%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX156^1 : 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 : n009.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 08:40:35 AM UTC 2026
% Result : Theorem 3.80s 0.84s
% Output : Refutation 3.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX156^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 16:09:00 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.23 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
% 0.21/0.35 % (4189454)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.35 % (4189463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=738322396:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.35 % (4189465)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.35 % (4189465)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
% 0.21/0.35 % (4189460)lrs+10_16_si=on:nwc=1.5:random_seed=2091549189:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.35 % (4189463)Instruction limit reached!
% 0.21/0.35 % (4189463)------------------------------
% 0.21/0.35 % (4189463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (4189463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (4189463)CaDiCaL version: 2.1.3
% 0.21/0.35 % (4189463)Termination reason: Instruction limit
% 0.21/0.35 % (4189463)Termination phase: Property scanning
% 0.21/0.35 % (4189463)Time elapsed: 0.006 s
% 0.21/0.35 % (4189459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1031891824:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.35 % (4189463)Peak memory usage: 10 MB
% 0.21/0.35 % (4189463)Instructions burned: 26 (million)
% 0.21/0.35 % (4189461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4018168237:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.35 % (4189462)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=2758124004: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)
% 0.21/0.35 % (4189464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2387895468:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.35 % (4189465)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=3498992165:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.35 % (4189461)Instruction limit reached!
% 0.21/0.35 % (4189461)------------------------------
% 0.21/0.35 % (4189461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (4189461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (4189461)CaDiCaL version: 2.1.3
% 0.21/0.35 % (4189461)Termination reason: Instruction limit
% 0.21/0.35 % (4189461)Termination phase: shuffling
% 0.21/0.35 % (4189461)Time elapsed: 0.002 s
% 0.21/0.35 % (4189461)Peak memory usage: 9 MB
% 0.21/0.35 % (4189461)Instructions burned: 4 (million)
% 0.21/0.35 % (4189460)Instruction limit reached!
% 0.21/0.35 % (4189460)------------------------------
% 0.21/0.35 % (4189460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (4189460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (4189460)CaDiCaL version: 2.1.3
% 0.21/0.35 % (4189460)Termination reason: Instruction limit
% 0.21/0.35 % (4189460)Termination phase: shuffling
% 0.21/0.35 % (4189460)Time elapsed: 0.008 s
% 0.21/0.35 % (4189460)Peak memory usage: 10 MB
% 0.21/0.35 % (4189460)Instructions burned: 19 (million)
% 0.21/0.35 % (4189471)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=91036741:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (4189471)Instruction limit reached!
% 0.21/0.35 % (4189471)------------------------------
% 0.21/0.35 % (4189471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (4189471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (4189471)CaDiCaL version: 2.1.3
% 0.21/0.35 % (4189471)Termination reason: Instruction limit
% 0.21/0.35 % (4189471)Termination phase: shuffling
% 0.21/0.35 % (4189471)Time elapsed: 0.001 s
% 0.21/0.35 % (4189471)Peak memory usage: 9 MB
% 0.21/0.35 % (4189471)Instructions burned: 4 (million)
% 0.21/0.35 % (4189474)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=765095026:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.82/0.39 % (4189475)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.39 % (4189477)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3428713724:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.82/0.39 % (4189474)Instruction limit reached!
% 0.82/0.39 % (4189474)------------------------------
% 0.82/0.39 % (4189474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.39 % (4189474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.39 % (4189474)CaDiCaL version: 2.1.3
% 0.82/0.39 % (4189474)Termination reason: Instruction limit
% 0.82/0.39 % (4189474)Termination phase: shuffling
% 0.82/0.39 % (4189474)Time elapsed: 0.003 s
% 0.82/0.39 % (4189474)Peak memory usage: 10 MB
% 0.82/0.39 % (4189474)Instructions burned: 7 (million)
% 0.82/0.39 % (4189475)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2331229280:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.82/0.39 % (4189477)Instruction limit reached!
% 0.82/0.39 % (4189477)------------------------------
% 0.82/0.39 % (4189477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.39 % (4189477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.39 % (4189477)CaDiCaL version: 2.1.3
% 0.82/0.39 % (4189477)Termination reason: Instruction limit
% 0.82/0.39 % (4189477)Termination phase: shuffling
% 0.82/0.39 % (4189477)Time elapsed: 0.003 s
% 0.82/0.39 % (4189477)Peak memory usage: 10 MB
% 0.82/0.39 % (4189477)Instructions burned: 13 (million)
% 0.82/0.39 % (4189475)Instruction limit reached!
% 0.82/0.39 % (4189475)------------------------------
% 0.82/0.39 % (4189475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.39 % (4189475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.39 % (4189475)CaDiCaL version: 2.1.3
% 0.82/0.39 % (4189475)Termination reason: Instruction limit
% 0.82/0.39 % (4189475)Termination phase: shuffling
% 0.82/0.39 % (4189475)Time elapsed: 0.004 s
% 0.82/0.39 % (4189475)Peak memory usage: 10 MB
% 0.82/0.39 % (4189475)Instructions burned: 9 (million)
% 0.82/0.39 % (4189464)Instruction limit reached!
% 0.82/0.39 % (4189464)------------------------------
% 0.82/0.39 % (4189464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.39 % (4189464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.39 % (4189464)CaDiCaL version: 2.1.3
% 0.82/0.39 % (4189464)Termination reason: Instruction limit
% 0.82/0.39 % (4189464)Termination phase: Preprocessing 3
% 0.82/0.39 % (4189464)Time elapsed: 0.034 s
% 0.82/0.39 % (4189464)Peak memory usage: 12 MB
% 0.82/0.39 % (4189464)Instructions burned: 75 (million)
% 0.82/0.39 % (4189482)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=1941511396:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.82/0.39 % (4189459)Instruction limit reached!
% 0.82/0.39 % (4189459)------------------------------
% 0.82/0.39 % (4189459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.39 % (4189459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.39 % (4189459)CaDiCaL version: 2.1.3
% 0.82/0.39 % (4189459)Termination reason: Instruction limit
% 0.82/0.39 % (4189459)Termination phase: Preprocessing 3
% 0.82/0.39 % (4189459)Time elapsed: 0.040 s
% 0.82/0.39 % (4189459)Peak memory usage: 13 MB
% 0.82/0.39 % (4189459)Instructions burned: 88 (million)
% 0.82/0.39 % (4189480)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
% 0.82/0.39 % (4189480)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.82/0.39 % (4189480)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3470394844:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.82/0.39 % (4189484)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.82/0.42 % (4189483)lrs+10_1_si=on:cs=on:random_seed=1013174945:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.82/0.42 % (4189484)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=54382691:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.82/0.42 % (4189483)Instruction limit reached!
% 0.82/0.42 % (4189483)------------------------------
% 0.82/0.42 % (4189483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189483)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189483)Termination reason: Instruction limit
% 0.82/0.42 % (4189483)Termination phase: shuffling
% 0.82/0.42 % (4189483)Time elapsed: 0.004 s
% 0.82/0.42 % (4189483)Peak memory usage: 9 MB
% 0.82/0.42 % (4189483)Instructions burned: 10 (million)
% 0.82/0.42 % (4189484)Instruction limit reached!
% 0.82/0.42 % (4189484)------------------------------
% 0.82/0.42 % (4189484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189484)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189484)Termination reason: Instruction limit
% 0.82/0.42 % (4189484)Termination phase: shuffling
% 0.82/0.42 % (4189484)Time elapsed: 0.003 s
% 0.82/0.42 % (4189484)Peak memory usage: 9 MB
% 0.82/0.42 % (4189484)Instructions burned: 5 (million)
% 0.82/0.42 % (4189482)Instruction limit reached!
