%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX163^1 : 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 : n001.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 08:40:36 AM UTC 2026
% Result : Theorem 46.03s 6.93s
% Output : Refutation 46.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX163^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:15:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.26 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
% 0.73/0.40 % (1435380)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.73/0.40 % (1435390)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=292035220:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.73/0.40 % (1435391)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.73/0.40 % (1435391)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
% 0.73/0.40 % (1435387)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=458877465:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.73/0.40 % (1435385)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2292444669:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.73/0.40 % (1435386)lrs+10_16_si=on:nwc=1.5:random_seed=3843396702:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.73/0.40 % (1435389)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=540242425:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.73/0.40 % (1435388)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=552253211: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)
% 0.73/0.40 % (1435391)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=1083783926:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.73/0.40 % (1435387)Instruction limit reached!
% 0.73/0.40 % (1435387)------------------------------
% 0.73/0.40 % (1435387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (1435387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (1435387)CaDiCaL version: 2.1.3
% 0.73/0.40 % (1435387)Termination reason: Instruction limit
% 0.73/0.40 % (1435387)Termination phase: shuffling
% 0.73/0.40 % (1435387)Time elapsed: 0.003 s
% 0.73/0.40 % (1435387)Peak memory usage: 9 MB
% 0.73/0.40 % (1435387)Instructions burned: 6 (million)
% 0.73/0.40 % (1435386)Instruction limit reached!
% 0.73/0.40 % (1435386)------------------------------
% 0.73/0.40 % (1435386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (1435386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (1435386)CaDiCaL version: 2.1.3
% 0.73/0.40 % (1435386)Termination reason: Instruction limit
% 0.73/0.40 % (1435386)Termination phase: shuffling
% 0.73/0.40 % (1435386)Time elapsed: 0.008 s
% 0.73/0.40 % (1435386)Peak memory usage: 10 MB
% 0.73/0.40 % (1435386)Instructions burned: 18 (million)
% 0.73/0.40 % (1435389)Instruction limit reached!
% 0.73/0.40 % (1435389)------------------------------
% 0.73/0.40 % (1435389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (1435389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (1435389)CaDiCaL version: 2.1.3
% 0.73/0.40 % (1435389)Termination reason: Instruction limit
% 0.73/0.40 % (1435389)Termination phase: Property scanning
% 0.73/0.40 % (1435389)Time elapsed: 0.011 s
% 0.73/0.40 % (1435389)Peak memory usage: 10 MB
% 0.73/0.40 % (1435389)Instructions burned: 25 (million)
% 0.73/0.40 % (1435390)Instruction limit reached!
% 0.73/0.40 % (1435390)------------------------------
% 0.73/0.40 % (1435390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (1435390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (1435390)CaDiCaL version: 2.1.3
% 0.73/0.40 % (1435390)Termination reason: Instruction limit
% 0.73/0.40 % (1435390)Termination phase: Preprocessing 3
% 0.73/0.40 % (1435390)Time elapsed: 0.018 s
% 0.73/0.40 % (1435390)Peak memory usage: 12 MB
% 0.73/0.40 % (1435390)Instructions burned: 76 (million)
% 0.73/0.40 % (1435401)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.40 % (1435401)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1107078824:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.73/0.44 % (1435399)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1320712308:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.44 % (1435401)Instruction limit reached!
% 0.73/0.44 % (1435401)------------------------------
% 0.73/0.44 % (1435401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.44 % (1435401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.44 % (1435401)CaDiCaL version: 2.1.3
% 0.73/0.44 % (1435401)Termination reason: Instruction limit
% 0.73/0.44 % (1435401)Termination phase: shuffling
% 0.73/0.44 % (1435401)Time elapsed: 0.002 s
% 0.73/0.44 % (1435401)Peak memory usage: 9 MB
% 0.73/0.44 % (1435401)Instructions burned: 10 (million)
% 0.73/0.44 % (1435399)Instruction limit reached!
% 0.73/0.44 % (1435399)------------------------------
% 0.73/0.44 % (1435399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.44 % (1435399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.44 % (1435399)CaDiCaL version: 2.1.3
% 0.73/0.44 % (1435399)Termination reason: Instruction limit
% 0.73/0.44 % (1435399)Termination phase: shuffling
% 0.73/0.44 % (1435399)Time elapsed: 0.001 s
% 0.73/0.44 % (1435399)Peak memory usage: 9 MB
% 0.73/0.44 % (1435399)Instructions burned: 3 (million)
% 0.73/0.44 % (1435400)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3692295496:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.73/0.44 % (1435402)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2879964501:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.73/0.44 % (1435400)Instruction limit reached!
% 0.73/0.44 % (1435400)------------------------------
% 0.73/0.44 % (1435400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.44 % (1435400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.44 % (1435400)CaDiCaL version: 2.1.3
% 0.73/0.44 % (1435400)Termination reason: Instruction limit
% 0.73/0.44 % (1435400)Termination phase: shuffling
% 0.73/0.44 % (1435400)Time elapsed: 0.005 s
% 0.73/0.44 % (1435400)Peak memory usage: 10 MB
% 0.73/0.44 % (1435400)Instructions burned: 12 (million)
% 0.73/0.44 % (1435405)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
% 0.73/0.44 % (1435405)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.44 % (1435405)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=661707240:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.73/0.44 % (1435402)Instruction limit reached!
% 0.73/0.44 % (1435402)------------------------------
% 0.73/0.44 % (1435402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.44 % (1435402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.44 % (1435402)CaDiCaL version: 2.1.3
% 0.73/0.44 % (1435402)Termination reason: Instruction limit
% 0.73/0.44 % (1435402)Termination phase: shuffling
% 0.73/0.44 % (1435402)Time elapsed: 0.006 s
% 0.73/0.44 % (1435402)Peak memory usage: 10 MB
% 0.73/0.44 % (1435402)Instructions burned: 12 (million)
% 0.73/0.44 % (1435405)Instruction limit reached!
% 0.73/0.44 % (1435405)------------------------------
% 0.73/0.44 % (1435405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.44 % (1435405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.44 % (1435405)CaDiCaL version: 2.1.3
% 0.73/0.44 % (1435405)Termination reason: Instruction limit
% 0.73/0.44 % (1435405)Termination phase: Property scanning
% 0.73/0.44 % (1435405)Time elapsed: 0.007 s
% 0.73/0.44 % (1435405)Peak memory usage: 10 MB
% 0.73/0.44 % (1435405)Instructions burned: 32 (million)
% 0.73/0.44 % (1435407)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=2532568909:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.73/0.44 % (1435411)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.73/0.47 % (1435409)lrs+10_1_si=on:cs=on:random_seed=1980647654:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.73/0.47 % (1435412)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1909780662:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.73/0.47 % (1435411)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=1236384047:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.47 % (1435409)Instruction limit reached!
% 0.73/0.47 % (1435409)------------------------------
% 0.73/0.47 % (1435409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (1435409)CaDiCaL version: 2.1.3
% 0.73/0.47 % (1435409)Termination reason: Instruction limit
% 0.73/0.47 % (1435409)Termination phase: shuffling
% 0.73/0.47 % (1435409)Time elapsed: 0.004 s
% 0.73/0.47 % (1435409)Peak memory usage: 9 MB
% 0.73/0.47 % (1435409)Instructions burned: 9 (million)
% 0.73/0.47 % (1435411)Instruction limit reached!
% 0.73/0.47 % (1435411)------------------------------
% 0.73/0.47 % (1435411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (1435411)CaDiCaL version: 2.1.3
% 0.73/0.47 % (1435411)Termination reason: Instruction limit
% 0.73/0.47 % (1435411)Termination phase: shuffling
% 0.73/0.47 % (1435411)Time elapsed: 0.002 s
% 0.73/0.47 % (1435411)Peak memory usage: 10 MB
% 0.73/0.47 % (1435411)Instructions burned: 3 (million)
% 0.73/0.47 % (1435385)Instruction limit reached!
% 0.73/0.47 % (1435385)------------------------------
% 0.73/0.47 % (1435385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (1435385)CaDiCaL version: 2.1.3
% 0.73/0.47 % (1435385)Termination reason: Instruction limit
% 0.73/0.47 % (1435385)Termination phase: Preprocessing 3
% 0.73/0.47 % (1435385)Time elapsed: 0.065 s
% 0.73/0.47 % (1435385)Peak memory usage: 12 MB
% 0.73/0.47 % (1435385)Instructions burned: 87 (million)
% 0.73/0.47 % (1435412)Instruction limit reached!
% 0.73/0.47 % (1435412)------------------------------
% 0.73/0.47 % (1435412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (1435412)CaDiCaL version: 2.1.3
% 0.73/0.47 % (1435412)Termination reason: Instruction limit
% 0.73/0.47 % (1435412)Termination phase: Property scanning
% 0.73/0.47 % (1435412)Time elapsed: 0.009 s
% 0.73/0.47 % (1435412)Peak memory usage: 11 MB
% 0.73/0.47 % (1435412)Instructions burned: 39 (million)
% 0.73/0.47 % (1435391)Instruction limit reached!
% 0.73/0.47 % (1435391)------------------------------
% 0.73/0.47 % (1435391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (1435391)CaDiCaL version: 2.1.3
% 0.73/0.47 % (1435391)Termination reason: Instruction limit
% 0.73/0.47 % (1435391)Termination phase: Property scanning
% 0.73/0.47 % (1435391)Time elapsed: 0.070 s
% 0.73/0.47 % (1435391)Peak memory usage: 13 MB
% 0.73/0.47 % (1435391)Instructions burned: 157 (million)
% 0.73/0.47 % (1435417)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3515192131:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.73/0.47 % (1435418)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=646548955:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.73/0.47 % (1435419)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=962665045:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.73/0.47 % (1435420)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4250746498:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.73/0.47 % (1435407)Instruction limit reached!
% 0.73/0.47 % (1435407)------------------------------
% 0.73/0.47 % (1435407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (1435407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (1435407)CaDiCaL version: 2.1.3
% 1.44/0.53 % (1435407)Termination reason: Instruction limit
% 1.44/0.53 % (1435407)Termination phase: Saturation
% 1.44/0.53 % (1435407)Time elapsed: 0.038 s
% 1.44/0.53 % (1435407)Peak memory usage: 12 MB
% 1.44/0.53 % (1435407)Instructions burned: 86 (million)
% 1.44/0.53 % (1435421)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=570220916:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.44/0.53 % (1435419)Instruction limit reached!
% 1.44/0.53 % (1435419)------------------------------
% 1.44/0.53 % (1435419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (1435419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (1435419)CaDiCaL version: 2.1.3
% 1.44/0.53 % (1435419)Termination reason: Instruction limit
% 1.44/0.53 % (1435419)Termination phase: shuffling
% 1.44/0.53 % (1435419)Time elapsed: 0.006 s
% 1.44/0.53 % (1435419)Peak memory usage: 10 MB
% 1.44/0.53 % (1435419)Instructions burned: 14 (million)
% 1.44/0.53 % (1435418)Instruction limit reached!
% 1.44/0.53 % (1435418)------------------------------
% 1.44/0.53 % (1435418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (1435418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (1435418)CaDiCaL version: 2.1.3
% 1.44/0.53 % (1435418)Termination reason: Instruction limit
% 1.44/0.53 % (1435418)Termination phase: Property scanning
% 1.44/0.53 % (1435418)Time elapsed: 0.011 s
% 1.44/0.53 % (1435418)Peak memory usage: 10 MB
% 1.44/0.53 % (1435418)Instructions burned: 25 (million)
% 1.44/0.53 % (1435421)Instruction limit reached!
% 1.44/0.53 % (1435421)------------------------------
% 1.44/0.53 % (1435421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (1435421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (1435421)CaDiCaL version: 2.1.3
% 1.44/0.53 % (1435421)Termination reason: Instruction limit
% 1.44/0.53 % (1435421)Termination phase: shuffling
% 1.44/0.53 % (1435421)Time elapsed: 0.007 s
% 1.44/0.53 % (1435421)Peak memory usage: 10 MB
% 1.44/0.53 % (1435421)Instructions burned: 16 (million)
% 1.44/0.53 % (1435428)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1688512464: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)
% 1.44/0.53 % (1435428)Instruction limit reached!
% 1.44/0.53 % (1435428)------------------------------
% 1.44/0.53 % (1435428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.53 % (1435428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.53 % (1435428)CaDiCaL version: 2.1.3
% 1.44/0.53 % (1435428)Termination reason: Instruction limit
% 1.44/0.53 % (1435428)Termination phase: shuffling
% 1.44/0.53 % (1435428)Time elapsed: 0.002 s
% 1.44/0.53 % (1435428)Peak memory usage: 10 MB
% 1.44/0.53 % (1435428)Instructions burned: 3 (million)
% 1.44/0.53 % (1435432)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1145387240:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.44/0.53 % (1435434)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3929311983:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.44/0.54 % (1435435)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=794144135:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.44/0.54 % (1435432)Instruction limit reached!
% 1.44/0.54 % (1435432)------------------------------
% 1.44/0.54 % (1435432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.54 % (1435432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.54 % (1435432)CaDiCaL version: 2.1.3
% 1.44/0.54 % (1435432)Termination reason: Instruction limit
% 1.44/0.54 % (1435432)Termination phase: shuffling
% 1.44/0.54 % (1435432)Time elapsed: 0.011 s
% 1.44/0.54 % (1435432)Peak memory usage: 10 MB
% 1.44/0.54 % (1435432)Instructions burned: 26 (million)
% 1.44/0.54 % (1435434)Instruction limit reached!
% 1.44/0.54 % (1435434)------------------------------
% 1.44/0.54 % (1435434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.54 % (1435434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.54 % (1435434)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435434)Termination reason: Instruction limit
% 2.01/0.60 % (1435434)Termination phase: shuffling
% 2.01/0.60 % (1435434)Time elapsed: 0.011 s
% 2.01/0.60 % (1435434)Peak memory usage: 10 MB
% 2.01/0.60 % (1435434)Instructions burned: 24 (million)
% 2.01/0.60 % (1435441)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
% 2.01/0.60 % (1435441)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.01/0.60 % (1435441)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=2248174735:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.01/0.60 % (1435417)Instruction limit reached!
% 2.01/0.60 % (1435417)------------------------------
% 2.01/0.60 % (1435417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.60 % (1435417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.60 % (1435417)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435417)Termination reason: Instruction limit
% 2.01/0.60 % (1435417)Termination phase: Saturation
% 2.01/0.60 % (1435417)Time elapsed: 0.061 s
% 2.01/0.60 % (1435417)Peak memory usage: 15 MB
% 2.01/0.60 % (1435417)Instructions burned: 253 (million)
% 2.01/0.60 % (1435441)Instruction limit reached!
% 2.01/0.60 % (1435441)------------------------------
% 2.01/0.60 % (1435441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.60 % (1435441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.60 % (1435441)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435441)Termination reason: Instruction limit
% 2.01/0.60 % (1435441)Termination phase: shuffling
% 2.01/0.60 % (1435441)Time elapsed: 0.006 s
% 2.01/0.60 % (1435441)Peak memory usage: 10 MB
% 2.01/0.60 % (1435441)Instructions burned: 14 (million)
% 2.01/0.60 % (1435450)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.01/0.60 % (1435450)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=664105191:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.01/0.60 % (1435451)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=2055186204:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.01/0.60 % (1435435)Instruction limit reached!
% 2.01/0.60 % (1435435)------------------------------
% 2.01/0.60 % (1435435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.60 % (1435435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.60 % (1435435)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435435)Termination reason: Instruction limit
% 2.01/0.60 % (1435435)Termination phase: Preprocessing 3
% 2.01/0.60 % (1435435)Time elapsed: 0.028 s
% 2.01/0.60 % (1435435)Peak memory usage: 11 MB
% 2.01/0.60 % (1435435)Instructions burned: 63 (million)
% 2.01/0.60 % (1435456)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2474770150:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.01/0.60 % (1435456)Instruction limit reached!
% 2.01/0.60 % (1435456)------------------------------
% 2.01/0.60 % (1435456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.60 % (1435456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.60 % (1435456)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435456)Termination reason: Instruction limit
% 2.01/0.60 % (1435456)Termination phase: shuffling
% 2.01/0.60 % (1435456)Time elapsed: 0.002 s
% 2.01/0.60 % (1435456)Peak memory usage: 10 MB
% 2.01/0.60 % (1435456)Instructions burned: 9 (million)
% 2.01/0.60 % (1435450)Instruction limit reached!
% 2.01/0.60 % (1435450)------------------------------
% 2.01/0.60 % (1435450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.01/0.60 % (1435450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.60 % (1435450)CaDiCaL version: 2.1.3
% 2.01/0.60 % (1435450)Termination reason: Instruction limit
% 2.01/0.60 % (1435450)Termination phase: shuffling
% 2.01/0.60 % (1435450)Time elapsed: 0.007 s
% 2.01/0.60 % (1435450)Peak memory usage: 10 MB
% 2.39/0.66 % (1435450)Instructions burned: 14 (million)
% 2.39/0.66 % (1435457)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=701649981:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.39/0.66 % (1435451)Instruction limit reached!
% 2.39/0.66 % (1435451)------------------------------
% 2.39/0.66 % (1435451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.66 % (1435451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.66 % (1435451)CaDiCaL version: 2.1.3
% 2.39/0.66 % (1435451)Termination reason: Instruction limit
% 2.39/0.66 % (1435451)Termination phase: Property scanning
% 2.39/0.66 % (1435451)Time elapsed: 0.014 s
% 2.39/0.66 % (1435451)Peak memory usage: 10 MB
% 2.39/0.66 % (1435451)Instructions burned: 33 (million)
% 2.39/0.66 % (1435466)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4103234342:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.39/0.66 % (1435465)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1362386790:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.39/0.66 % (1435457)Instruction limit reached!
% 2.39/0.66 % (1435457)------------------------------
% 2.39/0.66 % (1435457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.66 % (1435457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.66 % (1435457)CaDiCaL version: 2.1.3
% 2.39/0.66 % (1435457)Termination reason: Instruction limit
% 2.39/0.66 % (1435457)Termination phase: shuffling
% 2.39/0.66 % (1435457)Time elapsed: 0.011 s
% 2.39/0.66 % (1435457)Peak memory usage: 10 MB
% 2.39/0.66 % (1435457)Instructions burned: 25 (million)
% 2.39/0.66 % (1435467)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1688584373:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.39/0.66 % (1435465)Instruction limit reached!
% 2.39/0.66 % (1435465)------------------------------
% 2.39/0.66 % (1435465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.66 % (1435465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.66 % (1435465)CaDiCaL version: 2.1.3
% 2.39/0.66 % (1435465)Termination reason: Instruction limit
% 2.39/0.66 % (1435465)Termination phase: shuffling
% 2.39/0.66 % (1435465)Time elapsed: 0.009 s
% 2.39/0.66 % (1435465)Peak memory usage: 10 MB
% 2.39/0.66 % (1435465)Instructions burned: 20 (million)
% 2.39/0.66 % (1435473)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1592037748:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.39/0.66 % (1435478)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=19846412:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.39/0.66 % (1435485)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.39/0.66 % (1435485)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2735983952:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.39/0.66 % (1435485)Instruction limit reached!
% 2.39/0.66 % (1435485)------------------------------
% 2.39/0.66 % (1435485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.66 % (1435485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.66 % (1435485)CaDiCaL version: 2.1.3
% 2.39/0.66 % (1435485)Termination reason: Instruction limit
% 2.39/0.66 % (1435485)Termination phase: shuffling
% 2.39/0.66 % (1435485)Time elapsed: 0.004 s
% 2.39/0.66 % (1435485)Peak memory usage: 10 MB
% 2.39/0.66 % (1435485)Instructions burned: 8 (million)
% 2.39/0.66 % (1435478)Instruction limit reached!
% 2.39/0.66 % (1435478)------------------------------
% 2.39/0.66 % (1435478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.39/0.66 % (1435478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.66 % (1435478)CaDiCaL version: 2.1.3
% 2.39/0.66 % (1435478)Termination reason: Instruction limit
% 2.39/0.66 % (1435478)Termination phase: shuffling
% 2.39/0.66 % (1435478)Time elapsed: 0.019 s
% 2.39/0.66 % (1435478)Peak memory usage: 11 MB
% 2.39/0.66 % (1435478)Instructions burned: 43 (million)
% 2.39/0.66 % (1435499)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=270780176:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.56/0.76 % (1435503)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=1712371969: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)
% 2.56/0.76 % (1435467)Instruction limit reached!
% 2.56/0.76 % (1435467)------------------------------
% 2.56/0.76 % (1435467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.76 % (1435467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.76 % (1435467)CaDiCaL version: 2.1.3
% 2.56/0.76 % (1435467)Termination reason: Instruction limit
% 2.56/0.76 % (1435467)Termination phase: Function definition elimination
% 2.56/0.76 % (1435467)Time elapsed: 0.062 s
% 2.56/0.76 % (1435467)Peak memory usage: 13 MB
% 2.56/0.76 % (1435467)Instructions burned: 144 (million)
% 2.56/0.76 % (1435420)Instruction limit reached!
% 2.56/0.76 % (1435420)------------------------------
% 2.56/0.76 % (1435420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.76 % (1435420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.76 % (1435420)CaDiCaL version: 2.1.3
% 2.56/0.76 % (1435420)Termination reason: Instruction limit
% 2.56/0.76 % (1435420)Termination phase: Saturation
% 2.56/0.76 % (1435420)Time elapsed: 0.149 s
% 2.56/0.76 % (1435420)Peak memory usage: 16 MB
% 2.56/0.76 % (1435420)Instructions burned: 327 (million)
% 2.56/0.76 % (1435521)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.56/0.76 % (1435523)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1340240529:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.56/0.76 % (1435521)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2432366506:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.56/0.76 % (1435473)Instruction limit reached!
% 2.56/0.76 % (1435473)------------------------------
% 2.56/0.76 % (1435473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.76 % (1435473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.76 % (1435473)CaDiCaL version: 2.1.3
% 2.56/0.76 % (1435473)Termination reason: Instruction limit
% 2.56/0.76 % (1435473)Termination phase: Property scanning
% 2.56/0.76 % (1435473)Time elapsed: 0.083 s
% 2.56/0.76 % (1435473)Peak memory usage: 13 MB
% 2.56/0.76 % (1435473)Instructions burned: 194 (million)
% 2.56/0.76 % (1435521)Instruction limit reached!
% 2.56/0.76 % (1435521)------------------------------
% 2.56/0.76 % (1435521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.76 % (1435521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.76 % (1435521)CaDiCaL version: 2.1.3
% 2.56/0.76 % (1435521)Termination reason: Instruction limit
% 2.56/0.76 % (1435521)Termination phase: shuffling
% 2.56/0.76 % (1435521)Time elapsed: 0.006 s
% 2.56/0.76 % (1435521)Peak memory usage: 10 MB
% 2.56/0.76 % (1435521)Instructions burned: 7 (million)
% 2.56/0.76 % (1435523)Instruction limit reached!
% 2.56/0.76 % (1435523)------------------------------
% 2.56/0.76 % (1435523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.56/0.76 % (1435523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/0.76 % (1435523)CaDiCaL version: 2.1.3
% 2.56/0.76 % (1435523)Termination reason: Instruction limit
% 2.56/0.76 % (1435523)Termination phase: shuffling
% 2.56/0.76 % (1435523)Time elapsed: 0.010 s
% 2.56/0.76 % (1435523)Peak memory usage: 10 MB
% 2.56/0.76 % (1435523)Instructions burned: 24 (million)
% 2.56/0.76 % (1435531)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2787861353:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.56/0.76 % (1435532)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=1681648419:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.56/0.76 % (1435533)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=4193643166: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)
% 3.36/0.81 % (1435531)Instruction limit reached!
% 3.36/0.81 % (1435531)------------------------------
% 3.36/0.81 % (1435531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.81 % (1435531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.81 % (1435531)CaDiCaL version: 2.1.3
% 3.36/0.81 % (1435531)Termination reason: Instruction limit
% 3.36/0.81 % (1435531)Termination phase: shuffling
% 3.36/0.81 % (1435531)Time elapsed: 0.009 s
% 3.36/0.81 % (1435531)Peak memory usage: 10 MB
% 3.36/0.81 % (1435531)Instructions burned: 20 (million)
% 3.36/0.81 % (1435503)Instruction limit reached!
% 3.36/0.81 % (1435503)------------------------------
% 3.36/0.81 % (1435503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.81 % (1435503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.81 % (1435503)CaDiCaL version: 2.1.3
% 3.36/0.81 % (1435503)Termination reason: Instruction limit
% 3.36/0.81 % (1435503)Termination phase: Property scanning
% 3.36/0.81 % (1435503)Time elapsed: 0.073 s
% 3.36/0.81 % (1435503)Peak memory usage: 13 MB
% 3.36/0.81 % (1435503)Instructions burned: 170 (million)
% 3.36/0.81 % (1435499)Instruction limit reached!
% 3.36/0.81 % (1435499)------------------------------
% 3.36/0.81 % (1435499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.81 % (1435499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.81 % (1435499)CaDiCaL version: 2.1.3
% 3.36/0.81 % (1435499)Termination reason: Instruction limit
% 3.36/0.81 % (1435499)Termination phase: Saturation
% 3.36/0.81 % (1435499)Time elapsed: 0.088 s
% 3.36/0.81 % (1435499)Peak memory usage: 13 MB
% 3.36/0.81 % (1435499)Instructions burned: 183 (million)
% 3.36/0.81 % (1435544)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=1738104264: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)
% 3.36/0.81 % (1435547)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3753213166:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.36/0.81 % (1435388)Instruction limit reached!
% 3.36/0.81 % (1435388)------------------------------
% 3.36/0.81 % (1435388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.81 % (1435388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.81 % (1435388)CaDiCaL version: 2.1.3
% 3.36/0.81 % (1435388)Termination reason: Instruction limit
% 3.36/0.81 % (1435388)Termination phase: Saturation
% 3.36/0.81 % (1435388)Time elapsed: 0.325 s
% 3.36/0.81 % (1435388)Peak memory usage: 18 MB
% 3.36/0.81 % (1435388)Instructions burned: 634 (million)
% 3.36/0.81 % (1435551)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3424975086: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)
% 3.36/0.81 % (1435544)Instruction limit reached!
% 3.36/0.81 % (1435544)------------------------------
% 3.36/0.81 % (1435544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.81 % (1435544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.82 % (1435544)CaDiCaL version: 2.1.3
% 3.36/0.82 % (1435544)Termination reason: Instruction limit
% 3.36/0.82 % (1435544)Termination phase: SInE selection
% 3.36/0.82 % (1435544)Time elapsed: 0.019 s
% 3.36/0.82 % (1435544)Peak memory usage: 10 MB
% 3.36/0.82 % (1435544)Instructions burned: 45 (million)
% 3.36/0.82 % (1435551)Instruction limit reached!
% 3.36/0.82 % (1435551)------------------------------
% 3.36/0.82 % (1435551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.36/0.82 % (1435551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/0.82 % (1435551)CaDiCaL version: 2.1.3
% 3.36/0.82 % (1435551)Termination reason: Instruction limit
% 3.36/0.82 % (1435551)Termination phase: shuffling
% 3.36/0.82 % (1435551)Time elapsed: 0.009 s
% 3.36/0.82 % (1435551)Peak memory usage: 10 MB
% 3.36/0.82 % (1435551)Instructions burned: 22 (million)
% 3.36/0.82 % (1435560)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.36/0.82 % (1435560)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2332375876:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.78/0.99 % (1435561)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1121711857:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.78/0.99 % (1435561)Instruction limit reached!
% 3.78/0.99 % (1435561)------------------------------
% 3.78/0.99 % (1435561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435561)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435561)Termination reason: Instruction limit
% 3.78/0.99 % (1435561)Termination phase: shuffling
% 3.78/0.99 % (1435561)Time elapsed: 0.006 s
% 3.78/0.99 % (1435561)Peak memory usage: 10 MB
% 3.78/0.99 % (1435561)Instructions burned: 13 (million)
% 3.78/0.99 % (1435562)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=1794695338:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.78/0.99 % (1435571)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=4206402286:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.78/0.99 % (1435562)Instruction limit reached!
% 3.78/0.99 % (1435562)------------------------------
% 3.78/0.99 % (1435562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435562)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435562)Termination reason: Instruction limit
% 3.78/0.99 % (1435562)Termination phase: Property scanning
% 3.78/0.99 % (1435562)Time elapsed: 0.031 s
% 3.78/0.99 % (1435562)Peak memory usage: 11 MB
% 3.78/0.99 % (1435562)Instructions burned: 68 (million)
% 3.78/0.99 % (1435571)Instruction limit reached!
% 3.78/0.99 % (1435571)------------------------------
% 3.78/0.99 % (1435571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435571)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435571)Termination reason: Instruction limit
% 3.78/0.99 % (1435571)Termination phase: Preprocessing 3
% 3.78/0.99 % (1435571)Time elapsed: 0.022 s
% 3.78/0.99 % (1435571)Peak memory usage: 11 MB
% 3.78/0.99 % (1435571)Instructions burned: 51 (million)
% 3.78/0.99 % (1435584)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1390818876:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.78/0.99 % (1435585)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1082506157:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.78/0.99 % (1435584)Instruction limit reached!
% 3.78/0.99 % (1435584)------------------------------
% 3.78/0.99 % (1435584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435584)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435584)Termination reason: Instruction limit
% 3.78/0.99 % (1435584)Termination phase: Property scanning
% 3.78/0.99 % (1435584)Time elapsed: 0.017 s
% 3.78/0.99 % (1435584)Peak memory usage: 10 MB
% 3.78/0.99 % (1435584)Instructions burned: 33 (million)
% 3.78/0.99 % (1435560)Instruction limit reached!
% 3.78/0.99 % (1435560)------------------------------
% 3.78/0.99 % (1435560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435560)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435560)Termination reason: Instruction limit
% 3.78/0.99 % (1435560)Termination phase: Saturation
% 3.78/0.99 % (1435560)Time elapsed: 0.087 s
% 3.78/0.99 % (1435560)Peak memory usage: 14 MB
% 3.78/0.99 % (1435560)Instructions burned: 200 (million)
% 3.78/0.99 % (1435547)Refutation not found, incomplete strategy
% 3.78/0.99 % (1435547)------------------------------
% 3.78/0.99 % (1435547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.78/0.99 % (1435547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/0.99 % (1435547)CaDiCaL version: 2.1.3
% 3.78/0.99 % (1435547)Termination reason: Refutation not found, incomplete strategy
% 5.92/1.18 % (1435547)Time elapsed: 0.127 s
% 5.92/1.18 % (1435547)Peak memory usage: 16 MB
% 5.92/1.18 % (1435547)Instructions burned: 275 (million)
% 5.92/1.18 % (1435547)------------------------------
% 5.92/1.18 % (1435547)------------------------------
% 5.92/1.18 % (1435466)Instruction limit reached!
% 5.92/1.18 % (1435466)------------------------------
% 5.92/1.18 % (1435466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.92/1.18 % (1435466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.18 % (1435466)CaDiCaL version: 2.1.3
% 5.92/1.18 % (1435466)Termination reason: Instruction limit
% 5.92/1.18 % (1435466)Termination phase: Saturation
% 5.92/1.18 % (1435466)Time elapsed: 0.285 s
% 5.92/1.18 % (1435466)Peak memory usage: 14 MB
% 5.92/1.18 % (1435466)Instructions burned: 1245 (million)
% 5.92/1.18 % (1435596)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=3149697299:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 5.92/1.18 % (1435599)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=69316426:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 5.92/1.18 % (1435603)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1355608632:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 5.92/1.18 % (1435602)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.92/1.18 % (1435596)Instruction limit reached!
% 5.92/1.18 % (1435596)------------------------------
% 5.92/1.18 % (1435596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.92/1.18 % (1435596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.18 % (1435596)CaDiCaL version: 2.1.3
% 5.92/1.18 % (1435596)Termination reason: Instruction limit
% 5.92/1.18 % (1435596)Termination phase: Property scanning
% 5.92/1.18 % (1435596)Time elapsed: 0.016 s
% 5.92/1.18 % (1435596)Peak memory usage: 10 MB
% 5.92/1.18 % (1435596)Instructions burned: 37 (million)
% 5.92/1.18 % (1435602)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=194992438:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 5.92/1.18 % (1435585)Instruction limit reached!
% 5.92/1.18 % (1435585)------------------------------
% 5.92/1.18 % (1435585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.92/1.18 % (1435585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.18 % (1435585)CaDiCaL version: 2.1.3
% 5.92/1.18 % (1435585)Termination reason: Instruction limit
% 5.92/1.18 % (1435585)Termination phase: Property scanning
% 5.92/1.18 % (1435585)Time elapsed: 0.059 s
% 5.92/1.18 % (1435585)Peak memory usage: 12 MB
% 5.92/1.18 % (1435585)Instructions burned: 137 (million)
% 5.92/1.18 % (1435532)Instruction limit reached!
% 5.92/1.18 % (1435532)------------------------------
% 5.92/1.18 % (1435532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.92/1.18 % (1435532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.18 % (1435532)CaDiCaL version: 2.1.3
% 5.92/1.18 % (1435532)Termination reason: Instruction limit
% 5.92/1.18 % (1435532)Termination phase: Saturation
% 5.92/1.18 % (1435532)Time elapsed: 0.193 s
% 5.92/1.18 % (1435532)Peak memory usage: 15 MB
% 5.92/1.18 % (1435532)Instructions burned: 317 (million)
% 5.92/1.18 % (1435599)Instruction limit reached!
% 5.92/1.18 % (1435599)------------------------------
% 5.92/1.18 % (1435599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.92/1.18 % (1435599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.92/1.18 % (1435599)CaDiCaL version: 2.1.3
% 5.92/1.18 % (1435599)Termination reason: Instruction limit
% 5.92/1.18 % (1435599)Termination phase: Preprocessing 3
% 5.92/1.18 % (1435599)Time elapsed: 0.030 s
% 5.92/1.18 % (1435599)Peak memory usage: 12 MB
% 5.92/1.18 % (1435599)Instructions burned: 67 (million)
% 5.92/1.18 % (1435613)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3522689568:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 5.92/1.18 % (1435617)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2926409023:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 5.92/1.18 % (1435618)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2934271069:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 6.59/1.33 % (1435621)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2560617251:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 6.59/1.33 % (1435603)Instruction limit reached!
% 6.59/1.33 % (1435603)------------------------------
% 6.59/1.33 % (1435603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435603)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435603)Termination reason: Instruction limit
% 6.59/1.33 % (1435603)Termination phase: Saturation
% 6.59/1.33 % (1435603)Time elapsed: 0.065 s
% 6.59/1.33 % (1435603)Peak memory usage: 15 MB
% 6.59/1.33 % (1435603)Instructions burned: 251 (million)
% 6.59/1.33 % (1435613)Instruction limit reached!
% 6.59/1.33 % (1435613)------------------------------
% 6.59/1.33 % (1435613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435613)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435613)Termination reason: Instruction limit
% 6.59/1.33 % (1435613)Termination phase: Property scanning
% 6.59/1.33 % (1435613)Time elapsed: 0.043 s
% 6.59/1.33 % (1435613)Peak memory usage: 13 MB
% 6.59/1.33 % (1435613)Instructions burned: 96 (million)
% 6.59/1.33 % (1435632)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1951230377:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 6.59/1.33 % (1435633)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1215817431:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 6.59/1.33 % (1435602)Instruction limit reached!
% 6.59/1.33 % (1435602)------------------------------
% 6.59/1.33 % (1435602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435602)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435602)Termination reason: Instruction limit
% 6.59/1.33 % (1435602)Termination phase: Saturation
% 6.59/1.33 % (1435602)Time elapsed: 0.101 s
% 6.59/1.33 % (1435602)Peak memory usage: 12 MB
% 6.59/1.33 % (1435602)Instructions burned: 182 (million)
% 6.59/1.33 % (1435632)Instruction limit reached!
% 6.59/1.33 % (1435632)------------------------------
% 6.59/1.33 % (1435632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435632)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435632)Termination reason: Instruction limit
% 6.59/1.33 % (1435632)Termination phase: Saturation
% 6.59/1.33 % (1435632)Time elapsed: 0.032 s
% 6.59/1.33 % (1435632)Peak memory usage: 13 MB
% 6.59/1.33 % (1435632)Instructions burned: 132 (million)
% 6.59/1.33 % (1435633)Instruction limit reached!
% 6.59/1.33 % (1435633)------------------------------
% 6.59/1.33 % (1435633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435633)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435633)Termination reason: Instruction limit
% 6.59/1.33 % (1435633)Termination phase: Property scanning
% 6.59/1.33 % (1435633)Time elapsed: 0.021 s
% 6.59/1.33 % (1435633)Peak memory usage: 10 MB
% 6.59/1.33 % (1435633)Instructions burned: 45 (million)
% 6.59/1.33 % (1435641)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3458575412:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.59/1.33 % (1435642)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=529718921:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.59/1.33 % (1435643)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2380128625:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 6.59/1.33 % (1435643)Instruction limit reached!
% 6.59/1.33 % (1435643)------------------------------
% 6.59/1.33 % (1435643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.59/1.33 % (1435643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.59/1.33 % (1435643)CaDiCaL version: 2.1.3
% 6.59/1.33 % (1435643)Termination reason: Instruction limit
% 6.59/1.33 % (1435643)Termination phase: Property scanning
% 7.05/1.47 % (1435643)Time elapsed: 0.074 s
% 7.05/1.47 % (1435643)Peak memory usage: 13 MB
% 7.05/1.47 % (1435643)Instructions burned: 95 (million)
% 7.05/1.47 % (1435673)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=3635651841:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 7.05/1.47 % (1435617)Instruction limit reached!
% 7.05/1.47 % (1435617)------------------------------
% 7.05/1.47 % (1435617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.05/1.47 % (1435617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.05/1.47 % (1435617)CaDiCaL version: 2.1.3
% 7.05/1.47 % (1435617)Termination reason: Instruction limit
% 7.05/1.47 % (1435617)Termination phase: Saturation
% 7.05/1.47 % (1435617)Time elapsed: 0.238 s
% 7.05/1.47 % (1435617)Peak memory usage: 15 MB
% 7.05/1.47 % (1435617)Instructions burned: 428 (million)
% 7.05/1.47 % (1435673)Instruction limit reached!
% 7.05/1.47 % (1435673)------------------------------
% 7.05/1.47 % (1435673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.05/1.47 % (1435673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.05/1.47 % (1435673)CaDiCaL version: 2.1.3
% 7.05/1.47 % (1435673)Termination reason: Instruction limit
% 7.05/1.47 % (1435673)Termination phase: Property scanning
% 7.05/1.47 % (1435673)Time elapsed: 0.048 s
% 7.05/1.47 % (1435673)Peak memory usage: 11 MB
% 7.05/1.47 % (1435673)Instructions burned: 65 (million)
% 7.05/1.47 % (1435685)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=3019425746: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_2992 on theBenchmark for (2992ds/105Mi)
% 7.05/1.47 % (1435533)Instruction limit reached!
% 7.05/1.47 % (1435533)------------------------------
% 7.05/1.47 % (1435533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.05/1.47 % (1435533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.05/1.47 % (1435533)CaDiCaL version: 2.1.3
% 7.05/1.47 % (1435533)Termination reason: Instruction limit
% 7.05/1.47 % (1435533)Termination phase: Saturation
% 7.05/1.47 % (1435533)Time elapsed: 0.495 s
% 7.05/1.47 % (1435533)Peak memory usage: 19 MB
% 7.05/1.47 % (1435533)Instructions burned: 853 (million)
% 7.05/1.47 % (1435641)Refutation not found, incomplete strategy
% 7.05/1.47 % (1435641)------------------------------
% 7.05/1.47 % (1435641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.05/1.47 % (1435641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.05/1.47 % (1435641)CaDiCaL version: 2.1.3
% 7.05/1.47 % (1435641)Termination reason: Refutation not found, incomplete strategy
% 7.05/1.47 % (1435641)Time elapsed: 0.224 s
% 7.05/1.47 % (1435641)Peak memory usage: 18 MB
% 7.05/1.47 % (1435641)Instructions burned: 492 (million)
% 7.05/1.47 % (1435692)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=90009339:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 7.05/1.47 % (1435641)------------------------------
% 7.05/1.47 % (1435641)------------------------------
% 7.05/1.47 % (1435697)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=4156036370:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 7.05/1.47 % (1435705)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3321953428:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 7.05/1.47 % (1435685)Instruction limit reached!
% 7.05/1.47 % (1435685)------------------------------
% 7.05/1.47 % (1435685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.05/1.47 % (1435685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.05/1.47 % (1435685)CaDiCaL version: 2.1.3
% 7.05/1.47 % (1435685)Termination reason: Instruction limit
% 7.05/1.47 % (1435685)Termination phase: Saturation
% 7.05/1.47 % (1435685)Time elapsed: 0.077 s
% 7.05/1.47 % (1435685)Peak memory usage: 12 MB
% 7.05/1.47 % (1435685)Instructions burned: 105 (million)
% 7.05/1.47 % (1435621)Instruction limit reached!
% 7.05/1.47 % (1435621)------------------------------
% 8.22/1.65 % (1435621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435621)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435621)Termination reason: Instruction limit
% 8.22/1.65 % (1435621)Termination phase: Saturation
% 8.22/1.65 % (1435621)Time elapsed: 0.358 s
% 8.22/1.65 % (1435621)Peak memory usage: 17 MB
% 8.22/1.65 % (1435621)Instructions burned: 516 (million)
% 8.22/1.65 % (1435714)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=4099363665:cond=on:i=34:hud=10:nm=10:rtra=on_2991 on theBenchmark for (2991ds/34Mi)
% 8.22/1.65 % (1435714)Instruction limit reached!
% 8.22/1.65 % (1435714)------------------------------
% 8.22/1.65 % (1435714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435714)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435714)Termination reason: Instruction limit
% 8.22/1.65 % (1435714)Termination phase: Property scanning
% 8.22/1.65 % (1435714)Time elapsed: 0.017 s
% 8.22/1.65 % (1435714)Peak memory usage: 10 MB
% 8.22/1.65 % (1435714)Instructions burned: 35 (million)
% 8.22/1.65 % (1435716)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=613821502:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/91Mi)
% 8.22/1.65 % (1435724)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=2241954584:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2990 on theBenchmark for (2990ds/66Mi)
% 8.22/1.65 % (1435716)Instruction limit reached!
% 8.22/1.65 % (1435716)------------------------------
% 8.22/1.65 % (1435716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435716)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435716)Termination reason: Instruction limit
% 8.22/1.65 % (1435716)Termination phase: Preprocessing 3
% 8.22/1.65 % (1435716)Time elapsed: 0.074 s
% 8.22/1.65 % (1435716)Peak memory usage: 13 MB
% 8.22/1.65 % (1435716)Instructions burned: 91 (million)
% 8.22/1.65 % (1435642)Instruction limit reached!
% 8.22/1.65 % (1435642)------------------------------
% 8.22/1.65 % (1435642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435642)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435642)Termination reason: Instruction limit
% 8.22/1.65 % (1435642)Termination phase: Saturation
% 8.22/1.65 % (1435642)Time elapsed: 0.378 s
% 8.22/1.65 % (1435642)Peak memory usage: 17 MB
% 8.22/1.65 % (1435642)Instructions burned: 450 (million)
% 8.22/1.65 % (1435724)Instruction limit reached!
% 8.22/1.65 % (1435724)------------------------------
% 8.22/1.65 % (1435724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435724)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435724)Termination reason: Instruction limit
% 8.22/1.65 % (1435724)Termination phase: Saturation
% 8.22/1.65 % (1435724)Time elapsed: 0.054 s
% 8.22/1.65 % (1435724)Peak memory usage: 12 MB
% 8.22/1.65 % (1435724)Instructions burned: 67 (million)
% 8.22/1.65 % (1435744)lrs+10_1_sil=128000:si=on:urr=on:random_seed=3743452931:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/28Mi)
% 8.22/1.65 % (1435741)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1571912039:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2989 on theBenchmark for (2989ds/22Mi)
% 8.22/1.65 % (1435742)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=94353457:i=338:bd=all:ins=4:rtra=on_2989 on theBenchmark for (2989ds/338Mi)
% 8.22/1.65 % (1435705)Instruction limit reached!
% 8.22/1.65 % (1435705)------------------------------
% 8.22/1.65 % (1435705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.65 % (1435705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.65 % (1435705)CaDiCaL version: 2.1.3
% 8.22/1.65 % (1435705)Termination reason: Instruction limit
% 8.22/1.65 % (1435705)Termination phase: Saturation
% 8.22/1.65 % (1435705)Time elapsed: 0.185 s
% 8.67/1.86 % (1435705)Peak memory usage: 16 MB
% 8.67/1.86 % (1435705)Instructions burned: 495 (million)
% 8.67/1.86 % (1435744)Instruction limit reached!
% 8.67/1.86 % (1435744)------------------------------
% 8.67/1.86 % (1435744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.67/1.86 % (1435744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.67/1.86 % (1435744)CaDiCaL version: 2.1.3
% 8.67/1.86 % (1435744)Termination reason: Instruction limit
% 8.67/1.86 % (1435744)Termination phase: Property scanning
% 8.67/1.86 % (1435744)Time elapsed: 0.012 s
% 8.67/1.86 % (1435744)Peak memory usage: 10 MB
% 8.67/1.86 % (1435744)Instructions burned: 29 (million)
% 8.67/1.86 % (1435741)Instruction limit reached!
% 8.67/1.86 % (1435741)------------------------------
% 8.67/1.86 % (1435741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.67/1.86 % (1435741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.67/1.86 % (1435741)CaDiCaL version: 2.1.3
% 8.67/1.86 % (1435741)Termination reason: Instruction limit
% 8.67/1.86 % (1435741)Termination phase: shuffling
% 8.67/1.86 % (1435741)Time elapsed: 0.011 s
% 8.67/1.86 % (1435741)Peak memory usage: 10 MB
% 8.67/1.86 % (1435741)Instructions burned: 22 (million)
% 8.67/1.86 % (1435752)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 8.67/1.86 % (1435753)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=3183231190:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2989 on theBenchmark for (2989ds/340Mi)
% 8.67/1.86 % (1435752)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=2166461674:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2989 on theBenchmark for (2989ds/137Mi)
% 8.67/1.86 % (1435754)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=3250113673:i=227:sd=1:bd=all:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/227Mi)
% 8.67/1.86 % (1435754)Refutation not found, incomplete strategy
% 8.67/1.86 % (1435754)------------------------------
% 8.67/1.86 % (1435754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.67/1.86 % (1435754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.67/1.86 % (1435754)CaDiCaL version: 2.1.3
% 8.67/1.86 % (1435754)Termination reason: Refutation not found, incomplete strategy
% 8.67/1.86 % (1435754)Time elapsed: 0.056 s
% 8.67/1.86 % (1435754)Peak memory usage: 13 MB
% 8.67/1.86 % (1435754)Instructions burned: 66 (million)
% 8.67/1.86 % (1435754)------------------------------
% 8.67/1.86 % (1435754)------------------------------
% 8.67/1.86 % (1435752)Instruction limit reached!
% 8.67/1.86 % (1435752)------------------------------
% 8.67/1.86 % (1435752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.67/1.86 % (1435752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.67/1.86 % (1435752)CaDiCaL version: 2.1.3
% 8.67/1.86 % (1435752)Termination reason: Instruction limit
% 8.67/1.86 % (1435752)Termination phase: Saturation
% 8.67/1.86 % (1435752)Time elapsed: 0.074 s
% 8.67/1.86 % (1435752)Peak memory usage: 12 MB
% 8.67/1.86 % (1435752)Instructions burned: 138 (million)
% 8.67/1.86 % (1435697)Instruction limit reached!
% 8.67/1.86 % (1435697)------------------------------
% 8.67/1.86 % (1435697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.67/1.86 % (1435697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.67/1.86 % (1435697)CaDiCaL version: 2.1.3
% 8.67/1.86 % (1435697)Termination reason: Instruction limit
% 8.67/1.86 % (1435697)Termination phase: Saturation
% 8.67/1.86 % (1435697)Time elapsed: 0.307 s
% 8.67/1.86 % (1435697)Peak memory usage: 16 MB
% 8.67/1.86 % (1435697)Instructions burned: 375 (million)
% 8.67/1.86 % (1435767)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 8.67/1.86 % (1435767)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=942098695:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/373Mi)
% 8.67/1.86 % (1435768)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=1181521622:i=116:ep=RSTC:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/116Mi)
% 8.67/1.86 % (1435618)Instruction limit reached!
% 9.84/1.99 % (1435618)------------------------------
% 9.84/1.99 % (1435618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.84/1.99 % (1435618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/1.99 % (1435618)CaDiCaL version: 2.1.3
% 9.84/1.99 % (1435618)Termination reason: Instruction limit
% 9.84/1.99 % (1435618)Termination phase: Saturation
% 9.84/1.99 % (1435618)Time elapsed: 0.657 s
% 9.84/1.99 % (1435618)Peak memory usage: 19 MB
% 9.84/1.99 % (1435618)Instructions burned: 874 (million)
% 9.84/1.99 % (1435753)Instruction limit reached!
% 9.84/1.99 % (1435753)------------------------------
% 9.84/1.99 % (1435753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.84/1.99 % (1435753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/1.99 % (1435753)CaDiCaL version: 2.1.3
% 9.84/1.99 % (1435753)Termination reason: Instruction limit
% 9.84/1.99 % (1435753)Termination phase: Saturation
% 9.84/1.99 % (1435753)Time elapsed: 0.133 s
% 9.84/1.99 % (1435753)Peak memory usage: 16 MB
% 9.84/1.99 % (1435753)Instructions burned: 343 (million)
% 9.84/1.99 % (1435772)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=2435023152:i=575:rtra=on_2988 on theBenchmark for (2988ds/575Mi)
% 9.84/1.99 % (1435780)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=660343374: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_2987 on theBenchmark for (2987ds/9840Mi)
% 9.84/1.99 % (1435778)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3190605610:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2987 on theBenchmark for (2987ds/270Mi)
% 9.84/1.99 % (1435742)Instruction limit reached!
% 9.84/1.99 % (1435742)------------------------------
% 9.84/1.99 % (1435742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.84/1.99 % (1435742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/1.99 % (1435742)CaDiCaL version: 2.1.3
% 9.84/1.99 % (1435742)Termination reason: Instruction limit
% 9.84/1.99 % (1435742)Termination phase: Saturation
% 9.84/1.99 % (1435742)Time elapsed: 0.221 s
% 9.84/1.99 % (1435742)Peak memory usage: 18 MB
% 9.84/1.99 % (1435742)Instructions burned: 340 (million)
% 9.84/1.99 % (1435768)Instruction limit reached!
% 9.84/1.99 % (1435768)------------------------------
% 9.84/1.99 % (1435768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.84/1.99 % (1435768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/1.99 % (1435768)CaDiCaL version: 2.1.3
% 9.84/1.99 % (1435768)Termination reason: Instruction limit
% 9.84/1.99 % (1435768)Termination phase: Property scanning
% 9.84/1.99 % (1435768)Time elapsed: 0.118 s
% 9.84/1.99 % (1435768)Peak memory usage: 13 MB
% 9.84/1.99 % (1435768)Instructions burned: 116 (million)
% 9.84/1.99 % (1435788)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=171670799:i=421:rtra=on:ss=axioms_2987 on theBenchmark for (2987ds/421Mi)
% 9.84/1.99 % (1435791)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
% 9.84/1.99 % (1435791)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=1970565968:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/270Mi)
% 9.84/1.99 % (1435778)Instruction limit reached!
% 9.84/1.99 % (1435778)------------------------------
% 9.84/1.99 % (1435778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.84/1.99 % (1435778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/1.99 % (1435778)CaDiCaL version: 2.1.3
% 9.84/1.99 % (1435778)Termination reason: Instruction limit
% 9.84/1.99 % (1435778)Termination phase: Saturation
% 9.84/1.99 % (1435778)Time elapsed: 0.106 s
% 9.84/1.99 % (1435778)Peak memory usage: 13 MB
% 9.84/1.99 % (1435778)Instructions burned: 272 (million)
% 9.84/1.99 % (1435802)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3992083143:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2986 on theBenchmark for (2986ds/31Mi)
% 13.51/2.20 % (1435802)Instruction limit reached!
% 13.51/2.20 % (1435802)------------------------------
% 13.51/2.20 % (1435802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.51/2.20 % (1435802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.51/2.20 % (1435802)CaDiCaL version: 2.1.3
% 13.51/2.20 % (1435802)Termination reason: Instruction limit
% 13.51/2.20 % (1435802)Termination phase: Property scanning
% 13.51/2.20 % (1435802)Time elapsed: 0.013 s
% 13.51/2.20 % (1435802)Peak memory usage: 10 MB
% 13.51/2.20 % (1435802)Instructions burned: 31 (million)
% 13.51/2.20 % (1435806)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 13.51/2.20 % (1435806)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
% 13.51/2.20 % (1435767)Instruction limit reached!
% 13.51/2.20 % (1435767)------------------------------
% 13.51/2.20 % (1435767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.51/2.20 % (1435767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.51/2.20 % (1435767)CaDiCaL version: 2.1.3
% 13.51/2.20 % (1435767)Termination reason: Instruction limit
% 13.51/2.20 % (1435767)Termination phase: Saturation
% 13.51/2.20 % (1435767)Time elapsed: 0.232 s
% 13.51/2.20 % (1435767)Peak memory usage: 15 MB
% 13.51/2.20 % (1435767)Instructions burned: 373 (million)
% 13.51/2.20 % (1435806)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=3526109725:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2986 on theBenchmark for (2986ds/1440Mi)
% 13.51/2.20 % (1435809)dis+10_2_sil=128000:si=on:random_seed=1805301945:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2985 on theBenchmark for (2985ds/339Mi)
% 13.51/2.20 % (1435791)Instruction limit reached!
% 13.51/2.20 % (1435791)------------------------------
% 13.51/2.20 % (1435791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.51/2.20 % (1435791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.51/2.20 % (1435791)CaDiCaL version: 2.1.3
% 13.51/2.20 % (1435791)Termination reason: Instruction limit
% 13.51/2.20 % (1435791)Termination phase: Saturation
% 13.51/2.20 % (1435791)Time elapsed: 0.189 s
% 13.51/2.20 % (1435791)Peak memory usage: 15 MB
% 13.51/2.20 % (1435791)Instructions burned: 270 (million)
% 13.51/2.20 % (1435809)Instruction limit reached!
% 13.51/2.20 % (1435809)------------------------------
% 13.51/2.20 % (1435809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.51/2.20 % (1435809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.51/2.20 % (1435809)CaDiCaL version: 2.1.3
% 13.51/2.20 % (1435809)Termination reason: Instruction limit
% 13.51/2.20 % (1435809)Termination phase: Saturation
% 13.51/2.20 % (1435809)Time elapsed: 0.106 s
% 13.51/2.20 % (1435809)Peak memory usage: 14 MB
% 13.51/2.20 % (1435809)Instructions burned: 341 (million)
% 13.51/2.20 % (1435818)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=1745186529:i=111:add=on:fgj=on:rtra=on:fdi=1024_2984 on theBenchmark for (2984ds/111Mi)
% 13.51/2.20 % (1435788)Refutation not found, incomplete strategy
% 13.51/2.20 % (1435788)------------------------------
% 13.51/2.20 % (1435788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.51/2.20 % (1435788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.51/2.20 % (1435788)CaDiCaL version: 2.1.3
% 13.51/2.20 % (1435788)Termination reason: Refutation not found, incomplete strategy
% 13.51/2.20 % (1435788)Time elapsed: 0.241 s
% 13.51/2.20 % (1435788)Peak memory usage: 15 MB
% 13.51/2.20 % (1435788)Instructions burned: 353 (million)
% 13.51/2.20 % (1435819)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=2268434312:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/122Mi)
% 13.51/2.20 % (1435788)------------------------------
% 13.51/2.20 % (1435788)------------------------------
% 13.51/2.20 % (1435822)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=3590837701:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/136Mi)
% 13.51/2.20 % (1435819)Instruction limit reached!
% 14.08/2.34 % (1435819)------------------------------
% 14.08/2.34 % (1435819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.08/2.34 % (1435819)CaDiCaL version: 2.1.3
% 14.08/2.34 % (1435819)Termination reason: Instruction limit
% 14.08/2.34 % (1435819)Termination phase: Property scanning
% 14.08/2.34 % (1435819)Time elapsed: 0.029 s
% 14.08/2.34 % (1435819)Peak memory usage: 13 MB
% 14.08/2.34 % (1435819)Instructions burned: 125 (million)
% 14.08/2.34 % (1435824)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2974181565:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2984 on theBenchmark for (2984ds/232Mi)
% 14.08/2.34 % (1435818)Instruction limit reached!
% 14.08/2.34 % (1435818)------------------------------
% 14.08/2.34 % (1435818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.08/2.34 % (1435818)CaDiCaL version: 2.1.3
% 14.08/2.34 % (1435818)Termination reason: Instruction limit
% 14.08/2.34 % (1435818)Termination phase: Property scanning
% 14.08/2.34 % (1435818)Time elapsed: 0.049 s
% 14.08/2.34 % (1435818)Peak memory usage: 13 MB
% 14.08/2.34 % (1435818)Instructions burned: 111 (million)
% 14.08/2.34 % (1435772)Instruction limit reached!
% 14.08/2.34 % (1435772)------------------------------
% 14.08/2.34 % (1435772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.08/2.34 % (1435772)CaDiCaL version: 2.1.3
% 14.08/2.34 % (1435772)Termination reason: Instruction limit
% 14.08/2.34 % (1435772)Termination phase: Saturation
% 14.08/2.34 % (1435772)Time elapsed: 0.389 s
% 14.08/2.34 % (1435772)Peak memory usage: 18 MB
% 14.08/2.34 % (1435772)Instructions burned: 575 (million)
% 14.08/2.34 % (1435827)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 14.08/2.34 % (1435826)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=3137198376:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2983 on theBenchmark for (2983ds/1254Mi)
% 14.08/2.34 % (1435827)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=1155409278:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2983 on theBenchmark for (2983ds/281Mi)
% 14.08/2.34 % (1435822)Instruction limit reached!
% 14.08/2.34 % (1435822)------------------------------
% 14.08/2.34 % (1435822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.08/2.34 % (1435822)CaDiCaL version: 2.1.3
% 14.08/2.34 % (1435822)Termination reason: Instruction limit
% 14.08/2.34 % (1435822)Termination phase: Property scanning
% 14.08/2.34 % (1435822)Time elapsed: 0.062 s
% 14.08/2.34 % (1435822)Peak memory usage: 16 MB
% 14.08/2.34 % (1435822)Instructions burned: 136 (million)
% 14.08/2.34 % (1435824)Instruction limit reached!
% 14.08/2.34 % (1435824)------------------------------
% 14.08/2.34 % (1435824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.08/2.34 % (1435824)CaDiCaL version: 2.1.3
% 14.08/2.34 % (1435824)Termination reason: Instruction limit
% 14.08/2.34 % (1435824)Termination phase: Saturation
% 14.08/2.34 % (1435824)Time elapsed: 0.053 s
% 14.08/2.34 % (1435824)Peak memory usage: 14 MB
% 14.08/2.34 % (1435824)Instructions burned: 233 (million)
% 14.08/2.34 % (1435830)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2347925475:i=619:add=on:rtra=on_2983 on theBenchmark for (2983ds/619Mi)
% 14.08/2.34 % (1435831)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=3547012457:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2983 on theBenchmark for (2983ds/865Mi)
% 14.08/2.34 % (1435826)Refutation not found, incomplete strategy
% 14.08/2.34 % (1435826)------------------------------
% 14.08/2.34 % (1435826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.08/2.34 % (1435826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435826)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435826)Termination reason: Refutation not found, incomplete strategy
% 15.09/2.50 % (1435826)Time elapsed: 0.095 s
% 15.09/2.50 % (1435826)Peak memory usage: 15 MB
% 15.09/2.50 % (1435826)Instructions burned: 220 (million)
% 15.09/2.50 % (1435826)------------------------------
% 15.09/2.50 % (1435826)------------------------------
% 15.09/2.50 % (1435827)Instruction limit reached!
% 15.09/2.50 % (1435827)------------------------------
% 15.09/2.50 % (1435827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435827)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435827)Termination reason: Instruction limit
% 15.09/2.50 % (1435827)Termination phase: Saturation
% 15.09/2.50 % (1435827)Time elapsed: 0.116 s
% 15.09/2.50 % (1435827)Peak memory usage: 12 MB
% 15.09/2.50 % (1435827)Instructions burned: 283 (million)
% 15.09/2.50 % (1435849)lrs+10_1_sil=128000:si=on:urr=on:random_seed=34701921:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2982 on theBenchmark for (2982ds/212Mi)
% 15.09/2.50 % (1435858)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=2692828945:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2982 on theBenchmark for (2982ds/130Mi)
% 15.09/2.50 % (1435858)Instruction limit reached!
% 15.09/2.50 % (1435858)------------------------------
% 15.09/2.50 % (1435858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435858)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435858)Termination reason: Instruction limit
% 15.09/2.50 % (1435858)Termination phase: Property scanning
% 15.09/2.50 % (1435858)Time elapsed: 0.059 s
% 15.09/2.50 % (1435858)Peak memory usage: 13 MB
% 15.09/2.50 % (1435858)Instructions burned: 133 (million)
% 15.09/2.50 % (1435849)Instruction limit reached!
% 15.09/2.50 % (1435849)------------------------------
% 15.09/2.50 % (1435849)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435849)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435849)Termination reason: Instruction limit
% 15.09/2.50 % (1435849)Termination phase: Saturation
% 15.09/2.50 % (1435849)Time elapsed: 0.091 s
% 15.09/2.50 % (1435849)Peak memory usage: 14 MB
% 15.09/2.50 % (1435849)Instructions burned: 213 (million)
% 15.09/2.50 % (1435891)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2444422256:st=1.5:i=346:rtra=on:ss=axioms_2981 on theBenchmark for (2981ds/346Mi)
% 15.09/2.50 % (1435896)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=1639698731:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2981 on theBenchmark for (2981ds/152Mi)
% 15.09/2.50 % (1435891)Refutation not found, incomplete strategy
% 15.09/2.50 % (1435891)------------------------------
% 15.09/2.50 % (1435891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435891)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435891)Termination reason: Refutation not found, incomplete strategy
% 15.09/2.50 % (1435891)Time elapsed: 0.043 s
% 15.09/2.50 % (1435891)Peak memory usage: 13 MB
% 15.09/2.50 % (1435891)Instructions burned: 93 (million)
% 15.09/2.50 % (1435891)------------------------------
% 15.09/2.50 % (1435891)------------------------------
% 15.09/2.50 % (1435918)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4123263496:i=75:ep=R:rtra=on:ntd=on_2981 on theBenchmark for (2981ds/75Mi)
% 15.09/2.50 % (1435896)Instruction limit reached!
% 15.09/2.50 % (1435896)------------------------------
% 15.09/2.50 % (1435896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.09/2.50 % (1435896)CaDiCaL version: 2.1.3
% 15.09/2.50 % (1435896)Termination reason: Instruction limit
% 15.09/2.50 % (1435896)Termination phase: Inequality splitting
% 15.09/2.50 % (1435896)Time elapsed: 0.067 s
% 15.09/2.50 % (1435896)Peak memory usage: 13 MB
% 15.09/2.50 % (1435896)Instructions burned: 154 (million)
% 15.09/2.50 % (1435831)Instruction limit reached!
% 15.09/2.50 % (1435831)------------------------------
% 15.09/2.50 % (1435831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 15.09/2.50 % (1435831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435831)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435831)Termination reason: Instruction limit
% 16.62/2.80 % (1435831)Termination phase: Saturation
% 16.62/2.80 % (1435831)Time elapsed: 0.265 s
% 16.62/2.80 % (1435831)Peak memory usage: 20 MB
% 16.62/2.80 % (1435831)Instructions burned: 865 (million)
% 16.62/2.80 % (1435918)Instruction limit reached!
% 16.62/2.80 % (1435918)------------------------------
% 16.62/2.80 % (1435918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.62/2.80 % (1435918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435918)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435918)Termination reason: Instruction limit
% 16.62/2.80 % (1435918)Termination phase: Property scanning
% 16.62/2.80 % (1435918)Time elapsed: 0.032 s
% 16.62/2.80 % (1435918)Peak memory usage: 11 MB
% 16.62/2.80 % (1435918)Instructions burned: 77 (million)
% 16.62/2.80 % (1435930)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=2753531346:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/387Mi)
% 16.62/2.80 % (1435936)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=1433460511:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2980 on theBenchmark for (2980ds/148Mi)
% 16.62/2.80 % (1435937)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=3642607031:i=161:piset=and:rtra=on:ntd=on_2980 on theBenchmark for (2980ds/161Mi)
% 16.62/2.80 % (1435936)Instruction limit reached!
% 16.62/2.80 % (1435936)------------------------------
% 16.62/2.80 % (1435936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.62/2.80 % (1435936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435936)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435936)Termination reason: Instruction limit
% 16.62/2.80 % (1435936)Termination phase: Saturation
% 16.62/2.80 % (1435936)Time elapsed: 0.033 s
% 16.62/2.80 % (1435936)Peak memory usage: 12 MB
% 16.62/2.80 % (1435936)Instructions burned: 148 (million)
% 16.62/2.80 % (1435830)Instruction limit reached!
% 16.62/2.80 % (1435830)------------------------------
% 16.62/2.80 % (1435830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.62/2.80 % (1435830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435830)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435830)Termination reason: Instruction limit
% 16.62/2.80 % (1435830)Termination phase: Saturation
% 16.62/2.80 % (1435830)Time elapsed: 0.313 s
% 16.62/2.80 % (1435830)Peak memory usage: 18 MB
% 16.62/2.80 % (1435830)Instructions burned: 619 (million)
% 16.62/2.80 % (1435954)lrs+10_1_sil=128000:si=on:random_seed=3303726142:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2980 on theBenchmark for (2980ds/888Mi)
% 16.62/2.80 % (1435956)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=530348640:i=136:add=on:ins=4:rtra=on:sup=off_2980 on theBenchmark for (2980ds/136Mi)
% 16.62/2.80 % (1435937)Instruction limit reached!
