143 @ X142) @ X144))) | (((X138 @ X141 @ X139)) = ((X140 @ X141 @ X139)))) | (hoaslaminj != $true)) & (! [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) != ((ap @ X14 @ X12))) | (X11 = X14)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X11 : term,X14 : term,X12 : term,X13 : term] : ((((ap @ X11 @ X13)) = ((ap @ X14 @ X12))) & (X11 != X14))) & (? [X276 : term] : (((sub @ X276 @ id)) != X276) | ? [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) = ((ap @ X280 @ X277))) & (X279 != X280)) | ! [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 = X284) | (((ap @ (sub @ X284 @ id) @ X283)) != ((ap @ (sub @ X281 @ id) @ X282)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X276 : term] : (((sub @ X276 @ id)) = X276) & ! [X278 : term,X277 : term,X279 : term,X280 : term] : ((((ap @ X279 @ X278)) != ((ap @ X280 @ X277))) | (X279 = X280)) & ? [X282 : term,X281 : term,X283 : term,X284 : term] : ((X281 != X284) & (((ap @ (sub @ X284 @ id) @ X283)) = ((ap @ (sub @ X281 @ id) @ X282)))))) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) | ? [X290 : term] : ! [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) != ((X291 @ sh @ one)))) & (! [X290 : term] : ? [X291 : (subst > term > term)] : (((sub @ X290 @ (push @ one @ sh))) = ((X291 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X358 : d_term,X359 : d_term] : ((X358 = X359) | (((d2term @ X358)) != ((d2term @ X359)))) & ((hoasapinj2_lthm = $true) | (! [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 = X519) | (((ap @ X516 @ X517)) != ((ap @ X518 @ X519)))) & ? [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) = ((ap @ (sub @ X522 @ id) @ X521))) & (X520 != X521)))) & (? [X517 : term,X519 : term,X518 : term,X516 : term] : ((X517 != X519) & (((ap @ X516 @ X517)) = ((ap @ X518 @ X519)))) | ! [X521 : term,X520 : term,X523 : term,X522 : term] : ((((ap @ (sub @ X523 @ id) @ X520)) != ((ap @ (sub @ X522 @ id) @ X521))) | (X520 = X521)) | (hoasapinj2_lthm != $true)) & ((axvarcons = $true) | ? [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) != X510)) & (! [X510 : term,X511 : subst] : (((sub @ one @ (push @ X510 @ X511))) = X510) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & ((sP33 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP33 != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X336 : term] : ! [X337 : (subst > term > term)] : ? [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) != ((sub @ X336 @ (push @ X338 @ X339))))) & (! [X336 : term] : ? [X337 : (subst > term > term)] : ! [X338 : term,X339 : subst] : (((X337 @ X339 @ X338)) = ((sub @ X336 @ (push @ X338 @ X339)))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axvarid = $true) | ? [X327 : term] : (((sub @ X327 @ id)) != X327)) & (! [X327 : term] : (((sub @ X327 @ id)) = X327) | (axvarid != $true)) & ! [X4 : d_subst] : (d_id = X4) & ((hoasinduction_lem0_lthm = $true) | ? [X492 : (subst > term > subst > $o)] : ! [X493 : (term > $o)] : ? [X494 : term] : (((X492 @ id @ X494 @ id)) != ((X493 @ X494)))) & (! [X492 : (subst > term > subst > $o)] : ? [X493 : (term > $o)] : ! [X494 : term] : (((X492 @ id @ X494 @ id)) = ((X493 @ X494))) | (hoasinduction_lem0_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) = X396) & ? [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) != $true) & (((X398 @ X399)) = $true) & ! [X402 : term] : (((X401 @ X402)) = ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))))) & (? [X396 : term,X397 : subst] : (((sub @ one @ (push @ X396 @ X397))) != X396) | ! [X400 : subst,X399 : term,X398 : (term > $o),X401 : (term > $o)] : ((((X401 @ one)) = $true) | (((X398 @ X399)) != $true) | ? [X402 : term] : (((X401 @ X402)) != ((X398 @ (sub @ X402 @ (push @ X399 @ X400)))))) | (pushprop_lem1v2_lthm != $true)) & (apnotvar = $true) & (pushprop_gthm = $true) & (! [X318 : subst,X320 : term,X319 : (term > $o)] : ? [X321 : (term > $o)] : ! [X322 : term] : (((X321 @ X322)) = ((X319 @ (sub @ X322 @ (push @ X320 @ X318))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X318 : subst,X320 : term,X319 : (term > $o)] : ! [X321 : (term > $o)] : ? [X322 : term] : (((X321 @ X322)) != ((X319 @ (sub @ X322 @ (push @ X320 @ X318)))))) & (! [X342 : subst] : (((comp @ id @ X342)) = X342) | (axidl != $true)) & ((axidl = $true) | ? [X342 : subst] : (((comp @ id @ X342)) != X342)) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & ((substmonoid = $true) | ? [X326 : subst] : (((comp @ id @ X326)) != X326) | ? [X325 : subst] : (((comp @ X325 @ id)) != X325)) & ((! [X326 : subst] : (((comp @ id @ X326)) = X326) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325)) | (substmonoid != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP31 != $true)) & ((sP31 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) | (termmset != $true)) & ((termmset = $true) | ? [X328 : term] : (((sub @ X328 @ id)) != X328)) & (! [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) = X81) | (axscons != $true)) & ((axscons = $true) | ? [X81 : subst] : (((push @ (sub @ one @ X81) @ (comp @ sh @ X81))) != X81)) & ((sP30 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP30 != $true)) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X344 : (term > $o),X343 : term,X345 : subst] : ! [X346 : (term > $o)] : ? [X347 : term] : (((X346 @ X347)) != ((X344 @ (sub @ X347 @ (push @ X343 @ X345)))))) & (! [X344 : (term > $o),X343 : term,X345 : subst] : ? [X346 : (term > $o)] : ! [X347 : term] : (((X346 @ X347)) = ((X344 @ (sub @ X347 @ (push @ X343 @ X345))))) | (pushprop_lem0_lthm != $true)) & ! [X136 : subst] : ? [X137 : d_subst] : (((d2subst @ X137)) = X136) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | (sP28 != $true)) & ((sP28 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3a = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a != $true)) & (hoasapnotvar_lthm = $true) & ((induction = $true) | ? [X263 : term,X262 : (term > $o)] : ((((sP25 @ X262)) != $true) & (((X262 @ X263)) != $true) & ! [X267 : term] : ((((X262 @ X267)) = $true) | (((var @ X267)) != $true)) & ! [X266 : term] : ((((X262 @ X266)) != $true) | (((X262 @ (lam @ X266))) = $true)))) & (! [X263 : term,X262 : (term > $o)] : ((((sP25 @ X262)) = $true) | (((X262 @ X263)) = $true) | ? [X267 : term] : ((((X262 @ X267)) != $true) & (((var @ X267)) = $true)) | ? [X266 : term] : ((((X262 @ X266)) = $true) & (((X262 @ (lam @ X266))) != $true))) | (induction != $true)) & ((hoasapinj2 = $true) | ? [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 != X331) & (((ap @ (sub @ X333 @ id) @ X330)) = ((ap @ (sub @ X332 @ id) @ X331))))) & (! [X333 : term,X331 : term,X332 : term,X330 : term] : ((X330 = X331) | (((ap @ (sub @ X333 @ id) @ X330)) != ((ap @ (sub @ X332 @ id) @ X331)))) | (hoasapinj2 != $true)) & ((substmonoid_lthm = $true) | ((? [X479 : subst] : (((comp @ id @ X479)) != X479) | ? [X478 : subst] : (((comp @ X478 @ id)) != X478)) & ! [X476 : subst] : (((comp @ id @ X476)) = X476) & ! [X477 : subst] : (((comp @ X477 @ id)) = X477))) & ((! [X479 : subst] : (((comp @ id @ X479)) = X479) & ! [X478 : subst] : (((comp @ X478 @ id)) = X478)) | ? [X476 : subst] : (((comp @ id @ X476)) != X476) | ? [X477 : subst] : (((comp @ X477 @ id)) != X477) | (substmonoid_lthm != $true)) & ((sP24 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP24 != $true)) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & ((sP23 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP23 != $true)) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ! [X340 : term] : ? [X341 : d_term] : (((d2term @ X341)) = X340) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X480 : (subst > term > subst > $o)] : ? [X481 : (term > $o)] : ! [X482 : term] : (((X481 @ X482)) = ((X480 @ id @ X482 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X480 : (subst > term > subst > $o)] : ! [X481 : (term > $o)] : ? [X482 : term] : (((X481 @ X482)) != ((X480 @ id @ X482 @ id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction != $true)) & ((pushprop_lem1v2 = $true) | ? [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) != $true) & (((X434 @ X432)) = $true) & ! [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) = ((X433 @ X436))))) & (! [X434 : (term > $o),X435 : subst,X433 : (term > $o),X432 : term] : ((((X433 @ one)) = $true) | (((X434 @ X432)) != $true) | ? [X436 : term] : (((X434 @ (sub @ X436 @ (push @ X432 @ X435)))) != ((X433 @ X436)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ? [X334 : term] : ! [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) != ((X335 @ sh @ one)))) & (! [X334 : term] : ? [X335 : (subst > term > term)] : (((sub @ X334 @ (push @ one @ sh))) = ((X335 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X80 : d_subst,X79 : d_subst] : ((X79 = X80) | (((d2subst @ X79)) != ((d2subst @ X80)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj1 = $true) | ? [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 != X135) & (((ap @ (sub @ X135 @ id) @ X134)) = ((ap @ (sub @ X132 @ id) @ X133))))) & (! [X134 : term,X135 : term,X132 : term,X133 : term] : ((X132 = X135) | (((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X132 @ id) @ X133)))) | (hoasapinj1 != $true)) & ((hoaslamnotap = $true) | ? [X5 : (subst > term > term),X6 : term,X7 : term] : (! [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) = ((sub @ (X5 @ X9 @ X10) @ X8))) & (((lam @ (X5 @ sh @ one))) = ((ap @ (sub @ X6 @ id) @ X7))))) & (! [X5 : (subst > term > term),X6 : term,X7 : term] : (? [X8 : subst,X9 : subst,X10 : term] : (((X5 @ (comp @ X9 @ X8) @ (sub @ X10 @ X8))) != ((sub @ (X5 @ X9 @ X10) @ X8))) | (((lam @ (X5 @ sh @ one))) != ((ap @ (sub @ X6 @ id) @ X7)))) | (hoaslamnotap != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & (axmap = $true) & ((induction2_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (induction2_lthm != $true)) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X512 : term] : ! [X513 : (subst > term > term)] : ? [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) != ((sub @ X512 @ (push @ X515 @ X514))))) & (! [X512 : term] : ? [X513 : (subst > term > term)] : ! [X515 : term,X514 : subst] : (((X513 @ X514 @ X515)) = ((sub @ X512 @ (push @ X515 @ X514)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(flattening,[],[f276])).