% 0.82/0.42 % (4189482)------------------------------
% 0.82/0.42 % (4189482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189482)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189482)Termination reason: Instruction limit
% 0.82/0.42 % (4189482)Termination phase: Saturation
% 0.82/0.42 % (4189482)Time elapsed: 0.019 s
% 0.82/0.42 % (4189482)Peak memory usage: 12 MB
% 0.82/0.42 % (4189482)Instructions burned: 86 (million)
% 0.82/0.42 % (4189480)Instruction limit reached!
% 0.82/0.42 % (4189480)------------------------------
% 0.82/0.42 % (4189480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189480)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189480)Termination reason: Instruction limit
% 0.82/0.42 % (4189480)Termination phase: shuffling
% 0.82/0.42 % (4189480)Time elapsed: 0.013 s
% 0.82/0.42 % (4189480)Peak memory usage: 10 MB
% 0.82/0.42 % (4189480)Instructions burned: 30 (million)
% 0.82/0.42 % (4189486)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=271559987:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.82/0.42 % (4189492)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4212061160:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.82/0.42 % (4189465)Instruction limit reached!
% 0.82/0.42 % (4189465)------------------------------
% 0.82/0.42 % (4189465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189465)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189465)Termination reason: Instruction limit
% 0.82/0.42 % (4189465)Termination phase: Property scanning
% 0.82/0.42 % (4189465)Time elapsed: 0.069 s
% 0.82/0.42 % (4189465)Peak memory usage: 13 MB
% 0.82/0.42 % (4189465)Instructions burned: 157 (million)
% 0.82/0.42 % (4189492)Instruction limit reached!
% 0.82/0.42 % (4189492)------------------------------
% 0.82/0.42 % (4189492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.82/0.42 % (4189492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.82/0.42 % (4189492)CaDiCaL version: 2.1.3
% 0.82/0.42 % (4189492)Termination reason: Instruction limit
% 0.82/0.42 % (4189492)Termination phase: shuffling
% 0.82/0.42 % (4189492)Time elapsed: 0.003 s
% 0.82/0.42 % (4189492)Peak memory usage: 10 MB
% 0.82/0.42 % (4189492)Instructions burned: 15 (million)
% 0.82/0.42 % (4189490)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3309175697:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.82/0.42 % (4189486)Refutation not found, incomplete strategy
% 0.82/0.42 % (4189486)------------------------------
% 1.62/0.48 % (4189486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (4189486)CaDiCaL version: 2.1.3
% 1.62/0.48 % (4189486)Termination reason: Refutation not found, incomplete strategy
% 1.62/0.48 % (4189486)Time elapsed: 0.016 s
% 1.62/0.48 % (4189486)Peak memory usage: 12 MB
% 1.62/0.48 % (4189486)Instructions burned: 36 (million)
% 1.62/0.48 % (4189491)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=484916592:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.62/0.48 % (4189486)------------------------------
% 1.62/0.48 % (4189486)------------------------------
% 1.62/0.48 % (4189494)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2299610995:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.62/0.48 % (4189497)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3620108261: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)
% 1.62/0.48 % (4189497)Instruction limit reached!
% 1.62/0.48 % (4189497)------------------------------
% 1.62/0.48 % (4189497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (4189497)CaDiCaL version: 2.1.3
% 1.62/0.48 % (4189497)Termination reason: Instruction limit
% 1.62/0.48 % (4189497)Termination phase: shuffling
% 1.62/0.48 % (4189497)Time elapsed: 0.001 s
% 1.62/0.48 % (4189497)Peak memory usage: 9 MB
% 1.62/0.48 % (4189497)Instructions burned: 6 (million)
% 1.62/0.48 % (4189491)Instruction limit reached!
% 1.62/0.48 % (4189491)------------------------------
% 1.62/0.48 % (4189491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (4189491)CaDiCaL version: 2.1.3
% 1.62/0.48 % (4189491)Termination reason: Instruction limit
% 1.62/0.48 % (4189491)Termination phase: Property scanning
% 1.62/0.48 % (4189491)Time elapsed: 0.012 s
% 1.62/0.48 % (4189491)Peak memory usage: 10 MB
% 1.62/0.48 % (4189491)Instructions burned: 27 (million)
% 1.62/0.48 % (4189496)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2976402973:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.48 % (4189496)Instruction limit reached!
% 1.62/0.48 % (4189496)------------------------------
% 1.62/0.48 % (4189496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (4189496)CaDiCaL version: 2.1.3
% 1.62/0.48 % (4189496)Termination reason: Instruction limit
% 1.62/0.48 % (4189496)Termination phase: shuffling
% 1.62/0.48 % (4189496)Time elapsed: 0.006 s
% 1.62/0.48 % (4189496)Peak memory usage: 10 MB
% 1.62/0.48 % (4189496)Instructions burned: 15 (million)
% 1.62/0.48 % (4189503)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=16082804:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.62/0.48 % (4189501)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=460247544:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.62/0.48 % (4189503)Instruction limit reached!
% 1.62/0.48 % (4189503)------------------------------
% 1.62/0.48 % (4189503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (4189503)CaDiCaL version: 2.1.3
% 1.62/0.48 % (4189503)Termination reason: Instruction limit
% 1.62/0.48 % (4189503)Termination phase: shuffling
% 1.62/0.48 % (4189503)Time elapsed: 0.005 s
% 1.62/0.48 % (4189503)Peak memory usage: 10 MB
% 1.62/0.48 % (4189503)Instructions burned: 23 (million)
% 1.62/0.48 % (4189505)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3131604220:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.62/0.48 % (4189501)Instruction limit reached!
% 1.62/0.48 % (4189501)------------------------------
% 1.62/0.48 % (4189501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (4189501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (4189501)CaDiCaL version: 2.1.3
% 1.62/0.52 % (4189501)Termination reason: Instruction limit
% 1.62/0.52 % (4189501)Termination phase: shuffling
% 1.62/0.52 % (4189501)Time elapsed: 0.012 s
% 1.62/0.52 % (4189501)Peak memory usage: 10 MB
% 1.62/0.52 % (4189501)Instructions burned: 27 (million)
% 1.62/0.52 % (4189509)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.62/0.52 % (4189507)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
% 1.62/0.52 % (4189507)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.62/0.52 % (4189509)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=1583418766:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.62/0.52 % (4189509)Instruction limit reached!
% 1.62/0.52 % (4189509)------------------------------
% 1.62/0.52 % (4189509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (4189509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (4189509)CaDiCaL version: 2.1.3
% 1.62/0.52 % (4189509)Termination reason: Instruction limit
% 1.62/0.52 % (4189509)Termination phase: shuffling
% 1.62/0.52 % (4189509)Time elapsed: 0.002 s
% 1.62/0.52 % (4189509)Peak memory usage: 9 MB
% 1.62/0.52 % (4189509)Instructions burned: 9 (million)
% 1.62/0.52 % (4189507)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=2712530021:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.52 % (4189507)Instruction limit reached!
% 1.62/0.52 % (4189507)------------------------------
% 1.62/0.52 % (4189507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (4189507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (4189507)CaDiCaL version: 2.1.3
% 1.62/0.52 % (4189507)Termination reason: Instruction limit
% 1.62/0.52 % (4189507)Termination phase: shuffling
% 1.62/0.52 % (4189507)Time elapsed: 0.006 s
% 1.62/0.52 % (4189507)Peak memory usage: 10 MB
% 1.62/0.52 % (4189507)Instructions burned: 14 (million)
% 1.62/0.52 % (4189514)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3538778121:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.62/0.52 % (4189514)Instruction limit reached!