% 16.62/2.80 % (1435937)------------------------------
% 16.62/2.80 % (1435937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.62/2.80 % (1435937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435937)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435937)Termination reason: Instruction limit
% 16.62/2.80 % (1435937)Termination phase: Property scanning
% 16.62/2.80 % (1435937)Time elapsed: 0.070 s
% 16.62/2.80 % (1435937)Peak memory usage: 13 MB
% 16.62/2.80 % (1435937)Instructions burned: 163 (million)
% 16.62/2.80 % (1435959)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=2448994004:i=88:s2at=3:nm=2:rtra=on:rawr=on_2979 on theBenchmark for (2979ds/88Mi)
% 16.62/2.80 % (1435956)Instruction limit reached!
% 16.62/2.80 % (1435956)------------------------------
% 16.62/2.80 % (1435956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.62/2.80 % (1435956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.62/2.80 % (1435956)CaDiCaL version: 2.1.3
% 16.62/2.80 % (1435956)Termination reason: Instruction limit
% 16.62/2.80 % (1435956)Termination phase: Property scanning
% 16.62/2.80 % (1435956)Time elapsed: 0.060 s
% 16.62/2.80 % (1435956)Peak memory usage: 12 MB
% 16.62/2.80 % (1435956)Instructions burned: 138 (million)
% 16.62/2.80 % (1435961)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2090926922:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2979 on theBenchmark for (2979ds/93Mi)
% 17.32/3.01 % (1435959)Instruction limit reached!
% 17.32/3.01 % (1435959)------------------------------
% 17.32/3.01 % (1435959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435959)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435959)Termination reason: Instruction limit
% 17.32/3.01 % (1435959)Termination phase: Property scanning
% 17.32/3.01 % (1435959)Time elapsed: 0.036 s
% 17.32/3.01 % (1435959)Peak memory usage: 11 MB
% 17.32/3.01 % (1435959)Instructions burned: 89 (million)
% 17.32/3.01 % (1435930)Instruction limit reached!
% 17.32/3.01 % (1435930)------------------------------
% 17.32/3.01 % (1435930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435930)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435930)Termination reason: Instruction limit
% 17.32/3.01 % (1435930)Termination phase: Saturation
% 17.32/3.01 % (1435930)Time elapsed: 0.157 s
% 17.32/3.01 % (1435930)Peak memory usage: 12 MB
% 17.32/3.01 % (1435930)Instructions burned: 387 (million)
% 17.32/3.01 % (1435963)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1503784776:i=2186:rtra=on:ixr=off_2979 on theBenchmark for (2979ds/2186Mi)
% 17.32/3.01 % (1435961)Instruction limit reached!
% 17.32/3.01 % (1435961)------------------------------
% 17.32/3.01 % (1435961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435961)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435961)Termination reason: Instruction limit
% 17.32/3.01 % (1435961)Termination phase: Saturation
% 17.32/3.01 % (1435961)Time elapsed: 0.040 s
% 17.32/3.01 % (1435961)Peak memory usage: 12 MB
% 17.32/3.01 % (1435961)Instructions burned: 95 (million)
% 17.32/3.01 % (1435964)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3830285979:s2a=on:i=240:rtra=on:ntd=on_2979 on theBenchmark for (2979ds/240Mi)
% 17.32/3.01 % (1435806)Instruction limit reached!
% 17.32/3.01 % (1435806)------------------------------
% 17.32/3.01 % (1435806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435806)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435806)Termination reason: Instruction limit
% 17.32/3.01 % (1435806)Termination phase: Saturation
% 17.32/3.01 % (1435806)Time elapsed: 0.708 s
% 17.32/3.01 % (1435806)Peak memory usage: 22 MB
% 17.32/3.01 % (1435806)Instructions burned: 1441 (million)
% 17.32/3.01 % (1435971)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=1531185504:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2978 on theBenchmark for (2978ds/805Mi)
% 17.32/3.01 % (1435973)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 17.32/3.01 % (1435973)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=3834070721:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2978 on theBenchmark for (2978ds/391Mi)
% 17.32/3.01 % (1435964)Instruction limit reached!
% 17.32/3.01 % (1435964)------------------------------
% 17.32/3.01 % (1435964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435964)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435964)Termination reason: Instruction limit
% 17.32/3.01 % (1435964)Termination phase: Saturation
% 17.32/3.01 % (1435964)Time elapsed: 0.104 s
% 17.32/3.01 % (1435964)Peak memory usage: 14 MB
% 17.32/3.01 % (1435964)Instructions burned: 240 (million)
% 17.32/3.01 % (1435954)Instruction limit reached!
% 17.32/3.01 % (1435954)------------------------------
% 17.32/3.01 % (1435954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 17.32/3.01 % (1435954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.32/3.01 % (1435954)CaDiCaL version: 2.1.3
% 17.32/3.01 % (1435954)Termination reason: Instruction limit
% 17.32/3.01 % (1435954)Termination phase: Saturation
% 19.88/3.17 % (1435954)Time elapsed: 0.240 s
% 19.88/3.17 % (1435954)Peak memory usage: 19 MB
% 19.88/3.17 % (1435954)Instructions burned: 891 (million)
% 19.88/3.17 % (1436014)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=3696710084:i=355:av=off:fsr=off:rtra=on:ixr=off_2977 on theBenchmark for (2977ds/355Mi)
% 19.88/3.17 % (1436019)lrs+1010_5:1_sil=128000:si=on:uwa=interpreted_only:sac=on:slsq=on:random_seed=4080981175:lrd=on:i=314:sd=1:rtra=on:ss=axioms_2977 on theBenchmark for (2977ds/314Mi)
% 19.88/3.17 % (1435973)Instruction limit reached!
% 19.88/3.17 % (1435973)------------------------------
% 19.88/3.17 % (1435973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.88/3.17 % (1435973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.88/3.17 % (1435973)CaDiCaL version: 2.1.3
% 19.88/3.17 % (1435973)Termination reason: Instruction limit
% 19.88/3.17 % (1435973)Termination phase: Saturation
% 19.88/3.17 % (1435973)Time elapsed: 0.161 s
% 19.88/3.17 % (1435973)Peak memory usage: 13 MB
% 19.88/3.17 % (1435973)Instructions burned: 393 (million)
% 19.88/3.17 % (1436019)Refutation not found, incomplete strategy
% 19.88/3.17 % (1436019)------------------------------
% 19.88/3.17 % (1436019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.88/3.17 % (1436019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.88/3.17 % (1436019)CaDiCaL version: 2.1.3
% 19.88/3.17 % (1436019)Termination reason: Refutation not found, incomplete strategy
% 19.88/3.17 % (1436019)Time elapsed: 0.077 s
% 19.88/3.17 % (1436019)Peak memory usage: 15 MB
% 19.88/3.17 % (1436019)Instructions burned: 299 (million)
% 19.88/3.17 % (1436019)------------------------------
% 19.88/3.17 % (1436019)------------------------------
% 19.88/3.17 % (1436022)lrs+10_1_sil=128000:e2e=on:si=on:cbe=off:uwa=interpreted_only:cs=on:random_seed=2405309875:s2a=on:i=251:fsr=off:rtra=on_2976 on theBenchmark for (2976ds/251Mi)
% 19.88/3.17 % (1436023)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=3343435127: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_2976 on theBenchmark for (2976ds/2470Mi)
% 19.88/3.17 % (1436014)Instruction limit reached!
% 19.88/3.17 % (1436014)------------------------------
% 19.88/3.17 % (1436014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.88/3.17 % (1436014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.88/3.17 % (1436014)CaDiCaL version: 2.1.3
% 19.88/3.17 % (1436014)Termination reason: Instruction limit
% 19.88/3.17 % (1436014)Termination phase: Saturation
% 19.88/3.17 % (1436014)Time elapsed: 0.166 s
% 19.88/3.17 % (1436014)Peak memory usage: 15 MB
% 19.88/3.17 % (1436014)Instructions burned: 355 (million)
% 19.88/3.17 % (1436026)dis+10_6_sil=128000:si=on:sp=arity:bce=on:cbe=off:uwa=interpreted_only:slsqc=4:slsq=on:random_seed=2827281308:i=673:doe=on:fgj=on:piset=and:slsql=off:rtra=on:fdi=1024:ntd=on_2975 on theBenchmark for (2975ds/673Mi)
% 19.88/3.17 % (1436022)Instruction limit reached!
% 19.88/3.17 % (1436022)------------------------------
% 19.88/3.17 % (1436022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.88/3.17 % (1436022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.88/3.17 % (1436022)CaDiCaL version: 2.1.3
% 19.88/3.17 % (1436022)Termination reason: Instruction limit
% 19.88/3.17 % (1436022)Termination phase: Saturation
% 19.88/3.17 % (1436022)Time elapsed: 0.108 s
% 19.88/3.17 % (1436022)Peak memory usage: 14 MB
% 19.88/3.17 % (1436022)Instructions burned: 252 (million)
% 19.88/3.17 % (1436028)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=2701714242:i=116:ep=RSTC:rtra=on:ntd=on_2975 on theBenchmark for (2975ds/116Mi)
% 19.88/3.17 % (1436028)Instruction limit reached!
% 19.88/3.17 % (1436028)------------------------------
% 19.88/3.17 % (1436028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 19.88/3.17 % (1436028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.88/3.17 % (1436028)CaDiCaL version: 2.1.3
% 19.88/3.17 % (1436028)Termination reason: Instruction limit
% 19.88/3.17 % (1436028)Termination phase: Property scanning
% 19.88/3.17 % (1436028)Time elapsed: 0.051 s
% 19.88/3.17 % (1436028)Peak memory usage: 13 MB
% 19.88/3.17 % (1436028)Instructions burned: 117 (million)
% 19.88/3.17 % (1436030)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=2722886749:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2974 on theBenchmark for (2974ds/270Mi)
% 21.44/3.44 % (1435971)Instruction limit reached!
% 21.44/3.44 % (1435971)------------------------------
% 21.44/3.44 % (1435971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1435971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1435971)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1435971)Termination reason: Instruction limit
% 21.44/3.44 % (1435971)Termination phase: Saturation
% 21.44/3.44 % (1435971)Time elapsed: 0.399 s
% 21.44/3.44 % (1435971)Peak memory usage: 18 MB
% 21.44/3.44 % (1435971)Instructions burned: 806 (million)
% 21.44/3.44 % (1436032)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=121781510: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_2974 on theBenchmark for (2974ds/30Mi)
% 21.44/3.44 % (1436032)Instruction limit reached!
% 21.44/3.44 % (1436032)------------------------------
% 21.44/3.44 % (1436032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1436032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1436032)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1436032)Termination reason: Instruction limit
% 21.44/3.44 % (1436032)Termination phase: shuffling
% 21.44/3.44 % (1436032)Time elapsed: 0.013 s
% 21.44/3.44 % (1436032)Peak memory usage: 10 MB
% 21.44/3.44 % (1436032)Instructions burned: 31 (million)
% 21.44/3.44 % (1436034)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 21.44/3.44 % (1436034)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=986080301:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2974 on theBenchmark for (2974ds/39Mi)
% 21.44/3.44 % (1436034)Instruction limit reached!
% 21.44/3.44 % (1436034)------------------------------
% 21.44/3.44 % (1436034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1436034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1436034)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1436034)Termination reason: Instruction limit
% 21.44/3.44 % (1436034)Termination phase: Property scanning
% 21.44/3.44 % (1436034)Time elapsed: 0.017 s
% 21.44/3.44 % (1436034)Peak memory usage: 10 MB
% 21.44/3.44 % (1436034)Instructions burned: 41 (million)
% 21.44/3.44 % (1436036)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2519112768:i=365:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2973 on theBenchmark for (2973ds/365Mi)
% 21.44/3.44 % (1436030)Instruction limit reached!
% 21.44/3.44 % (1436030)------------------------------
% 21.44/3.44 % (1436030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1436030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1436030)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1436030)Termination reason: Instruction limit
% 21.44/3.44 % (1436030)Termination phase: Saturation
% 21.44/3.44 % (1436030)Time elapsed: 0.111 s
% 21.44/3.44 % (1436030)Peak memory usage: 12 MB
% 21.44/3.44 % (1436030)Instructions burned: 272 (million)
% 21.44/3.44 % (1436038)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1307864725:i=158:av=off:rtra=on_2973 on theBenchmark for (2973ds/158Mi)
% 21.44/3.44 % (1436038)Instruction limit reached!
% 21.44/3.44 % (1436038)------------------------------
% 21.44/3.44 % (1436038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1436038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1436038)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1436038)Termination reason: Instruction limit
% 21.44/3.44 % (1436038)Termination phase: Saturation
% 21.44/3.44 % (1436038)Time elapsed: 0.069 s
% 21.44/3.44 % (1436038)Peak memory usage: 14 MB
% 21.44/3.44 % (1436038)Instructions burned: 158 (million)
% 21.44/3.44 % (1436026)Instruction limit reached!
% 21.44/3.44 % (1436026)------------------------------
% 21.44/3.44 % (1436026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 21.44/3.44 % (1436026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.44/3.44 % (1436026)CaDiCaL version: 2.1.3
% 21.44/3.44 % (1436026)Termination reason: Instruction limit
% 22.28/3.53 % (1436026)Termination phase: Saturation
% 22.28/3.53 % (1436026)Time elapsed: 0.311 s
% 22.28/3.53 % (1436026)Peak memory usage: 17 MB
% 22.28/3.53 % (1436026)Instructions burned: 674 (million)
% 22.28/3.53 % (1436040)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
% 22.28/3.53 % (1436040)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=1628629872:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/252Mi)
% 22.28/3.53 % (1436041)lrs+10_1_cnfonf=off:si=on:sos=on:uwa=off:random_seed=2268847448:i=213:rtra=on:ss=axioms_2972 on theBenchmark for (2972ds/213Mi)
% 22.28/3.53 % (1436041)Refutation not found, incomplete strategy
% 22.28/3.53 % (1436041)------------------------------
% 22.28/3.53 % (1436041)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.28/3.53 % (1436041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.28/3.53 % (1436041)CaDiCaL version: 2.1.3
% 22.28/3.53 % (1436041)Termination reason: Refutation not found, incomplete strategy
% 22.28/3.53 % (1436041)Time elapsed: 0.019 s
% 22.28/3.53 % (1436041)Peak memory usage: 13 MB
% 22.28/3.53 % (1436041)Instructions burned: 40 (million)
% 22.28/3.53 % (1436041)------------------------------
% 22.28/3.53 % (1436041)------------------------------
% 22.28/3.53 % (1436036)Instruction limit reached!
% 22.28/3.53 % (1436036)------------------------------
% 22.28/3.53 % (1436036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.28/3.53 % (1436036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.28/3.53 % (1436036)CaDiCaL version: 2.1.3
% 22.28/3.53 % (1436036)Termination reason: Instruction limit
% 22.28/3.53 % (1436036)Termination phase: Saturation
% 22.28/3.53 % (1436036)Time elapsed: 0.160 s
% 22.28/3.53 % (1436036)Peak memory usage: 16 MB
% 22.28/3.53 % (1436036)Instructions burned: 365 (million)
% 22.28/3.53 % (1436044)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=352472203:st=3:i=160:s2at=3:bd=preordered:nm=16:rtra=on:ss=axioms:ntd=on_2972 on theBenchmark for (2972ds/160Mi)
% 22.28/3.53 % (1436045)lrs+1010_2:3_sil=128000:cnfonf=off:e2e=on:si=on:sp=unary_first:uwa=off:br=off:lftc=80:random_seed=3887658052:hsq=on:hsqr=16,1:i=763:kws=inv_frequency:piset=and:bd=all:rtra=on:ntd=on_2972 on theBenchmark for (2972ds/763Mi)
% 22.28/3.53 % (1436040)Instruction limit reached!
% 22.28/3.53 % (1436040)------------------------------
% 22.28/3.53 % (1436040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.28/3.53 % (1436040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.28/3.53 % (1436040)CaDiCaL version: 2.1.3
% 22.28/3.53 % (1436040)Termination reason: Instruction limit
% 22.28/3.53 % (1436040)Termination phase: Saturation
% 22.28/3.53 % (1436040)Time elapsed: 0.111 s
% 22.28/3.53 % (1436040)Peak memory usage: 15 MB
% 22.28/3.53 % (1436040)Instructions burned: 252 (million)
% 22.28/3.53 % (1436044)Instruction limit reached!
% 22.28/3.53 % (1436044)------------------------------
% 22.28/3.53 % (1436044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.28/3.53 % (1436044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.28/3.53 % (1436044)CaDiCaL version: 2.1.3
% 22.28/3.53 % (1436044)Termination reason: Instruction limit
% 22.28/3.53 % (1436044)Termination phase: Function definition elimination
% 22.28/3.53 % (1436044)Time elapsed: 0.069 s
% 22.28/3.53 % (1436044)Peak memory usage: 13 MB
% 22.28/3.53 % (1436044)Instructions burned: 160 (million)
% 22.28/3.53 % (1436048)WARNING Broken Constraint: if ho_split_queue_layered_arrangement(off) has been set then ho_split_queue(off) is equal to on
% 22.28/3.53 % (1436049)dis+1002_1_drc=ordering:cnfonf=lazy_not_gen_be_off:si=on:lma=off:cbe=off:uwa=off:random_seed=3337741469:s2a=on:i=386:rtra=on:ntd=on_2971 on theBenchmark for (2971ds/386Mi)
% 22.28/3.53 % (1436048)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=2447942931: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)
% 22.28/3.53 % (1436023)Instruction limit reached!
% 22.28/3.53 % (1436023)------------------------------
% 22.28/3.53 % (1436023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1436023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1436023)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1436023)Termination reason: Instruction limit
% 23.21/3.62 % (1436023)Termination phase: Saturation
% 23.21/3.62 % (1436023)Time elapsed: 0.567 s
% 23.21/3.62 % (1436023)Peak memory usage: 18 MB
% 23.21/3.62 % (1436023)Instructions burned: 2473 (million)
% 23.21/3.62 % (1436052)dis+10_128_to=lpo:sil=128000:si=on:spb=intro:uwa=off:random_seed=2477474210:i=300:piset=and:nm=32:rtra=on_2970 on theBenchmark for (2970ds/300Mi)
% 23.21/3.62 % (1436052)Instruction limit reached!
% 23.21/3.62 % (1436052)------------------------------
% 23.21/3.62 % (1436052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1436052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1436052)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1436052)Termination reason: Instruction limit
% 23.21/3.62 % (1436052)Termination phase: Saturation
% 23.21/3.62 % (1436052)Time elapsed: 0.066 s
% 23.21/3.62 % (1436052)Peak memory usage: 14 MB
% 23.21/3.62 % (1436052)Instructions burned: 304 (million)
% 23.21/3.62 % (1436048)Instruction limit reached!
% 23.21/3.62 % (1436048)------------------------------
% 23.21/3.62 % (1436048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1436048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1436048)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1436048)Termination reason: Instruction limit
% 23.21/3.62 % (1436048)Termination phase: Saturation
% 23.21/3.62 % (1436048)Time elapsed: 0.104 s
% 23.21/3.62 % (1436048)Peak memory usage: 14 MB
% 23.21/3.62 % (1436048)Instructions burned: 237 (million)
% 23.21/3.62 % (1436054)dis+1010_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:urr=on:random_seed=1824311404:st=5:s2a=on:i=567:sd=2:rtra=on:ss=axioms_2970 on theBenchmark for (2970ds/567Mi)
% 23.21/3.62 % (1436056)lrs+1010_1_si=on:uwa=one_side_interpreted:random_seed=3063856508:s2a=on:i=379:sd=1:rtra=on:ss=axioms:sgt=128_2970 on theBenchmark for (2970ds/379Mi)
% 23.21/3.62 % (1436049)Instruction limit reached!
% 23.21/3.62 % (1436049)------------------------------
% 23.21/3.62 % (1436049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1436049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1436049)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1436049)Termination reason: Instruction limit
% 23.21/3.62 % (1436049)Termination phase: Saturation
% 23.21/3.62 % (1436049)Time elapsed: 0.157 s
% 23.21/3.62 % (1436049)Peak memory usage: 12 MB
% 23.21/3.62 % (1436049)Instructions burned: 387 (million)
% 23.21/3.62 % (1435963)Instruction limit reached!
% 23.21/3.62 % (1435963)------------------------------
% 23.21/3.62 % (1435963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1435963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1435963)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1435963)Termination reason: Instruction limit
% 23.21/3.62 % (1435963)Termination phase: Saturation
% 23.21/3.62 % (1435963)Time elapsed: 0.942 s
% 23.21/3.62 % (1435963)Peak memory usage: 15 MB
% 23.21/3.62 % (1435963)Instructions burned: 2187 (million)
% 23.21/3.62 % (1436059)ott+10_1_to=lpo:sil=128000:e2e=on:si=on:sos=on:uwa=off:sac=on:random_seed=4236087346:i=478:bd=all:rtra=on_2969 on theBenchmark for (2969ds/478Mi)
% 23.21/3.62 % (1436058)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=3993259696: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)
% 23.21/3.62 % (1436054)Instruction limit reached!
% 23.21/3.62 % (1436054)------------------------------
% 23.21/3.62 % (1436054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 23.21/3.62 % (1436054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.21/3.62 % (1436054)CaDiCaL version: 2.1.3
% 23.21/3.62 % (1436054)Termination reason: Instruction limit
% 23.21/3.62 % (1436054)Termination phase: Saturation
% 23.21/3.62 % (1436054)Time elapsed: 0.123 s
% 23.21/3.62 % (1436054)Peak memory usage: 12 MB
% 23.21/3.62 % (1436054)Instructions burned: 571 (million)
% 23.21/3.62 % (1436062)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3844029029:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2968 on theBenchmark for (2968ds/445Mi)
% 23.21/3.62 % (1436045)Instruction limit reached!
% 23.21/3.62 % (1436045)------------------------------
% 24.51/3.94 % (1436045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436045)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436045)Termination reason: Instruction limit
% 24.51/3.94 % (1436045)Termination phase: Saturation
% 24.51/3.94 % (1436045)Time elapsed: 0.370 s
% 24.51/3.94 % (1436045)Peak memory usage: 17 MB
% 24.51/3.94 % (1436045)Instructions burned: 764 (million)
% 24.51/3.94 % (1436056)Instruction limit reached!
% 24.51/3.94 % (1436056)------------------------------
% 24.51/3.94 % (1436056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436056)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436056)Termination reason: Instruction limit
% 24.51/3.94 % (1436056)Termination phase: Saturation
% 24.51/3.94 % (1436056)Time elapsed: 0.169 s
% 24.51/3.94 % (1436056)Peak memory usage: 16 MB
% 24.51/3.94 % (1436056)Instructions burned: 379 (million)
% 24.51/3.94 % (1436064)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=2099436807:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2968 on theBenchmark for (2968ds/71Mi)
% 24.51/3.94 % (1436065)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=105396130:i=302:sd=2:bd=preordered:rtra=on:ss=axioms_2968 on theBenchmark for (2968ds/302Mi)
% 24.51/3.94 % (1436064)Instruction limit reached!
% 24.51/3.94 % (1436064)------------------------------
% 24.51/3.94 % (1436064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436064)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436064)Termination reason: Instruction limit
% 24.51/3.94 % (1436064)Termination phase: Property scanning
% 24.51/3.94 % (1436064)Time elapsed: 0.030 s
% 24.51/3.94 % (1436064)Peak memory usage: 11 MB
% 24.51/3.94 % (1436064)Instructions burned: 72 (million)
% 24.51/3.94 % (1436062)Instruction limit reached!
% 24.51/3.94 % (1436062)------------------------------
% 24.51/3.94 % (1436062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436062)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436062)Termination reason: Instruction limit
% 24.51/3.94 % (1436062)Termination phase: Saturation
% 24.51/3.94 % (1436062)Time elapsed: 0.110 s
% 24.51/3.94 % (1436062)Peak memory usage: 16 MB
% 24.51/3.94 % (1436062)Instructions burned: 447 (million)
% 24.51/3.94 % (1436068)lrs+10_1_sil=128000:fde=none:cnfonf=off:si=on:uwa=off:random_seed=3040426036:s2a=on:i=4980:sd=2:bd=all:rtra=on:ss=axioms:ntd=on_2967 on theBenchmark for (2967ds/4980Mi)
% 24.51/3.94 % (1436069)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
% 24.51/3.94 % (1436069)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 24.51/3.94 % (1436069)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=483324079:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2967 on theBenchmark for (2967ds/100Mi)
% 24.51/3.94 % (1436068)Refutation not found, incomplete strategy
% 24.51/3.94 % (1436068)------------------------------
% 24.51/3.94 % (1436068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436068)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436068)Termination reason: Refutation not found, incomplete strategy
% 24.51/3.94 % (1436068)Time elapsed: 0.019 s
% 24.51/3.94 % (1436068)Peak memory usage: 12 MB
% 24.51/3.94 % (1436068)Instructions burned: 42 (million)
% 24.51/3.94 % (1436058)Instruction limit reached!
% 24.51/3.94 % (1436058)------------------------------
% 24.51/3.94 % (1436058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.51/3.94 % (1436058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.51/3.94 % (1436058)CaDiCaL version: 2.1.3
% 24.51/3.94 % (1436058)Termination reason: Instruction limit
% 24.51/3.94 % (1436058)Termination phase: Saturation
% 24.51/3.94 % (1436058)Time elapsed: 0.200 s
% 27.23/4.13 % (1436058)Peak memory usage: 17 MB
% 27.23/4.13 % (1436058)Instructions burned: 429 (million)
% 27.23/4.13 % (1436068)------------------------------
% 27.23/4.13 % (1436068)------------------------------
% 27.23/4.13 % (1436069)Instruction limit reached!
% 27.23/4.13 % (1436069)------------------------------
% 27.23/4.13 % (1436069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.23/4.13 % (1436069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.23/4.13 % (1436069)CaDiCaL version: 2.1.3
% 27.23/4.13 % (1436069)Termination reason: Instruction limit
% 27.23/4.13 % (1436069)Termination phase: Twee Goal Transformation
% 27.23/4.13 % (1436069)Time elapsed: 0.022 s
% 27.23/4.13 % (1436069)Peak memory usage: 11 MB
% 27.23/4.13 % (1436069)Instructions burned: 104 (million)
% 27.23/4.13 % (1436074)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=187856181:i=493:s2at=5:kws=frequency:doe=on:rtra=on:er=known_2967 on theBenchmark for (2967ds/493Mi)
% 27.23/4.13 % (1436073)lrs+10_1_to=lpo:sil=128000:cnfonf=off:si=on:sp=unary_first:sos=all:spb=goal:uwa=off:random_seed=437102757:i=289:rtra=on_2967 on theBenchmark for (2967ds/289Mi)
% 27.23/4.13 % (1436072)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=34734445:i=76:piset=equals:rtra=on:ntd=on_2967 on theBenchmark for (2967ds/76Mi)
% 27.23/4.13 % (1436059)Instruction limit reached!
% 27.23/4.13 % (1436059)------------------------------
% 27.23/4.13 % (1436059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.23/4.13 % (1436059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.23/4.13 % (1436059)CaDiCaL version: 2.1.3
% 27.23/4.13 % (1436059)Termination reason: Instruction limit
% 27.23/4.13 % (1436059)Termination phase: Saturation
% 27.23/4.13 % (1436059)Time elapsed: 0.232 s
% 27.23/4.13 % (1436059)Peak memory usage: 18 MB
% 27.23/4.13 % (1436059)Instructions burned: 478 (million)
% 27.23/4.13 % (1436078)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=3382120791:cond=on:i=34:hud=10:nm=10:rtra=on_2967 on theBenchmark for (2967ds/34Mi)
% 27.23/4.13 % (1436072)Instruction limit reached!
% 27.23/4.13 % (1436072)------------------------------
% 27.23/4.13 % (1436072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.23/4.13 % (1436072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.23/4.13 % (1436072)CaDiCaL version: 2.1.3
% 27.23/4.13 % (1436072)Termination reason: Instruction limit
% 27.23/4.13 % (1436072)Termination phase: Property scanning
% 27.23/4.13 % (1436072)Time elapsed: 0.032 s
% 27.23/4.13 % (1436072)Peak memory usage: 10 MB
% 27.23/4.13 % (1436072)Instructions burned: 77 (million)
% 27.23/4.13 % (1436078)Instruction limit reached!
% 27.23/4.13 % (1436078)------------------------------
% 27.23/4.13 % (1436078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.23/4.13 % (1436078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.23/4.13 % (1436078)CaDiCaL version: 2.1.3
% 27.23/4.13 % (1436078)Termination reason: Instruction limit
% 27.23/4.13 % (1436078)Termination phase: Property scanning
% 27.23/4.13 % (1436078)Time elapsed: 0.015 s
% 27.23/4.13 % (1436078)Peak memory usage: 10 MB
% 27.23/4.13 % (1436078)Instructions burned: 35 (million)
% 27.23/4.13 % (1436080)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 27.23/4.13 % (1436080)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=2955481829:i=372:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2966 on theBenchmark for (2966ds/372Mi)
% 27.23/4.13 % (1436065)Instruction limit reached!
% 27.23/4.13 % (1436065)------------------------------
% 27.23/4.13 % (1436065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.23/4.13 % (1436065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.23/4.13 % (1436065)CaDiCaL version: 2.1.3
% 27.23/4.13 % (1436065)Termination reason: Instruction limit
% 27.23/4.13 % (1436065)Termination phase: Saturation
% 27.23/4.13 % (1436065)Time elapsed: 0.140 s
% 27.23/4.13 % (1436065)Peak memory usage: 14 MB
% 27.23/4.13 % (1436065)Instructions burned: 303 (million)
% 27.23/4.13 % (1436081)lrs+1002_1024_sil=128000:tgt=ground:e2e=on:si=on:uwa=interpreted_only:fd=off:nwc=1:random_seed=2697585601:cts=off:avsq=on:i=670:avsqr=1,16:nm=16:rtra=on_2966 on theBenchmark for (2966ds/670Mi)
% 28.39/4.50 % (1436083)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1195637589:hsq=on:st=2:i=647:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2966 on theBenchmark for (2966ds/647Mi)
% 28.39/4.50 % (1436074)Instruction limit reached!
% 28.39/4.50 % (1436074)------------------------------
% 28.39/4.50 % (1436074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.39/4.50 % (1436074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.50 % (1436074)CaDiCaL version: 2.1.3
% 28.39/4.50 % (1436074)Termination reason: Instruction limit
% 28.39/4.50 % (1436074)Termination phase: Saturation
% 28.39/4.50 % (1436074)Time elapsed: 0.132 s
% 28.39/4.50 % (1436074)Peak memory usage: 15 MB
% 28.39/4.50 % (1436074)Instructions burned: 493 (million)
% 28.39/4.50 % (1436073)Instruction limit reached!
% 28.39/4.50 % (1436073)------------------------------
% 28.39/4.50 % (1436073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.39/4.50 % (1436073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.50 % (1436073)CaDiCaL version: 2.1.3
% 28.39/4.50 % (1436073)Termination reason: Instruction limit
% 28.39/4.50 % (1436073)Termination phase: Saturation
% 28.39/4.50 % (1436073)Time elapsed: 0.133 s
% 28.39/4.50 % (1436073)Peak memory usage: 15 MB
% 28.39/4.50 % (1436073)Instructions burned: 290 (million)
% 28.39/4.50 % (1436086)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=1159467157:i=857:add=off:kws=frequency:rtra=on:ntd=on_2965 on theBenchmark for (2965ds/857Mi)
% 28.39/4.50 % (1436087)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=4114190485:i=693:add=off:fsr=off:rtra=on:fe=abstraction:ntd=on_2965 on theBenchmark for (2965ds/693Mi)
% 28.39/4.50 % (1436080)Instruction limit reached!
% 28.39/4.50 % (1436080)------------------------------
% 28.39/4.50 % (1436080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.39/4.50 % (1436080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.50 % (1436080)CaDiCaL version: 2.1.3
% 28.39/4.50 % (1436080)Termination reason: Instruction limit
% 28.39/4.50 % (1436080)Termination phase: Saturation
% 28.39/4.50 % (1436080)Time elapsed: 0.168 s
% 28.39/4.50 % (1436080)Peak memory usage: 16 MB
% 28.39/4.50 % (1436080)Instructions burned: 373 (million)
% 28.39/4.50 % (1436090)dis+10_7_sil=128000:cnfonf=lazy_gen:si=on:sos=on:random_seed=2726381190:i=285:hud=10:bd=all:rtra=on:ss=axioms_2964 on theBenchmark for (2964ds/285Mi)
% 28.39/4.50 % (1436086)Instruction limit reached!
% 28.39/4.50 % (1436086)------------------------------
% 28.39/4.50 % (1436086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.39/4.50 % (1436086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.50 % (1436086)CaDiCaL version: 2.1.3
% 28.39/4.50 % (1436086)Termination reason: Instruction limit
% 28.39/4.50 % (1436086)Termination phase: Saturation
% 28.39/4.50 % (1436086)Time elapsed: 0.216 s
% 28.39/4.50 % (1436086)Peak memory usage: 18 MB
% 28.39/4.50 % (1436086)Instructions burned: 860 (million)
% 28.39/4.50 % (1436090)Instruction limit reached!
% 28.39/4.50 % (1436090)------------------------------
% 28.39/4.50 % (1436090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 28.39/4.50 % (1436090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.50 % (1436090)CaDiCaL version: 2.1.3
% 28.39/4.50 % (1436090)Termination reason: Instruction limit
% 28.39/4.50 % (1436090)Termination phase: Saturation
% 28.39/4.50 % (1436090)Time elapsed: 0.127 s
% 28.39/4.50 % (1436090)Peak memory usage: 15 MB
% 28.39/4.50 % (1436090)Instructions burned: 285 (million)
% 28.39/4.50 % (1436092)WARNING Broken Constraint: if ho_split_queue_ratios(23,10) has been set then ho_split_queue(off) is equal to on
% 28.39/4.50 % (1436092)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=2971076742: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)
% 28.39/4.50 % (1436092)Instruction limit reached!
% 28.39/4.50 % (1436092)------------------------------
% 29.84/4.68 % (1436092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436092)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436092)Termination reason: Instruction limit
% 29.84/4.68 % (1436092)Termination phase: Preprocessing 3
% 29.84/4.68 % (1436092)Time elapsed: 0.013 s
% 29.84/4.68 % (1436092)Peak memory usage: 11 MB
% 29.84/4.68 % (1436092)Instructions burned: 54 (million)
% 29.84/4.68 % (1436081)Instruction limit reached!
% 29.84/4.68 % (1436081)------------------------------
% 29.84/4.68 % (1436081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436081)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436081)Termination reason: Instruction limit
% 29.84/4.68 % (1436081)Termination phase: Saturation
% 29.84/4.68 % (1436081)Time elapsed: 0.320 s
% 29.84/4.68 % (1436081)Peak memory usage: 18 MB
% 29.84/4.68 % (1436081)Instructions burned: 671 (million)
% 29.84/4.68 % (1436093)dis+10_1_si=on:random_seed=1562002187:i=407:sd=4:rtra=on:ss=axioms:sgt=20_2963 on theBenchmark for (2963ds/407Mi)
% 29.84/4.68 % (1436083)Instruction limit reached!
% 29.84/4.68 % (1436083)------------------------------
% 29.84/4.68 % (1436083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436083)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436083)Termination reason: Instruction limit
% 29.84/4.68 % (1436083)Termination phase: Saturation
% 29.84/4.68 % (1436083)Time elapsed: 0.315 s
% 29.84/4.68 % (1436083)Peak memory usage: 18 MB
% 29.84/4.68 % (1436083)Instructions burned: 647 (million)
% 29.84/4.68 % (1436095)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=686783321:i=2240:bs=unit_only:ins=25:rtra=on:ntd=on_2963 on theBenchmark for (2963ds/2240Mi)
% 29.84/4.68 % (1436097)lrs+10_1_sil=128000:e2e=on:si=on:uwa=interpreted_only:random_seed=2077939760:st=2:i=336:sd=1:rtra=on:ss=axioms:ntd=on_2963 on theBenchmark for (2963ds/336Mi)
% 29.84/4.68 % (1436098)lrs+10_1_to=lpo:sil=128000:fde=none:cnfonf=off:si=on:sp=unary_first:urr=on:uwa=one_side_constant:random_seed=3982613123:s2a=on:i=1142:s2at=3:bd=all:rtra=on_2963 on theBenchmark for (2963ds/1142Mi)
% 29.84/4.68 % (1436087)Instruction limit reached!
% 29.84/4.68 % (1436087)------------------------------
% 29.84/4.68 % (1436087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436087)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436087)Termination reason: Instruction limit
% 29.84/4.68 % (1436087)Termination phase: Saturation
% 29.84/4.68 % (1436087)Time elapsed: 0.284 s
% 29.84/4.68 % (1436087)Peak memory usage: 13 MB
% 29.84/4.68 % (1436087)Instructions burned: 693 (million)
% 29.84/4.68 % (1436102)dis+1002_1_sil=128000:si=on:uwa=off:random_seed=1534601070:st=3:i=376:sd=4:rtra=on:ss=axioms:ntd=on_2962 on theBenchmark for (2962ds/376Mi)
% 29.84/4.68 % (1436097)Instruction limit reached!
% 29.84/4.68 % (1436097)------------------------------
% 29.84/4.68 % (1436097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436097)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436097)Termination reason: Instruction limit
% 29.84/4.68 % (1436097)Termination phase: Saturation
% 29.84/4.68 % (1436097)Time elapsed: 0.149 s
% 29.84/4.68 % (1436097)Peak memory usage: 16 MB
% 29.84/4.68 % (1436097)Instructions burned: 338 (million)
% 29.84/4.68 % (1436093)Instruction limit reached!
% 29.84/4.68 % (1436093)------------------------------
% 29.84/4.68 % (1436093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.84/4.68 % (1436093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.84/4.68 % (1436093)CaDiCaL version: 2.1.3
% 29.84/4.68 % (1436093)Termination reason: Instruction limit
% 29.84/4.68 % (1436093)Termination phase: Saturation
% 29.84/4.68 % (1436093)Time elapsed: 0.178 s
% 29.84/4.68 % (1436093)Peak memory usage: 16 MB
% 29.84/4.68 % (1436093)Instructions burned: 408 (million)
% 29.84/4.68 % (1436104)dis+1002_4:1_anc=none:sil=128000:sas=cadical:si=on:sp=weighted_frequency:sos=on:uwa=one_side_interpreted:random_seed=1748280635:i=766:bd=all:rtra=on_2961 on theBenchmark for (2961ds/766Mi)
% 30.71/4.88 % (1436105)WARNING Broken Constraint: if avatar_split_queue_cutoffs(4) has been set then avatar_split_queue(off) is equal to on
% 30.71/4.88 % (1436105)lrs+10_1_to=kbo:si=on:sp=const_frequency:sos=on:spb=non_intro:uwa=hol:avsqc=4:random_seed=781504579: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_2961 on theBenchmark for (2961ds/959Mi)
% 30.71/4.88 % (1436102)Instruction limit reached!
% 30.71/4.88 % (1436102)------------------------------
% 30.71/4.88 % (1436102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1436102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.71/4.88 % (1436102)CaDiCaL version: 2.1.3
% 30.71/4.88 % (1436102)Termination reason: Instruction limit
% 30.71/4.88 % (1436102)Termination phase: Saturation
% 30.71/4.88 % (1436102)Time elapsed: 0.167 s
% 30.71/4.88 % (1436102)Peak memory usage: 16 MB
% 30.71/4.88 % (1436102)Instructions burned: 376 (million)
% 30.71/4.88 % (1436108)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=789679191:i=6359:add=on:kws=inv_frequency:aac=none:rtra=on:c=on:er=filter:ntd=on_2960 on theBenchmark for (2960ds/6359Mi)
% 30.71/4.88 % (1435692)Instruction limit reached!
% 30.71/4.88 % (1435692)------------------------------
% 30.71/4.88 % (1435692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1435692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.71/4.88 % (1435692)CaDiCaL version: 2.1.3
% 30.71/4.88 % (1435692)Termination reason: Instruction limit
% 30.71/4.88 % (1435692)Termination phase: Saturation
% 30.71/4.88 % (1435692)Time elapsed: 3.220 s
% 30.71/4.88 % (1435692)Peak memory usage: 34 MB
% 30.71/4.88 % (1435692)Instructions burned: 5755 (million)
% 30.71/4.88 % (1436110)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2913254470: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)
% 30.71/4.88 % (1436110)Instruction limit reached!
% 30.71/4.88 % (1436110)------------------------------
% 30.71/4.88 % (1436110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1436110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.71/4.88 % (1436110)CaDiCaL version: 2.1.3
% 30.71/4.88 % (1436110)Termination reason: Instruction limit
% 30.71/4.88 % (1436110)Termination phase: SInE selection
% 30.71/4.88 % (1436110)Time elapsed: 0.015 s
% 30.71/4.88 % (1436110)Peak memory usage: 10 MB
% 30.71/4.88 % (1436110)Instructions burned: 35 (million)
% 30.71/4.88 % (1436112)dis+10_1_sfv=off:sil=128000:cnfonf=lazy_gen:si=on:uwa=off:nwc=1:chr=on:random_seed=2722188492:hsq=on:hsqr=1,8:i=53:hsql=off:bd=all:rtra=on:ixr=off_2958 on theBenchmark for (2958ds/53Mi)
% 30.71/4.88 % (1436112)Instruction limit reached!
% 30.71/4.88 % (1436112)------------------------------
% 30.71/4.88 % (1436112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1436112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.71/4.88 % (1436112)CaDiCaL version: 2.1.3
% 30.71/4.88 % (1436112)Termination reason: Instruction limit
% 30.71/4.88 % (1436112)Termination phase: Property scanning
% 30.71/4.88 % (1436112)Time elapsed: 0.023 s
% 30.71/4.88 % (1436112)Peak memory usage: 10 MB
% 30.71/4.88 % (1436112)Instructions burned: 55 (million)
% 30.71/4.88 % (1436114)dis+21_1_sil=128000:tgt=full:fde=none:e2e=on:si=on:urr=on:uwa=interpreted_only:s2agt=32:sac=on:random_seed=1446410162:s2a=on:i=876:s2at=6:nm=2:rtra=on_2958 on theBenchmark for (2958ds/876Mi)
% 30.71/4.88 % (1436104)Instruction limit reached!
% 30.71/4.88 % (1436104)------------------------------
% 30.71/4.88 % (1436104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1436104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.71/4.88 % (1436104)CaDiCaL version: 2.1.3
% 30.71/4.88 % (1436104)Termination reason: Instruction limit
% 30.71/4.88 % (1436104)Termination phase: Saturation
% 30.71/4.88 % (1436104)Time elapsed: 0.365 s
% 30.71/4.88 % (1436104)Peak memory usage: 19 MB
% 30.71/4.88 % (1436104)Instructions burned: 766 (million)
% 30.71/4.88 % (1436098)Instruction limit reached!
% 30.71/4.88 % (1436098)------------------------------
% 30.71/4.88 % (1436098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 30.71/4.88 % (1436098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436098)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436098)Termination reason: Instruction limit
% 31.91/5.02 % (1436098)Termination phase: Saturation
% 31.91/5.02 % (1436098)Time elapsed: 0.533 s
% 31.91/5.02 % (1436098)Peak memory usage: 19 MB
% 31.91/5.02 % (1436098)Instructions burned: 1143 (million)
% 31.91/5.02 % (1436117)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 31.91/5.02 % (1436116)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2066003526:i=57:ep=R:rtra=on:ntd=on_2957 on theBenchmark for (2957ds/57Mi)
% 31.91/5.02 % (1436117)dis+1002_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_min:sos=on:fd=preordered:slsqc=2:chr=on:random_seed=3909827584:i=306:bd=all:rtra=on_2957 on theBenchmark for (2957ds/306Mi)
% 31.91/5.02 % (1436116)Instruction limit reached!
% 31.91/5.02 % (1436116)------------------------------
% 31.91/5.02 % (1436116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.91/5.02 % (1436116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436116)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436116)Termination reason: Instruction limit
% 31.91/5.02 % (1436116)Termination phase: Property scanning
% 31.91/5.02 % (1436116)Time elapsed: 0.025 s
% 31.91/5.02 % (1436116)Peak memory usage: 11 MB
% 31.91/5.02 % (1436116)Instructions burned: 59 (million)
% 31.91/5.02 % (1436120)dis+10_8:1_sil=128000:si=on:uwa=off:random_seed=1394520343:i=262:sd=2:bd=preordered:rtra=on:ss=axioms:sgt=8_2957 on theBenchmark for (2957ds/262Mi)
% 31.91/5.02 % (1436105)Instruction limit reached!
% 31.91/5.02 % (1436105)------------------------------
% 31.91/5.02 % (1436105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.91/5.02 % (1436105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436105)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436105)Termination reason: Instruction limit
% 31.91/5.02 % (1436105)Termination phase: Saturation
% 31.91/5.02 % (1436105)Time elapsed: 0.424 s
% 31.91/5.02 % (1436105)Peak memory usage: 20 MB
% 31.91/5.02 % (1436105)Instructions burned: 961 (million)
% 31.91/5.02 % (1436122)WARNING Broken Constraint: if ho_split_queue_ratios(1,3) has been set then ho_split_queue(off) is equal to on
% 31.91/5.02 % (1436122)ott+1002_16_sil=128000:si=on:random_seed=4025908631:hsqr=1,3:i=409:add=on:rtra=on:fe=abstraction_2957 on theBenchmark for (2957ds/409Mi)
% 31.91/5.02 % (1436095)Instruction limit reached!
% 31.91/5.02 % (1436095)------------------------------
% 31.91/5.02 % (1436095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.91/5.02 % (1436095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436095)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436095)Termination reason: Instruction limit
% 31.91/5.02 % (1436095)Termination phase: Saturation
% 31.91/5.02 % (1436095)Time elapsed: 0.709 s
% 31.91/5.02 % (1436095)Peak memory usage: 23 MB
% 31.91/5.02 % (1436095)Instructions burned: 2240 (million)
% 31.91/5.02 % (1436117)Instruction limit reached!
% 31.91/5.02 % (1436117)------------------------------
% 31.91/5.02 % (1436117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.91/5.02 % (1436117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436117)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436117)Termination reason: Instruction limit
% 31.91/5.02 % (1436117)Termination phase: Saturation
% 31.91/5.02 % (1436117)Time elapsed: 0.141 s
% 31.91/5.02 % (1436117)Peak memory usage: 15 MB
% 31.91/5.02 % (1436117)Instructions burned: 306 (million)
% 31.91/5.02 % (1436124)dis+10_1_sil=128000:plsq=on:si=on:plsqr=32,1:uwa=off:random_seed=1842393047:s2a=on:i=381:rtra=on_2956 on theBenchmark for (2956ds/381Mi)
% 31.91/5.02 % (1436120)Instruction limit reached!
% 31.91/5.02 % (1436120)------------------------------
% 31.91/5.02 % (1436120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 31.91/5.02 % (1436120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.91/5.02 % (1436120)CaDiCaL version: 2.1.3
% 31.91/5.02 % (1436120)Termination reason: Instruction limit
% 31.91/5.02 % (1436120)Termination phase: Saturation
% 31.91/5.02 % (1436120)Time elapsed: 0.114 s
% 31.91/5.02 % (1436120)Peak memory usage: 15 MB
% 31.91/5.02 % (1436120)Instructions burned: 263 (million)
% 31.91/5.02 % (1436125)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1003948081:cond=on:i=324:rtra=on:ntd=on_2956 on theBenchmark for (2956ds/324Mi)
% 34.15/5.18 % (1436127)lrs+10_1_sil=128000:fde=none:si=on:sos=on:spb=goal_then_units:urr=on:random_seed=1789903409:i=240:kws=inv_precedence:rtra=on_2955 on theBenchmark for (2955ds/240Mi)
% 34.15/5.18 % (1436124)Instruction limit reached!
% 34.15/5.18 % (1436124)------------------------------
% 34.15/5.18 % (1436124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.15/5.18 % (1436124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.15/5.18 % (1436124)CaDiCaL version: 2.1.3
% 34.15/5.18 % (1436124)Termination reason: Instruction limit
% 34.15/5.18 % (1436124)Termination phase: Saturation
% 34.15/5.18 % (1436124)Time elapsed: 0.091 s
% 34.15/5.18 % (1436124)Peak memory usage: 17 MB
% 34.15/5.18 % (1436124)Instructions burned: 381 (million)
% 34.15/5.18 % (1436122)Instruction limit reached!
% 34.15/5.18 % (1436122)------------------------------
% 34.15/5.18 % (1436122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.15/5.18 % (1436122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.15/5.18 % (1436122)CaDiCaL version: 2.1.3
% 34.15/5.18 % (1436122)Termination reason: Instruction limit
% 34.15/5.18 % (1436122)Termination phase: Saturation
% 34.15/5.18 % (1436122)Time elapsed: 0.183 s
% 34.15/5.18 % (1436122)Peak memory usage: 16 MB
% 34.15/5.18 % (1436122)Instructions burned: 411 (million)
% 34.15/5.18 % (1436130)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 34.15/5.18 % (1436130)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3603341529:cts=off:uwa_fpi=on:i=124:av=off:fsr=off:rtra=on:ntd=on_2955 on theBenchmark for (2955ds/124Mi)
% 34.15/5.18 % (1436131)lrs+1010_2_to=lpo:cnfonf=off:e2e=on:si=on:random_seed=4109949088:uwa_fpi=on:i=223:bd=all:rtra=on:fe=abstraction:ntd=on_2955 on theBenchmark for (2955ds/223Mi)
% 34.15/5.18 % (1436130)Instruction limit reached!
% 34.15/5.18 % (1436130)------------------------------
% 34.15/5.18 % (1436130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.15/5.18 % (1436130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.15/5.18 % (1436130)CaDiCaL version: 2.1.3
% 34.15/5.18 % (1436130)Termination reason: Instruction limit
% 34.15/5.18 % (1436130)Termination phase: Property scanning
% 34.15/5.18 % (1436130)Time elapsed: 0.029 s
% 34.15/5.18 % (1436130)Peak memory usage: 13 MB
% 34.15/5.18 % (1436130)Instructions burned: 128 (million)
% 34.15/5.18 % (1436127)Instruction limit reached!
% 34.15/5.18 % (1436127)------------------------------
% 34.15/5.18 % (1436127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.15/5.18 % (1436127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.15/5.18 % (1436127)CaDiCaL version: 2.1.3
% 34.15/5.18 % (1436127)Termination reason: Instruction limit
% 34.15/5.18 % (1436127)Termination phase: Saturation
% 34.15/5.18 % (1436127)Time elapsed: 0.115 s
% 34.15/5.18 % (1436127)Peak memory usage: 16 MB
% 34.15/5.18 % (1436127)Instructions burned: 240 (million)
% 34.15/5.18 % (1436134)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1981266413:s2a=on:i=282:kws=inv_frequency:bd=all:rtra=on_2954 on theBenchmark for (2954ds/282Mi)
% 34.15/5.18 % (1436125)Instruction limit reached!
% 34.15/5.18 % (1436125)------------------------------
% 34.15/5.18 % (1436125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.15/5.18 % (1436125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.15/5.18 % (1436125)CaDiCaL version: 2.1.3
% 34.15/5.18 % (1436125)Termination reason: Instruction limit
% 34.15/5.18 % (1436125)Termination phase: Saturation
% 34.15/5.18 % (1436125)Time elapsed: 0.151 s
% 34.15/5.18 % (1436125)Peak memory usage: 16 MB
% 34.15/5.18 % (1436125)Instructions burned: 325 (million)
% 34.15/5.18 % (1436136)lrs+10_1_sil=128000:tgt=ground:cnfonf=conj_eager:si=on:random_seed=3870946424:s2a=on:i=464:kws=frequency:bd=all:rtra=on:ss=axioms_2954 on theBenchmark for (2954ds/464Mi)
% 34.15/5.18 % (1436137)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=2954171832:i=88:s2at=3:nm=2:rtra=on:rawr=on_2954 on theBenchmark for (2954ds/88Mi)
% 34.15/5.18 % (1436114)Instruction limit reached!
% 34.15/5.18 % (1436114)------------------------------
% 34.15/5.18 % (1436114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.33/5.54 % (1436114)CaDiCaL version: 2.1.3
% 36.33/5.54 % (1436114)Termination reason: Instruction limit
% 36.33/5.54 % (1436114)Termination phase: Saturation
% 36.33/5.54 % (1436114)Time elapsed: 0.439 s
% 36.33/5.54 % (1436114)Peak memory usage: 17 MB
% 36.33/5.54 % (1436114)Instructions burned: 878 (million)
% 36.33/5.54 % (1436134)Instruction limit reached!
% 36.33/5.54 % (1436134)------------------------------
% 36.33/5.54 % (1436134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.33/5.54 % (1436134)CaDiCaL version: 2.1.3
% 36.33/5.54 % (1436134)Termination reason: Instruction limit
% 36.33/5.54 % (1436134)Termination phase: Saturation
% 36.33/5.54 % (1436134)Time elapsed: 0.067 s
% 36.33/5.54 % (1436134)Peak memory usage: 15 MB
% 36.33/5.54 % (1436134)Instructions burned: 285 (million)
% 36.33/5.54 % (1436131)Instruction limit reached!
% 36.33/5.54 % (1436131)------------------------------
% 36.33/5.54 % (1436131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.33/5.54 % (1436131)CaDiCaL version: 2.1.3
% 36.33/5.54 % (1436131)Termination reason: Instruction limit
% 36.33/5.54 % (1436131)Termination phase: Saturation
% 36.33/5.54 % (1436131)Time elapsed: 0.097 s
% 36.33/5.54 % (1436131)Peak memory usage: 14 MB
% 36.33/5.54 % (1436131)Instructions burned: 224 (million)
% 36.33/5.54 % (1436137)Instruction limit reached!
% 36.33/5.54 % (1436137)------------------------------
% 36.33/5.54 % (1436137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.33/5.54 % (1436137)CaDiCaL version: 2.1.3
% 36.33/5.54 % (1436137)Termination reason: Instruction limit
% 36.33/5.54 % (1436137)Termination phase: Property scanning
% 36.33/5.54 % (1436137)Time elapsed: 0.037 s
% 36.33/5.54 % (1436137)Peak memory usage: 11 MB
% 36.33/5.54 % (1436137)Instructions burned: 90 (million)
% 36.33/5.54 % (1436141)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 36.33/5.54 % (1436141)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=3180731812:i=4386:hud=10:nm=16:av=off:rtra=on:ntd=on_2953 on theBenchmark for (2953ds/4386Mi)
% 36.33/5.54 % (1436140)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2314471337:s2a=on:cond=on:i=280:add=on:bd=preordered:rtra=on:er=filter_2953 on theBenchmark for (2953ds/280Mi)
% 36.33/5.54 % (1436142)WARNING Broken Constraint: if lookahaed_delay(10) has been set then selection(21) is not lookahead selection
% 36.33/5.54 % (1436142)WARNING Broken Constraint: if mono_ep(off) has been set then equality_proxy(off) is not equal to off
% 36.33/5.54 % (1436142)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=2415618655: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)
% 36.33/5.54 % (1436143)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=1633696938:i=73:rtra=on_2953 on theBenchmark for (2953ds/73Mi)
% 36.33/5.54 % (1436143)Instruction limit reached!
% 36.33/5.54 % (1436143)------------------------------
% 36.33/5.54 % (1436143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 36.33/5.54 % (1436143)CaDiCaL version: 2.1.3
% 36.33/5.54 % (1436143)Termination reason: Instruction limit
% 36.33/5.54 % (1436143)Termination phase: Preprocessing 3
% 36.33/5.54 % (1436143)Time elapsed: 0.032 s
% 36.33/5.54 % (1436143)Peak memory usage: 12 MB
% 36.33/5.54 % (1436143)Instructions burned: 73 (million)
% 36.33/5.54 % (1436148)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=3839803654:cts=off:i=176:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2953 on theBenchmark for (2953ds/176Mi)
% 36.33/5.54 % (1436140)Instruction limit reached!
% 36.33/5.54 % (1436140)------------------------------
% 36.33/5.54 % (1436140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 36.33/5.54 % (1436140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.06/5.80 % (1436140)CaDiCaL version: 2.1.3
% 38.06/5.80 % (1436140)Termination reason: Instruction limit
% 38.06/5.80 % (1436140)Termination phase: Saturation
% 38.06/5.80 % (1436140)Time elapsed: 0.116 s
% 38.06/5.80 % (1436140)Peak memory usage: 13 MB
% 38.06/5.80 % (1436140)Instructions burned: 282 (million)
% 38.06/5.80 % (1436150)WARNING Broken Constraint: if sine_tolerance(12) has been set then sine_selection(off) is not equal to off
% 38.06/5.80 % (1436148)Instruction limit reached!
% 38.06/5.80 % (1436148)------------------------------
% 38.06/5.80 % (1436148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.06/5.80 % (1436148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.06/5.80 % (1436148)CaDiCaL version: 2.1.3
% 38.06/5.80 % (1436148)Termination reason: Instruction limit
% 38.06/5.80 % (1436148)Termination phase: Saturation
% 38.06/5.80 % (1436148)Time elapsed: 0.072 s
% 38.06/5.80 % (1436148)Peak memory usage: 12 MB
% 38.06/5.80 % (1436148)Instructions burned: 178 (million)
% 38.06/5.80 % (1436150)dis+1010_128_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=hol:nwc=2:flr=on:random_seed=2060337715:st=12:uwa_fpi=on:i=39:nm=40:ins=7:rtra=on_2952 on theBenchmark for (2952ds/39Mi)
% 38.06/5.80 % (1436136)Instruction limit reached!
% 38.06/5.80 % (1436136)------------------------------
% 38.06/5.80 % (1436136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.06/5.80 % (1436136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.06/5.80 % (1436136)CaDiCaL version: 2.1.3
% 38.06/5.80 % (1436136)Termination reason: Instruction limit
% 38.06/5.80 % (1436136)Termination phase: Saturation
% 38.06/5.80 % (1436136)Time elapsed: 0.210 s
% 38.06/5.80 % (1436136)Peak memory usage: 15 MB
% 38.06/5.80 % (1436136)Instructions burned: 465 (million)
% 38.06/5.80 % (1436150)Instruction limit reached!
% 38.06/5.80 % (1436150)------------------------------
% 38.06/5.80 % (1436150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.06/5.80 % (1436150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.06/5.80 % (1436150)CaDiCaL version: 2.1.3
% 38.06/5.80 % (1436150)Termination reason: Instruction limit
% 38.06/5.80 % (1436150)Termination phase: Property scanning
% 38.06/5.80 % (1436150)Time elapsed: 0.017 s
% 38.06/5.80 % (1436150)Peak memory usage: 10 MB
% 38.06/5.80 % (1436150)Instructions burned: 41 (million)
% 38.06/5.80 % (1436151)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=761317183:i=708:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2952 on theBenchmark for (2952ds/708Mi)
% 38.06/5.80 % (1436153)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
% 38.06/5.80 % (1436153)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=2977199069:avsq=on:i=252:s2at=3:avsqr=1,16:rtra=on:ntd=on_2952 on theBenchmark for (2952ds/252Mi)
% 38.06/5.80 % (1436154)dis+10_4_sil=128000:tgt=full:fde=unused:cnfonf=lazy_not_gen:sas=cadical:si=on:uwa=off:sac=on:random_seed=986267197:i=823:fsr=off:rtra=on_2952 on theBenchmark for (2952ds/823Mi)
% 38.06/5.80 % (1436142)Instruction limit reached!
% 38.06/5.80 % (1436142)------------------------------
% 38.06/5.80 % (1436142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.06/5.80 % (1436142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 38.06/5.80 % (1436142)CaDiCaL version: 2.1.3
% 38.06/5.80 % (1436142)Termination reason: Instruction limit
% 38.06/5.80 % (1436142)Termination phase: Saturation
% 38.06/5.80 % (1436142)Time elapsed: 0.223 s
% 38.06/5.80 % (1436142)Peak memory usage: 17 MB
% 38.06/5.80 % (1436142)Instructions burned: 485 (million)
% 38.06/5.80 % (1436158)WARNING Broken Constraint: lrs_first_time_check(100) is less than 100
% 38.06/5.80 % (1436158)lrs+1010_7_anc=all_dependent:sil=128000:cnfonf=lazy_not_gen:si=on:urr=on:rp=on:sac=on:lftc=100:random_seed=545615538:lrd=on:st=3:i=16202:add=on:sd=3:kws=frequency:rtra=on:ss=axioms_2951 on theBenchmark for (2951ds/16202Mi)
% 38.06/5.80 % (1436153)Instruction limit reached!
% 38.06/5.80 % (1436153)------------------------------
% 38.06/5.80 % (1436153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 38.06/5.80 % (1436153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.39 % (1436153)CaDiCaL version: 2.1.3
% 42.52/6.39 % (1436153)Termination reason: Instruction limit
% 42.52/6.39 % (1436153)Termination phase: Saturation
% 42.52/6.39 % (1436153)Time elapsed: 0.112 s
% 42.52/6.39 % (1436153)Peak memory usage: 15 MB
% 42.52/6.39 % (1436153)Instructions burned: 252 (million)
% 42.52/6.39 % (1436160)dis+10_1_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:uwa=off:random_seed=2401614128:s2a=on:i=300:s2at=10:bd=all:rtra=on:ntd=on_2950 on theBenchmark for (2950ds/300Mi)
% 42.52/6.39 % (1436160)Instruction limit reached!
% 42.52/6.39 % (1436160)------------------------------
% 42.52/6.39 % (1436160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.39 % (1436160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.39 % (1436160)CaDiCaL version: 2.1.3
% 42.52/6.39 % (1436160)Termination reason: Instruction limit
% 42.52/6.39 % (1436160)Termination phase: Saturation
% 42.52/6.39 % (1436160)Time elapsed: 0.122 s
% 42.52/6.39 % (1436160)Peak memory usage: 12 MB
% 42.52/6.39 % (1436160)Instructions burned: 301 (million)
% 42.52/6.39 % (1436162)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(2) has been set then positive_literal_split_queue(off) is equal to on
% 42.52/6.39 % (1436162)WARNING Broken Constraint: if ho_split_queue_lambda_weight(0) has been set then ho_split_queue(off) is equal to on
% 42.52/6.39 % (1436162)dis+1010_1_anc=none:sil=128000:plsqc=2:sas=cadical:si=on:hsqlw=0:uwa=one_side_interpreted:sac=on:random_seed=2883420285:i=177:add=on:bd=preordered:rtra=on:rawr=on_2949 on theBenchmark for (2949ds/177Mi)
% 42.52/6.39 % (1436151)Instruction limit reached!
% 42.52/6.39 % (1436151)------------------------------
% 42.52/6.39 % (1436151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.39 % (1436151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.39 % (1436151)CaDiCaL version: 2.1.3
% 42.52/6.39 % (1436151)Termination reason: Instruction limit
% 42.52/6.39 % (1436151)Termination phase: Saturation
% 42.52/6.39 % (1436151)Time elapsed: 0.322 s
% 42.52/6.39 % (1436151)Peak memory usage: 18 MB
% 42.52/6.39 % (1436151)Instructions burned: 708 (million)
% 42.52/6.39 % (1436164)lrs+10_1_cnfonf=conj_eager:si=on:random_seed=1223331707:st=1.5:s2a=on:i=715:rtra=on:ss=axioms_2948 on theBenchmark for (2948ds/715Mi)
% 42.52/6.39 % (1436154)Instruction limit reached!
% 42.52/6.39 % (1436154)------------------------------
% 42.52/6.39 % (1436154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.39 % (1436154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.39 % (1436154)CaDiCaL version: 2.1.3
% 42.52/6.39 % (1436154)Termination reason: Instruction limit
% 42.52/6.39 % (1436154)Termination phase: Saturation
% 42.52/6.39 % (1436154)Time elapsed: 0.333 s
% 42.52/6.39 % (1436154)Peak memory usage: 13 MB
% 42.52/6.39 % (1436154)Instructions burned: 823 (million)
% 42.52/6.39 % (1436162)Instruction limit reached!
% 42.52/6.39 % (1436162)------------------------------
% 42.52/6.39 % (1436162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 42.52/6.39 % (1436162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 42.52/6.39 % (1436162)CaDiCaL version: 2.1.3
% 42.52/6.39 % (1436162)Termination reason: Instruction limit
% 42.52/6.39 % (1436162)Termination phase: Property scanning
% 42.52/6.39 % (1436162)Time elapsed: 0.076 s
% 42.52/6.39 % (1436162)Peak memory usage: 13 MB
% 42.52/6.39 % (1436162)Instructions burned: 179 (million)
% 42.52/6.39 % (1436166)WARNING Broken Constraint: if positive_literal_split_queue_cutoffs(3) has been set then positive_literal_split_queue(off) is equal to on
% 42.52/6.39 % (1436166)WARNING Broken Constraint: if positive_literal_split_queue_ratios(19,3) has been set then positive_literal_split_queue(off) is equal to on
% 42.52/6.39 % (1436166)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=2199415546:i=230:add=on:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2948 on theBenchmark for (2948ds/230Mi)
% 42.52/6.39 % (1436167)dis+32_3_cha=on:sil=128000:drc=off:si=on:cbe=off:uwa=interpreted_only:nwc=3:random_seed=771375472: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)
% 42.52/6.39 % (1436166)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 42.52/6.39 % (1436166)Instruction limit reached!