% 47.53/7.12 thf(f278,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & (? [X0 : subst,X1 : term] : (((sub @ one @ (push @ X1 @ X0))) != X1) | ? [X2 : term,X3 : subst] : (((comp @ sh @ (push @ X2 @ X3))) != X3) | ! [X4 : term,X5 : subst,X6 : (term > $o),X7 : (term > $o),X8 : term] : (($true = ((X6 @ (sub @ X4 @ (push @ X8 @ X5))))) | (((X7 @ X4)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X9 : subst,X10 : term] : (((sub @ one @ (push @ X10 @ X9))) = X10) & ! [X11 : term,X12 : subst] : (((comp @ sh @ (push @ X11 @ X12))) = X12) & ? [X13 : term,X14 : subst,X15 : (term > $o),X16 : (term > $o),X17 : term] : ((((X15 @ (sub @ X13 @ (push @ X17 @ X14)))) != $true) & (((X16 @ X13)) = $true)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) | ? [X18 : term,X19 : (term > $o),X20 : (term > $o),X21 : term,X22 : subst] : ((((X19 @ X18)) = $true) & (((X20 @ (sub @ X18 @ (push @ X21 @ X22)))) != $true))) & (! [X23 : term,X24 : (term > $o),X25 : (term > $o),X26 : term,X27 : subst] : ((((X24 @ X23)) != $true) | (((X25 @ (sub @ X23 @ (push @ X26 @ X27)))) = $true)) | (pushprop_lem1 != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((laminj = $true) | ? [X28 : term,X29 : term] : ((((lam @ X29)) = ((lam @ X28))) & (X28 != X29))) & (! [X30 : term,X31 : term] : ((((lam @ X30)) != ((lam @ X31))) | (X30 = X31)) | (laminj != $true)) & (! [X32 : term,X33 : term,X34 : term,X35 : term] : ((X32 = X33) | (((ap @ X34 @ X33)) != ((ap @ X35 @ X32)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X36 : term,X37 : term,X38 : term,X39 : term] : ((X36 != X37) & (((ap @ X38 @ X37)) = ((ap @ X39 @ X36))))) & ((axshiftcons = $true) | ? [X40 : term,X41 : subst] : (((comp @ sh @ (push @ X40 @ X41))) != X41)) & (! [X42 : term,X43 : subst] : (((comp @ sh @ (push @ X42 @ X43))) = X43) | (axshiftcons != $true)) & ((sP61 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP61 != $true)) & ((sP60 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP60 != $true)) & ((sP55 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP55 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X44 : (subst > term > subst > $o),X45 : term] : ((((X44 @ id @ X45 @ id)) != $true) & ! [X46 : term,X47 : term] : ((((X44 @ id @ (ap @ (sub @ X46 @ id) @ X47) @ id)) = $true) | (((X44 @ id @ X46 @ id)) != $true) | (((X44 @ id @ X47 @ id)) != $true)) & (((sP51 @ X44)) != $true))) & (! [X48 : (subst > term > subst > $o),X49 : term] : ((((X48 @ id @ X49 @ id)) = $true) | ? [X50 : term,X51 : term] : ((((X48 @ id @ (ap @ (sub @ X50 @ id) @ X51) @ id)) != $true) & (((X48 @ id @ X50 @ id)) = $true) & (((X48 @ id @ X51 @ id)) = $true)) | (((sP51 @ X48)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X52 : term,X53 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) | (shinj != $true)) & ((shinj = $true) | ? [X54 : term,X55 : term] : ((((sub @ X55 @ sh)) = ((sub @ X54 @ sh))) & (X54 != X55))) & (! [X56 : subst] : (((comp @ X56 @ id)) = X56) | (axidr != $true)) & ((axidr = $true) | ? [X57 : subst] : (((comp @ X57 @ id)) != X57)) & (axabs = $true) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((induction2lem = $true) | (sP41 != $true)) & ((sP41 = $true) | (induction2lem != $true)) & (ulamvarind = $true) & ((termmset_lthm = $true) | (! [X58 : term] : (((sub @ X58 @ id)) = X58) & ? [X59 : term] : (((sub @ X59 @ id)) != X59))) & (? [X60 : term] : (((sub @ X60 @ id)) != X60) | ! [X61 : term] : (((sub @ X61 @ id)) = X61) | (termmset_lthm != $true)) & ! [X62 : d_term] : (d_one = X62) & ((sP39 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP39 != $true)) & ((sP37 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP37 != $true)) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((hoaslaminj = $true) | ? [X63 : (subst > term > term),X64 : term,X65 : subst,X66 : (subst > term > term)] : ((((lam @ (X66 @ sh @ one))) = ((lam @ (X63 @ sh @ one)))) & ! [X67 : subst,X68 : term,X69 : subst] : (((X66 @ (comp @ X69 @ X67) @ (sub @ X68 @ X67))) = ((sub @ (X66 @ X69 @ X68) @ X67))) & ! [X70 : subst,X71 : term,X72 : subst] : (((sub @ (X63 @ X70 @ X71) @ X72)) = ((X63 @ (comp @ X70 @ X72) @ (sub @ X71 @ X72)))) & (((X63 @ X65 @ X64)) != ((X66 @ X65 @ X64))))) & (! [X73 : (subst > term > term),X74 : term,X75 : subst,X76 : (subst > term > term)] : ((((lam @ (X76 @ sh @ one))) != ((lam @ (X73 @ sh @ one)))) | ? [X77 : subst,X78 : term,X79 : subst] : (((X76 @ (comp @ X79 @ X77) @ (sub @ X78 @ X77))) != ((sub @ (X76 @ X79 @ X78) @ X77))) | ? [X80 : subst,X81 : term,X82 : subst] : (((sub @ (X73 @ X80 @ X81) @ X82)) != ((X73 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82)))) | (((X76 @ X75 @ X74)) = ((X73 @ X75 @ X74)))) | (hoaslaminj != $true)) & (! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X84 @ X85)) != ((ap @ X83 @ X86))) | (X83 = X84)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X87 : term,X88 : term,X89 : term,X90 : term] : ((((ap @ X88 @ X89)) = ((ap @ X87 @ X90))) & (X87 != X88))) & (? [X91 : term] : (((sub @ X91 @ id)) != X91) | ? [X92 : term,X93 : term,X94 : term,X95 : term] : ((((ap @ X95 @ X93)) = ((ap @ X94 @ X92))) & (X94 != X95)) | ! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X97 = X99) | (((ap @ (sub @ X97 @ id) @ X96)) != ((ap @ (sub @ X99 @ id) @ X98)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X100 : term] : (((sub @ X100 @ id)) = X100) & ! [X101 : term,X102 : term,X103 : term,X104 : term] : ((((ap @ X103 @ X101)) != ((ap @ X104 @ X102))) | (X103 = X104)) & ? [X105 : term,X106 : term,X107 : term,X108 : term] : ((X106 != X108) & (((ap @ (sub @ X106 @ id) @ X105)) = ((ap @ (sub @ X108 @ id) @ X107)))))) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) | ? [X109 : term] : ! [X110 : (subst > term > term)] : (((sub @ X109 @ (push @ one @ sh))) != ((X110 @ sh @ one)))) & (! [X111 : term] : ? [X112 : (subst > term > term)] : (((X112 @ sh @ one)) = ((sub @ X111 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X113 : d_term,X114 : d_term] : ((X113 = X114) | (((d2term @ X113)) != ((d2term @ X114)))) & ((hoasapinj2_lthm = $true) | (! [X115 : term,X116 : term,X117 : term,X118 : term] : ((X115 = X116) | (((ap @ X117 @ X116)) != ((ap @ X118 @ X115)))) & ? [X119 : term,X120 : term,X121 : term,X122 : term] : ((((ap @ (sub @ X122 @ id) @ X119)) = ((ap @ (sub @ X121 @ id) @ X120))) & (X119 != X120)))) & (? [X123 : term,X124 : term,X125 : term,X126 : term] : ((X123 != X124) & (((ap @ X125 @ X124)) = ((ap @ X126 @ X123)))) | ! [X127 : term,X128 : term,X129 : term,X130 : term] : ((((ap @ (sub @ X130 @ id) @ X127)) != ((ap @ (sub @ X129 @ id) @ X128))) | (X127 = X128)) | (hoasapinj2_lthm != $true)) & ((axvarcons = $true) | ? [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) != X131)) & (! [X133 : term,X134 : subst] : (((sub @ one @ (push @ X133 @ X134))) = X133) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & ((sP33 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP33 != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X135 : term] : ! [X136 : (subst > term > term)] : ? [X137 : term,X138 : subst] : (((sub @ X135 @ (push @ X137 @ X138))) != ((X136 @ X138 @ X137)))) & (! [X139 : term] : ? [X140 : (subst > term > term)] : ! [X141 : term,X142 : subst] : (((X140 @ X142 @ X141)) = ((sub @ X139 @ (push @ X141 @ X142)))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axvarid = $true) | ? [X143 : term] : (((sub @ X143 @ id)) != X143)) & (! [X144 : term] : (((sub @ X144 @ id)) = X144) | (axvarid != $true)) & ! [X145 : d_subst] : (d_id = X145) & ((hoasinduction_lem0_lthm = $true) | ? [X146 : (subst > term > subst > $o)] : ! [X147 : (term > $o)] : ? [X148 : term] : (((X146 @ id @ X148 @ id)) != ((X147 @ X148)))) & (! [X149 : (subst > term > subst > $o)] : ? [X150 : (term > $o)] : ! [X151 : term] : (((X150 @ X151)) = ((X149 @ id @ X151 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) = X152) & ? [X154 : subst,X155 : term,X156 : (term > $o),X157 : (term > $o)] : (($true != ((X157 @ one))) & (((X156 @ X155)) = $true) & ! [X158 : term] : (((X157 @ X158)) = ((X156 @ (sub @ X158 @ (push @ X155 @ X154)))))))) & (? [X159 : term,X160 : subst] : (((sub @ one @ (push @ X159 @ X160))) != X159) | ! [X161 : subst,X162 : term,X163 : (term > $o),X164 : (term > $o)] : (($true = ((X164 @ one))) | (((X163 @ X162)) != $true) | ? [X165 : term] : (((X163 @ (sub @ X165 @ (push @ X162 @ X161)))) != ((X164 @ X165)))) | (pushprop_lem1v2_lthm != $true)) & (apnotvar = $true) & (pushprop_gthm = $true) & (! [X166 : subst,X167 : term,X168 : (term > $o)] : ? [X169 : (term > $o)] : ! [X170 : term] : (((X168 @ (sub @ X170 @ (push @ X167 @ X166)))) = ((X169 @ X170))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X171 : subst,X172 : term,X173 : (term > $o)] : ! [X174 : (term > $o)] : ? [X175 : term] : (((X174 @ X175)) != ((X173 @ (sub @ X175 @ (push @ X172 @ X171)))))) & (! [X176 : subst] : (((comp @ id @ X176)) = X176) | (axidl != $true)) & ((axidl = $true) | ? [X177 : subst] : (((comp @ id @ X177)) != X177)) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & ((substmonoid = $true) | ? [X178 : subst] : (((comp @ id @ X178)) != X178) | ? [X179 : subst] : (((comp @ X179 @ id)) != X179)) & ((! [X180 : subst] : (((comp @ id @ X180)) = X180) & ! [X181 : subst] : (((comp @ X181 @ id)) = X181)) | (substmonoid != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP31 != $true)) & ((sP31 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (! [X182 : term] : (((sub @ X182 @ id)) = X182) | (termmset != $true)) & ((termmset = $true) | ? [X183 : term] : (((sub @ X183 @ id)) != X183)) & (! [X184 : subst] : (((push @ (sub @ one @ X184) @ (comp @ sh @ X184))) = X184) | (axscons != $true)) & ((axscons = $true) | ? [X185 : subst] : (((push @ (sub @ one @ X185) @ (comp @ sh @ X185))) != X185)) & ((sP30 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP30 != $true)) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem0_lthm = $true) | ? [X186 : (term > $o),X187 : term,X188 : subst] : ! [X189 : (term > $o)] : ? [X190 : term] : (((X186 @ (sub @ X190 @ (push @ X187 @ X188)))) != ((X189 @ X190)))) & (! [X191 : (term > $o),X192 : term,X193 : subst] : ? [X194 : (term > $o)] : ! [X195 : term] : (((X194 @ X195)) = ((X191 @ (sub @ X195 @ (push @ X192 @ X193))))) | (pushprop_lem0_lthm != $true)) & ! [X196 : subst] : ? [X197 : d_subst] : (((d2subst @ X197)) = X196) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | (sP28 != $true)) & ((sP28 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3a = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a != $true)) & (hoasapnotvar_lthm = $true) & ((induction = $true) | ? [X198 : term,X199 : (term > $o)] : ((((sP25 @ X199)) != $true) & (((X199 @ X198)) != $true) & ! [X200 : term] : ((((X199 @ X200)) = $true) | (((var @ X200)) != $true)) & ! [X201 : term] : ((((X199 @ X201)) != $true) | (((X199 @ (lam @ X201))) = $true)))) & (! [X202 : term,X203 : (term > $o)] : ((((sP25 @ X203)) = $true) | (((X203 @ X202)) = $true) | ? [X204 : term] : ((((X203 @ X204)) != $true) & (((var @ X204)) = $true)) | ? [X205 : term] : ((((X203 @ X205)) = $true) & (((X203 @ (lam @ X205))) != $true))) | (induction != $true)) & ((hoasapinj2 = $true) | ? [X206 : term,X207 : term,X208 : term,X209 : term] : ((X207 != X209) & (((ap @ (sub @ X208 @ id) @ X207)) = ((ap @ (sub @ X206 @ id) @ X209))))) & (! [X210 : term,X211 : term,X212 : term,X213 : term] : ((X211 = X213) | (((ap @ (sub @ X212 @ id) @ X211)) != ((ap @ (sub @ X210 @ id) @ X213)))) | (hoasapinj2 != $true)) & ((substmonoid_lthm = $true) | ((? [X214 : subst] : (((comp @ id @ X214)) != X214) | ? [X215 : subst] : (((comp @ X215 @ id)) != X215)) & ! [X216 : subst] : (((comp @ id @ X216)) = X216) & ! [X217 : subst] : (((comp @ X217 @ id)) = X217))) & ((! [X218 : subst] : (((comp @ id @ X218)) = X218) & ! [X219 : subst] : (((comp @ X219 @ id)) = X219)) | ? [X220 : subst] : (((comp @ id @ X220)) != X220) | ? [X221 : subst] : (((comp @ X221 @ id)) != X221) | (substmonoid_lthm != $true)) & ((sP24 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP24 != $true)) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & ((sP23 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP23 != $true)) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ! [X222 : term] : ? [X223 : d_term] : (((d2term @ X223)) = X222) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X224 : (subst > term > subst > $o)] : ? [X225 : (term > $o)] : ! [X226 : term] : (((X224 @ id @ X226 @ id)) = ((X225 @ X226))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X227 : (subst > term > subst > $o)] : ! [X228 : (term > $o)] : ? [X229 : term] : (((X227 @ id @ X229 @ id)) != ((X228 @ X229)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction != $true)) & ((pushprop_lem1v2 = $true) | ? [X230 : (term > $o),X231 : subst,X232 : (term > $o),X233 : term] : ((((X232 @ one)) != $true) & (((X230 @ X233)) = $true) & ! [X234 : term] : (((X230 @ (sub @ X234 @ (push @ X233 @ X231)))) = ((X232 @ X234))))) & (! [X235 : (term > $o),X236 : subst,X237 : (term > $o),X238 : term] : ((((X237 @ one)) = $true) | (((X235 @ X238)) != $true) | ? [X239 : term] : (((X237 @ X239)) != ((X235 @ (sub @ X239 @ (push @ X238 @ X236)))))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ? [X240 : term] : ! [X241 : (subst > term > term)] : (((sub @ X240 @ (push @ one @ sh))) != ((X241 @ sh @ one)))) & (! [X242 : term] : ? [X243 : (subst > term > term)] : (((sub @ X242 @ (push @ one @ sh))) = ((X243 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X244 : d_subst,X245 : d_subst] : ((X244 = X245) | (((d2subst @ X244)) != ((d2subst @ X245)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj1 = $true) | ? [X246 : term,X247 : term,X248 : term,X249 : term] : ((X247 != X248) & (((ap @ (sub @ X247 @ id) @ X246)) = ((ap @ (sub @ X248 @ id) @ X249))))) & (! [X250 : term,X251 : term,X252 : term,X253 : term] : ((X251 = X252) | (((ap @ (sub @ X251 @ id) @ X250)) != ((ap @ (sub @ X252 @ id) @ X253)))) | (hoasapinj1 != $true)) & ((hoaslamnotap = $true) | ? [X254 : (subst > term > term),X255 : term,X256 : term] : (! [X257 : subst,X258 : subst,X259 : term] : (((sub @ (X254 @ X258 @ X259) @ X257)) = ((X254 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257)))) & (((ap @ (sub @ X255 @ id) @ X256)) = ((lam @ (X254 @ sh @ one)))))) & (! [X260 : (subst > term > term),X261 : term,X262 : term] : (? [X263 : subst,X264 : subst,X265 : term] : (((X260 @ (comp @ X264 @ X263) @ (sub @ X265 @ X263))) != ((sub @ (X260 @ X264 @ X265) @ X263))) | (((lam @ (X260 @ sh @ one))) != ((ap @ (sub @ X261 @ id) @ X262)))) | (hoaslamnotap != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & (axmap = $true) & ((induction2_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (induction2_lthm != $true)) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X266 : term] : ! [X267 : (subst > term > term)] : ? [X268 : term,X269 : subst] : (((sub @ X266 @ (push @ X268 @ X269))) != ((X267 @ X269 @ X268)))) & (! [X270 : term] : ? [X271 : (subst > term > term)] : ! [X272 : term,X273 : subst] : (((X271 @ X273 @ X272)) = ((sub @ X270 @ (push @ X272 @ X273)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(rectify,[],[f277])).
% 47.53/7.12 thf(f279,plain,(
% 47.53/7.12 (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar = $true) & ((((sub @ one @ (push @ sK479 @ sK478))) != sK479) | (((comp @ sh @ (push @ sK480 @ sK481))) != sK481) | ! [X4 : term,X5 : subst,X6 : (term > $o),X7 : (term > $o),X8 : term] : (($true = ((X6 @ (sub @ X4 @ (push @ X8 @ X5))))) | (((X7 @ X4)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X9 : subst,X10 : term] : (((sub @ one @ (push @ X10 @ X9))) = X10) & ! [X11 : term,X12 : subst] : (((comp @ sh @ (push @ X11 @ X12))) = X12) & ((((sK484 @ (sub @ sK482 @ (push @ sK486 @ sK483)))) != $true) & (((sK485 @ sK482)) = $true)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1 = $true) | ((((sK488 @ sK487)) = $true) & (((sK489 @ (sub @ sK487 @ (push @ sK490 @ sK491)))) != $true))) & (! [X23 : term,X24 : (term > $o),X25 : (term > $o),X26 : term,X27 : subst] : ((((X24 @ X23)) != $true) | (((X25 @ (sub @ X23 @ (push @ X26 @ X27)))) = $true)) | (pushprop_lem1 != $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslaminj_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((laminj = $true) | ((((lam @ sK493)) = ((lam @ sK492))) & (sK493 != sK492))) & (! [X30 : term,X31 : term] : ((((lam @ X30)) != ((lam @ X31))) | (X30 = X31)) | (laminj != $true)) & (! [X32 : term,X33 : term,X34 : term,X35 : term] : ((X32 = X33) | (((ap @ X34 @ X33)) != ((ap @ X35 @ X32)))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK494 != sK495) & (((ap @ sK496 @ sK495)) = ((ap @ sK497 @ sK494))))) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK498 @ sK499))) != sK499)) & (! [X42 : term,X43 : subst] : (((comp @ sh @ (push @ X42 @ X43))) = X43) | (axshiftcons != $true)) & ((sP61 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP61 != $true)) & ((sP60 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP60 != $true)) & ((sP55 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP55 != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK500 @ id @ sK501 @ id)) != $true) & ! [X46 : term,X47 : term] : ((((sK500 @ id @ (ap @ (sub @ X46 @ id) @ X47) @ id)) = $true) | (((sK500 @ id @ X46 @ id)) != $true) | ($true != ((sK500 @ id @ X47 @ id)))) & (((sP51 @ sK500)) != $true))) & (! [X48 : (subst > term > subst > $o),X49 : term] : ((((X48 @ id @ X49 @ id)) = $true) | ((((X48 @ id @ (ap @ (sub @ (sK502 @ X48) @ id) @ (sK503 @ X48)) @ id)) != $true) & (((X48 @ id @ (sK502 @ X48) @ id)) = $true) & (((X48 @ id @ (sK503 @ X48) @ id)) = $true)) | (((sP51 @ X48)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X52 : term,X53 : term] : ((((sub @ X52 @ sh)) != ((sub @ X53 @ sh))) | (X52 = X53)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK505 @ sh)) = ((sub @ sK504 @ sh))) & (sK504 != sK505))) & (! [X56 : subst] : (((comp @ X56 @ id)) = X56) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK506 @ id)) != sK506)) & (axabs = $true) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((induction2lem = $true) | (sP41 != $true)) & ((sP41 = $true) | (induction2lem != $true)) & (ulamvarind = $true) & ((termmset_lthm = $true) | (! [X58 : term] : (((sub @ X58 @ id)) = X58) & (sK507 != ((sub @ sK507 @ id))))) & ((sK508 != ((sub @ sK508 @ id))) | ! [X61 : term] : (((sub @ X61 @ id)) = X61) | (termmset_lthm != $true)) & ! [X62 : d_term] : (d_one = X62) & ((sP39 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP39 != $true)) & ((sP37 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP37 != $true)) & ((sP35 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP35 != $true)) & ((hoaslaminj = $true) | ((((lam @ (sK512 @ sh @ one))) = ((lam @ (sK509 @ sh @ one)))) & ! [X67 : subst,X68 : term,X69 : subst] : (((sub @ (sK512 @ X69 @ X68) @ X67)) = ((sK512 @ (comp @ X69 @ X67) @ (sub @ X68 @ X67)))) & ! [X70 : subst,X71 : term,X72 : subst] : (((sK509 @ (comp @ X70 @ X72) @ (sub @ X71 @ X72))) = ((sub @ (sK509 @ X70 @ X71) @ X72))) & (((sK512 @ sK511 @ sK510)) != ((sK509 @ sK511 @ sK510))))) & (! [X73 : (subst > term > term),X74 : term,X75 : subst,X76 : (subst > term > term)] : ((((lam @ (X76 @ sh @ one))) != ((lam @ (X73 @ sh @ one)))) | (((X76 @ (comp @ (sK515 @ X76) @ (sK513 @ X76)) @ (sub @ (sK514 @ X76) @ (sK513 @ X76)))) != ((sub @ (X76 @ (sK515 @ X76) @ (sK514 @ X76)) @ (sK513 @ X76)))) | (((sub @ (X73 @ (sK516 @ X73) @ (sK517 @ X73)) @ (sK518 @ X73))) != ((X73 @ (comp @ (sK516 @ X73) @ (sK518 @ X73)) @ (sub @ (sK517 @ X73) @ (sK518 @ X73))))) | (((X76 @ X75 @ X74)) = ((X73 @ X75 @ X74)))) | (hoaslaminj != $true)) & (! [X83 : term,X84 : term,X85 : term,X86 : term] : ((((ap @ X84 @ X85)) != ((ap @ X83 @ X86))) | (X83 = X84)) | (apinj1 != $true)) & ((apinj1 = $true) | ((((ap @ sK519 @ sK522)) = ((ap @ sK520 @ sK521))) & (sK519 != sK520))) & ((sK523 != ((sub @ sK523 @ id))) | ((((ap @ sK526 @ sK524)) = ((ap @ sK527 @ sK525))) & (sK527 != sK526)) | ! [X96 : term,X97 : term,X98 : term,X99 : term] : ((X97 = X99) | (((ap @ (sub @ X97 @ id) @ X96)) != ((ap @ (sub @ X99 @ id) @ X98)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X100 : term] : (((sub @ X100 @ id)) = X100) & ! [X101 : term,X102 : term,X103 : term,X104 : term] : ((((ap @ X103 @ X101)) != ((ap @ X104 @ X102))) | (X103 = X104)) & ((sK531 != sK529) & (((ap @ (sub @ sK531 @ id) @ sK530)) = ((ap @ (sub @ sK529 @ id) @ sK528)))))) & (hoaslamnotap_gthm = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3b = $true) | ! [X110 : (subst > term > term)] : (((X110 @ sh @ one)) != ((sub @ sK532 @ (push @ one @ sh))))) & (! [X111 : term] : (((sK533 @ X111 @ sh @ one)) = ((sub @ X111 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (pushprop_lem2v2 = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & ! [X113 : d_term,X114 : d_term] : ((X113 = X114) | (((d2term @ X113)) != ((d2term @ X114)))) & ((hoasapinj2_lthm = $true) | (! [X115 : term,X116 : term,X117 : term,X118 : term] : ((X115 = X116) | (((ap @ X117 @ X116)) != ((ap @ X118 @ X115)))) & ((((ap @ (sub @ sK536 @ id) @ sK535)) = ((ap @ (sub @ sK537 @ id) @ sK534))) & (sK534 != sK535)))) & (((sK539 != sK538) & (((ap @ sK541 @ sK538)) = ((ap @ sK540 @ sK539)))) | ! [X127 : term,X128 : term,X129 : term,X130 : term] : ((((ap @ (sub @ X130 @ id) @ X127)) != ((ap @ (sub @ X129 @ id) @ X128))) | (X127 = X128)) | (hoasapinj2_lthm != $true)) & ((axvarcons = $true) | (((sub @ one @ (push @ sK542 @ sK543))) != sK542)) & (! [X133 : term,X134 : subst] : (((sub @ one @ (push @ X133 @ X134))) = X133) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & ((sP33 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP33 != $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X136 : (subst > term > term)] : (((sub @ sK544 @ (push @ (sK545 @ X136) @ (sK546 @ X136)))) != ((X136 @ (sK546 @ X136) @ (sK545 @ X136))))) & (! [X139 : term] : ! [X141 : term,X142 : subst] : (((sK547 @ X139 @ X142 @ X141)) = ((sub @ X139 @ (push @ X141 @ X142)))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axvarid = $true) | (((sub @ sK548 @ id)) != sK548)) & (! [X144 : term] : (((sub @ X144 @ id)) = X144) | (axvarid != $true)) & ! [X145 : d_subst] : (d_id = X145) & ((hoasinduction_lem0_lthm = $true) | ! [X147 : (term > $o)] : (((sK549 @ id @ (sK550 @ X147) @ id)) != ((X147 @ (sK550 @ X147))))) & (! [X149 : (subst > term > subst > $o)] : ! [X151 : term] : (((sK551 @ X149 @ X151)) = ((X149 @ id @ X151 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) = X152) & ((((sK555 @ one)) != $true) & (((sK554 @ sK553)) = $true) & ! [X158 : term] : (((sK554 @ (sub @ X158 @ (push @ sK553 @ sK552)))) = ((sK555 @ X158)))))) & ((sK556 != ((sub @ one @ (push @ sK556 @ sK557)))) | ! [X161 : subst,X162 : term,X163 : (term > $o),X164 : (term > $o)] : (($true = ((X164 @ one))) | (((X163 @ X162)) != $true) | (((X163 @ (sub @ (sK558 @ X164 @ X163 @ X162 @ X161) @ (push @ X162 @ X161)))) != ((X164 @ (sK558 @ X164 @ X163 @ X162 @ X161))))) | (pushprop_lem1v2_lthm != $true)) & (apnotvar = $true) & (pushprop_gthm = $true) & (! [X166 : subst,X167 : term,X168 : (term > $o)] : ! [X170 : term] : (((X168 @ (sub @ X170 @ (push @ X167 @ X166)))) = ((sK559 @ X168 @ X167 @ X166 @ X170))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X174 : (term > $o)] : (((X174 @ (sK563 @ X174))) != ((sK562 @ (sub @ (sK563 @ X174) @ (push @ sK561 @ sK560)))))) & (! [X176 : subst] : (((comp @ id @ X176)) = X176) | (axidl != $true)) & ((axidl = $true) | (((comp @ id @ sK564)) != sK564)) & (hoasinduction_lem2v2_gthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (one = ((d2term @ d_one))) & ((substmonoid = $true) | (((comp @ id @ sK565)) != sK565) | (sK566 != ((comp @ sK566 @ id)))) & ((! [X180 : subst] : (((comp @ id @ X180)) = X180) & ! [X181 : subst] : (((comp @ X181 @ id)) = X181)) | (substmonoid != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP31 != $true)) & ((sP31 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (axvarshift = $true) & (pushprop_lem2v2_gthm = $true) & (axclos = $true) & (pushprop_lthm = $true) & (! [X182 : term] : (((sub @ X182 @ id)) = X182) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK567 @ id)) != sK567)) & (! [X184 : subst] : (((push @ (sub @ one @ X184) @ (comp @ sh @ X184))) = X184) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK568) @ (comp @ sh @ sK568))) != sK568)) & ((sP30 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP30 != $true)) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem0_lthm = $true) | ! [X189 : (term > $o)] : (((sK569 @ (sub @ (sK572 @ X189) @ (push @ sK570 @ sK571)))) != ((X189 @ (sK572 @ X189))))) & (! [X191 : (term > $o),X192 : term,X193 : subst] : ! [X195 : term] : (((sK573 @ X193 @ X192 @ X191 @ X195)) = ((X191 @ (sub @ X195 @ (push @ X192 @ X193))))) | (pushprop_lem0_lthm != $true)) & ! [X196 : subst] : (((d2subst @ (sK574 @ X196))) = X196) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | (sP28 != $true)) & ((sP28 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lem3v2_lthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3a = $true) | (sP26 != $true)) & ((sP26 = $true) | (hoasinduction_lem3a != $true)) & (hoasapnotvar_lthm = $true) & ((induction = $true) | ((((sP25 @ sK576)) != $true) & (((sK576 @ sK575)) != $true) & ! [X200 : term] : ((((sK576 @ X200)) = $true) | (((var @ X200)) != $true)) & ! [X201 : term] : ((((sK576 @ X201)) != $true) | (((sK576 @ (lam @ X201))) = $true)))) & (! [X202 : term,X203 : (term > $o)] : ((((sP25 @ X203)) = $true) | (((X203 @ X202)) = $true) | ((((X203 @ (sK577 @ X203))) != $true) & (((var @ (sK577 @ X203))) = $true)) | ((((X203 @ (sK578 @ X203))) = $true) & (((X203 @ (lam @ (sK578 @ X203)))) != $true))) | (induction != $true)) & ((hoasapinj2 = $true) | ((sK582 != sK580) & (((ap @ (sub @ sK581 @ id) @ sK580)) = ((ap @ (sub @ sK579 @ id) @ sK582))))) & (! [X210 : term,X211 : term,X212 : term,X213 : term] : ((X211 = X213) | (((ap @ (sub @ X212 @ id) @ X211)) != ((ap @ (sub @ X210 @ id) @ X213)))) | (hoasapinj2 != $true)) & ((substmonoid_lthm = $true) | (((((comp @ id @ sK583)) != sK583) | (((comp @ sK584 @ id)) != sK584)) & ! [X216 : subst] : (((comp @ id @ X216)) = X216) & ! [X217 : subst] : (((comp @ X217 @ id)) = X217))) & ((! [X218 : subst] : (((comp @ id @ X218)) = X218) & ! [X219 : subst] : (((comp @ X219 @ id)) = X219)) | (((comp @ id @ sK585)) != sK585) | (sK586 != ((comp @ sK586 @ id))) | (substmonoid_lthm != $true)) & ((sP24 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP24 != $true)) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & ((sP23 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP23 != $true)) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ! [X222 : term] : (((d2term @ (sK587 @ X222))) = X222) & (hoasapnotvar_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem1_gthm = $true) & (induction2lem_gthm = $true) & (! [X224 : (subst > term > subst > $o)] : ! [X226 : term] : (((X224 @ id @ X226 @ id)) = ((sK588 @ X224 @ X226))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X228 : (term > $o)] : (((sK589 @ id @ (sK590 @ X228) @ id)) != ((X228 @ (sK590 @ X228))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((hoasinduction = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction != $true)) & ((pushprop_lem1v2 = $true) | ((((sK593 @ one)) != $true) & (((sK591 @ sK594)) = $true) & ! [X234 : term] : (((sK593 @ X234)) = ((sK591 @ (sub @ X234 @ (push @ sK594 @ sK592))))))) & (! [X235 : (term > $o),X236 : subst,X237 : (term > $o),X238 : term] : ((((X237 @ one)) = $true) | (((X235 @ X238)) != $true) | (((X237 @ (sK595 @ X238 @ X237 @ X236 @ X235))) != ((X235 @ (sub @ (sK595 @ X238 @ X237 @ X236 @ X235) @ (push @ X238 @ X236)))))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3b_lthm = $true) | ! [X241 : (subst > term > term)] : (((X241 @ sh @ one)) != ((sub @ sK596 @ (push @ one @ sh))))) & (! [X242 : term] : (((sub @ X242 @ (push @ one @ sh))) = ((sK597 @ X242 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3v2a = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X244 : d_subst,X245 : d_subst] : ((X244 = X245) | (((d2subst @ X244)) != ((d2subst @ X245)))) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasapinj1 = $true) | ((sK600 != sK599) & (((ap @ (sub @ sK599 @ id) @ sK598)) = ((ap @ (sub @ sK600 @ id) @ sK601))))) & (! [X250 : term,X251 : term,X252 : term,X253 : term] : ((X251 = X252) | (((ap @ (sub @ X251 @ id) @ X250)) != ((ap @ (sub @ X252 @ id) @ X253)))) | (hoasapinj1 != $true)) & ((hoaslamnotap = $true) | (! [X257 : subst,X258 : subst,X259 : term] : (((sub @ (sK602 @ X258 @ X259) @ X257)) = ((sK602 @ (comp @ X258 @ X257) @ (sub @ X259 @ X257)))) & (((ap @ (sub @ sK603 @ id) @ sK604)) = ((lam @ (sK602 @ sh @ one)))))) & (! [X260 : (subst > term > term),X261 : term,X262 : term] : ((((X260 @ (comp @ (sK606 @ X260) @ (sK605 @ X260)) @ (sub @ (sK607 @ X260) @ (sK605 @ X260)))) != ((sub @ (X260 @ (sK606 @ X260) @ (sK607 @ X260)) @ (sK605 @ X260)))) | (((lam @ (X260 @ sh @ one))) != ((ap @ (sub @ X261 @ id) @ X262)))) | (hoaslamnotap != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axapp = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((sP8 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP8 != $true)) & (axmap = $true) & ((induction2_lthm = $true) | (sP6 != $true)) & ((sP6 = $true) | (induction2_lthm != $true)) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (lamnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X267 : (subst > term > term)] : (((sub @ sK608 @ (push @ (sK609 @ X267) @ (sK610 @ X267)))) != ((X267 @ (sK610 @ X267) @ (sK609 @ X267))))) & (! [X270 : term] : ! [X272 : term,X273 : subst] : (((sub @ X270 @ (push @ X272 @ X273))) = ((sK611 @ X270 @ X273 @ X272))) | (hoasinduction_lem3v2_f_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_gthm = $true)),
% 47.53/7.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,vAPP,vAPP,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,vAPP,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,vAPP,vAPP,vAPP,sK548,sK549,vAPP,vAPP,sK552,sK553,sK554,sK555,sK556,sK557,vAPP,vAPP,sK560,sK561,sK562,vAPP,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,vAPP,vAPP,vAPP,sK575,sK576,vAPP,vAPP,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,vAPP,vAPP,sK589,vAPP,sK591,sK592,sK593,sK594,vAPP,sK596,vAPP,sK598,sK599,sK600,sK601,sK602,sK603,sK604,vAPP,vAPP,vAPP,sK608,vAPP,vAPP,vAPP]),skolemize(X0,sK478),skolemize(X1,sK479),skolemize(X2,sK480),skolemize(X3,sK481),skolemize(X13,sK482),skolemize(X14,sK483),skolemize(X15,sK484),skolemize(X16,sK485),skolemize(X17,sK486),skolemize(X18,sK487),skolemize(X19,sK488),skolemize(X20,sK489),skolemize(X21,sK490),skolemize(X22,sK491),skolemize(X28,sK492),skolemize(X29,sK493),skolemize(X36,sK494),skolemize(X37,sK495),skolemize(X38,sK496),skolemize(X39,sK497),skolemize(X40,sK498),skolemize(X41,sK499),skolemize(X44,sK500),skolemize(X45,sK501),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X54,sK504),skolemize(X55,sK505),skolemize(X57,sK506),skolemize(X59,sK507),skolemize(X60,sK508),skolemize(X63,sK509),skolemize(X64,sK510),skolemize(X65,sK511),skolemize(X66,sK512),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X87,sK519),skolemize(X88,sK520),skolemize(X89,sK521),skolemize(X90,sK522),skolemize(X91,sK523),skolemize(X92,sK524),skolemize(X93,sK525),skolemize(X94,sK526),skolemize(X95,sK527),skolemize(X105,sK528),skolemize(X106,sK529),skolemize(X107,sK530),skolemize(X108,sK531),skolemize(X109,sK532),skolemize(X21,sK72 @ X11),skolemize(X119,sK534),skolemize(X120,sK535),skolemize(X121,sK536),skolemize(X122,sK537),skolemize(X123,sK538),skolemize(X124,sK539),skolemize(X125,sK540),skolemize(X126,sK541),skolemize(X131,sK542),skolemize(X132,sK543),skolemize(X135,sK544),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X143,sK548),skolemize(X146,sK549),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X154,sK552),skolemize(X155,sK553),skolemize(X156,sK554),skolemize(X157,sK555),skolemize(X159,sK556),skolemize(X160,sK557),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X171,sK560),skolemize(X172,sK561),skolemize(X173,sK562),skolemize(X21,sK72 @ X11),skolemize(X177,sK564),skolemize(X178,sK565),skolemize(X179,sK566),skolemize(X183,sK567),skolemize(X185,sK568),skolemize(X186,sK569),skolemize(X187,sK570),skolemize(X188,sK571),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X198,sK575),skolemize(X199,sK576),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X206,sK579),skolemize(X207,sK580),skolemize(X208,sK581),skolemize(X209,sK582),skolemize(X214,sK583),skolemize(X215,sK584),skolemize(X220,sK585),skolemize(X221,sK586),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X227,sK589),skolemize(X21,sK72 @ X11),skolemize(X230,sK591),skolemize(X231,sK592),skolemize(X232,sK593),skolemize(X233,sK594),skolemize(X21,sK72 @ X11),skolemize(X240,sK596),skolemize(X21,sK72 @ X11),skolemize(X246,sK598),skolemize(X247,sK599),skolemize(X248,sK600),skolemize(X249,sK601),skolemize(X254,sK602),skolemize(X255,sK603),skolemize(X256,sK604),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X266,sK608),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11),skolemize(X21,sK72 @ X11)],[f278])).