% 1.62/0.52 % (4189514)------------------------------
% 1.62/0.52 % (4189514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (4189514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (4189514)CaDiCaL version: 2.1.3
% 1.62/0.52 % (4189514)Termination reason: Instruction limit
% 1.62/0.52 % (4189514)Termination phase: shuffling
% 1.62/0.52 % (4189514)Time elapsed: 0.002 s
% 1.62/0.52 % (4189514)Peak memory usage: 10 MB
% 1.62/0.52 % (4189514)Instructions burned: 8 (million)
% 1.62/0.52 % (4189511)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=2457608487:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.62/0.52 % (4189505)Instruction limit reached!
% 1.62/0.52 % (4189505)------------------------------
% 1.62/0.52 % (4189505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (4189505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (4189505)CaDiCaL version: 2.1.3
% 1.62/0.52 % (4189505)Termination reason: Instruction limit
% 1.62/0.52 % (4189505)Termination phase: Preprocessing 3
% 1.62/0.52 % (4189505)Time elapsed: 0.027 s
% 1.62/0.52 % (4189505)Peak memory usage: 11 MB
% 1.62/0.52 % (4189505)Instructions burned: 61 (million)
% 1.62/0.52 % (4189517)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3779595806:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.62/0.52 % (4189515)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2226316799:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.62/0.52 % (4189511)Instruction limit reached!
% 1.62/0.52 % (4189511)------------------------------
% 2.32/0.59 % (4189511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189511)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189511)Termination reason: Instruction limit
% 2.32/0.59 % (4189511)Termination phase: Property scanning
% 2.32/0.59 % (4189511)Time elapsed: 0.014 s
% 2.32/0.59 % (4189511)Peak memory usage: 10 MB
% 2.32/0.59 % (4189511)Instructions burned: 32 (million)
% 2.32/0.59 % (4189517)Instruction limit reached!
% 2.32/0.59 % (4189517)------------------------------
% 2.32/0.59 % (4189517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189517)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189517)Termination reason: Instruction limit
% 2.32/0.59 % (4189517)Termination phase: shuffling
% 2.32/0.59 % (4189517)Time elapsed: 0.005 s
% 2.32/0.59 % (4189517)Peak memory usage: 10 MB
% 2.32/0.59 % (4189517)Instructions burned: 24 (million)
% 2.32/0.59 % (4189515)Instruction limit reached!
% 2.32/0.59 % (4189515)------------------------------
% 2.32/0.59 % (4189515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189515)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189515)Termination reason: Instruction limit
% 2.32/0.59 % (4189515)Termination phase: shuffling
% 2.32/0.59 % (4189515)Time elapsed: 0.010 s
% 2.32/0.59 % (4189515)Peak memory usage: 10 MB
% 2.32/0.59 % (4189515)Instructions burned: 24 (million)
% 2.32/0.59 % (4189519)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1943366474:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.32/0.59 % (4189522)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3154625880:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.32/0.59 % (4189523)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2131227564:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.32/0.59 % (4189524)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1883721238:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.32/0.59 % (4189490)Instruction limit reached!
% 2.32/0.59 % (4189490)------------------------------
% 2.32/0.59 % (4189490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189490)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189490)Termination reason: Instruction limit
% 2.32/0.59 % (4189490)Termination phase: Saturation
% 2.32/0.59 % (4189490)Time elapsed: 0.109 s
% 2.32/0.59 % (4189490)Peak memory usage: 15 MB
% 2.32/0.59 % (4189490)Instructions burned: 249 (million)
% 2.32/0.59 % (4189522)Instruction limit reached!
% 2.32/0.59 % (4189522)------------------------------
% 2.32/0.59 % (4189522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189522)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189522)Termination reason: Instruction limit
% 2.32/0.59 % (4189522)Termination phase: Function definition elimination
% 2.32/0.59 % (4189522)Time elapsed: 0.035 s
% 2.32/0.59 % (4189522)Peak memory usage: 13 MB
% 2.32/0.59 % (4189522)Instructions burned: 145 (million)
% 2.32/0.59 % (4189524)Instruction limit reached!
% 2.32/0.59 % (4189524)------------------------------
% 2.32/0.59 % (4189524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.32/0.59 % (4189524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.59 % (4189524)CaDiCaL version: 2.1.3
% 2.32/0.59 % (4189524)Termination reason: Instruction limit
% 2.32/0.59 % (4189524)Termination phase: Naming
% 2.32/0.59 % (4189524)Time elapsed: 0.019 s
% 2.32/0.59 % (4189524)Peak memory usage: 11 MB
% 2.32/0.59 % (4189524)Instructions burned: 42 (million)
% 2.32/0.59 % (4189529)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.32/0.59 % (4189530)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4022260291:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.32/0.59 % (4189529)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=588063417:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.72/0.67 % (4189529)Instruction limit reached!
% 2.72/0.67 % (4189529)------------------------------
% 2.72/0.67 % (4189529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.67 % (4189529)CaDiCaL version: 2.1.3
% 2.72/0.67 % (4189529)Termination reason: Instruction limit
% 2.72/0.67 % (4189529)Termination phase: shuffling
% 2.72/0.67 % (4189529)Time elapsed: 0.003 s
% 2.72/0.67 % (4189529)Peak memory usage: 10 MB
% 2.72/0.67 % (4189529)Instructions burned: 7 (million)
% 2.72/0.67 % (4189531)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=264570661: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)
% 2.72/0.67 % (4189530)Refutation not found, incomplete strategy
% 2.72/0.67 % (4189530)------------------------------
% 2.72/0.67 % (4189530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.67 % (4189530)CaDiCaL version: 2.1.3
% 2.72/0.67 % (4189530)Termination reason: Refutation not found, incomplete strategy
% 2.72/0.67 % (4189530)Time elapsed: 0.009 s
% 2.72/0.67 % (4189530)Peak memory usage: 13 MB
% 2.72/0.67 % (4189530)Instructions burned: 37 (million)
% 2.72/0.67 % (4189530)------------------------------
% 2.72/0.67 % (4189530)------------------------------
% 2.72/0.67 % (4189534)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.72/0.67 % (4189534)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1463787275:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.72/0.67 % (4189494)Instruction limit reached!
% 2.72/0.67 % (4189494)------------------------------
% 2.72/0.67 % (4189494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.67 % (4189494)CaDiCaL version: 2.1.3
% 2.72/0.67 % (4189494)Termination reason: Instruction limit
% 2.72/0.67 % (4189494)Termination phase: Saturation
% 2.72/0.67 % (4189494)Time elapsed: 0.148 s
% 2.72/0.67 % (4189494)Peak memory usage: 16 MB
% 2.72/0.67 % (4189494)Instructions burned: 328 (million)
% 2.72/0.67 % (4189534)Instruction limit reached!
% 2.72/0.67 % (4189534)------------------------------
% 2.72/0.67 % (4189534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.67 % (4189534)CaDiCaL version: 2.1.3
% 2.72/0.67 % (4189534)Termination reason: Instruction limit
% 2.72/0.67 % (4189534)Termination phase: shuffling
% 2.72/0.67 % (4189534)Time elapsed: 0.003 s
% 2.72/0.67 % (4189534)Peak memory usage: 10 MB
% 2.72/0.67 % (4189534)Instructions burned: 6 (million)
% 2.72/0.67 % (4189536)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=246858489:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.72/0.67 % (4189538)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=681616133:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.72/0.67 % (4189536)Instruction limit reached!