% 42.52/6.39 % (1436166)------------------------------
% 45.17/6.84 % (1436166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.17/6.84 % (1436166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.17/6.84 % (1436166)CaDiCaL version: 2.1.3
% 45.17/6.84 % (1436166)Termination reason: Instruction limit
% 45.17/6.84 % (1436166)Termination phase: Saturation
% 45.17/6.84 % (1436166)Time elapsed: 0.115 s
% 45.17/6.84 % (1436166)Peak memory usage: 16 MB
% 45.17/6.84 % (1436166)Instructions burned: 231 (million)
% 45.17/6.84 % (1436170)WARNING Broken Constraint: if lrs_retroactive_deletes(on) has been set then saturation_algorithm(otter) is equal to lrs
% 45.17/6.84 % (1436170)ott+2_2:1_sil=128000:tgt=full:drc=off:si=on:lma=off:urr=on:cbe=off:uwa=interpreted_only:random_seed=1733543815:lrd=on:i=841:nm=0:rtra=on_2947 on theBenchmark for (2947ds/841Mi)
% 45.17/6.84 % (1436164)Instruction limit reached!
% 45.17/6.84 % (1436164)------------------------------
% 45.17/6.84 % (1436164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.17/6.84 % (1436164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.17/6.84 % (1436164)CaDiCaL version: 2.1.3
% 45.17/6.84 % (1436164)Termination reason: Instruction limit
% 45.17/6.84 % (1436164)Termination phase: Saturation
% 45.17/6.84 % (1436164)Time elapsed: 0.315 s
% 45.17/6.84 % (1436164)Peak memory usage: 16 MB
% 45.17/6.84 % (1436164)Instructions burned: 715 (million)
% 45.17/6.84 % (1436167)Instruction limit reached!
% 45.17/6.84 % (1436167)------------------------------
% 45.17/6.84 % (1436167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.17/6.84 % (1436167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.17/6.84 % (1436167)CaDiCaL version: 2.1.3
% 45.17/6.84 % (1436167)Termination reason: Instruction limit
% 45.17/6.84 % (1436167)Termination phase: Saturation
% 45.17/6.84 % (1436167)Time elapsed: 0.297 s
% 45.17/6.84 % (1436167)Peak memory usage: 17 MB
% 45.17/6.84 % (1436167)Instructions burned: 606 (million)
% 45.17/6.84 % (1436172)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2805177915:i=445:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2945 on theBenchmark for (2945ds/445Mi)
% 45.17/6.84 % (1436173)ott+1003_1_to=kbo:cnfonf=lazy_pi_sigma_gen:si=on:sp=weighted_frequency:spb=units:urr=on:cbe=off:random_seed=3193407741:uwa_fpi=on:i=71:hud=10:rtra=on:ixr=off_2945 on theBenchmark for (2945ds/71Mi)
% 45.17/6.84 % (1436141)Instruction limit reached!
% 45.17/6.84 % (1436141)------------------------------
% 45.17/6.84 % (1436141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.17/6.84 % (1436141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.17/6.84 % (1436141)CaDiCaL version: 2.1.3
% 45.17/6.84 % (1436141)Termination reason: Instruction limit
% 45.17/6.84 % (1436141)Termination phase: Saturation
% 45.17/6.84 % (1436141)Time elapsed: 0.857 s
% 45.17/6.84 % (1436141)Peak memory usage: 18 MB
% 45.17/6.84 % (1436141)Instructions burned: 4390 (million)
% 45.17/6.84 % (1436176)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
% 45.17/6.84 % (1436176)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 45.17/6.84 % (1436176)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3401819052:i=100:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2945 on theBenchmark for (2945ds/100Mi)
% 45.17/6.84 % (1436173)Instruction limit reached!
% 45.17/6.84 % (1436173)------------------------------
% 45.17/6.84 % (1436173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 45.17/6.84 % (1436173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 45.17/6.84 % (1436173)CaDiCaL version: 2.1.3
% 45.17/6.84 % (1436173)Termination reason: Instruction limit
% 45.17/6.84 % (1436173)Termination phase: Property scanning
% 45.17/6.84 % (1436173)Time elapsed: 0.029 s
% 45.17/6.84 % (1436173)Peak memory usage: 11 MB
% 45.17/6.84 % (1436173)Instructions burned: 72 (million)
% 45.17/6.84 % (1436178)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(3) has been set then sine_level_split_queue(off) is equal to on
% 45.17/6.84 % (1436178)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=3520115516:i=1352:add=on:aac=none:rtra=on_2944 on theBenchmark for (2944ds/1352Mi)
% 46.03/6.93 % (1436176)Instruction limit reached!
% 46.03/6.93 % (1436176)------------------------------
% 46.03/6.93 % (1436176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436176)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436176)Termination reason: Instruction limit
% 46.03/6.93 % (1436176)Termination phase: Twee Goal Transformation
% 46.03/6.93 % (1436176)Time elapsed: 0.042 s
% 46.03/6.93 % (1436176)Peak memory usage: 11 MB
% 46.03/6.93 % (1436176)Instructions burned: 101 (million)
% 46.03/6.93 % (1436180)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=1677859589:hsq=on:hsqr=16,1:s2a=on:i=646:nm=16:rtra=on:gtg=exists_top:proc=on_2944 on theBenchmark for (2944ds/646Mi)
% 46.03/6.93 % (1436170)Instruction limit reached!
% 46.03/6.93 % (1436170)------------------------------
% 46.03/6.93 % (1436170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436170)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436170)Termination reason: Instruction limit
% 46.03/6.93 % (1436170)Termination phase: Property scanning
% 46.03/6.93 % (1436170)Time elapsed: 0.341 s
% 46.03/6.93 % (1436170)Peak memory usage: 16 MB
% 46.03/6.93 % (1436170)Instructions burned: 842 (million)
% 46.03/6.93 % (1436182)lrs+10_1_sil=128000:si=on:uwa=all:random_seed=662142703:i=1924:sd=2:kws=precedence:bd=all:rtra=on:ss=axioms:sgt=16_2943 on theBenchmark for (2943ds/1924Mi)
% 46.03/6.93 % (1436172)Instruction limit reached!
% 46.03/6.93 % (1436172)------------------------------
% 46.03/6.93 % (1436172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436172)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436172)Termination reason: Instruction limit
% 46.03/6.93 % (1436172)Termination phase: Saturation
% 46.03/6.93 % (1436172)Time elapsed: 0.201 s
% 46.03/6.93 % (1436172)Peak memory usage: 16 MB
% 46.03/6.93 % (1436172)Instructions burned: 446 (million)
% 46.03/6.93 % (1436184)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=402728411:hsq=on:i=984:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2943 on theBenchmark for (2943ds/984Mi)
% 46.03/6.93 % (1436180)Instruction limit reached!
% 46.03/6.93 % (1436180)------------------------------
% 46.03/6.93 % (1436180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436180)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436180)Termination reason: Instruction limit
% 46.03/6.93 % (1436180)Termination phase: Saturation
% 46.03/6.93 % (1436180)Time elapsed: 0.186 s
% 46.03/6.93 % (1436180)Peak memory usage: 17 MB
% 46.03/6.93 % (1436180)Instructions burned: 647 (million)
% 46.03/6.93 % (1436186)dis+10_128_sil=128000:drc=ordering:fde=unused:si=on:lma=off:uwa=interpreted_only:avsqc=4:random_seed=2038776979:avsq=on:i=592:add=off:kws=inv_frequency:bd=preordered:rtra=on_2942 on theBenchmark for (2942ds/592Mi)
% 46.03/6.93 % (1436186)Instruction limit reached!
% 46.03/6.93 % (1436186)------------------------------
% 46.03/6.93 % (1436186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436186)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436186)Termination reason: Instruction limit
% 46.03/6.93 % (1436186)Termination phase: Saturation
% 46.03/6.93 % (1436186)Time elapsed: 0.142 s
% 46.03/6.93 % (1436186)Peak memory usage: 17 MB
% 46.03/6.93 % (1436186)Instructions burned: 593 (million)
% 46.03/6.93 % (1436188)dis+1010_7_si=on:uwa=off:nwc=1.2:random_seed=1246718126:st=2.5:i=872:sd=4:fsr=off:rtra=on:ss=axioms:c=on:ntd=on_2940 on theBenchmark for (2940ds/872Mi)
% 46.03/6.93 % (1436184)Instruction limit reached!
% 46.03/6.93 % (1436184)------------------------------
% 46.03/6.93 % (1436184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436184)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436184)Termination reason: Instruction limit
% 46.03/6.93 % (1436184)Termination phase: Saturation
% 46.03/6.93 % (1436184)Time elapsed: 0.425 s
% 46.03/6.93 % (1436184)Peak memory usage: 20 MB
% 46.03/6.93 % (1436184)Instructions burned: 984 (million)
% 46.03/6.93 % (1436178)Instruction limit reached!
% 46.03/6.93 % (1436178)------------------------------
% 46.03/6.93 % (1436178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436178)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436178)Termination reason: Instruction limit
% 46.03/6.93 % (1436178)Termination phase: Saturation
% 46.03/6.93 % (1436178)Time elapsed: 0.599 s
% 46.03/6.93 % (1436178)Peak memory usage: 23 MB
% 46.03/6.93 % (1436178)Instructions burned: 1355 (million)
% 46.03/6.93 % (1436190)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 46.03/6.93 % (1436190)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=4011796423:i=999:add=on:rtra=on_2938 on theBenchmark for (2938ds/999Mi)
% 46.03/6.93 % (1436188)Instruction limit reached!
% 46.03/6.93 % (1436188)------------------------------
% 46.03/6.93 % (1436188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436188)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436188)Termination reason: Instruction limit
% 46.03/6.93 % (1436188)Termination phase: Saturation
% 46.03/6.93 % (1436188)Time elapsed: 0.228 s
% 46.03/6.93 % (1436188)Peak memory usage: 19 MB
% 46.03/6.93 % (1436188)Instructions burned: 875 (million)
% 46.03/6.93 % (1436191)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 46.03/6.93 % (1436191)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=3704420138:i=244:add=off:piset=or:nm=10:fsr=off:rtra=on:c=on_2938 on theBenchmark for (2938ds/244Mi)
% 46.03/6.93 % (1436193)ott+1003_1_anc=all:sil=128000:si=on:sos=on:random_seed=2705566403:cts=off:i=113:fsr=off:rtra=on:fe=abstraction_2938 on theBenchmark for (2938ds/113Mi)
% 46.03/6.93 % (1436193)Instruction limit reached!
% 46.03/6.93 % (1436193)------------------------------
% 46.03/6.93 % (1436193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436193)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436193)Termination reason: Instruction limit
% 46.03/6.93 % (1436193)Termination phase: Property scanning
% 46.03/6.93 % (1436193)Time elapsed: 0.027 s
% 46.03/6.93 % (1436193)Peak memory usage: 12 MB
% 46.03/6.93 % (1436193)Instructions burned: 113 (million)
% 46.03/6.93 % (1436196)lrs+10_1_sil=128000:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1831248471:i=7795:sd=2:nm=16:rtra=on:ss=axioms_2938 on theBenchmark for (2938ds/7795Mi)
% 46.03/6.93 % (1436191)Instruction limit reached!
% 46.03/6.93 % (1436191)------------------------------
% 46.03/6.93 % (1436191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436191)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436191)Termination reason: Instruction limit
% 46.03/6.93 % (1436191)Termination phase: Saturation
% 46.03/6.93 % (1436191)Time elapsed: 0.110 s
% 46.03/6.93 % (1436191)Peak memory usage: 16 MB
% 46.03/6.93 % (1436191)Instructions burned: 246 (million)
% 46.03/6.93 % (1436198)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2303601349:st=2:i=5026:sd=1:rtra=on:ss=axioms_2937 on theBenchmark for (2937ds/5026Mi)
% 46.03/6.93 % (1436182)Instruction limit reached!
% 46.03/6.93 % (1436182)------------------------------
% 46.03/6.93 % (1436182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436182)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436182)Termination reason: Instruction limit
% 46.03/6.93 % (1436182)Termination phase: Saturation
% 46.03/6.93 % (1436182)Time elapsed: 0.894 s
% 46.03/6.93 % (1436182)Peak memory usage: 23 MB
% 46.03/6.93 % (1436182)Instructions burned: 1925 (million)
% 46.03/6.93 % (1436200)WARNING Broken Constraint: if ho_split_queue_ratios(1,4) has been set then ho_split_queue(off) is equal to on
% 46.03/6.93 % (1436200)dis+1004_8_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_frequency:sos=on:uwa=off:random_seed=2637096258:hsqr=1,4:i=763:bd=preordered:nm=0:rtra=on:bet=on:ss=axioms_2934 on theBenchmark for (2934ds/763Mi)
% 46.03/6.93 % (1436108) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1435380-1436108"...
% 46.03/6.93 % (1436190)Instruction limit reached!
% 46.03/6.93 % (1436190)------------------------------
% 46.03/6.93 % (1436190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.93 % (1436190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.93 % (1436190)CaDiCaL version: 2.1.3
% 46.03/6.93 % (1436190)Termination reason: Instruction limit
% 46.03/6.93 % (1436190)Termination phase: Saturation
% 46.03/6.93 % (1436190)Time elapsed: 0.481 s
% 46.03/6.93 % (1436190)Peak memory usage: 15 MB
% 46.03/6.93 % (1436190)Instructions burned: 1001 (million)
% 46.03/6.93 % (1436202)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1322008925:hsq=on:st=2:i=1144:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2933 on theBenchmark for (2933ds/1144Mi)
% 46.03/6.93 % (1436108)...printing done.
% 46.03/6.93 % (1436108)Refutation found. Thanks to Tanya!
% 46.03/6.93 % SZS status Theorem for theBenchmark
% 46.03/6.93 % SZS output start Proof for theBenchmark
% 46.03/6.93 thf(type_def_5, type, term: $tType).
% 46.03/6.93 thf(type_def_6, type, subst: $tType).
% 46.03/6.93 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 46.03/6.93 thf(type_def_8, type, d_term: $tType).
% 46.03/6.93 thf(type_def_9, type, d_subst: $tType).
% 46.03/6.93 thf(func_def_0, type, one: term).
% 46.03/6.93 thf(func_def_1, type, ap: (term > term > term)).
% 46.03/6.93 thf(func_def_2, type, lam: (term > term)).
% 46.03/6.93 thf(func_def_3, type, sub: (term > subst > term)).
% 46.03/6.93 thf(func_def_4, type, id: subst).
% 46.03/6.93 thf(func_def_5, type, sh: subst).
% 46.03/6.93 thf(func_def_6, type, push: (term > subst > subst)).
% 46.03/6.93 thf(func_def_7, type, comp: (subst > subst > subst)).
% 46.03/6.93 thf(func_def_8, type, var: (term > $o)).
% 46.03/6.93 thf(func_def_9, type, pushprop_lem1v2: $o).
% 46.03/6.93 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 46.03/6.93 thf(func_def_11, type, axmap: $o).
% 46.03/6.93 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 46.03/6.93 thf(func_def_13, type, shinj: $o).
% 46.03/6.93 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 46.03/6.93 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 46.03/6.93 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 46.03/6.93 thf(func_def_17, type, induction2lem: $o).
% 46.03/6.93 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 46.03/6.93 thf(func_def_19, type, axvarshift: $o).
% 46.03/6.93 thf(func_def_20, type, hoasapinj2: $o).
% 46.03/6.93 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 46.03/6.93 thf(func_def_22, type, hoasapinj1: $o).
% 46.03/6.93 thf(func_def_23, type, ulamvar1: $o).
% 46.03/6.93 thf(func_def_24, type, induction2lem_lthm: $o).
% 46.03/6.93 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 46.03/6.93 thf(func_def_26, type, apnotvar: $o).
% 46.03/6.93 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 46.03/6.93 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 46.03/6.93 thf(func_def_29, type, hoasinduction_lthm: $o).
% 46.03/6.93 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 46.03/6.93 thf(func_def_31, type, hoaslaminj: $o).
% 46.03/6.93 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 46.03/6.93 thf(func_def_33, type, induction2lem_gthm: $o).
% 46.03/6.93 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 46.03/6.93 thf(func_def_35, type, hoasinduction_lem3: $o).
% 46.03/6.93 thf(func_def_36, type, hoasinduction_lem2: $o).
% 46.03/6.93 thf(func_def_37, type, termmset_lthm: $o).
% 46.03/6.93 thf(func_def_38, type, hoasinduction_lem1: $o).
% 46.03/6.93 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 46.03/6.93 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 46.03/6.93 thf(func_def_41, type, hoasapnotvar: $o).
% 46.03/6.93 thf(func_def_42, type, hoasinduction_lem0: $o).
% 46.03/6.93 thf(func_def_43, type, hoasinduction: $o).
% 46.03/6.93 thf(func_def_44, type, hoasinduction_gthm: $o).
% 46.03/6.93 thf(func_def_45, type, axapp: $o).
% 46.03/6.93 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 46.03/6.93 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 46.03/6.93 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 46.03/6.93 thf(func_def_49, type, ulamvarind: $o).
% 46.03/6.93 thf(func_def_50, type, induction: $o).
% 46.03/6.93 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 46.03/6.93 thf(func_def_52, type, termmset_gthm: $o).
% 46.03/6.93 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 46.03/6.93 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 46.03/6.93 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 46.03/6.93 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 46.03/6.93 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 46.03/6.93 thf(func_def_58, type, pushprop_lem2v2: $o).
% 46.03/6.93 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 46.03/6.93 thf(func_def_60, type, axclos: $o).
% 46.03/6.93 thf(func_def_61, type, axassoc: $o).
% 46.03/6.93 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 46.03/6.93 thf(func_def_63, type, pushprop_lthm: $o).
% 46.03/6.93 thf(func_def_64, type, apinj2: $o).
% 46.03/6.93 thf(func_def_65, type, apinj1: $o).
% 46.03/6.93 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 46.03/6.93 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 46.03/6.93 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 46.03/6.93 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 46.03/6.93 thf(func_def_70, type, axvarcons: $o).
% 46.03/6.93 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 46.03/6.93 thf(func_def_72, type, axscons: $o).
% 46.03/6.93 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 46.03/6.93 thf(func_def_74, type, axidr: $o).
% 46.03/6.93 thf(func_def_75, type, pushprop_lem1: $o).
% 46.03/6.93 thf(func_def_76, type, laminj: $o).
% 46.03/6.93 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 46.03/6.93 thf(func_def_78, type, pushprop_lem0: $o).
% 46.03/6.93 thf(func_def_79, type, pushprop_gthm: $o).
% 46.03/6.93 thf(func_def_80, type, axabs: $o).
% 46.03/6.93 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 46.03/6.93 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 46.03/6.93 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 46.03/6.93 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 46.03/6.93 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 46.03/6.93 thf(func_def_86, type, lamnotap: $o).
% 46.03/6.93 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 46.03/6.93 thf(func_def_88, type, hoaslamnotvar: $o).
% 46.03/6.93 thf(func_def_89, type, axidl: $o).
% 46.03/6.93 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 46.03/6.93 thf(func_def_91, type, induction2_lthm: $o).
% 46.03/6.93 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 46.03/6.93 thf(func_def_93, type, substmonoid_lthm: $o).
% 46.03/6.93 thf(func_def_94, type, pushprop: $o).
% 46.03/6.93 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 46.03/6.93 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 46.03/6.93 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 46.03/6.93 thf(func_def_98, type, substmonoid: $o).
% 46.03/6.93 thf(func_def_99, type, lamnotvar: $o).
% 46.03/6.93 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 46.03/6.93 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 46.03/6.93 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 46.03/6.93 thf(func_def_103, type, induction2_gthm: $o).
% 46.03/6.93 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 46.03/6.93 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_106, type, hoaslamnotap: $o).
% 46.03/6.93 thf(func_def_107, type, substmonoid_gthm: $o).
% 46.03/6.93 thf(func_def_108, type, ulamvarsh: $o).
% 46.03/6.93 thf(func_def_109, type, induction2: $o).
% 46.03/6.93 thf(func_def_110, type, pushprop_lem3v2: $o).
% 46.03/6.93 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 46.03/6.93 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 46.03/6.93 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 46.03/6.93 thf(func_def_114, type, axshiftcons: $o).
% 46.03/6.93 thf(func_def_115, type, termmset: $o).
% 46.03/6.93 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 46.03/6.93 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 46.03/6.93 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 46.03/6.93 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 46.03/6.93 thf(func_def_120, type, axvarid: $o).
% 46.03/6.93 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 46.03/6.93 thf(func_def_122, type, d2term: (d_term > term)).
% 46.03/6.93 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 46.03/6.93 thf(func_def_124, type, d_one: d_term).
% 46.03/6.93 thf(func_def_125, type, d_id: d_subst).
% 46.03/6.93 thf(func_def_129, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 46.03/6.93 thf(func_def_130, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 46.03/6.93 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 46.03/6.93 thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
% 46.03/6.93 thf(func_def_133, type, db1: !>[X0: $tType]:(X0)).
% 46.03/6.93 thf(func_def_134, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 46.03/6.93 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 46.03/6.93 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 46.03/6.93 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_138, type, sP1: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_139, type, sP2: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_140, type, sP3: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_141, type, sP4: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_142, type, sP5: $o).
% 46.03/6.93 thf(func_def_143, type, sP6: $o).
% 46.03/6.93 thf(func_def_144, type, sP7: $o).
% 46.03/6.93 thf(func_def_145, type, sP8: $o).
% 46.03/6.93 thf(func_def_146, type, sP9: $o).
% 46.03/6.93 thf(func_def_147, type, sP10: $o).
% 46.03/6.93 thf(func_def_148, type, sP11: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_149, type, sP12: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_150, type, sP13: $o).
% 46.03/6.93 thf(func_def_151, type, sP14: $o).
% 46.03/6.93 thf(func_def_152, type, sP15: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_153, type, sP16: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_154, type, sP17: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_155, type, sP18: $o).
% 46.03/6.93 thf(func_def_156, type, sP19: $o).
% 46.03/6.93 thf(func_def_157, type, sP20: $o).
% 46.03/6.93 thf(func_def_158, type, sP21: $o).
% 46.03/6.93 thf(func_def_159, type, sP22: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_160, type, sP23: $o).
% 46.03/6.93 thf(func_def_161, type, sP24: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_162, type, sP25: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_163, type, sP26: $o).
% 46.03/6.93 thf(func_def_164, type, sP27: $o).
% 46.03/6.93 thf(func_def_165, type, sP28: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_166, type, sP29: $o).
% 46.03/6.93 thf(func_def_167, type, sP30: $o).
% 46.03/6.93 thf(func_def_168, type, sP31: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_169, type, sP32: $o).
% 46.03/6.93 thf(func_def_170, type, sP33: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_171, type, sP34: $o).
% 46.03/6.93 thf(func_def_172, type, sP35: $o).
% 46.03/6.93 thf(func_def_173, type, sP36: $o).
% 46.03/6.93 thf(func_def_174, type, sP37: $o).
% 46.03/6.93 thf(func_def_175, type, sP38: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_176, type, sP39: $o).
% 46.03/6.93 thf(func_def_177, type, sP40: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_178, type, sP41: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_179, type, sP42: $o).
% 46.03/6.93 thf(func_def_180, type, sP43: $o).
% 46.03/6.93 thf(func_def_181, type, sP44: $o).
% 46.03/6.93 thf(func_def_182, type, sP45: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_183, type, sP46: $o).
% 46.03/6.93 thf(func_def_184, type, sP47: $o).
% 46.03/6.93 thf(func_def_185, type, sP48: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_186, type, sP49: $o).
% 46.03/6.93 thf(func_def_187, type, sP50: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_188, type, sP51: ((term > $o) > $o)).
% 46.03/6.93 thf(func_def_189, type, sP52: $o).
% 46.03/6.93 thf(func_def_190, type, sP53: $o).
% 46.03/6.93 thf(func_def_191, type, sP54: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_192, type, sP55: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_193, type, sP56: $o).
% 46.03/6.93 thf(func_def_194, type, sP57: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_195, type, sP58: $o).
% 46.03/6.93 thf(func_def_196, type, sP59: ((subst > term > subst > $o) > $o)).
% 46.03/6.93 thf(func_def_197, type, sP60: $o).
% 46.03/6.93 thf(func_def_198, type, sK61: (term > $o)).
% 46.03/6.93 thf(func_def_199, type, sK62: term).
% 46.03/6.93 thf(func_def_200, type, sK63: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_201, type, sK64: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_202, type, sK65: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_203, type, sK66: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_204, type, sK67: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_205, type, sK68: (term > subst > term > term)).
% 46.03/6.93 thf(func_def_206, type, sK69: term).
% 46.03/6.93 thf(func_def_207, type, sK70: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_209, type, sK72: (term > (term > $o) > term)).
% 46.03/6.93 thf(func_def_210, type, sK73: term).
% 46.03/6.93 thf(func_def_211, type, sK74: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_212, type, sK75: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_213, type, sK76: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_214, type, sK77: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_215, type, sK78: term).
% 46.03/6.93 thf(func_def_216, type, sK79: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_217, type, sK80: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_218, type, sK81: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_219, type, sK82: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_220, type, sK83: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_221, type, sK84: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_222, type, sK85: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_223, type, sK86: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_224, type, sK87: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_225, type, sK88: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_226, type, sK89: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_227, type, sK90: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_228, type, sK91: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_229, type, sK92: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_230, type, sK93: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_231, type, sK94: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_232, type, sK95: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_233, type, sK96: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_234, type, sK97: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_235, type, sK98: subst).
% 46.03/6.93 thf(func_def_236, type, sK99: term).
% 46.03/6.93 thf(func_def_237, type, sK100: subst).
% 46.03/6.93 thf(func_def_238, type, sK101: term).
% 46.03/6.93 thf(func_def_239, type, sK102: term).
% 46.03/6.93 thf(func_def_240, type, sK103: (term > $o)).
% 46.03/6.93 thf(func_def_241, type, sK104: subst).
% 46.03/6.93 thf(func_def_242, type, sK105: (term > $o)).
% 46.03/6.93 thf(func_def_243, type, sK106: subst).
% 46.03/6.93 thf(func_def_244, type, sK107: term).
% 46.03/6.93 thf(func_def_245, type, sK108: (term > term)).
% 46.03/6.93 thf(func_def_246, type, sK109: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_247, type, sK110: (subst > (term > $o) > term)).
% 46.03/6.93 thf(func_def_248, type, sK111: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_249, type, sK112: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_250, type, sK113: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_251, type, sK114: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_252, type, sK115: subst).
% 46.03/6.93 thf(func_def_253, type, sK116: term).
% 46.03/6.93 thf(func_def_254, type, sK117: (term > $o)).
% 46.03/6.93 thf(func_def_255, type, sK118: (term > term)).
% 46.03/6.93 thf(func_def_256, type, sK119: ((term > $o) > subst > term)).
% 46.03/6.93 thf(func_def_257, type, sK120: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_258, type, sK121: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_259, type, sK122: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_260, type, sK123: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_261, type, sK124: term).
% 46.03/6.93 thf(func_def_262, type, sK125: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_263, type, sK126: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_264, type, sK127: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_265, type, sK128: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_266, type, sK129: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_267, type, sK130: (term > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_268, type, sK131: (term > $o)).
% 46.03/6.93 thf(func_def_269, type, sK132: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_270, type, sK133: term).
% 46.03/6.93 thf(func_def_271, type, sK134: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_272, type, sK135: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_273, type, sK136: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_274, type, sK137: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_275, type, sK138: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_276, type, sK139: (term > (term > $o) > term)).
% 46.03/6.93 thf(func_def_277, type, sK140: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_278, type, sK141: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_279, type, sK142: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_280, type, sK143: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_281, type, sK144: term).
% 46.03/6.93 thf(func_def_282, type, sK145: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_283, type, sK146: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_284, type, sK147: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_285, type, sK148: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_286, type, sK149: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_287, type, sK150: ((subst > term > subst > $o) > term > $o)).
% 46.03/6.93 thf(func_def_288, type, sK151: term).
% 46.03/6.93 thf(func_def_289, type, sK152: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_290, type, sK153: term).
% 46.03/6.93 thf(func_def_291, type, sK154: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_292, type, sK155: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_293, type, sK156: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_294, type, sK157: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_295, type, sK158: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_296, type, sK159: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_297, type, sK160: term).
% 46.03/6.93 thf(func_def_298, type, sK161: (term > $o)).
% 46.03/6.93 thf(func_def_299, type, sK162: (term > term)).
% 46.03/6.93 thf(func_def_300, type, sK163: (term > (term > $o) > term)).
% 46.03/6.93 thf(func_def_301, type, sK164: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_302, type, sK165: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_303, type, sK166: (term > $o)).
% 46.03/6.93 thf(func_def_304, type, sK167: term).
% 46.03/6.93 thf(func_def_305, type, sK168: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_306, type, sK169: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_307, type, sK170: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_308, type, sK171: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_309, type, sK172: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_310, type, sK173: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_311, type, sK174: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_312, type, sK175: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_313, type, sK176: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_314, type, sK177: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_315, type, sK178: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_317, type, sK180: term).
% 46.03/6.93 thf(func_def_318, type, sK181: (term > $o)).
% 46.03/6.93 thf(func_def_319, type, sK182: (term > term)).
% 46.03/6.93 thf(func_def_320, type, sK183: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_321, type, sK184: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_322, type, sK185: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_323, type, sK186: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_324, type, sK187: term).
% 46.03/6.93 thf(func_def_325, type, sK188: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_326, type, sK189: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_327, type, sK190: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_328, type, sK191: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_329, type, sK192: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_330, type, sK193: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_331, type, sK194: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_332, type, sK195: term).
% 46.03/6.93 thf(func_def_333, type, sK196: (term > $o)).
% 46.03/6.93 thf(func_def_334, type, sK197: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_335, type, sK198: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_336, type, sK199: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_337, type, sK200: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_338, type, sK201: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_339, type, sK202: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_340, type, sK203: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_341, type, sK204: ((term > $o) > term > term)).
% 46.03/6.93 thf(func_def_342, type, sK205: term).
% 46.03/6.93 thf(func_def_343, type, sK206: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_344, type, sK207: term).
% 46.03/6.93 thf(func_def_345, type, sK208: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_346, type, sK209: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_347, type, sK210: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_348, type, sK211: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_349, type, sK212: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_350, type, sK213: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_351, type, sK214: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_352, type, sK215: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_354, type, sK217: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_355, type, sK218: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_356, type, sK219: term).
% 46.03/6.93 thf(func_def_357, type, sK220: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_358, type, sK221: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_359, type, sK222: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_360, type, sK223: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_361, type, sK224: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_362, type, sK225: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_363, type, sK226: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_364, type, sK227: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_365, type, sK228: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_366, type, sK229: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_367, type, sK230: term).
% 46.03/6.93 thf(func_def_368, type, sK231: (term > $o)).
% 46.03/6.93 thf(func_def_369, type, sK232: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_370, type, sK233: term).
% 46.03/6.93 thf(func_def_371, type, sK234: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_372, type, sK235: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_373, type, sK236: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_374, type, sK237: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_375, type, sK238: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_376, type, sK239: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_379, type, sK242: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_380, type, sK243: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_381, type, sK244: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_382, type, sK245: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_383, type, sK246: term).
% 46.03/6.93 thf(func_def_384, type, sK247: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_385, type, sK248: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_386, type, sK249: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_387, type, sK250: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_388, type, sK251: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_389, type, sK252: (term > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_390, type, sK253: term).
% 46.03/6.93 thf(func_def_391, type, sK254: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_392, type, sK255: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_393, type, sK256: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_394, type, sK257: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_395, type, sK258: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_396, type, sK259: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_397, type, sK260: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_398, type, sK261: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_399, type, sK262: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_400, type, sK263: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_401, type, sK264: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_402, type, sK265: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_403, type, sK266: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_404, type, sK267: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_405, type, sK268: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_406, type, sK269: (subst > (term > $o) > term)).
% 46.03/6.93 thf(func_def_407, type, sK270: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_408, type, sK271: term).
% 46.03/6.93 thf(func_def_409, type, sK272: (term > $o)).
% 46.03/6.93 thf(func_def_410, type, sK273: subst).
% 46.03/6.93 thf(func_def_411, type, sK274: (term > term)).
% 46.03/6.93 thf(func_def_412, type, sK275: term).
% 46.03/6.93 thf(func_def_413, type, sK276: term).
% 46.03/6.93 thf(func_def_414, type, sK277: (term > $o)).
% 46.03/6.93 thf(func_def_415, type, sK278: (term > term)).
% 46.03/6.93 thf(func_def_416, type, sK279: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_417, type, sK280: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_418, type, sK281: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_419, type, sK282: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_420, type, sK283: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_421, type, sK284: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_422, type, sK285: term).
% 46.03/6.93 thf(func_def_423, type, sK286: term).
% 46.03/6.93 thf(func_def_424, type, sK287: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_425, type, sK288: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_426, type, sK289: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_427, type, sK290: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_428, type, sK291: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_429, type, sK292: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_430, type, sK293: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_431, type, sK294: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_432, type, sK295: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_433, type, sK296: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_434, type, sK297: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_435, type, sK298: (subst > term > term)).
% 46.03/6.93 thf(func_def_436, type, sK299: subst).
% 46.03/6.93 thf(func_def_437, type, sK300: term).
% 46.03/6.93 thf(func_def_438, type, sK301: (subst > term > term)).
% 46.03/6.93 thf(func_def_439, type, sK302: subst).
% 46.03/6.93 thf(func_def_440, type, sK303: term).
% 46.03/6.93 thf(func_def_441, type, sK304: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_442, type, sK305: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_443, type, sK306: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_444, type, sK307: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_445, type, sK308: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_446, type, sK309: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_447, type, sK310: term).
% 46.03/6.93 thf(func_def_448, type, sK311: term).
% 46.03/6.93 thf(func_def_449, type, sK312: term).
% 46.03/6.93 thf(func_def_450, type, sK313: subst).
% 46.03/6.93 thf(func_def_451, type, sK314: ((subst > term > subst > $o) > term > $o)).
% 46.03/6.93 thf(func_def_452, type, sK315: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_453, type, sK316: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_454, type, sK317: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_455, type, sK318: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_456, type, sK319: (term > $o)).
% 46.03/6.93 thf(func_def_457, type, sK320: term).
% 46.03/6.93 thf(func_def_458, type, sK321: (term > term)).
% 46.03/6.93 thf(func_def_459, type, sK322: term).
% 46.03/6.93 thf(func_def_460, type, sK323: term).
% 46.03/6.93 thf(func_def_461, type, sK324: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_462, type, sK325: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_463, type, sK326: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_464, type, sK327: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_465, type, sK328: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_466, type, sK329: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_467, type, sK330: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_468, type, sK331: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_469, type, sK332: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_470, type, sK333: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_471, type, sK334: ((subst > term > subst > $o) > (term > $o) > term)).
% 46.03/6.93 thf(func_def_472, type, sK335: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_473, type, sK336: ((term > $o) > term > term)).
% 46.03/6.93 thf(func_def_474, type, sK337: term).
% 46.03/6.93 thf(func_def_475, type, sK338: (term > $o)).
% 46.03/6.93 thf(func_def_476, type, sK339: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_477, type, sK340: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_478, type, sK341: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_479, type, sK342: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_480, type, sK343: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_481, type, sK344: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_482, type, sK345: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_483, type, sK346: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_484, type, sK347: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_485, type, sK348: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_486, type, sK349: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_487, type, sK350: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_488, type, sK351: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_489, type, sK352: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_490, type, sK353: term).
% 46.03/6.93 thf(func_def_491, type, sK354: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_492, type, sK355: ((subst > term > term) > term > subst)).
% 46.03/6.93 thf(func_def_493, type, sK356: ((subst > term > term) > term > term)).
% 46.03/6.93 thf(func_def_494, type, sK357: ((subst > term > term) > term > subst)).
% 46.03/6.93 thf(func_def_495, type, sK358: ((subst > term > term) > term > subst)).
% 46.03/6.93 thf(func_def_496, type, sK359: ((subst > term > term) > term > subst)).
% 46.03/6.93 thf(func_def_497, type, sK360: ((subst > term > term) > term > term)).
% 46.03/6.93 thf(func_def_498, type, sK361: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_499, type, sK362: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_500, type, sK363: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_501, type, sK364: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_502, type, sK365: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_503, type, sK366: term).
% 46.03/6.93 thf(func_def_504, type, sK367: (term > $o)).
% 46.03/6.93 thf(func_def_505, type, sK368: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_506, type, sK369: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_507, type, sK370: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_508, type, sK371: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_509, type, sK372: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_510, type, sK373: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_511, type, sK374: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_512, type, sK375: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_513, type, sK376: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_514, type, sK377: ((term > $o) > term > term)).
% 46.03/6.93 thf(func_def_515, type, sK378: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_516, type, sK379: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_517, type, sK380: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_518, type, sK381: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_519, type, sK382: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_520, type, sK383: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_521, type, sK384: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_522, type, sK385: term).
% 46.03/6.93 thf(func_def_523, type, sK386: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_524, type, sK387: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_525, type, sK388: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_526, type, sK389: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_527, type, sK390: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_528, type, sK391: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_529, type, sK392: ((subst > term > subst > $o) > term > term)).
% 46.03/6.93 thf(func_def_530, type, sK393: term).
% 46.03/6.93 thf(func_def_531, type, sK394: (term > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_532, type, sK395: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_533, type, sK396: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_534, type, sK397: term).
% 46.03/6.93 thf(func_def_535, type, sK398: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_536, type, sK399: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_537, type, sK400: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_538, type, sK401: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_539, type, sK402: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_540, type, sK403: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_541, type, sK404: term).
% 46.03/6.93 thf(func_def_542, type, sK405: (term > $o)).
% 46.03/6.93 thf(func_def_543, type, sK406: (term > term)).
% 46.03/6.93 thf(func_def_544, type, sK407: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_545, type, sK408: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_546, type, sK409: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_547, type, sK410: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_548, type, sK411: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_549, type, sK412: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_550, type, sK413: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_551, type, sK414: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_552, type, sK415: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_553, type, sK416: term).
% 46.03/6.93 thf(func_def_554, type, sK417: term).
% 46.03/6.93 thf(func_def_555, type, sK418: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_556, type, sK419: term).
% 46.03/6.93 thf(func_def_557, type, sK420: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_558, type, sK421: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_559, type, sK422: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_560, type, sK423: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_562, type, sK425: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_563, type, sK426: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_564, type, sK427: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_565, type, sK428: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_567, type, sK430: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_568, type, sK431: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_569, type, sK432: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_571, type, sK434: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_572, type, sK435: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_573, type, sK436: ((subst > term > subst > $o) > subst)).
% 46.03/6.93 thf(func_def_574, type, sK437: (term > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_575, type, sK438: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_576, type, sK439: term).
% 46.03/6.93 thf(func_def_577, type, sK440: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_578, type, sK441: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_579, type, sK442: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_580, type, sK443: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_581, type, sK444: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_582, type, sK445: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_583, type, sK446: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_584, type, sK447: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_585, type, sK448: ((term > $o) > term)).
% 46.03/6.93 thf(func_def_586, type, sK449: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_587, type, sK450: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_588, type, sK451: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_589, type, sK452: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_590, type, sK453: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_591, type, sK454: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_592, type, sK455: ((subst > term > subst > $o) > term)).
% 46.03/6.93 thf(func_def_593, type, sK456: term).
% 46.03/6.93 thf(func_def_594, type, sK457: (subst > term > subst > $o)).
% 46.03/6.93 thf(func_def_595, type, sK458: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_596, type, sK459: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_597, type, sK460: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_598, type, sK461: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_599, type, sK462: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.93 thf(func_def_600, type, sK463: term).
% 46.03/6.93 thf(func_def_601, type, sK464: (term > $o)).
% 46.03/6.93 thf(func_def_602, type, sK465: subst).
% 46.03/6.93 thf(func_def_603, type, sK466: (term > $o)).
% 46.03/6.93 thf(func_def_604, type, sK467: term).
% 46.03/6.93 thf(func_def_605, type, sK468: (term > subst > term > term)).
% 46.03/6.93 thf(func_def_606, type, sK469: term).
% 46.03/6.93 thf(func_def_607, type, sK470: ((subst > term > term) > term)).
% 46.03/6.93 thf(func_def_608, type, sK471: ((subst > term > term) > subst)).
% 46.03/6.93 thf(func_def_609, type, sK472: term).
% 46.03/6.93 thf(func_def_610, type, sK473: (term > $o)).
% 46.03/6.93 thf(func_def_611, type, sK474: subst).
% 46.03/6.93 thf(func_def_612, type, sK475: (term > $o)).
% 46.03/6.93 thf(func_def_613, type, sK476: ((term > $o) > subst > (term > $o) > term > term)).
% 46.03/6.93 thf(func_def_614, type, sK477: (term > $o)).
% 46.03/6.93 thf(func_def_615, type, sK478: term).
% 46.03/6.93 thf(func_def_616, type, sK479: subst).
% 46.03/6.93 thf(func_def_617, type, sK480: (term > $o)).
% 46.03/6.93 thf(func_def_618, type, sK481: subst).
% 46.03/6.93 thf(func_def_619, type, sK482: term).
% 46.03/6.93 thf(func_def_620, type, sK483: ((term > $o) > subst > term > (term > $o) > term)).
% 46.03/6.93 thf(func_def_621, type, sK484: term).
% 46.03/6.93 thf(func_def_622, type, sK485: term).
% 46.03/6.93 thf(func_def_623, type, sK486: (term > $o)).
% 46.03/6.93 thf(func_def_624, type, sK487: term).
% 46.03/6.93 thf(func_def_625, type, sK488: subst).
% 46.03/6.94 thf(func_def_626, type, sK489: term).
% 46.03/6.94 thf(func_def_627, type, sK490: (term > $o)).
% 46.03/6.94 thf(func_def_628, type, sK491: subst).
% 46.03/6.94 thf(func_def_629, type, sK492: term).
% 46.03/6.94 thf(func_def_630, type, sK493: term).
% 46.03/6.94 thf(func_def_631, type, sK494: subst).
% 46.03/6.94 thf(func_def_632, type, sK495: term).
% 46.03/6.94 thf(func_def_633, type, sK496: (subst > term > term)).
% 46.03/6.94 thf(func_def_634, type, sK497: term).
% 46.03/6.94 thf(func_def_635, type, sK498: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_636, type, sK499: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_637, type, sK500: ((subst > term > term) > term)).
% 46.03/6.94 thf(func_def_638, type, sK501: term).
% 46.03/6.94 thf(func_def_639, type, sK502: term).
% 46.03/6.94 thf(func_def_640, type, sK503: subst).
% 46.03/6.94 thf(func_def_641, type, sK504: term).
% 46.03/6.94 thf(func_def_642, type, sK505: (term > subst > term > term)).
% 46.03/6.94 thf(func_def_643, type, sK506: term).
% 46.03/6.94 thf(func_def_644, type, sK507: subst).
% 46.03/6.94 thf(func_def_645, type, sK508: (term > subst > term > term)).
% 46.03/6.94 thf(func_def_646, type, sK509: term).
% 46.03/6.94 thf(func_def_647, type, sK510: ((subst > term > term) > term)).
% 46.03/6.94 thf(func_def_648, type, sK511: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_649, type, sK512: subst).
% 46.03/6.94 thf(func_def_650, type, sK513: term).
% 46.03/6.94 thf(func_def_651, type, sK514: term).
% 46.03/6.94 thf(func_def_652, type, sK515: term).
% 46.03/6.94 thf(func_def_653, type, sK516: term).
% 46.03/6.94 thf(func_def_654, type, sK517: term).
% 46.03/6.94 thf(func_def_655, type, sK518: (subst > term > subst > $o)).
% 46.03/6.94 thf(func_def_656, type, sK519: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_657, type, sK520: ((subst > term > subst > $o) > term > $o)).
% 46.03/6.94 thf(func_def_658, type, sK521: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_659, type, sK522: ((subst > term > term) > term)).
% 46.03/6.94 thf(func_def_660, type, sK523: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_661, type, sK524: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_662, type, sK525: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_663, type, sK526: ((subst > term > term) > term)).
% 46.03/6.94 thf(func_def_664, type, sK527: term).
% 46.03/6.94 thf(func_def_665, type, sK528: (subst > term > term)).
% 46.03/6.94 thf(func_def_666, type, sK529: (subst > term > term)).
% 46.03/6.94 thf(func_def_667, type, sK530: subst).
% 46.03/6.94 thf(func_def_668, type, sK531: (term > subst > term > term)).
% 46.03/6.94 thf(func_def_669, type, sK532: term).
% 46.03/6.94 thf(func_def_670, type, sK533: term).
% 46.03/6.94 thf(func_def_671, type, sK534: term).
% 46.03/6.94 thf(func_def_672, type, sK535: term).
% 46.03/6.94 thf(func_def_673, type, sK536: term).
% 46.03/6.94 thf(func_def_674, type, sK537: term).
% 46.03/6.94 thf(func_def_675, type, sK538: (term > (term > $o) > subst > term > $o)).
% 46.03/6.94 thf(func_def_676, type, sK539: subst).
% 46.03/6.94 thf(func_def_677, type, sK540: (term > $o)).
% 46.03/6.94 thf(func_def_678, type, sK541: term).
% 46.03/6.94 thf(func_def_679, type, sK542: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_680, type, sK543: (subst > term > subst > $o)).
% 46.03/6.94 thf(func_def_681, type, sK544: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_682, type, sK545: ((subst > term > subst > $o) > term > $o)).
% 46.03/6.94 thf(func_def_683, type, sK546: subst).
% 46.03/6.94 thf(func_def_684, type, sK547: term).
% 46.03/6.94 thf(func_def_685, type, sK548: ((term > $o) > term > subst > term > $o)).
% 46.03/6.94 thf(func_def_686, type, sK549: subst).
% 46.03/6.94 thf(func_def_687, type, sK550: term).
% 46.03/6.94 thf(func_def_688, type, sK551: (term > $o)).
% 46.03/6.94 thf(func_def_689, type, sK552: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_690, type, sK553: (subst > d_subst)).
% 46.03/6.94 thf(func_def_691, type, sK554: term).
% 46.03/6.94 thf(func_def_692, type, sK555: term).
% 46.03/6.94 thf(func_def_693, type, sK556: term).
% 46.03/6.94 thf(func_def_694, type, sK557: term).
% 46.03/6.94 thf(func_def_695, type, sK558: term).
% 46.03/6.94 thf(func_def_696, type, sK559: term).
% 46.03/6.94 thf(func_def_697, type, sK560: term).
% 46.03/6.94 thf(func_def_698, type, sK561: term).
% 46.03/6.94 thf(func_def_699, type, sK562: subst).
% 46.03/6.94 thf(func_def_700, type, sK563: subst).
% 46.03/6.94 thf(func_def_701, type, sK564: (term > $o)).
% 46.03/6.94 thf(func_def_702, type, sK565: term).
% 46.03/6.94 thf(func_def_703, type, sK566: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_704, type, sK567: ((term > $o) > term)).
% 46.03/6.94 thf(func_def_705, type, sK568: subst).
% 46.03/6.94 thf(func_def_706, type, sK569: subst).
% 46.03/6.94 thf(func_def_707, type, sK570: subst).
% 46.03/6.94 thf(func_def_708, type, sK571: subst).
% 46.03/6.94 thf(func_def_709, type, sK572: (term > d_term)).
% 46.03/6.94 thf(func_def_710, type, sK573: subst).
% 46.03/6.94 thf(func_def_711, type, sK574: term).
% 46.03/6.94 thf(func_def_712, type, sK575: term).
% 46.03/6.94 thf(func_def_713, type, sK576: term).
% 46.03/6.94 thf(func_def_714, type, sK577: term).
% 46.03/6.94 thf(func_def_715, type, sK578: term).
% 46.03/6.94 thf(func_def_716, type, sK579: term).
% 46.03/6.94 thf(func_def_717, type, sK580: term).
% 46.03/6.94 thf(func_def_718, type, sK581: term).
% 46.03/6.94 thf(func_def_719, type, sK582: term).
% 46.03/6.94 thf(func_def_720, type, sK583: term).
% 46.03/6.94 thf(func_def_721, type, sK584: term).
% 46.03/6.94 thf(func_def_722, type, sK585: term).
% 46.03/6.94 thf(func_def_723, type, sK586: term).
% 46.03/6.94 thf(func_def_724, type, sK587: term).
% 46.03/6.94 thf(func_def_725, type, sK588: term).
% 46.03/6.94 thf(func_def_726, type, sK589: term).
% 46.03/6.94 thf(func_def_727, type, sK590: term).
% 46.03/6.94 thf(func_def_728, type, sK591: term).
% 46.03/6.94 thf(func_def_729, type, sK592: term).
% 46.03/6.94 thf(func_def_730, type, sK593: (term > $o)).
% 46.03/6.94 thf(func_def_731, type, sK594: (subst > term > subst > $o)).
% 46.03/6.94 thf(func_def_732, type, sK595: term).
% 46.03/6.94 thf(func_def_733, type, sK596: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_734, type, sK597: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_735, type, sK598: ((subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_736, type, sK599: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_737, type, sK600: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_738, type, sK601: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_739, type, sK602: ((subst > term > subst > $o) > subst)).
% 46.03/6.94 thf(func_def_740, type, sK603: ((subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_741, type, sK604: (term > (term > $o) > term)).
% 46.03/6.94 thf(func_def_742, type, sK605: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_743, type, sK606: ((subst > term > term) > term)).
% 46.03/6.94 thf(func_def_744, type, sK607: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_745, type, sK608: ((subst > term > term) > subst)).
% 46.03/6.94 thf(func_def_746, type, sK609: ((subst > term > subst > $o) > subst > term > term)).
% 46.03/6.94 thf(func_def_747, type, vNOT: ($o > $o)).
% 46.03/6.94 thf(func_def_748, type, sK610: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_749, type, sK611: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_750, type, sK612: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_751, type, sK613: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_752, type, sK614: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_753, type, sK615: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_754, type, sK616: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(func_def_755, type, sK617: ((term > $o) > (subst > term > subst > $o) > term)).
% 46.03/6.94 thf(f1,axiom,(
% 46.03/6.94 ~ulamvar1 & (one = ((d2term @ d_one))) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id))) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : ((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)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3aa) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & pushprop_lem2v2_lthm & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id))) & hoaslamnotap_lthm & (! [X46 : term,X18 : (subst > term > term),X47 : term] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & substmonoid_gthm & ~lamnotap & (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] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [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) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X30 @ id))))))) & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X26 : (term > $o),X14 : subst,X13 : term,X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & (id = ((d2subst @ d_id))) & pushprop_lthm_orig & hoaslamnotvar & pushprop_lem3v2 & pushprop_lthm & axclos & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))))) <=> induction2_lthm) & hoasapnotvar & (hoasinduction_lem3v2a <=> ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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)))) & (! [X10 : (term > $o),X21 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) <=> induction) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [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)))) => ! [X31 : (subst > term > term),X18 : (subst > term > term),X33 : term,X32 : subst] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) <=> induction2) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (sh = ((d2subst @ d_id))) & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & ! [X5 : d_subst] : (X5 = d_id) & hoasapnotvar_gthm & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X48)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [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))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))))) <=> hoasinduction_lem3v2_lthm) & axapp & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((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)] : ((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)))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : 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))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id))))) <=> hoasinduction_lem3_lthm) & hoaslamnotvar_lthm & pushprop_lem1v2_gthm & axmap & hoaslamnotap_gthm & (apinj2 <=> ! [X19 : term,X15 : term,X13 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X14 : subst,X11 : (term > $o),X10 : (term > $o),X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & (hoasapinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & pushprop_lem2v2 & pushprop_lem0_gthm & (hoasinduction_lthm <=> (! [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 @ X15) | ~(X10 @ X13))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id)) => (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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)) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ 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))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [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,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))))) & (pushprop_lem1 <=> ! [X26 : (term > $o),X13 : term,X14 : subst,X15 : term,X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & ulamvarsh & induction2_gthm & axabs & (! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) <=> hoasinduction) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & lamnotvar & hoasinduction_lem1 & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : 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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))) & hoasapnotvar_lthm & (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term),X35 : term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X36 : subst,X37 : term,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)))) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id))) & (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)))))))) & apnotvar & ulamvarind & (! [X31 : (subst > term > term),X18 : (subst > term > term),X32 : subst,X33 : term] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslaminj) & hoasapinj2_gthm & (induction2lem <=> ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))))) & (! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & hoasinduction_lem2v2_gthm & ! [X1 : d_term] : (X1 = d_one) & hoasinduction_lem3b_gthm & (! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3a) & hoasinduction_lem2_lthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (apinj1 <=> ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & induction2lem_gthm & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (shinj <=> ! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [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,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3v2) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((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))) | (X11 @ (lam @ X29)))))) & axvarshift & pushprop_lem3v2_lthm & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21)) => ! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))))))) <=> induction2lem_lthm) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X10 : (term > $o),X14 : subst,X13 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one)) <=> pushprop_lem1v2) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & hoasinduction_lem3a_gthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((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)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id)))))) <=> hoasinduction_lthm_3) & ((! [X15 : term,X20 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X15 : term,X19 : term,X20 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) <=> hoasapinj2_lthm) & hoasapinj1_gthm & axassoc & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & termmset_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & hoasinduction_lem1v2_gthm & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & ((! [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)] : ((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)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [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)))))))) <=> hoasinduction_lem3a_lthm) & (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & hoaslaminj_gthm & pushprop_lem2v2_gthm & (pushprop_lem0 <=> ! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & hoaslamnotvar_gthm & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & hoasinduction_lem2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1_lthm & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoasapinj2 <=> ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3_gthm & (hoasinduction_lem2v2 <=> ! [X11 : (term > $o),X44 : term,X45 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_lem3v2_gthm & (laminj <=> ! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & hoasinduction_lem1v2 & hoasinduction_lem1_gthm & ~(var @ (d2term @ d_one)) & pushprop_gthm & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))),
% 46.03/6.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 46.03/6.94 thf(f2,conjecture,(
% 46.03/6.94 (hoasinduction_lem3v2 = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X5 : subst,X2 : subst,X4 : subst,X3 : term] : ((X0 @ X2 @ X3 @ (comp @ X5 @ X4)) => (X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4)) => (! [X5 : subst,X3 : term,X4 : subst,X2 : subst] : ((X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4) => (X0 @ X2 @ X3 @ (comp @ X5 @ X4))) => (! [X6 : (subst > term > term)] : (! [X3 : term,X4 : subst,X2 : subst] : (((sub @ (X6 @ X2 @ X3) @ X4)) = ((X6 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X6 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X6 @ X2 @ X3)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X3 : term] : (! [X7 : term] : ((X1 @ X7) => (X1 @ (sub @ X3 @ (push @ X7 @ id)))) => (X1 @ (lam @ X3))))))))),
% 46.03/6.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2)).
% 46.03/6.94 thf(f3,negated_conjecture,(
% 46.03/6.94 ~ (hoasinduction_lem3v2 = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X5 : subst,X2 : subst,X4 : subst,X3 : term] : ((X0 @ X2 @ X3 @ (comp @ X5 @ X4)) => (X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4)) => (! [X5 : subst,X3 : term,X4 : subst,X2 : subst] : ((X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4) => (X0 @ X2 @ X3 @ (comp @ X5 @ X4))) => (! [X6 : (subst > term > term)] : (! [X3 : term,X4 : subst,X2 : subst] : (((sub @ (X6 @ X2 @ X3) @ X4)) = ((X6 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4)))) => (! [X3 : term] : ((X0 @ id @ X3 @ id) => (X0 @ id @ (X6 @ id @ X3) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X2 : subst, X3 : term] : ((X6 @ X2 @ X3)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X3 : term] : (! [X7 : term] : ((X1 @ X7) => (X1 @ (sub @ X3 @ (push @ X7 @ id)))) => (X1 @ (lam @ X3))))))))),
% 46.03/6.94 inference(negated_conjecture,[status(cth)],[f2])).