% 47.53/7.12 thf(f288,plain,(
% 47.53/7.12 (((sP0 @ sK62)) != $true) | (sP2 = $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f81])).
% 47.53/7.12 thf(f291,plain,(
% 47.53/7.12 (sP2 = $true) | (((sK62 @ id @ sK63 @ id)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f81])).
% 47.53/7.12 thf(f302,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X1 @ (comp @ (sK78 @ X1) @ (sK77 @ X1)) @ (sub @ (sK76 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK78 @ X1) @ (sK76 @ X1)) @ (sK77 @ X1)))) | (((sP0 @ X0)) = $true) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true) | (((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f87])).
% 47.53/7.12 thf(f304,plain,(
% 47.53/7.12 (hoasinduction != $true) | (sP2 != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f88])).
% 47.53/7.12 thf(f445,plain,(
% 47.53/7.12 ( ! [X3 : term,X0 : (subst > term > subst > $o),X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) = $true) | (((X0 @ id @ X3 @ id)) != $true) | (((sP45 @ X0)) != $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f143])).
% 47.53/7.12 thf(f446,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (ap @ (sub @ (sK192 @ X0) @ id) @ (sK193 @ X0)) @ id)) != $true) | (((sP45 @ X0)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f143])).
% 47.53/7.12 thf(f447,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((sP45 @ X0)) = $true) | (((X0 @ id @ (sK192 @ X0) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f143])).
% 47.53/7.12 thf(f492,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true) | (sP36 = $true) | (((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ (sK225 @ X11 @ id @ X13) @ id)) = $true) | (((X11 @ id @ (lam @ X10) @ id)) = $true) | (sP37 != $true) | (((sub @ sK224 @ id)) != sK224)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f168])).
% 47.53/7.12 thf(f494,plain,(
% 47.53/7.12 (sP37 = $true) | (((sK219 @ id @ (lam @ sK218) @ id)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f168])).
% 47.53/7.12 thf(f497,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK221 @ X3) @ (sK223 @ X3)) @ (sK222 @ X3))) != ((X3 @ (comp @ (sK221 @ X3) @ (sK222 @ X3)) @ (sub @ (sK223 @ X3) @ (sK222 @ X3))))) | (sP37 = $true) | (((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK219 @ id @ (sK220 @ X3) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f168])).
% 47.53/7.12 thf(f500,plain,(
% 47.53/7.12 (sP36 != $true) | (((sK229 @ id @ (lam @ (sub @ sK230 @ (push @ one @ sh))) @ id)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f171])).
% 47.53/7.12 thf(f501,plain,(
% 47.53/7.12 ( ! [X11 : (subst > term > term)] : ((((X11 @ (comp @ (sK233 @ X11) @ (sK231 @ X11)) @ (sub @ (sK232 @ X11) @ (sK231 @ X11)))) != ((sub @ (X11 @ (sK233 @ X11) @ (sK232 @ X11)) @ (sK231 @ X11)))) | (((sK229 @ id @ (sK234 @ X11) @ id)) = $true) | (((sK229 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true) | (sP36 != $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f171])).
% 47.53/7.12 thf(f503,plain,(
% 47.53/7.12 ( ! [X10 : term] : ((((sK229 @ id @ X10 @ id)) != $true) | (((sK229 @ id @ (sub @ sK230 @ (push @ X10 @ id)) @ id)) = $true) | (sP36 != $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f171])).
% 47.53/7.12 thf(f597,plain,(
% 47.53/7.12 ( ! [X8 : (subst > term > subst > $o),X9 : term] : ((sP26 != $true) | (((X8 @ id @ (lam @ (sK317 @ X8 @ sh @ one)) @ id)) != $true) | (((X8 @ id @ (lam @ X9) @ id)) = $true) | (((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f202])).
% 47.53/7.12 thf(f599,plain,(
% 47.53/7.12 ( ! [X2 : (subst > term > term)] : ((((sK311 @ id @ (sK313 @ X2) @ id)) = $true) | (((sK311 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (sP26 = $true) | (((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2)))))) )),
% 47.53/7.12 inference(cnf_transformation,[],[f202])).
% 47.53/7.12 thf(f601,plain,(
% 47.53/7.12 (sP26 = $true) | (((sK311 @ id @ (lam @ sK312) @ id)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f202])).
% 47.53/7.12 thf(f609,plain,(
% 47.53/7.12 ( ! [X8 : term,X9 : (subst > term > subst > $o),X15 : term] : ((((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | (((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true) | (sP24 != $true) | (((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (sK327 @ X9 @ X8) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f208])).
% 47.53/7.12 thf(f612,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((sP24 = $true) | (((sub @ (X3 @ (sK325 @ X3) @ (sK324 @ X3)) @ (sK323 @ X3))) != ((X3 @ (comp @ (sK325 @ X3) @ (sK323 @ X3)) @ (sub @ (sK324 @ X3) @ (sK323 @ X3))))) | (((sK322 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK322 @ id @ (sK326 @ X3) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f208])).
% 47.53/7.12 thf(f614,plain,(
% 47.53/7.12 (((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id)) != $true) | (sP24 = $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f208])).
% 47.53/7.12 thf(f645,plain,(
% 47.53/7.12 (sP21 = $true) | (((sK358 @ id @ sK357 @ id)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f218])).
% 47.53/7.12 thf(f648,plain,(
% 47.53/7.12 (sP21 = $true) | (((sP20 @ sK358)) != $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f218])).
% 47.53/7.12 thf(f654,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP20 @ X0)) = $true) | (((sub @ (X1 @ (sK371 @ X1) @ (sK369 @ X1)) @ (sK370 @ X1))) != ((X1 @ (comp @ (sK371 @ X1) @ (sK370 @ X1)) @ (sub @ (sK369 @ X1) @ (sK370 @ X1))))) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((X0 @ id @ (sK368 @ X1 @ X0) @ id)) = $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f221])).
% 47.53/7.12 thf(f839,plain,(
% 47.53/7.12 (sP21 != $true) | (hoasinduction = $true)),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f850,plain,(
% 47.53/7.12 ( ! [X222 : term] : ((((d2term @ (sK587 @ X222))) = X222)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f864,plain,(
% 47.53/7.12 ( ! [X212 : term,X213 : term,X210 : term,X211 : term] : ((X211 = X213) | (((ap @ (sub @ X212 @ id) @ X211)) != ((ap @ (sub @ X210 @ id) @ X213))) | (hoasapinj2 != $true)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f866,plain,(
% 47.53/7.12 (hoasapinj2 = $true) | (sK582 != sK580)),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f904,plain,(
% 47.53/7.12 (one = ((d2term @ d_one)))),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f968,plain,(
% 47.53/7.12 ( ! [X62 : d_term] : ((d_one = X62)) )),
% 47.53/7.12 inference(cnf_transformation,[],[f279])).
% 47.53/7.12 thf(f1062,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP0 @ X0)) = $true) | (((X1 @ (comp @ (sK78 @ X1) @ (sK77 @ X1)) @ (sub @ (sK76 @ X1) @ (sK77 @ X1)))) != ((sub @ (X1 @ (sK78 @ X1) @ (sK76 @ X1)) @ (sK77 @ X1)))) | (((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true) | (((X0 @ id @ (hoaslam @ id @ X1) @ id)) = $true)) )),
% 47.53/7.12 inference(beta-eta_normalization,[],[f302])).
% 47.53/7.12 thf(f1224,definition,(
% 47.53/7.12 spl612_13 <=> (sP26 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_13])],[avatar_definition])).
% 47.53/7.12 thf(f1228,definition,(
% 47.53/7.12 spl612_14 <=> ! [X2 : (subst > term > term)] : ((((sK311 @ id @ (sK313 @ X2) @ id)) = $true) | (((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2))))) | (((sK311 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_14])],[avatar_definition])).
% 47.53/7.12 thf(f1229,plain,(
% 47.53/7.12 ( ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2))))) | (((sK311 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (((sK311 @ id @ (sK313 @ X2) @ id)) = $true)) ) | ~spl612_14),
% 47.53/7.12 inference(avatar_component_clause,[],[f1228])).
% 47.53/7.12 thf(f1230,plain,(
% 47.53/7.12 spl612_13 | spl612_14),
% 47.53/7.12 inference(avatar_split_clause,[],[f599,f1228,f1224])).
% 47.53/7.12 thf(f1564,definition,(
% 47.53/7.12 spl612_95 <=> (sP21 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_95])],[avatar_definition])).
% 47.53/7.12 thf(f1568,definition,(
% 47.53/7.12 spl612_96 <=> (hoasinduction = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_96])],[avatar_definition])).
% 47.53/7.12 thf(f1685,definition,(
% 47.53/7.12 spl612_124 <=> (sP2 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_124])],[avatar_definition])).
% 47.53/7.12 thf(f1730,definition,(
% 47.53/7.12 spl612_134 <=> ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK221 @ X3) @ (sK223 @ X3)) @ (sK222 @ X3))) != ((X3 @ (comp @ (sK221 @ X3) @ (sK222 @ X3)) @ (sub @ (sK223 @ X3) @ (sK222 @ X3))))) | (((sK219 @ id @ (sK220 @ X3) @ id)) = $true) | (((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_134])],[avatar_definition])).
% 47.53/7.12 thf(f1731,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK221 @ X3) @ (sK223 @ X3)) @ (sK222 @ X3))) != ((X3 @ (comp @ (sK221 @ X3) @ (sK222 @ X3)) @ (sub @ (sK223 @ X3) @ (sK222 @ X3))))) | (((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK219 @ id @ (sK220 @ X3) @ id)) = $true)) ) | ~spl612_134),
% 47.53/7.12 inference(avatar_component_clause,[],[f1730])).
% 47.53/7.12 thf(f1733,definition,(
% 47.53/7.12 spl612_135 <=> (sP37 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_135])],[avatar_definition])).
% 47.53/7.12 thf(f1736,plain,(
% 47.53/7.12 spl612_134 | spl612_135),
% 47.53/7.12 inference(avatar_split_clause,[],[f497,f1733,f1730])).
% 47.53/7.12 thf(f1781,definition,(
% 47.53/7.12 spl612_147 <=> (((sP20 @ sK358)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_147])],[avatar_definition])).
% 47.53/7.12 thf(f1784,plain,(
% 47.53/7.12 spl612_95 | ~spl612_147),
% 47.53/7.12 inference(avatar_split_clause,[],[f648,f1781,f1564])).
% 47.53/7.12 thf(f1794,definition,(
% 47.53/7.12 spl612_150 <=> (((sK358 @ id @ sK357 @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_150])],[avatar_definition])).
% 47.53/7.12 thf(f1796,plain,(
% 47.53/7.12 (((sK358 @ id @ sK357 @ id)) != $true) | spl612_150),
% 47.53/7.12 inference(avatar_component_clause,[],[f1794])).
% 47.53/7.12 thf(f1797,plain,(
% 47.53/7.12 spl612_95 | ~spl612_150),
% 47.53/7.12 inference(avatar_split_clause,[],[f645,f1794,f1564])).