% 2.72/0.67 % (4189536)------------------------------
% 2.72/0.67 % (4189536)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/0.67 % (4189536)CaDiCaL version: 2.1.3
% 2.72/0.67 % (4189536)Termination reason: Instruction limit
% 2.72/0.67 % (4189536)Termination phase: shuffling
% 2.72/0.67 % (4189536)Time elapsed: 0.009 s
% 2.72/0.67 % (4189536)Peak memory usage: 10 MB
% 2.72/0.67 % (4189536)Instructions burned: 22 (million)
% 2.72/0.67 % (4189538)Instruction limit reached!
% 2.72/0.67 % (4189538)------------------------------
% 2.72/0.67 % (4189538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.72/0.67 % (4189538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.72 % (4189538)CaDiCaL version: 2.1.3
% 3.17/0.72 % (4189538)Termination reason: Instruction limit
% 3.17/0.72 % (4189538)Termination phase: shuffling
% 3.17/0.72 % (4189538)Time elapsed: 0.004 s
% 3.17/0.72 % (4189538)Peak memory usage: 10 MB
% 3.17/0.72 % (4189538)Instructions burned: 19 (million)
% 3.17/0.72 % (4189540)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=2293481097:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.17/0.72 % (4189523)Instruction limit reached!
% 3.17/0.72 % (4189523)------------------------------
% 3.17/0.72 % (4189523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.72 % (4189523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.72 % (4189523)CaDiCaL version: 2.1.3
% 3.17/0.72 % (4189523)Termination reason: Instruction limit
% 3.17/0.72 % (4189523)Termination phase: Property scanning
% 3.17/0.72 % (4189523)Time elapsed: 0.084 s
% 3.17/0.72 % (4189523)Peak memory usage: 13 MB
% 3.17/0.72 % (4189523)Instructions burned: 194 (million)
% 3.17/0.72 % (4189543)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=3554719781:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.17/0.72 % (4189542)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=1504345933:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.17/0.72 % (4189543)Instruction limit reached!
% 3.17/0.72 % (4189543)------------------------------
% 3.17/0.72 % (4189543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.72 % (4189543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.72 % (4189543)CaDiCaL version: 2.1.3
% 3.17/0.72 % (4189543)Termination reason: Instruction limit
% 3.17/0.72 % (4189543)Termination phase: Preprocessing 1
% 3.17/0.72 % (4189543)Time elapsed: 0.010 s
% 3.17/0.72 % (4189543)Peak memory usage: 10 MB
% 3.17/0.72 % (4189543)Instructions burned: 47 (million)
% 3.17/0.72 % (4189545)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1626219440:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 3.17/0.72 % (4189548)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3550451845: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)
% 3.17/0.72 % (4189548)Instruction limit reached!
% 3.17/0.72 % (4189548)------------------------------
% 3.17/0.72 % (4189548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.72 % (4189548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.72 % (4189548)CaDiCaL version: 2.1.3
% 3.17/0.72 % (4189548)Termination reason: Instruction limit
% 3.17/0.72 % (4189548)Termination phase: shuffling
% 3.17/0.72 % (4189548)Time elapsed: 0.005 s
% 3.17/0.72 % (4189548)Peak memory usage: 10 MB
% 3.17/0.72 % (4189548)Instructions burned: 22 (million)
% 3.17/0.72 % (4189531)Instruction limit reached!
% 3.17/0.72 % (4189531)------------------------------
% 3.17/0.72 % (4189531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.72 % (4189531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.72 % (4189531)CaDiCaL version: 2.1.3
% 3.17/0.72 % (4189531)Termination reason: Instruction limit
% 3.17/0.72 % (4189531)Termination phase: Property scanning
% 3.17/0.72 % (4189531)Time elapsed: 0.073 s
% 3.17/0.72 % (4189531)Peak memory usage: 13 MB
% 3.17/0.72 % (4189531)Instructions burned: 172 (million)
% 3.17/0.72 % (4189551)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.17/0.72 % (4189551)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=697793671:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.17/0.72 % (4189552)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2760091188:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.17/0.72 % (4189552)Instruction limit reached!
% 3.17/0.72 % (4189552)------------------------------
% 3.80/0.82 % (4189552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189552)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189552)Termination reason: Instruction limit
% 3.80/0.82 % (4189552)Termination phase: shuffling
% 3.80/0.82 % (4189552)Time elapsed: 0.006 s
% 3.80/0.82 % (4189552)Peak memory usage: 10 MB
% 3.80/0.82 % (4189552)Instructions burned: 14 (million)
% 3.80/0.82 % (4189555)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=3408011696:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.80/0.82 % (4189462)Instruction limit reached!
% 3.80/0.82 % (4189462)------------------------------
% 3.80/0.82 % (4189462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189462)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189462)Termination reason: Instruction limit
% 3.80/0.82 % (4189462)Termination phase: Saturation
% 3.80/0.82 % (4189462)Time elapsed: 0.334 s
% 3.80/0.82 % (4189462)Peak memory usage: 18 MB
% 3.80/0.82 % (4189462)Instructions burned: 635 (million)
% 3.80/0.82 % (4189551)Instruction limit reached!
% 3.80/0.82 % (4189551)------------------------------
% 3.80/0.82 % (4189551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189551)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189551)Termination reason: Instruction limit
% 3.80/0.82 % (4189551)Termination phase: Saturation
% 3.80/0.82 % (4189551)Time elapsed: 0.045 s
% 3.80/0.82 % (4189551)Peak memory usage: 14 MB
% 3.80/0.82 % (4189551)Instructions burned: 201 (million)
% 3.80/0.82 % (4189558)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1699667298:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.80/0.82 % (4189557)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=4217343039:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.80/0.82 % (4189558)Instruction limit reached!
% 3.80/0.82 % (4189558)------------------------------
% 3.80/0.82 % (4189558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189558)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189558)Termination reason: Instruction limit
% 3.80/0.82 % (4189558)Termination phase: Property scanning
% 3.80/0.82 % (4189558)Time elapsed: 0.007 s
% 3.80/0.82 % (4189558)Peak memory usage: 10 MB
% 3.80/0.82 % (4189558)Instructions burned: 33 (million)
% 3.80/0.82 % (4189555)Instruction limit reached!
% 3.80/0.82 % (4189555)------------------------------
% 3.80/0.82 % (4189555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189555)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189555)Termination reason: Instruction limit
% 3.80/0.82 % (4189555)Termination phase: Property scanning
% 3.80/0.82 % (4189555)Time elapsed: 0.029 s
% 3.80/0.82 % (4189555)Peak memory usage: 11 MB
% 3.80/0.82 % (4189555)Instructions burned: 68 (million)
% 3.80/0.82 % (4189561)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3007023151:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 3.80/0.82 % (4189557)Instruction limit reached!
% 3.80/0.82 % (4189557)------------------------------
% 3.80/0.82 % (4189557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.82 % (4189557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.82 % (4189557)CaDiCaL version: 2.1.3
% 3.80/0.82 % (4189557)Termination reason: Instruction limit
% 3.80/0.82 % (4189557)Termination phase: Preprocessing 3
% 3.80/0.82 % (4189557)Time elapsed: 0.022 s
% 3.80/0.82 % (4189557)Peak memory usage: 11 MB
% 3.80/0.82 % (4189557)Instructions burned: 51 (million)
% 3.80/0.82 % (4189562)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=1026972996:cond=on:i=34:hud=10:nm=10:rtra=on_2996 on theBenchmark for (2996ds/34Mi)
% 3.80/0.82 % (4189545)Refutation not found, incomplete strategy
% 3.80/0.84 % (4189545)------------------------------
% 3.80/0.84 % (4189545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189545)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189545)Termination reason: Refutation not found, incomplete strategy
% 3.80/0.84 % (4189545)Time elapsed: 0.121 s
% 3.80/0.84 % (4189545)Peak memory usage: 16 MB
% 3.80/0.84 % (4189545)Instructions burned: 268 (million)
% 3.80/0.84 % (4189545)------------------------------
% 3.80/0.84 % (4189545)------------------------------
% 3.80/0.84 % (4189562)Instruction limit reached!