% 46.03/6.94 thf(f4,plain,(
% 46.03/6.94 ~ulamvar1 & (one = ((d2term @ d_one))) & (hoasinduction_lem3 <=> ! [X0 : term,X1 : (subst > term > subst > $o)] : (~ ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((X1 @ X3 @ X4 @ (comp @ X2 @ X5)) | ~(X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) | ~ ! [X6 : (subst > term > term)] : (~ ! [X7 : term] : ((X1 @ id @ (X6 @ id @ X7) @ id) | ~(X1 @ id @ X7 @ id)) | ~ ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) | (X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) | ~ ! [X11 : term] : (~(X1 @ id @ X11 @ id) | (X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : ((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13) | ~(X1 @ X14 @ X12 @ (comp @ X15 @ X13))) | (X1 @ id @ (lam @ X0) @ id))) & (hoasinduction_lem3b_lthm <=> ! [X16 : term] : ~ ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh))))) & (substmonoid <=> (! [X18 : subst] : (((comp @ id @ X18)) = X18) & ! [X19 : subst] : (((comp @ X19 @ id)) = X19))) & (! [X20 : term,X21 : (subst > term > subst > $o)] : ((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id) | ~ ! [X22 : term] : (~(X21 @ id @ X22 @ id) | (X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) | ~ ! [X23 : (subst > term > term)] : ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X24 : term] : ((X21 @ id @ (X23 @ id @ X24) @ id) | ~(X21 @ id @ X24 @ id)) | ~ ! [X25 : subst,X26 : term,X27 : subst] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))))) <=> hoasinduction_lem3aa) & ((! [X28 : subst] : (((comp @ id @ X28)) = X28) => (! [X29 : subst] : (((comp @ X29 @ id)) = X29) => (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)))) <=> substmonoid_lthm) & pushprop_lem2v2_lthm & (hoasinduction_lem2 <=> ! [X32 : (subst > term > subst > $o),X33 : term,X34 : term] : (~ ! [X35 : term,X36 : term] : (~(X32 @ id @ X36 @ id) | ~(X32 @ id @ X35 @ id) | (X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) | ~(X32 @ id @ X33 @ id) | ~ ! [X37 : term,X38 : subst,X39 : subst,X40 : subst] : (~(X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40) | (X32 @ X38 @ X37 @ (comp @ X39 @ X40))) | (X32 @ id @ (ap @ X33 @ X34) @ id) | ~ ! [X41 : term,X42 : subst,X43 : subst,X44 : subst] : ((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44) | ~(X32 @ X43 @ X41 @ (comp @ X42 @ X44))) | ~(X32 @ id @ X34 @ id))) & hoaslamnotap_lthm & (! [X45 : term,X46 : (subst > term > term),X47 : term] : (~ ! [X48 : term,X49 : subst,X50 : subst] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))) | (((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47)))) <=> hoaslamnotap) & (hoasapinj1_lthm <=> (! [X51 : term] : (((sub @ X51 @ id)) = X51) => (! [X52 : term,X53 : term,X54 : term,X55 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))) => ! [X56 : term,X57 : term,X58 : term,X59 : term] : ((X58 = X59) | (((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & substmonoid_gthm & ~lamnotap & (hoasinduction_no_psi_cond_lthm <=> (! [X60 : (subst > term > subst > $o)] : ~ ! [X61 : (term > $o)] : ~ ! [X62 : term] : (((X60 @ id @ X62 @ id)) = ((X61 @ X62))) => (! [X63 : term,X64 : (term > $o)] : (~ ! [X65 : term] : ((X64 @ (lam @ X65)) | ~ ! [X66 : term] : ((X64 @ (sub @ X65 @ (push @ X66 @ id))) | ~(X64 @ X66))) | (X64 @ X63) | ~ ! [X67 : term,X68 : term] : (~(X64 @ X68) | (X64 @ (ap @ X67 @ X68)) | ~(X64 @ X67)) | ~ ! [X69 : term] : (~(var @ X69) | (X64 @ X69))) => (! [X70 : term] : (((sub @ X70 @ id)) = X70) => (! [X71 : (subst > term > subst > $o),X72 : term,X73 : (term > $o)] : ((X73 @ (lam @ X72)) | ~ ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) | ~ ! [X75 : term] : (~(X73 @ X75) | (X73 @ (sub @ X72 @ (push @ X75 @ id)))) | ~ ! [X76 : (subst > term > term)] : (~ ! [X77 : subst,X78 : subst,X79 : term] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) = ((sub @ (X76 @ X78 @ X79) @ X77))) | (X71 @ id @ (lam @ (X76 @ sh @ one)) @ id) | ~ ! [X80 : term] : ((X71 @ id @ (X76 @ id @ X80) @ id) | ~(X71 @ id @ X80 @ id)))) => ! [X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : term,X84 : term] : (~(X82 @ id @ X84 @ id) | ~(X82 @ id @ X83 @ id) | (X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) | ~ ! [X85 : (subst > term > term)] : ((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id) | ~ ! [X86 : term] : ((X82 @ id @ (X85 @ id @ X86) @ id) | ~(X82 @ id @ X86 @ id)) | ~ ! [X87 : subst,X88 : subst,X89 : term] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88))))) | (X82 @ id @ X81 @ id))))))) & (pushprop_lem1_lthm <=> (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : term,X95 : (term > $o),X96 : subst,X97 : term,X98 : (term > $o)] : (~(X98 @ X97) | (X95 @ (sub @ X97 @ (push @ X94 @ X96))))))) & (id = ((d2subst @ d_id))) & pushprop_lthm_orig & hoaslamnotvar & pushprop_lem3v2 & pushprop_lthm & axclos & ((! [X99 : term] : (((sub @ X99 @ id)) = X99) => (! [X100 : term,X101 : subst,X102 : (term > $o)] : (~ ! [X103 : term,X104 : term] : (~(X102 @ X104) | ~(X102 @ X103) | (X102 @ (ap @ X103 @ X104))) | (X102 @ (sub @ X100 @ X101)) | ~ ! [X105 : term] : ((X102 @ (sub @ X105 @ X101)) | ~(var @ X105)) | ~ ! [X106 : term] : ((X102 @ (lam @ X106)) | ~ ! [X107 : term] : ((X102 @ (sub @ X106 @ (push @ X107 @ id))) | ~(X102 @ X107)))) => ! [X108 : (term > $o),X109 : term] : ((X108 @ X109) | ~ ! [X110 : term] : ((X108 @ (lam @ X110)) | ~ ! [X111 : term] : ((X108 @ (sub @ X110 @ (push @ X111 @ id))) | ~(X108 @ X111))) | ~ ! [X112 : term,X113 : term] : (~(X108 @ X112) | (X108 @ (ap @ X113 @ X112)) | ~(X108 @ X113)) | ~ ! [X114 : term] : (~(var @ X114) | (X108 @ X114))))) <=> induction2_lthm) & hoasapnotvar & (hoasinduction_lem3v2a <=> ! [X115 : (term > $o),X116 : (subst > term > subst > $o),X117 : term] : (~ ! [X118 : term] : (~(X115 @ X118) | (X115 @ (sub @ X117 @ (push @ X118 @ id)))) | (X115 @ (lam @ X117)) | ~ ! [X119 : term] : (((X116 @ id @ X119 @ id)) = ((X115 @ X119))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X121 : term] : ((X116 @ id @ (X120 @ id @ X121) @ id) | ~(X116 @ id @ X121 @ id)) | ~ ! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) | (X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)))) & (! [X125 : (term > $o),X126 : term] : (~ ! [X127 : term,X128 : term] : (~(X125 @ X128) | (X125 @ (ap @ X128 @ X127)) | ~(X125 @ X127)) | ~ ! [X129 : term] : (~(var @ X129) | (X125 @ X129)) | (X125 @ X126) | ~ ! [X130 : term] : ((X125 @ (lam @ X130)) | ~(X125 @ X130))) <=> induction) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X133 : subst,X134 : term] : (((comp @ sh @ (push @ X134 @ X133))) = X133) => (! [X135 : term,X136 : term] : ((X135 = X136) | (((lam @ X135)) != ((lam @ X136)))) => ! [X137 : (subst > term > term),X138 : (subst > term > term),X139 : term,X140 : subst] : ((((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))) | ~ ! [X141 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) = ((sub @ (X138 @ X143 @ X142) @ X141))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | ~ ! [X144 : term,X145 : subst,X146 : subst] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) = ((sub @ (X137 @ X146 @ X144) @ X145))))))) <=> hoaslaminj_lthm) & (! [X147 : (term > $o),X148 : term] : (~ ! [X149 : term,X150 : term] : (~(X147 @ X149) | (X147 @ (ap @ X149 @ X150)) | ~(X147 @ X150)) | ~ ! [X151 : term] : (~ ! [X152 : term] : (~(X147 @ X152) | (X147 @ (sub @ X151 @ (push @ X152 @ id)))) | (X147 @ (lam @ X151))) | (X147 @ X148) | ~ ! [X153 : term] : (~(var @ X153) | (X147 @ X153))) <=> induction2) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> termmset) & (sh = ((d2subst @ d_id))) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> axscons) & ! [X156 : d_subst] : (d_id = X156) & hoasapnotvar_gthm & (! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158) <=> axvarcons) & ((! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (term > $o),X162 : (subst > term > subst > $o)] : ((X161 @ (lam @ X160)) | ~ ! [X163 : subst,X164 : subst,X165 : term,X166 : subst] : ((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163) | ~(X162 @ X164 @ X165 @ (comp @ X166 @ X163))) | ~ ! [X167 : subst,X168 : subst,X169 : subst,X170 : term] : ((X162 @ X169 @ X170 @ (comp @ X168 @ X167)) | ~(X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167)) | ~ ! [X171 : term] : (((X162 @ id @ X171 @ id)) = ((X161 @ X171))) | ~ ! [X172 : (subst > term > term)] : ((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id) | ~ ! [X173 : term,X174 : subst,X175 : subst] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) | ~ ! [X176 : term] : (~(X162 @ id @ X176 @ id) | (X162 @ id @ (X172 @ id @ X176) @ id))) | ~ ! [X177 : term] : (~(X161 @ X177) | (X161 @ (sub @ X160 @ (push @ X177 @ id)))))) <=> hoasinduction_lem3v2_lthm) & axapp & ((! [X178 : term] : (((sub @ X178 @ id)) = X178) => (! [X179 : term,X180 : (subst > term > subst > $o)] : ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id) | ~ ! [X181 : term] : (~(X180 @ id @ X181 @ id) | (X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) | ~ ! [X182 : (subst > term > term)] : ((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id) | ~ ! [X183 : term,X184 : subst,X185 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) = ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ~ ! [X186 : term] : ((X180 @ id @ (X182 @ id @ X186) @ id) | ~(X180 @ id @ X186 @ id)))) => ! [X187 : (subst > term > subst > $o),X188 : term] : (~ ! [X189 : (subst > term > term)] : ((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id) | ~ ! [X190 : subst,X191 : subst,X192 : term] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190)))) | ~ ! [X193 : term] : (~(X187 @ id @ X193 @ id) | (X187 @ id @ (X189 @ id @ X193) @ id))) | ~ ! [X194 : subst,X195 : term,X196 : subst,X197 : subst] : ((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194) | ~(X187 @ X197 @ X195 @ (comp @ X196 @ X194))) | ~ ! [X198 : term,X199 : subst,X200 : subst,X201 : subst] : ((X187 @ X200 @ X198 @ (comp @ X201 @ X199)) | ~(X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) | (X187 @ id @ (lam @ X188) @ id) | ~ ! [X202 : term] : (~(X187 @ id @ X202 @ id) | (X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id))))) <=> hoasinduction_lem3_lthm) & hoaslamnotvar_lthm & pushprop_lem1v2_gthm & axmap & hoaslamnotap_gthm & (apinj2 <=> ! [X203 : term,X204 : term,X205 : term,X206 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203))))) & ((! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) => ! [X209 : subst,X210 : (term > $o),X211 : (term > $o),X212 : term] : (~(X211 @ X212) | (X210 @ one) | ~ ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209))))))) <=> pushprop_lem1v2_lthm) & pushprop_lem1_gthm & (hoasapinj1 <=> ! [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & pushprop_lem2v2 & pushprop_lem0_gthm & (hoasinduction_lthm <=> (! [X218 : term,X219 : (term > $o)] : (~ ! [X220 : term] : (~(var @ X220) | (X219 @ X220)) | (X219 @ X218) | ~ ! [X221 : term] : (~ ! [X222 : term] : (~(X219 @ X222) | (X219 @ (sub @ X221 @ (push @ X222 @ id)))) | (X219 @ (lam @ X221))) | ~ ! [X223 : term,X224 : term] : ((X219 @ (ap @ X223 @ X224)) | ~(X219 @ X224) | ~(X219 @ X223))) => (! [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (~(X225 @ id @ X227 @ id) | ~(X225 @ id @ X226 @ id) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : (~(X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229) | (X225 @ X230 @ X231 @ (comp @ X228 @ X229))) | ~ ! [X232 : term,X233 : term] : (~(X225 @ id @ X233 @ id) | ~(X225 @ id @ X232 @ id) | (X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) | ~ ! [X234 : subst,X235 : subst,X236 : term,X237 : subst] : ((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237) | ~(X225 @ X235 @ X236 @ (comp @ X234 @ X237))) | (X225 @ id @ (ap @ X226 @ X227) @ id)) => (! [X238 : term,X239 : (subst > term > subst > $o)] : (~ ! [X240 : (subst > term > term)] : (~ ! [X241 : term] : ((X239 @ id @ (X240 @ id @ X241) @ id) | ~(X239 @ id @ X241 @ id)) | ~ ! [X242 : subst,X243 : term,X244 : subst] : (((sub @ (X240 @ X242 @ X243) @ X244)) = ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | (X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)) | ~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (~(X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248) | (X239 @ X245 @ X247 @ (comp @ X246 @ X248))) | (X239 @ id @ (lam @ X238) @ id) | ~ ! [X249 : term] : ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id) | ~(X239 @ id @ X249 @ id)) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~(X239 @ X250 @ X251 @ (comp @ X252 @ X253)) | (X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253))) => ! [X254 : (subst > term > subst > $o),X255 : term] : (~ ! [X256 : subst,X257 : subst,X258 : term,X259 : subst] : ((X254 @ X259 @ X258 @ (comp @ X257 @ X256)) | ~(X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) | ~ ! [X260 : (subst > term > term)] : (~ ! [X261 : term] : (~(X254 @ id @ X261 @ id) | (X254 @ id @ (X260 @ id @ X261) @ id)) | (X254 @ id @ (lam @ (X260 @ sh @ one)) @ id) | ~ ! [X262 : subst,X263 : subst,X264 : term] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262)))) | (X254 @ id @ X255 @ id) | ~ ! [X265 : term] : (~(var @ (sub @ X265 @ id)) | (X254 @ id @ X265 @ id)) | ~ ! [X266 : term,X267 : term] : (~(X254 @ id @ X266 @ id) | (X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id) | ~(X254 @ id @ X267 @ id)) | ~ ! [X268 : subst,X269 : subst,X270 : subst,X271 : term] : ((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269) | ~(X254 @ X270 @ X271 @ (comp @ X268 @ X269)))))))) & (pushprop_lem1 <=> ! [X272 : (term > $o),X273 : term,X274 : subst,X275 : term,X276 : (term > $o)] : (~(X276 @ X273) | (X272 @ (sub @ X273 @ (push @ X275 @ X274))))) & ulamvarsh & induction2_gthm & axabs & (! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term] : ((X277 @ id @ X279 @ id) | ~(var @ (sub @ X279 @ id))) | ~ ! [X280 : (subst > term > term)] : (~ ! [X281 : term,X282 : subst,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) | (X277 @ id @ (lam @ (X280 @ sh @ one)) @ id) | ~ ! [X284 : term] : ((X277 @ id @ (X280 @ id @ X284) @ id) | ~(X277 @ id @ X284 @ id))) | ~ ! [X285 : subst,X286 : term,X287 : subst,X288 : subst] : ((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287) | ~(X277 @ X288 @ X286 @ (comp @ X285 @ X287))) | (X277 @ id @ X278 @ id) | ~ ! [X289 : term,X290 : subst,X291 : subst,X292 : subst] : (~(X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290) | (X277 @ X291 @ X289 @ (comp @ X292 @ X290))) | ~ ! [X293 : term,X294 : term] : (~(X277 @ id @ X294 @ id) | ~(X277 @ id @ X293 @ id) | (X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))) <=> hoasinduction) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : ~ ! [X297 : subst,X298 : term] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> hoasinduction_lem3v2_f) & lamnotvar & hoasinduction_lem1 & (hoasinduction_no_psi_cond <=> ! [X299 : (subst > term > subst > $o),X300 : term] : (~ ! [X301 : (subst > term > term)] : (~ ! [X302 : subst,X303 : subst,X304 : term] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) | ~ ! [X305 : term] : (~(X299 @ id @ X305 @ id) | (X299 @ id @ (X301 @ id @ X305) @ id)) | (X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) | (X299 @ id @ X300 @ id) | ~ ! [X306 : term,X307 : term] : (~(X299 @ id @ X306 @ id) | (X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id) | ~(X299 @ id @ X307 @ id)))) & hoasapnotvar_lthm & (hoasinduction_lem3aaa <=> ! [X308 : (subst > term > subst > $o),X309 : term] : (~ ! [X310 : term] : (~(X308 @ id @ X310 @ id) | (X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) | ~ ! [X311 : (subst > term > term),X312 : term] : ((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id) | ~ ! [X313 : term] : ((X308 @ id @ (X311 @ id @ X313) @ id) | ~(X308 @ id @ X313 @ id)) | ~ ! [X314 : term,X315 : subst,X316 : subst] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | ~ ! [X317 : subst,X318 : term,X319 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319)))) | (X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))) & (pushprop_p_and_p_prime = (^[X320 : term, X321 : subst, X322 : (term > $o), X323 : (term > $o)] : (! [X324 : term] : (((X322 @ (sub @ X324 @ (push @ X320 @ X321)))) = ((X323 @ X324)))))) & apnotvar & ulamvarind & (! [X325 : (subst > term > term),X326 : (subst > term > term),X327 : subst,X328 : term] : (~ ! [X329 : term,X330 : subst,X331 : subst] : (((sub @ (X326 @ X331 @ X329) @ X330)) = ((X326 @ (comp @ X331 @ X330) @ (sub @ X329 @ X330)))) | (((X325 @ X327 @ X328)) = ((X326 @ X327 @ X328))) | (((lam @ (X325 @ sh @ one))) != ((lam @ (X326 @ sh @ one)))) | ~ ! [X332 : subst,X333 : term,X334 : subst] : (((sub @ (X325 @ X334 @ X333) @ X332)) = ((X325 @ (comp @ X334 @ X332) @ (sub @ X333 @ X332))))) <=> hoaslaminj) & hoasapinj2_gthm & (induction2lem <=> ! [X335 : (term > $o),X336 : subst,X337 : term] : (~ ! [X338 : term,X339 : term] : (~(X335 @ X339) | (X335 @ (ap @ X338 @ X339)) | ~(X335 @ X338)) | (X335 @ (sub @ X337 @ X336)) | ~ ! [X340 : term] : ((X335 @ (sub @ X340 @ X336)) | ~(var @ X340)) | ~ ! [X341 : term] : (~ ! [X342 : term] : ((X335 @ (sub @ X341 @ (push @ X342 @ id))) | ~(X335 @ X342)) | (X335 @ (lam @ X341))))) & (! [X343 : term,X344 : subst,X345 : (term > $o)] : ~ ! [X346 : (term > $o)] : ~ ! [X347 : term] : (((X346 @ X347)) = ((X345 @ (sub @ X347 @ (push @ X343 @ X344))))) <=> pushprop_lem0_lthm) & hoasinduction_lem2v2_gthm & ! [X348 : d_term] : (d_one = X348) & hoasinduction_lem3b_gthm & (! [X349 : (subst > term > subst > $o),X350 : term] : ((X349 @ id @ (lam @ X350) @ id) | ~ ! [X351 : term] : (~(X349 @ id @ X351 @ id) | (X349 @ id @ (sub @ X350 @ (push @ X351 @ id)) @ id)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : term] : ((X349 @ id @ (X352 @ id @ X353) @ id) | ~(X349 @ id @ X353 @ id)) | ~ ! [X354 : term,X355 : subst,X356 : subst] : (((sub @ (X352 @ X356 @ X354) @ X355)) = ((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355)))) | (X349 @ id @ (lam @ (X352 @ sh @ one)) @ id))) <=> hoasinduction_lem3a) & hoasinduction_lem2_lthm & ! [X357 : subst] : ? [X358 : d_subst] : (((d2subst @ X358)) = X357) & (apinj1 <=> ! [X359 : term,X360 : term,X361 : term,X362 : term] : ((((ap @ X360 @ X362)) != ((ap @ X359 @ X361))) | (X359 = X360))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop & (termmset_lthm <=> (! [X363 : term] : (((sub @ X363 @ id)) = X363) => ! [X364 : term] : (((sub @ X364 @ id)) = X364))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & induction2lem_gthm & ((^[X365 : (subst > term > subst > $o), X366 : (term > $o)] : (! [X367 : term] : (((X365 @ id @ X367 @ id)) = ((X366 @ X367))))) = hoasinduction_p_and_p_prime) & (shinj <=> ! [X368 : term,X369 : term] : ((X368 = X369) | (((sub @ X368 @ sh)) != ((sub @ X369 @ sh))))) & ! [X370 : d_term,X371 : d_term] : ((((d2term @ X371)) = ((d2term @ X370))) => (X370 = X371)) & (! [X372 : (term > $o),X373 : (subst > term > subst > $o),X374 : term] : (~ ! [X375 : subst,X376 : term,X377 : subst,X378 : subst] : (~(X373 @ X377 @ X376 @ (comp @ X378 @ X375)) | (X373 @ (comp @ X377 @ X378) @ (sub @ X376 @ X378) @ X375)) | (X372 @ (lam @ X374)) | ~ ! [X379 : term] : (((X372 @ X379)) = ((X373 @ id @ X379 @ id))) | ~ ! [X380 : term] : (~(X372 @ X380) | (X372 @ (sub @ X374 @ (push @ X380 @ id)))) | ~ ! [X381 : subst,X382 : subst,X383 : term,X384 : subst] : ((X373 @ X384 @ X383 @ (comp @ X381 @ X382)) | ~(X373 @ (comp @ X384 @ X381) @ (sub @ X383 @ X381) @ X382)) | ~ ! [X385 : (subst > term > term)] : ((X373 @ id @ (lam @ (X385 @ sh @ one)) @ id) | ~ ! [X386 : term] : ((X373 @ id @ (X385 @ id @ X386) @ id) | ~(X373 @ id @ X386 @ id)) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X389 @ X388) @ (sub @ X387 @ X388))) = ((sub @ (X385 @ X389 @ X387) @ X388))))) <=> hoasinduction_lem3v2) & (! [X390 : term] : ~ ! [X391 : (subst > term > term)] : (((X391 @ sh @ one)) != ((sub @ X390 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & hoasinduction_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X392 : term] : ~ ! [X393 : (subst > term > term)] : ~ ! [X394 : subst,X395 : term] : (((X393 @ X394 @ X395)) = ((sub @ X392 @ (push @ X395 @ X394)))) => (! [X396 : term] : (((sub @ X396 @ id)) = X396) => ! [X397 : (subst > term > subst > $o),X398 : (term > $o),X399 : term] : (~ ! [X400 : term] : ((X398 @ (sub @ X399 @ (push @ X400 @ id))) | ~(X398 @ X400)) | ~ ! [X401 : term] : (((X397 @ id @ X401 @ id)) = ((X398 @ X401))) | ~ ! [X402 : (subst > term > term)] : (~ ! [X403 : subst,X404 : term,X405 : subst] : (((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403))) = ((sub @ (X402 @ X405 @ X404) @ X403))) | (X397 @ id @ (lam @ (X402 @ sh @ one)) @ id) | ~ ! [X406 : term] : (~(X397 @ id @ X406 @ id) | (X397 @ id @ (X402 @ id @ X406) @ id))) | (X398 @ (lam @ X399)))))) & axvarshift & pushprop_lem3v2_lthm & (axidr <=> ! [X407 : subst] : (((comp @ X407 @ id)) = X407)) & ((! [X408 : subst,X409 : term] : (((sub @ one @ (push @ X409 @ X408))) = X409) => (! [X410 : subst,X411 : term] : (((comp @ sh @ (push @ X411 @ X410))) = X410) => (! [X412 : subst] : (((comp @ X412 @ id)) = X412) => (! [X413 : (term > $o),X414 : term] : (~ ! [X415 : term,X416 : term] : (~(X413 @ X416) | ~(X413 @ X415) | (X413 @ (ap @ X416 @ X415))) | ~ ! [X417 : term] : ((X413 @ X417) | ~(var @ X417)) | ~ ! [X418 : term] : (~(X413 @ X418) | (X413 @ (lam @ X418))) | (X413 @ X414)) => ! [X419 : subst,X420 : (term > $o),X421 : term] : (~ ! [X422 : term,X423 : term] : ((X420 @ (ap @ X422 @ X423)) | ~(X420 @ X422) | ~(X420 @ X423)) | ~ ! [X424 : term] : (~ ! [X425 : term] : ((X420 @ (sub @ X424 @ (push @ X425 @ id))) | ~(X420 @ X425)) | (X420 @ (lam @ X424))) | ~ ! [X426 : term] : ((X420 @ (sub @ X426 @ X419)) | ~(var @ X426)) | (X420 @ (sub @ X421 @ X419))))))) <=> induction2lem_lthm) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X427 : (term > $o),X428 : subst,X429 : term,X430 : (term > $o)] : (~ ! [X431 : term] : (((X430 @ X431)) = ((X427 @ (sub @ X431 @ (push @ X429 @ X428))))) | ~(X427 @ X429) | (X430 @ one)) <=> pushprop_lem1v2) & ! [X432 : d_subst,X433 : d_subst] : ((((d2subst @ X432)) = ((d2subst @ X433))) => (X432 = X433)) & (! [X434 : term,X435 : subst] : (((comp @ sh @ (push @ X434 @ X435))) = X435) <=> axshiftcons) & hoasinduction_lem3a_gthm & ((! [X436 : (subst > term > subst > $o)] : ~ ! [X437 : (term > $o)] : ~ ! [X438 : term] : (((X437 @ X438)) = ((X436 @ id @ X438 @ id))) => (! [X439 : term,X440 : (term > $o)] : (~ ! [X441 : term] : ((X440 @ (lam @ X441)) | ~ ! [X442 : term] : (~(X440 @ X442) | (X440 @ (sub @ X441 @ (push @ X442 @ id))))) | ~ ! [X443 : term,X444 : term] : (~(X440 @ X443) | ~(X440 @ X444) | (X440 @ (ap @ X444 @ X443))) | ~ ! [X445 : term] : ((X440 @ X445) | ~(var @ X445)) | (X440 @ X439)) => (! [X446 : term] : (((sub @ X446 @ id)) = X446) => (! [X447 : (term > $o),X448 : term,X449 : (subst > term > subst > $o)] : (~ ! [X450 : term] : ((X447 @ (sub @ X448 @ (push @ X450 @ id))) | ~(X447 @ X450)) | ~ ! [X451 : (subst > term > term)] : ((X449 @ id @ (lam @ (X451 @ sh @ one)) @ id) | ~ ! [X452 : term] : (~(X449 @ id @ X452 @ id) | (X449 @ id @ (X451 @ id @ X452) @ id)) | ~ ! [X453 : subst,X454 : subst,X455 : term] : (((X451 @ (comp @ X453 @ X454) @ (sub @ X455 @ X454))) = ((sub @ (X451 @ X453 @ X455) @ X454)))) | (X447 @ (lam @ X448)) | ~ ! [X456 : term] : (((X447 @ X456)) = ((X449 @ id @ X456 @ id)))) => ! [X457 : term,X458 : (subst > term > subst > $o)] : (~ ! [X459 : subst,X460 : subst,X461 : subst,X462 : term] : ((X458 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460) @ X459) | ~(X458 @ X461 @ X462 @ (comp @ X460 @ X459))) | ~ ! [X463 : term] : (~(var @ (sub @ X463 @ id)) | (X458 @ id @ X463 @ id)) | ~ ! [X464 : term,X465 : subst,X466 : subst,X467 : subst] : ((X458 @ X466 @ X464 @ (comp @ X467 @ X465)) | ~(X458 @ (comp @ X466 @ X467) @ (sub @ X464 @ X467) @ X465)) | ~ ! [X468 : (subst > term > term)] : ((X458 @ id @ (lam @ (X468 @ sh @ one)) @ id) | ~ ! [X469 : term,X470 : subst,X471 : subst] : (((X468 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471))) = ((sub @ (X468 @ X470 @ X469) @ X471))) | ~ ! [X472 : term] : (~(X458 @ id @ X472 @ id) | (X458 @ id @ (X468 @ id @ X472) @ id))) | ~ ! [X473 : term,X474 : term] : ((X458 @ id @ (ap @ (sub @ X473 @ id) @ X474) @ id) | ~(X458 @ id @ X473 @ id) | ~(X458 @ id @ X474 @ id)) | (X458 @ id @ X457 @ id)))))) <=> hoasinduction_lthm_3) & ((! [X475 : term,X476 : term,X477 : term,X478 : term] : ((X476 = X477) | (((ap @ X478 @ X477)) != ((ap @ X475 @ X476)))) => ! [X479 : term,X480 : term,X481 : term,X482 : term] : ((((ap @ (sub @ X482 @ id) @ X480)) != ((ap @ (sub @ X479 @ id) @ X481))) | (X480 = X481))) <=> hoasapinj2_lthm) & hoasapinj1_gthm & axassoc & ! [X483 : term] : ? [X484 : d_term] : (((d2term @ X484)) = X483) & termmset_gthm & (! [X485 : (subst > term > subst > $o)] : ~ ! [X486 : (term > $o)] : ~ ! [X487 : term] : (((X485 @ id @ X487 @ id)) = ((X486 @ X487))) <=> hoasinduction_lem0) & hoasinduction_lem1v2_gthm & (axidl <=> ! [X488 : subst] : (((comp @ id @ X488)) = X488)) & ((! [X489 : term] : (((sub @ X489 @ id)) = X489) => (! [X490 : (subst > term > subst > $o),X491 : term] : ((X490 @ id @ (lam @ (sub @ X491 @ (push @ one @ sh))) @ id) | ~ ! [X492 : (subst > term > term)] : ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id) | ~ ! [X493 : subst,X494 : term,X495 : subst] : (((X492 @ (comp @ X495 @ X493) @ (sub @ X494 @ X493))) = ((sub @ (X492 @ X495 @ X494) @ X493))) | ~ ! [X496 : term] : ((X490 @ id @ (X492 @ id @ X496) @ id) | ~(X490 @ id @ X496 @ id))) | ~ ! [X497 : term] : (~(X490 @ id @ X497 @ id) | (X490 @ id @ (sub @ X491 @ (push @ X497 @ id)) @ id))) => ! [X498 : (subst > term > subst > $o),X499 : term] : (~ ! [X500 : term] : (~(X498 @ id @ X500 @ id) | (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) | (X498 @ id @ (lam @ X499) @ id) | ~ ! [X501 : (subst > term > term)] : ((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id) | ~ ! [X502 : term] : (~(X498 @ id @ X502 @ id) | (X498 @ id @ (X501 @ id @ X502) @ id)) | ~ ! [X503 : subst,X504 : term,X505 : subst] : (((sub @ (X501 @ X503 @ X504) @ X505)) = ((X501 @ (comp @ X503 @ X505) @ (sub @ X504 @ X505)))))))) <=> hoasinduction_lem3a_lthm) & (! [X506 : (subst > term > subst > $o),X507 : term] : (~ ! [X508 : term] : (~(X506 @ id @ X508 @ id) | (X506 @ id @ (sub @ X507 @ (push @ X508 @ id)) @ id)) | ~ ! [X509 : (subst > term > term)] : (~ ! [X510 : term] : (~(X506 @ id @ X510 @ id) | (X506 @ id @ (X509 @ id @ X510) @ id)) | ~ ! [X511 : term,X512 : subst,X513 : subst] : (((X509 @ (comp @ X512 @ X513) @ (sub @ X511 @ X513))) = ((sub @ (X509 @ X512 @ X511) @ X513))) | (X506 @ id @ (lam @ (X509 @ sh @ one)) @ id)) | (X506 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & hoaslaminj_gthm & pushprop_lem2v2_gthm & (pushprop_lem0 <=> ! [X514 : (term > $o),X515 : subst,X516 : term] : ~ ! [X517 : (term > $o)] : ~ ! [X518 : term] : (((X517 @ X518)) = ((X514 @ (sub @ X518 @ (push @ X516 @ X515)))))) & hoaslamnotvar_gthm & (hoaslam = (^[X519 : subst, X520 : (subst > term > term)] : ((d2term @ d_one)))) & hoasinduction_lem2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1_lthm & (axvarid <=> ! [X521 : term] : (((sub @ X521 @ id)) = X521)) & (hoasapinj2 <=> ! [X522 : term,X523 : term,X524 : term,X525 : term] : ((X522 = X523) | (((ap @ (sub @ X524 @ id) @ X523)) != ((ap @ (sub @ X525 @ id) @ X522))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem3_gthm & (hoasinduction_lem2v2 <=> ! [X526 : (term > $o),X527 : term,X528 : term,X529 : (subst > term > subst > $o)] : (~ ! [X530 : term,X531 : term] : ((X529 @ id @ (ap @ (sub @ X531 @ id) @ X530) @ id) | ~(X529 @ id @ X531 @ id) | ~(X529 @ id @ X530 @ id)) | ~(X526 @ X527) | (X526 @ (ap @ X527 @ X528)) | ~ ! [X532 : subst,X533 : subst,X534 : term,X535 : subst] : (~(X529 @ X535 @ X534 @ (comp @ X533 @ X532)) | (X529 @ (comp @ X535 @ X533) @ (sub @ X534 @ X533) @ X532)) | ~ ! [X536 : subst,X537 : subst,X538 : term,X539 : subst] : (~(X529 @ (comp @ X539 @ X536) @ (sub @ X538 @ X536) @ X537) | (X529 @ X539 @ X538 @ (comp @ X536 @ X537))) | ~(X526 @ X528) | ~ ! [X540 : term] : (((X529 @ id @ X540 @ id)) = ((X526 @ X540))))) & (! [X541 : term] : ~ ! [X542 : (subst > term > term)] : ~ ! [X543 : term,X544 : subst] : (((X542 @ X544 @ X543)) = ((sub @ X541 @ (push @ X543 @ X544)))) <=> hoasinduction_lem3v2_f_lthm) & hoasinduction_lem3v2_gthm & (laminj <=> ! [X545 : term,X546 : term] : ((((lam @ X546)) != ((lam @ X545))) | (X545 = X546))) & hoasinduction_lem1v2 & hoasinduction_lem1_gthm & ~(var @ (d2term @ d_one)) & pushprop_gthm & (hoasinduction_lem0_lthm <=> ! [X547 : (subst > term > subst > $o)] : ~ ! [X548 : (term > $o)] : ~ ! [X549 : term] : (((X547 @ id @ X549 @ id)) = ((X548 @ X549))))),
% 46.03/6.94 inference(rectify,[],[f1])).
% 46.03/6.94 thf(f5,plain,(
% 46.03/6.94 ~ (ulamvar1 = $true) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) <=> ! [X0 : term,X1 : (subst > term > subst > $o)] : (~ ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) = $true) | ~ (((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) = $true)) | ~ ! [X6 : (subst > term > term)] : (~ ! [X7 : term] : ((((X1 @ id @ (X6 @ id @ X7) @ id)) = $true) | ~ (((X1 @ id @ X7 @ id)) = $true)) | ~ ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) | (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true)) | ~ ! [X11 : term] : (~ (((X1 @ id @ X11 @ id)) = $true) | (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) = $true)) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : ((((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) = $true) | ~ (((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) = $true)) | (((X1 @ id @ (lam @ X0) @ id)) = $true))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X16 : term] : ~ ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & (! [X20 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X22 : term] : (~ (((X21 @ id @ X22 @ id)) = $true) | (((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) = $true)) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))))) <=> (hoasinduction_lem3aa = $true)) & ((! [X28 : subst] : (((comp @ id @ X28)) = X28) => (! [X29 : subst] : (((comp @ X29 @ id)) = X29) => (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)))) <=> (substmonoid_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X32 : (subst > term > subst > $o),X33 : term,X34 : term] : (~ ! [X35 : term,X36 : term] : (~ (((X32 @ id @ X36 @ id)) = $true) | ~ (((X32 @ id @ X35 @ id)) = $true) | (((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) = $true)) | ~ (((X32 @ id @ X33 @ id)) = $true) | ~ ! [X37 : term,X38 : subst,X39 : subst,X40 : subst] : (~ (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) = $true) | ($true = ((X32 @ X38 @ X37 @ (comp @ X39 @ X40))))) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | ~ ! [X41 : term,X42 : subst,X43 : subst,X44 : subst] : ((((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) = $true) | ~ (((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) = $true)) | ~ (((X32 @ id @ X34 @ id)) = $true))) & (hoaslamnotap_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X45 : term,X46 : (subst > term > term),X47 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ~ ! [X50 : subst,X49 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))))) & ((hoasapinj1_lthm = $true) <=> (! [X51 : term] : (((sub @ X51 @ id)) = X51) => (! [X55 : term,X54 : term,X53 : term,X52 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))) => ! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (substmonoid_gthm = $true) & ~ (lamnotap = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X60 : (subst > term > subst > $o)] : ~ ! [X61 : (term > $o)] : ~ ! [X62 : term] : (((X60 @ id @ X62 @ id)) = ((X61 @ X62))) => (! [X63 : term,X64 : (term > $o)] : (~ ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ~ ! [X66 : term] : ((((X64 @ (sub @ X65 @ (push @ X66 @ id)))) = $true) | ~ (((X64 @ X66)) = $true))) | (((X64 @ X63)) = $true) | ~ ! [X67 : term,X68 : term] : (~ (((X64 @ X68)) = $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | ~ (((X64 @ X67)) = $true)) | ~ ! [X69 : term] : (~ (((var @ X69)) = $true) | (((X64 @ X69)) = $true))) => (! [X70 : term] : (((sub @ X70 @ id)) = X70) => (! [X71 : (subst > term > subst > $o),X72 : term,X73 : (term > $o)] : ((((X73 @ (lam @ X72))) = $true) | ~ ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) | ~ ! [X75 : term] : (~ (((X73 @ X75)) = $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) | ~ ! [X76 : (subst > term > term)] : (~ ! [X79 : term,X78 : subst,X77 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) = ((sub @ (X76 @ X78 @ X79) @ X77))) | (((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ~ ! [X80 : term] : (($true = ((X71 @ id @ (X76 @ id @ X80) @ id))) | ~ (((X71 @ id @ X80 @ id)) = $true)))) => ! [X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : term,X84 : term] : (~ (((X82 @ id @ X84 @ id)) = $true) | ~ (((X82 @ id @ X83 @ id)) = $true) | (((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) = $true)) | ~ ! [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true) | ~ ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | ~ (((X82 @ id @ X86 @ id)) = $true)) | ~ ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88))))) | (((X82 @ id @ X81 @ id)) = $true))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : term,X95 : (term > $o),X96 : subst,X97 : term,X98 : (term > $o)] : (~ (((X98 @ X97)) = $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true))))) & (((d2subst @ d_id)) = id) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (axclos = $true) & ((! [X99 : term] : (((sub @ X99 @ id)) = X99) => (! [X100 : term,X101 : subst,X102 : (term > $o)] : (~ ! [X103 : term,X104 : term] : (~ (((X102 @ X104)) = $true) | ~ (((X102 @ X103)) = $true) | (((X102 @ (ap @ X103 @ X104))) = $true)) | (((X102 @ (sub @ X100 @ X101))) = $true) | ~ ! [X105 : term] : ((((X102 @ (sub @ X105 @ X101))) = $true) | ~ (((var @ X105)) = $true)) | ~ ! [X106 : term] : ((((X102 @ (lam @ X106))) = $true) | ~ ! [X107 : term] : ((((X102 @ (sub @ X106 @ (push @ X107 @ id)))) = $true) | ~ (((X102 @ X107)) = $true)))) => ! [X108 : (term > $o),X109 : term] : ((((X108 @ X109)) = $true) | ~ ! [X110 : term] : ((((X108 @ (lam @ X110))) = $true) | ~ ! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | ~ (((X108 @ X111)) = $true))) | ~ ! [X112 : term,X113 : term] : (~ (((X108 @ X112)) = $true) | (((X108 @ (ap @ X113 @ X112))) = $true) | ~ (((X108 @ X113)) = $true)) | ~ ! [X114 : term] : (~ (((var @ X114)) = $true) | (((X108 @ X114)) = $true))))) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X115 : (term > $o),X116 : (subst > term > subst > $o),X117 : term] : (~ ! [X118 : term] : (~ (((X115 @ X118)) = $true) | (((X115 @ (sub @ X117 @ (push @ X118 @ id)))) = $true)) | (((X115 @ (lam @ X117))) = $true) | ~ ! [X119 : term] : (((X116 @ id @ X119 @ id)) = ((X115 @ X119))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | ~ (((X116 @ id @ X121 @ id)) = $true)) | ~ ! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) | (((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true)))) & (! [X125 : (term > $o),X126 : term] : (~ ! [X127 : term,X128 : term] : (~ (((X125 @ X128)) = $true) | (((X125 @ (ap @ X128 @ X127))) = $true) | ~ (((X125 @ X127)) = $true)) | ~ ! [X129 : term] : (~ (((var @ X129)) = $true) | ($true = ((X125 @ X129)))) | (((X125 @ X126)) = $true) | ~ ! [X130 : term] : ((((X125 @ (lam @ X130))) = $true) | ~ (((X125 @ X130)) = $true))) <=> (induction = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) = X133) => (! [X135 : term,X136 : term] : ((((lam @ X135)) != ((lam @ X136))) | (X135 = X136)) => ! [X138 : (subst > term > term),X140 : subst,X137 : (subst > term > term),X139 : term] : (~ ! [X141 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) = ((sub @ (X138 @ X143 @ X142) @ X141))) | ~ ! [X144 : term,X146 : subst,X145 : subst] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) = ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (! [X147 : (term > $o),X148 : term] : (~ ! [X149 : term,X150 : term] : (~ (((X147 @ X149)) = $true) | (((X147 @ (ap @ X149 @ X150))) = $true) | ~ (((X147 @ X150)) = $true)) | ~ ! [X151 : term] : (~ ! [X152 : term] : (~ (((X147 @ X152)) = $true) | (((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true)) | (((X147 @ (lam @ X151))) = $true)) | ($true = ((X147 @ X148))) | ~ ! [X153 : term] : (~ (((var @ X153)) = $true) | (((X147 @ X153)) = $true))) <=> (induction2 = $true)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & (((d2subst @ d_id)) = sh) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & ! [X156 : d_subst] : (d_id = X156) & (hoasapnotvar_gthm = $true) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & ((! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (term > $o),X162 : (subst > term > subst > $o)] : ((((X161 @ (lam @ X160))) = $true) | ~ ! [X163 : subst,X164 : subst,X165 : term,X166 : subst] : ((((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) = $true) | ~ (((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) = $true)) | ~ ! [X167 : subst,X168 : subst,X169 : subst,X170 : term] : ((((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) = $true) | ~ ($true = ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167)))) | ~ ! [X171 : term] : (((X162 @ id @ X171 @ id)) = ((X161 @ X171))) | ~ ! [X172 : (subst > term > term)] : ((((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) = $true) | ~ ! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) | ~ ! [X176 : term] : (~ (((X162 @ id @ X176 @ id)) = $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true))) | ~ ! [X177 : term] : (~ (((X161 @ X177)) = $true) | (((X161 @ (sub @ X160 @ (push @ X177 @ id)))) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (axapp = $true) & ((! [X178 : term] : (((sub @ X178 @ id)) = X178) => (! [X179 : term,X180 : (subst > term > subst > $o)] : (($true = ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id))) | ~ ! [X181 : term] : (~ (((X180 @ id @ X181 @ id)) = $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) | ~ ! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X183 : term,X185 : subst,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) = ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ~ ! [X186 : term] : (($true = ((X180 @ id @ (X182 @ id @ X186) @ id))) | ~ (((X180 @ id @ X186 @ id)) = $true)))) => ! [X187 : (subst > term > subst > $o),X188 : term] : (~ ! [X189 : (subst > term > term)] : ((((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true) | ~ ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190)))) | ~ ! [X193 : term] : (~ (((X187 @ id @ X193 @ id)) = $true) | (((X187 @ id @ (X189 @ id @ X193) @ id)) = $true))) | ~ ! [X194 : subst,X195 : term,X196 : subst,X197 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) = $true) | ~ (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) = $true)) | ~ ! [X198 : term,X199 : subst,X200 : subst,X201 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) = $true) | ~ (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) = $true)) | ($true = ((X187 @ id @ (lam @ X188) @ id))) | ~ ! [X202 : term] : (~ (((X187 @ id @ X202 @ id)) = $true) | (((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (axmap = $true) & (hoaslamnotap_gthm = $true) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & ((! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) => ! [X209 : subst,X210 : (term > $o),X211 : (term > $o),X212 : term] : (~ (((X211 @ X212)) = $true) | ($true = ((X210 @ one))) | ~ ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209))))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (pushprop_lem2v2 = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X218 : term,X219 : (term > $o)] : (~ ! [X220 : term] : (~ (((var @ X220)) = $true) | (((X219 @ X220)) = $true)) | (((X219 @ X218)) = $true) | ~ ! [X221 : term] : (~ ! [X222 : term] : (~ (((X219 @ X222)) = $true) | (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) | (((X219 @ (lam @ X221))) = $true)) | ~ ! [X223 : term,X224 : term] : (($true = ((X219 @ (ap @ X223 @ X224)))) | ~ ($true = ((X219 @ X224))) | ~ (((X219 @ X223)) = $true))) => (! [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (~ (((X225 @ id @ X227 @ id)) = $true) | ~ (((X225 @ id @ X226 @ id)) = $true) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : (~ (((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) = $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true)) | ~ ! [X232 : term,X233 : term] : (~ (((X225 @ id @ X233 @ id)) = $true) | ~ (((X225 @ id @ X232 @ id)) = $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)) | ~ ! [X234 : subst,X235 : subst,X236 : term,X237 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | ~ (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) = $true)) | (((X225 @ id @ (ap @ X226 @ X227) @ id)) = $true)) => (! [X238 : term,X239 : (subst > term > subst > $o)] : (~ ! [X240 : (subst > term > term)] : (~ ! [X241 : term] : ((((X239 @ id @ (X240 @ id @ X241) @ id)) = $true) | ~ (((X239 @ id @ X241 @ id)) = $true)) | ~ ! [X242 : subst,X244 : subst,X243 : term] : (((sub @ (X240 @ X242 @ X243) @ X244)) = ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)))) | ~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (~ ($true = ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true)) | (((X239 @ id @ (lam @ X238) @ id)) = $true) | ~ ! [X249 : term] : (($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id))) | ~ (((X239 @ id @ X249 @ id)) = $true)) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~ (((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) = $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true))) => ! [X254 : (subst > term > subst > $o),X255 : term] : (~ ! [X256 : subst,X257 : subst,X258 : term,X259 : subst] : ((((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) = $true) | ~ (((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) = $true)) | ~ ! [X260 : (subst > term > term)] : (~ ! [X261 : term] : (~ (((X254 @ id @ X261 @ id)) = $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true)) | (((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) = $true) | ~ ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262)))) | (((X254 @ id @ X255 @ id)) = $true) | ~ ! [X265 : term] : (~ (((var @ (sub @ X265 @ id))) = $true) | (((X254 @ id @ X265 @ id)) = $true)) | ~ ! [X266 : term,X267 : term] : (~ (((X254 @ id @ X266 @ id)) = $true) | (((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) = $true) | ~ (((X254 @ id @ X267 @ id)) = $true)) | ~ ! [X268 : subst,X269 : subst,X270 : subst,X271 : term] : ((((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) = $true) | ~ (((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true))))))) & ((pushprop_lem1 = $true) <=> ! [X272 : (term > $o),X273 : term,X274 : subst,X275 : term,X276 : (term > $o)] : (~ (((X276 @ X273)) = $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true))) & (ulamvarsh = $true) & (induction2_gthm = $true) & (axabs = $true) & (! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term] : ((((X277 @ id @ X279 @ id)) = $true) | ~ (((var @ (sub @ X279 @ id))) = $true)) | ~ ! [X280 : (subst > term > term)] : (~ ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) | (((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X284 : term] : (($true = ((X277 @ id @ (X280 @ id @ X284) @ id))) | ~ (((X277 @ id @ X284 @ id)) = $true))) | ~ ! [X285 : subst,X286 : term,X287 : subst,X288 : subst] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) = $true) | ~ (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) = $true)) | (((X277 @ id @ X278 @ id)) = $true) | ~ ! [X289 : term,X290 : subst,X291 : subst,X292 : subst] : (~ ($true = ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290))) | (((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) = $true)) | ~ ! [X293 : term,X294 : term] : (~ (((X277 @ id @ X294 @ id)) = $true) | ~ (((X277 @ id @ X293 @ id)) = $true) | ($true = ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))))) <=> (hoasinduction = $true)) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : ~ ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X299 : (subst > term > subst > $o),X300 : term] : (~ ! [X301 : (subst > term > term)] : (~ ! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) | ~ ! [X305 : term] : (~ ($true = ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true)) | (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true)) | (((X299 @ id @ X300 @ id)) = $true) | ~ ! [X306 : term,X307 : term] : (~ (((X299 @ id @ X306 @ id)) = $true) | ($true = ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) | ~ (((X299 @ id @ X307 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X308 : (subst > term > subst > $o),X309 : term] : (~ ! [X310 : term] : (~ (((X308 @ id @ X310 @ id)) = $true) | (((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) = $true)) | ~ ! [X311 : (subst > term > term),X312 : term] : ((((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) = $true) | ~ ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | ~ (((X308 @ id @ X313 @ id)) = $true)) | ~ ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | ~ ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319)))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & (ulamvarind = $true) & (! [X325 : (subst > term > term),X326 : (subst > term > term),X327 : subst,X328 : term] : (~ ! [X329 : term,X330 : subst,X331 : subst] : (((sub @ (X326 @ X331 @ X329) @ X330)) = ((X326 @ (comp @ X331 @ X330) @ (sub @ X329 @ X330)))) | (((X325 @ X327 @ X328)) = ((X326 @ X327 @ X328))) | (((lam @ (X325 @ sh @ one))) != ((lam @ (X326 @ sh @ one)))) | ~ ! [X332 : subst,X333 : term,X334 : subst] : (((sub @ (X325 @ X334 @ X333) @ X332)) = ((X325 @ (comp @ X334 @ X332) @ (sub @ X333 @ X332))))) <=> (hoaslaminj = $true)) & (hoasapinj2_gthm = $true) & ((induction2lem = $true) <=> ! [X335 : (term > $o),X336 : subst,X337 : term] : (~ ! [X338 : term,X339 : term] : (~ (((X335 @ X339)) = $true) | (((X335 @ (ap @ X338 @ X339))) = $true) | ~ (((X335 @ X338)) = $true)) | (((X335 @ (sub @ X337 @ X336))) = $true) | ~ ! [X340 : term] : ((((X335 @ (sub @ X340 @ X336))) = $true) | ~ (((var @ X340)) = $true)) | ~ ! [X341 : term] : (~ ! [X342 : term] : ((((X335 @ (sub @ X341 @ (push @ X342 @ id)))) = $true) | ~ (((X335 @ X342)) = $true)) | (((X335 @ (lam @ X341))) = $true)))) & (! [X343 : term,X344 : subst,X345 : (term > $o)] : ~ ! [X346 : (term > $o)] : ~ ! [X347 : term] : (((X346 @ X347)) = ((X345 @ (sub @ X347 @ (push @ X343 @ X344))))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X348 : d_term] : (d_one = X348) & (hoasinduction_lem3b_gthm = $true) & (! [X349 : (subst > term > subst > $o),X350 : term] : (($true = ((X349 @ id @ (lam @ X350) @ id))) | ~ ! [X351 : term] : (~ (((X349 @ id @ X351 @ id)) = $true) | (((X349 @ id @ (sub @ X350 @ (push @ X351 @ id)) @ id)) = $true)) | ~ ! [X352 : (subst > term > term)] : (~ ! [X353 : term] : ((((X349 @ id @ (X352 @ id @ X353) @ id)) = $true) | ~ (((X349 @ id @ X353 @ id)) = $true)) | ~ ! [X354 : term,X355 : subst,X356 : subst] : (((sub @ (X352 @ X356 @ X354) @ X355)) = ((X352 @ (comp @ X356 @ X355) @ (sub @ X354 @ X355)))) | ($true = ((X349 @ id @ (lam @ (X352 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem2_lthm = $true) & ! [X357 : subst] : ? [X358 : d_subst] : (((d2subst @ X358)) = X357) & ((apinj1 = $true) <=> ! [X359 : term,X360 : term,X361 : term,X362 : term] : ((((ap @ X360 @ X362)) != ((ap @ X359 @ X361))) | (X359 = X360))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & ((termmset_lthm = $true) <=> (! [X363 : term] : (((sub @ X363 @ id)) = X363) => ! [X364 : term] : (((sub @ X364 @ id)) = X364))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (induction2lem_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((shinj = $true) <=> ! [X368 : term,X369 : term] : ((X368 = X369) | (((sub @ X368 @ sh)) != ((sub @ X369 @ sh))))) & ! [X370 : d_term,X371 : d_term] : ((((d2term @ X371)) = ((d2term @ X370))) => (X370 = X371)) & (! [X372 : (term > $o),X373 : (subst > term > subst > $o),X374 : term] : (~ ! [X375 : subst,X376 : term,X377 : subst,X378 : subst] : (~ (((X373 @ X377 @ X376 @ (comp @ X378 @ X375))) = $true) | (((X373 @ (comp @ X377 @ X378) @ (sub @ X376 @ X378) @ X375)) = $true)) | (((X372 @ (lam @ X374))) = $true) | ~ ! [X379 : term] : (((X372 @ X379)) = ((X373 @ id @ X379 @ id))) | ~ ! [X380 : term] : (~ (((X372 @ X380)) = $true) | (((X372 @ (sub @ X374 @ (push @ X380 @ id)))) = $true)) | ~ ! [X381 : subst,X382 : subst,X383 : term,X384 : subst] : ((((X373 @ X384 @ X383 @ (comp @ X381 @ X382))) = $true) | ~ (((X373 @ (comp @ X384 @ X381) @ (sub @ X383 @ X381) @ X382)) = $true)) | ~ ! [X385 : (subst > term > term)] : ((((X373 @ id @ (lam @ (X385 @ sh @ one)) @ id)) = $true) | ~ ! [X386 : term] : (($true = ((X373 @ id @ (X385 @ id @ X386) @ id))) | ~ (((X373 @ id @ X386 @ id)) = $true)) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X389 @ X388) @ (sub @ X387 @ X388))) = ((sub @ (X385 @ X389 @ X387) @ X388))))) <=> (hoasinduction_lem3v2 = $true)) & (! [X390 : term] : ~ ! [X391 : (subst > term > term)] : (((X391 @ sh @ one)) != ((sub @ X390 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X392 : term] : ~ ! [X393 : (subst > term > term)] : ~ ! [X394 : subst,X395 : term] : (((X393 @ X394 @ X395)) = ((sub @ X392 @ (push @ X395 @ X394)))) => (! [X396 : term] : (((sub @ X396 @ id)) = X396) => ! [X397 : (subst > term > subst > $o),X398 : (term > $o),X399 : term] : (~ ! [X400 : term] : ((((X398 @ (sub @ X399 @ (push @ X400 @ id)))) = $true) | ~ (((X398 @ X400)) = $true)) | ~ ! [X401 : term] : (((X397 @ id @ X401 @ id)) = ((X398 @ X401))) | ~ ! [X402 : (subst > term > term)] : (~ ! [X403 : subst,X404 : term,X405 : subst] : (((X402 @ (comp @ X405 @ X403) @ (sub @ X404 @ X403))) = ((sub @ (X402 @ X405 @ X404) @ X403))) | (((X397 @ id @ (lam @ (X402 @ sh @ one)) @ id)) = $true) | ~ ! [X406 : term] : (~ (((X397 @ id @ X406 @ id)) = $true) | (((X397 @ id @ (X402 @ id @ X406) @ id)) = $true))) | (((X398 @ (lam @ X399))) = $true))))) & (axvarshift = $true) & (pushprop_lem3v2_lthm = $true) & ((axidr = $true) <=> ! [X407 : subst] : (((comp @ X407 @ id)) = X407)) & ((! [X408 : subst,X409 : term] : (((sub @ one @ (push @ X409 @ X408))) = X409) => (! [X410 : subst,X411 : term] : (((comp @ sh @ (push @ X411 @ X410))) = X410) => (! [X412 : subst] : (((comp @ X412 @ id)) = X412) => (! [X413 : (term > $o),X414 : term] : (~ ! [X415 : term,X416 : term] : (~ (((X413 @ X416)) = $true) | ~ (((X413 @ X415)) = $true) | (((X413 @ (ap @ X416 @ X415))) = $true)) | ~ ! [X417 : term] : (($true = ((X413 @ X417))) | ~ ($true = ((var @ X417)))) | ~ ! [X418 : term] : (~ ($true = ((X413 @ X418))) | (((X413 @ (lam @ X418))) = $true)) | (((X413 @ X414)) = $true)) => ! [X419 : subst,X420 : (term > $o),X421 : term] : (~ ! [X422 : term,X423 : term] : ((((X420 @ (ap @ X422 @ X423))) = $true) | ~ (((X420 @ X422)) = $true) | ~ (((X420 @ X423)) = $true)) | ~ ! [X424 : term] : (~ ! [X425 : term] : ((((X420 @ (sub @ X424 @ (push @ X425 @ id)))) = $true) | ~ (((X420 @ X425)) = $true)) | (((X420 @ (lam @ X424))) = $true)) | ~ ! [X426 : term] : ((((X420 @ (sub @ X426 @ X419))) = $true) | ~ (((var @ X426)) = $true)) | (((X420 @ (sub @ X421 @ X419))) = $true)))))) <=> (induction2lem_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X427 : (term > $o),X428 : subst,X429 : term,X430 : (term > $o)] : (~ ! [X431 : term] : (((X430 @ X431)) = ((X427 @ (sub @ X431 @ (push @ X429 @ X428))))) | ~ (((X427 @ X429)) = $true) | (((X430 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & ! [X432 : d_subst,X433 : d_subst] : ((((d2subst @ X432)) = ((d2subst @ X433))) => (X432 = X433)) & (! [X434 : term,X435 : subst] : (((comp @ sh @ (push @ X434 @ X435))) = X435) <=> (axshiftcons = $true)) & (hoasinduction_lem3a_gthm = $true) & ((! [X436 : (subst > term > subst > $o)] : ~ ! [X437 : (term > $o)] : ~ ! [X438 : term] : (((X437 @ X438)) = ((X436 @ id @ X438 @ id))) => (! [X439 : term,X440 : (term > $o)] : (~ ! [X441 : term] : ((((X440 @ (lam @ X441))) = $true) | ~ ! [X442 : term] : (~ (((X440 @ X442)) = $true) | (((X440 @ (sub @ X441 @ (push @ X442 @ id)))) = $true))) | ~ ! [X443 : term,X444 : term] : (~ (((X440 @ X443)) = $true) | ~ (((X440 @ X444)) = $true) | (((X440 @ (ap @ X444 @ X443))) = $true)) | ~ ! [X445 : term] : ((((X440 @ X445)) = $true) | ~ (((var @ X445)) = $true)) | (((X440 @ X439)) = $true)) => (! [X446 : term] : (((sub @ X446 @ id)) = X446) => (! [X447 : (term > $o),X448 : term,X449 : (subst > term > subst > $o)] : (~ ! [X450 : term] : ((((X447 @ (sub @ X448 @ (push @ X450 @ id)))) = $true) | ~ (((X447 @ X450)) = $true)) | ~ ! [X451 : (subst > term > term)] : (($true = ((X449 @ id @ (lam @ (X451 @ sh @ one)) @ id))) | ~ ! [X452 : term] : (~ (((X449 @ id @ X452 @ id)) = $true) | (((X449 @ id @ (X451 @ id @ X452) @ id)) = $true)) | ~ ! [X453 : subst,X454 : subst,X455 : term] : (((X451 @ (comp @ X453 @ X454) @ (sub @ X455 @ X454))) = ((sub @ (X451 @ X453 @ X455) @ X454)))) | (((X447 @ (lam @ X448))) = $true) | ~ ! [X456 : term] : (((X447 @ X456)) = ((X449 @ id @ X456 @ id)))) => ! [X457 : term,X458 : (subst > term > subst > $o)] : (~ ! [X459 : subst,X460 : subst,X461 : subst,X462 : term] : ((((X458 @ (comp @ X461 @ X460) @ (sub @ X462 @ X460) @ X459)) = $true) | ~ (((X458 @ X461 @ X462 @ (comp @ X460 @ X459))) = $true)) | ~ ! [X463 : term] : (~ (((var @ (sub @ X463 @ id))) = $true) | ($true = ((X458 @ id @ X463 @ id)))) | ~ ! [X464 : term,X465 : subst,X466 : subst,X467 : subst] : ((((X458 @ X466 @ X464 @ (comp @ X467 @ X465))) = $true) | ~ (((X458 @ (comp @ X466 @ X467) @ (sub @ X464 @ X467) @ X465)) = $true)) | ~ ! [X468 : (subst > term > term)] : ((((X458 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true) | ~ ! [X469 : term,X470 : subst,X471 : subst] : (((X468 @ (comp @ X470 @ X471) @ (sub @ X469 @ X471))) = ((sub @ (X468 @ X470 @ X469) @ X471))) | ~ ! [X472 : term] : (~ ($true = ((X458 @ id @ X472 @ id))) | (((X458 @ id @ (X468 @ id @ X472) @ id)) = $true))) | ~ ! [X473 : term,X474 : term] : ((((X458 @ id @ (ap @ (sub @ X473 @ id) @ X474) @ id)) = $true) | ~ (((X458 @ id @ X473 @ id)) = $true) | ~ (((X458 @ id @ X474 @ id)) = $true)) | (((X458 @ id @ X457 @ id)) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & ((! [X475 : term,X476 : term,X477 : term,X478 : term] : ((X476 = X477) | (((ap @ X478 @ X477)) != ((ap @ X475 @ X476)))) => ! [X479 : term,X480 : term,X481 : term,X482 : term] : ((((ap @ (sub @ X482 @ id) @ X480)) != ((ap @ (sub @ X479 @ id) @ X481))) | (X480 = X481))) <=> (hoasapinj2_lthm = $true)) & (hoasapinj1_gthm = $true) & (axassoc = $true) & ! [X483 : term] : ? [X484 : d_term] : (((d2term @ X484)) = X483) & (termmset_gthm = $true) & (! [X485 : (subst > term > subst > $o)] : ~ ! [X486 : (term > $o)] : ~ ! [X487 : term] : (((X485 @ id @ X487 @ id)) = ((X486 @ X487))) <=> (hoasinduction_lem0 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((axidl = $true) <=> ! [X488 : subst] : (((comp @ id @ X488)) = X488)) & ((! [X489 : term] : (((sub @ X489 @ id)) = X489) => (! [X490 : (subst > term > subst > $o),X491 : term] : (($true = ((X490 @ id @ (lam @ (sub @ X491 @ (push @ one @ sh))) @ id))) | ~ ! [X492 : (subst > term > term)] : (($true = ((X490 @ id @ (lam @ (X492 @ sh @ one)) @ id))) | ~ ! [X493 : subst,X494 : term,X495 : subst] : (((X492 @ (comp @ X495 @ X493) @ (sub @ X494 @ X493))) = ((sub @ (X492 @ X495 @ X494) @ X493))) | ~ ! [X496 : term] : (($true = ((X490 @ id @ (X492 @ id @ X496) @ id))) | ~ (((X490 @ id @ X496 @ id)) = $true))) | ~ ! [X497 : term] : (~ (((X490 @ id @ X497 @ id)) = $true) | (((X490 @ id @ (sub @ X491 @ (push @ X497 @ id)) @ id)) = $true))) => ! [X498 : (subst > term > subst > $o),X499 : term] : (~ ! [X500 : term] : (~ (((X498 @ id @ X500 @ id)) = $true) | (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) = $true)) | (((X498 @ id @ (lam @ X499) @ id)) = $true) | ~ ! [X501 : (subst > term > term)] : ((((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) = $true) | ~ ! [X502 : term] : (~ (((X498 @ id @ X502 @ id)) = $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) | ~ ! [X503 : subst,X504 : term,X505 : subst] : (((sub @ (X501 @ X503 @ X504) @ X505)) = ((X501 @ (comp @ X503 @ X505) @ (sub @ X504 @ X505)))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X506 : (subst > term > subst > $o),X507 : term] : (~ ! [X508 : term] : (~ (((X506 @ id @ X508 @ id)) = $true) | (((X506 @ id @ (sub @ X507 @ (push @ X508 @ id)) @ id)) = $true)) | ~ ! [X509 : (subst > term > term)] : (~ ! [X510 : term] : (~ (((X506 @ id @ X510 @ id)) = $true) | ($true = ((X506 @ id @ (X509 @ id @ X510) @ id)))) | ~ ! [X511 : term,X512 : subst,X513 : subst] : (((X509 @ (comp @ X512 @ X513) @ (sub @ X511 @ X513))) = ((sub @ (X509 @ X512 @ X511) @ X513))) | (((X506 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true)) | (((X506 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X514 : (term > $o),X515 : subst,X516 : term] : ~ ! [X517 : (term > $o)] : ~ ! [X518 : term] : (((X517 @ X518)) = ((X514 @ (sub @ X518 @ (push @ X516 @ X515)))))) & (hoaslamnotvar_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoasinduction_lem1_lthm = $true) & ((axvarid = $true) <=> ! [X521 : term] : (((sub @ X521 @ id)) = X521)) & ((hoasapinj2 = $true) <=> ! [X522 : term,X523 : term,X524 : term,X525 : term] : ((X522 = X523) | (((ap @ (sub @ X524 @ id) @ X523)) != ((ap @ (sub @ X525 @ id) @ X522))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X526 : (term > $o),X527 : term,X528 : term,X529 : (subst > term > subst > $o)] : (~ ! [X530 : term,X531 : term] : ((((X529 @ id @ (ap @ (sub @ X531 @ id) @ X530) @ id)) = $true) | ~ (((X529 @ id @ X531 @ id)) = $true) | ~ (((X529 @ id @ X530 @ id)) = $true)) | ~ (((X526 @ X527)) = $true) | (((X526 @ (ap @ X527 @ X528))) = $true) | ~ ! [X532 : subst,X533 : subst,X534 : term,X535 : subst] : (~ (((X529 @ X535 @ X534 @ (comp @ X533 @ X532))) = $true) | (((X529 @ (comp @ X535 @ X533) @ (sub @ X534 @ X533) @ X532)) = $true)) | ~ ! [X536 : subst,X537 : subst,X538 : term,X539 : subst] : (~ (((X529 @ (comp @ X539 @ X536) @ (sub @ X538 @ X536) @ X537)) = $true) | (((X529 @ X539 @ X538 @ (comp @ X536 @ X537))) = $true)) | ~ (((X526 @ X528)) = $true) | ~ ! [X540 : term] : (((X529 @ id @ X540 @ id)) = ((X526 @ X540))))) & (! [X541 : term] : ~ ! [X542 : (subst > term > term)] : ~ ! [X543 : term,X544 : subst] : (((X542 @ X544 @ X543)) = ((sub @ X541 @ (push @ X543 @ X544)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((laminj = $true) <=> ! [X545 : term,X546 : term] : ((((lam @ X546)) != ((lam @ X545))) | (X545 = X546))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X547 : (subst > term > subst > $o)] : ~ ! [X548 : (term > $o)] : ~ ! [X549 : term] : (((X547 @ id @ X549 @ id)) = ((X548 @ X549))))),
% 46.03/6.94 inference(fool_elimination,[],[f4])).
% 46.03/6.94 thf(f6,plain,(
% 46.03/6.94 ~ (hoasinduction_lem3v2 = ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X2 : subst,X3 : subst,X4 : subst,X5 : term] : ((X0 @ X3 @ X5 @ (comp @ X2 @ X4)) => (X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) => (! [X6 : subst,X7 : term,X8 : subst,X9 : subst] : ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8) => (X0 @ X9 @ X7 @ (comp @ X6 @ X8))) => (! [X10 : (subst > term > term)] : (! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) => (! [X14 : term] : ((X0 @ id @ X14 @ id) => (X0 @ id @ (X10 @ id @ X14) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X15 : subst, X16 : term] : ((X10 @ X15 @ X16)))) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X17 : term] : (! [X18 : term] : ((X1 @ X18) => (X1 @ (sub @ X17 @ (push @ X18 @ id)))) => (X1 @ (lam @ X17))))))))),
% 46.03/6.94 inference(rectify,[],[f3])).
% 46.03/6.94 thf(f7,plain,(
% 46.03/6.94 ~((hoasinduction_lem3v2 = $true) <=> ! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X5 : term,X2 : subst,X3 : subst,X4 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) => (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) = $true)) => (! [X6 : subst,X8 : subst,X9 : subst,X7 : term] : (($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8))) => (((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) = $true)) => (! [X10 : (subst > term > term)] : (! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) => (! [X14 : term] : ((((X0 @ id @ X14 @ id)) = $true) => (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) = $true))) => ((((hoasinduction_p_and_p_prime @ X0 @ X1)) = $true) => ! [X17 : term] : (! [X18 : term] : ((((X1 @ X18)) = $true) => (((X1 @ (sub @ X17 @ (push @ X18 @ id)))) = $true)) => (((X1 @ (lam @ X17))) = $true)))))))),
% 46.03/6.94 inference(fool_elimination,[],[f6])).