% 47.53/7.12 thf(f1859,definition,(
% 47.53/7.12 spl612_165 <=> (sP36 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_165])],[avatar_definition])).
% 47.53/7.12 thf(f1912,definition,(
% 47.53/7.12 spl612_178 <=> (((sub @ sK224 @ id)) = sK224)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_178])],[avatar_definition])).
% 47.53/7.12 thf(f1914,plain,(
% 47.53/7.12 (((sub @ sK224 @ id)) != sK224) | spl612_178),
% 47.53/7.12 inference(avatar_component_clause,[],[f1912])).
% 47.53/7.12 thf(f1926,definition,(
% 47.53/7.12 spl612_181 <=> ! [X11 : (subst > term > term)] : ((((X11 @ (comp @ (sK233 @ X11) @ (sK231 @ X11)) @ (sub @ (sK232 @ X11) @ (sK231 @ X11)))) != ((sub @ (X11 @ (sK233 @ X11) @ (sK232 @ X11)) @ (sK231 @ X11)))) | (((sK229 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true) | (((sK229 @ id @ (sK234 @ X11) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_181])],[avatar_definition])).
% 47.53/7.12 thf(f1927,plain,(
% 47.53/7.12 ( ! [X11 : (subst > term > term)] : ((((X11 @ (comp @ (sK233 @ X11) @ (sK231 @ X11)) @ (sub @ (sK232 @ X11) @ (sK231 @ X11)))) != ((sub @ (X11 @ (sK233 @ X11) @ (sK232 @ X11)) @ (sK231 @ X11)))) | (((sK229 @ id @ (sK234 @ X11) @ id)) = $true) | (((sK229 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true)) ) | ~spl612_181),
% 47.53/7.12 inference(avatar_component_clause,[],[f1926])).
% 47.53/7.12 thf(f1928,plain,(
% 47.53/7.12 ~spl612_165 | spl612_181),
% 47.53/7.12 inference(avatar_split_clause,[],[f501,f1926,f1859])).
% 47.53/7.12 thf(f1954,definition,(
% 47.53/7.12 spl612_188 <=> (sP24 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_188])],[avatar_definition])).
% 47.53/7.12 thf(f1958,definition,(
% 47.53/7.12 spl612_189 <=> ! [X9 : (subst > term > subst > $o),X8 : term,X15 : term] : ((((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | (((X9 @ id @ (sK327 @ X9 @ X8) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_189])],[avatar_definition])).
% 47.53/7.12 thf(f1959,plain,(
% 47.53/7.12 ( ! [X8 : term,X9 : (subst > term > subst > $o),X15 : term] : ((((X9 @ id @ (sK327 @ X9 @ X8) @ id)) = $true) | (((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | (((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true)) ) | ~spl612_189),
% 47.53/7.12 inference(avatar_component_clause,[],[f1958])).
% 47.53/7.12 thf(f1960,plain,(
% 47.53/7.12 ~spl612_188 | spl612_189),
% 47.53/7.12 inference(avatar_split_clause,[],[f609,f1958,f1954])).
% 47.53/7.12 thf(f1974,definition,(
% 47.53/7.12 spl612_193 <=> ! [X9 : term,X8 : (subst > term > subst > $o)] : ((((X8 @ id @ (lam @ (sK317 @ X8 @ sh @ one)) @ id)) != $true) | (((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true) | (((X8 @ id @ (lam @ X9) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_193])],[avatar_definition])).
% 47.53/7.12 thf(f1975,plain,(
% 47.53/7.12 ( ! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ (sK317 @ X8 @ sh @ one)) @ id)) != $true) | (((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true) | (((X8 @ id @ (lam @ X9) @ id)) = $true)) ) | ~spl612_193),
% 47.53/7.12 inference(avatar_component_clause,[],[f1974])).
% 47.53/7.12 thf(f1976,plain,(
% 47.53/7.12 ~spl612_13 | spl612_193),
% 47.53/7.12 inference(avatar_split_clause,[],[f597,f1974,f1224])).
% 47.53/7.12 thf(f2374,plain,(
% 47.53/7.12 ~spl612_95 | spl612_96),
% 47.53/7.12 inference(avatar_split_clause,[],[f839,f1568,f1564])).
% 47.53/7.12 thf(f2452,definition,(
% 47.53/7.12 spl612_304 <=> (((sK219 @ id @ (lam @ sK218) @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_304])],[avatar_definition])).
% 47.53/7.12 thf(f2454,plain,(
% 47.53/7.12 (((sK219 @ id @ (lam @ sK218) @ id)) != $true) | spl612_304),
% 47.53/7.12 inference(avatar_component_clause,[],[f2452])).
% 47.53/7.12 thf(f2455,plain,(
% 47.53/7.12 spl612_135 | ~spl612_304),
% 47.53/7.12 inference(avatar_split_clause,[],[f494,f2452,f1733])).
% 47.53/7.12 thf(f2628,definition,(
% 47.53/7.12 spl612_344 <=> (((sK62 @ id @ sK63 @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_344])],[avatar_definition])).
% 47.53/7.12 thf(f2630,plain,(
% 47.53/7.12 (((sK62 @ id @ sK63 @ id)) != $true) | spl612_344),
% 47.53/7.12 inference(avatar_component_clause,[],[f2628])).
% 47.53/7.12 thf(f2631,plain,(
% 47.53/7.12 ~spl612_344 | spl612_124),
% 47.53/7.12 inference(avatar_split_clause,[],[f291,f1685,f2628])).
% 47.53/7.12 thf(f2985,definition,(
% 47.53/7.12 spl612_426 <=> (((sP0 @ sK62)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_426])],[avatar_definition])).
% 47.53/7.12 thf(f2987,plain,(
% 47.53/7.12 (((sP0 @ sK62)) != $true) | spl612_426),
% 47.53/7.12 inference(avatar_component_clause,[],[f2985])).
% 47.53/7.12 thf(f2988,plain,(
% 47.53/7.12 spl612_124 | ~spl612_426),
% 47.53/7.12 inference(avatar_split_clause,[],[f288,f2985,f1685])).
% 47.53/7.12 thf(f3046,definition,(
% 47.53/7.12 spl612_440 <=> ! [X10 : term] : ((((sK229 @ id @ X10 @ id)) != $true) | (((sK229 @ id @ (sub @ sK230 @ (push @ X10 @ id)) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_440])],[avatar_definition])).
% 47.53/7.12 thf(f3047,plain,(
% 47.53/7.12 ( ! [X10 : term] : ((((sK229 @ id @ X10 @ id)) != $true) | (((sK229 @ id @ (sub @ sK230 @ (push @ X10 @ id)) @ id)) = $true)) ) | ~spl612_440),
% 47.53/7.12 inference(avatar_component_clause,[],[f3046])).
% 47.53/7.12 thf(f3048,plain,(
% 47.53/7.12 ~spl612_165 | spl612_440),
% 47.53/7.12 inference(avatar_split_clause,[],[f503,f3046,f1859])).
% 47.53/7.12 thf(f3157,definition,(
% 47.53/7.12 spl612_465 <=> (((sK229 @ id @ (lam @ (sub @ sK230 @ (push @ one @ sh))) @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_465])],[avatar_definition])).
% 47.53/7.12 thf(f3159,plain,(
% 47.53/7.12 (((sK229 @ id @ (lam @ (sub @ sK230 @ (push @ one @ sh))) @ id)) != $true) | spl612_465),
% 47.53/7.12 inference(avatar_component_clause,[],[f3157])).
% 47.53/7.12 thf(f3160,plain,(
% 47.53/7.12 ~spl612_165 | ~spl612_465),
% 47.53/7.12 inference(avatar_split_clause,[],[f500,f3157,f1859])).
% 47.53/7.12 thf(f3184,definition,(
% 47.53/7.12 spl612_471 <=> (((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_471])],[avatar_definition])).
% 47.53/7.12 thf(f3186,plain,(
% 47.53/7.12 (((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id)) != $true) | spl612_471),
% 47.53/7.12 inference(avatar_component_clause,[],[f3184])).
% 47.53/7.12 thf(f3187,plain,(
% 47.53/7.12 ~spl612_471 | spl612_188),
% 47.53/7.12 inference(avatar_split_clause,[],[f614,f1954,f3184])).
% 47.53/7.12 thf(f3198,definition,(
% 47.53/7.12 spl612_474 <=> (hoasapinj2 = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_474])],[avatar_definition])).
% 47.53/7.12 thf(f3276,definition,(
% 47.53/7.12 spl612_492 <=> ! [X130 : term,X128 : term,X129 : term,X127 : term] : ((X127 = X128) | (((ap @ (sub @ X130 @ id) @ X127)) != ((ap @ (sub @ X129 @ id) @ X128))))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_492])],[avatar_definition])).
% 47.53/7.12 thf(f3277,plain,(
% 47.53/7.12 ( ! [X127 : term,X130 : term,X128 : term,X129 : term] : ((X127 = X128) | (((ap @ (sub @ X130 @ id) @ X127)) != ((ap @ (sub @ X129 @ id) @ X128)))) ) | ~spl612_492),
% 47.53/7.12 inference(avatar_component_clause,[],[f3276])).
% 47.53/7.12 thf(f3284,definition,(
% 47.53/7.12 spl612_494 <=> ! [X13 : term,X11 : (subst > term > subst > $o),X10 : term] : ((((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true) | (((X11 @ id @ (lam @ X10) @ id)) = $true) | (((X11 @ id @ (sK225 @ X11 @ id @ X13) @ id)) = $true) | (((X11 @ id @ X13 @ id)) != $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_494])],[avatar_definition])).
% 47.53/7.12 thf(f3285,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ (lam @ X10) @ id)) = $true) | (((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true) | (((X11 @ id @ (sK225 @ X11 @ id @ X13) @ id)) = $true)) ) | ~spl612_494),
% 47.53/7.12 inference(avatar_component_clause,[],[f3284])).
% 47.53/7.12 thf(f3286,plain,(
% 47.53/7.12 spl612_165 | ~spl612_178 | ~spl612_135 | spl612_494),
% 47.53/7.12 inference(avatar_split_clause,[],[f492,f3284,f1733,f1912,f1859])).
% 47.53/7.12 thf(f3477,definition,(
% 47.53/7.12 spl612_538 <=> (sK582 = sK580)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_538])],[avatar_definition])).
% 47.53/7.12 thf(f3479,plain,(
% 47.53/7.12 (sK582 != sK580) | spl612_538),
% 47.53/7.12 inference(avatar_component_clause,[],[f3477])).
% 47.53/7.12 thf(f3480,plain,(
% 47.53/7.12 spl612_474 | ~spl612_538),
% 47.53/7.12 inference(avatar_split_clause,[],[f866,f3477,f3198])).
% 47.53/7.12 thf(f3563,plain,(
% 47.53/7.12 spl612_492 | ~spl612_474),
% 47.53/7.12 inference(avatar_split_clause,[],[f864,f3198,f3276])).
% 47.53/7.12 thf(f3616,definition,(
% 47.53/7.12 spl612_569 <=> (((sK311 @ id @ (lam @ sK312) @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_569])],[avatar_definition])).
% 47.53/7.12 thf(f3618,plain,(
% 47.53/7.12 (((sK311 @ id @ (lam @ sK312) @ id)) != $true) | spl612_569),
% 47.53/7.12 inference(avatar_component_clause,[],[f3616])).
% 47.53/7.12 thf(f3619,plain,(
% 47.53/7.12 spl612_13 | ~spl612_569),
% 47.53/7.12 inference(avatar_split_clause,[],[f601,f3616,f1224])).
% 47.53/7.12 thf(f3651,definition,(
% 47.53/7.12 spl612_577 <=> ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK325 @ X3) @ (sK324 @ X3)) @ (sK323 @ X3))) != ((X3 @ (comp @ (sK325 @ X3) @ (sK323 @ X3)) @ (sub @ (sK324 @ X3) @ (sK323 @ X3))))) | (((sK322 @ id @ (sK326 @ X3) @ id)) = $true) | (((sK322 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true))),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_577])],[avatar_definition])).