% 3.80/0.84 % (4189562)------------------------------
% 3.80/0.84 % (4189562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189562)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189562)Termination reason: Instruction limit
% 3.80/0.84 % (4189562)Termination phase: Property scanning
% 3.80/0.84 % (4189562)Time elapsed: 0.015 s
% 3.80/0.84 % (4189562)Peak memory usage: 10 MB
% 3.80/0.84 % (4189562)Instructions burned: 36 (million)
% 3.80/0.84 % (4189565)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3096189294:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.80/0.84 % (4189561)Instruction limit reached!
% 3.80/0.84 % (4189561)------------------------------
% 3.80/0.84 % (4189561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189561)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189561)Termination reason: Instruction limit
% 3.80/0.84 % (4189561)Termination phase: Property scanning
% 3.80/0.84 % (4189561)Time elapsed: 0.031 s
% 3.80/0.84 % (4189561)Peak memory usage: 13 MB
% 3.80/0.84 % (4189561)Instructions burned: 137 (million)
% 3.80/0.84 % (4189566)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.80/0.84 % (4189569)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1166678564:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.80/0.84 % (4189566)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=1452264509:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.80/0.84 % (4189567)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=299293147:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.80/0.84 % (4189540)Instruction limit reached!
% 3.80/0.84 % (4189540)------------------------------
% 3.80/0.84 % (4189540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189540)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189540)Termination reason: Instruction limit
% 3.80/0.84 % (4189540)Termination phase: Saturation
% 3.80/0.84 % (4189540)Time elapsed: 0.174 s
% 3.80/0.84 % (4189540)Peak memory usage: 15 MB
% 3.80/0.84 % (4189540)Instructions burned: 318 (million)
% 3.80/0.84 % (4189565)Instruction limit reached!
% 3.80/0.84 % (4189565)------------------------------
% 3.80/0.84 % (4189565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189565)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189565)Termination reason: Instruction limit
% 3.80/0.84 % (4189565)Termination phase: Preprocessing 3
% 3.80/0.84 % (4189565)Time elapsed: 0.029 s
% 3.80/0.84 % (4189565)Peak memory usage: 12 MB
% 3.80/0.84 % (4189565)Instructions burned: 67 (million)
% 3.80/0.84 % (4189569)Instruction limit reached!
% 3.80/0.84 % (4189569)------------------------------
% 3.80/0.84 % (4189569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189569)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189569)Termination reason: Instruction limit
% 3.80/0.84 % (4189569)Termination phase: Property scanning
% 3.80/0.84 % (4189569)Time elapsed: 0.024 s
% 3.80/0.84 % (4189569)Peak memory usage: 12 MB
% 3.80/0.84 % (4189569)Instructions burned: 101 (million)
% 3.80/0.84 % (4189573)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=2399174281:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.80/0.84 % (4189575)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=866014773:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/515Mi)
% 3.80/0.84 % (4189574)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=558314336:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 3.80/0.84 % (4189573)Refutation not found, incomplete strategy
% 3.80/0.84 % (4189573)------------------------------
% 3.80/0.84 % (4189573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189573)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189573)Termination reason: Refutation not found, incomplete strategy
% 3.80/0.84 % (4189573)Time elapsed: 0.017 s
% 3.80/0.84 % (4189573)Peak memory usage: 13 MB
% 3.80/0.84 % (4189573)Instructions burned: 37 (million)
% 3.80/0.84 % (4189573)------------------------------
% 3.80/0.84 % (4189573)------------------------------
% 3.80/0.84 % (4189579)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3480669914:st=1.5:i=130:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/130Mi)
% 3.80/0.84 % (4189566)Instruction limit reached!
% 3.80/0.84 % (4189566)------------------------------
% 3.80/0.84 % (4189566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189566)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189566)Termination reason: Instruction limit
% 3.80/0.84 % (4189566)Termination phase: Saturation
% 3.80/0.84 % (4189566)Time elapsed: 0.075 s
% 3.80/0.84 % (4189566)Peak memory usage: 12 MB
% 3.80/0.84 % (4189566)Instructions burned: 182 (million)
% 3.80/0.84 % (4189581)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=754298349:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 3.80/0.84 % (4189579)Refutation not found, incomplete strategy
% 3.80/0.84 % (4189579)------------------------------
% 3.80/0.84 % (4189579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189579)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189579)Termination reason: Refutation not found, incomplete strategy
% 3.80/0.84 % (4189579)Time elapsed: 0.028 s
% 3.80/0.84 % (4189579)Peak memory usage: 13 MB
% 3.80/0.84 % (4189579)Instructions burned: 66 (million)
% 3.80/0.84 % (4189579)------------------------------
% 3.80/0.84 % (4189579)------------------------------
% 3.80/0.84 % (4189567)Instruction limit reached!
% 3.80/0.84 % (4189567)------------------------------
% 3.80/0.84 % (4189567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189567)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189567)Termination reason: Instruction limit
% 3.80/0.84 % (4189567)Termination phase: Saturation
% 3.80/0.84 % (4189567)Time elapsed: 0.106 s
% 3.80/0.84 % (4189567)Peak memory usage: 15 MB
% 3.80/0.84 % (4189567)Instructions burned: 246 (million)
% 3.80/0.84 % (4189581)Instruction limit reached!
% 3.80/0.84 % (4189581)------------------------------
% 3.80/0.84 % (4189581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.84 % (4189581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.84 % (4189581)CaDiCaL version: 2.1.3
% 3.80/0.84 % (4189581)Termination reason: Instruction limit
% 3.80/0.84 % (4189581)Termination phase: Property scanning
% 3.80/0.84 % (4189581)Time elapsed: 0.019 s
% 3.80/0.84 % (4189581)Peak memory usage: 10 MB
% 3.80/0.84 % (4189581)Instructions burned: 46 (million)
% 3.80/0.84 % (4189583)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3496395049:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 3.80/0.84 % (4189575) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4189454-4189575"...
% 3.80/0.84 % (4189584)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=496827316:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 3.80/0.84 % (4189585)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=891270991:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 3.80/0.84 % (4189575)...printing done.
% 3.80/0.84 % (4189575)Refutation found. Thanks to Tanya!
% 3.80/0.84 % SZS status Theorem for theBenchmark
% 3.80/0.84 % SZS output start Proof for theBenchmark
% 3.80/0.84 thf(type_def_5, type, term: $tType).
% 3.80/0.84 thf(type_def_6, type, subst: $tType).
% 3.80/0.84 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 3.80/0.84 thf(type_def_8, type, d_term: $tType).
% 3.80/0.84 thf(type_def_9, type, d_subst: $tType).
% 3.80/0.84 thf(func_def_0, type, one: term).
% 3.80/0.84 thf(func_def_1, type, ap: (term > term > term)).
% 3.80/0.84 thf(func_def_2, type, lam: (term > term)).
% 3.80/0.84 thf(func_def_3, type, sub: (term > subst > term)).
% 3.80/0.84 thf(func_def_4, type, id: subst).
% 3.80/0.84 thf(func_def_5, type, sh: subst).
% 3.80/0.84 thf(func_def_6, type, push: (term > subst > subst)).
% 3.80/0.84 thf(func_def_7, type, comp: (subst > subst > subst)).
% 3.80/0.84 thf(func_def_8, type, var: (term > $o)).
% 3.80/0.84 thf(func_def_9, type, pushprop_lem1v2: $o).
% 3.80/0.84 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 3.80/0.84 thf(func_def_11, type, axmap: $o).