% 46.03/6.94 thf(f8,plain,(
% 46.03/6.94 ~ (ulamvar1 = $true) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) <=> ! [X0 : term,X1 : (subst > term > subst > $o)] : (~ ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) = $true) | ~ (((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) = $true)) | ~ ! [X6 : (subst > term > term)] : (~ ! [X7 : term] : ((((X1 @ id @ (X6 @ id @ X7) @ id)) = $true) | ~ (((X1 @ id @ X7 @ id)) = $true)) | ~ ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) | (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true)) | ~ ! [X11 : term] : (~ (((X1 @ id @ X11 @ id)) = $true) | (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) = $true)) | ~ ! [X12 : term,X13 : subst,X14 : subst,X15 : subst] : ((((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) = $true) | ~ (((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) = $true)) | (((X1 @ id @ (lam @ X0) @ id)) = $true))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X16 : term] : ~ ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh))))) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & (! [X20 : term,X21 : (subst > term > subst > $o)] : ((((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X22 : term] : (~ (((X21 @ id @ X22 @ id)) = $true) | (((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) = $true)) | ~ ! [X23 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | ~ (((X21 @ id @ X24 @ id)) = $true)) | ~ ! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))))) <=> (hoasinduction_lem3aa = $true)) & ((! [X28 : subst] : (((comp @ id @ X28)) = X28) => (! [X29 : subst] : (((comp @ X29 @ id)) = X29) => (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)))) <=> (substmonoid_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X32 : (subst > term > subst > $o),X33 : term,X34 : term] : (~ ! [X35 : term,X36 : term] : (~ (((X32 @ id @ X36 @ id)) = $true) | ~ (((X32 @ id @ X35 @ id)) = $true) | (((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) = $true)) | ~ (((X32 @ id @ X33 @ id)) = $true) | ~ ! [X37 : term,X38 : subst,X39 : subst,X40 : subst] : (~ (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) = $true) | ($true = ((X32 @ X38 @ X37 @ (comp @ X39 @ X40))))) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | ~ ! [X41 : term,X42 : subst,X43 : subst,X44 : subst] : ((((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) = $true) | ~ (((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) = $true)) | ~ (((X32 @ id @ X34 @ id)) = $true))) & (hoaslamnotap_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X45 : term,X46 : (subst > term > term),X47 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ~ ! [X50 : subst,X49 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))))) & ((hoasapinj1_lthm = $true) <=> (! [X51 : term] : (((sub @ X51 @ id)) = X51) => (! [X55 : term,X54 : term,X53 : term,X52 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))) => ! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (substmonoid_gthm = $true) & ~ (lamnotap = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X60 : (subst > term > subst > $o)] : ~ ! [X61 : (term > $o)] : ~ ! [X62 : term] : (((X60 @ id @ X62 @ id)) = ((X61 @ X62))) => (! [X63 : term,X64 : (term > $o)] : (~ ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ~ ! [X66 : term] : ((((X64 @ (sub @ X65 @ (push @ X66 @ id)))) = $true) | ~ (((X64 @ X66)) = $true))) | (((X64 @ X63)) = $true) | ~ ! [X67 : term,X68 : term] : (~ (((X64 @ X68)) = $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | ~ (((X64 @ X67)) = $true)) | ~ ! [X69 : term] : (~ (((var @ X69)) = $true) | (((X64 @ X69)) = $true))) => (! [X70 : term] : (((sub @ X70 @ id)) = X70) => (! [X71 : (subst > term > subst > $o),X72 : term,X73 : (term > $o)] : ((((X73 @ (lam @ X72))) = $true) | ~ ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) | ~ ! [X75 : term] : (~ (((X73 @ X75)) = $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) | ~ ! [X76 : (subst > term > term)] : (~ ! [X79 : term,X78 : subst,X77 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) = ((sub @ (X76 @ X78 @ X79) @ X77))) | (((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ~ ! [X80 : term] : (($true = ((X71 @ id @ (X76 @ id @ X80) @ id))) | ~ (((X71 @ id @ X80 @ id)) = $true)))) => ! [X81 : term,X82 : (subst > term > subst > $o)] : (~ ! [X83 : term,X84 : term] : (~ (((X82 @ id @ X84 @ id)) = $true) | ~ (((X82 @ id @ X83 @ id)) = $true) | (((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) = $true)) | ~ ! [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true) | ~ ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | ~ (((X82 @ id @ X86 @ id)) = $true)) | ~ ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88))))) | (((X82 @ id @ X81 @ id)) = $true))))))) & ((pushprop_lem1_lthm = $true) <=> (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : term,X95 : (term > $o),X96 : subst,X97 : term,X98 : (term > $o)] : (~ (((X98 @ X97)) = $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true))))) & (((d2subst @ d_id)) = id) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (pushprop_lem3v2 = $true) & (pushprop_lthm = $true) & (axclos = $true) & ((! [X99 : term] : (((sub @ X99 @ id)) = X99) => (! [X100 : term,X101 : subst,X102 : (term > $o)] : (~ ! [X103 : term,X104 : term] : (~ (((X102 @ X104)) = $true) | ~ (((X102 @ X103)) = $true) | (((X102 @ (ap @ X103 @ X104))) = $true)) | (((X102 @ (sub @ X100 @ X101))) = $true) | ~ ! [X105 : term] : ((((X102 @ (sub @ X105 @ X101))) = $true) | ~ (((var @ X105)) = $true)) | ~ ! [X106 : term] : ((((X102 @ (lam @ X106))) = $true) | ~ ! [X107 : term] : ((((X102 @ (sub @ X106 @ (push @ X107 @ id)))) = $true) | ~ (((X102 @ X107)) = $true)))) => ! [X108 : (term > $o),X109 : term] : ((((X108 @ X109)) = $true) | ~ ! [X110 : term] : ((((X108 @ (lam @ X110))) = $true) | ~ ! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | ~ (((X108 @ X111)) = $true))) | ~ ! [X112 : term,X113 : term] : (~ (((X108 @ X112)) = $true) | (((X108 @ (ap @ X113 @ X112))) = $true) | ~ (((X108 @ X113)) = $true)) | ~ ! [X114 : term] : (~ (((var @ X114)) = $true) | (((X108 @ X114)) = $true))))) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X115 : (term > $o),X116 : (subst > term > subst > $o),X117 : term] : (~ ! [X118 : term] : (~ (((X115 @ X118)) = $true) | (((X115 @ (sub @ X117 @ (push @ X118 @ id)))) = $true)) | (((X115 @ (lam @ X117))) = $true) | ~ ! [X119 : term] : (((X116 @ id @ X119 @ id)) = ((X115 @ X119))) | ~ ! [X120 : (subst > term > term)] : (~ ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | ~ (((X116 @ id @ X121 @ id)) = $true)) | ~ ! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) | (((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true)))) & (! [X125 : (term > $o),X126 : term] : (~ ! [X127 : term,X128 : term] : (~ (((X125 @ X128)) = $true) | (((X125 @ (ap @ X128 @ X127))) = $true) | ~ (((X125 @ X127)) = $true)) | ~ ! [X129 : term] : (~ (((var @ X129)) = $true) | ($true = ((X125 @ X129)))) | (((X125 @ X126)) = $true) | ~ ! [X130 : term] : ((((X125 @ (lam @ X130))) = $true) | ~ (((X125 @ X130)) = $true))) <=> (induction = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) = X133) => (! [X135 : term,X136 : term] : ((((lam @ X135)) != ((lam @ X136))) | (X135 = X136)) => ! [X138 : (subst > term > term),X140 : subst,X137 : (subst > term > term),X139 : term] : (~ ! [X141 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) = ((sub @ (X138 @ X143 @ X142) @ X141))) | ~ ! [X144 : term,X146 : subst,X145 : subst] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) = ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (! [X147 : (term > $o),X148 : term] : (~ ! [X149 : term,X150 : term] : (~ (((X147 @ X149)) = $true) | (((X147 @ (ap @ X149 @ X150))) = $true) | ~ (((X147 @ X150)) = $true)) | ~ ! [X151 : term] : (~ ! [X152 : term] : (~ (((X147 @ X152)) = $true) | (((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true)) | (((X147 @ (lam @ X151))) = $true)) | ($true = ((X147 @ X148))) | ~ ! [X153 : term] : (~ (((var @ X153)) = $true) | (((X147 @ X153)) = $true))) <=> (induction2 = $true)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & (((d2subst @ d_id)) = sh) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & ! [X156 : d_subst] : (d_id = X156) & (hoasapnotvar_gthm = $true) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & ((! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (term > $o),X162 : (subst > term > subst > $o)] : ((((X161 @ (lam @ X160))) = $true) | ~ ! [X163 : subst,X164 : subst,X165 : term,X166 : subst] : ((((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) = $true) | ~ (((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) = $true)) | ~ ! [X167 : subst,X168 : subst,X169 : subst,X170 : term] : ((((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) = $true) | ~ ($true = ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167)))) | ~ ! [X171 : term] : (((X162 @ id @ X171 @ id)) = ((X161 @ X171))) | ~ ! [X172 : (subst > term > term)] : ((((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) = $true) | ~ ! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) | ~ ! [X176 : term] : (~ (((X162 @ id @ X176 @ id)) = $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true))) | ~ ! [X177 : term] : (~ (((X161 @ X177)) = $true) | (((X161 @ (sub @ X160 @ (push @ X177 @ id)))) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (axapp = $true) & ((! [X178 : term] : (((sub @ X178 @ id)) = X178) => (! [X179 : term,X180 : (subst > term > subst > $o)] : (($true = ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id))) | ~ ! [X181 : term] : (~ (((X180 @ id @ X181 @ id)) = $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) | ~ ! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X183 : term,X185 : subst,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) = ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ~ ! [X186 : term] : (($true = ((X180 @ id @ (X182 @ id @ X186) @ id))) | ~ (((X180 @ id @ X186 @ id)) = $true)))) => ! [X187 : (subst > term > subst > $o),X188 : term] : (~ ! [X189 : (subst > term > term)] : ((((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true) | ~ ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190)))) | ~ ! [X193 : term] : (~ (((X187 @ id @ X193 @ id)) = $true) | (((X187 @ id @ (X189 @ id @ X193) @ id)) = $true))) | ~ ! [X194 : subst,X195 : term,X196 : subst,X197 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) = $true) | ~ (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) = $true)) | ~ ! [X198 : term,X199 : subst,X200 : subst,X201 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) = $true) | ~ (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) = $true)) | ($true = ((X187 @ id @ (lam @ X188) @ id))) | ~ ! [X202 : term] : (~ (((X187 @ id @ X202 @ id)) = $true) | (((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) = $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (axmap = $true) & (hoaslamnotap_gthm = $true) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & ((! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) => ! [X209 : subst,X210 : (term > $o),X211 : (term > $o),X212 : term] : (~ (((X211 @ X212)) = $true) | ($true = ((X210 @ one))) | ~ ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209))))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (pushprop_lem2v2 = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X218 : term,X219 : (term > $o)] : (~ ! [X220 : term] : (~ (((var @ X220)) = $true) | (((X219 @ X220)) = $true)) | (((X219 @ X218)) = $true) | ~ ! [X221 : term] : (~ ! [X222 : term] : (~ (((X219 @ X222)) = $true) | (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) | (((X219 @ (lam @ X221))) = $true)) | ~ ! [X223 : term,X224 : term] : (($true = ((X219 @ (ap @ X223 @ X224)))) | ~ ($true = ((X219 @ X224))) | ~ (((X219 @ X223)) = $true))) => (! [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (~ (((X225 @ id @ X227 @ id)) = $true) | ~ (((X225 @ id @ X226 @ id)) = $true) | ~ ! [X228 : subst,X229 : subst,X230 : subst,X231 : term] : (~ (((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) = $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true)) | ~ ! [X232 : term,X233 : term] : (~ (((X225 @ id @ X233 @ id)) = $true) | ~ (((X225 @ id @ X232 @ id)) = $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)) | ~ ! [X234 : subst,X235 : subst,X236 : term,X237 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | ~ (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) = $true)) | (((X225 @ id @ (ap @ X226 @ X227) @ id)) = $true)) => (! [X238 : term,X239 : (subst > term > subst > $o)] : (~ ! [X240 : (subst > term > term)] : (~ ! [X241 : term] : ((((X239 @ id @ (X240 @ id @ X241) @ id)) = $true) | ~ (((X239 @ id @ X241 @ id)) = $true)) | ~ ! [X242 : subst,X244 : subst,X243 : term] : (((sub @ (X240 @ X242 @ X243) @ X244)) = ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)))) | ~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (~ ($true = ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true)) | (((X239 @ id @ (lam @ X238) @ id)) = $true) | ~ ! [X249 : term] : (($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id))) | ~ (((X239 @ id @ X249 @ id)) = $true)) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (~ (((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) = $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true))) => ! [X254 : (subst > term > subst > $o),X255 : term] : (~ ! [X256 : subst,X257 : subst,X258 : term,X259 : subst] : ((((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) = $true) | ~ (((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) = $true)) | ~ ! [X260 : (subst > term > term)] : (~ ! [X261 : term] : (~ (((X254 @ id @ X261 @ id)) = $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true)) | (((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) = $true) | ~ ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262)))) | (((X254 @ id @ X255 @ id)) = $true) | ~ ! [X265 : term] : (~ (((var @ (sub @ X265 @ id))) = $true) | (((X254 @ id @ X265 @ id)) = $true)) | ~ ! [X266 : term,X267 : term] : (~ (((X254 @ id @ X266 @ id)) = $true) | (((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) = $true) | ~ (((X254 @ id @ X267 @ id)) = $true)) | ~ ! [X268 : subst,X269 : subst,X270 : subst,X271 : term] : ((((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) = $true) | ~ (((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true))))))) & ((pushprop_lem1 = $true) <=> ! [X272 : (term > $o),X273 : term,X274 : subst,X275 : term,X276 : (term > $o)] : (~ (((X276 @ X273)) = $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true))) & (ulamvarsh = $true) & (induction2_gthm = $true) & (axabs = $true) & (! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term] : ((((X277 @ id @ X279 @ id)) = $true) | ~ (((var @ (sub @ X279 @ id))) = $true)) | ~ ! [X280 : (subst > term > term)] : (~ ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) | (((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X284 : term] : (($true = ((X277 @ id @ (X280 @ id @ X284) @ id))) | ~ (((X277 @ id @ X284 @ id)) = $true))) | ~ ! [X285 : subst,X286 : term,X287 : subst,X288 : subst] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) = $true) | ~ (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) = $true)) | (((X277 @ id @ X278 @ id)) = $true) | ~ ! [X289 : term,X290 : subst,X291 : subst,X292 : subst] : (~ ($true = ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290))) | (((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) = $true)) | ~ ! [X293 : term,X294 : term] : (~ (((X277 @ id @ X294 @ id)) = $true) | ~ (((X277 @ id @ X293 @ id)) = $true) | ($true = ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))))) <=> (hoasinduction = $true)) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : ~ ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X299 : (subst > term > subst > $o),X300 : term] : (~ ! [X301 : (subst > term > term)] : (~ ! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) | ~ ! [X305 : term] : (~ ($true = ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true)) | (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true)) | (((X299 @ id @ X300 @ id)) = $true) | ~ ! [X306 : term,X307 : term] : (~ (((X299 @ id @ X306 @ id)) = $true) | ($true = ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) | ~ (((X299 @ id @ X307 @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X308 : (subst > term > subst > $o),X309 : term] : (~ ! [X310 : term] : (~ (((X308 @ id @ X310 @ id)) = $true) | (((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) = $true)) | ~ ! [X311 : (subst > term > term),X312 : term] : ((((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) = $true) | ~ ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | ~ (((X308 @ id @ X313 @ id)) = $true)) | ~ ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | ~ ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319)))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & (ulamvarind = $true) & ((hoaslaminj = $true) <=> ! [X322 : subst,X321 : (subst > term > term),X323 : term,X320 : (subst > term > term)] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one)))) | ~ ! [X324 : term,X325 : subst,X326 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) = ((sub @ (X321 @ X326 @ X324) @ X325))) | ~ ! [X327 : subst,X328 : term,X329 : subst] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) = ((sub @ (X320 @ X329 @ X328) @ X327))))) & (hoasapinj2_gthm = $true) & ((induction2lem = $true) <=> ! [X330 : (term > $o),X331 : subst,X332 : term] : (~ ! [X333 : term,X334 : term] : (~ ($true = ((X330 @ X334))) | (((X330 @ (ap @ X333 @ X334))) = $true) | ~ (((X330 @ X333)) = $true)) | (((X330 @ (sub @ X332 @ X331))) = $true) | ~ ! [X335 : term] : ((((X330 @ (sub @ X335 @ X331))) = $true) | ~ (((var @ X335)) = $true)) | ~ ! [X336 : term] : (~ ! [X337 : term] : ((((X330 @ (sub @ X336 @ (push @ X337 @ id)))) = $true) | ~ ($true = ((X330 @ X337)))) | (((X330 @ (lam @ X336))) = $true)))) & (! [X338 : term,X339 : subst,X340 : (term > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem3b_gthm = $true) & (! [X344 : (subst > term > subst > $o),X345 : term] : ((((X344 @ id @ (lam @ X345) @ id)) = $true) | ~ ! [X346 : term] : (~ (((X344 @ id @ X346 @ id)) = $true) | (((X344 @ id @ (sub @ X345 @ (push @ X346 @ id)) @ id)) = $true)) | ~ ! [X347 : (subst > term > term)] : (~ ! [X348 : term] : ((((X344 @ id @ (X347 @ id @ X348) @ id)) = $true) | ~ (((X344 @ id @ X348 @ id)) = $true)) | ~ ! [X350 : subst,X351 : subst,X349 : term] : (((X347 @ (comp @ X351 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X347 @ X351 @ X349) @ X350))) | (((X344 @ id @ (lam @ (X347 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem2_lthm = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & ((apinj1 = $true) <=> ! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & ((! [X358 : term] : (((sub @ X358 @ id)) = X358) => ! [X359 : term] : (((sub @ X359 @ id)) = X359)) <=> (termmset_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (induction2lem_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((shinj = $true) <=> ! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh))))) & ! [X363 : d_term,X362 : d_term] : ((((d2term @ X362)) = ((d2term @ X363))) => (X362 = X363)) & (! [X364 : (term > $o),X365 : (subst > term > subst > $o),X366 : term] : (~ ! [X367 : subst,X368 : term,X369 : subst,X370 : subst] : (~ (((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) = $true) | (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) = $true)) | (((X364 @ (lam @ X366))) = $true) | ~ ! [X371 : term] : (((X364 @ X371)) = ((X365 @ id @ X371 @ id))) | ~ ! [X372 : term] : (~ (((X364 @ X372)) = $true) | (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) = $true)) | ~ ! [X373 : subst,X374 : subst,X375 : term,X376 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) = $true) | ~ (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) = $true)) | ~ ! [X377 : (subst > term > term)] : ((((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X378 : term] : ((((X365 @ id @ (X377 @ id @ X378) @ id)) = $true) | ~ (((X365 @ id @ X378 @ id)) = $true)) | ~ ! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X382 : term] : ~ ! [X383 : (subst > term > term)] : (((X383 @ sh @ one)) != ((sub @ X382 @ (push @ one @ sh))))) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X384 : term] : ~ ! [X385 : (subst > term > term)] : ~ ! [X386 : subst,X387 : term] : (((X385 @ X386 @ X387)) = ((sub @ X384 @ (push @ X387 @ X386)))) => (! [X388 : term] : (((sub @ X388 @ id)) = X388) => ! [X389 : (subst > term > subst > $o),X390 : (term > $o),X391 : term] : (~ ! [X392 : term] : ((((X390 @ (sub @ X391 @ (push @ X392 @ id)))) = $true) | ~ (((X390 @ X392)) = $true)) | ~ ! [X393 : term] : (((X389 @ id @ X393 @ id)) = ((X390 @ X393))) | ~ ! [X394 : (subst > term > term)] : (~ ! [X396 : term,X397 : subst,X395 : subst] : (((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395))) = ((sub @ (X394 @ X397 @ X396) @ X395))) | (((X389 @ id @ (lam @ (X394 @ sh @ one)) @ id)) = $true) | ~ ! [X398 : term] : (~ (((X389 @ id @ X398 @ id)) = $true) | (((X389 @ id @ (X394 @ id @ X398) @ id)) = $true))) | (((X390 @ (lam @ X391))) = $true))))) & (axvarshift = $true) & (pushprop_lem3v2_lthm = $true) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) <=> (axidr = $true)) & ((! [X400 : subst,X401 : term] : (((sub @ one @ (push @ X401 @ X400))) = X401) => (! [X402 : subst,X403 : term] : (((comp @ sh @ (push @ X403 @ X402))) = X402) => (! [X404 : subst] : (((comp @ X404 @ id)) = X404) => (! [X405 : (term > $o),X406 : term] : (~ ! [X407 : term,X408 : term] : (~ (((X405 @ X408)) = $true) | ~ (((X405 @ X407)) = $true) | (((X405 @ (ap @ X408 @ X407))) = $true)) | ~ ! [X409 : term] : ((((X405 @ X409)) = $true) | ~ (((var @ X409)) = $true)) | ~ ! [X410 : term] : (~ (((X405 @ X410)) = $true) | (((X405 @ (lam @ X410))) = $true)) | (((X405 @ X406)) = $true)) => ! [X411 : subst,X412 : (term > $o),X413 : term] : (~ ! [X414 : term,X415 : term] : ((((X412 @ (ap @ X414 @ X415))) = $true) | ~ ($true = ((X412 @ X414))) | ~ ($true = ((X412 @ X415)))) | ~ ! [X416 : term] : (~ ! [X417 : term] : ((((X412 @ (sub @ X416 @ (push @ X417 @ id)))) = $true) | ~ ($true = ((X412 @ X417)))) | (((X412 @ (lam @ X416))) = $true)) | ~ ! [X418 : term] : ((((X412 @ (sub @ X418 @ X411))) = $true) | ~ (((var @ X418)) = $true)) | (((X412 @ (sub @ X413 @ X411))) = $true)))))) <=> (induction2lem_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X419 : (term > $o),X420 : subst,X421 : term,X422 : (term > $o)] : (~ ! [X423 : term] : (((X422 @ X423)) = ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))) | ~ (((X419 @ X421)) = $true) | (((X422 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) = ((d2subst @ X425))) => (X424 = X425)) & ((axshiftcons = $true) <=> ! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427)) & (hoasinduction_lem3a_gthm = $true) & ((! [X428 : (subst > term > subst > $o)] : ~ ! [X429 : (term > $o)] : ~ ! [X430 : term] : (((X429 @ X430)) = ((X428 @ id @ X430 @ id))) => (! [X431 : term,X432 : (term > $o)] : (~ ! [X433 : term] : ((((X432 @ (lam @ X433))) = $true) | ~ ! [X434 : term] : (~ (((X432 @ X434)) = $true) | (((X432 @ (sub @ X433 @ (push @ X434 @ id)))) = $true))) | ~ ! [X435 : term,X436 : term] : (~ (((X432 @ X435)) = $true) | ~ (((X432 @ X436)) = $true) | (((X432 @ (ap @ X436 @ X435))) = $true)) | ~ ! [X437 : term] : ((((X432 @ X437)) = $true) | ~ (((var @ X437)) = $true)) | (((X432 @ X431)) = $true)) => (! [X438 : term] : (((sub @ X438 @ id)) = X438) => (! [X439 : (term > $o),X440 : term,X441 : (subst > term > subst > $o)] : (~ ! [X442 : term] : ((((X439 @ (sub @ X440 @ (push @ X442 @ id)))) = $true) | ~ (((X439 @ X442)) = $true)) | ~ ! [X443 : (subst > term > term)] : ((((X441 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true) | ~ ! [X444 : term] : (~ ($true = ((X441 @ id @ X444 @ id))) | (((X441 @ id @ (X443 @ id @ X444) @ id)) = $true)) | ~ ! [X445 : subst,X447 : term,X446 : subst] : (((X443 @ (comp @ X445 @ X446) @ (sub @ X447 @ X446))) = ((sub @ (X443 @ X445 @ X447) @ X446)))) | (((X439 @ (lam @ X440))) = $true) | ~ ! [X448 : term] : (((X439 @ X448)) = ((X441 @ id @ X448 @ id)))) => ! [X449 : term,X450 : (subst > term > subst > $o)] : (~ ! [X451 : subst,X452 : subst,X453 : subst,X454 : term] : ((((X450 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452) @ X451)) = $true) | ~ (((X450 @ X453 @ X454 @ (comp @ X452 @ X451))) = $true)) | ~ ! [X455 : term] : (~ (((var @ (sub @ X455 @ id))) = $true) | (((X450 @ id @ X455 @ id)) = $true)) | ~ ! [X456 : term,X457 : subst,X458 : subst,X459 : subst] : ((((X450 @ X458 @ X456 @ (comp @ X459 @ X457))) = $true) | ~ (((X450 @ (comp @ X458 @ X459) @ (sub @ X456 @ X459) @ X457)) = $true)) | ~ ! [X460 : (subst > term > term)] : ((((X450 @ id @ (lam @ (X460 @ sh @ one)) @ id)) = $true) | ~ ! [X461 : term,X462 : subst,X463 : subst] : (((X460 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))) = ((sub @ (X460 @ X462 @ X461) @ X463))) | ~ ! [X464 : term] : (~ (((X450 @ id @ X464 @ id)) = $true) | (((X450 @ id @ (X460 @ id @ X464) @ id)) = $true))) | ~ ! [X465 : term,X466 : term] : ((((X450 @ id @ (ap @ (sub @ X465 @ id) @ X466) @ id)) = $true) | ~ (((X450 @ id @ X465 @ id)) = $true) | ~ (((X450 @ id @ X466 @ id)) = $true)) | (((X450 @ id @ X449 @ id)) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasapinj2_lthm = $true) <=> (! [X470 : term,X469 : term,X468 : term,X467 : term] : ((((ap @ X467 @ X468)) != ((ap @ X470 @ X469))) | (X468 = X469)) => ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))))) & (hoasapinj1_gthm = $true) & (axassoc = $true) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (termmset_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X477 : (subst > term > subst > $o)] : ~ ! [X478 : (term > $o)] : ~ ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) <=> (axidl = $true)) & ((! [X481 : term] : (((sub @ X481 @ id)) = X481) => (! [X482 : (subst > term > subst > $o),X483 : term] : ((((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X484 : (subst > term > term)] : ((((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ~ ! [X485 : subst,X486 : term,X487 : subst] : (((sub @ (X484 @ X487 @ X486) @ X485)) = ((X484 @ (comp @ X487 @ X485) @ (sub @ X486 @ X485)))) | ~ ! [X488 : term] : ((((X482 @ id @ (X484 @ id @ X488) @ id)) = $true) | ~ (((X482 @ id @ X488 @ id)) = $true))) | ~ ! [X489 : term] : (~ (((X482 @ id @ X489 @ id)) = $true) | (((X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)) = $true))) => ! [X490 : (subst > term > subst > $o),X491 : term] : (~ ! [X492 : term] : (~ (((X490 @ id @ X492 @ id)) = $true) | ($true = ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id)))) | (((X490 @ id @ (lam @ X491) @ id)) = $true) | ~ ! [X493 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) = $true) | ~ ! [X494 : term] : (~ ($true = ((X490 @ id @ X494 @ id))) | (((X490 @ id @ (X493 @ id @ X494) @ id)) = $true)) | ~ ! [X495 : subst,X496 : term,X497 : subst] : (((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X493 @ X495 @ X496) @ X497))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X498 : (subst > term > subst > $o),X499 : term] : (~ ! [X500 : term] : (~ (((X498 @ id @ X500 @ id)) = $true) | (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) = $true)) | ~ ! [X501 : (subst > term > term)] : (~ ! [X502 : term] : (~ (((X498 @ id @ X502 @ id)) = $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) | ~ ! [X504 : subst,X503 : term,X505 : subst] : (((sub @ (X501 @ X504 @ X503) @ X505)) = ((X501 @ (comp @ X504 @ X505) @ (sub @ X503 @ X505)))) | (((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) = $true)) | (((X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X508 : term,X507 : subst,X506 : (term > $o)] : ~ ! [X509 : (term > $o)] : ~ ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510)))) & (hoaslamnotvar_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoasinduction_lem1_lthm = $true) & ((axvarid = $true) <=> ! [X511 : term] : (((sub @ X511 @ id)) = X511)) & ((hoasapinj2 = $true) <=> ! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X516 : (term > $o),X517 : term,X518 : term,X519 : (subst > term > subst > $o)] : (~ ! [X520 : term,X521 : term] : ((((X519 @ id @ (ap @ (sub @ X521 @ id) @ X520) @ id)) = $true) | ~ ($true = ((X519 @ id @ X521 @ id))) | ~ (((X519 @ id @ X520 @ id)) = $true)) | ~ (((X516 @ X517)) = $true) | ($true = ((X516 @ (ap @ X517 @ X518)))) | ~ ! [X522 : subst,X523 : subst,X524 : term,X525 : subst] : (~ (((X519 @ X525 @ X524 @ (comp @ X523 @ X522))) = $true) | (((X519 @ (comp @ X525 @ X523) @ (sub @ X524 @ X523) @ X522)) = $true)) | ~ ! [X526 : subst,X527 : subst,X528 : term,X529 : subst] : (~ (((X519 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)) = $true) | (((X519 @ X529 @ X528 @ (comp @ X526 @ X527))) = $true)) | ~ (((X516 @ X518)) = $true) | ~ ! [X530 : term] : (((X516 @ X530)) = ((X519 @ id @ X530 @ id))))) & (! [X531 : term] : ~ ! [X532 : (subst > term > term)] : ~ ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((laminj = $true) <=> ! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536))) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem1_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X537 : (subst > term > subst > $o)] : ~ ! [X538 : (term > $o)] : ~ ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id))))),
% 46.03/6.94 inference(rectify,[],[f5])).
% 46.03/6.94 thf(f9,plain,(
% 46.03/6.94 ((hoasinduction_no_psi_cond = $true) <=> ! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ~ ! [X301 : (subst > term > term)] : ((((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true) | ~ ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true)) | ~ ! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303))))) | ~ ! [X306 : term,X307 : term] : (($true = ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) | (((X299 @ id @ X306 @ id)) != $true) | (((X299 @ id @ X307 @ id)) != $true)))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X309 : term,X308 : (subst > term > subst > $o)] : (~ ! [X310 : term] : ((((X308 @ id @ X310 @ id)) != $true) | (((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) = $true)) | ~ ! [X311 : (subst > term > term),X312 : term] : (~ ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) | (((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) = $true) | ~ ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | (((X308 @ id @ X313 @ id)) != $true)) | ~ ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319)))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))))) & (pushprop_lem2v2_lthm = $true) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & (axabs = $true) & ((laminj = $true) <=> ! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536))) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X382 : term] : ~ ! [X383 : (subst > term > term)] : (((X383 @ sh @ one)) != ((sub @ X382 @ (push @ one @ sh))))) & (! [X344 : (subst > term > subst > $o),X345 : term] : (~ ! [X347 : (subst > term > term)] : (~ ! [X348 : term] : ((((X344 @ id @ X348 @ id)) != $true) | (((X344 @ id @ (X347 @ id @ X348) @ id)) = $true)) | ~ ! [X350 : subst,X351 : subst,X349 : term] : (((X347 @ (comp @ X351 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X347 @ X351 @ X349) @ X350))) | (((X344 @ id @ (lam @ (X347 @ sh @ one)) @ id)) = $true)) | (((X344 @ id @ (lam @ X345) @ id)) = $true) | ~ ! [X346 : term] : ((((X344 @ id @ (sub @ X345 @ (push @ X346 @ id)) @ id)) = $true) | (((X344 @ id @ X346 @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) = X133) => (! [X135 : term,X136 : term] : ((((lam @ X135)) != ((lam @ X136))) | (X135 = X136)) => ! [X138 : (subst > term > term),X140 : subst,X137 : (subst > term > term),X139 : term] : (~ ! [X141 : subst,X142 : term,X143 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) = ((sub @ (X138 @ X143 @ X142) @ X141))) | ~ ! [X144 : term,X146 : subst,X145 : subst] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) = ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & ((axshiftcons = $true) <=> ! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427)) & ((hoasinduction_lthm = $true) <=> (! [X219 : (term > $o),X218 : term] : ((((X219 @ X218)) = $true) | ~ ! [X221 : term] : (~ ! [X222 : term] : ((((X219 @ (sub @ X221 @ (push @ X222 @ id)))) = $true) | (((X219 @ X222)) != $true)) | (((X219 @ (lam @ X221))) = $true)) | ~ ! [X223 : term,X224 : term] : ((((X219 @ X223)) != $true) | ($true != ((X219 @ X224))) | ($true = ((X219 @ (ap @ X223 @ X224))))) | ~ ! [X220 : term] : ((((X219 @ X220)) = $true) | (((var @ X220)) != $true))) => (! [X225 : (subst > term > subst > $o),X227 : term,X226 : term] : (~ ! [X236 : term,X234 : subst,X237 : subst,X235 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) != $true)) | (((X225 @ id @ (ap @ X226 @ X227) @ id)) = $true) | ~ ! [X233 : term,X232 : term] : ((((X225 @ id @ X232 @ id)) != $true) | (((X225 @ id @ X233 @ id)) != $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)) | (((X225 @ id @ X227 @ id)) != $true) | (((X225 @ id @ X226 @ id)) != $true) | ~ ! [X229 : subst,X230 : subst,X228 : subst,X231 : term] : ((((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) != $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true))) => (! [X239 : (subst > term > subst > $o),X238 : term] : (~ ! [X249 : term] : ((((X239 @ id @ X249 @ id)) != $true) | ($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id)))) | ~ ! [X253 : subst,X252 : subst,X250 : subst,X251 : term] : ((((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) != $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true)) | (((X239 @ id @ (lam @ X238) @ id)) = $true) | ~ ! [X240 : (subst > term > term)] : (($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id))) | ~ ! [X242 : subst,X244 : subst,X243 : term] : (((sub @ (X240 @ X242 @ X243) @ X244)) = ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ~ ! [X241 : term] : ((((X239 @ id @ X241 @ id)) != $true) | (((X239 @ id @ (X240 @ id @ X241) @ id)) = $true))) | ~ ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (($true != ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true))) => ! [X254 : (subst > term > subst > $o),X255 : term] : (~ ! [X258 : term,X257 : subst,X259 : subst,X256 : subst] : ((((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) != $true) | (((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) = $true)) | ~ ! [X265 : term] : ((((var @ (sub @ X265 @ id))) != $true) | (((X254 @ id @ X265 @ id)) = $true)) | (((X254 @ id @ X255 @ id)) = $true) | ~ ! [X260 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) = $true) | ~ ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262))) | ~ ! [X261 : term] : ((((X254 @ id @ X261 @ id)) != $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true))) | ~ ! [X268 : subst,X269 : subst,X271 : term,X270 : subst] : ((((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) != $true) | (((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) = $true)) | ~ ! [X266 : term,X267 : term] : ((((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) = $true) | (((X254 @ id @ X266 @ id)) != $true) | (((X254 @ id @ X267 @ id)) != $true))))))) & ((! [X28 : subst] : (((comp @ id @ X28)) = X28) => (! [X29 : subst] : (((comp @ X29 @ id)) = X29) => (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)))) <=> (substmonoid_lthm = $true)) & ! [X363 : d_term,X362 : d_term] : ((((d2term @ X362)) = ((d2term @ X363))) => (X362 = X363)) & ((hoaslamnotap = $true) <=> ! [X45 : term,X46 : (subst > term > term),X47 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ~ ! [X50 : subst,X49 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))))) & ((hoaslaminj = $true) <=> ! [X322 : subst,X321 : (subst > term > term),X323 : term,X320 : (subst > term > term)] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one)))) | ~ ! [X324 : term,X325 : subst,X326 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) = ((sub @ (X321 @ X326 @ X324) @ X325))) | ~ ! [X327 : subst,X328 : term,X329 : subst] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) = ((sub @ (X320 @ X329 @ X328) @ X327))))) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((induction2lem = $true) <=> ! [X331 : subst,X330 : (term > $o),X332 : term] : (~ ! [X333 : term,X334 : term] : ((((X330 @ X333)) != $true) | ($true != ((X330 @ X334))) | (((X330 @ (ap @ X333 @ X334))) = $true)) | ~ ! [X336 : term] : (~ ! [X337 : term] : ((((X330 @ (sub @ X336 @ (push @ X337 @ id)))) = $true) | ($true != ((X330 @ X337)))) | (((X330 @ (lam @ X336))) = $true)) | ~ ! [X335 : term] : ((((X330 @ (sub @ X335 @ X331))) = $true) | (((var @ X335)) != $true)) | (((X330 @ (sub @ X332 @ X331))) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) <=> ! [X20 : term,X21 : (subst > term > subst > $o)] : (~ ! [X23 : (subst > term > term)] : (~ ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) | (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25)))) | ~ ! [X22 : term] : ((((X21 @ id @ X22 @ id)) != $true) | (((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) = $true)) | (((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true))) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (pushprop_lem1v2_gthm = $true) & ((induction2 = $true) <=> ! [X147 : (term > $o),X148 : term] : (~ ! [X150 : term,X149 : term] : ((((X147 @ X149)) != $true) | (((X147 @ (ap @ X149 @ X150))) = $true) | (((X147 @ X150)) != $true)) | ~ ! [X151 : term] : (~ ! [X152 : term] : ((((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true) | (((X147 @ X152)) != $true)) | (((X147 @ (lam @ X151))) = $true)) | ($true = ((X147 @ X148))) | ~ ! [X153 : term] : ((((X147 @ X153)) = $true) | (((var @ X153)) != $true)))) & ((apinj1 = $true) <=> ! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356))))) & (hoasinduction_lem2v2_gthm = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & ((pushprop_lem1v2_lthm = $true) <=> (! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) => ! [X211 : (term > $o),X209 : subst,X210 : (term > $o),X212 : term] : ((((X211 @ X212)) != $true) | ($true = ((X210 @ one))) | ~ ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) <=> (axidr = $true)) & (pushprop_lthm_orig = $true) & (lamnotap != $true) & ((hoasapinj2 = $true) <=> ! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512))))) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem3v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslamnotvar_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X470 : term,X469 : term,X468 : term,X467 : term] : ((((ap @ X467 @ X468)) != ((ap @ X470 @ X469))) | (X468 = X469)) => ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))))) & ((induction = $true) <=> ! [X125 : (term > $o),X126 : term] : (~ ! [X127 : term,X128 : term] : ((((X125 @ X127)) != $true) | (((X125 @ X128)) != $true) | (((X125 @ (ap @ X128 @ X127))) = $true)) | ~ ! [X130 : term] : ((((X125 @ (lam @ X130))) = $true) | (((X125 @ X130)) != $true)) | ~ ! [X129 : term] : ((((var @ X129)) != $true) | ($true = ((X125 @ X129)))) | (((X125 @ X126)) = $true))) & (! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) <=> (pushprop_lem1 = $true)) & ((! [X99 : term] : (((sub @ X99 @ id)) = X99) => (! [X100 : term,X101 : subst,X102 : (term > $o)] : (~ ! [X105 : term] : ((((var @ X105)) != $true) | (((X102 @ (sub @ X105 @ X101))) = $true)) | ~ ! [X106 : term] : ((((X102 @ (lam @ X106))) = $true) | ~ ! [X107 : term] : ((((X102 @ X107)) != $true) | (((X102 @ (sub @ X106 @ (push @ X107 @ id)))) = $true))) | ~ ! [X104 : term,X103 : term] : ((((X102 @ X104)) != $true) | (((X102 @ (ap @ X103 @ X104))) = $true) | (((X102 @ X103)) != $true)) | (((X102 @ (sub @ X100 @ X101))) = $true)) => ! [X108 : (term > $o),X109 : term] : (~ ! [X114 : term] : ((((X108 @ X114)) = $true) | (((var @ X114)) != $true)) | ~ ! [X110 : term] : ((((X108 @ (lam @ X110))) = $true) | ~ ! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | (((X108 @ X111)) != $true))) | ~ ! [X112 : term,X113 : term] : ((((X108 @ X113)) != $true) | (((X108 @ X112)) != $true) | (((X108 @ (ap @ X113 @ X112))) = $true)) | (((X108 @ X109)) = $true)))) <=> (induction2_lthm = $true)) & (hoasapnotvar_lthm = $true) & (! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X280 : (subst > term > term)] : ((((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X284 : term] : ((((X277 @ id @ X284 @ id)) != $true) | ($true = ((X277 @ id @ (X280 @ id @ X284) @ id)))) | ~ ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282)))) | ~ ! [X291 : subst,X290 : subst,X292 : subst,X289 : term] : ((((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) = $true) | ($true != ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290)))) | ~ ! [X293 : term,X294 : term] : (($true = ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id))) | (((X277 @ id @ X294 @ id)) != $true) | (((X277 @ id @ X293 @ id)) != $true)) | ~ ! [X279 : term] : ((((var @ (sub @ X279 @ id))) != $true) | (((X277 @ id @ X279 @ id)) = $true)) | ~ ! [X287 : subst,X288 : subst,X285 : subst,X286 : term] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) = $true) | (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) != $true)) | (((X277 @ id @ X278 @ id)) = $true)) <=> (hoasinduction = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X60 : (subst > term > subst > $o)] : ~ ! [X61 : (term > $o)] : ~ ! [X62 : term] : (((X60 @ id @ X62 @ id)) = ((X61 @ X62))) => (! [X63 : term,X64 : (term > $o)] : (~ ! [X68 : term,X67 : term] : ((((X64 @ X68)) != $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | (((X64 @ X67)) != $true)) | ~ ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ~ ! [X66 : term] : ((((X64 @ X66)) != $true) | (((X64 @ (sub @ X65 @ (push @ X66 @ id)))) = $true))) | ~ ! [X69 : term] : ((((X64 @ X69)) = $true) | (((var @ X69)) != $true)) | (((X64 @ X63)) = $true)) => (! [X70 : term] : (((sub @ X70 @ id)) = X70) => (! [X72 : term,X73 : (term > $o),X71 : (subst > term > subst > $o)] : ((((X73 @ (lam @ X72))) = $true) | ~ ! [X75 : term] : ((((X73 @ X75)) != $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) | ~ ! [X76 : (subst > term > term)] : ((((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true) | ~ ! [X79 : term,X78 : subst,X77 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) = ((sub @ (X76 @ X78 @ X79) @ X77))) | ~ ! [X80 : term] : (($true = ((X71 @ id @ (X76 @ id @ X80) @ id))) | (((X71 @ id @ X80 @ id)) != $true))) | ~ ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id)))) => ! [X82 : (subst > term > subst > $o),X81 : term] : (~ ! [X84 : term,X83 : term] : ((((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) = $true) | (((X82 @ id @ X83 @ id)) != $true) | (((X82 @ id @ X84 @ id)) != $true)) | ~ ! [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) = $true) | ~ ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88)))) | ~ ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X82 @ id @ X86 @ id)) != $true))) | (((X82 @ id @ X81 @ id)) = $true))))))) & (axclos = $true) & (! [X516 : (term > $o),X518 : term,X519 : (subst > term > subst > $o),X517 : term] : ((((X516 @ X517)) != $true) | ($true = ((X516 @ (ap @ X517 @ X518)))) | ~ ! [X529 : subst,X527 : subst,X526 : subst,X528 : term] : ((((X519 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)) != $true) | (((X519 @ X529 @ X528 @ (comp @ X526 @ X527))) = $true)) | ~ ! [X530 : term] : (((X516 @ X530)) = ((X519 @ id @ X530 @ id))) | (((X516 @ X518)) != $true) | ~ ! [X521 : term,X520 : term] : ((((X519 @ id @ (ap @ (sub @ X521 @ id) @ X520) @ id)) = $true) | ($true != ((X519 @ id @ X521 @ id))) | (((X519 @ id @ X520 @ id)) != $true)) | ~ ! [X523 : subst,X522 : subst,X525 : subst,X524 : term] : ((((X519 @ X525 @ X524 @ (comp @ X523 @ X522))) != $true) | (((X519 @ (comp @ X525 @ X523) @ (sub @ X524 @ X523) @ X522)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasapinj1_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X508 : term,X507 : subst,X506 : (term > $o)] : ~ ! [X509 : (term > $o)] : ~ ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510)))) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : ~ ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem3v2 = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X481 : term] : (((sub @ X481 @ id)) = X481) => (! [X482 : (subst > term > subst > $o),X483 : term] : (~ ! [X484 : (subst > term > term)] : (~ ! [X488 : term] : ((((X482 @ id @ X488 @ id)) != $true) | (((X482 @ id @ (X484 @ id @ X488) @ id)) = $true)) | (((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ~ ! [X485 : subst,X486 : term,X487 : subst] : (((sub @ (X484 @ X487 @ X486) @ X485)) = ((X484 @ (comp @ X487 @ X485) @ (sub @ X486 @ X485))))) | (((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X489 : term] : ((((X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)) = $true) | (((X482 @ id @ X489 @ id)) != $true))) => ! [X491 : term,X490 : (subst > term > subst > $o)] : ((((X490 @ id @ (lam @ X491) @ id)) = $true) | ~ ! [X493 : (subst > term > term)] : ((((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) = $true) | ~ ! [X495 : subst,X496 : term,X497 : subst] : (((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X493 @ X495 @ X496) @ X497))) | ~ ! [X494 : term] : (($true != ((X490 @ id @ X494 @ id))) | (((X490 @ id @ (X493 @ id @ X494) @ id)) = $true))) | ~ ! [X492 : term] : ((((X490 @ id @ X492 @ id)) != $true) | ($true = ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id)))))))) & (! [X338 : term,X339 : subst,X340 : (term > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X16 : term] : ~ ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh))))) & (hoasapnotvar_gthm = $true) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) = ((d2subst @ X425))) => (X424 = X425)) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & ((shinj = $true) <=> ! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh))))) & (hoaslamnotvar = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X1 : (subst > term > subst > $o),X0 : term] : (~ ! [X13 : subst,X14 : subst,X15 : subst,X12 : term] : ((((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) != $true) | (((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) = $true)) | (((X1 @ id @ (lam @ X0) @ id)) = $true) | ~ ! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) != $true) | (((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) = $true)) | ~ ! [X11 : term] : ((((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) = $true) | (((X1 @ id @ X11 @ id)) != $true)) | ~ ! [X6 : (subst > term > term)] : (~ ! [X7 : term] : ((((X1 @ id @ X7 @ id)) != $true) | (((X1 @ id @ (X6 @ id @ X7) @ id)) = $true)) | ~ ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) | (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) = $true)))) & (termmset_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & (pushprop_lem2v2 = $true) & (ulamvarsh = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem0 = $true) <=> ! [X477 : (subst > term > subst > $o)] : ~ ! [X478 : (term > $o)] : ~ ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id)))) & (hoaslamnotap_lthm = $true) & (induction2_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (axvarshift = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) <=> (axidl = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((! [X400 : subst,X401 : term] : (((sub @ one @ (push @ X401 @ X400))) = X401) => (! [X402 : subst,X403 : term] : (((comp @ sh @ (push @ X403 @ X402))) = X402) => (! [X404 : subst] : (((comp @ X404 @ id)) = X404) => (! [X406 : term,X405 : (term > $o)] : ((((X405 @ X406)) = $true) | ~ ! [X409 : term] : ((((var @ X409)) != $true) | (((X405 @ X409)) = $true)) | ~ ! [X410 : term] : ((((X405 @ X410)) != $true) | (((X405 @ (lam @ X410))) = $true)) | ~ ! [X408 : term,X407 : term] : ((((X405 @ (ap @ X408 @ X407))) = $true) | (((X405 @ X407)) != $true) | (((X405 @ X408)) != $true))) => ! [X411 : subst,X412 : (term > $o),X413 : term] : (~ ! [X416 : term] : ((((X412 @ (lam @ X416))) = $true) | ~ ! [X417 : term] : (($true != ((X412 @ X417))) | (((X412 @ (sub @ X416 @ (push @ X417 @ id)))) = $true))) | ~ ! [X418 : term] : ((((var @ X418)) != $true) | (((X412 @ (sub @ X418 @ X411))) = $true)) | (((X412 @ (sub @ X413 @ X411))) = $true) | ~ ! [X415 : term,X414 : term] : (($true != ((X412 @ X415))) | ($true != ((X412 @ X414))) | (((X412 @ (ap @ X414 @ X415))) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X51 : term] : (((sub @ X51 @ id)) = X51) => (! [X55 : term,X54 : term,X53 : term,X52 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))) => ! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X33 : term,X32 : (subst > term > subst > $o),X34 : term] : (~ ! [X35 : term,X36 : term] : ((((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) = $true) | (((X32 @ id @ X35 @ id)) != $true) | (((X32 @ id @ X36 @ id)) != $true)) | ~ ! [X41 : term,X43 : subst,X42 : subst,X44 : subst] : ((((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) != $true) | (((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) = $true)) | (((X32 @ id @ X33 @ id)) != $true) | (((X32 @ id @ X34 @ id)) != $true) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | ~ ! [X38 : subst,X37 : term,X40 : subst,X39 : subst] : (($true = ((X32 @ X38 @ X37 @ (comp @ X39 @ X40)))) | (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) != $true)))) & ((! [X358 : term] : (((sub @ X358 @ id)) = X358) => ! [X359 : term] : (((sub @ X359 @ id)) = X359)) <=> (termmset_lthm = $true)) & ((! [X384 : term] : ~ ! [X385 : (subst > term > term)] : ~ ! [X386 : subst,X387 : term] : (((X385 @ X386 @ X387)) = ((sub @ X384 @ (push @ X387 @ X386)))) => (! [X388 : term] : (((sub @ X388 @ id)) = X388) => ! [X390 : (term > $o),X391 : term,X389 : (subst > term > subst > $o)] : (~ ! [X392 : term] : ((((X390 @ (sub @ X391 @ (push @ X392 @ id)))) = $true) | (((X390 @ X392)) != $true)) | ~ ! [X394 : (subst > term > term)] : (~ ! [X396 : term,X397 : subst,X395 : subst] : (((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395))) = ((sub @ (X394 @ X397 @ X396) @ X395))) | (((X389 @ id @ (lam @ (X394 @ sh @ one)) @ id)) = $true) | ~ ! [X398 : term] : ((((X389 @ id @ (X394 @ id @ X398) @ id)) = $true) | (((X389 @ id @ X398 @ id)) != $true))) | ~ ! [X393 : term] : (((X389 @ id @ X393 @ id)) = ((X390 @ X393))) | (((X390 @ (lam @ X391))) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (lamnotvar = $true) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (pushprop_gthm = $true) & (ulamvar1 != $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & ((! [X178 : term] : (((sub @ X178 @ id)) = X178) => (! [X179 : term,X180 : (subst > term > subst > $o)] : (~ ! [X181 : term] : ((((X180 @ id @ X181 @ id)) != $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) | ~ ! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ~ ! [X183 : term,X185 : subst,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) = ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ~ ! [X186 : term] : ((((X180 @ id @ X186 @ id)) != $true) | ($true = ((X180 @ id @ (X182 @ id @ X186) @ id))))) | ($true = ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id)))) => ! [X188 : term,X187 : (subst > term > subst > $o)] : (~ ! [X189 : (subst > term > term)] : (~ ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190)))) | (((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true) | ~ ! [X193 : term] : ((((X187 @ id @ (X189 @ id @ X193) @ id)) = $true) | (((X187 @ id @ X193 @ id)) != $true))) | ~ ! [X202 : term] : ((((X187 @ id @ X202 @ id)) != $true) | (((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) = $true)) | ~ ! [X198 : term,X201 : subst,X200 : subst,X199 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) = $true) | (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) != $true)) | ~ ! [X196 : subst,X197 : subst,X195 : term,X194 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) = $true) | (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) != $true)) | ($true = ((X187 @ id @ (lam @ X188) @ id)))))) <=> (hoasinduction_lem3_lthm = $true)) & (apnotvar = $true) & (! [X364 : (term > $o),X366 : term,X365 : (subst > term > subst > $o)] : (~ ! [X367 : subst,X369 : subst,X370 : subst,X368 : term] : ((((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) = $true) | (((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) != $true)) | ~ ! [X375 : term,X373 : subst,X374 : subst,X376 : subst] : ((((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) != $true) | (((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) = $true)) | ~ ! [X371 : term] : (((X364 @ X371)) = ((X365 @ id @ X371 @ id))) | ~ ! [X372 : term] : ((((X364 @ (sub @ X366 @ (push @ X372 @ id)))) = $true) | (((X364 @ X372)) != $true)) | ~ ! [X377 : (subst > term > term)] : (~ ! [X378 : term] : ((((X365 @ id @ X378 @ id)) != $true) | (((X365 @ id @ (X377 @ id @ X378) @ id)) = $true)) | (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true) | ~ ! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380))))) | (((X364 @ (lam @ X366))) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X419 : (term > $o),X421 : term,X422 : (term > $o),X420 : subst] : (~ ! [X423 : term] : (((X422 @ X423)) = ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))) | (((X419 @ X421)) != $true) | (((X422 @ one)) = $true))) & (! [X531 : term] : ~ ! [X532 : (subst > term > term)] : ~ ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((! [X428 : (subst > term > subst > $o)] : ~ ! [X429 : (term > $o)] : ~ ! [X430 : term] : (((X429 @ X430)) = ((X428 @ id @ X430 @ id))) => (! [X431 : term,X432 : (term > $o)] : (~ ! [X436 : term,X435 : term] : ((((X432 @ X435)) != $true) | (((X432 @ (ap @ X436 @ X435))) = $true) | (((X432 @ X436)) != $true)) | (((X432 @ X431)) = $true) | ~ ! [X433 : term] : ((((X432 @ (lam @ X433))) = $true) | ~ ! [X434 : term] : ((((X432 @ X434)) != $true) | (((X432 @ (sub @ X433 @ (push @ X434 @ id)))) = $true))) | ~ ! [X437 : term] : ((((X432 @ X437)) = $true) | (((var @ X437)) != $true))) => (! [X438 : term] : (((sub @ X438 @ id)) = X438) => (! [X441 : (subst > term > subst > $o),X439 : (term > $o),X440 : term] : (~ ! [X443 : (subst > term > term)] : ((((X441 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true) | ~ ! [X445 : subst,X447 : term,X446 : subst] : (((X443 @ (comp @ X445 @ X446) @ (sub @ X447 @ X446))) = ((sub @ (X443 @ X445 @ X447) @ X446))) | ~ ! [X444 : term] : ((((X441 @ id @ (X443 @ id @ X444) @ id)) = $true) | ($true != ((X441 @ id @ X444 @ id))))) | (((X439 @ (lam @ X440))) = $true) | ~ ! [X442 : term] : ((((X439 @ (sub @ X440 @ (push @ X442 @ id)))) = $true) | (((X439 @ X442)) != $true)) | ~ ! [X448 : term] : (((X439 @ X448)) = ((X441 @ id @ X448 @ id)))) => ! [X450 : (subst > term > subst > $o),X449 : term] : (~ ! [X455 : term] : ((((X450 @ id @ X455 @ id)) = $true) | (((var @ (sub @ X455 @ id))) != $true)) | (((X450 @ id @ X449 @ id)) = $true) | ~ ! [X460 : (subst > term > term)] : (~ ! [X461 : term,X462 : subst,X463 : subst] : (((X460 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))) = ((sub @ (X460 @ X462 @ X461) @ X463))) | ~ ! [X464 : term] : ((((X450 @ id @ (X460 @ id @ X464) @ id)) = $true) | (((X450 @ id @ X464 @ id)) != $true)) | (((X450 @ id @ (lam @ (X460 @ sh @ one)) @ id)) = $true)) | ~ ! [X451 : subst,X452 : subst,X454 : term,X453 : subst] : ((((X450 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452) @ X451)) = $true) | (((X450 @ X453 @ X454 @ (comp @ X452 @ X451))) != $true)) | ~ ! [X457 : subst,X458 : subst,X456 : term,X459 : subst] : ((((X450 @ (comp @ X458 @ X459) @ (sub @ X456 @ X459) @ X457)) != $true) | (((X450 @ X458 @ X456 @ (comp @ X459 @ X457))) = $true)) | ~ ! [X465 : term,X466 : term] : ((((X450 @ id @ X465 @ id)) != $true) | (((X450 @ id @ (ap @ (sub @ X465 @ id) @ X466) @ id)) = $true) | (((X450 @ id @ X466 @ id)) != $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X156 : d_subst] : (d_id = X156) & ((hoasinduction_lem0_lthm = $true) <=> ! [X537 : (subst > term > subst > $o)] : ~ ! [X538 : (term > $o)] : ~ ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id)))) & (! [X116 : (subst > term > subst > $o),X115 : (term > $o),X117 : term] : (~ ! [X120 : (subst > term > term)] : ((((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) = $true) | ~ ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | (((X116 @ id @ X121 @ id)) != $true)) | ~ ! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124))))) | (((X115 @ (lam @ X117))) = $true) | ~ ! [X119 : term] : (((X116 @ id @ X119 @ id)) = ((X115 @ X119))) | ~ ! [X118 : term] : ((((X115 @ X118)) != $true) | (((X115 @ (sub @ X117 @ (push @ X118 @ id)))) = $true))) <=> (hoasinduction_lem3v2a = $true)) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X159 : term] : (((sub @ X159 @ id)) = X159) => ! [X160 : term,X161 : (term > $o),X162 : (subst > term > subst > $o)] : ((((X161 @ (lam @ X160))) = $true) | ~ ! [X177 : term] : ((((X161 @ (sub @ X160 @ (push @ X177 @ id)))) = $true) | (((X161 @ X177)) != $true)) | ~ ! [X172 : (subst > term > term)] : (~ ! [X176 : term] : ((((X162 @ id @ X176 @ id)) != $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true)) | ~ ! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) | (((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) = $true)) | ~ ! [X170 : term,X167 : subst,X168 : subst,X169 : subst] : ((((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) = $true) | ($true != ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167)))) | ~ ! [X171 : term] : (((X162 @ id @ X171 @ id)) = ((X161 @ X171))) | ~ ! [X164 : subst,X163 : subst,X166 : subst,X165 : term] : ((((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) = $true) | (((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) != $true))))) & (! [X498 : (subst > term > subst > $o),X499 : term] : (~ ! [X501 : (subst > term > term)] : (~ ! [X502 : term] : ((((X498 @ id @ X502 @ id)) != $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) | (((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) = $true) | ~ ! [X504 : subst,X503 : term,X505 : subst] : (((sub @ (X501 @ X504 @ X503) @ X505)) = ((X501 @ (comp @ X504 @ X505) @ (sub @ X503 @ X505))))) | ~ ! [X500 : term] : ((((X498 @ id @ X500 @ id)) != $true) | (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) = $true)) | (((X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (axapp = $true) & ((axvarid = $true) <=> ! [X511 : term] : (((sub @ X511 @ id)) = X511))),
% 46.03/6.94 inference(flattening,[],[f8])).
% 46.03/6.94 thf(f10,plain,(
% 46.03/6.94 ~((hoasinduction_lem3v2 = $true) <=> ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (! [X5 : term,X2 : subst,X3 : subst,X4 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) => (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) = $true)) => (! [X6 : subst,X8 : subst,X9 : subst,X7 : term] : (($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8))) => (((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) = $true)) => (! [X10 : (subst > term > term)] : (! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) => (! [X14 : term] : ((((X0 @ id @ X14 @ id)) = $true) => (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true)) => (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) = $true))) => ((((hoasinduction_p_and_p_prime @ X0 @ X1)) = $true) => ! [X15 : term] : (! [X16 : term] : ((((X1 @ X16)) = $true) => (((X1 @ (sub @ X15 @ (push @ X16 @ id)))) = $true)) => (((X1 @ (lam @ X15))) = $true)))))))),
% 46.03/6.94 inference(rectify,[],[f7])).