% 47.53/7.12 thf(f3652,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sub @ (X3 @ (sK325 @ X3) @ (sK324 @ X3)) @ (sK323 @ X3))) != ((X3 @ (comp @ (sK325 @ X3) @ (sK323 @ X3)) @ (sub @ (sK324 @ X3) @ (sK323 @ X3))))) | (((sK322 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK322 @ id @ (sK326 @ X3) @ id)) = $true)) ) | ~spl612_577),
% 47.53/7.12 inference(avatar_component_clause,[],[f3651])).
% 47.53/7.12 thf(f3653,plain,(
% 47.53/7.12 spl612_577 | spl612_188),
% 47.53/7.12 inference(avatar_split_clause,[],[f612,f1954,f3651])).
% 47.53/7.12 thf(f3842,plain,(
% 47.53/7.12 ~spl612_124 | ~spl612_96),
% 47.53/7.12 inference(avatar_split_clause,[],[f304,f1568,f1685])).
% 47.53/7.12 thf(f3935,plain,(
% 47.53/7.12 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 47.53/7.12 inference(superposition,[],[f904,f968])).
% 47.53/7.12 thf(f3953,plain,(
% 47.53/7.12 ( ! [X222 : term] : ((one = X222)) )),
% 47.53/7.12 inference(forward_demodulation,[],[f850,f3935])).
% 47.53/7.12 thf(f3964,plain,(
% 47.53/7.12 (one != sK580) | spl612_538),
% 47.53/7.12 inference(superposition,[],[f3479,f3953])).
% 47.53/7.12 thf(f3967,plain,(
% 47.53/7.12 $false | spl612_538),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f3964,f3953])).
% 47.53/7.12 thf(f3968,plain,(
% 47.53/7.12 spl612_538),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f3967])).
% 47.53/7.12 thf(f3973,plain,(
% 47.53/7.12 ( ! [X127 : term,X130 : term,X128 : term] : ((one != ((ap @ (sub @ X130 @ id) @ X127))) | (X127 = X128)) ) | ~spl612_492),
% 47.53/7.12 inference(forward_demodulation,[],[f3277,f3953])).
% 47.53/7.12 thf(f3978,plain,(
% 47.53/7.12 ( ! [X127 : term,X128 : term] : ((X127 = X128)) ) | ~spl612_492),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f3973,f3953])).
% 47.53/7.12 thf(f4156,plain,(
% 47.53/7.12 (((sK358 @ id @ one @ id)) != $true) | spl612_150),
% 47.53/7.12 inference(forward_demodulation,[],[f1796,f3953])).
% 47.53/7.12 thf(f4453,plain,(
% 47.53/7.12 (((sK311 @ id @ one @ id)) != $true) | spl612_569),
% 47.53/7.12 inference(forward_demodulation,[],[f3618,f3953])).
% 47.53/7.12 thf(f4454,plain,(
% 47.53/7.12 ( ! [X0 : term] : ((((sK311 @ id @ X0 @ id)) != $true)) ) | spl612_569),
% 47.53/7.12 inference(superposition,[],[f4453,f3953])).
% 47.53/7.12 thf(f4616,plain,(
% 47.53/7.12 (((sK229 @ id @ one @ id)) != $true) | spl612_465),
% 47.53/7.12 inference(forward_demodulation,[],[f3159,f3953])).
% 47.53/7.12 thf(f4652,plain,(
% 47.53/7.12 ( ! [X10 : term] : ((((sK229 @ id @ X10 @ id)) != $true) | (((sK229 @ id @ one @ id)) = $true)) ) | ~spl612_440),
% 47.53/7.12 inference(forward_demodulation,[],[f3047,f3953])).
% 47.53/7.12 thf(f4653,plain,(
% 47.53/7.12 ( ! [X10 : term] : ((((sK229 @ id @ X10 @ id)) != $true)) ) | (~spl612_440 | spl612_465)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f4652,f4616])).
% 47.53/7.12 thf(f5520,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ one @ id)) = $true) | (((sP45 @ X0)) = $true)) )),
% 47.53/7.12 inference(forward_demodulation,[],[f447,f3953])).
% 47.53/7.12 thf(f6899,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ one @ id)) != $true) | (((sP45 @ X0)) = $true)) )),
% 47.53/7.12 inference(forward_demodulation,[],[f446,f3953])).
% 47.53/7.12 thf(f6900,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((sP45 @ X0)) = $true)) )),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f6899,f5520])).
% 47.53/7.12 thf(f7466,plain,(
% 47.53/7.12 ( ! [X3 : term,X0 : (subst > term > subst > $o),X4 : term] : ((((X0 @ id @ (ap @ (sub @ X3 @ id) @ X4) @ id)) = $true) | (((X0 @ id @ X3 @ id)) != $true) | (((X0 @ id @ X4 @ id)) != $true)) )),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f445,f6900])).
% 47.53/7.12 thf(f7467,plain,(
% 47.53/7.12 ( ! [X3 : term,X0 : (subst > term > subst > $o),X4 : term] : ((((X0 @ id @ one @ id)) = $true) | (((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ X3 @ id)) != $true)) )),
% 47.53/7.12 inference(forward_demodulation,[],[f7466,f3953])).
% 47.53/7.12 thf(f7655,plain,(
% 47.53/7.12 ( ! [X8 : term,X9 : (subst > term > subst > $o),X15 : term] : ((((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true) | (((X9 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ one @ id)) = $true)) ) | ~spl612_189),
% 47.53/7.12 inference(forward_demodulation,[],[f1959,f3953])).
% 47.53/7.12 thf(f7656,plain,(
% 47.53/7.12 ( ! [X9 : (subst > term > subst > $o),X15 : term] : ((((X9 @ id @ (sK328 @ X9 @ id @ X15) @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ one @ id)) = $true)) ) | ~spl612_189),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7655,f7467])).
% 47.53/7.12 thf(f7657,plain,(
% 47.53/7.12 ( ! [X9 : (subst > term > subst > $o),X15 : term] : ((((X9 @ id @ one @ id)) = $true) | (((X9 @ id @ X15 @ id)) != $true)) ) | ~spl612_189),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7656,f7467])).
% 47.53/7.12 thf(f7834,plain,(
% 47.53/7.12 ( ! [X2 : (subst > term > term)] : ((((sK311 @ id @ (sK313 @ X2) @ id)) = $true) | (((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2)))))) ) | (~spl612_14 | spl612_569)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f1229,f4454])).
% 47.53/7.12 thf(f7835,plain,(
% 47.53/7.12 ( ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK314 @ X2) @ (sK316 @ X2)) @ (sK315 @ X2))) != ((X2 @ (comp @ (sK314 @ X2) @ (sK315 @ X2)) @ (sub @ (sK316 @ X2) @ (sK315 @ X2)))))) ) | (~spl612_14 | spl612_569)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7834,f4454])).
% 47.53/7.12 thf(f7836,plain,(
% 47.53/7.12 $false | (~spl612_14 | ~spl612_492 | spl612_569)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7835,f3978])).
% 47.53/7.12 thf(f7837,plain,(
% 47.53/7.12 ~spl612_14 | ~spl612_492 | spl612_569),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f7836])).
% 47.53/7.12 thf(f7843,plain,(
% 47.53/7.12 ( ! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ X9) @ id)) = $true) | (((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true) | (((X8 @ id @ one @ id)) != $true)) ) | ~spl612_193),
% 47.53/7.12 inference(forward_demodulation,[],[f1975,f3953])).
% 47.53/7.12 thf(f7847,plain,(
% 47.53/7.12 ( ! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ X9) @ id)) = $true) | (((X8 @ id @ (sub @ X9 @ (push @ (sK318 @ X9 @ X8) @ id)) @ id)) != $true)) ) | (~spl612_189 | ~spl612_193)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7843,f7657])).
% 47.53/7.12 thf(f7850,plain,(
% 47.53/7.12 ( ! [X8 : (subst > term > subst > $o),X9 : term] : ((((X8 @ id @ (lam @ X9) @ id)) = $true) | (((X8 @ id @ one @ id)) != $true)) ) | (~spl612_189 | ~spl612_193)),
% 47.53/7.12 inference(forward_demodulation,[],[f7847,f3953])).
% 47.53/7.12 thf(f7991,plain,(
% 47.53/7.12 ( ! [X11 : (subst > term > term)] : ((((sK229 @ id @ (lam @ (X11 @ sh @ one)) @ id)) = $true) | (((sK229 @ id @ (sK234 @ X11) @ id)) = $true)) ) | (~spl612_181 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f1927,f3978])).
% 47.53/7.12 thf(f7992,plain,(
% 47.53/7.12 ( ! [X11 : (subst > term > term)] : ((((sK229 @ id @ (sK234 @ X11) @ id)) = $true)) ) | (~spl612_181 | ~spl612_440 | spl612_465 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7991,f4653])).
% 47.53/7.12 thf(f7993,plain,(
% 47.53/7.12 $false | (~spl612_181 | ~spl612_440 | spl612_465 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f7992,f4653])).
% 47.53/7.12 thf(f7994,plain,(
% 47.53/7.12 ~spl612_181 | ~spl612_440 | spl612_465 | ~spl612_492),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f7993])).
% 47.53/7.12 thf(f7998,plain,(
% 47.53/7.12 $false | (spl612_178 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f1914,f3978])).
% 47.53/7.12 thf(f7999,plain,(
% 47.53/7.12 spl612_178 | ~spl612_492),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f7998])).
% 47.53/7.12 thf(f8009,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ one @ id)) = $true) | (((X11 @ id @ (lam @ X10) @ id)) = $true) | (((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true)) ) | ~spl612_494),
% 47.53/7.12 inference(forward_demodulation,[],[f3285,f3953])).
% 47.53/7.12 thf(f8012,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ (lam @ X10) @ id)) = $true) | (((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ (sub @ X10 @ (push @ (sK226 @ X11 @ X10) @ id)) @ id)) != $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_494)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f8009,f7850])).
% 47.53/7.12 thf(f8015,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ X13 @ id)) != $true) | (((X11 @ id @ one @ id)) != $true) | (((X11 @ id @ (lam @ X10) @ id)) = $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_494)),
% 47.53/7.12 inference(forward_demodulation,[],[f8012,f3953])).
% 47.53/7.12 thf(f8018,plain,(
% 47.53/7.12 ( ! [X10 : term,X11 : (subst > term > subst > $o),X13 : term] : ((((X11 @ id @ (lam @ X10) @ id)) = $true) | (((X11 @ id @ X13 @ id)) != $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_494)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f8015,f7657])).
% 47.53/7.12 thf(f8161,plain,(
% 47.53/7.12 (((sK219 @ id @ one @ id)) != $true) | spl612_304),
% 47.53/7.12 inference(forward_demodulation,[],[f2454,f3953])).
% 47.53/7.12 thf(f8163,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sK219 @ id @ (sK220 @ X3) @ id)) = $true) | (((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) ) | (~spl612_134 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f1731,f3978])).
% 47.53/7.12 thf(f8166,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK219 @ id @ one @ id)) = $true)) ) | (~spl612_134 | ~spl612_492)),
% 47.53/7.12 inference(forward_demodulation,[],[f8163,f3953])).
% 47.53/7.12 thf(f8169,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sK219 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true)) ) | (~spl612_134 | ~spl612_189 | ~spl612_193 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f8166,f7850])).
% 47.53/7.12 thf(f8170,plain,(
% 47.53/7.12 (((sK219 @ id @ one @ id)) = $true) | (~spl612_134 | ~spl612_189 | ~spl612_193 | ~spl612_492)),
% 47.53/7.12 inference(forward_demodulation,[],[f8169,f3953])).
% 47.53/7.12 thf(f8223,plain,(
% 47.53/7.12 $false | (~spl612_134 | ~spl612_189 | ~spl612_193 | spl612_304 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f8170,f8161])).
% 47.53/7.12 thf(f8224,plain,(
% 47.53/7.12 ~spl612_134 | ~spl612_189 | ~spl612_193 | spl612_304 | ~spl612_492),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f8223])).
% 47.53/7.12 thf(f9577,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((sub @ (X1 @ (sK371 @ X1) @ (sK369 @ X1)) @ (sK370 @ X1))) != ((X1 @ (comp @ (sK371 @ X1) @ (sK370 @ X1)) @ (sub @ (sK369 @ X1) @ (sK370 @ X1))))) | (((sP20 @ X0)) = $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_494)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f654,f8018])).
% 47.53/7.12 thf(f9578,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((sP20 @ X0)) = $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f9577,f3978])).