% 3.80/0.84 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 3.80/0.84 thf(func_def_13, type, shinj: $o).
% 3.80/0.84 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 3.80/0.84 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 3.80/0.84 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 3.80/0.84 thf(func_def_17, type, induction2lem: $o).
% 3.80/0.84 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 3.80/0.84 thf(func_def_19, type, axvarshift: $o).
% 3.80/0.84 thf(func_def_20, type, hoasapinj2: $o).
% 3.80/0.84 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 3.80/0.84 thf(func_def_22, type, hoasapinj1: $o).
% 3.80/0.84 thf(func_def_23, type, ulamvar1: $o).
% 3.80/0.84 thf(func_def_24, type, induction2lem_lthm: $o).
% 3.80/0.84 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 3.80/0.84 thf(func_def_26, type, apnotvar: $o).
% 3.80/0.84 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 3.80/0.84 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 3.80/0.84 thf(func_def_29, type, hoasinduction_lthm: $o).
% 3.80/0.84 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 3.80/0.84 thf(func_def_31, type, hoaslaminj: $o).
% 3.80/0.84 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 3.80/0.84 thf(func_def_33, type, induction2lem_gthm: $o).
% 3.80/0.84 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 3.80/0.84 thf(func_def_35, type, hoasinduction_lem3: $o).
% 3.80/0.84 thf(func_def_36, type, hoasinduction_lem2: $o).
% 3.80/0.84 thf(func_def_37, type, termmset_lthm: $o).
% 3.80/0.84 thf(func_def_38, type, hoasinduction_lem1: $o).
% 3.80/0.84 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 3.80/0.84 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 3.80/0.84 thf(func_def_41, type, hoasapnotvar: $o).
% 3.80/0.84 thf(func_def_42, type, hoasinduction_lem0: $o).
% 3.80/0.84 thf(func_def_43, type, hoasinduction: $o).
% 3.80/0.84 thf(func_def_44, type, hoasinduction_gthm: $o).
% 3.80/0.84 thf(func_def_45, type, axapp: $o).
% 3.80/0.84 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 3.80/0.84 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 3.80/0.84 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 3.80/0.84 thf(func_def_49, type, ulamvarind: $o).
% 3.80/0.84 thf(func_def_50, type, induction: $o).
% 3.80/0.84 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 3.80/0.84 thf(func_def_52, type, termmset_gthm: $o).
% 3.80/0.84 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 3.80/0.84 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 3.80/0.84 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 3.80/0.84 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 3.80/0.84 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 3.80/0.84 thf(func_def_58, type, pushprop_lem2v2: $o).
% 3.80/0.84 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 3.80/0.84 thf(func_def_60, type, axclos: $o).
% 3.80/0.84 thf(func_def_61, type, axassoc: $o).
% 3.80/0.84 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 3.80/0.84 thf(func_def_63, type, pushprop_lthm: $o).
% 3.80/0.84 thf(func_def_64, type, apinj2: $o).
% 3.80/0.84 thf(func_def_65, type, apinj1: $o).
% 3.80/0.84 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 3.80/0.84 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 3.80/0.84 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 3.80/0.84 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 3.80/0.84 thf(func_def_70, type, axvarcons: $o).
% 3.80/0.84 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 3.80/0.84 thf(func_def_72, type, axscons: $o).
% 3.80/0.84 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 3.80/0.84 thf(func_def_74, type, axidr: $o).
% 3.80/0.84 thf(func_def_75, type, pushprop_lem1: $o).
% 3.80/0.84 thf(func_def_76, type, laminj: $o).
% 3.80/0.84 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 3.80/0.84 thf(func_def_78, type, pushprop_lem0: $o).
% 3.80/0.84 thf(func_def_79, type, pushprop_gthm: $o).
% 3.80/0.84 thf(func_def_80, type, axabs: $o).
% 3.80/0.84 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 3.80/0.84 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 3.80/0.84 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 3.80/0.84 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 3.80/0.84 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 3.80/0.84 thf(func_def_86, type, lamnotap: $o).
% 3.80/0.84 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 3.80/0.84 thf(func_def_88, type, hoaslamnotvar: $o).
% 3.80/0.84 thf(func_def_89, type, axidl: $o).
% 3.80/0.84 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 3.80/0.84 thf(func_def_91, type, induction2_lthm: $o).
% 3.80/0.84 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 3.80/0.84 thf(func_def_93, type, substmonoid_lthm: $o).
% 3.80/0.84 thf(func_def_94, type, pushprop: $o).
% 3.80/0.84 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 3.80/0.84 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 3.80/0.84 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 3.80/0.84 thf(func_def_98, type, substmonoid: $o).
% 3.80/0.84 thf(func_def_99, type, lamnotvar: $o).
% 3.80/0.84 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 3.80/0.84 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 3.80/0.84 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 3.80/0.84 thf(func_def_103, type, induction2_gthm: $o).
% 3.80/0.84 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 3.80/0.84 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_106, type, hoaslamnotap: $o).
% 3.80/0.84 thf(func_def_107, type, substmonoid_gthm: $o).
% 3.80/0.84 thf(func_def_108, type, ulamvarsh: $o).
% 3.80/0.84 thf(func_def_109, type, induction2: $o).
% 3.80/0.84 thf(func_def_110, type, pushprop_lem3v2: $o).
% 3.80/0.84 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 3.80/0.84 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 3.80/0.84 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 3.80/0.84 thf(func_def_114, type, axshiftcons: $o).
% 3.80/0.84 thf(func_def_115, type, termmset: $o).
% 3.80/0.84 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 3.80/0.84 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 3.80/0.84 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 3.80/0.84 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 3.80/0.84 thf(func_def_120, type, axvarid: $o).
% 3.80/0.84 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 3.80/0.84 thf(func_def_122, type, d2term: (d_term > term)).
% 3.80/0.84 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 3.80/0.84 thf(func_def_124, type, d_one: d_term).
% 3.80/0.84 thf(func_def_125, type, d_id: d_subst).
% 3.80/0.84 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.80/0.84 thf(func_def_128, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.80/0.84 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)).
% 3.80/0.84 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 3.80/0.84 thf(func_def_131, type, db3: !>[X0: $tType]:(X0)).
% 3.80/0.84 thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
% 3.80/0.84 thf(func_def_133, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.80/0.84 thf(func_def_136, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.80/0.84 thf(func_def_137, type, db4: !>[X0: $tType]:(X0)).
% 3.80/0.84 thf(func_def_138, type, sP0: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_139, type, sP1: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_140, type, sP2: $o).
% 3.80/0.84 thf(func_def_141, type, sP3: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_142, type, sP4: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_143, type, sP5: $o).
% 3.80/0.84 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_145, type, sP7: ((term > $o) > subst > $o)).
% 3.80/0.84 thf(func_def_146, type, sP8: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_147, type, sP9: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_148, type, sP10: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_149, type, sP11: $o).
% 3.80/0.84 thf(func_def_150, type, sP12: $o).
% 3.80/0.84 thf(func_def_151, type, sP13: $o).
% 3.80/0.84 thf(func_def_152, type, sP14: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_153, type, sP15: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_156, type, sP18: $o).
% 3.80/0.84 thf(func_def_157, type, sP19: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_158, type, sP20: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_159, type, sP21: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_160, type, sP22: $o).
% 3.80/0.84 thf(func_def_161, type, sP23: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_162, type, sP24: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_163, type, sP25: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_164, type, sP26: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_166, type, sP28: $o).
% 3.80/0.84 thf(func_def_167, type, sP29: $o).
% 3.80/0.84 thf(func_def_168, type, sP30: $o).