% 46.03/6.94 thf(f11,plain,(
% 46.03/6.94 ((hoasinduction_no_psi_cond = $true) <=> ! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) & (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) != $true) & ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true))) | ? [X306 : term,X307 : term] : (($true != ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) & (((X299 @ id @ X306 @ id)) = $true) & (((X299 @ id @ X307 @ id)) = $true)))) & (axassoc = $true) & (((d2subst @ d_id)) = sh) & (axmap = $true) & (! [X309 : term,X308 : (subst > term > subst > $o)] : (? [X312 : term,X311 : (subst > term > term)] : ((((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) != $true) & ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319))) & ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | (((X308 @ id @ X313 @ id)) != $true))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))) | ? [X310 : term] : ((((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) != $true) & (((X308 @ id @ X310 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_lem2v2_lthm = $true) & (ulamvarind = $true) & (pushprop_lem2v2_gthm = $true) & (axabs = $true) & ((laminj = $true) <=> ! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536))) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & (hoasinduction_gthm = $true) & (! [X382 : term] : ? [X383 : (subst > term > term)] : (((X383 @ sh @ one)) = ((sub @ X382 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X345 : term,X344 : (subst > term > subst > $o)] : (? [X347 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X350 : subst,X351 : subst,X349 : term] : (((X347 @ (comp @ X351 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X347 @ X351 @ X349) @ X350))) & ! [X348 : term] : ((((X344 @ id @ X348 @ id)) != $true) | (((X344 @ id @ (X347 @ id @ X348) @ id)) = $true))) | (((X344 @ id @ (lam @ X345) @ id)) = $true) | ? [X346 : term] : ((((X344 @ id @ X346 @ id)) = $true) & (((X344 @ id @ (sub @ X345 @ (push @ X346 @ id)) @ id)) != $true)))) & ((((! [X138 : (subst > term > term),X140 : subst,X139 : term,X137 : (subst > term > term)] : (? [X146 : subst,X145 : subst,X144 : term] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) != ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))) | ? [X143 : subst,X142 : term,X141 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) != ((sub @ (X138 @ X143 @ X142) @ X141)))) | ? [X136 : term,X135 : term] : ((X135 != X136) & (((lam @ X135)) = ((lam @ X136))))) | ? [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) != X133)) | ? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131)) <=> (hoaslaminj_lthm = $true)) & ((axshiftcons = $true) <=> ! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427)) & ((hoasinduction_lthm = $true) <=> (((! [X254 : (subst > term > subst > $o),X255 : term] : (? [X269 : subst,X271 : term,X268 : subst,X270 : subst] : ((((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) != $true) & (((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true)) | ? [X260 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) != $true) & ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262))) & ! [X261 : term] : ((((X254 @ id @ X261 @ id)) != $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true))) | ? [X265 : term] : ((((X254 @ id @ X265 @ id)) != $true) & (((var @ (sub @ X265 @ id))) = $true)) | (((X254 @ id @ X255 @ id)) = $true) | ? [X258 : term,X256 : subst,X259 : subst,X257 : subst] : ((((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) = $true) & (((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) != $true)) | ? [X267 : term,X266 : term] : ((((X254 @ id @ X266 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & (((X254 @ id @ X267 @ id)) = $true))) | ? [X239 : (subst > term > subst > $o),X238 : term] : (! [X240 : (subst > term > term)] : (? [X241 : term] : ((((X239 @ id @ X241 @ id)) = $true) & (((X239 @ id @ (X240 @ id @ X241) @ id)) != $true)) | ? [X244 : subst,X243 : term,X242 : subst] : (((sub @ (X240 @ X242 @ X243) @ X244)) != ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)))) & ! [X253 : subst,X252 : subst,X250 : subst,X251 : term] : ((((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) != $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true)) & ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (($true != ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true)) & ! [X249 : term] : ((((X239 @ id @ X249 @ id)) != $true) | ($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id)))) & (((X239 @ id @ (lam @ X238) @ id)) != $true))) | ? [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (! [X236 : term,X234 : subst,X237 : subst,X235 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) != $true)) & ! [X233 : term,X232 : term] : ((((X225 @ id @ X232 @ id)) != $true) | (((X225 @ id @ X233 @ id)) != $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)) & (((X225 @ id @ X226 @ id)) = $true) & (((X225 @ id @ X227 @ id)) = $true) & (((X225 @ id @ (ap @ X226 @ X227) @ id)) != $true) & ! [X229 : subst,X230 : subst,X228 : subst,X231 : term] : ((((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) != $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true)))) | ? [X218 : term,X219 : (term > $o)] : (! [X223 : term,X224 : term] : ((((X219 @ X223)) != $true) | ($true != ((X219 @ X224))) | ($true = ((X219 @ (ap @ X223 @ X224))))) & ! [X221 : term] : ((((X219 @ (lam @ X221))) = $true) | ? [X222 : term] : ((((X219 @ X222)) = $true) & (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) != $true))) & ! [X220 : term] : ((((X219 @ X220)) = $true) | (((var @ X220)) != $true)) & (((X219 @ X218)) != $true)))) & ((((! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)) | ? [X29 : subst] : (((comp @ X29 @ id)) != X29)) | ? [X28 : subst] : (((comp @ id @ X28)) != X28)) <=> (substmonoid_lthm = $true)) & ! [X362 : d_term,X363 : d_term] : ((X362 = X363) | (((d2term @ X362)) != ((d2term @ X363)))) & ((hoaslamnotap = $true) <=> ! [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ? [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) != ((sub @ (X46 @ X50 @ X48) @ X49))))) & (! [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | ? [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) != ((sub @ (X321 @ X326 @ X324) @ X325))) | ? [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) != ((sub @ (X320 @ X329 @ X328) @ X327))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one))))) <=> (hoaslaminj = $true)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)) | ? [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) != X92)) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91)) <=> (pushprop_lem1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((induction2lem = $true) <=> ! [X331 : subst,X332 : term,X330 : (term > $o)] : (? [X335 : term] : ((((X330 @ (sub @ X335 @ X331))) != $true) & (((var @ X335)) = $true)) | ? [X334 : term,X333 : term] : (($true = ((X330 @ X334))) & (((X330 @ (ap @ X333 @ X334))) != $true) & (((X330 @ X333)) = $true)) | ? [X336 : term] : (! [X337 : term] : ((((X330 @ (sub @ X336 @ (push @ X337 @ id)))) = $true) | ($true != ((X330 @ X337)))) & (((X330 @ (lam @ X336))) != $true)) | (((X330 @ (sub @ X332 @ X331))) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X21 : (subst > term > subst > $o),X20 : term] : (? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X22 : term] : ((((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) != $true) & (((X21 @ id @ X22 @ id)) = $true)) | (((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (pushprop_lem1v2_gthm = $true) & ((induction2 = $true) <=> ! [X148 : term,X147 : (term > $o)] : (($true = ((X147 @ X148))) | ? [X151 : term] : (! [X152 : term] : ((((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true) | (((X147 @ X152)) != $true)) & (((X147 @ (lam @ X151))) != $true)) | ? [X150 : term,X149 : term] : ((((X147 @ X149)) = $true) & (((X147 @ (ap @ X149 @ X150))) != $true) & (((X147 @ X150)) = $true)) | ? [X153 : term] : ((((var @ X153)) = $true) & (((X147 @ X153)) != $true)))) & ((apinj1 = $true) <=> ! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356))))) & (hoasinduction_lem2v2_gthm = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & ((pushprop_lem1v2_lthm = $true) <=> (? [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) != X208) | ! [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true = ((X210 @ one))) | (((X211 @ X212)) != $true) | ? [X213 : term] : (((X210 @ X213)) != ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) <=> (axidr = $true)) & (pushprop_lthm_orig = $true) & (lamnotap != $true) & ((hoasapinj2 = $true) <=> ! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512))))) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem3v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoaslamnotvar_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 != X469) & (((ap @ X467 @ X468)) = ((ap @ X470 @ X469)))) | ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))))) & ((induction = $true) <=> ! [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) = $true) | ? [X130 : term] : ((((X125 @ (lam @ X130))) != $true) & (((X125 @ X130)) = $true)) | ? [X128 : term,X127 : term] : ((((X125 @ X127)) = $true) & (((X125 @ (ap @ X128 @ X127))) != $true) & (((X125 @ X128)) = $true)) | ? [X129 : term] : ((((var @ X129)) = $true) & ($true != ((X125 @ X129)))))) & (! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) <=> (pushprop_lem1 = $true)) & (((! [X109 : term,X108 : (term > $o)] : (? [X110 : term] : (! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | (((X108 @ X111)) != $true)) & (((X108 @ (lam @ X110))) != $true)) | ? [X114 : term] : ((((X108 @ X114)) != $true) & (((var @ X114)) = $true)) | (((X108 @ X109)) = $true) | ? [X113 : term,X112 : term] : ((((X108 @ X113)) = $true) & (((X108 @ (ap @ X113 @ X112))) != $true) & (((X108 @ X112)) = $true))) | ? [X100 : term,X102 : (term > $o),X101 : subst] : (! [X105 : term] : ((((var @ X105)) != $true) | (((X102 @ (sub @ X105 @ X101))) = $true)) & ! [X106 : term] : (? [X107 : term] : ((((X102 @ X107)) = $true) & (((X102 @ (sub @ X106 @ (push @ X107 @ id)))) != $true)) | (((X102 @ (lam @ X106))) = $true)) & (((X102 @ (sub @ X100 @ X101))) != $true) & ! [X104 : term,X103 : term] : ((((X102 @ X104)) != $true) | (((X102 @ (ap @ X103 @ X104))) = $true) | (((X102 @ X103)) != $true)))) | ? [X99 : term] : (((sub @ X99 @ id)) != X99)) <=> (induction2_lthm = $true)) & (hoasapnotvar_lthm = $true) & (! [X278 : term,X277 : (subst > term > subst > $o)] : (? [X292 : subst,X289 : term,X290 : subst,X291 : subst] : (($true = ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290))) & (((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) != $true)) | (((X277 @ id @ X278 @ id)) = $true) | ? [X287 : subst,X286 : term,X285 : subst,X288 : subst] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) != $true) & (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) = $true)) | ? [X294 : term,X293 : term] : ((((X277 @ id @ X293 @ id)) = $true) & (((X277 @ id @ X294 @ id)) = $true) & ($true != ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)))) | ? [X279 : term] : ((((X277 @ id @ X279 @ id)) != $true) & (((var @ (sub @ X279 @ id))) = $true)) | ? [X280 : (subst > term > term)] : (! [X284 : term] : ((((X277 @ id @ X284 @ id)) != $true) | ($true = ((X277 @ id @ (X280 @ id @ X284) @ id)))) & ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) & (((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X81 : term,X82 : (subst > term > subst > $o)] : ((((X82 @ id @ X81 @ id)) = $true) | ? [X84 : term,X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) & (((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true)) | ? [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88)))) & ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X82 @ id @ X86 @ id)) != $true)))) | ? [X73 : (term > $o),X72 : term,X71 : (subst > term > subst > $o)] : (! [X75 : term] : ((((X73 @ X75)) != $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) & ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) & (((X73 @ (lam @ X72))) != $true) & ! [X76 : (subst > term > term)] : (? [X79 : term,X77 : subst,X78 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) != ((sub @ (X76 @ X78 @ X79) @ X77))) | ? [X80 : term] : ((((X71 @ id @ X80 @ id)) = $true) & ($true != ((X71 @ id @ (X76 @ id @ X80) @ id)))) | (((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true)))) | ? [X70 : term] : (((sub @ X70 @ id)) != X70)) | ? [X63 : term,X64 : (term > $o)] : ((((X64 @ X63)) != $true) & ! [X68 : term,X67 : term] : ((((X64 @ X68)) != $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | (((X64 @ X67)) != $true)) & ! [X69 : term] : ((((X64 @ X69)) = $true) | (((var @ X69)) != $true)) & ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ? [X66 : term] : ((((X64 @ X66)) = $true) & (((X64 @ (sub @ X65 @ (push @ X66 @ id)))) != $true))))) | ? [X60 : (subst > term > subst > $o)] : ! [X61 : (term > $o)] : ? [X62 : term] : (((X60 @ id @ X62 @ id)) != ((X61 @ X62))))) & (axclos = $true) & (! [X518 : term,X516 : (term > $o),X519 : (subst > term > subst > $o),X517 : term] : (($true = ((X516 @ (ap @ X517 @ X518)))) | ? [X529 : subst,X526 : subst,X527 : subst,X528 : term] : ((((X519 @ X529 @ X528 @ (comp @ X526 @ X527))) != $true) & (((X519 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)) = $true)) | ? [X523 : subst,X522 : subst,X524 : term,X525 : subst] : ((((X519 @ (comp @ X525 @ X523) @ (sub @ X524 @ X523) @ X522)) != $true) & (((X519 @ X525 @ X524 @ (comp @ X523 @ X522))) = $true)) | ? [X530 : term] : (((X516 @ X530)) != ((X519 @ id @ X530 @ id))) | ? [X520 : term,X521 : term] : ((((X519 @ id @ (ap @ (sub @ X521 @ id) @ X520) @ id)) != $true) & ($true = ((X519 @ id @ X521 @ id))) & (((X519 @ id @ X520 @ id)) = $true)) | (((X516 @ X517)) != $true) | (((X516 @ X518)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasapinj1_gthm = $true) & (! [X507 : subst,X506 : (term > $o),X508 : term] : ? [X509 : (term > $o)] : ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X295 : term] : ? [X296 : (subst > term > term)] : ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem3v2 = $true) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X491 : term,X490 : (subst > term > subst > $o)] : (? [X493 : (subst > term > term)] : (! [X494 : term] : (($true != ((X490 @ id @ X494 @ id))) | (((X490 @ id @ (X493 @ id @ X494) @ id)) = $true)) & ! [X495 : subst,X496 : term,X497 : subst] : (((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X493 @ X495 @ X496) @ X497))) & (((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) != $true)) | (((X490 @ id @ (lam @ X491) @ id)) = $true) | ? [X492 : term] : ((((X490 @ id @ X492 @ id)) = $true) & ($true != ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id))))) | ? [X482 : (subst > term > subst > $o),X483 : term] : ((((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id)) != $true) & ! [X489 : term] : ((((X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)) = $true) | (((X482 @ id @ X489 @ id)) != $true)) & ! [X484 : (subst > term > term)] : (? [X485 : subst,X487 : subst,X486 : term] : (((sub @ (X484 @ X487 @ X486) @ X485)) != ((X484 @ (comp @ X487 @ X485) @ (sub @ X486 @ X485)))) | (((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ? [X488 : term] : ((((X482 @ id @ X488 @ id)) = $true) & (((X482 @ id @ (X484 @ id @ X488) @ id)) != $true))))) | ? [X481 : term] : (((sub @ X481 @ id)) != X481))) & (! [X339 : subst,X338 : term,X340 : (term > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lthm = $true) & (! [X16 : term] : ? [X17 : (subst > term > term)] : (((X17 @ sh @ one)) = ((sub @ X16 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasapnotvar_gthm = $true) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) != ((d2subst @ X425))) | (X424 = X425)) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & ((shinj = $true) <=> ! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh))))) & (hoaslamnotvar = $true) & (hoasinduction_lem1 = $true) & (! [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ (lam @ X0) @ id)) = $true) | ? [X11 : term] : ((((X1 @ id @ X11 @ id)) = $true) & (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) != $true)) | ? [X4 : term,X5 : subst,X2 : subst,X3 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) != $true) & (((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) = $true)) | ? [X15 : subst,X14 : subst,X12 : term,X13 : subst] : ((((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) != $true) & (((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) = $true)) | ? [X6 : (subst > term > term)] : (! [X7 : term] : ((((X1 @ id @ X7 @ id)) != $true) | (((X1 @ id @ (X6 @ id @ X7) @ id)) = $true)) & ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) & (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3 = $true)) & (termmset_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & (pushprop_lem2v2 = $true) & (ulamvarsh = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem0 = $true) <=> ! [X477 : (subst > term > subst > $o)] : ? [X478 : (term > $o)] : ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id)))) & (hoaslamnotap_lthm = $true) & (induction2_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (axvarshift = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) <=> (axidl = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2_gthm = $true) & (((((! [X412 : (term > $o),X411 : subst,X413 : term] : (? [X414 : term,X415 : term] : ((((X412 @ (ap @ X414 @ X415))) != $true) & ($true = ((X412 @ X414))) & ($true = ((X412 @ X415)))) | ? [X416 : term] : (! [X417 : term] : (($true != ((X412 @ X417))) | (((X412 @ (sub @ X416 @ (push @ X417 @ id)))) = $true)) & (((X412 @ (lam @ X416))) != $true)) | (((X412 @ (sub @ X413 @ X411))) = $true) | ? [X418 : term] : ((((var @ X418)) = $true) & (((X412 @ (sub @ X418 @ X411))) != $true))) | ? [X406 : term,X405 : (term > $o)] : (! [X409 : term] : ((((var @ X409)) != $true) | (((X405 @ X409)) = $true)) & ! [X408 : term,X407 : term] : ((((X405 @ (ap @ X408 @ X407))) = $true) | (((X405 @ X407)) != $true) | (((X405 @ X408)) != $true)) & (((X405 @ X406)) != $true) & ! [X410 : term] : ((((X405 @ X410)) != $true) | (((X405 @ (lam @ X410))) = $true)))) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404)) | ? [X402 : subst,X403 : term] : (((comp @ sh @ (push @ X403 @ X402))) != X402)) | ? [X400 : subst,X401 : term] : (((sub @ one @ (push @ X401 @ X400))) != X401)) <=> (induction2lem_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((hoasapinj1_lthm = $true) <=> ((! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59)) | ? [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 != X54) & (((ap @ X52 @ X55)) = ((ap @ X54 @ X53))))) | ? [X51 : term] : (((sub @ X51 @ id)) != X51))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X34 : term,X33 : term,X32 : (subst > term > subst > $o)] : (? [X35 : term,X36 : term] : ((((X32 @ id @ X36 @ id)) = $true) & (((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) != $true) & (((X32 @ id @ X35 @ id)) = $true)) | (((X32 @ id @ X34 @ id)) != $true) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | (((X32 @ id @ X33 @ id)) != $true) | ? [X39 : subst,X37 : term,X40 : subst,X38 : subst] : (($true != ((X32 @ X38 @ X37 @ (comp @ X39 @ X40)))) & (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) = $true)) | ? [X41 : term,X43 : subst,X44 : subst,X42 : subst] : ((((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) = $true) & (((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) != $true)))) & ((! [X359 : term] : (((sub @ X359 @ id)) = X359) | ? [X358 : term] : (((sub @ X358 @ id)) != X358)) <=> (termmset_lthm = $true)) & (((! [X390 : (term > $o),X391 : term,X389 : (subst > term > subst > $o)] : (? [X394 : (subst > term > term)] : (! [X396 : term,X397 : subst,X395 : subst] : (((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395))) = ((sub @ (X394 @ X397 @ X396) @ X395))) & ! [X398 : term] : ((((X389 @ id @ (X394 @ id @ X398) @ id)) = $true) | (((X389 @ id @ X398 @ id)) != $true)) & (((X389 @ id @ (lam @ (X394 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : (((X389 @ id @ X393 @ id)) != ((X390 @ X393))) | ? [X392 : term] : ((((X390 @ (sub @ X391 @ (push @ X392 @ id)))) != $true) & (((X390 @ X392)) = $true)) | (((X390 @ (lam @ X391))) = $true)) | ? [X388 : term] : (((sub @ X388 @ id)) != X388)) | ? [X384 : term] : ! [X385 : (subst > term > term)] : ? [X386 : subst,X387 : term] : (((X385 @ X386 @ X387)) != ((sub @ X384 @ (push @ X387 @ X386))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (lamnotvar = $true) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (pushprop_gthm = $true) & (ulamvar1 != $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((d2subst @ d_id)) = id) & (((! [X188 : term,X187 : (subst > term > subst > $o)] : (? [X198 : term,X200 : subst,X201 : subst,X199 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) != $true) & (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) = $true)) | ? [X197 : subst,X195 : term,X196 : subst,X194 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) != $true) & (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) = $true)) | ? [X202 : term] : ((((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) != $true) & (((X187 @ id @ X202 @ id)) = $true)) | ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X187 @ id @ (X189 @ id @ X193) @ id)) = $true) | (((X187 @ id @ X193 @ id)) != $true)) & (((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) != $true) & ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190))))) | ($true = ((X187 @ id @ (lam @ X188) @ id)))) | ? [X179 : term,X180 : (subst > term > subst > $o)] : (! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ? [X185 : subst,X183 : term,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) != ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ? [X186 : term] : ((((X180 @ id @ X186 @ id)) = $true) & ($true != ((X180 @ id @ (X182 @ id @ X186) @ id))))) & ! [X181 : term] : ((((X180 @ id @ X181 @ id)) != $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) & ($true != ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id))))) | ? [X178 : term] : (((sub @ X178 @ id)) != X178)) <=> (hoasinduction_lem3_lthm = $true)) & (apnotvar = $true) & (! [X365 : (subst > term > subst > $o),X366 : term,X364 : (term > $o)] : (? [X373 : subst,X376 : subst,X375 : term,X374 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) != $true) & (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) = $true)) | ? [X377 : (subst > term > term)] : (! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) & ! [X378 : term] : ((((X365 @ id @ X378 @ id)) != $true) | (((X365 @ id @ (X377 @ id @ X378) @ id)) = $true)) & (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true)) | (((X364 @ (lam @ X366))) = $true) | ? [X371 : term] : (((X364 @ X371)) != ((X365 @ id @ X371 @ id))) | ? [X369 : subst,X370 : subst,X367 : subst,X368 : term] : ((((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) = $true) & (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) != $true)) | ? [X372 : term] : ((((X364 @ X372)) = $true) & (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) = $true) | (((X419 @ X421)) != $true) | ? [X423 : term] : (((X422 @ X423)) != ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))))) & (! [X531 : term] : ? [X532 : (subst > term > term)] : ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (((((! [X449 : term,X450 : (subst > term > subst > $o)] : (? [X466 : term,X465 : term] : ((((X450 @ id @ X466 @ id)) = $true) & (((X450 @ id @ X465 @ id)) = $true) & (((X450 @ id @ (ap @ (sub @ X465 @ id) @ X466) @ id)) != $true)) | ? [X460 : (subst > term > term)] : (! [X464 : term] : ((((X450 @ id @ (X460 @ id @ X464) @ id)) = $true) | (((X450 @ id @ X464 @ id)) != $true)) & (((X450 @ id @ (lam @ (X460 @ sh @ one)) @ id)) != $true) & ! [X461 : term,X462 : subst,X463 : subst] : (((X460 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))) = ((sub @ (X460 @ X462 @ X461) @ X463)))) | ? [X459 : subst,X458 : subst,X457 : subst,X456 : term] : ((((X450 @ X458 @ X456 @ (comp @ X459 @ X457))) != $true) & (((X450 @ (comp @ X458 @ X459) @ (sub @ X456 @ X459) @ X457)) = $true)) | ? [X453 : subst,X454 : term,X451 : subst,X452 : subst] : ((((X450 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452) @ X451)) != $true) & (((X450 @ X453 @ X454 @ (comp @ X452 @ X451))) = $true)) | (((X450 @ id @ X449 @ id)) = $true) | ? [X455 : term] : ((((var @ (sub @ X455 @ id))) = $true) & (((X450 @ id @ X455 @ id)) != $true))) | ? [X440 : term,X439 : (term > $o),X441 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X440))) != $true) & ! [X448 : term] : (((X439 @ X448)) = ((X441 @ id @ X448 @ id))) & ! [X443 : (subst > term > term)] : (? [X444 : term] : (($true = ((X441 @ id @ X444 @ id))) & (((X441 @ id @ (X443 @ id @ X444) @ id)) != $true)) | ? [X446 : subst,X447 : term,X445 : subst] : (((X443 @ (comp @ X445 @ X446) @ (sub @ X447 @ X446))) != ((sub @ (X443 @ X445 @ X447) @ X446))) | (((X441 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true)) & ! [X442 : term] : ((((X439 @ (sub @ X440 @ (push @ X442 @ id)))) = $true) | (((X439 @ X442)) != $true)))) | ? [X438 : term] : (((sub @ X438 @ id)) != X438)) | ? [X432 : (term > $o),X431 : term] : ((((X432 @ X431)) != $true) & ! [X436 : term,X435 : term] : ((((X432 @ X435)) != $true) | (((X432 @ (ap @ X436 @ X435))) = $true) | (((X432 @ X436)) != $true)) & ! [X437 : term] : ((((X432 @ X437)) = $true) | (((var @ X437)) != $true)) & ! [X433 : term] : (? [X434 : term] : ((((X432 @ X434)) = $true) & (((X432 @ (sub @ X433 @ (push @ X434 @ id)))) != $true)) | (((X432 @ (lam @ X433))) = $true)))) | ? [X428 : (subst > term > subst > $o)] : ! [X429 : (term > $o)] : ? [X430 : term] : (((X429 @ X430)) != ((X428 @ id @ X430 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ! [X156 : d_subst] : (d_id = X156) & ((hoasinduction_lem0_lthm = $true) <=> ! [X537 : (subst > term > subst > $o)] : ? [X538 : (term > $o)] : ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id)))) & (! [X117 : term,X115 : (term > $o),X116 : (subst > term > subst > $o)] : (? [X119 : term] : (((X116 @ id @ X119 @ id)) != ((X115 @ X119))) | ? [X120 : (subst > term > term)] : (! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) & ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | (((X116 @ id @ X121 @ id)) != $true)) & (((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) != $true)) | ? [X118 : term] : ((((X115 @ (sub @ X117 @ (push @ X118 @ id)))) != $true) & (((X115 @ X118)) = $true)) | (((X115 @ (lam @ X117))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (substmonoid_gthm = $true) & ((! [X161 : (term > $o),X162 : (subst > term > subst > $o),X160 : term] : ((((X161 @ (lam @ X160))) = $true) | ? [X163 : subst,X165 : term,X166 : subst,X164 : subst] : ((((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) = $true) & (((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) != $true)) | ? [X171 : term] : (((X162 @ id @ X171 @ id)) != ((X161 @ X171))) | ? [X172 : (subst > term > term)] : (! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) & ! [X176 : term] : ((((X162 @ id @ X176 @ id)) != $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true)) & (((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)) | ? [X177 : term] : ((((X161 @ X177)) = $true) & (((X161 @ (sub @ X160 @ (push @ X177 @ id)))) != $true)) | ? [X168 : subst,X170 : term,X169 : subst,X167 : subst] : (($true = ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167))) & (((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) != $true))) | ? [X159 : term] : (((sub @ X159 @ id)) != X159)) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X498 : (subst > term > subst > $o),X499 : term] : (? [X501 : (subst > term > term)] : (! [X502 : term] : ((((X498 @ id @ X502 @ id)) != $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) & ! [X504 : subst,X503 : term,X505 : subst] : (((sub @ (X501 @ X504 @ X503) @ X505)) = ((X501 @ (comp @ X504 @ X505) @ (sub @ X503 @ X505)))) & (((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) != $true)) | ? [X500 : term] : ((((X498 @ id @ X500 @ id)) = $true) & (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) != $true)) | (((X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) = $true))) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (axapp = $true) & ((axvarid = $true) <=> ! [X511 : term] : (((sub @ X511 @ id)) = X511))),
% 46.03/6.94 inference(ennf_transformation,[],[f9])).
% 46.03/6.94 thf(f12,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((? [X388 : term] : (((sub @ X388 @ id)) != X388) | ! [X390 : (term > $o),X391 : term,X389 : (subst > term > subst > $o)] : (? [X394 : (subst > term > term)] : (! [X396 : term,X397 : subst,X395 : subst] : (((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395))) = ((sub @ (X394 @ X397 @ X396) @ X395))) & ! [X398 : term] : ((((X389 @ id @ (X394 @ id @ X398) @ id)) = $true) | (((X389 @ id @ X398 @ id)) != $true)) & (((X389 @ id @ (lam @ (X394 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : (((X389 @ id @ X393 @ id)) != ((X390 @ X393))) | ? [X392 : term] : ((((X390 @ (sub @ X391 @ (push @ X392 @ id)))) != $true) & (((X390 @ X392)) = $true)) | (((X390 @ (lam @ X391))) = $true)) | ? [X384 : term] : ! [X385 : (subst > term > term)] : ? [X386 : subst,X387 : term] : (((X385 @ X386 @ X387)) != ((sub @ X384 @ (push @ X387 @ X386))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) & (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) != $true) & ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true))) | ? [X306 : term,X307 : term] : (($true != ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) & (((X299 @ id @ X306 @ id)) = $true) & (((X299 @ id @ X307 @ id)) = $true)))) & (! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X531 : term] : ? [X532 : (subst > term > term)] : ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) = $true) | (((X419 @ X421)) != $true) | ? [X423 : term] : (((X422 @ X423)) != ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))))) & (! [X278 : term,X277 : (subst > term > subst > $o)] : (? [X292 : subst,X289 : term,X290 : subst,X291 : subst] : (($true = ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290))) & (((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) != $true)) | (((X277 @ id @ X278 @ id)) = $true) | ? [X287 : subst,X286 : term,X285 : subst,X288 : subst] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) != $true) & (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) = $true)) | ? [X294 : term,X293 : term] : ((((X277 @ id @ X293 @ id)) = $true) & (((X277 @ id @ X294 @ id)) = $true) & ($true != ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)))) | ? [X279 : term] : ((((X277 @ id @ X279 @ id)) != $true) & (((var @ (sub @ X279 @ id))) = $true)) | ? [X280 : (subst > term > term)] : (! [X284 : term] : ((((X277 @ id @ X284 @ id)) != $true) | ($true = ((X277 @ id @ (X280 @ id @ X284) @ id)))) & ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) & (((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction = $true)) & (pushprop_lthm = $true) & ((induction2lem_lthm = $true) <=> (? [X400 : subst,X401 : term] : (((sub @ one @ (push @ X401 @ X400))) != X401) | ? [X402 : subst,X403 : term] : (((comp @ sh @ (push @ X403 @ X402))) != X402) | ? [X406 : term,X405 : (term > $o)] : (! [X409 : term] : ((((var @ X409)) != $true) | (((X405 @ X409)) = $true)) & ! [X408 : term,X407 : term] : ((((X405 @ (ap @ X408 @ X407))) = $true) | (((X405 @ X407)) != $true) | (((X405 @ X408)) != $true)) & (((X405 @ X406)) != $true) & ! [X410 : term] : ((((X405 @ X410)) != $true) | (((X405 @ (lam @ X410))) = $true))) | ! [X412 : (term > $o),X411 : subst,X413 : term] : (? [X414 : term,X415 : term] : ((((X412 @ (ap @ X414 @ X415))) != $true) & ($true = ((X412 @ X414))) & ($true = ((X412 @ X415)))) | ? [X416 : term] : (! [X417 : term] : (($true != ((X412 @ X417))) | (((X412 @ (sub @ X416 @ (push @ X417 @ id)))) = $true)) & (((X412 @ (lam @ X416))) != $true)) | (((X412 @ (sub @ X413 @ X411))) = $true) | ? [X418 : term] : ((((var @ X418)) = $true) & (((X412 @ (sub @ X418 @ X411))) != $true))) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404))) & ((induction2lem = $true) <=> ! [X331 : subst,X332 : term,X330 : (term > $o)] : (? [X335 : term] : ((((X330 @ (sub @ X335 @ X331))) != $true) & (((var @ X335)) = $true)) | ? [X334 : term,X333 : term] : (($true = ((X330 @ X334))) & (((X330 @ (ap @ X333 @ X334))) != $true) & (((X330 @ X333)) = $true)) | ? [X336 : term] : (! [X337 : term] : ((((X330 @ (sub @ X336 @ (push @ X337 @ id)))) = $true) | ($true != ((X330 @ X337)))) & (((X330 @ (lam @ X336))) != $true)) | (((X330 @ (sub @ X332 @ X331))) = $true))) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) != X208) | ! [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true = ((X210 @ one))) | (((X211 @ X212)) != $true) | ? [X213 : term] : (((X210 @ X213)) != ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & ((shinj = $true) <=> ! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh))))) & (! [X21 : (subst > term > subst > $o),X20 : term] : (? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X22 : term] : ((((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) != $true) & (((X21 @ id @ X22 @ id)) = $true)) | (((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91) | ! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)) | ? [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) != X92))) & ((hoaslamnotap = $true) <=> ! [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ? [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) != ((sub @ (X46 @ X50 @ X48) @ X49))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X161 : (term > $o),X162 : (subst > term > subst > $o),X160 : term] : ((((X161 @ (lam @ X160))) = $true) | ? [X163 : subst,X165 : term,X166 : subst,X164 : subst] : ((((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) = $true) & (((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) != $true)) | ? [X171 : term] : (((X162 @ id @ X171 @ id)) != ((X161 @ X171))) | ? [X172 : (subst > term > term)] : (! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) & ! [X176 : term] : ((((X162 @ id @ X176 @ id)) != $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true)) & (((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)) | ? [X177 : term] : ((((X161 @ X177)) = $true) & (((X161 @ (sub @ X160 @ (push @ X177 @ id)))) != $true)) | ? [X168 : subst,X170 : term,X169 : subst,X167 : subst] : (($true = ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167))) & (((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) != $true))) | ? [X159 : term] : (((sub @ X159 @ id)) != X159)) <=> (hoasinduction_lem3v2_lthm = $true)) & ((laminj = $true) <=> ! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536))) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & ((? [X70 : term] : (((sub @ X70 @ id)) != X70) | ? [X63 : term,X64 : (term > $o)] : ((((X64 @ X63)) != $true) & ! [X68 : term,X67 : term] : ((((X64 @ X68)) != $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | (((X64 @ X67)) != $true)) & ! [X69 : term] : ((((X64 @ X69)) = $true) | (((var @ X69)) != $true)) & ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ? [X66 : term] : ((((X64 @ X66)) = $true) & (((X64 @ (sub @ X65 @ (push @ X66 @ id)))) != $true)))) | ? [X60 : (subst > term > subst > $o)] : ! [X61 : (term > $o)] : ? [X62 : term] : (((X60 @ id @ X62 @ id)) != ((X61 @ X62))) | ! [X81 : term,X82 : (subst > term > subst > $o)] : ((((X82 @ id @ X81 @ id)) = $true) | ? [X84 : term,X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) & (((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true)) | ? [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88)))) & ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X82 @ id @ X86 @ id)) != $true)))) | ? [X73 : (term > $o),X72 : term,X71 : (subst > term > subst > $o)] : (! [X75 : term] : ((((X73 @ X75)) != $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) & ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) & (((X73 @ (lam @ X72))) != $true) & ! [X76 : (subst > term > term)] : (? [X79 : term,X77 : subst,X78 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) != ((sub @ (X76 @ X78 @ X79) @ X77))) | ? [X80 : term] : ((((X71 @ id @ X80 @ id)) = $true) & ($true != ((X71 @ id @ (X76 @ id @ X80) @ id)))) | (((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X16 : term] : ? [X17 : (subst > term > term)] : (((X17 @ sh @ one)) = ((sub @ X16 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) <=> (axidr = $true)) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) != ((d2subst @ X425))) | (X424 = X425)) & (hoasapnotvar = $true) & (! [X295 : term] : ? [X296 : (subst > term > term)] : ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X156 : d_subst] : (d_id = X156) & ((axshiftcons = $true) <=> ! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427)) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) <=> ! [X148 : term,X147 : (term > $o)] : (($true = ((X147 @ X148))) | ? [X151 : term] : (! [X152 : term] : ((((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true) | (((X147 @ X152)) != $true)) & (((X147 @ (lam @ X151))) != $true)) | ? [X150 : term,X149 : term] : ((((X147 @ X149)) = $true) & (((X147 @ (ap @ X149 @ X150))) != $true) & (((X147 @ X150)) = $true)) | ? [X153 : term] : ((((var @ X153)) = $true) & (((X147 @ X153)) != $true)))) & ((apinj1 = $true) <=> ! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356))))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X345 : term,X344 : (subst > term > subst > $o)] : (? [X347 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X350 : subst,X351 : subst,X349 : term] : (((X347 @ (comp @ X351 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X347 @ X351 @ X349) @ X350))) & ! [X348 : term] : ((((X344 @ id @ X348 @ id)) != $true) | (((X344 @ id @ (X347 @ id @ X348) @ id)) = $true))) | (((X344 @ id @ (lam @ X345) @ id)) = $true) | ? [X346 : term] : ((((X344 @ id @ X346 @ id)) = $true) & (((X344 @ id @ (sub @ X345 @ (push @ X346 @ id)) @ id)) != $true)))) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem0 = $true) <=> ! [X477 : (subst > term > subst > $o)] : ? [X478 : (term > $o)] : ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id)))) & (! [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | ? [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) != ((sub @ (X321 @ X326 @ X324) @ X325))) | ? [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) != ((sub @ (X320 @ X329 @ X328) @ X327))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one))))) <=> (hoaslaminj = $true)) & (! [X117 : term,X115 : (term > $o),X116 : (subst > term > subst > $o)] : (? [X119 : term] : (((X116 @ id @ X119 @ id)) != ((X115 @ X119))) | ? [X120 : (subst > term > term)] : (! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) & ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | (((X116 @ id @ X121 @ id)) != $true)) & (((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) != $true)) | ? [X118 : term] : ((((X115 @ (sub @ X117 @ (push @ X118 @ id)))) != $true) & (((X115 @ X118)) = $true)) | (((X115 @ (lam @ X117))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (! [X382 : term] : ? [X383 : (subst > term > term)] : (((X383 @ sh @ one)) = ((sub @ X382 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & ((axvarid = $true) <=> ! [X511 : term] : (((sub @ X511 @ id)) = X511)) & ((? [X179 : term,X180 : (subst > term > subst > $o)] : (! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ? [X185 : subst,X183 : term,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) != ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ? [X186 : term] : ((((X180 @ id @ X186 @ id)) = $true) & ($true != ((X180 @ id @ (X182 @ id @ X186) @ id))))) & ! [X181 : term] : ((((X180 @ id @ X181 @ id)) != $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) & ($true != ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id)))) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ! [X188 : term,X187 : (subst > term > subst > $o)] : (? [X198 : term,X200 : subst,X201 : subst,X199 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) != $true) & (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) = $true)) | ? [X197 : subst,X195 : term,X196 : subst,X194 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) != $true) & (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) = $true)) | ? [X202 : term] : ((((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) != $true) & (((X187 @ id @ X202 @ id)) = $true)) | ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X187 @ id @ (X189 @ id @ X193) @ id)) = $true) | (((X187 @ id @ X193 @ id)) != $true)) & (((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) != $true) & ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190))))) | ($true = ((X187 @ id @ (lam @ X188) @ id))))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem1_gthm = $true) & (! [X518 : term,X516 : (term > $o),X519 : (subst > term > subst > $o),X517 : term] : (($true = ((X516 @ (ap @ X517 @ X518)))) | ? [X529 : subst,X526 : subst,X527 : subst,X528 : term] : ((((X519 @ X529 @ X528 @ (comp @ X526 @ X527))) != $true) & (((X519 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)) = $true)) | ? [X523 : subst,X522 : subst,X524 : term,X525 : subst] : ((((X519 @ (comp @ X525 @ X523) @ (sub @ X524 @ X523) @ X522)) != $true) & (((X519 @ X525 @ X524 @ (comp @ X523 @ X522))) = $true)) | ? [X530 : term] : (((X516 @ X530)) != ((X519 @ id @ X530 @ id))) | ? [X520 : term,X521 : term] : ((((X519 @ id @ (ap @ (sub @ X521 @ id) @ X520) @ id)) != $true) & ($true = ((X519 @ id @ X521 @ id))) & (((X519 @ id @ X520 @ id)) = $true)) | (((X516 @ X517)) != $true) | (((X516 @ X518)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X498 : (subst > term > subst > $o),X499 : term] : (? [X501 : (subst > term > term)] : (! [X502 : term] : ((((X498 @ id @ X502 @ id)) != $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) & ! [X504 : subst,X503 : term,X505 : subst] : (((sub @ (X501 @ X504 @ X503) @ X505)) = ((X501 @ (comp @ X504 @ X505) @ (sub @ X503 @ X505)))) & (((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) != $true)) | ? [X500 : term] : ((((X498 @ id @ X500 @ id)) = $true) & (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) != $true)) | (((X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) = $true))) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (! [X507 : subst,X506 : (term > $o),X508 : term] : ? [X509 : (term > $o)] : ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510))) <=> (pushprop_lem0 = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X537 : (subst > term > subst > $o)] : ? [X538 : (term > $o)] : ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X339 : subst,X338 : term,X340 : (term > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) <=> (pushprop_lem0_lthm = $true)) & (! [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ (lam @ X0) @ id)) = $true) | ? [X11 : term] : ((((X1 @ id @ X11 @ id)) = $true) & (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) != $true)) | ? [X4 : term,X5 : subst,X2 : subst,X3 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) != $true) & (((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) = $true)) | ? [X15 : subst,X14 : subst,X12 : term,X13 : subst] : ((((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) != $true) & (((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) = $true)) | ? [X6 : (subst > term > term)] : (! [X7 : term] : ((((X1 @ id @ X7 @ id)) != $true) | (((X1 @ id @ (X6 @ id @ X7) @ id)) = $true)) & ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) & (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3 = $true)) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((? [X100 : term,X102 : (term > $o),X101 : subst] : (! [X105 : term] : ((((var @ X105)) != $true) | (((X102 @ (sub @ X105 @ X101))) = $true)) & ! [X106 : term] : (? [X107 : term] : ((((X102 @ X107)) = $true) & (((X102 @ (sub @ X106 @ (push @ X107 @ id)))) != $true)) | (((X102 @ (lam @ X106))) = $true)) & (((X102 @ (sub @ X100 @ X101))) != $true) & ! [X104 : term,X103 : term] : ((((X102 @ X104)) != $true) | (((X102 @ (ap @ X103 @ X104))) = $true) | (((X102 @ X103)) != $true))) | ? [X99 : term] : (((sub @ X99 @ id)) != X99) | ! [X109 : term,X108 : (term > $o)] : (? [X110 : term] : (! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | (((X108 @ X111)) != $true)) & (((X108 @ (lam @ X110))) != $true)) | ? [X114 : term] : ((((X108 @ X114)) != $true) & (((var @ X114)) = $true)) | (((X108 @ X109)) = $true) | ? [X113 : term,X112 : term] : ((((X108 @ X113)) = $true) & (((X108 @ (ap @ X113 @ X112))) != $true) & (((X108 @ X112)) = $true)))) <=> (induction2_lthm = $true)) & (apnotvar = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X34 : term,X33 : term,X32 : (subst > term > subst > $o)] : (? [X35 : term,X36 : term] : ((((X32 @ id @ X36 @ id)) = $true) & (((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) != $true) & (((X32 @ id @ X35 @ id)) = $true)) | (((X32 @ id @ X34 @ id)) != $true) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | (((X32 @ id @ X33 @ id)) != $true) | ? [X39 : subst,X37 : term,X40 : subst,X38 : subst] : (($true != ((X32 @ X38 @ X37 @ (comp @ X39 @ X40)))) & (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) = $true)) | ? [X41 : term,X43 : subst,X44 : subst,X42 : subst] : ((((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) = $true) & (((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) != $true)))) & ((? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131) | ! [X138 : (subst > term > term),X140 : subst,X139 : term,X137 : (subst > term > term)] : (? [X146 : subst,X145 : subst,X144 : term] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) != ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))) | ? [X143 : subst,X142 : term,X141 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) != ((sub @ (X138 @ X143 @ X142) @ X141)))) | ? [X136 : term,X135 : term] : ((X135 != X136) & (((lam @ X135)) = ((lam @ X136)))) | ? [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) != X133)) <=> (hoaslaminj_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512))))) & ((hoasinduction_lthm_3 = $true) <=> (? [X428 : (subst > term > subst > $o)] : ! [X429 : (term > $o)] : ? [X430 : term] : (((X429 @ X430)) != ((X428 @ id @ X430 @ id))) | ? [X432 : (term > $o),X431 : term] : ((((X432 @ X431)) != $true) & ! [X436 : term,X435 : term] : ((((X432 @ X435)) != $true) | (((X432 @ (ap @ X436 @ X435))) = $true) | (((X432 @ X436)) != $true)) & ! [X437 : term] : ((((X432 @ X437)) = $true) | (((var @ X437)) != $true)) & ! [X433 : term] : (? [X434 : term] : ((((X432 @ X434)) = $true) & (((X432 @ (sub @ X433 @ (push @ X434 @ id)))) != $true)) | (((X432 @ (lam @ X433))) = $true))) | ! [X449 : term,X450 : (subst > term > subst > $o)] : (? [X466 : term,X465 : term] : ((((X450 @ id @ X466 @ id)) = $true) & (((X450 @ id @ X465 @ id)) = $true) & (((X450 @ id @ (ap @ (sub @ X465 @ id) @ X466) @ id)) != $true)) | ? [X460 : (subst > term > term)] : (! [X464 : term] : ((((X450 @ id @ (X460 @ id @ X464) @ id)) = $true) | (((X450 @ id @ X464 @ id)) != $true)) & (((X450 @ id @ (lam @ (X460 @ sh @ one)) @ id)) != $true) & ! [X461 : term,X462 : subst,X463 : subst] : (((X460 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))) = ((sub @ (X460 @ X462 @ X461) @ X463)))) | ? [X459 : subst,X458 : subst,X457 : subst,X456 : term] : ((((X450 @ X458 @ X456 @ (comp @ X459 @ X457))) != $true) & (((X450 @ (comp @ X458 @ X459) @ (sub @ X456 @ X459) @ X457)) = $true)) | ? [X453 : subst,X454 : term,X451 : subst,X452 : subst] : ((((X450 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452) @ X451)) != $true) & (((X450 @ X453 @ X454 @ (comp @ X452 @ X451))) = $true)) | (((X450 @ id @ X449 @ id)) = $true) | ? [X455 : term] : ((((var @ (sub @ X455 @ id))) = $true) & (((X450 @ id @ X455 @ id)) != $true))) | ? [X438 : term] : (((sub @ X438 @ id)) != X438) | ? [X440 : term,X439 : (term > $o),X441 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X440))) != $true) & ! [X448 : term] : (((X439 @ X448)) = ((X441 @ id @ X448 @ id))) & ! [X443 : (subst > term > term)] : (? [X444 : term] : (($true = ((X441 @ id @ X444 @ id))) & (((X441 @ id @ (X443 @ id @ X444) @ id)) != $true)) | ? [X446 : subst,X447 : term,X445 : subst] : (((X443 @ (comp @ X445 @ X446) @ (sub @ X447 @ X446))) != ((sub @ (X443 @ X445 @ X447) @ X446))) | (((X441 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true)) & ! [X442 : term] : ((((X439 @ (sub @ X440 @ (push @ X442 @ id)))) = $true) | (((X439 @ X442)) != $true))))) & (! [X309 : term,X308 : (subst > term > subst > $o)] : (? [X312 : term,X311 : (subst > term > term)] : ((((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) != $true) & ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319))) & ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | (((X308 @ id @ X313 @ id)) != $true))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))) | ? [X310 : term] : ((((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) != $true) & (((X308 @ id @ X310 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X365 : (subst > term > subst > $o),X366 : term,X364 : (term > $o)] : (? [X373 : subst,X376 : subst,X375 : term,X374 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) != $true) & (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) = $true)) | ? [X377 : (subst > term > term)] : (! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) & ! [X378 : term] : ((((X365 @ id @ X378 @ id)) != $true) | (((X365 @ id @ (X377 @ id @ X378) @ id)) = $true)) & (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true)) | (((X364 @ (lam @ X366))) = $true) | ? [X371 : term] : (((X364 @ X371)) != ((X365 @ id @ X371 @ id))) | ? [X369 : subst,X370 : subst,X367 : subst,X368 : term] : ((((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) = $true) & (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) != $true)) | ? [X372 : term] : ((((X364 @ X372)) = $true) & (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & ((induction = $true) <=> ! [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) = $true) | ? [X130 : term] : ((((X125 @ (lam @ X130))) != $true) & (((X125 @ X130)) = $true)) | ? [X128 : term,X127 : term] : ((((X125 @ X127)) = $true) & (((X125 @ (ap @ X128 @ X127))) != $true) & (((X125 @ X128)) = $true)) | ? [X129 : term] : ((((var @ X129)) = $true) & ($true != ((X125 @ X129)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((? [X482 : (subst > term > subst > $o),X483 : term] : ((((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id)) != $true) & ! [X489 : term] : ((((X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)) = $true) | (((X482 @ id @ X489 @ id)) != $true)) & ! [X484 : (subst > term > term)] : (? [X485 : subst,X487 : subst,X486 : term] : (((sub @ (X484 @ X487 @ X486) @ X485)) != ((X484 @ (comp @ X487 @ X485) @ (sub @ X486 @ X485)))) | (((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ? [X488 : term] : ((((X482 @ id @ X488 @ id)) = $true) & (((X482 @ id @ (X484 @ id @ X488) @ id)) != $true)))) | ! [X491 : term,X490 : (subst > term > subst > $o)] : (? [X493 : (subst > term > term)] : (! [X494 : term] : (($true != ((X490 @ id @ X494 @ id))) | (((X490 @ id @ (X493 @ id @ X494) @ id)) = $true)) & ! [X495 : subst,X496 : term,X497 : subst] : (((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X493 @ X495 @ X496) @ X497))) & (((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) != $true)) | (((X490 @ id @ (lam @ X491) @ id)) = $true) | ? [X492 : term] : ((((X490 @ id @ X492 @ id)) = $true) & ($true != ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id))))) | ? [X481 : term] : (((sub @ X481 @ id)) != X481)) <=> (hoasinduction_lem3a_lthm = $true)) & ((substmonoid_lthm = $true) <=> (? [X29 : subst] : (((comp @ X29 @ id)) != X29) | (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)) | ? [X28 : subst] : (((comp @ id @ X28)) != X28))) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (hoasapinj1_gthm = $true) & ! [X362 : d_term,X363 : d_term] : ((X362 = X363) | (((d2term @ X362)) != ((d2term @ X363)))) & (pushprop_lem2v2_gthm = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) <=> (axidl = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 != X469) & (((ap @ X467 @ X468)) = ((ap @ X470 @ X469)))) | ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))))) & ((! [X359 : term] : (((sub @ X359 @ id)) = X359) | ? [X358 : term] : (((sub @ X358 @ id)) != X358)) <=> (termmset_lthm = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) <=> (! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59)) | ? [X51 : term] : (((sub @ X51 @ id)) != X51) | ? [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 != X54) & (((ap @ X52 @ X55)) = ((ap @ X54 @ X53)))))) & ((hoasinduction_lthm = $true) <=> (! [X254 : (subst > term > subst > $o),X255 : term] : (? [X269 : subst,X271 : term,X268 : subst,X270 : subst] : ((((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) != $true) & (((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true)) | ? [X260 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) != $true) & ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262))) & ! [X261 : term] : ((((X254 @ id @ X261 @ id)) != $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true))) | ? [X265 : term] : ((((X254 @ id @ X265 @ id)) != $true) & (((var @ (sub @ X265 @ id))) = $true)) | (((X254 @ id @ X255 @ id)) = $true) | ? [X258 : term,X256 : subst,X259 : subst,X257 : subst] : ((((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) = $true) & (((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) != $true)) | ? [X267 : term,X266 : term] : ((((X254 @ id @ X266 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & (((X254 @ id @ X267 @ id)) = $true))) | ? [X218 : term,X219 : (term > $o)] : (! [X223 : term,X224 : term] : ((((X219 @ X223)) != $true) | ($true != ((X219 @ X224))) | ($true = ((X219 @ (ap @ X223 @ X224))))) & ! [X221 : term] : ((((X219 @ (lam @ X221))) = $true) | ? [X222 : term] : ((((X219 @ X222)) = $true) & (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) != $true))) & ! [X220 : term] : ((((X219 @ X220)) = $true) | (((var @ X220)) != $true)) & (((X219 @ X218)) != $true)) | ? [X239 : (subst > term > subst > $o),X238 : term] : (! [X240 : (subst > term > term)] : (? [X241 : term] : ((((X239 @ id @ X241 @ id)) = $true) & (((X239 @ id @ (X240 @ id @ X241) @ id)) != $true)) | ? [X244 : subst,X243 : term,X242 : subst] : (((sub @ (X240 @ X242 @ X243) @ X244)) != ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)))) & ! [X253 : subst,X252 : subst,X250 : subst,X251 : term] : ((((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) != $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true)) & ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (($true != ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true)) & ! [X249 : term] : ((((X239 @ id @ X249 @ id)) != $true) | ($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id)))) & (((X239 @ id @ (lam @ X238) @ id)) != $true)) | ? [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (! [X236 : term,X234 : subst,X237 : subst,X235 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) != $true)) & ! [X233 : term,X232 : term] : ((((X225 @ id @ X232 @ id)) != $true) | (((X225 @ id @ X233 @ id)) != $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)) & (((X225 @ id @ X226 @ id)) = $true) & (((X225 @ id @ X227 @ id)) = $true) & (((X225 @ id @ (ap @ X226 @ X227) @ id)) != $true) & ! [X229 : subst,X230 : subst,X228 : subst,X231 : term] : ((((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) != $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true)))))),
% 46.03/6.94 inference(flattening,[],[f11])).
% 46.03/6.94 thf(f13,plain,(
% 46.03/6.94 (hoasinduction_lem3v2 = $true) <~> ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : ((((! [X15 : term] : ((((X1 @ (lam @ X15))) = $true) | ? [X16 : term] : ((((X1 @ (sub @ X15 @ (push @ X16 @ id)))) != $true) & (((X1 @ X16)) = $true))) | (((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true)) | ? [X10 : (subst > term > term)] : (((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) != $true) & ! [X14 : term] : ((((X0 @ id @ X14 @ id)) != $true) | (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true))) & ! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))))) | ? [X9 : subst,X8 : subst,X6 : subst,X7 : term] : ((((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) != $true) & ($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8))))) | ? [X4 : subst,X3 : subst,X5 : term,X2 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) != $true)))),
% 46.03/6.94 inference(ennf_transformation,[],[f10])).
% 46.03/6.94 thf(f14,plain,(
% 46.03/6.94 (hoasinduction_lem3v2 = $true) <~> ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (? [X4 : subst,X3 : subst,X5 : term,X2 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) != $true)) | (((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true) | ? [X10 : (subst > term > term)] : (! [X14 : term] : ((((X0 @ id @ X14 @ id)) != $true) | (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true)) & ! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) != $true)) | ? [X9 : subst,X8 : subst,X6 : subst,X7 : term] : ((((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) != $true) & ($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8)))) | ! [X15 : term] : ((((X1 @ (lam @ X15))) = $true) | ? [X16 : term] : ((((X1 @ (sub @ X15 @ (push @ X16 @ id)))) != $true) & (((X1 @ X16)) = $true))))),
% 46.03/6.94 inference(flattening,[],[f13])).
% 46.03/6.94 thf(f15,definition,(
% 46.03/6.94 ! [X225 : (subst > term > subst > $o)] : ((((sP0 @ X225)) = $true) <=> ! [X233 : term,X232 : term] : ((((X225 @ id @ X232 @ id)) != $true) | (((X225 @ id @ X233 @ id)) != $true) | (((X225 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f16,definition,(
% 46.03/6.94 ! [X239 : (subst > term > subst > $o)] : (($true = ((sP1 @ X239))) <=> ! [X240 : (subst > term > term)] : (? [X241 : term] : ((((X239 @ id @ X241 @ id)) = $true) & (((X239 @ id @ (X240 @ id @ X241) @ id)) != $true)) | ? [X244 : subst,X243 : term,X242 : subst] : (((sub @ (X240 @ X242 @ X243) @ X244)) != ((X240 @ (comp @ X242 @ X244) @ (sub @ X243 @ X244)))) | ($true = ((X239 @ id @ (lam @ (X240 @ sh @ one)) @ id)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f17,definition,(
% 46.03/6.94 ! [X219 : (term > $o)] : ((((sP2 @ X219)) = $true) <=> ! [X223 : term,X224 : term] : ((((X219 @ X223)) != $true) | ($true != ((X219 @ X224))) | ($true = ((X219 @ (ap @ X223 @ X224))))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f18,definition,(
% 46.03/6.94 ! [X254 : (subst > term > subst > $o)] : ((((sP3 @ X254)) = $true) <=> ? [X267 : term,X266 : term] : ((((X254 @ id @ X266 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & (((X254 @ id @ X267 @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f19,definition,(
% 46.03/6.94 ! [X254 : (subst > term > subst > $o)] : ((((sP4 @ X254)) = $true) <=> ? [X260 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X260 @ sh @ one)) @ id)) != $true) & ! [X262 : subst,X264 : term,X263 : subst] : (((X260 @ (comp @ X263 @ X262) @ (sub @ X264 @ X262))) = ((sub @ (X260 @ X263 @ X264) @ X262))) & ! [X261 : term] : ((((X254 @ id @ X261 @ id)) != $true) | (((X254 @ id @ (X260 @ id @ X261) @ id)) = $true))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f20,definition,(
% 46.03/6.94 (sP5 = $true) <=> ? [X239 : (subst > term > subst > $o),X238 : term] : (($true = ((sP1 @ X239))) & ! [X253 : subst,X252 : subst,X250 : subst,X251 : term] : ((((X239 @ X250 @ X251 @ (comp @ X252 @ X253))) != $true) | (((X239 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252) @ X253)) = $true)) & ! [X245 : subst,X246 : subst,X247 : term,X248 : subst] : (($true != ((X239 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246) @ X248))) | (((X239 @ X245 @ X247 @ (comp @ X246 @ X248))) = $true)) & ! [X249 : term] : ((((X239 @ id @ X249 @ id)) != $true) | ($true = ((X239 @ id @ (sub @ X238 @ (push @ X249 @ id)) @ id)))) & (((X239 @ id @ (lam @ X238) @ id)) != $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f21,definition,(
% 46.03/6.94 (sP6 = $true) <=> ! [X254 : (subst > term > subst > $o),X255 : term] : (? [X269 : subst,X271 : term,X268 : subst,X270 : subst] : ((((X254 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269)) != $true) & (((X254 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true)) | (((sP4 @ X254)) = $true) | ? [X265 : term] : ((((X254 @ id @ X265 @ id)) != $true) & (((var @ (sub @ X265 @ id))) = $true)) | (((X254 @ id @ X255 @ id)) = $true) | ? [X258 : term,X256 : subst,X259 : subst,X257 : subst] : ((((X254 @ (comp @ X259 @ X257) @ (sub @ X258 @ X257) @ X256)) = $true) & (((X254 @ X259 @ X258 @ (comp @ X257 @ X256))) != $true)) | (((sP3 @ X254)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f22,definition,(
% 46.03/6.94 (sP7 = $true) <=> ? [X225 : (subst > term > subst > $o),X226 : term,X227 : term] : (! [X236 : term,X234 : subst,X237 : subst,X235 : subst] : ((((X225 @ (comp @ X235 @ X234) @ (sub @ X236 @ X234) @ X237)) = $true) | (((X225 @ X235 @ X236 @ (comp @ X234 @ X237))) != $true)) & (((sP0 @ X225)) = $true) & (((X225 @ id @ X226 @ id)) = $true) & (((X225 @ id @ X227 @ id)) = $true) & (((X225 @ id @ (ap @ X226 @ X227) @ id)) != $true) & ! [X229 : subst,X230 : subst,X228 : subst,X231 : term] : ((((X225 @ (comp @ X230 @ X228) @ (sub @ X231 @ X228) @ X229)) != $true) | (((X225 @ X230 @ X231 @ (comp @ X228 @ X229))) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f23,definition,(
% 46.03/6.94 ($true = sP8) <=> ((sP6 = $true) | ? [X218 : term,X219 : (term > $o)] : ((((sP2 @ X219)) = $true) & ! [X221 : term] : ((((X219 @ (lam @ X221))) = $true) | ? [X222 : term] : ((((X219 @ X222)) = $true) & (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) != $true))) & ! [X220 : term] : ((((X219 @ X220)) = $true) | (((var @ X220)) != $true)) & (((X219 @ X218)) != $true)) | (sP5 = $true) | (sP7 = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f24,definition,(
% 46.03/6.94 (sP9 = $true) <=> ? [X482 : (subst > term > subst > $o),X483 : term] : ((((X482 @ id @ (lam @ (sub @ X483 @ (push @ one @ sh))) @ id)) != $true) & ! [X489 : term] : ((((X482 @ id @ (sub @ X483 @ (push @ X489 @ id)) @ id)) = $true) | (((X482 @ id @ X489 @ id)) != $true)) & ! [X484 : (subst > term > term)] : (? [X485 : subst,X487 : subst,X486 : term] : (((sub @ (X484 @ X487 @ X486) @ X485)) != ((X484 @ (comp @ X487 @ X485) @ (sub @ X486 @ X485)))) | (((X482 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ? [X488 : term] : ((((X482 @ id @ X488 @ id)) = $true) & (((X482 @ id @ (X484 @ id @ X488) @ id)) != $true))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f25,definition,(
% 46.03/6.94 (sP10 = $true) <=> ((sP9 = $true) | ! [X491 : term,X490 : (subst > term > subst > $o)] : (? [X493 : (subst > term > term)] : (! [X494 : term] : (($true != ((X490 @ id @ X494 @ id))) | (((X490 @ id @ (X493 @ id @ X494) @ id)) = $true)) & ! [X495 : subst,X496 : term,X497 : subst] : (((X493 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X493 @ X495 @ X496) @ X497))) & (((X490 @ id @ (lam @ (X493 @ sh @ one)) @ id)) != $true)) | (((X490 @ id @ (lam @ X491) @ id)) = $true) | ? [X492 : term] : ((((X490 @ id @ X492 @ id)) = $true) & ($true != ((X490 @ id @ (sub @ X491 @ (push @ X492 @ id)) @ id))))) | ? [X481 : term] : (((sub @ X481 @ id)) != X481))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f26,definition,(
% 46.03/6.94 ! [X125 : (term > $o)] : (($true = ((sP11 @ X125))) <=> ? [X128 : term,X127 : term] : ((((X125 @ X127)) = $true) & (((X125 @ (ap @ X128 @ X127))) != $true) & (((X125 @ X128)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f27,definition,(
% 46.03/6.94 ! [X365 : (subst > term > subst > $o)] : ((((sP12 @ X365)) = $true) <=> ? [X377 : (subst > term > term)] : (! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) & ! [X378 : term] : ((((X365 @ id @ X378 @ id)) != $true) | (((X365 @ id @ (X377 @ id @ X378) @ id)) = $true)) & (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f28,definition,(
% 46.03/6.94 ($true = sP13) <=> ! [X365 : (subst > term > subst > $o),X366 : term,X364 : (term > $o)] : (? [X373 : subst,X376 : subst,X375 : term,X374 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) != $true) & (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) = $true)) | (((sP12 @ X365)) = $true) | (((X364 @ (lam @ X366))) = $true) | ? [X371 : term] : (((X364 @ X371)) != ((X365 @ id @ X371 @ id))) | ? [X369 : subst,X370 : subst,X367 : subst,X368 : term] : ((((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) = $true) & (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) != $true)) | ? [X372 : term] : ((((X364 @ X372)) = $true) & (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f29,definition,(
% 46.03/6.94 (sP14 = $true) <=> ! [X309 : term,X308 : (subst > term > subst > $o)] : (? [X312 : term,X311 : (subst > term > term)] : ((((X308 @ id @ (lam @ (X311 @ sh @ one)) @ id)) != $true) & ! [X319 : subst,X318 : term,X317 : subst] : (((sub @ (sub @ X312 @ (push @ X318 @ X317)) @ X319)) = ((sub @ (X311 @ X317 @ X318) @ X319))) & ! [X316 : subst,X315 : subst,X314 : term] : (((sub @ X312 @ (push @ (sub @ X314 @ X316) @ (comp @ X315 @ X316)))) = ((X311 @ (comp @ X315 @ X316) @ (sub @ X314 @ X316)))) & ! [X313 : term] : ((((X308 @ id @ (X311 @ id @ X313) @ id)) = $true) | (((X308 @ id @ X313 @ id)) != $true))) | ($true = ((X308 @ id @ (lam @ (sub @ X309 @ (push @ one @ sh))) @ id))) | ? [X310 : term] : ((((X308 @ id @ (sub @ X309 @ (push @ X310 @ id)) @ id)) != $true) & (((X308 @ id @ X310 @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f30,definition,(
% 46.03/6.94 ! [X450 : (subst > term > subst > $o)] : ((((sP15 @ X450)) = $true) <=> ? [X460 : (subst > term > term)] : (! [X464 : term] : ((((X450 @ id @ (X460 @ id @ X464) @ id)) = $true) | (((X450 @ id @ X464 @ id)) != $true)) & (((X450 @ id @ (lam @ (X460 @ sh @ one)) @ id)) != $true) & ! [X461 : term,X462 : subst,X463 : subst] : (((X460 @ (comp @ X462 @ X463) @ (sub @ X461 @ X463))) = ((sub @ (X460 @ X462 @ X461) @ X463)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f31,definition,(
% 46.03/6.94 ! [X450 : (subst > term > subst > $o)] : ((((sP16 @ X450)) = $true) <=> ? [X466 : term,X465 : term] : ((((X450 @ id @ X466 @ id)) = $true) & (((X450 @ id @ X465 @ id)) = $true) & (((X450 @ id @ (ap @ (sub @ X465 @ id) @ X466) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f32,definition,(
% 46.03/6.94 ! [X432 : (term > $o)] : ((((sP17 @ X432)) = $true) <=> ! [X436 : term,X435 : term] : ((((X432 @ X435)) != $true) | (((X432 @ (ap @ X436 @ X435))) = $true) | (((X432 @ X436)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f33,definition,(
% 46.03/6.94 ($true = sP18) <=> ? [X440 : term,X439 : (term > $o),X441 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X440))) != $true) & ! [X448 : term] : (((X439 @ X448)) = ((X441 @ id @ X448 @ id))) & ! [X443 : (subst > term > term)] : (? [X444 : term] : (($true = ((X441 @ id @ X444 @ id))) & (((X441 @ id @ (X443 @ id @ X444) @ id)) != $true)) | ? [X446 : subst,X447 : term,X445 : subst] : (((X443 @ (comp @ X445 @ X446) @ (sub @ X447 @ X446))) != ((sub @ (X443 @ X445 @ X447) @ X446))) | (((X441 @ id @ (lam @ (X443 @ sh @ one)) @ id)) = $true)) & ! [X442 : term] : ((((X439 @ (sub @ X440 @ (push @ X442 @ id)))) = $true) | (((X439 @ X442)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f34,definition,(
% 46.03/6.94 (sP19 = $true) <=> ! [X449 : term,X450 : (subst > term > subst > $o)] : ((((sP16 @ X450)) = $true) | (((sP15 @ X450)) = $true) | ? [X459 : subst,X458 : subst,X457 : subst,X456 : term] : ((((X450 @ X458 @ X456 @ (comp @ X459 @ X457))) != $true) & (((X450 @ (comp @ X458 @ X459) @ (sub @ X456 @ X459) @ X457)) = $true)) | ? [X453 : subst,X454 : term,X451 : subst,X452 : subst] : ((((X450 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452) @ X451)) != $true) & (((X450 @ X453 @ X454 @ (comp @ X452 @ X451))) = $true)) | (((X450 @ id @ X449 @ id)) = $true) | ? [X455 : term] : ((((var @ (sub @ X455 @ id))) = $true) & (((X450 @ id @ X455 @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f35,definition,(
% 46.03/6.94 (sP20 = $true) <=> (? [X428 : (subst > term > subst > $o)] : ! [X429 : (term > $o)] : ? [X430 : term] : (((X429 @ X430)) != ((X428 @ id @ X430 @ id))) | ? [X432 : (term > $o),X431 : term] : ((((X432 @ X431)) != $true) & (((sP17 @ X432)) = $true) & ! [X437 : term] : ((((X432 @ X437)) = $true) | (((var @ X437)) != $true)) & ! [X433 : term] : (? [X434 : term] : ((((X432 @ X434)) = $true) & (((X432 @ (sub @ X433 @ (push @ X434 @ id)))) != $true)) | (((X432 @ (lam @ X433))) = $true))) | (sP19 = $true) | ? [X438 : term] : (((sub @ X438 @ id)) != X438) | ($true = sP18))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f36,definition,(
% 46.03/6.94 (sP21 = $true) <=> (? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131) | ! [X138 : (subst > term > term),X140 : subst,X139 : term,X137 : (subst > term > term)] : (? [X146 : subst,X145 : subst,X144 : term] : (((X137 @ (comp @ X146 @ X145) @ (sub @ X144 @ X145))) != ((sub @ (X137 @ X146 @ X144) @ X145))) | (((X137 @ X140 @ X139)) = ((X138 @ X140 @ X139))) | (((lam @ (X138 @ sh @ one))) != ((lam @ (X137 @ sh @ one)))) | ? [X143 : subst,X142 : term,X141 : subst] : (((X138 @ (comp @ X143 @ X141) @ (sub @ X142 @ X141))) != ((sub @ (X138 @ X143 @ X142) @ X141)))) | ? [X136 : term,X135 : term] : ((X135 != X136) & (((lam @ X135)) = ((lam @ X136)))) | ? [X134 : term,X133 : subst] : (((comp @ sh @ (push @ X134 @ X133))) != X133))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f37,definition,(
% 46.03/6.94 ! [X32 : (subst > term > subst > $o)] : ((((sP22 @ X32)) = $true) <=> ? [X35 : term,X36 : term] : ((((X32 @ id @ X36 @ id)) = $true) & (((X32 @ id @ (ap @ (sub @ X35 @ id) @ X36) @ id)) != $true) & (((X32 @ id @ X35 @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f38,definition,(
% 46.03/6.94 (sP23 = $true) <=> ! [X34 : term,X33 : term,X32 : (subst > term > subst > $o)] : ((((sP22 @ X32)) = $true) | (((X32 @ id @ X34 @ id)) != $true) | (((X32 @ id @ (ap @ X33 @ X34) @ id)) = $true) | (((X32 @ id @ X33 @ id)) != $true) | ? [X39 : subst,X37 : term,X40 : subst,X38 : subst] : (($true != ((X32 @ X38 @ X37 @ (comp @ X39 @ X40)))) & (((X32 @ (comp @ X38 @ X39) @ (sub @ X37 @ X39) @ X40)) = $true)) | ? [X41 : term,X43 : subst,X44 : subst,X42 : subst] : ((((X32 @ X43 @ X41 @ (comp @ X42 @ X44))) = $true) & (((X32 @ (comp @ X43 @ X42) @ (sub @ X41 @ X42) @ X44)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f39,definition,(
% 46.03/6.94 ! [X108 : (term > $o)] : ((((sP24 @ X108)) = $true) <=> ? [X113 : term,X112 : term] : ((((X108 @ X113)) = $true) & (((X108 @ (ap @ X113 @ X112))) != $true) & (((X108 @ X112)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f40,definition,(
% 46.03/6.94 ! [X102 : (term > $o)] : ((((sP25 @ X102)) = $true) <=> ! [X104 : term,X103 : term] : ((((X102 @ X104)) != $true) | (((X102 @ (ap @ X103 @ X104))) = $true) | (((X102 @ X103)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f41,definition,(
% 46.03/6.94 (sP26 = $true) <=> ! [X109 : term,X108 : (term > $o)] : (? [X110 : term] : (! [X111 : term] : ((((X108 @ (sub @ X110 @ (push @ X111 @ id)))) = $true) | (((X108 @ X111)) != $true)) & (((X108 @ (lam @ X110))) != $true)) | ? [X114 : term] : ((((X108 @ X114)) != $true) & (((var @ X114)) = $true)) | (((X108 @ X109)) = $true) | (((sP24 @ X108)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f42,definition,(
% 46.03/6.94 (sP27 = $true) <=> (? [X100 : term,X102 : (term > $o),X101 : subst] : (! [X105 : term] : ((((var @ X105)) != $true) | (((X102 @ (sub @ X105 @ X101))) = $true)) & ! [X106 : term] : (? [X107 : term] : ((((X102 @ X107)) = $true) & (((X102 @ (sub @ X106 @ (push @ X107 @ id)))) != $true)) | (((X102 @ (lam @ X106))) = $true)) & (((X102 @ (sub @ X100 @ X101))) != $true) & (((sP25 @ X102)) = $true)) | ? [X99 : term] : (((sub @ X99 @ id)) != X99) | (sP26 = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f43,definition,(
% 46.03/6.94 ! [X1 : (subst > term > subst > $o)] : ((((sP28 @ X1)) = $true) <=> ? [X6 : (subst > term > term)] : (! [X7 : term] : ((((X1 @ id @ X7 @ id)) != $true) | (((X1 @ id @ (X6 @ id @ X7) @ id)) = $true)) & ! [X8 : subst,X9 : term,X10 : subst] : (((sub @ (X6 @ X8 @ X9) @ X10)) = ((X6 @ (comp @ X8 @ X10) @ (sub @ X9 @ X10)))) & (((X1 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f44,definition,(
% 46.03/6.94 (sP29 = $true) <=> ! [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ (lam @ X0) @ id)) = $true) | ? [X11 : term] : ((((X1 @ id @ X11 @ id)) = $true) & (((X1 @ id @ (sub @ X0 @ (push @ X11 @ id)) @ id)) != $true)) | ? [X4 : term,X5 : subst,X2 : subst,X3 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X2 @ X5))) != $true) & (((X1 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X5)) = $true)) | ? [X15 : subst,X14 : subst,X12 : term,X13 : subst] : ((((X1 @ (comp @ X14 @ X15) @ (sub @ X12 @ X15) @ X13)) != $true) & (((X1 @ X14 @ X12 @ (comp @ X15 @ X13))) = $true)) | (((sP28 @ X1)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f45,definition,(
% 46.03/6.94 (sP30 = $true) <=> ! [X498 : (subst > term > subst > $o),X499 : term] : (? [X501 : (subst > term > term)] : (! [X502 : term] : ((((X498 @ id @ X502 @ id)) != $true) | (((X498 @ id @ (X501 @ id @ X502) @ id)) = $true)) & ! [X504 : subst,X503 : term,X505 : subst] : (((sub @ (X501 @ X504 @ X503) @ X505)) = ((X501 @ (comp @ X504 @ X505) @ (sub @ X503 @ X505)))) & (((X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) != $true)) | ? [X500 : term] : ((((X498 @ id @ X500 @ id)) = $true) & (((X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) != $true)) | (((X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f46,definition,(
% 46.03/6.94 ! [X519 : (subst > term > subst > $o)] : ((((sP31 @ X519)) = $true) <=> ? [X520 : term,X521 : term] : ((((X519 @ id @ (ap @ (sub @ X521 @ id) @ X520) @ id)) != $true) & ($true = ((X519 @ id @ X521 @ id))) & (((X519 @ id @ X520 @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f47,definition,(
% 46.03/6.94 (sP32 = $true) <=> ! [X518 : term,X516 : (term > $o),X519 : (subst > term > subst > $o),X517 : term] : (($true = ((X516 @ (ap @ X517 @ X518)))) | ? [X529 : subst,X526 : subst,X527 : subst,X528 : term] : ((((X519 @ X529 @ X528 @ (comp @ X526 @ X527))) != $true) & (((X519 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)) = $true)) | ? [X523 : subst,X522 : subst,X524 : term,X525 : subst] : ((((X519 @ (comp @ X525 @ X523) @ (sub @ X524 @ X523) @ X522)) != $true) & (((X519 @ X525 @ X524 @ (comp @ X523 @ X522))) = $true)) | ? [X530 : term] : (((X516 @ X530)) != ((X519 @ id @ X530 @ id))) | (((sP31 @ X519)) = $true) | (((X516 @ X517)) != $true) | (((X516 @ X518)) != $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f48,definition,(
% 46.03/6.94 ! [X187 : (subst > term > subst > $o)] : ((((sP33 @ X187)) = $true) <=> ? [X189 : (subst > term > term)] : (! [X193 : term] : ((((X187 @ id @ (X189 @ id @ X193) @ id)) = $true) | (((X187 @ id @ X193 @ id)) != $true)) & (((X187 @ id @ (lam @ (X189 @ sh @ one)) @ id)) != $true) & ! [X192 : term,X191 : subst,X190 : subst] : (((sub @ (X189 @ X191 @ X192) @ X190)) = ((X189 @ (comp @ X191 @ X190) @ (sub @ X192 @ X190))))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f49,definition,(
% 46.03/6.94 (sP34 = $true) <=> ? [X179 : term,X180 : (subst > term > subst > $o)] : (! [X182 : (subst > term > term)] : ((((X180 @ id @ (lam @ (X182 @ sh @ one)) @ id)) = $true) | ? [X185 : subst,X183 : term,X184 : subst] : (((sub @ (X182 @ X185 @ X183) @ X184)) != ((X182 @ (comp @ X185 @ X184) @ (sub @ X183 @ X184)))) | ? [X186 : term] : ((((X180 @ id @ X186 @ id)) = $true) & ($true != ((X180 @ id @ (X182 @ id @ X186) @ id))))) & ! [X181 : term] : ((((X180 @ id @ X181 @ id)) != $true) | (((X180 @ id @ (sub @ X179 @ (push @ X181 @ id)) @ id)) = $true)) & ($true != ((X180 @ id @ (lam @ (sub @ X179 @ (push @ one @ sh))) @ id))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f50,definition,(
% 46.03/6.94 (sP35 = $true) <=> ((sP34 = $true) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ! [X188 : term,X187 : (subst > term > subst > $o)] : (? [X198 : term,X200 : subst,X201 : subst,X199 : subst] : ((((X187 @ X200 @ X198 @ (comp @ X201 @ X199))) != $true) & (((X187 @ (comp @ X200 @ X201) @ (sub @ X198 @ X201) @ X199)) = $true)) | ? [X197 : subst,X195 : term,X196 : subst,X194 : subst] : ((((X187 @ (comp @ X197 @ X196) @ (sub @ X195 @ X196) @ X194)) != $true) & (((X187 @ X197 @ X195 @ (comp @ X196 @ X194))) = $true)) | ? [X202 : term] : ((((X187 @ id @ (sub @ X188 @ (push @ X202 @ id)) @ id)) != $true) & (((X187 @ id @ X202 @ id)) = $true)) | (((sP33 @ X187)) = $true) | ($true = ((X187 @ id @ (lam @ X188) @ id)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f51,definition,(
% 46.03/6.94 (sP36 = $true) <=> ! [X117 : term,X115 : (term > $o),X116 : (subst > term > subst > $o)] : (? [X119 : term] : (((X116 @ id @ X119 @ id)) != ((X115 @ X119))) | ? [X120 : (subst > term > term)] : (! [X122 : subst,X123 : term,X124 : subst] : (((sub @ (X120 @ X122 @ X123) @ X124)) = ((X120 @ (comp @ X122 @ X124) @ (sub @ X123 @ X124)))) & ! [X121 : term] : ((((X116 @ id @ (X120 @ id @ X121) @ id)) = $true) | (((X116 @ id @ X121 @ id)) != $true)) & (((X116 @ id @ (lam @ (X120 @ sh @ one)) @ id)) != $true)) | ? [X118 : term] : ((((X115 @ (sub @ X117 @ (push @ X118 @ id)))) != $true) & (((X115 @ X118)) = $true)) | (((X115 @ (lam @ X117))) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f52,definition,(
% 46.03/6.94 ($true = sP37) <=> ! [X345 : term,X344 : (subst > term > subst > $o)] : (? [X347 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X350 : subst,X351 : subst,X349 : term] : (((X347 @ (comp @ X351 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X347 @ X351 @ X349) @ X350))) & ! [X348 : term] : ((((X344 @ id @ X348 @ id)) != $true) | (((X344 @ id @ (X347 @ id @ X348) @ id)) = $true))) | (((X344 @ id @ (lam @ X345) @ id)) = $true) | ? [X346 : term] : ((((X344 @ id @ X346 @ id)) = $true) & (((X344 @ id @ (sub @ X345 @ (push @ X346 @ id)) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f53,definition,(
% 46.03/6.94 ! [X147 : (term > $o)] : ((((sP38 @ X147)) = $true) <=> ? [X150 : term,X149 : term] : ((((X147 @ X149)) = $true) & (((X147 @ (ap @ X149 @ X150))) != $true) & (((X147 @ X150)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f54,definition,(
% 46.03/6.94 (sP39 = $true) <=> ! [X148 : term,X147 : (term > $o)] : (($true = ((X147 @ X148))) | ? [X151 : term] : (! [X152 : term] : ((((X147 @ (sub @ X151 @ (push @ X152 @ id)))) = $true) | (((X147 @ X152)) != $true)) & (((X147 @ (lam @ X151))) != $true)) | (((sP38 @ X147)) = $true) | ? [X153 : term] : ((((var @ X153)) = $true) & (((X147 @ X153)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f55,definition,(
% 46.03/6.94 ! [X82 : (subst > term > subst > $o)] : ((((sP40 @ X82)) = $true) <=> ? [X85 : (subst > term > term)] : ((((X82 @ id @ (lam @ (X85 @ sh @ one)) @ id)) != $true) & ! [X87 : subst,X89 : term,X88 : subst] : (((sub @ (X85 @ X87 @ X89) @ X88)) = ((X85 @ (comp @ X87 @ X88) @ (sub @ X89 @ X88)))) & ! [X86 : term] : ((((X82 @ id @ (X85 @ id @ X86) @ id)) = $true) | (((X82 @ id @ X86 @ id)) != $true))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f56,definition,(
% 46.03/6.94 ! [X64 : (term > $o)] : ((((sP41 @ X64)) = $true) <=> ! [X68 : term,X67 : term] : ((((X64 @ X68)) != $true) | (((X64 @ (ap @ X67 @ X68))) = $true) | (((X64 @ X67)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f57,definition,(
% 46.03/6.94 (sP42 = $true) <=> ? [X73 : (term > $o),X72 : term,X71 : (subst > term > subst > $o)] : (! [X75 : term] : ((((X73 @ X75)) != $true) | ($true = ((X73 @ (sub @ X72 @ (push @ X75 @ id)))))) & ! [X74 : term] : (((X73 @ X74)) = ((X71 @ id @ X74 @ id))) & (((X73 @ (lam @ X72))) != $true) & ! [X76 : (subst > term > term)] : (? [X79 : term,X77 : subst,X78 : subst] : (((X76 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77))) != ((sub @ (X76 @ X78 @ X79) @ X77))) | ? [X80 : term] : ((((X71 @ id @ X80 @ id)) = $true) & ($true != ((X71 @ id @ (X76 @ id @ X80) @ id)))) | (((X71 @ id @ (lam @ (X76 @ sh @ one)) @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f58,definition,(
% 46.03/6.94 (sP43 = $true) <=> ? [X63 : term,X64 : (term > $o)] : ((((X64 @ X63)) != $true) & (((sP41 @ X64)) = $true) & ! [X69 : term] : ((((X64 @ X69)) = $true) | (((var @ X69)) != $true)) & ! [X65 : term] : ((((X64 @ (lam @ X65))) = $true) | ? [X66 : term] : ((((X64 @ X66)) = $true) & (((X64 @ (sub @ X65 @ (push @ X66 @ id)))) != $true))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f59,definition,(
% 46.03/6.94 (sP44 = $true) <=> (? [X70 : term] : (((sub @ X70 @ id)) != X70) | (sP43 = $true) | ? [X60 : (subst > term > subst > $o)] : ! [X61 : (term > $o)] : ? [X62 : term] : (((X60 @ id @ X62 @ id)) != ((X61 @ X62))) | ! [X81 : term,X82 : (subst > term > subst > $o)] : ((((X82 @ id @ X81 @ id)) = $true) | ? [X84 : term,X83 : term] : ((((X82 @ id @ X83 @ id)) = $true) & (((X82 @ id @ (ap @ (sub @ X83 @ id) @ X84) @ id)) != $true) & (((X82 @ id @ X84 @ id)) = $true)) | (((sP40 @ X82)) = $true)) | (sP42 = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f60,definition,(
% 46.03/6.94 ! [X162 : (subst > term > subst > $o)] : (($true = ((sP45 @ X162))) <=> ? [X172 : (subst > term > term)] : (! [X175 : subst,X174 : subst,X173 : term] : (((sub @ (X172 @ X175 @ X173) @ X174)) = ((X172 @ (comp @ X175 @ X174) @ (sub @ X173 @ X174)))) & ! [X176 : term] : ((((X162 @ id @ X176 @ id)) != $true) | (((X162 @ id @ (X172 @ id @ X176) @ id)) = $true)) & (((X162 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f61,definition,(
% 46.03/6.94 (sP46 = $true) <=> (! [X161 : (term > $o),X162 : (subst > term > subst > $o),X160 : term] : ((((X161 @ (lam @ X160))) = $true) | ? [X163 : subst,X165 : term,X166 : subst,X164 : subst] : ((((X162 @ X164 @ X165 @ (comp @ X166 @ X163))) = $true) & (((X162 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X163)) != $true)) | ? [X171 : term] : (((X162 @ id @ X171 @ id)) != ((X161 @ X171))) | ($true = ((sP45 @ X162))) | ? [X177 : term] : ((((X161 @ X177)) = $true) & (((X161 @ (sub @ X160 @ (push @ X177 @ id)))) != $true)) | ? [X168 : subst,X170 : term,X169 : subst,X167 : subst] : (($true = ((X162 @ (comp @ X169 @ X168) @ (sub @ X170 @ X168) @ X167))) & (((X162 @ X169 @ X170 @ (comp @ X168 @ X167))) != $true))) | ? [X159 : term] : (((sub @ X159 @ id)) != X159))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f62,definition,(
% 46.03/6.94 (sP47 = $true) <=> ! [X21 : (subst > term > subst > $o),X20 : term] : (? [X23 : (subst > term > term)] : (! [X25 : subst,X27 : subst,X26 : term] : (((X23 @ (comp @ X27 @ X25) @ (sub @ X26 @ X25))) = ((sub @ (X23 @ X27 @ X26) @ X25))) & ! [X24 : term] : ((((X21 @ id @ (X23 @ id @ X24) @ id)) = $true) | (((X21 @ id @ X24 @ id)) != $true)) & (((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X22 : term] : ((((X21 @ id @ (sub @ X20 @ (push @ X22 @ id)) @ id)) != $true) & (((X21 @ id @ X22 @ id)) = $true)) | (((X21 @ id @ (lam @ (sub @ X20 @ (push @ one @ sh))) @ id)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f63,definition,(
% 46.03/6.94 ! [X330 : (term > $o)] : ((((sP48 @ X330)) = $true) <=> ? [X334 : term,X333 : term] : (($true = ((X330 @ X334))) & (((X330 @ (ap @ X333 @ X334))) != $true) & (((X330 @ X333)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f64,definition,(
% 46.03/6.94 (sP49 = $true) <=> ! [X331 : subst,X332 : term,X330 : (term > $o)] : (? [X335 : term] : ((((X330 @ (sub @ X335 @ X331))) != $true) & (((var @ X335)) = $true)) | (((sP48 @ X330)) = $true) | ? [X336 : term] : (! [X337 : term] : ((((X330 @ (sub @ X336 @ (push @ X337 @ id)))) = $true) | ($true != ((X330 @ X337)))) & (((X330 @ (lam @ X336))) != $true)) | (((X330 @ (sub @ X332 @ X331))) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f65,definition,(
% 46.03/6.94 ! [X412 : (term > $o)] : ((((sP50 @ X412)) = $true) <=> ? [X414 : term,X415 : term] : ((((X412 @ (ap @ X414 @ X415))) != $true) & ($true = ((X412 @ X414))) & ($true = ((X412 @ X415)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f66,definition,(
% 46.03/6.94 ! [X405 : (term > $o)] : ((((sP51 @ X405)) = $true) <=> ! [X408 : term,X407 : term] : ((((X405 @ (ap @ X408 @ X407))) = $true) | (((X405 @ X407)) != $true) | (((X405 @ X408)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f67,definition,(
% 46.03/6.94 ($true = sP52) <=> ! [X412 : (term > $o),X411 : subst,X413 : term] : ((((sP50 @ X412)) = $true) | ? [X416 : term] : (! [X417 : term] : (($true != ((X412 @ X417))) | (((X412 @ (sub @ X416 @ (push @ X417 @ id)))) = $true)) & (((X412 @ (lam @ X416))) != $true)) | (((X412 @ (sub @ X413 @ X411))) = $true) | ? [X418 : term] : ((((var @ X418)) = $true) & (((X412 @ (sub @ X418 @ X411))) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f68,definition,(
% 46.03/6.94 (sP53 = $true) <=> (? [X400 : subst,X401 : term] : (((sub @ one @ (push @ X401 @ X400))) != X401) | ? [X402 : subst,X403 : term] : (((comp @ sh @ (push @ X403 @ X402))) != X402) | ? [X406 : term,X405 : (term > $o)] : (! [X409 : term] : ((((var @ X409)) != $true) | (((X405 @ X409)) = $true)) & (((sP51 @ X405)) = $true) & (((X405 @ X406)) != $true) & ! [X410 : term] : ((((X405 @ X410)) != $true) | (((X405 @ (lam @ X410))) = $true))) | ($true = sP52) | ? [X404 : subst] : (((comp @ X404 @ id)) != X404))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f69,definition,(
% 46.03/6.94 ! [X277 : (subst > term > subst > $o)] : ((((sP54 @ X277)) = $true) <=> ? [X280 : (subst > term > term)] : (! [X284 : term] : ((((X277 @ id @ X284 @ id)) != $true) | ($true = ((X277 @ id @ (X280 @ id @ X284) @ id)))) & ! [X282 : subst,X281 : term,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) & (((X277 @ id @ (lam @ (X280 @ sh @ one)) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f70,definition,(
% 46.03/6.94 ! [X277 : (subst > term > subst > $o)] : ((((sP55 @ X277)) = $true) <=> ? [X294 : term,X293 : term] : ((((X277 @ id @ X293 @ id)) = $true) & (((X277 @ id @ X294 @ id)) = $true) & ($true != ((X277 @ id @ (ap @ (sub @ X293 @ id) @ X294) @ id)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f71,definition,(
% 46.03/6.94 (sP56 = $true) <=> ! [X278 : term,X277 : (subst > term > subst > $o)] : (? [X292 : subst,X289 : term,X290 : subst,X291 : subst] : (($true = ((X277 @ (comp @ X291 @ X292) @ (sub @ X289 @ X292) @ X290))) & (((X277 @ X291 @ X289 @ (comp @ X292 @ X290))) != $true)) | (((X277 @ id @ X278 @ id)) = $true) | ? [X287 : subst,X286 : term,X285 : subst,X288 : subst] : ((((X277 @ (comp @ X288 @ X285) @ (sub @ X286 @ X285) @ X287)) != $true) & (((X277 @ X288 @ X286 @ (comp @ X285 @ X287))) = $true)) | (((sP55 @ X277)) = $true) | ? [X279 : term] : ((((X277 @ id @ X279 @ id)) != $true) & (((var @ (sub @ X279 @ id))) = $true)) | (((sP54 @ X277)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f72,definition,(
% 46.03/6.94 ! [X299 : (subst > term > subst > $o)] : ((((sP57 @ X299)) = $true) <=> ? [X306 : term,X307 : term] : (($true != ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) & (((X299 @ id @ X306 @ id)) = $true) & (((X299 @ id @ X307 @ id)) = $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f73,definition,(
% 46.03/6.94 (sP58 = $true) <=> (? [X388 : term] : (((sub @ X388 @ id)) != X388) | ! [X390 : (term > $o),X391 : term,X389 : (subst > term > subst > $o)] : (? [X394 : (subst > term > term)] : (! [X396 : term,X397 : subst,X395 : subst] : (((X394 @ (comp @ X397 @ X395) @ (sub @ X396 @ X395))) = ((sub @ (X394 @ X397 @ X396) @ X395))) & ! [X398 : term] : ((((X389 @ id @ (X394 @ id @ X398) @ id)) = $true) | (((X389 @ id @ X398 @ id)) != $true)) & (((X389 @ id @ (lam @ (X394 @ sh @ one)) @ id)) != $true)) | ? [X393 : term] : (((X389 @ id @ X393 @ id)) != ((X390 @ X393))) | ? [X392 : term] : ((((X390 @ (sub @ X391 @ (push @ X392 @ id)))) != $true) & (((X390 @ X392)) = $true)) | (((X390 @ (lam @ X391))) = $true)) | ? [X384 : term] : ! [X385 : (subst > term > term)] : ? [X386 : subst,X387 : term] : (((X385 @ X386 @ X387)) != ((sub @ X384 @ (push @ X387 @ X386)))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f74,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((sP58 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) & (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) != $true) & ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true))) | (((sP57 @ X299)) = $true))) & (! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X531 : term] : ? [X532 : (subst > term > term)] : ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) = $true) | (((X419 @ X421)) != $true) | ? [X423 : term] : (((X422 @ X423)) != ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))))) & ((sP56 = $true) <=> (hoasinduction = $true)) & (pushprop_lthm = $true) & ((induction2lem_lthm = $true) <=> (sP53 = $true)) & ((induction2lem = $true) <=> (sP49 = $true)) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) != X208) | ! [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true = ((X210 @ one))) | (((X211 @ X212)) != $true) | ? [X213 : term] : (((X210 @ X213)) != ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & ((shinj = $true) <=> ! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh))))) & ((sP47 = $true) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91) | ! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)) | ? [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) != X92))) & ((hoaslamnotap = $true) <=> ! [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ? [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) != ((sub @ (X46 @ X50 @ X48) @ X49))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((sP46 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & ((laminj = $true) <=> ! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536))) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) <=> (axscons = $true)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) <=> (termmset = $true)) & ((sP44 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X16 : term] : ? [X17 : (subst > term > term)] : (((X17 @ sh @ one)) = ((sub @ X16 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) <=> (axidr = $true)) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) != ((d2subst @ X425))) | (X424 = X425)) & (hoasapnotvar = $true) & (! [X295 : term] : ? [X296 : (subst > term > term)] : ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) <=> (hoasinduction_lem3v2_f = $true)) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X156 : d_subst] : (d_id = X156) & ((axshiftcons = $true) <=> ! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427)) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) <=> (sP39 = $true)) & ((apinj1 = $true) <=> ! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356))))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP37)) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem0 = $true) <=> ! [X477 : (subst > term > subst > $o)] : ? [X478 : (term > $o)] : ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id)))) & (! [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | ? [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) != ((sub @ (X321 @ X326 @ X324) @ X325))) | ? [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) != ((sub @ (X320 @ X329 @ X328) @ X327))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one))))) <=> (hoaslaminj = $true)) & ((sP36 = $true) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (! [X382 : term] : ? [X383 : (subst > term > term)] : (((X383 @ sh @ one)) = ((sub @ X382 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & ((axvarid = $true) <=> ! [X511 : term] : (((sub @ X511 @ id)) = X511)) & ((sP35 = $true) <=> (hoasinduction_lem3_lthm = $true)) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem1_gthm = $true) & ((sP32 = $true) <=> (hoasinduction_lem2v2 = $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP30 = $true)) & ((hoasapinj1 = $true) <=> ! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215))))) & (! [X507 : subst,X506 : (term > $o),X508 : term] : ? [X509 : (term > $o)] : ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510))) <=> (pushprop_lem0 = $true)) & (termmset_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X537 : (subst > term > subst > $o)] : ? [X538 : (term > $o)] : ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & ((axvarcons = $true) <=> ! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X339 : subst,X338 : term,X340 : (term > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) <=> (pushprop_lem0_lthm = $true)) & ((sP29 = $true) <=> (hoasinduction_lem3 = $true)) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((sP27 = $true) <=> (induction2_lthm = $true)) & (apnotvar = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) <=> (apinj2 = $true)) & ((hoasinduction_lem2 = $true) <=> (sP23 = $true)) & ((sP21 = $true) <=> (hoaslaminj_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512))))) & ((hoasinduction_lthm_3 = $true) <=> (sP20 = $true)) & ((sP14 = $true) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP13) <=> (hoasinduction_lem3v2 = $true)) & ((substmonoid = $true) <=> (! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18))) & ((induction = $true) <=> ! [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) = $true) | ? [X130 : term] : ((((X125 @ (lam @ X130))) != $true) & (((X125 @ X130)) = $true)) | ($true = ((sP11 @ X125))) | ? [X129 : term] : ((((var @ X129)) = $true) & ($true != ((X125 @ X129)))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP10 = $true) <=> (hoasinduction_lem3a_lthm = $true)) & ((substmonoid_lthm = $true) <=> (? [X29 : subst] : (((comp @ X29 @ id)) != X29) | (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)) | ? [X28 : subst] : (((comp @ id @ X28)) != X28))) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (hoasapinj1_gthm = $true) & ! [X362 : d_term,X363 : d_term] : ((X362 = X363) | (((d2term @ X362)) != ((d2term @ X363)))) & (pushprop_lem2v2_gthm = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) <=> (axidl = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 != X469) & (((ap @ X467 @ X468)) = ((ap @ X470 @ X469)))) | ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))))) & ((! [X359 : term] : (((sub @ X359 @ id)) = X359) | ? [X358 : term] : (((sub @ X358 @ id)) != X358)) <=> (termmset_lthm = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) <=> (! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59)) | ? [X51 : term] : (((sub @ X51 @ id)) != X51) | ? [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 != X54) & (((ap @ X52 @ X55)) = ((ap @ X54 @ X53)))))) & ((hoasinduction_lthm = $true) <=> ($true = sP8))),
% 46.03/6.94 inference(definition_folding,[],[f12,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,f18,f17,f16,f15])).