% 47.53/7.12 thf(f9579,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ one @ id)) = $true) | (((sP20 @ X0)) = $true)) ) | (~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494)),
% 47.53/7.12 inference(forward_demodulation,[],[f9578,f3953])).
% 47.53/7.12 thf(f9601,plain,(
% 47.53/7.12 (((sP20 @ sK358)) = $true) | ($true != $true) | (spl612_150 | ~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494)),
% 47.53/7.12 inference(superposition,[],[f4156,f9579])).
% 47.53/7.12 thf(f9650,plain,(
% 47.53/7.12 (((sP20 @ sK358)) = $true) | (spl612_150 | ~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494)),
% 47.53/7.12 inference(trivial_inequality_removal,[],[f9601])).
% 47.53/7.12 thf(f9713,plain,(
% 47.53/7.12 spl612_147 | spl612_150 | ~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494),
% 47.53/7.12 inference(avatar_split_clause,[],[f9650,f3284,f3276,f1974,f1958,f1794,f1781])).
% 47.53/7.12 thf(f9722,plain,(
% 47.53/7.12 (((sK62 @ id @ one @ id)) != $true) | spl612_344),
% 47.53/7.12 inference(forward_demodulation,[],[f2630,f3953])).
% 47.53/7.12 thf(f10109,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (sK75 @ X1 @ X0) @ id)) = $true) | (((X0 @ id @ (hoaslam @ id @ X1) @ id)) = $true) | (((sP0 @ X0)) = $true)) ) | ~spl612_492),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f1062,f3978])).
% 47.53/7.12 thf(f10110,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (hoaslam @ id @ X1) @ id)) = $true) | (((X0 @ id @ one @ id)) = $true) | (((sP0 @ X0)) = $true)) ) | ~spl612_492),
% 47.53/7.12 inference(forward_demodulation,[],[f10109,f3953])).
% 47.53/7.12 thf(f10111,plain,(
% 47.53/7.12 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ one @ id)) = $true) | (((sP0 @ X0)) = $true)) ) | (~spl612_189 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f10110,f7657])).
% 47.53/7.12 thf(f10132,plain,(
% 47.53/7.12 (((sP0 @ sK62)) = $true) | ($true != $true) | (~spl612_189 | spl612_344 | ~spl612_492)),
% 47.53/7.12 inference(superposition,[],[f9722,f10111])).
% 47.53/7.12 thf(f10216,plain,(
% 47.53/7.12 (((sP0 @ sK62)) = $true) | (~spl612_189 | spl612_344 | ~spl612_492)),
% 47.53/7.12 inference(trivial_inequality_removal,[],[f10132])).
% 47.53/7.12 thf(f10232,plain,(
% 47.53/7.12 $false | (~spl612_189 | spl612_344 | spl612_426 | ~spl612_492)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f10216,f2987])).
% 47.53/7.12 thf(f10233,plain,(
% 47.53/7.12 ~spl612_189 | spl612_344 | spl612_426 | ~spl612_492),
% 47.53/7.12 inference(avatar_contradiction_clause,[],[f10232])).
% 47.53/7.12 thf(f10243,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sK322 @ id @ (lam @ (X3 @ sh @ one)) @ id)) = $true) | (((sK322 @ id @ (sK326 @ X3) @ id)) = $true)) ) | (~spl612_492 | ~spl612_577)),
% 47.53/7.12 inference(forward_subsumption_resolution,[],[f3652,f3978])).
% 47.53/7.12 thf(f10260,plain,(
% 47.53/7.12 (((sK322 @ id @ one @ id)) != $true) | spl612_471),
% 47.53/7.12 inference(forward_demodulation,[],[f3186,f3953])).
% 47.53/7.12 thf(f10301,plain,(
% 47.53/7.12 ( ! [X3 : (subst > term > term)] : ((((sK322 @ id @ (sK326 @ X3) @ id)) = $true) | (((sK322 @ id @ one @ id)) = $true)) ) | (~spl612_492 | ~spl612_577)),
% 47.53/7.12 inference(forward_demodulation,[],[f10243,f3953])).
% 47.53/7.12 thf(f10305,definition,(
% 47.53/7.12 spl612_723 <=> (((sK322 @ id @ one @ id)) = $true)),
% 47.53/7.12 introduced(definition,[new_symbols(definition,[spl612_723])],[avatar_definition])).
% 47.53/7.12 thf(f10318,plain,(
% 47.53/7.12 ~spl612_723 | spl612_471),
% 47.53/7.12 inference(avatar_split_clause,[],[f10260,f3184,f10305])).
% 47.53/7.12 thf(f10481,plain,(
% 47.53/7.12 (((sK322 @ id @ one @ id)) = $true) | (((sK322 @ id @ one @ id)) = $true) | (~spl612_492 | ~spl612_577)),
% 47.53/7.12 inference(forward_demodulation,[],[f10301,f3953])).
% 47.53/7.12 thf(f10482,plain,(
% 47.53/7.12 (((sK322 @ id @ one @ id)) = $true) | (~spl612_492 | ~spl612_577)),
% 47.53/7.12 inference(duplicate_literal_removal,[],[f10481])).
% 47.53/7.12 thf(f10508,plain,(
% 47.53/7.12 spl612_723 | ~spl612_492 | ~spl612_577),
% 47.53/7.12 inference(avatar_split_clause,[],[f10482,f3651,f3276,f10305])).
% 47.53/7.12 cnf(s7, plain, spl612_13 | spl612_14, inference(sat_conversion,[],[f1230])).
% 47.53/7.12 cnf(s90, plain, spl612_134 | spl612_135, inference(sat_conversion,[],[f1736])).
% 47.53/7.12 cnf(s100, plain, spl612_95 | ~spl612_147, inference(sat_conversion,[],[f1784])).
% 47.53/7.12 cnf(s103, plain, spl612_95 | ~spl612_150, inference(sat_conversion,[],[f1797])).
% 47.53/7.12 cnf(s130, plain, ~spl612_165 | spl612_181, inference(sat_conversion,[],[f1928])).
% 47.53/7.12 cnf(s136, plain, ~spl612_188 | spl612_189, inference(sat_conversion,[],[f1960])).
% 47.53/7.12 cnf(s140, plain, ~spl612_13 | spl612_193, inference(sat_conversion,[],[f1976])).
% 47.53/7.12 cnf(s229, plain, ~spl612_95 | spl612_96, inference(sat_conversion,[],[f2374])).
% 47.53/7.12 cnf(s246, plain, spl612_135 | ~spl612_304, inference(sat_conversion,[],[f2455])).
% 47.53/7.12 cnf(s288, plain, spl612_124 | ~spl612_344, inference(sat_conversion,[],[f2631])).
% 47.53/7.12 cnf(s379, plain, spl612_124 | ~spl612_426, inference(sat_conversion,[],[f2988])).
% 47.53/7.12 cnf(s393, plain, ~spl612_165 | spl612_440, inference(sat_conversion,[],[f3048])).
% 47.53/7.12 cnf(s422, plain, ~spl612_165 | ~spl612_465, inference(sat_conversion,[],[f3160])).
% 47.53/7.12 cnf(s430, plain, spl612_188 | ~spl612_471, inference(sat_conversion,[],[f3187])).
% 47.53/7.12 cnf(s452, plain, ~spl612_135 | spl612_165 | ~spl612_178 | spl612_494, inference(sat_conversion,[],[f3286])).
% 47.53/7.12 cnf(s496, plain, spl612_474 | ~spl612_538, inference(sat_conversion,[],[f3480])).
% 47.53/7.12 cnf(s518, plain, ~spl612_474 | spl612_492, inference(sat_conversion,[],[f3563])).
% 47.53/7.12 cnf(s534, plain, spl612_13 | ~spl612_569, inference(sat_conversion,[],[f3619])).
% 47.53/7.12 cnf(s543, plain, spl612_188 | spl612_577, inference(sat_conversion,[],[f3653])).
% 47.53/7.12 cnf(s590, plain, ~spl612_96 | ~spl612_124, inference(sat_conversion,[],[f3842])).
% 47.53/7.12 cnf(s618, plain, spl612_538, inference(sat_conversion,[],[f3968])).
% 47.53/7.12 cnf(s740, plain, ~spl612_14 | ~spl612_492 | spl612_569, inference(sat_conversion,[],[f7837])).
% 47.53/7.12 cnf(s741, plain, ~spl612_181 | ~spl612_440 | spl612_465 | ~spl612_492, inference(sat_conversion,[],[f7994])).
% 47.53/7.12 cnf(s742, plain, spl612_178 | ~spl612_492, inference(sat_conversion,[],[f7999])).
% 47.53/7.12 cnf(s755, plain, ~spl612_134 | ~spl612_189 | ~spl612_193 | spl612_304 | ~spl612_492, inference(sat_conversion,[],[f8224])).
% 47.53/7.12 cnf(s815, plain, spl612_147 | spl612_150 | ~spl612_189 | ~spl612_193 | ~spl612_492 | ~spl612_494, inference(sat_conversion,[],[f9713])).
% 47.53/7.12 cnf(s856, plain, ~spl612_189 | spl612_344 | spl612_426 | ~spl612_492, inference(sat_conversion,[],[f10233])).
% 47.53/7.12 cnf(s861, plain, spl612_471 | ~spl612_723, inference(sat_conversion,[],[f10318])).
% 47.53/7.12 cnf(s871, plain, ~spl612_492 | ~spl612_577 | spl612_723, inference(sat_conversion,[],[f10508])).
% 47.53/7.12 cnf(s873, plain, spl612_474, inference(rat,[],[s496,s618])).
% 47.53/7.12 cnf(s874, plain, spl612_492, inference(rat,[],[s518,s873])).
% 47.53/7.12 cnf(s877, plain, spl612_178, inference(rat,[],[s742,s874])).
% 47.53/7.12 cnf(s907, plain, ~spl612_135 | spl612_165 | spl612_494, inference(rat,[],[s452,s877])).
% 47.53/7.12 cnf(s999, plain, spl612_13, inference(rat,[],[s740,s7,s534,s874])).
% 47.53/7.12 cnf(s1005, plain, spl612_193, inference(rat,[],[s140,s999])).
% 47.53/7.12 cnf(s1018, plain, ~spl612_165, inference(rat,[],[s741,s130,s393,s422,s874])).
% 47.53/7.12 cnf(s1025, plain, spl612_188, inference(rat,[],[s861,s871,s430,s543,s874])).
% 47.53/7.12 cnf(s1032, plain, spl612_189, inference(rat,[],[s136,s1025])).
% 47.53/7.12 cnf(s1033, plain, spl612_135, inference(rat,[],[s755,s90,s246,s1005,s1032,s874])).
% 47.53/7.12 cnf(s1038, plain, spl612_494, inference(rat,[],[s907,s1018,s1033])).
% 47.53/7.12 cnf(s1052, plain, spl612_95, inference(rat,[],[s815,s100,s103,s1032,s1038,s874,s1005])).
% 47.53/7.12 cnf(s1061, plain, spl612_96, inference(rat,[],[s229,s1052])).
% 47.53/7.12 cnf(s1062, plain, ~spl612_124, inference(rat,[],[s590,s1061])).
% 47.53/7.12 cnf(s1065, plain, ~spl612_426, inference(rat,[],[s379,s1062])).
% 47.53/7.12 cnf(s1066, plain, ~spl612_344, inference(rat,[],[s288,s1062])).
% 47.53/7.12 cnf(s1069, plain, $false, inference(rat,[],[s856,s874,s1032,s1065,s1066])).
% 47.53/7.12 thf(f10554,plain,(
% 47.53/7.12 $false),
% 47.53/7.12 inference(avatar_sat_refutation,[],[s1069])).
% 47.53/7.12 % SZS output end Proof for theBenchmark
% 47.53/7.12 % (2686150)------------------------------
% 47.53/7.12 % (2686150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 47.53/7.12 % (2686150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 47.53/7.12 % (2686150)CaDiCaL version: 2.1.3
% 47.53/7.12 % (2686150)Termination reason: Refutation
% 47.53/7.12 % (2686150)Time elapsed: 0.397 s
% 47.53/7.12 % (2686150)Peak memory usage: 19 MB
% 47.53/7.12 % (2686150)Instructions burned: 860 (million)
% 47.53/7.12 % (2685728)Success in time 6.846 s
% 47.53/7.12 % Vampire exiting
%------------------------------------------------------------------------------