% 3.80/0.84 thf(func_def_169, type, sP31: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_171, type, sP33: $o).
% 3.80/0.84 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_174, type, sP36: (term > (subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_176, type, sP38: $o).
% 3.80/0.84 thf(func_def_177, type, sP39: $o).
% 3.80/0.84 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_180, type, sP42: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_181, type, sP43: $o).
% 3.80/0.84 thf(func_def_182, type, sP44: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_185, type, sP47: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_186, type, sP48: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_187, type, sP49: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_188, type, sP50: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_189, type, sP51: $o).
% 3.80/0.84 thf(func_def_190, type, sP52: $o).
% 3.80/0.84 thf(func_def_191, type, sP53: $o).
% 3.80/0.84 thf(func_def_192, type, sP54: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_193, type, sP55: $o).
% 3.80/0.84 thf(func_def_194, type, sP56: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_195, type, sP57: (term > (term > $o) > $o)).
% 3.80/0.84 thf(func_def_196, type, sP58: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_197, type, sP59: $o).
% 3.80/0.84 thf(func_def_198, type, sP60: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_199, type, sP61: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_200, type, sP62: $o).
% 3.80/0.84 thf(func_def_201, type, sP63: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_202, type, sP64: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_203, type, sP65: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_204, type, sP66: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_205, type, sP67: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_206, type, sP68: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_207, type, sP69: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_208, type, sP70: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_209, type, sP71: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_210, type, sP72: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_211, type, sP73: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_212, type, sP74: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_213, type, sP75: $o).
% 3.80/0.84 thf(func_def_214, type, sP76: $o).
% 3.80/0.84 thf(func_def_215, type, sP77: $o).
% 3.80/0.84 thf(func_def_216, type, sP78: $o).
% 3.80/0.84 thf(func_def_217, type, sP79: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_218, type, sP80: $o).
% 3.80/0.84 thf(func_def_219, type, sP81: $o).
% 3.80/0.84 thf(func_def_220, type, sP82: $o).
% 3.80/0.84 thf(func_def_221, type, sP83: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_222, type, sP84: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_223, type, sP85: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_224, type, sP86: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_225, type, sP87: $o).
% 3.80/0.84 thf(func_def_226, type, sP88: $o).
% 3.80/0.84 thf(func_def_227, type, sP89: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_228, type, sP90: $o).
% 3.80/0.84 thf(func_def_229, type, sP91: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_230, type, sP92: $o).
% 3.80/0.84 thf(func_def_231, type, sP93: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_232, type, sP94: $o).
% 3.80/0.84 thf(func_def_233, type, sP95: $o).
% 3.80/0.84 thf(func_def_234, type, sP96: $o).
% 3.80/0.84 thf(func_def_235, type, sP97: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_236, type, sP98: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_237, type, sP99: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_238, type, sP100: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_239, type, sP101: $o).
% 3.80/0.84 thf(func_def_240, type, sP102: $o).
% 3.80/0.84 thf(func_def_241, type, sP103: $o).
% 3.80/0.84 thf(func_def_242, type, sP104: $o).
% 3.80/0.84 thf(func_def_243, type, sP105: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_244, type, sP106: ((term > $o) > $o)).
% 3.80/0.84 thf(func_def_245, type, sP107: $o).
% 3.80/0.84 thf(func_def_246, type, sP108: ((subst > term > subst > $o) > $o)).
% 3.80/0.84 thf(func_def_247, type, sP109: $o).
% 3.80/0.84 thf(func_def_248, type, sK110: term).
% 3.80/0.84 thf(func_def_249, type, sK111: (term > $o)).
% 3.80/0.84 thf(func_def_250, type, sK112: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_251, type, sK113: ((term > $o) > term > term)).
% 3.80/0.84 thf(func_def_252, type, sK114: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.80/0.84 thf(func_def_253, type, sK115: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_254, type, sK116: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_255, type, sK117: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_256, type, sK118: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_258, type, sK120: (term > $o)).
% 3.80/0.84 thf(func_def_259, type, sK121: term).
% 3.80/0.84 thf(func_def_260, type, sK122: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_261, type, sK123: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_262, type, sK124: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_263, type, sK125: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_264, type, sK126: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_265, type, sK127: term).
% 3.80/0.84 thf(func_def_266, type, sK128: term).
% 3.80/0.84 thf(func_def_267, type, sK129: subst).
% 3.80/0.84 thf(func_def_268, type, sK130: term).
% 3.80/0.84 thf(func_def_269, type, sK131: subst).
% 3.80/0.84 thf(func_def_270, type, sK132: term).
% 3.80/0.84 thf(func_def_271, type, sK133: (subst > term > term)).
% 3.80/0.84 thf(func_def_272, type, sK134: term).
% 3.80/0.84 thf(func_def_273, type, sK135: (subst > term > term)).
% 3.80/0.84 thf(func_def_274, type, sK136: subst).
% 3.80/0.84 thf(func_def_275, type, sK137: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_276, type, sK138: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_277, type, sK139: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_278, type, sK140: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_279, type, sK141: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_280, type, sK142: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_281, type, sK143: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_282, type, sK144: (term > $o)).
% 3.80/0.84 thf(func_def_283, type, sK145: term).
% 3.80/0.84 thf(func_def_284, type, sK146: subst).
% 3.80/0.84 thf(func_def_285, type, sK147: term).
% 3.80/0.84 thf(func_def_286, type, sK148: (term > $o)).
% 3.80/0.84 thf(func_def_287, type, sK149: ((term > $o) > subst > term)).
% 3.80/0.84 thf(func_def_288, type, sK150: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_289, type, sK151: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_290, type, sK152: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_291, type, sK153: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_292, type, sK154: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_293, type, sK155: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_294, type, sK156: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_295, type, sK157: term).
% 3.80/0.84 thf(func_def_296, type, sK158: term).
% 3.80/0.84 thf(func_def_297, type, sK159: term).
% 3.80/0.84 thf(func_def_298, type, sK160: term).
% 3.80/0.84 thf(func_def_299, type, sK161: term).
% 3.80/0.84 thf(func_def_300, type, sK162: term).
% 3.80/0.84 thf(func_def_301, type, sK163: term).
% 3.80/0.84 thf(func_def_302, type, sK164: term).
% 3.80/0.84 thf(func_def_303, type, sK165: term).
% 3.80/0.84 thf(func_def_304, type, sK166: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_305, type, sK167: ((subst > term > subst > $o) > term > term)).
% 3.80/0.84 thf(func_def_306, type, sK168: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_307, type, sK169: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_308, type, sK170: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_309, type, sK171: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_311, type, sK173: term).
% 3.80/0.84 thf(func_def_312, type, sK174: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > term > term)).
% 3.80/0.84 thf(func_def_314, type, sK176: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_315, type, sK177: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_316, type, sK178: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_317, type, sK179: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_319, type, sK181: term).
% 3.80/0.84 thf(func_def_320, type, sK182: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_321, type, sK183: (term > $o)).
% 3.80/0.84 thf(func_def_322, type, sK184: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_323, type, sK185: ((term > $o) > term > term)).
% 3.80/0.84 thf(func_def_324, type, sK186: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_325, type, sK187: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_326, type, sK188: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_327, type, sK189: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_329, type, sK191: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_330, type, sK192: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_331, type, sK193: term).
% 3.80/0.84 thf(func_def_332, type, sK194: term).
% 3.80/0.84 thf(func_def_333, type, sK195: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > term > term)).
% 3.80/0.84 thf(func_def_335, type, sK197: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_336, type, sK198: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_337, type, sK199: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_338, type, sK200: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_341, type, sK203: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_342, type, sK204: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_343, type, sK205: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_344, type, sK206: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_347, type, sK209: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_348, type, sK210: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_349, type, sK211: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_350, type, sK212: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_351, type, sK213: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_352, type, sK214: term).