% 46.03/6.94 thf(f75,definition,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : ((((sP59 @ X0)) = $true) <=> ? [X10 : (subst > term > term)] : (! [X14 : term] : ((((X0 @ id @ X14 @ id)) != $true) | (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true)) & ! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) != $true)))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f76,definition,(
% 46.03/6.94 (sP60 = $true) <=> ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (? [X4 : subst,X3 : subst,X5 : term,X2 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) != $true)) | (((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true) | (((sP59 @ X0)) = $true) | ? [X9 : subst,X8 : subst,X6 : subst,X7 : term] : ((((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) != $true) & ($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8)))) | ! [X15 : term] : ((((X1 @ (lam @ X15))) = $true) | ? [X16 : term] : ((((X1 @ (sub @ X15 @ (push @ X16 @ id)))) != $true) & (((X1 @ X16)) = $true))))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 46.03/6.94 thf(f77,plain,(
% 46.03/6.94 (hoasinduction_lem3v2 = $true) <~> (sP60 = $true)),
% 46.03/6.94 inference(definition_folding,[],[f14,f76,f75])).
% 46.03/6.94 thf(f82,plain,(
% 46.03/6.94 ! [X299 : (subst > term > subst > $o)] : (((((sP57 @ X299)) = $true) | ! [X306 : term,X307 : term] : (($true = ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) | (((X299 @ id @ X306 @ id)) != $true) | (((X299 @ id @ X307 @ id)) != $true))) & (? [X306 : term,X307 : term] : (($true != ((X299 @ id @ (ap @ (sub @ X307 @ id) @ X306) @ id))) & (((X299 @ id @ X306 @ id)) = $true) & (((X299 @ id @ X307 @ id)) = $true)) | (((sP57 @ X299)) != $true)))),
% 46.03/6.94 inference(nnf_transformation,[],[f72])).
% 46.03/6.94 thf(f83,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : (((((sP57 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id)) = $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ X2 @ id)) != $true))) & (? [X3 : term,X4 : term] : ((((X0 @ id @ (ap @ (sub @ X4 @ id) @ X3) @ id)) != $true) & (((X0 @ id @ X3 @ id)) = $true) & (((X0 @ id @ X4 @ id)) = $true)) | (((sP57 @ X0)) != $true)))),
% 46.03/6.94 inference(rectify,[],[f82])).
% 46.03/6.94 thf(f84,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : (((((sP57 @ X0)) = $true) | ! [X1 : term,X2 : term] : ((((X0 @ id @ (ap @ (sub @ X2 @ id) @ X1) @ id)) = $true) | (((X0 @ id @ X1 @ id)) != $true) | (((X0 @ id @ X2 @ id)) != $true))) & (((((X0 @ id @ (ap @ (sub @ (sK77 @ X0) @ id) @ (sK76 @ X0)) @ id)) != $true) & (((X0 @ id @ (sK76 @ X0) @ id)) = $true) & (((X0 @ id @ (sK77 @ X0) @ id)) = $true)) | (((sP57 @ X0)) != $true)))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27)],[f83])).
% 46.03/6.94 thf(f221,plain,(
% 46.03/6.94 (($true = sP13) | ? [X365 : (subst > term > subst > $o),X366 : term,X364 : (term > $o)] : (! [X373 : subst,X376 : subst,X375 : term,X374 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) = $true) | (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) != $true)) & (((sP12 @ X365)) != $true) & (((X364 @ (lam @ X366))) != $true) & ! [X371 : term] : (((X364 @ X371)) = ((X365 @ id @ X371 @ id))) & ! [X369 : subst,X370 : subst,X367 : subst,X368 : term] : ((((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) != $true) | (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) = $true)) & ! [X372 : term] : ((((X364 @ X372)) != $true) | (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) = $true)))) & (! [X365 : (subst > term > subst > $o),X366 : term,X364 : (term > $o)] : (? [X373 : subst,X376 : subst,X375 : term,X374 : subst] : ((((X365 @ X376 @ X375 @ (comp @ X373 @ X374))) != $true) & (((X365 @ (comp @ X376 @ X373) @ (sub @ X375 @ X373) @ X374)) = $true)) | (((sP12 @ X365)) = $true) | (((X364 @ (lam @ X366))) = $true) | ? [X371 : term] : (((X364 @ X371)) != ((X365 @ id @ X371 @ id))) | ? [X369 : subst,X370 : subst,X367 : subst,X368 : term] : ((((X365 @ X369 @ X368 @ (comp @ X370 @ X367))) = $true) & (((X365 @ (comp @ X369 @ X370) @ (sub @ X368 @ X370) @ X367)) != $true)) | ? [X372 : term] : ((((X364 @ X372)) = $true) & (((X364 @ (sub @ X366 @ (push @ X372 @ id)))) != $true))) | ($true != sP13))),
% 46.03/6.94 inference(nnf_transformation,[],[f28])).
% 46.03/6.94 thf(f222,plain,(
% 46.03/6.94 (($true = sP13) | ? [X0 : (subst > term > subst > $o),X1 : term,X2 : (term > $o)] : (! [X3 : subst,X4 : subst,X5 : term,X6 : subst] : ((((X0 @ X4 @ X5 @ (comp @ X3 @ X6))) = $true) | (((X0 @ (comp @ X4 @ X3) @ (sub @ X5 @ X3) @ X6)) != $true)) & ($true != ((sP12 @ X0))) & (((X2 @ (lam @ X1))) != $true) & ! [X7 : term] : (((X2 @ X7)) = ((X0 @ id @ X7 @ id))) & ! [X8 : subst,X9 : subst,X10 : subst,X11 : term] : ((((X0 @ X8 @ X11 @ (comp @ X9 @ X10))) != $true) | (((X0 @ (comp @ X8 @ X9) @ (sub @ X11 @ X9) @ X10)) = $true)) & ! [X12 : term] : ((((X2 @ X12)) != $true) | (((X2 @ (sub @ X1 @ (push @ X12 @ id)))) = $true)))) & (! [X13 : (subst > term > subst > $o),X14 : term,X15 : (term > $o)] : (? [X16 : subst,X17 : subst,X18 : term,X19 : subst] : ((((X13 @ X17 @ X18 @ (comp @ X16 @ X19))) != $true) & (((X13 @ (comp @ X17 @ X16) @ (sub @ X18 @ X16) @ X19)) = $true)) | (((sP12 @ X13)) = $true) | (((X15 @ (lam @ X14))) = $true) | ? [X20 : term] : (((X13 @ id @ X20 @ id)) != ((X15 @ X20))) | ? [X21 : subst,X22 : subst,X23 : subst,X24 : term] : ((((X13 @ X21 @ X24 @ (comp @ X22 @ X23))) = $true) & ($true != ((X13 @ (comp @ X21 @ X22) @ (sub @ X24 @ X22) @ X23)))) | ? [X25 : term] : ((((X15 @ X25)) = $true) & (((X15 @ (sub @ X14 @ (push @ X25 @ id)))) != $true))) | ($true != sP13))),
% 46.03/6.94 inference(rectify,[],[f221])).
% 46.03/6.94 thf(f223,plain,(
% 46.03/6.94 (($true = sP13) | (! [X3 : subst,X4 : subst,X5 : term,X6 : subst] : ((((sK365 @ X4 @ X5 @ (comp @ X3 @ X6))) = $true) | (((sK365 @ (comp @ X4 @ X3) @ (sub @ X5 @ X3) @ X6)) != $true)) & (((sP12 @ sK365)) != $true) & (((sK367 @ (lam @ sK366))) != $true) & ! [X7 : term] : (((sK367 @ X7)) = ((sK365 @ id @ X7 @ id))) & ! [X8 : subst,X9 : subst,X10 : subst,X11 : term] : ((((sK365 @ X8 @ X11 @ (comp @ X9 @ X10))) != $true) | (((sK365 @ (comp @ X8 @ X9) @ (sub @ X11 @ X9) @ X10)) = $true)) & ! [X12 : term] : ((((sK367 @ X12)) != $true) | (((sK367 @ (sub @ sK366 @ (push @ X12 @ id)))) = $true)))) & (! [X13 : (subst > term > subst > $o),X14 : term,X15 : (term > $o)] : (((((X13 @ (sK369 @ X13) @ (sK370 @ X13) @ (comp @ (sK368 @ X13) @ (sK371 @ X13)))) != $true) & (((X13 @ (comp @ (sK369 @ X13) @ (sK368 @ X13)) @ (sub @ (sK370 @ X13) @ (sK368 @ X13)) @ (sK371 @ X13))) = $true)) | (((sP12 @ X13)) = $true) | (((X15 @ (lam @ X14))) = $true) | (((X13 @ id @ (sK372 @ X15 @ X13) @ id)) != ((X15 @ (sK372 @ X15 @ X13)))) | ((((X13 @ (sK373 @ X13) @ (sK376 @ X13) @ (comp @ (sK374 @ X13) @ (sK375 @ X13)))) = $true) & (((X13 @ (comp @ (sK373 @ X13) @ (sK374 @ X13)) @ (sub @ (sK376 @ X13) @ (sK374 @ X13)) @ (sK375 @ X13))) != $true)) | ((((X15 @ (sK377 @ X15 @ X14))) = $true) & (((X15 @ (sub @ X14 @ (push @ (sK377 @ X15 @ X14) @ id)))) != $true))) | ($true != sP13))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK365,sK366,sK367,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK365),skolemize(X1,sK366),skolemize(X2,sK367),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27)],[f222])).
% 46.03/6.94 thf(f224,plain,(
% 46.03/6.94 ! [X365 : (subst > term > subst > $o)] : (((((sP12 @ X365)) = $true) | ! [X377 : (subst > term > term)] : (? [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) != ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) | ? [X378 : term] : ((((X365 @ id @ X378 @ id)) = $true) & (((X365 @ id @ (X377 @ id @ X378) @ id)) != $true)) | (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) = $true))) & (? [X377 : (subst > term > term)] : (! [X380 : subst,X379 : term,X381 : subst] : (((sub @ (X377 @ X381 @ X379) @ X380)) = ((X377 @ (comp @ X381 @ X380) @ (sub @ X379 @ X380)))) & ! [X378 : term] : ((((X365 @ id @ X378 @ id)) != $true) | (((X365 @ id @ (X377 @ id @ X378) @ id)) = $true)) & (((X365 @ id @ (lam @ (X377 @ sh @ one)) @ id)) != $true)) | (((sP12 @ X365)) != $true)))),
% 46.03/6.94 inference(nnf_transformation,[],[f27])).
% 46.03/6.94 thf(f225,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP12 @ X0))) | ! [X1 : (subst > term > term)] : (? [X2 : subst,X3 : term,X4 : subst] : (((X1 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) != ((sub @ (X1 @ X4 @ X3) @ X2))) | ? [X5 : term] : ((((X0 @ id @ X5 @ id)) = $true) & (((X0 @ id @ (X1 @ id @ X5) @ id)) != $true)) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true))) & (? [X6 : (subst > term > term)] : (! [X7 : subst,X8 : term,X9 : subst] : (((sub @ (X6 @ X9 @ X8) @ X7)) = ((X6 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)))) & ! [X10 : term] : ((((X0 @ id @ X10 @ id)) != $true) | (((X0 @ id @ (X6 @ id @ X10) @ id)) = $true)) & (((X0 @ id @ (lam @ (X6 @ sh @ one)) @ id)) != $true)) | ($true != ((sP12 @ X0)))))),
% 46.03/6.94 inference(rectify,[],[f224])).
% 46.03/6.94 thf(f226,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : ((($true = ((sP12 @ X0))) | ! [X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK380 @ X1) @ (sK379 @ X1)) @ (sK378 @ X1))) != ((X1 @ (comp @ (sK380 @ X1) @ (sK378 @ X1)) @ (sub @ (sK379 @ X1) @ (sK378 @ X1))))) | ((((X0 @ id @ (sK381 @ X1 @ X0) @ id)) = $true) & (((X0 @ id @ (X1 @ id @ (sK381 @ X1 @ X0)) @ id)) != $true)) | (((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true))) & ((! [X7 : subst,X8 : term,X9 : subst] : (((sub @ (sK382 @ X0 @ X9 @ X8) @ X7)) = ((sK382 @ X0 @ (comp @ X9 @ X7) @ (sub @ X8 @ X7)))) & ! [X10 : term] : ((((X0 @ id @ X10 @ id)) != $true) | (((X0 @ id @ (sK382 @ X0 @ id @ X10) @ id)) = $true)) & (((X0 @ id @ (lam @ (sK382 @ X0 @ sh @ one)) @ id)) != $true)) | ($true != ((sP12 @ X0)))))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27)],[f225])).
% 46.03/6.94 thf(f265,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((sP58 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP58 != $true))) & (((hoasinduction_no_psi_cond = $true) | ? [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) != $true) & ! [X301 : (subst > term > term)] : (? [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) != ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) | (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true) | ? [X305 : term] : (($true = ((X299 @ id @ X305 @ id))) & (((X299 @ id @ (X301 @ id @ X305) @ id)) != $true))) & (((sP57 @ X299)) != $true))) & (! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) & (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) != $true) & ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true))) | (((sP57 @ X299)) = $true)) | (hoasinduction_no_psi_cond != $true))) & ((! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) = $true) & (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) != $true)))) & (hoaslamnotap_gthm = $true) & ((! [X531 : term] : ? [X532 : (subst > term > term)] : ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X531 : term] : ! [X532 : (subst > term > term)] : ? [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) != ((X532 @ X534 @ X533))))) & (((pushprop_lem1v2 = $true) | ? [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) != $true) & (((X419 @ X421)) = $true) & ! [X423 : term] : (((X422 @ X423)) = ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))))) & (! [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) = $true) | (((X419 @ X421)) != $true) | ? [X423 : term] : (((X422 @ X423)) != ((X419 @ (sub @ X423 @ (push @ X421 @ X420)))))) | (pushprop_lem1v2 != $true))) & (((sP56 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP56 != $true))) & (pushprop_lthm = $true) & (((induction2lem_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (induction2lem_lthm != $true))) & (((induction2lem = $true) | (sP49 != $true)) & ((sP49 = $true) | (induction2lem != $true))) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) & ? [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true != ((X210 @ one))) & (((X211 @ X212)) = $true) & ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & ((? [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) != X208) | ! [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true = ((X210 @ one))) | (((X211 @ X212)) != $true) | ? [X213 : term] : (((X210 @ X213)) != ((X211 @ (sub @ X213 @ (push @ X212 @ X209))))))) | (pushprop_lem1v2_lthm != $true))) & (((shinj = $true) | ? [X360 : term,X361 : term] : ((X360 != X361) & (((sub @ X360 @ sh)) = ((sub @ X361 @ sh))))) & (! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh)))) | (shinj != $true))) & (((sP47 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP47 != $true))) & (((pushprop_lem1_lthm = $true) | (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) & ? [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) = $true) & (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) != $true)) & ! [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) = X92))) & ((? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91) | ! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)) | ? [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) != X92)) | (pushprop_lem1_lthm != $true))) & (((hoaslamnotap = $true) | ? [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) = ((ap @ (sub @ X45 @ id) @ X47))) & ! [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))))) & (! [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ? [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) != ((sub @ (X46 @ X50 @ X48) @ X49)))) | (hoaslamnotap != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((sP46 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP46 != $true))) & (((laminj = $true) | ? [X536 : term,X535 : term] : ((((lam @ X535)) = ((lam @ X536))) & (X535 != X536))) & (! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536)) | (laminj != $true))) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & ((! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) | (axscons != $true)) & ((axscons = $true) | ? [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) != X155))) & ((! [X154 : term] : (((sub @ X154 @ id)) = X154) | (termmset != $true)) & ((termmset = $true) | ? [X154 : term] : (((sub @ X154 @ id)) != X154))) & (((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true))) & ((! [X16 : term] : ? [X17 : (subst > term > term)] : (((X17 @ sh @ one)) = ((sub @ X16 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X16 : term] : ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X399 : subst] : (((comp @ X399 @ id)) = X399) | (axidr != $true)) & ((axidr = $true) | ? [X399 : subst] : (((comp @ X399 @ id)) != X399))) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) != ((d2subst @ X425))) | (X424 = X425)) & (hoasapnotvar = $true) & ((! [X295 : term] : ? [X296 : (subst > term > term)] : ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X295 : term] : ! [X296 : (subst > term > term)] : ? [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) != ((sub @ X295 @ (push @ X298 @ X297)))))) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X156 : d_subst] : (d_id = X156) & (((axshiftcons = $true) | ? [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) != X427)) & (! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427) | (axshiftcons != $true))) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & (((induction2 = $true) | (sP39 != $true)) & ((sP39 = $true) | (induction2 != $true))) & (((apinj1 = $true) | ? [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 != X355) & (((ap @ X355 @ X357)) = ((ap @ X354 @ X356))))) & (! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356)))) | (apinj1 != $true))) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3a != $true))) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & (((hoasinduction_lem0 = $true) | ? [X477 : (subst > term > subst > $o)] : ! [X478 : (term > $o)] : ? [X479 : term] : (((X478 @ X479)) != ((X477 @ id @ X479 @ id)))) & (! [X477 : (subst > term > subst > $o)] : ? [X478 : (term > $o)] : ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id))) | (hoasinduction_lem0 != $true))) & ((! [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | ? [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) != ((sub @ (X321 @ X326 @ X324) @ X325))) | ? [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) != ((sub @ (X320 @ X329 @ X328) @ X327))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) != ((X321 @ X322 @ X323))) & ! [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) = ((sub @ (X321 @ X326 @ X324) @ X325))) & ! [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) = ((sub @ (X320 @ X329 @ X328) @ X327))) & (((lam @ (X320 @ sh @ one))) = ((lam @ (X321 @ sh @ one))))))) & (((sP36 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP36 != $true))) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & ((! [X382 : term] : ? [X383 : (subst > term > term)] : (((X383 @ sh @ one)) = ((sub @ X382 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X382 : term] : ! [X383 : (subst > term > term)] : (((X383 @ sh @ one)) != ((sub @ X382 @ (push @ one @ sh)))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & (((axvarid = $true) | ? [X511 : term] : (((sub @ X511 @ id)) != X511)) & (! [X511 : term] : (((sub @ X511 @ id)) = X511) | (axvarid != $true))) & (((sP35 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP35 != $true))) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem1_gthm = $true) & (((sP32 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP32 != $true))) & (one = ((d2term @ d_one))) & (((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (((hoasapinj1 = $true) | ? [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 != X216) & (((ap @ (sub @ X214 @ id) @ X217)) = ((ap @ (sub @ X216 @ id) @ X215))))) & (! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215)))) | (hoasapinj1 != $true))) & ((! [X507 : subst,X506 : (term > $o),X508 : term] : ? [X509 : (term > $o)] : ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X507 : subst,X506 : (term > $o),X508 : term] : ! [X509 : (term > $o)] : ? [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) != ((X509 @ X510))))) & (termmset_gthm = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X537 : (subst > term > subst > $o)] : ! [X538 : (term > $o)] : ? [X539 : term] : (((X538 @ X539)) != ((X537 @ id @ X539 @ id)))) & (! [X537 : (subst > term > subst > $o)] : ? [X538 : (term > $o)] : ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id))) | (hoasinduction_lem0_lthm != $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & (((axvarcons = $true) | ? [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) != X158)) & (! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158) | (axvarcons != $true))) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & ((! [X339 : subst,X338 : term,X340 : (term > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X339 : subst,X338 : term,X340 : (term > $o)] : ! [X341 : (term > $o)] : ? [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) != ((X341 @ X342))))) & (((sP29 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP29 != $true))) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & (((sP27 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP27 != $true))) & (apnotvar = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & ((! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 != X206) & (((ap @ X204 @ X206)) = ((ap @ X205 @ X203)))))) & (((hoasinduction_lem2 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem2 != $true))) & (((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true))) & (((hoasapinj2 = $true) | ? [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 != X513) & (((ap @ (sub @ X514 @ id) @ X513)) = ((ap @ (sub @ X515 @ id) @ X512))))) & (! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512)))) | (hoasapinj2 != $true))) & (((hoasinduction_lthm_3 = $true) | (sP20 != $true)) & ((sP20 = $true) | (hoasinduction_lthm_3 != $true))) & (((sP14 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP14 != $true))) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((($true = sP13) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP13))) & (((substmonoid = $true) | (? [X19 : subst] : (((comp @ X19 @ id)) != X19) | ? [X18 : subst] : (((comp @ id @ X18)) != X18))) & ((! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18)) | (substmonoid != $true))) & (((induction = $true) | ? [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) != $true) & ! [X130 : term] : ((((X125 @ (lam @ X130))) = $true) | (((X125 @ X130)) != $true)) & ($true != ((sP11 @ X125))) & ! [X129 : term] : ((((var @ X129)) != $true) | ($true = ((X125 @ X129)))))) & (! [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) = $true) | ? [X130 : term] : ((((X125 @ (lam @ X130))) != $true) & (((X125 @ X130)) = $true)) | ($true = ((sP11 @ X125))) | ? [X129 : term] : ((((var @ X129)) = $true) & ($true != ((X125 @ X129))))) | (induction != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true))) & (((substmonoid_lthm = $true) | (! [X29 : subst] : (((comp @ X29 @ id)) = X29) & (? [X30 : subst] : (((comp @ id @ X30)) != X30) | ? [X31 : subst] : (((comp @ X31 @ id)) != X31)) & ! [X28 : subst] : (((comp @ id @ X28)) = X28))) & ((? [X29 : subst] : (((comp @ X29 @ id)) != X29) | (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)) | ? [X28 : subst] : (((comp @ id @ X28)) != X28)) | (substmonoid_lthm != $true))) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (hoasapinj1_gthm = $true) & ! [X362 : d_term,X363 : d_term] : ((X362 = X363) | (((d2term @ X362)) != ((d2term @ X363)))) & (pushprop_lem2v2_gthm = $true) & ((! [X480 : subst] : (((comp @ id @ X480)) = X480) | (axidl != $true)) & ((axidl = $true) | ? [X480 : subst] : (((comp @ id @ X480)) != X480))) & (hoasinduction_lem3_gthm = $true) & (((hoasapinj2_lthm = $true) | (! [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 = X469) | (((ap @ X467 @ X468)) != ((ap @ X470 @ X469)))) & ? [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 != X473) & (((ap @ (sub @ X471 @ id) @ X473)) = ((ap @ (sub @ X474 @ id) @ X472)))))) & ((? [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 != X469) & (((ap @ X467 @ X468)) = ((ap @ X470 @ X469)))) | ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472))))) | (hoasapinj2_lthm != $true))) & (((! [X359 : term] : (((sub @ X359 @ id)) = X359) | ? [X358 : term] : (((sub @ X358 @ id)) != X358)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X359 : term] : (((sub @ X359 @ id)) != X359) & ! [X358 : term] : (((sub @ X358 @ id)) = X358)))) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoasapinj1_lthm = $true) | (? [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) = ((ap @ (sub @ X58 @ id) @ X57))) & (X58 != X59)) & ! [X51 : term] : (((sub @ X51 @ id)) = X51) & ! [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))))) & ((! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59)) | ? [X51 : term] : (((sub @ X51 @ id)) != X51) | ? [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 != X54) & (((ap @ X52 @ X55)) = ((ap @ X54 @ X53))))) | (hoasapinj1_lthm != $true))) & (((hoasinduction_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lthm != $true)))),
% 46.03/6.94 inference(nnf_transformation,[],[f74])).
% 46.03/6.94 thf(f266,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((sP58 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP58 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) != $true) & ! [X301 : (subst > term > term)] : (? [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) != ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) | (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true) | ? [X305 : term] : (($true = ((X299 @ id @ X305 @ id))) & (((X299 @ id @ (X301 @ id @ X305) @ id)) != $true))) & (((sP57 @ X299)) != $true))) & (! [X300 : term,X299 : (subst > term > subst > $o)] : ((((X299 @ id @ X300 @ id)) = $true) | ? [X301 : (subst > term > term)] : (! [X303 : subst,X304 : term,X302 : subst] : (((sub @ (X301 @ X302 @ X304) @ X303)) = ((X301 @ (comp @ X302 @ X303) @ (sub @ X304 @ X303)))) & (((X299 @ id @ (lam @ (X301 @ sh @ one)) @ id)) != $true) & ! [X305 : term] : (($true != ((X299 @ id @ X305 @ id))) | (((X299 @ id @ (X301 @ id @ X305) @ id)) = $true))) | (((sP57 @ X299)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) != $true) | (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X275 : term,X276 : (term > $o),X274 : subst,X272 : (term > $o),X273 : term] : ((((X276 @ X273)) = $true) & (((X272 @ (sub @ X273 @ (push @ X275 @ X274)))) != $true))) & (hoaslamnotap_gthm = $true) & (! [X531 : term] : ? [X532 : (subst > term > term)] : ! [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) = ((X532 @ X534 @ X533))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X531 : term] : ! [X532 : (subst > term > term)] : ? [X533 : term,X534 : subst] : (((sub @ X531 @ (push @ X533 @ X534))) != ((X532 @ X534 @ X533)))) & ((pushprop_lem1v2 = $true) | ? [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) != $true) & (((X419 @ X421)) = $true) & ! [X423 : term] : (((X422 @ X423)) = ((X419 @ (sub @ X423 @ (push @ X421 @ X420))))))) & (! [X421 : term,X419 : (term > $o),X420 : subst,X422 : (term > $o)] : ((((X422 @ one)) = $true) | (((X419 @ X421)) != $true) | ? [X423 : term] : (((X422 @ X423)) != ((X419 @ (sub @ X423 @ (push @ X421 @ X420)))))) | (pushprop_lem1v2 != $true)) & ((sP56 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP56 != $true)) & (pushprop_lthm = $true) & ((induction2lem_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (induction2lem_lthm != $true)) & ((induction2lem = $true) | (sP49 != $true)) & ((sP49 = $true) | (induction2lem != $true)) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) = X208) & ? [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true != ((X210 @ one))) & (((X211 @ X212)) = $true) & ! [X213 : term] : (((X210 @ X213)) = ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))))) & (? [X207 : subst,X208 : term] : (((sub @ one @ (push @ X208 @ X207))) != X208) | ! [X210 : (term > $o),X212 : term,X209 : subst,X211 : (term > $o)] : (($true = ((X210 @ one))) | (((X211 @ X212)) != $true) | ? [X213 : term] : (((X210 @ X213)) != ((X211 @ (sub @ X213 @ (push @ X212 @ X209)))))) | (pushprop_lem1v2_lthm != $true)) & ((shinj = $true) | ? [X360 : term,X361 : term] : ((X360 != X361) & (((sub @ X360 @ sh)) = ((sub @ X361 @ sh))))) & (! [X360 : term,X361 : term] : ((X360 = X361) | (((sub @ X360 @ sh)) != ((sub @ X361 @ sh)))) | (shinj != $true)) & ((sP47 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP47 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) & ? [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) = $true) & (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) != $true)) & ! [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) = X92))) & (? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91) | ! [X98 : (term > $o),X94 : term,X96 : subst,X97 : term,X95 : (term > $o)] : ((((X98 @ X97)) != $true) | (((X95 @ (sub @ X97 @ (push @ X94 @ X96)))) = $true)) | ? [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) != X92) | (pushprop_lem1_lthm != $true)) & ((hoaslamnotap = $true) | ? [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) = ((ap @ (sub @ X45 @ id) @ X47))) & ! [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) = ((sub @ (X46 @ X50 @ X48) @ X49))))) & (! [X47 : term,X46 : (subst > term > term),X45 : term] : ((((lam @ (X46 @ sh @ one))) != ((ap @ (sub @ X45 @ id) @ X47))) | ? [X49 : subst,X50 : subst,X48 : term] : (((X46 @ (comp @ X50 @ X49) @ (sub @ X48 @ X49))) != ((sub @ (X46 @ X50 @ X48) @ X49)))) | (hoaslamnotap != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((sP46 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP46 != $true)) & ((laminj = $true) | ? [X536 : term,X535 : term] : ((((lam @ X535)) = ((lam @ X536))) & (X535 != X536))) & (! [X536 : term,X535 : term] : ((((lam @ X535)) != ((lam @ X536))) | (X535 = X536)) | (laminj != $true)) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) = X155) | (axscons != $true)) & ((axscons = $true) | ? [X155 : subst] : (((push @ (sub @ one @ X155) @ (comp @ sh @ X155))) != X155)) & (! [X154 : term] : (((sub @ X154 @ id)) = X154) | (termmset != $true)) & ((termmset = $true) | ? [X154 : term] : (((sub @ X154 @ id)) != X154)) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & (! [X16 : term] : ? [X17 : (subst > term > term)] : (((X17 @ sh @ one)) = ((sub @ X16 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X16 : term] : ! [X17 : (subst > term > term)] : (((X17 @ sh @ one)) != ((sub @ X16 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X399 : subst] : (((comp @ X399 @ id)) = X399) | (axidr != $true)) & ((axidr = $true) | ? [X399 : subst] : (((comp @ X399 @ id)) != X399)) & ! [X424 : d_subst,X425 : d_subst] : ((((d2subst @ X424)) != ((d2subst @ X425))) | (X424 = X425)) & (hoasapnotvar = $true) & (! [X295 : term] : ? [X296 : (subst > term > term)] : ! [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) = ((sub @ X295 @ (push @ X298 @ X297)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X295 : term] : ! [X296 : (subst > term > term)] : ? [X298 : term,X297 : subst] : (((X296 @ X297 @ X298)) != ((sub @ X295 @ (push @ X298 @ X297))))) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X156 : d_subst] : (d_id = X156) & ((axshiftcons = $true) | ? [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) != X427)) & (! [X427 : subst,X426 : term] : (((comp @ sh @ (push @ X426 @ X427))) = X427) | (axshiftcons != $true)) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) | (sP39 != $true)) & ((sP39 = $true) | (induction2 != $true)) & ((apinj1 = $true) | ? [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 != X355) & (((ap @ X355 @ X357)) = ((ap @ X354 @ X356))))) & (! [X357 : term,X354 : term,X355 : term,X356 : term] : ((X354 = X355) | (((ap @ X355 @ X357)) != ((ap @ X354 @ X356)))) | (apinj1 != $true)) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3a != $true)) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem0 = $true) | ? [X477 : (subst > term > subst > $o)] : ! [X478 : (term > $o)] : ? [X479 : term] : (((X478 @ X479)) != ((X477 @ id @ X479 @ id)))) & (! [X477 : (subst > term > subst > $o)] : ? [X478 : (term > $o)] : ! [X479 : term] : (((X478 @ X479)) = ((X477 @ id @ X479 @ id))) | (hoasinduction_lem0 != $true)) & (! [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) = ((X321 @ X322 @ X323))) | ? [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) != ((sub @ (X321 @ X326 @ X324) @ X325))) | ? [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) != ((sub @ (X320 @ X329 @ X328) @ X327))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X321 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X323 : term,X321 : (subst > term > term),X320 : (subst > term > term),X322 : subst] : ((((X320 @ X322 @ X323)) != ((X321 @ X322 @ X323))) & ! [X326 : subst,X324 : term,X325 : subst] : (((X321 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325))) = ((sub @ (X321 @ X326 @ X324) @ X325))) & ! [X327 : subst,X329 : subst,X328 : term] : (((X320 @ (comp @ X329 @ X327) @ (sub @ X328 @ X327))) = ((sub @ (X320 @ X329 @ X328) @ X327))) & (((lam @ (X320 @ sh @ one))) = ((lam @ (X321 @ sh @ one)))))) & ((sP36 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP36 != $true)) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (! [X382 : term] : ? [X383 : (subst > term > term)] : (((X383 @ sh @ one)) = ((sub @ X382 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X382 : term] : ! [X383 : (subst > term > term)] : (((X383 @ sh @ one)) != ((sub @ X382 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & ((axvarid = $true) | ? [X511 : term] : (((sub @ X511 @ id)) != X511)) & (! [X511 : term] : (((sub @ X511 @ id)) = X511) | (axvarid != $true)) & ((sP35 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP35 != $true)) & ! [X343 : d_term] : (d_one = X343) & (hoasinduction_lem1_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP32 != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasapinj1 = $true) | ? [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 != X216) & (((ap @ (sub @ X214 @ id) @ X217)) = ((ap @ (sub @ X216 @ id) @ X215))))) & (! [X217 : term,X216 : term,X214 : term,X215 : term] : ((X214 = X216) | (((ap @ (sub @ X214 @ id) @ X217)) != ((ap @ (sub @ X216 @ id) @ X215)))) | (hoasapinj1 != $true)) & (! [X507 : subst,X506 : (term > $o),X508 : term] : ? [X509 : (term > $o)] : ! [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) = ((X509 @ X510))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X507 : subst,X506 : (term > $o),X508 : term] : ! [X509 : (term > $o)] : ? [X510 : term] : (((X506 @ (sub @ X510 @ (push @ X508 @ X507)))) != ((X509 @ X510)))) & (termmset_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X537 : (subst > term > subst > $o)] : ! [X538 : (term > $o)] : ? [X539 : term] : (((X538 @ X539)) != ((X537 @ id @ X539 @ id)))) & (! [X537 : (subst > term > subst > $o)] : ? [X538 : (term > $o)] : ! [X539 : term] : (((X538 @ X539)) = ((X537 @ id @ X539 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & ((axvarcons = $true) | ? [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) != X158)) & (! [X157 : subst,X158 : term] : (((sub @ one @ (push @ X158 @ X157))) = X158) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X339 : subst,X338 : term,X340 : (term > $o)] : ? [X341 : (term > $o)] : ! [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) = ((X341 @ X342))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X339 : subst,X338 : term,X340 : (term > $o)] : ! [X341 : (term > $o)] : ? [X342 : term] : (((X340 @ (sub @ X342 @ (push @ X338 @ X339)))) != ((X341 @ X342)))) & ((sP29 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP29 != $true)) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((sP27 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP27 != $true)) & (apnotvar = $true) & ! [X352 : subst] : ? [X353 : d_subst] : (((d2subst @ X353)) = X352) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 = X206) | (((ap @ X204 @ X206)) != ((ap @ X205 @ X203)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X204 : term,X206 : term,X203 : term,X205 : term] : ((X203 != X206) & (((ap @ X204 @ X206)) = ((ap @ X205 @ X203))))) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & ((hoasapinj2 = $true) | ? [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 != X513) & (((ap @ (sub @ X514 @ id) @ X513)) = ((ap @ (sub @ X515 @ id) @ X512))))) & (! [X514 : term,X515 : term,X513 : term,X512 : term] : ((X512 = X513) | (((ap @ (sub @ X514 @ id) @ X513)) != ((ap @ (sub @ X515 @ id) @ X512)))) | (hoasapinj2 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP20 != $true)) & ((sP20 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP14 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP14 != $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP13) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP13)) & ((substmonoid = $true) | ? [X19 : subst] : (((comp @ X19 @ id)) != X19) | ? [X18 : subst] : (((comp @ id @ X18)) != X18)) & ((! [X19 : subst] : (((comp @ X19 @ id)) = X19) & ! [X18 : subst] : (((comp @ id @ X18)) = X18)) | (substmonoid != $true)) & ((induction = $true) | ? [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) != $true) & ! [X130 : term] : ((((X125 @ (lam @ X130))) = $true) | (((X125 @ X130)) != $true)) & ($true != ((sP11 @ X125))) & ! [X129 : term] : ((((var @ X129)) != $true) | ($true = ((X125 @ X129)))))) & (! [X125 : (term > $o),X126 : term] : ((((X125 @ X126)) = $true) | ? [X130 : term] : ((((X125 @ (lam @ X130))) != $true) & (((X125 @ X130)) = $true)) | ($true = ((sP11 @ X125))) | ? [X129 : term] : ((((var @ X129)) = $true) & ($true != ((X125 @ X129))))) | (induction != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & ((substmonoid_lthm = $true) | (! [X29 : subst] : (((comp @ X29 @ id)) = X29) & (? [X30 : subst] : (((comp @ id @ X30)) != X30) | ? [X31 : subst] : (((comp @ X31 @ id)) != X31)) & ! [X28 : subst] : (((comp @ id @ X28)) = X28))) & (? [X29 : subst] : (((comp @ X29 @ id)) != X29) | (! [X30 : subst] : (((comp @ id @ X30)) = X30) & ! [X31 : subst] : (((comp @ X31 @ id)) = X31)) | ? [X28 : subst] : (((comp @ id @ X28)) != X28) | (substmonoid_lthm != $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X475 : term] : ? [X476 : d_term] : (((d2term @ X476)) = X475) & (hoasapinj1_gthm = $true) & ! [X362 : d_term,X363 : d_term] : ((X362 = X363) | (((d2term @ X362)) != ((d2term @ X363)))) & (pushprop_lem2v2_gthm = $true) & (! [X480 : subst] : (((comp @ id @ X480)) = X480) | (axidl != $true)) & ((axidl = $true) | ? [X480 : subst] : (((comp @ id @ X480)) != X480)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 = X469) | (((ap @ X467 @ X468)) != ((ap @ X470 @ X469)))) & ? [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 != X473) & (((ap @ (sub @ X471 @ id) @ X473)) = ((ap @ (sub @ X474 @ id) @ X472)))))) & (? [X467 : term,X469 : term,X468 : term,X470 : term] : ((X468 != X469) & (((ap @ X467 @ X468)) = ((ap @ X470 @ X469)))) | ! [X474 : term,X472 : term,X471 : term,X473 : term] : ((X472 = X473) | (((ap @ (sub @ X471 @ id) @ X473)) != ((ap @ (sub @ X474 @ id) @ X472)))) | (hoasapinj2_lthm != $true)) & (! [X359 : term] : (((sub @ X359 @ id)) = X359) | ? [X358 : term] : (((sub @ X358 @ id)) != X358) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X359 : term] : (((sub @ X359 @ id)) != X359) & ! [X358 : term] : (((sub @ X358 @ id)) = X358))) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) | (? [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) = ((ap @ (sub @ X58 @ id) @ X57))) & (X58 != X59)) & ! [X51 : term] : (((sub @ X51 @ id)) = X51) & ! [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 = X54) | (((ap @ X52 @ X55)) != ((ap @ X54 @ X53)))))) & (! [X56 : term,X57 : term,X59 : term,X58 : term] : ((((ap @ (sub @ X59 @ id) @ X56)) != ((ap @ (sub @ X58 @ id) @ X57))) | (X58 = X59)) | ? [X51 : term] : (((sub @ X51 @ id)) != X51) | ? [X53 : term,X52 : term,X55 : term,X54 : term] : ((X52 != X54) & (((ap @ X52 @ X55)) = ((ap @ X54 @ X53)))) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lthm != $true))),
% 46.03/6.94 inference(flattening,[],[f265])).
% 46.03/6.94 thf(f267,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((sP58 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP58 != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ X0 @ id)) != $true) & ! [X2 : (subst > term > term)] : (? [X3 : subst,X4 : term,X5 : subst] : (((X2 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) != ((sub @ (X2 @ X5 @ X4) @ X3))) | (((X1 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | ? [X6 : term] : (($true = ((X1 @ id @ X6 @ id))) & (((X1 @ id @ (X2 @ id @ X6) @ id)) != $true))) & (((sP57 @ X1)) != $true))) & (! [X7 : term,X8 : (subst > term > subst > $o)] : ((((X8 @ id @ X7 @ id)) = $true) | ? [X9 : (subst > term > term)] : (! [X10 : subst,X11 : term,X12 : subst] : (((X9 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10))) = ((sub @ (X9 @ X12 @ X11) @ X10))) & (((X8 @ id @ (lam @ (X9 @ sh @ one)) @ id)) != $true) & ! [X13 : term] : ((((X8 @ id @ X13 @ id)) != $true) | (((X8 @ id @ (X9 @ id @ X13) @ id)) = $true))) | (((sP57 @ X8)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X14 : term,X15 : (term > $o),X16 : subst,X17 : (term > $o),X18 : term] : ((((X15 @ X18)) != $true) | (((X17 @ (sub @ X18 @ (push @ X14 @ X16)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X19 : term,X20 : (term > $o),X21 : subst,X22 : (term > $o),X23 : term] : ((((X20 @ X23)) = $true) & (((X22 @ (sub @ X23 @ (push @ X19 @ X21)))) != $true))) & (hoaslamnotap_gthm = $true) & (! [X24 : term] : ? [X25 : (subst > term > term)] : ! [X26 : term,X27 : subst] : (((sub @ X24 @ (push @ X26 @ X27))) = ((X25 @ X27 @ X26))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X28 : term] : ! [X29 : (subst > term > term)] : ? [X30 : term,X31 : subst] : (((sub @ X28 @ (push @ X30 @ X31))) != ((X29 @ X31 @ X30)))) & ((pushprop_lem1v2 = $true) | ? [X32 : term,X33 : (term > $o),X34 : subst,X35 : (term > $o)] : ((((X35 @ one)) != $true) & (((X33 @ X32)) = $true) & ! [X36 : term] : (((X33 @ (sub @ X36 @ (push @ X32 @ X34)))) = ((X35 @ X36))))) & (! [X37 : term,X38 : (term > $o),X39 : subst,X40 : (term > $o)] : ((((X40 @ one)) = $true) | (((X38 @ X37)) != $true) | ? [X41 : term] : (((X38 @ (sub @ X41 @ (push @ X37 @ X39)))) != ((X40 @ X41)))) | (pushprop_lem1v2 != $true)) & ((sP56 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP56 != $true)) & (pushprop_lthm = $true) & ((induction2lem_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (induction2lem_lthm != $true)) & ((induction2lem = $true) | (sP49 != $true)) & ((sP49 = $true) | (induction2lem != $true)) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X42 : subst,X43 : term] : (((sub @ one @ (push @ X43 @ X42))) = X43) & ? [X44 : (term > $o),X45 : term,X46 : subst,X47 : (term > $o)] : ((((X44 @ one)) != $true) & (((X47 @ X45)) = $true) & ! [X48 : term] : (((X47 @ (sub @ X48 @ (push @ X45 @ X46)))) = ((X44 @ X48)))))) & (? [X49 : subst,X50 : term] : (((sub @ one @ (push @ X50 @ X49))) != X50) | ! [X51 : (term > $o),X52 : term,X53 : subst,X54 : (term > $o)] : ((((X51 @ one)) = $true) | (((X54 @ X52)) != $true) | ? [X55 : term] : (((X54 @ (sub @ X55 @ (push @ X52 @ X53)))) != ((X51 @ X55)))) | (pushprop_lem1v2_lthm != $true)) & ((shinj = $true) | ? [X56 : term,X57 : term] : ((X56 != X57) & (((sub @ X56 @ sh)) = ((sub @ X57 @ sh))))) & (! [X58 : term,X59 : term] : ((X58 = X59) | (((sub @ X58 @ sh)) != ((sub @ X59 @ sh)))) | (shinj != $true)) & ((sP47 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP47 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X60 : subst,X61 : term] : (((sub @ one @ (push @ X61 @ X60))) = X61) & ? [X62 : (term > $o),X63 : term,X64 : subst,X65 : term,X66 : (term > $o)] : ((((X62 @ X65)) = $true) & (((X66 @ (sub @ X65 @ (push @ X63 @ X64)))) != $true)) & ! [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) = X68))) & (? [X69 : subst,X70 : term] : (((sub @ one @ (push @ X70 @ X69))) != X70) | ! [X71 : (term > $o),X72 : term,X73 : subst,X74 : term,X75 : (term > $o)] : ((((X71 @ X74)) != $true) | (((X75 @ (sub @ X74 @ (push @ X72 @ X73)))) = $true)) | ? [X76 : term,X77 : subst] : (((comp @ sh @ (push @ X76 @ X77))) != X77) | (pushprop_lem1_lthm != $true)) & ((hoaslamnotap = $true) | ? [X78 : term,X79 : (subst > term > term),X80 : term] : ((((lam @ (X79 @ sh @ one))) = ((ap @ (sub @ X80 @ id) @ X78))) & ! [X81 : subst,X82 : subst,X83 : term] : (((X79 @ (comp @ X82 @ X81) @ (sub @ X83 @ X81))) = ((sub @ (X79 @ X82 @ X83) @ X81))))) & (! [X84 : term,X85 : (subst > term > term),X86 : term] : ((((ap @ (sub @ X86 @ id) @ X84)) != ((lam @ (X85 @ sh @ one)))) | ? [X87 : subst,X88 : subst,X89 : term] : (((sub @ (X85 @ X88 @ X89) @ X87)) != ((X85 @ (comp @ X88 @ X87) @ (sub @ X89 @ X87))))) | (hoaslamnotap != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((sP46 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP46 != $true)) & ((laminj = $true) | ? [X90 : term,X91 : term] : ((((lam @ X91)) = ((lam @ X90))) & (X90 != X91))) & (! [X92 : term,X93 : term] : ((((lam @ X93)) != ((lam @ X92))) | (X92 = X93)) | (laminj != $true)) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X94 : subst] : (((push @ (sub @ one @ X94) @ (comp @ sh @ X94))) = X94) | (axscons != $true)) & ((axscons = $true) | ? [X95 : subst] : (((push @ (sub @ one @ X95) @ (comp @ sh @ X95))) != X95)) & (! [X96 : term] : (((sub @ X96 @ id)) = X96) | (termmset != $true)) & ((termmset = $true) | ? [X97 : term] : (((sub @ X97 @ id)) != X97)) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & (! [X98 : term] : ? [X99 : (subst > term > term)] : (((sub @ X98 @ (push @ one @ sh))) = ((X99 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X100 : term] : ! [X101 : (subst > term > term)] : (((X101 @ sh @ one)) != ((sub @ X100 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X102 : subst] : (((comp @ X102 @ id)) = X102) | (axidr != $true)) & ((axidr = $true) | ? [X103 : subst] : (((comp @ X103 @ id)) != X103)) & ! [X104 : d_subst,X105 : d_subst] : ((((d2subst @ X105)) != ((d2subst @ X104))) | (X104 = X105)) & (hoasapnotvar = $true) & (! [X106 : term] : ? [X107 : (subst > term > term)] : ! [X108 : term,X109 : subst] : (((X107 @ X109 @ X108)) = ((sub @ X106 @ (push @ X108 @ X109)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X110 : term] : ! [X111 : (subst > term > term)] : ? [X112 : term,X113 : subst] : (((X111 @ X113 @ X112)) != ((sub @ X110 @ (push @ X112 @ X113))))) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X114 : d_subst] : (d_id = X114) & ((axshiftcons = $true) | ? [X115 : subst,X116 : term] : (((comp @ sh @ (push @ X116 @ X115))) != X115)) & (! [X117 : subst,X118 : term] : (((comp @ sh @ (push @ X118 @ X117))) = X117) | (axshiftcons != $true)) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) | (sP39 != $true)) & ((sP39 = $true) | (induction2 != $true)) & ((apinj1 = $true) | ? [X119 : term,X120 : term,X121 : term,X122 : term] : ((X120 != X121) & (((ap @ X121 @ X119)) = ((ap @ X120 @ X122))))) & (! [X123 : term,X124 : term,X125 : term,X126 : term] : ((X124 = X125) | (((ap @ X124 @ X126)) != ((ap @ X125 @ X123)))) | (apinj1 != $true)) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3a != $true)) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem0 = $true) | ? [X127 : (subst > term > subst > $o)] : ! [X128 : (term > $o)] : ? [X129 : term] : (((X127 @ id @ X129 @ id)) != ((X128 @ X129)))) & (! [X130 : (subst > term > subst > $o)] : ? [X131 : (term > $o)] : ! [X132 : term] : (((X130 @ id @ X132 @ id)) = ((X131 @ X132))) | (hoasinduction_lem0 != $true)) & (! [X133 : term,X134 : (subst > term > term),X135 : (subst > term > term),X136 : subst] : ((((X134 @ X136 @ X133)) = ((X135 @ X136 @ X133))) | ? [X137 : subst,X138 : term,X139 : subst] : (((sub @ (X134 @ X137 @ X138) @ X139)) != ((X134 @ (comp @ X137 @ X139) @ (sub @ X138 @ X139)))) | ? [X140 : subst,X141 : subst,X142 : term] : (((sub @ (X135 @ X141 @ X142) @ X140)) != ((X135 @ (comp @ X141 @ X140) @ (sub @ X142 @ X140)))) | (((lam @ (X134 @ sh @ one))) != ((lam @ (X135 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X143 : term,X144 : (subst > term > term),X145 : (subst > term > term),X146 : subst] : ((((X144 @ X146 @ X143)) != ((X145 @ X146 @ X143))) & ! [X147 : subst,X148 : term,X149 : subst] : (((X144 @ (comp @ X147 @ X149) @ (sub @ X148 @ X149))) = ((sub @ (X144 @ X147 @ X148) @ X149))) & ! [X150 : subst,X151 : subst,X152 : term] : (((sub @ (X145 @ X151 @ X152) @ X150)) = ((X145 @ (comp @ X151 @ X150) @ (sub @ X152 @ X150)))) & (((lam @ (X144 @ sh @ one))) = ((lam @ (X145 @ sh @ one)))))) & ((sP36 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP36 != $true)) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (! [X153 : term] : ? [X154 : (subst > term > term)] : (((X154 @ sh @ one)) = ((sub @ X153 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X155 : term] : ! [X156 : (subst > term > term)] : (((X156 @ sh @ one)) != ((sub @ X155 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & ((axvarid = $true) | ? [X157 : term] : (((sub @ X157 @ id)) != X157)) & (! [X158 : term] : (((sub @ X158 @ id)) = X158) | (axvarid != $true)) & ((sP35 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP35 != $true)) & ! [X159 : d_term] : (d_one = X159) & (hoasinduction_lem1_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP32 != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasapinj1 = $true) | ? [X160 : term,X161 : term,X162 : term,X163 : term] : ((X161 != X162) & (((ap @ (sub @ X162 @ id) @ X160)) = ((ap @ (sub @ X161 @ id) @ X163))))) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X165 = X166) | (((ap @ (sub @ X165 @ id) @ X167)) != ((ap @ (sub @ X166 @ id) @ X164)))) | (hoasapinj1 != $true)) & (! [X168 : subst,X169 : (term > $o),X170 : term] : ? [X171 : (term > $o)] : ! [X172 : term] : (((X171 @ X172)) = ((X169 @ (sub @ X172 @ (push @ X170 @ X168))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X173 : subst,X174 : (term > $o),X175 : term] : ! [X176 : (term > $o)] : ? [X177 : term] : (((X176 @ X177)) != ((X174 @ (sub @ X177 @ (push @ X175 @ X173)))))) & (termmset_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X178 : (subst > term > subst > $o)] : ! [X179 : (term > $o)] : ? [X180 : term] : (((X179 @ X180)) != ((X178 @ id @ X180 @ id)))) & (! [X181 : (subst > term > subst > $o)] : ? [X182 : (term > $o)] : ! [X183 : term] : (((X181 @ id @ X183 @ id)) = ((X182 @ X183))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & ((axvarcons = $true) | ? [X184 : subst,X185 : term] : (((sub @ one @ (push @ X185 @ X184))) != X185)) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X188 : subst,X189 : term,X190 : (term > $o)] : ? [X191 : (term > $o)] : ! [X192 : term] : (((X190 @ (sub @ X192 @ (push @ X189 @ X188)))) = ((X191 @ X192))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X193 : subst,X194 : term,X195 : (term > $o)] : ! [X196 : (term > $o)] : ? [X197 : term] : (((X196 @ X197)) != ((X195 @ (sub @ X197 @ (push @ X194 @ X193)))))) & ((sP29 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP29 != $true)) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((sP27 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP27 != $true)) & (apnotvar = $true) & ! [X198 : subst] : ? [X199 : d_subst] : (((d2subst @ X199)) = X198) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X200 : term,X201 : term,X202 : term,X203 : term] : ((X201 = X202) | (((ap @ X203 @ X202)) != ((ap @ X200 @ X201)))) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X204 : term,X205 : term,X206 : term,X207 : term] : ((X205 != X206) & (((ap @ X204 @ X205)) = ((ap @ X207 @ X206))))) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & ((hoasapinj2 = $true) | ? [X208 : term,X209 : term,X210 : term,X211 : term] : ((X210 != X211) & (((ap @ (sub @ X209 @ id) @ X211)) = ((ap @ (sub @ X208 @ id) @ X210))))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((X214 = X215) | (((ap @ (sub @ X212 @ id) @ X214)) != ((ap @ (sub @ X213 @ id) @ X215)))) | (hoasapinj2 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP20 != $true)) & ((sP20 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP14 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP14 != $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP13) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP13)) & ((substmonoid = $true) | ? [X216 : subst] : (((comp @ X216 @ id)) != X216) | ? [X217 : subst] : (((comp @ id @ X217)) != X217)) & ((! [X218 : subst] : (((comp @ X218 @ id)) = X218) & ! [X219 : subst] : (((comp @ id @ X219)) = X219)) | (substmonoid != $true)) & ((induction = $true) | ? [X220 : (term > $o),X221 : term] : ((((X220 @ X221)) != $true) & ! [X222 : term] : ((((X220 @ (lam @ X222))) = $true) | (((X220 @ X222)) != $true)) & (((sP11 @ X220)) != $true) & ! [X223 : term] : ((((var @ X223)) != $true) | (((X220 @ X223)) = $true)))) & (! [X224 : (term > $o),X225 : term] : ((((X224 @ X225)) = $true) | ? [X226 : term] : ((((X224 @ (lam @ X226))) != $true) & ($true = ((X224 @ X226)))) | (((sP11 @ X224)) = $true) | ? [X227 : term] : ((((var @ X227)) = $true) & (((X224 @ X227)) != $true))) | (induction != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & ((substmonoid_lthm = $true) | (! [X228 : subst] : (((comp @ X228 @ id)) = X228) & (? [X229 : subst] : (((comp @ id @ X229)) != X229) | ? [X230 : subst] : (((comp @ X230 @ id)) != X230)) & ! [X231 : subst] : (((comp @ id @ X231)) = X231))) & (? [X232 : subst] : (((comp @ X232 @ id)) != X232) | (! [X233 : subst] : (((comp @ id @ X233)) = X233) & ! [X234 : subst] : (((comp @ X234 @ id)) = X234)) | ? [X235 : subst] : (((comp @ id @ X235)) != X235) | (substmonoid_lthm != $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X236 : term] : ? [X237 : d_term] : (((d2term @ X237)) = X236) & (hoasapinj1_gthm = $true) & ! [X238 : d_term,X239 : d_term] : ((X238 = X239) | (((d2term @ X238)) != ((d2term @ X239)))) & (pushprop_lem2v2_gthm = $true) & (! [X240 : subst] : (((comp @ id @ X240)) = X240) | (axidl != $true)) & ((axidl = $true) | ? [X241 : subst] : (((comp @ id @ X241)) != X241)) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X243 = X244) | (((ap @ X245 @ X243)) != ((ap @ X242 @ X244)))) & ? [X246 : term,X247 : term,X248 : term,X249 : term] : ((X247 != X249) & (((ap @ (sub @ X246 @ id) @ X247)) = ((ap @ (sub @ X248 @ id) @ X249)))))) & (? [X250 : term,X251 : term,X252 : term,X253 : term] : ((X251 != X252) & (((ap @ X250 @ X252)) = ((ap @ X253 @ X251)))) | ! [X254 : term,X255 : term,X256 : term,X257 : term] : ((X255 = X257) | (((ap @ (sub @ X256 @ id) @ X257)) != ((ap @ (sub @ X254 @ id) @ X255)))) | (hoasapinj2_lthm != $true)) & (! [X258 : term] : (((sub @ X258 @ id)) = X258) | ? [X259 : term] : (((sub @ X259 @ id)) != X259) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X260 : term] : (((sub @ X260 @ id)) != X260) & ! [X261 : term] : (((sub @ X261 @ id)) = X261))) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) | (? [X262 : term,X263 : term,X264 : term,X265 : term] : ((((ap @ (sub @ X264 @ id) @ X262)) = ((ap @ (sub @ X265 @ id) @ X263))) & (X264 != X265)) & ! [X266 : term] : (((sub @ X266 @ id)) = X266) & ! [X267 : term,X268 : term,X269 : term,X270 : term] : ((X268 = X270) | (((ap @ X270 @ X267)) != ((ap @ X268 @ X269)))))) & (! [X271 : term,X272 : term,X273 : term,X274 : term] : ((((ap @ (sub @ X273 @ id) @ X271)) != ((ap @ (sub @ X274 @ id) @ X272))) | (X273 = X274)) | ? [X275 : term] : (((sub @ X275 @ id)) != X275) | ? [X276 : term,X277 : term,X278 : term,X279 : term] : ((X277 != X279) & (((ap @ X279 @ X276)) = ((ap @ X277 @ X278)))) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lthm != $true))),
% 46.03/6.94 inference(rectify,[],[f266])).
% 46.03/6.94 thf(f268,plain,(
% 46.03/6.94 (hoasinduction_gthm = $true) & (ulamvarind = $true) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((sP58 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP58 != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK457 @ id @ sK456 @ id)) != $true) & ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2))))) | (((sK457 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | ((((sK457 @ id @ (sK461 @ X2) @ id)) = $true) & (((sK457 @ id @ (X2 @ id @ (sK461 @ X2)) @ id)) != $true))) & (((sP57 @ sK457)) != $true))) & (! [X7 : term,X8 : (subst > term > subst > $o)] : ((((X8 @ id @ X7 @ id)) = $true) | (! [X10 : subst,X11 : term,X12 : subst] : (((sK462 @ X8 @ (comp @ X12 @ X10) @ (sub @ X11 @ X10))) = ((sub @ (sK462 @ X8 @ X12 @ X11) @ X10))) & (((X8 @ id @ (lam @ (sK462 @ X8 @ sh @ one)) @ id)) != $true) & ! [X13 : term] : ((((X8 @ id @ X13 @ id)) != $true) | (((X8 @ id @ (sK462 @ X8 @ id @ X13) @ id)) = $true))) | (((sP57 @ X8)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X14 : term,X15 : (term > $o),X16 : subst,X17 : (term > $o),X18 : term] : ((((X15 @ X18)) != $true) | (((X17 @ (sub @ X18 @ (push @ X14 @ X16)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK464 @ sK467)) = $true) & (((sK466 @ (sub @ sK467 @ (push @ sK463 @ sK465)))) != $true))) & (hoaslamnotap_gthm = $true) & (! [X24 : term] : ! [X26 : term,X27 : subst] : (((sK468 @ X24 @ X27 @ X26)) = ((sub @ X24 @ (push @ X26 @ X27)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X29 : (subst > term > term)] : (((sub @ sK469 @ (push @ (sK470 @ X29) @ (sK471 @ X29)))) != ((X29 @ (sK471 @ X29) @ (sK470 @ X29))))) & ((pushprop_lem1v2 = $true) | ((((sK475 @ one)) != $true) & ($true = ((sK473 @ sK472))) & ! [X36 : term] : (((sK475 @ X36)) = ((sK473 @ (sub @ X36 @ (push @ sK472 @ sK474))))))) & (! [X37 : term,X38 : (term > $o),X39 : subst,X40 : (term > $o)] : ((((X40 @ one)) = $true) | (((X38 @ X37)) != $true) | (((X40 @ (sK476 @ X40 @ X39 @ X38 @ X37))) != ((X38 @ (sub @ (sK476 @ X40 @ X39 @ X38 @ X37) @ (push @ X37 @ X39)))))) | (pushprop_lem1v2 != $true)) & ((sP56 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP56 != $true)) & (pushprop_lthm = $true) & ((induction2lem_lthm = $true) | (sP53 != $true)) & ((sP53 = $true) | (induction2lem_lthm != $true)) & ((induction2lem = $true) | (sP49 != $true)) & ((sP49 = $true) | (induction2lem != $true)) & (axassoc = $true) & (axabs = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X42 : subst,X43 : term] : (((sub @ one @ (push @ X43 @ X42))) = X43) & ((((sK477 @ one)) != $true) & (((sK480 @ sK478)) = $true) & ! [X48 : term] : (((sK477 @ X48)) = ((sK480 @ (sub @ X48 @ (push @ sK478 @ sK479)))))))) & ((((sub @ one @ (push @ sK482 @ sK481))) != sK482) | ! [X51 : (term > $o),X52 : term,X53 : subst,X54 : (term > $o)] : ((((X51 @ one)) = $true) | (((X54 @ X52)) != $true) | (((X51 @ (sK483 @ X54 @ X53 @ X52 @ X51))) != ((X54 @ (sub @ (sK483 @ X54 @ X53 @ X52 @ X51) @ (push @ X52 @ X53)))))) | (pushprop_lem1v2_lthm != $true)) & ((shinj = $true) | ((sK484 != sK485) & (((sub @ sK484 @ sh)) = ((sub @ sK485 @ sh))))) & (! [X58 : term,X59 : term] : ((X58 = X59) | (((sub @ X58 @ sh)) != ((sub @ X59 @ sh)))) | (shinj != $true)) & ((sP47 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP47 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X60 : subst,X61 : term] : (((sub @ one @ (push @ X61 @ X60))) = X61) & ((((sK486 @ sK489)) = $true) & (((sK490 @ (sub @ sK489 @ (push @ sK487 @ sK488)))) != $true)) & ! [X67 : term,X68 : subst] : (((comp @ sh @ (push @ X67 @ X68))) = X68))) & ((sK492 != ((sub @ one @ (push @ sK492 @ sK491)))) | ! [X71 : (term > $o),X72 : term,X73 : subst,X74 : term,X75 : (term > $o)] : ((((X71 @ X74)) != $true) | (((X75 @ (sub @ X74 @ (push @ X72 @ X73)))) = $true)) | (((comp @ sh @ (push @ sK493 @ sK494))) != sK494) | (pushprop_lem1_lthm != $true)) & ((hoaslamnotap = $true) | ((((ap @ (sub @ sK497 @ id) @ sK495)) = ((lam @ (sK496 @ sh @ one)))) & ! [X81 : subst,X82 : subst,X83 : term] : (((sK496 @ (comp @ X82 @ X81) @ (sub @ X83 @ X81))) = ((sub @ (sK496 @ X82 @ X83) @ X81))))) & (! [X84 : term,X85 : (subst > term > term),X86 : term] : ((((ap @ (sub @ X86 @ id) @ X84)) != ((lam @ (X85 @ sh @ one)))) | (((sub @ (X85 @ (sK499 @ X85) @ (sK500 @ X85)) @ (sK498 @ X85))) != ((X85 @ (comp @ (sK499 @ X85) @ (sK498 @ X85)) @ (sub @ (sK500 @ X85) @ (sK498 @ X85)))))) | (hoaslamnotap != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((sP46 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP46 != $true)) & ((laminj = $true) | ((((lam @ sK502)) = ((lam @ sK501))) & (sK501 != sK502))) & (! [X92 : term,X93 : term] : ((((lam @ X93)) != ((lam @ X92))) | (X92 = X93)) | (laminj != $true)) & (axapp = $true) & (lamnotap != $true) & (((var @ (d2term @ d_one))) != $true) & (hoasinduction_lem1v2 = $true) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X94 : subst] : (((push @ (sub @ one @ X94) @ (comp @ sh @ X94))) = X94) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK503) @ (comp @ sh @ sK503))) != sK503)) & (! [X96 : term] : (((sub @ X96 @ id)) = X96) | (termmset != $true)) & ((termmset = $true) | (sK504 != ((sub @ sK504 @ id)))) & ((sP44 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP44 != $true)) & (! [X98 : term] : (((sK505 @ X98 @ sh @ one)) = ((sub @ X98 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X101 : (subst > term > term)] : (((X101 @ sh @ one)) != ((sub @ sK506 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X102 : subst] : (((comp @ X102 @ id)) = X102) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK507 @ id)) != sK507)) & ! [X104 : d_subst,X105 : d_subst] : ((((d2subst @ X105)) != ((d2subst @ X104))) | (X104 = X105)) & (hoasapnotvar = $true) & (! [X106 : term] : ! [X108 : term,X109 : subst] : (((sK508 @ X106 @ X109 @ X108)) = ((sub @ X106 @ (push @ X108 @ X109)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X111 : (subst > term > term)] : (((X111 @ (sK511 @ X111) @ (sK510 @ X111))) != ((sub @ sK509 @ (push @ (sK510 @ X111) @ (sK511 @ X111)))))) & (axclos = $true) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (lamnotvar = $true) & (hoasinduction_lem1 = $true) & ! [X114 : d_subst] : (d_id = X114) & ((axshiftcons = $true) | (sK512 != ((comp @ sh @ (push @ sK513 @ sK512))))) & (! [X117 : subst,X118 : term] : (((comp @ sh @ (push @ X118 @ X117))) = X117) | (axshiftcons != $true)) & (hoaslamnotvar_lthm = $true) & (axvarshift = $true) & (hoasinduction_lem3a_gthm = $true) & ((induction2 = $true) | (sP39 != $true)) & ((sP39 = $true) | (induction2 != $true)) & ((apinj1 = $true) | ((sK516 != sK515) & (((ap @ sK516 @ sK514)) = ((ap @ sK515 @ sK517))))) & (! [X123 : term,X124 : term,X125 : term,X126 : term] : ((X124 = X125) | (((ap @ X124 @ X126)) != ((ap @ X125 @ X123)))) | (apinj1 != $true)) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3a != $true)) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_lem0 = $true) | ! [X128 : (term > $o)] : (((sK518 @ id @ (sK519 @ X128) @ id)) != ((X128 @ (sK519 @ X128))))) & (! [X130 : (subst > term > subst > $o)] : ! [X132 : term] : (((X130 @ id @ X132 @ id)) = ((sK520 @ X130 @ X132))) | (hoasinduction_lem0 != $true)) & (! [X133 : term,X134 : (subst > term > term),X135 : (subst > term > term),X136 : subst] : ((((X134 @ X136 @ X133)) = ((X135 @ X136 @ X133))) | (((sub @ (X134 @ (sK521 @ X134) @ (sK522 @ X134)) @ (sK523 @ X134))) != ((X134 @ (comp @ (sK521 @ X134) @ (sK523 @ X134)) @ (sub @ (sK522 @ X134) @ (sK523 @ X134))))) | (((sub @ (X135 @ (sK525 @ X135) @ (sK526 @ X135)) @ (sK524 @ X135))) != ((X135 @ (comp @ (sK525 @ X135) @ (sK524 @ X135)) @ (sub @ (sK526 @ X135) @ (sK524 @ X135))))) | (((lam @ (X134 @ sh @ one))) != ((lam @ (X135 @ sh @ one))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((sK529 @ sK530 @ sK527)) != ((sK528 @ sK530 @ sK527))) & ! [X147 : subst,X148 : term,X149 : subst] : (((sub @ (sK528 @ X147 @ X148) @ X149)) = ((sK528 @ (comp @ X147 @ X149) @ (sub @ X148 @ X149)))) & ! [X150 : subst,X151 : subst,X152 : term] : (((sK529 @ (comp @ X151 @ X150) @ (sub @ X152 @ X150))) = ((sub @ (sK529 @ X151 @ X152) @ X150))) & (((lam @ (sK529 @ sh @ one))) = ((lam @ (sK528 @ sh @ one)))))) & ((sP36 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP36 != $true)) & (pushprop_gthm = $true) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (! [X153 : term] : (((sK531 @ X153 @ sh @ one)) = ((sub @ X153 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X156 : (subst > term > term)] : (((X156 @ sh @ one)) != ((sub @ sK532 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2_lthm = $true) & (substmonoid_gthm = $true) & ((axvarid = $true) | (((sub @ sK533 @ id)) != sK533)) & (! [X158 : term] : (((sub @ X158 @ id)) = X158) | (axvarid != $true)) & ((sP35 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP35 != $true)) & ! [X159 : d_term] : (d_one = X159) & (hoasinduction_lem1_gthm = $true) & ((sP32 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP32 != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3aa_lthm = $true) | (sP30 != $true)) & ((sP30 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasapinj1 = $true) | ((sK536 != sK535) & (((ap @ (sub @ sK536 @ id) @ sK534)) = ((ap @ (sub @ sK535 @ id) @ sK537))))) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X165 = X166) | (((ap @ (sub @ X165 @ id) @ X167)) != ((ap @ (sub @ X166 @ id) @ X164)))) | (hoasapinj1 != $true)) & (! [X168 : subst,X169 : (term > $o),X170 : term] : ! [X172 : term] : (((sK538 @ X170 @ X169 @ X168 @ X172)) = ((X169 @ (sub @ X172 @ (push @ X170 @ X168))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X176 : (term > $o)] : (((X176 @ (sK542 @ X176))) != ((sK540 @ (sub @ (sK542 @ X176) @ (push @ sK541 @ sK539)))))) & (termmset_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X179 : (term > $o)] : (((X179 @ (sK544 @ X179))) != ((sK543 @ id @ (sK544 @ X179) @ id)))) & (! [X181 : (subst > term > subst > $o)] : ! [X183 : term] : (((X181 @ id @ X183 @ id)) = ((sK545 @ X181 @ X183))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarsh = $true) & ((axvarcons = $true) | (sK547 != ((sub @ one @ (push @ sK547 @ sK546))))) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (! [X188 : subst,X189 : term,X190 : (term > $o)] : ! [X192 : term] : (((X190 @ (sub @ X192 @ (push @ X189 @ X188)))) = ((sK548 @ X190 @ X189 @ X188 @ X192))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X196 : (term > $o)] : (((sK551 @ (sub @ (sK552 @ X196) @ (push @ sK550 @ sK549)))) != ((X196 @ (sK552 @ X196))))) & ((sP29 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP29 != $true)) & (induction2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((sP27 = $true) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (sP27 != $true)) & (apnotvar = $true) & ! [X198 : subst] : (((d2subst @ (sK553 @ X198))) = X198) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X200 : term,X201 : term,X202 : term,X203 : term] : ((X201 = X202) | (((ap @ X203 @ X202)) != ((ap @ X200 @ X201)))) | (apinj2 != $true)) & ((apinj2 = $true) | ((sK555 != sK556) & (((ap @ sK557 @ sK556)) = ((ap @ sK554 @ sK555))))) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & ((hoasapinj2 = $true) | ((sK561 != sK560) & (((ap @ (sub @ sK559 @ id) @ sK561)) = ((ap @ (sub @ sK558 @ id) @ sK560))))) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((X214 = X215) | (((ap @ (sub @ X212 @ id) @ X214)) != ((ap @ (sub @ X213 @ id) @ X215)))) | (hoasapinj2 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP20 != $true)) & ((sP20 = $true) | (hoasinduction_lthm_3 != $true)) & ((sP14 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP14 != $true)) & (hoasinduction_lem2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (($true = sP13) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ($true != sP13)) & ((substmonoid = $true) | (sK562 != ((comp @ sK562 @ id))) | (sK563 != ((comp @ id @ sK563)))) & ((! [X218 : subst] : (((comp @ X218 @ id)) = X218) & ! [X219 : subst] : (((comp @ id @ X219)) = X219)) | (substmonoid != $true)) & ((induction = $true) | ((((sK564 @ sK565)) != $true) & ! [X222 : term] : ((((sK564 @ (lam @ X222))) = $true) | (((sK564 @ X222)) != $true)) & (((sP11 @ sK564)) != $true) & ! [X223 : term] : ((((var @ X223)) != $true) | (((sK564 @ X223)) = $true)))) & (! [X224 : (term > $o),X225 : term] : ((((X224 @ X225)) = $true) | ((((X224 @ (lam @ (sK566 @ X224)))) != $true) & (((X224 @ (sK566 @ X224))) = $true)) | (((sP11 @ X224)) = $true) | ((((var @ (sK567 @ X224))) = $true) & ($true != ((X224 @ (sK567 @ X224)))))) | (induction != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axmap = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((sP10 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP10 != $true)) & ((substmonoid_lthm = $true) | (! [X228 : subst] : (((comp @ X228 @ id)) = X228) & ((sK568 != ((comp @ id @ sK568))) | (((comp @ sK569 @ id)) != sK569)) & ! [X231 : subst] : (((comp @ id @ X231)) = X231))) & ((((comp @ sK570 @ id)) != sK570) | (! [X233 : subst] : (((comp @ id @ X233)) = X233) & ! [X234 : subst] : (((comp @ X234 @ id)) = X234)) | (sK571 != ((comp @ id @ sK571))) | (substmonoid_lthm != $true)) & (pushprop_lem0_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1_gthm = $true) & ! [X236 : term] : (((d2term @ (sK572 @ X236))) = X236) & (hoasapinj1_gthm = $true) & ! [X238 : d_term,X239 : d_term] : ((X238 = X239) | (((d2term @ X238)) != ((d2term @ X239)))) & (pushprop_lem2v2_gthm = $true) & (! [X240 : subst] : (((comp @ id @ X240)) = X240) | (axidl != $true)) & ((axidl = $true) | (sK573 != ((comp @ id @ sK573)))) & (hoasinduction_lem3_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X242 : term,X243 : term,X244 : term,X245 : term] : ((X243 = X244) | (((ap @ X245 @ X243)) != ((ap @ X242 @ X244)))) & ((sK575 != sK577) & (((ap @ (sub @ sK576 @ id) @ sK577)) = ((ap @ (sub @ sK574 @ id) @ sK575)))))) & (((sK580 != sK579) & (((ap @ sK578 @ sK580)) = ((ap @ sK581 @ sK579)))) | ! [X254 : term,X255 : term,X256 : term,X257 : term] : ((X255 = X257) | (((ap @ (sub @ X256 @ id) @ X257)) != ((ap @ (sub @ X254 @ id) @ X255)))) | (hoasapinj2_lthm != $true)) & (! [X258 : term] : (((sub @ X258 @ id)) = X258) | (sK582 != ((sub @ sK582 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK583 @ id)) != sK583) & ! [X261 : term] : (((sub @ X261 @ id)) = X261))) & (hoasapnotvar_lthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasapinj1_lthm = $true) | (((((ap @ (sub @ sK587 @ id) @ sK585)) = ((ap @ (sub @ sK586 @ id) @ sK584))) & (sK586 != sK587)) & ! [X266 : term] : (((sub @ X266 @ id)) = X266) & ! [X267 : term,X268 : term,X269 : term,X270 : term] : ((X268 = X270) | (((ap @ X270 @ X267)) != ((ap @ X268 @ X269)))))) & (! [X271 : term,X272 : term,X273 : term,X274 : term] : ((((ap @ (sub @ X273 @ id) @ X271)) != ((ap @ (sub @ X274 @ id) @ X272))) | (X273 = X274)) | (sK588 != ((sub @ sK588 @ id))) | ((sK592 != sK590) & (((ap @ sK590 @ sK591)) = ((ap @ sK592 @ sK589)))) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lthm != $true))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK456,sK457,vAPP,vAPP,vAPP,vAPP,vAPP,sK463,sK464,sK465,sK466,sK467,vAPP,sK469,vAPP,vAPP,sK472,sK473,sK474,sK475,vAPP,sK477,sK478,sK479,sK480,sK481,sK482,vAPP,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,vAPP,vAPP,sK501,sK502,sK503,sK504,vAPP,sK506,sK507,vAPP,sK509,vAPP,vAPP,sK512,sK513,sK514,sK515,sK516,sK517,sK518,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK527,sK528,sK529,sK530,vAPP,sK532,sK533,sK534,sK535,sK536,sK537,vAPP,sK539,sK540,sK541,vAPP,sK543,vAPP,vAPP,sK546,sK547,vAPP,sK549,sK550,sK551,vAPP,vAPP,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,vAPP,vAPP,sK568,sK569,sK570,sK571,vAPP,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,sK586,sK587,sK588,sK589,sK590,sK591,sK592]),skolemize(X0,sK456),skolemize(X1,sK457),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X19,sK463),skolemize(X20,sK464),skolemize(X21,sK465),skolemize(X22,sK466),skolemize(X23,sK467),skolemize(X29,sK75 @ X27),skolemize(X28,sK469),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X32,sK472),skolemize(X33,sK473),skolemize(X34,sK474),skolemize(X35,sK475),skolemize(X29,sK75 @ X27),skolemize(X44,sK477),skolemize(X45,sK478),skolemize(X46,sK479),skolemize(X47,sK480),skolemize(X49,sK481),skolemize(X50,sK482),skolemize(X29,sK75 @ X27),skolemize(X56,sK484),skolemize(X57,sK485),skolemize(X62,sK486),skolemize(X63,sK487),skolemize(X64,sK488),skolemize(X65,sK489),skolemize(X66,sK490),skolemize(X69,sK491),skolemize(X70,sK492),skolemize(X76,sK493),skolemize(X77,sK494),skolemize(X78,sK495),skolemize(X79,sK496),skolemize(X80,sK497),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X90,sK501),skolemize(X91,sK502),skolemize(X95,sK503),skolemize(X97,sK504),skolemize(X29,sK75 @ X27),skolemize(X100,sK506),skolemize(X103,sK507),skolemize(X29,sK75 @ X27),skolemize(X110,sK509),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X115,sK512),skolemize(X116,sK513),skolemize(X119,sK514),skolemize(X120,sK515),skolemize(X121,sK516),skolemize(X122,sK517),skolemize(X127,sK518),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X143,sK527),skolemize(X144,sK528),skolemize(X145,sK529),skolemize(X146,sK530),skolemize(X29,sK75 @ X27),skolemize(X155,sK532),skolemize(X157,sK533),skolemize(X160,sK534),skolemize(X161,sK535),skolemize(X162,sK536),skolemize(X163,sK537),skolemize(X29,sK75 @ X27),skolemize(X173,sK539),skolemize(X174,sK540),skolemize(X175,sK541),skolemize(X29,sK75 @ X27),skolemize(X178,sK543),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X184,sK546),skolemize(X185,sK547),skolemize(X29,sK75 @ X27),skolemize(X193,sK549),skolemize(X194,sK550),skolemize(X195,sK551),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X204,sK554),skolemize(X205,sK555),skolemize(X206,sK556),skolemize(X207,sK557),skolemize(X208,sK558),skolemize(X209,sK559),skolemize(X210,sK560),skolemize(X211,sK561),skolemize(X216,sK562),skolemize(X217,sK563),skolemize(X220,sK564),skolemize(X221,sK565),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X229,sK568),skolemize(X230,sK569),skolemize(X232,sK570),skolemize(X235,sK571),skolemize(X29,sK75 @ X27),skolemize(X241,sK573),skolemize(X246,sK574),skolemize(X247,sK575),skolemize(X248,sK576),skolemize(X249,sK577),skolemize(X250,sK578),skolemize(X251,sK579),skolemize(X252,sK580),skolemize(X253,sK581),skolemize(X259,sK582),skolemize(X260,sK583),skolemize(X262,sK584),skolemize(X263,sK585),skolemize(X264,sK586),skolemize(X265,sK587),skolemize(X275,sK588),skolemize(X276,sK589),skolemize(X277,sK590),skolemize(X278,sK591),skolemize(X279,sK592)],[f267])).
% 46.03/6.94 thf(f269,plain,(
% 46.03/6.94 ((sP60 = $true) | ? [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (! [X4 : subst,X3 : subst,X5 : term,X2 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) != $true) | (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) = $true)) & (((hoasinduction_p_and_p_prime @ X0 @ X1)) = $true) & (((sP59 @ X0)) != $true) & ! [X9 : subst,X8 : subst,X6 : subst,X7 : term] : ((((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) = $true) | ($true != ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8)))) & ? [X15 : term] : ((((X1 @ (lam @ X15))) != $true) & ! [X16 : term] : ((((X1 @ (sub @ X15 @ (push @ X16 @ id)))) = $true) | (((X1 @ X16)) != $true))))) & (! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (? [X4 : subst,X3 : subst,X5 : term,X2 : subst] : ((((X0 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true) & (((X0 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4)) != $true)) | (((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true) | (((sP59 @ X0)) = $true) | ? [X9 : subst,X8 : subst,X6 : subst,X7 : term] : ((((X0 @ X9 @ X7 @ (comp @ X6 @ X8))) != $true) & ($true = ((X0 @ (comp @ X9 @ X6) @ (sub @ X7 @ X6) @ X8)))) | ! [X15 : term] : ((((X1 @ (lam @ X15))) = $true) | ? [X16 : term] : ((((X1 @ (sub @ X15 @ (push @ X16 @ id)))) != $true) & (((X1 @ X16)) = $true)))) | (sP60 != $true))),
% 46.03/6.94 inference(nnf_transformation,[],[f76])).
% 46.03/6.94 thf(f270,plain,(
% 46.03/6.94 ((sP60 = $true) | ? [X0 : (term > $o),X1 : (subst > term > subst > $o)] : (! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((((X1 @ X3 @ X4 @ (comp @ X5 @ X2))) != $true) | (((X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)) = $true)) & (((hoasinduction_p_and_p_prime @ X1 @ X0)) = $true) & (((sP59 @ X1)) != $true) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X1 @ X6 @ X9 @ (comp @ X8 @ X7))) = $true) | (((X1 @ (comp @ X6 @ X8) @ (sub @ X9 @ X8) @ X7)) != $true)) & ? [X10 : term] : ((((X0 @ (lam @ X10))) != $true) & ! [X11 : term] : ((((X0 @ (sub @ X10 @ (push @ X11 @ id)))) = $true) | (((X0 @ X11)) != $true))))) & (! [X12 : (term > $o),X13 : (subst > term > subst > $o)] : (? [X14 : subst,X15 : subst,X16 : term,X17 : subst] : ((((X13 @ X15 @ X16 @ (comp @ X17 @ X14))) = $true) & (((X13 @ (comp @ X15 @ X17) @ (sub @ X16 @ X17) @ X14)) != $true)) | (((hoasinduction_p_and_p_prime @ X13 @ X12)) != $true) | (((sP59 @ X13)) = $true) | ? [X18 : subst,X19 : subst,X20 : subst,X21 : term] : ((((X13 @ X18 @ X21 @ (comp @ X20 @ X19))) != $true) & (((X13 @ (comp @ X18 @ X20) @ (sub @ X21 @ X20) @ X19)) = $true)) | ! [X22 : term] : ((((X12 @ (lam @ X22))) = $true) | ? [X23 : term] : ((((X12 @ (sub @ X22 @ (push @ X23 @ id)))) != $true) & (((X12 @ X23)) = $true)))) | (sP60 != $true))),
% 46.03/6.94 inference(rectify,[],[f269])).
% 46.03/6.94 thf(f271,plain,(
% 46.03/6.94 ((sP60 = $true) | (! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : (($true != ((sK594 @ X3 @ X4 @ (comp @ X5 @ X2)))) | (((sK594 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)) = $true)) & (((hoasinduction_p_and_p_prime @ sK594 @ sK593)) = $true) & (((sP59 @ sK594)) != $true) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((sK594 @ X6 @ X9 @ (comp @ X8 @ X7))) = $true) | (((sK594 @ (comp @ X6 @ X8) @ (sub @ X9 @ X8) @ X7)) != $true)) & ((((sK593 @ (lam @ sK595))) != $true) & ! [X11 : term] : ((((sK593 @ (sub @ sK595 @ (push @ X11 @ id)))) = $true) | (((sK593 @ X11)) != $true))))) & (! [X12 : (term > $o),X13 : (subst > term > subst > $o)] : (((((X13 @ (sK597 @ X13) @ (sK598 @ X13) @ (comp @ (sK599 @ X13) @ (sK596 @ X13)))) = $true) & ($true != ((X13 @ (comp @ (sK597 @ X13) @ (sK599 @ X13)) @ (sub @ (sK598 @ X13) @ (sK599 @ X13)) @ (sK596 @ X13))))) | (((hoasinduction_p_and_p_prime @ X13 @ X12)) != $true) | (((sP59 @ X13)) = $true) | ((((X13 @ (sK600 @ X13) @ (sK603 @ X13) @ (comp @ (sK602 @ X13) @ (sK601 @ X13)))) != $true) & (((X13 @ (comp @ (sK600 @ X13) @ (sK602 @ X13)) @ (sub @ (sK603 @ X13) @ (sK602 @ X13)) @ (sK601 @ X13))) = $true)) | ! [X22 : term] : ((((X12 @ (lam @ X22))) = $true) | ((((X12 @ (sub @ X22 @ (push @ (sK604 @ X22 @ X12) @ id)))) != $true) & (((X12 @ (sK604 @ X22 @ X12))) = $true)))) | (sP60 != $true))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK593,sK594,sK595,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK593),skolemize(X1,sK594),skolemize(X10,sK595),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27)],[f270])).
% 46.03/6.94 thf(f272,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : (((((sP59 @ X0)) = $true) | ! [X10 : (subst > term > term)] : (? [X14 : term] : ((((X0 @ id @ X14 @ id)) = $true) & (((X0 @ id @ (X10 @ id @ X14) @ id)) != $true)) | ? [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) != ((sub @ (X10 @ X13 @ X11) @ X12))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) = $true))) & (? [X10 : (subst > term > term)] : (! [X14 : term] : ((((X0 @ id @ X14 @ id)) != $true) | (((X0 @ id @ (X10 @ id @ X14) @ id)) = $true)) & ! [X11 : term,X12 : subst,X13 : subst] : (((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))) = ((sub @ (X10 @ X13 @ X11) @ X12))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X10 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP59 @ X0)) != $true)))),
% 46.03/6.94 inference(nnf_transformation,[],[f75])).
% 46.03/6.94 thf(f273,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : (((((sP59 @ 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] : (((X1 @ (comp @ X5 @ X4) @ (sub @ X3 @ X4))) != ((sub @ (X1 @ X5 @ 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] : (((sub @ (X6 @ X10 @ X8) @ X9)) = ((X6 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9)))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X6 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP59 @ X0)) != $true)))),
% 46.03/6.94 inference(rectify,[],[f272])).
% 46.03/6.94 thf(f274,plain,(
% 46.03/6.94 ! [X0 : (subst > term > subst > $o)] : (((((sP59 @ X0)) = $true) | ! [X1 : (subst > term > term)] : (((((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) & (((X0 @ id @ (X1 @ id @ (sK605 @ X1 @ X0)) @ id)) != $true)) | (((sub @ (X1 @ (sK608 @ X1) @ (sK606 @ X1)) @ (sK607 @ X1))) != ((X1 @ (comp @ (sK608 @ X1) @ (sK607 @ X1)) @ (sub @ (sK606 @ X1) @ (sK607 @ X1))))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true))) & ((! [X7 : term] : ((((X0 @ id @ X7 @ id)) != $true) | (((X0 @ id @ (sK609 @ X0 @ id @ X7) @ id)) = $true)) & ! [X8 : term,X9 : subst,X10 : subst] : (((sK609 @ X0 @ (comp @ X10 @ X9) @ (sub @ X8 @ X9))) = ((sub @ (sK609 @ X0 @ X10 @ X8) @ X9))) & (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK609 @ X0 @ Y0 @ Y1))))) @ id)) != $true)) | (((sP59 @ X0)) != $true)))),
% 46.03/6.94 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27),skolemize(X29,sK75 @ X27)],[f273])).
% 46.03/6.94 thf(f275,plain,(
% 46.03/6.94 ((sP60 != $true) | (hoasinduction_lem3v2 != $true)) & ((sP60 = $true) | (hoasinduction_lem3v2 = $true))),
% 46.03/6.94 inference(nnf_transformation,[],[f77])).
% 46.03/6.94 thf(f291,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o)] : ((((X0 @ id @ (ap @ (sub @ (sK77 @ X0) @ id) @ (sK76 @ X0)) @ id)) != $true) | (((sP57 @ X0)) != $true)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f84])).
% 46.03/6.94 thf(f658,plain,(
% 46.03/6.94 ( ! [X7 : term] : ((((sK367 @ X7)) = ((sK365 @ id @ X7 @ id))) | ($true = sP13)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f223])).
% 46.03/6.94 thf(f659,plain,(
% 46.03/6.94 (((sK367 @ (lam @ sK366))) != $true) | ($true = sP13)),
% 46.03/6.94 inference(cnf_transformation,[],[f223])).
% 46.03/6.94 thf(f660,plain,(
% 46.03/6.94 ($true = sP13) | (((sP12 @ sK365)) != $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f223])).
% 46.03/6.94 thf(f666,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((sub @ (X1 @ (sK380 @ X1) @ (sK379 @ X1)) @ (sK378 @ X1))) != ((X1 @ (comp @ (sK380 @ X1) @ (sK378 @ X1)) @ (sub @ (sK379 @ X1) @ (sK378 @ X1))))) | (((X0 @ id @ (sK381 @ X1 @ X0) @ id)) = $true) | ($true = ((sP12 @ X0)))) )),
% 46.03/6.94 inference(cnf_transformation,[],[f226])).
% 46.03/6.94 thf(f789,plain,(
% 46.03/6.94 ( ! [X236 : term] : ((((d2term @ (sK572 @ X236))) = X236)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f815,plain,(
% 46.03/6.94 (hoasinduction_lem3v2 = $true) | ($true != sP13)),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f817,plain,(
% 46.03/6.94 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f834,plain,(
% 46.03/6.94 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2))))))))),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f835,plain,(
% 46.03/6.94 ( ! [X198 : subst] : ((((d2subst @ (sK553 @ X198))) = X198)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f862,plain,(
% 46.03/6.94 (one = ((d2term @ d_one)))),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f866,plain,(
% 46.03/6.94 ( ! [X159 : d_term] : ((d_one = X159)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f873,plain,(
% 46.03/6.94 (((d2subst @ d_id)) = id)),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f905,plain,(
% 46.03/6.94 ( ! [X114 : d_subst] : ((d_id = X114)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f978,plain,(
% 46.03/6.94 ( ! [X8 : (subst > term > subst > $o),X7 : term] : ((((X8 @ id @ (lam @ (sK462 @ X8 @ sh @ one)) @ id)) != $true) | (((sP57 @ X8)) = $true) | (((X8 @ id @ X7 @ id)) = $true) | (hoasinduction_no_psi_cond != $true)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f982,plain,(
% 46.03/6.94 ( ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2))))) | (((sK457 @ id @ (sK461 @ X2) @ id)) = $true) | (((sK457 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (hoasinduction_no_psi_cond = $true)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f983,plain,(
% 46.03/6.94 (((sK457 @ id @ sK456 @ id)) != $true) | (hoasinduction_no_psi_cond = $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f268])).
% 46.03/6.94 thf(f999,plain,(
% 46.03/6.94 (((sK593 @ (lam @ sK595))) != $true) | (sP60 = $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f271])).
% 46.03/6.94 thf(f1001,plain,(
% 46.03/6.94 (sP60 = $true) | (((sP59 @ sK594)) != $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f271])).
% 46.03/6.94 thf(f1002,plain,(
% 46.03/6.94 (sP60 = $true) | (((hoasinduction_p_and_p_prime @ sK594 @ sK593)) = $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f271])).
% 46.03/6.94 thf(f1008,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sP59 @ X0)) = $true) | (((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) | (((sub @ (X1 @ (sK608 @ X1) @ (sK606 @ X1)) @ (sK607 @ X1))) != ((X1 @ (comp @ (sK608 @ X1) @ (sK607 @ X1)) @ (sub @ (sK606 @ X1) @ (sK607 @ X1))))) | (((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)) = $true)) )),
% 46.03/6.94 inference(cnf_transformation,[],[f274])).
% 46.03/6.94 thf(f1010,plain,(
% 46.03/6.94 (hoasinduction_lem3v2 != $true) | (sP60 != $true)),
% 46.03/6.94 inference(cnf_transformation,[],[f275])).
% 46.03/6.94 thf(f1013,plain,(
% 46.03/6.94 ((((^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2))))))) @ sK594 @ sK593)) = $true) | (sP60 = $true)),
% 46.03/6.94 inference(definition_unfolding,[],[f1002,f834])).
% 46.03/6.94 thf(f1022,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK608 @ X1) @ (sK606 @ X1)) @ (sK607 @ X1))) != ((X1 @ (comp @ (sK608 @ X1) @ (sK607 @ X1)) @ (sub @ (sK606 @ X1) @ (sK607 @ X1))))) | (((sP59 @ X0)) = $true) | (((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) | ($true = ((X0 @ id @ ((^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id)))) )),
% 46.03/6.94 inference(definition_unfolding,[],[f1008,f817])).
% 46.03/6.94 thf(f1119,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) | (((sub @ (X1 @ (sK608 @ X1) @ (sK606 @ X1)) @ (sK607 @ X1))) != ((X1 @ (comp @ (sK608 @ X1) @ (sK607 @ X1)) @ (sub @ (sK606 @ X1) @ (sK607 @ X1))))) | ($true = ((X0 @ id @ (d2term @ d_one) @ id))) | (((sP59 @ X0)) = $true)) )),
% 46.03/6.94 inference(beta-eta_normalization,[],[f1022])).
% 46.03/6.94 thf(f1138,plain,(
% 46.03/6.94 (sP60 = $true) | (((!! @ term @ (^[Y0 : term]: ((sK594 @ id @ Y0 @ id) = (sK593 @ Y0))))) = $true)),
% 46.03/6.94 inference(beta-eta_normalization,[],[f1013])).
% 46.03/6.94 thf(f1139,plain,(
% 46.03/6.94 ( ! [X1 : term] : (((((^[Y0 : term]: ((sK594 @ id @ Y0 @ id) = (sK593 @ Y0))) @ X1)) = $true) | (sP60 = $true)) )),
% 46.03/6.94 inference(pi_proxy_clausification,[],[f1138])).
% 46.03/6.94 thf(f1140,plain,(
% 46.03/6.94 ( ! [X1 : term] : ((sP60 = $true) | ((((sK594 @ id @ X1 @ id) = (sK593 @ X1))) = $true)) )),
% 46.03/6.94 inference(beta-eta_normalization,[],[f1139])).
% 46.03/6.94 thf(f1141,plain,(
% 46.03/6.94 ( ! [X1 : term] : ((((sK593 @ X1)) = ((sK594 @ id @ X1 @ id))) | (sP60 = $true)) )),
% 46.03/6.94 inference(equality_proxy_clausification,[],[f1140])).
% 46.03/6.94 thf(f1142,plain,(
% 46.03/6.94 ( ! [X1 : term] : ((sP60 = $true) | ($false = ((sK594 @ id @ X1 @ id))) | (((sK593 @ X1)) = $true)) )),
% 46.03/6.94 inference(iff_proxy_clausification,[],[f1141])).
% 46.03/6.94 thf(f1190,plain,(
% 46.03/6.94 ( ! [X7 : term] : (($false = ((sK365 @ id @ X7 @ id))) | ($true = sP13) | (((sK367 @ X7)) = $true)) )),
% 46.03/6.94 inference(iff_proxy_clausification,[],[f658])).
% 46.03/6.94 thf(f1493,definition,(
% 46.03/6.94 spl618_75 <=> (sP60 = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_75])],[avatar_definition])).
% 46.03/6.94 thf(f1748,definition,(
% 46.03/6.94 spl618_139 <=> ($true = sP13)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_139])],[avatar_definition])).
% 46.03/6.94 thf(f1751,definition,(
% 46.03/6.94 spl618_140 <=> (hoasinduction_lem3v2 = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_140])],[avatar_definition])).
% 46.03/6.94 thf(f1809,definition,(
% 46.03/6.94 spl618_155 <=> (hoasinduction_no_psi_cond = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_155])],[avatar_definition])).
% 46.03/6.94 thf(f1857,definition,(
% 46.03/6.94 spl618_167 <=> (((sP59 @ sK594)) = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_167])],[avatar_definition])).
% 46.03/6.94 thf(f1859,plain,(
% 46.03/6.94 spl618_75 | ~spl618_167),
% 46.03/6.94 inference(avatar_split_clause,[],[f1001,f1857,f1493])).
% 46.03/6.94 thf(f2333,definition,(
% 46.03/6.94 spl618_282 <=> (((sK593 @ (lam @ sK595))) = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_282])],[avatar_definition])).
% 46.03/6.94 thf(f2334,plain,(
% 46.03/6.94 (((sK593 @ (lam @ sK595))) != $true) | spl618_282),
% 46.03/6.94 inference(avatar_component_clause,[],[f2333])).
% 46.03/6.94 thf(f2335,plain,(
% 46.03/6.94 spl618_75 | ~spl618_282),
% 46.03/6.94 inference(avatar_split_clause,[],[f999,f2333,f1493])).
% 46.03/6.94 thf(f2409,definition,(
% 46.03/6.94 spl618_299 <=> (((sK367 @ (lam @ sK366))) = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_299])],[avatar_definition])).
% 46.03/6.94 thf(f2410,plain,(
% 46.03/6.94 (((sK367 @ (lam @ sK366))) != $true) | spl618_299),
% 46.03/6.94 inference(avatar_component_clause,[],[f2409])).
% 46.03/6.94 thf(f2411,plain,(
% 46.03/6.94 spl618_139 | ~spl618_299),
% 46.03/6.94 inference(avatar_split_clause,[],[f659,f2409,f1748])).
% 46.03/6.94 thf(f2774,definition,(
% 46.03/6.94 spl618_386 <=> ! [X1 : term] : (($false = ((sK594 @ id @ X1 @ id))) | (((sK593 @ X1)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_386])],[avatar_definition])).
% 46.03/6.94 thf(f2775,plain,(
% 46.03/6.94 ( ! [X1 : term] : ((((sK593 @ X1)) = $true) | ($false = ((sK594 @ id @ X1 @ id)))) ) | ~spl618_386),
% 46.03/6.94 inference(avatar_component_clause,[],[f2774])).
% 46.03/6.94 thf(f2776,plain,(
% 46.03/6.94 spl618_75 | spl618_386),
% 46.03/6.94 inference(avatar_split_clause,[],[f1142,f2774,f1493])).
% 46.03/6.94 thf(f2826,definition,(
% 46.03/6.94 spl618_398 <=> ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2))))) | (((sK457 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true) | (((sK457 @ id @ (sK461 @ X2) @ id)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_398])],[avatar_definition])).
% 46.03/6.94 thf(f2827,plain,(
% 46.03/6.94 ( ! [X2 : (subst > term > term)] : ((((sK457 @ id @ (sK461 @ X2) @ id)) = $true) | (((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2))))) | (((sK457 @ id @ (lam @ (X2 @ sh @ one)) @ id)) = $true)) ) | ~spl618_398),
% 46.03/6.94 inference(avatar_component_clause,[],[f2826])).
% 46.03/6.94 thf(f2828,plain,(
% 46.03/6.94 spl618_155 | spl618_398),
% 46.03/6.94 inference(avatar_split_clause,[],[f982,f2826,f1809])).
% 46.03/6.94 thf(f3307,definition,(
% 46.03/6.94 spl618_513 <=> (((sP12 @ sK365)) = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_513])],[avatar_definition])).
% 46.03/6.94 thf(f3308,plain,(
% 46.03/6.94 (((sP12 @ sK365)) != $true) | spl618_513),
% 46.03/6.94 inference(avatar_component_clause,[],[f3307])).
% 46.03/6.94 thf(f3309,plain,(
% 46.03/6.94 ~spl618_513 | spl618_139),
% 46.03/6.94 inference(avatar_split_clause,[],[f660,f1748,f3307])).
% 46.03/6.94 thf(f3336,definition,(
% 46.03/6.94 spl618_520 <=> ! [X8 : (subst > term > subst > $o),X7 : term] : ((((X8 @ id @ (lam @ (sK462 @ X8 @ sh @ one)) @ id)) != $true) | (((X8 @ id @ X7 @ id)) = $true) | (((sP57 @ X8)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_520])],[avatar_definition])).
% 46.03/6.94 thf(f3337,plain,(
% 46.03/6.94 ( ! [X8 : (subst > term > subst > $o),X7 : term] : ((((X8 @ id @ (lam @ (sK462 @ X8 @ sh @ one)) @ id)) != $true) | (((sP57 @ X8)) = $true) | (((X8 @ id @ X7 @ id)) = $true)) ) | ~spl618_520),
% 46.03/6.94 inference(avatar_component_clause,[],[f3336])).
% 46.03/6.94 thf(f3338,plain,(
% 46.03/6.94 spl618_520 | ~spl618_155),
% 46.03/6.94 inference(avatar_split_clause,[],[f978,f1809,f3336])).
% 46.03/6.94 thf(f3555,definition,(
% 46.03/6.94 spl618_571 <=> ! [X7 : term] : (($false = ((sK365 @ id @ X7 @ id))) | (((sK367 @ X7)) = $true))),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_571])],[avatar_definition])).
% 46.03/6.94 thf(f3556,plain,(
% 46.03/6.94 ( ! [X7 : term] : (($false = ((sK365 @ id @ X7 @ id))) | (((sK367 @ X7)) = $true)) ) | ~spl618_571),
% 46.03/6.94 inference(avatar_component_clause,[],[f3555])).
% 46.03/6.94 thf(f3557,plain,(
% 46.03/6.94 spl618_571 | spl618_139),
% 46.03/6.94 inference(avatar_split_clause,[],[f1190,f1748,f3555])).
% 46.03/6.94 thf(f3696,definition,(
% 46.03/6.94 spl618_604 <=> (((sK457 @ id @ sK456 @ id)) = $true)),
% 46.03/6.94 introduced(definition,[new_symbols(definition,[spl618_604])],[avatar_definition])).
% 46.03/6.94 thf(f3697,plain,(
% 46.03/6.94 (((sK457 @ id @ sK456 @ id)) != $true) | spl618_604),
% 46.03/6.94 inference(avatar_component_clause,[],[f3696])).
% 46.03/6.94 thf(f3698,plain,(
% 46.03/6.94 spl618_155 | ~spl618_604),
% 46.03/6.94 inference(avatar_split_clause,[],[f983,f3696,f1809])).
% 46.03/6.94 thf(f3783,plain,(
% 46.03/6.94 ~spl618_75 | ~spl618_140),
% 46.03/6.94 inference(avatar_split_clause,[],[f1010,f1751,f1493])).
% 46.03/6.94 thf(f3784,plain,(
% 46.03/6.94 spl618_140 | ~spl618_139),
% 46.03/6.94 inference(avatar_split_clause,[],[f815,f1748,f1751])).
% 46.03/6.94 thf(f3917,plain,(
% 46.03/6.94 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 46.03/6.94 inference(constrained_superposition,[],[f862,f866])).
% 46.03/6.94 thf(f3920,plain,(
% 46.03/6.94 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 46.03/6.94 inference(constrained_superposition,[],[f873,f905])).
% 46.03/6.94 thf(f3937,plain,(
% 46.03/6.94 ( ! [X0 : term] : ((one = X0)) )),
% 46.03/6.94 inference(constrained_superposition,[],[f789,f3917])).
% 46.03/6.94 thf(f3939,plain,(
% 46.03/6.94 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 46.03/6.94 inference(constrained_superposition,[],[f3937,f3937])).
% 46.03/6.94 thf(f4001,plain,(
% 46.03/6.94 ( ! [X0 : subst] : ((id = X0)) )),
% 46.03/6.94 inference(constrained_superposition,[],[f835,f3920])).
% 46.03/6.94 thf(f4215,plain,(
% 46.03/6.94 ( ! [X0 : subst] : (($true != ((sK457 @ X0 @ sK456 @ X0)))) ) | spl618_604),
% 46.03/6.94 inference(constrained_superposition,[],[f3697,f4001])).
% 46.03/6.94 thf(f4251,plain,(
% 46.03/6.94 ( ! [X0 : term,X1 : subst] : ((((sK457 @ X1 @ X0 @ X1)) != $true)) ) | spl618_604),
% 46.03/6.94 inference(constrained_superposition,[],[f4215,f3939])).
% 46.03/6.94 thf(f7532,plain,(
% 46.03/6.94 ( ! [X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ X0 @ id)) != $true) | (((sP57 @ X1)) != $true)) )),
% 46.03/6.94 inference(constrained_superposition,[],[f291,f3939])).
% 46.03/6.94 thf(f13698,plain,(
% 46.03/6.94 ( ! [X0 : term] : ((((sK593 @ X0)) != $true)) ) | spl618_282),
% 46.03/6.94 inference(constrained_superposition,[],[f2334,f3939])).
% 46.03/6.94 thf(f15115,plain,(
% 46.03/6.94 ( ! [X1 : term] : (($false = ((sK594 @ id @ X1 @ id)))) ) | (spl618_282 | ~spl618_386)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f2775,f13698])).
% 46.03/6.94 thf(f52190,plain,(
% 46.03/6.94 ( ! [X2 : (subst > term > term)] : ((((sK457 @ id @ (sK461 @ X2) @ id)) = $true) | (((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2)))))) ) | (~spl618_398 | spl618_604)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f2827,f4251])).
% 46.03/6.94 thf(f52191,plain,(
% 46.03/6.94 ( ! [X2 : (subst > term > term)] : ((((sub @ (X2 @ (sK460 @ X2) @ (sK459 @ X2)) @ (sK458 @ X2))) != ((X2 @ (comp @ (sK460 @ X2) @ (sK458 @ X2)) @ (sub @ (sK459 @ X2) @ (sK458 @ X2)))))) ) | (~spl618_398 | spl618_604)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f52190,f4251])).
% 46.03/6.94 thf(f52192,plain,(
% 46.03/6.94 $false | (~spl618_398 | spl618_604)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f52191,f3939])).
% 46.03/6.94 thf(f52193,plain,(
% 46.03/6.94 ~spl618_398 | spl618_604),
% 46.03/6.94 inference(avatar_contradiction_clause,[],[f52192])).
% 46.03/6.94 thf(f52195,plain,(
% 46.03/6.94 ( ! [X8 : (subst > term > subst > $o),X7 : term] : ((((X8 @ id @ (lam @ (sK462 @ X8 @ sh @ one)) @ id)) != $true) | (((X8 @ id @ X7 @ id)) = $true)) ) | ~spl618_520),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f3337,f7532])).
% 46.03/6.94 thf(f52213,plain,(
% 46.03/6.94 ( ! [X2 : term,X0 : term,X1 : (subst > term > subst > $o)] : ((((X1 @ id @ X0 @ id)) != $true) | (((X1 @ id @ X2 @ id)) = $true)) ) | ~spl618_520),
% 46.03/6.94 inference(constrained_superposition,[],[f52195,f3939])).
% 46.03/6.94 thf(f73878,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) | (((sub @ (X1 @ (sK608 @ X1) @ (sK606 @ X1)) @ (sK607 @ X1))) != ((X1 @ (comp @ (sK608 @ X1) @ (sK607 @ X1)) @ (sub @ (sK606 @ X1) @ (sK607 @ X1))))) | (((sP59 @ X0)) = $true)) ) | ~spl618_520),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f1119,f52213])).
% 46.03/6.94 thf(f73879,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (sK605 @ X1 @ X0) @ id)) = $true) | (((sP59 @ X0)) = $true)) ) | ~spl618_520),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f73878,f3939])).
% 46.03/6.94 thf(f74022,plain,(
% 46.03/6.94 ($false = $true) | (((sP59 @ sK594)) = $true) | (spl618_282 | ~spl618_386 | ~spl618_520)),
% 46.03/6.94 inference(constrained_superposition,[],[f15115,f73879])).
% 46.03/6.94 thf(f74352,plain,(
% 46.03/6.94 (((sP59 @ sK594)) = $true) | (spl618_282 | ~spl618_386 | ~spl618_520)),
% 46.03/6.94 inference(trivial_inequality_removal,[],[f74022])).
% 46.03/6.94 thf(f74459,plain,(
% 46.03/6.94 spl618_167 | spl618_282 | ~spl618_386 | ~spl618_520),
% 46.03/6.94 inference(avatar_split_clause,[],[f74352,f3336,f2774,f2333,f1857])).
% 46.03/6.94 thf(f74574,plain,(
% 46.03/6.94 ( ! [X0 : term] : ((((sK367 @ X0)) != $true)) ) | spl618_299),
% 46.03/6.94 inference(constrained_superposition,[],[f2410,f3939])).
% 46.03/6.94 thf(f127649,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | (((sub @ (X1 @ (sK380 @ X1) @ (sK379 @ X1)) @ (sK378 @ X1))) != ((X1 @ (comp @ (sK380 @ X1) @ (sK378 @ X1)) @ (sub @ (sK379 @ X1) @ (sK378 @ X1))))) | ($true = ((sP12 @ X0)))) ) | ~spl618_520),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f666,f52213])).
% 46.03/6.94 thf(f127650,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > subst > $o),X1 : (subst > term > term)] : ((((X0 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ($true = ((sP12 @ X0)))) ) | ~spl618_520),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f127649,f3939])).
% 46.03/6.94 thf(f127711,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > term)] : ((((sK367 @ (lam @ (X0 @ sh @ one)))) = $true) | (((sP12 @ sK365)) = $true) | ($false = $true)) ) | (~spl618_520 | ~spl618_571)),
% 46.03/6.94 inference(constrained_superposition,[],[f127650,f3556])).
% 46.03/6.94 thf(f128113,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > term)] : ((((sP12 @ sK365)) = $true) | (((sK367 @ (lam @ (X0 @ sh @ one)))) = $true)) ) | (~spl618_520 | ~spl618_571)),
% 46.03/6.94 inference(trivial_inequality_removal,[],[f127711])).
% 46.03/6.94 thf(f128190,plain,(
% 46.03/6.94 ( ! [X0 : (subst > term > term)] : ((((sK367 @ (lam @ (X0 @ sh @ one)))) = $true)) ) | (spl618_513 | ~spl618_520 | ~spl618_571)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f128113,f3308])).
% 46.03/6.94 thf(f128203,plain,(
% 46.03/6.94 $false | (spl618_299 | spl618_513 | ~spl618_520 | ~spl618_571)),
% 46.03/6.94 inference(forward_subsumption_resolution,[],[f128190,f74574])).
% 46.03/6.94 thf(f128204,plain,(
% 46.03/6.94 spl618_299 | spl618_513 | ~spl618_520 | ~spl618_571),
% 46.03/6.94 inference(avatar_contradiction_clause,[],[f128203])).
% 46.03/6.94 cnf(s113, plain, spl618_75 | ~spl618_167, inference(sat_conversion,[],[f1859])).
% 46.03/6.94 cnf(s224, plain, spl618_75 | ~spl618_282, inference(sat_conversion,[],[f2335])).
% 46.03/6.94 cnf(s243, plain, spl618_139 | ~spl618_299, inference(sat_conversion,[],[f2411])).
% 46.03/6.94 cnf(s336, plain, spl618_75 | spl618_386, inference(sat_conversion,[],[f2776])).
% 46.03/6.94 cnf(s348, plain, spl618_155 | spl618_398, inference(sat_conversion,[],[f2828])).
% 46.03/6.94 cnf(s474, plain, spl618_139 | ~spl618_513, inference(sat_conversion,[],[f3309])).
% 46.03/6.94 cnf(s481, plain, ~spl618_155 | spl618_520, inference(sat_conversion,[],[f3338])).
% 46.03/6.94 cnf(s537, plain, spl618_139 | spl618_571, inference(sat_conversion,[],[f3557])).
% 46.03/6.94 cnf(s574, plain, spl618_155 | ~spl618_604, inference(sat_conversion,[],[f3698])).
% 46.03/6.94 cnf(s598, plain, ~spl618_75 | ~spl618_140, inference(sat_conversion,[],[f3783])).
% 46.03/6.94 cnf(s599, plain, ~spl618_139 | spl618_140, inference(sat_conversion,[],[f3784])).
% 46.03/6.94 cnf(s1617, plain, ~spl618_398 | spl618_604, inference(sat_conversion,[],[f52193])).
% 46.03/6.94 cnf(s2268, plain, spl618_167 | spl618_282 | ~spl618_386 | ~spl618_520, inference(sat_conversion,[],[f74459])).
% 46.03/6.94 cnf(s3993, plain, spl618_299 | spl618_513 | ~spl618_520 | ~spl618_571, inference(sat_conversion,[],[f128204])).
% 46.03/6.94 cnf(s4251, plain, spl618_155, inference(rat,[],[s1617,s348,s574])).
% 46.03/6.94 cnf(s4253, plain, spl618_520, inference(rat,[],[s481,s4251])).
% 46.03/6.94 cnf(s4295, plain, spl618_75, inference(rat,[],[s2268,s113,s224,s336,s4253])).
% 46.03/6.94 cnf(s4296, plain, ~spl618_140, inference(rat,[],[s598,s4295])).
% 46.03/6.94 cnf(s4313, plain, ~spl618_139, inference(rat,[],[s599,s4296])).
% 46.03/6.94 cnf(s4314, plain, spl618_571, inference(rat,[],[s537,s4313])).
% 46.03/6.94 cnf(s4317, plain, ~spl618_513, inference(rat,[],[s474,s4313])).
% 46.03/6.94 cnf(s4319, plain, ~spl618_299, inference(rat,[],[s243,s4313])).
% 46.03/6.94 cnf(s4321, plain, $false, inference(rat,[],[s3993,s4314,s4253,s4317,s4319])).
% 46.03/6.94 thf(f128205,plain,(
% 46.03/6.94 $false),
% 46.03/6.94 inference(avatar_sat_refutation,[],[s4321])).
% 46.03/6.94 % SZS output end Proof for theBenchmark
% 46.03/6.94 % (1436108)------------------------------
% 46.03/6.94 % (1436108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 46.03/6.94 % (1436108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 46.03/6.94 % (1436108)CaDiCaL version: 2.1.3
% 46.03/6.94 % (1436108)Termination reason: Refutation
% 46.03/6.94 % (1436108)Time elapsed: 2.718 s
% 46.03/6.94 % (1436108)Peak memory usage: 41 MB
% 46.03/6.94 % (1436108)Instructions burned: 5626 (million)
% 46.03/6.94 % (1435380)Success in time 6.662 s
% 46.03/6.94 % Vampire exiting
%------------------------------------------------------------------------------