% 3.80/0.84 thf(func_def_353, type, sK215: term).
% 3.80/0.84 thf(func_def_354, type, sK216: term).
% 3.80/0.84 thf(func_def_355, type, sK217: term).
% 3.80/0.84 thf(func_def_356, type, sK218: term).
% 3.80/0.84 thf(func_def_357, type, sK219: term).
% 3.80/0.84 thf(func_def_358, type, sK220: term).
% 3.80/0.84 thf(func_def_359, type, sK221: term).
% 3.80/0.84 thf(func_def_360, type, sK222: term).
% 3.80/0.84 thf(func_def_361, type, sK223: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_362, type, sK224: term).
% 3.80/0.84 thf(func_def_363, type, sK225: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_364, type, sK226: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_365, type, sK227: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_366, type, sK228: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_367, type, sK229: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_369, type, sK231: term).
% 3.80/0.84 thf(func_def_370, type, sK232: (term > $o)).
% 3.80/0.84 thf(func_def_371, type, sK233: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_372, type, sK234: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_373, type, sK235: term).
% 3.80/0.84 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_375, type, sK237: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_376, type, sK238: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_378, type, sK240: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_379, type, sK241: term).
% 3.80/0.84 thf(func_def_380, type, sK242: term).
% 3.80/0.84 thf(func_def_381, type, sK243: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_382, type, sK244: term).
% 3.80/0.84 thf(func_def_383, type, sK245: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_386, type, sK248: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_387, type, sK249: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_388, type, sK250: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_389, type, sK251: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_390, type, sK252: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_396, type, sK258: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_397, type, sK259: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_398, type, sK260: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_399, type, sK261: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_400, type, sK262: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_404, type, sK266: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_406, type, sK268: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_407, type, sK269: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_408, type, sK270: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_409, type, sK271: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_410, type, sK272: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_411, type, sK273: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_412, type, sK274: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_413, type, sK275: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_414, type, sK276: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_415, type, sK277: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_416, type, sK278: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_417, type, sK279: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_418, type, sK280: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_419, type, sK281: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_422, type, sK284: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_423, type, sK285: (term > $o)).
% 3.80/0.84 thf(func_def_424, type, sK286: term).
% 3.80/0.84 thf(func_def_425, type, sK287: subst).
% 3.80/0.84 thf(func_def_426, type, sK288: (subst > (term > $o) > term)).
% 3.80/0.84 thf(func_def_427, type, sK289: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_428, type, sK290: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_429, type, sK291: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_430, type, sK292: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_431, type, sK293: (term > $o)).
% 3.80/0.84 thf(func_def_432, type, sK294: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_433, type, sK295: term).
% 3.80/0.84 thf(func_def_434, type, sK296: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_438, type, sK300: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.80/0.84 thf(func_def_439, type, sK301: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_440, type, sK302: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_443, type, sK305: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_444, type, sK306: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_445, type, sK307: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_446, type, sK308: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_447, type, sK309: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_449, type, sK311: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_450, type, sK312: term).
% 3.80/0.84 thf(func_def_451, type, sK313: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_452, type, sK314: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_453, type, sK315: ((subst > term > term) > term > subst)).
% 3.80/0.84 thf(func_def_454, type, sK316: ((subst > term > term) > term > subst)).
% 3.80/0.84 thf(func_def_455, type, sK317: ((subst > term > term) > term > term)).
% 3.80/0.84 thf(func_def_456, type, sK318: ((subst > term > term) > term > term)).
% 3.80/0.84 thf(func_def_457, type, sK319: ((subst > term > term) > term > subst)).
% 3.80/0.84 thf(func_def_458, type, sK320: ((subst > term > term) > term > subst)).
% 3.80/0.84 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_461, type, sK323: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_462, type, sK324: term).
% 3.80/0.84 thf(func_def_463, type, sK325: (term > $o)).
% 3.80/0.84 thf(func_def_464, type, sK326: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_465, type, sK327: ((term > $o) > term > term)).
% 3.80/0.84 thf(func_def_466, type, sK328: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_467, type, sK329: term).
% 3.80/0.84 thf(func_def_468, type, sK330: (term > $o)).
% 3.80/0.84 thf(func_def_469, type, sK331: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_470, type, sK332: term).
% 3.80/0.84 thf(func_def_471, type, sK333: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_473, type, sK335: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_474, type, sK336: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_475, type, sK337: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_476, type, sK338: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_477, type, sK339: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_478, type, sK340: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_479, type, sK341: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_480, type, sK342: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_481, type, sK343: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_482, type, sK344: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_483, type, sK345: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_484, type, sK346: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_485, type, sK347: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_486, type, sK348: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_487, type, sK349: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_488, type, sK350: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_489, type, sK351: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_490, type, sK352: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_491, type, sK353: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_492, type, sK354: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_493, type, sK355: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_494, type, sK356: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_495, type, sK357: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_496, type, sK358: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_497, type, sK359: term).
% 3.80/0.84 thf(func_def_498, type, sK360: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_499, type, sK361: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_503, type, sK365: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_507, type, sK369: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_508, type, sK370: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_509, type, sK371: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_510, type, sK372: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > term > term)).
% 3.80/0.84 thf(func_def_513, type, sK375: term).
% 3.80/0.84 thf(func_def_514, type, sK376: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_515, type, sK377: term).
% 3.80/0.84 thf(func_def_516, type, sK378: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_520, type, sK382: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_521, type, sK383: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_522, type, sK384: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_523, type, sK385: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_524, type, sK386: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_525, type, sK387: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_526, type, sK388: (term > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_527, type, sK389: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_531, type, sK393: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_532, type, sK394: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_533, type, sK395: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_534, type, sK396: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_535, type, sK397: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_536, type, sK398: term).
% 3.80/0.84 thf(func_def_537, type, sK399: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_538, type, sK400: term).
% 3.80/0.84 thf(func_def_539, type, sK401: (term > $o)).
% 3.80/0.84 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_541, type, sK403: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_544, type, sK406: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_547, type, sK409: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_548, type, sK410: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_549, type, sK411: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_551, type, sK413: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_552, type, sK414: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_553, type, sK415: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_554, type, sK416: (term > $o)).
% 3.80/0.84 thf(func_def_555, type, sK417: term).
% 3.80/0.84 thf(func_def_556, type, sK418: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_557, type, sK419: term).
% 3.80/0.84 thf(func_def_558, type, sK420: (term > $o)).
% 3.80/0.84 thf(func_def_559, type, sK421: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_560, type, sK422: term).
% 3.80/0.84 thf(func_def_561, type, sK423: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_562, type, sK424: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_563, type, sK425: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_565, type, sK427: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_566, type, sK428: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_567, type, sK429: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_568, type, sK430: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_569, type, sK431: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_570, type, sK432: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_571, type, sK433: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_572, type, sK434: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_573, type, sK435: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_574, type, sK436: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_575, type, sK437: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_576, type, sK438: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_577, type, sK439: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_578, type, sK440: term).
% 3.80/0.84 thf(func_def_579, type, sK441: (term > $o)).
% 3.80/0.84 thf(func_def_580, type, sK442: ((term > $o) > term > term)).
% 3.80/0.84 thf(func_def_581, type, sK443: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_585, type, sK447: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_588, type, sK450: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_589, type, sK451: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_590, type, sK452: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_591, type, sK453: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_592, type, sK454: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_593, type, sK455: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_595, type, sK457: term).
% 3.80/0.84 thf(func_def_596, type, sK458: (subst > term > subst > $o)).
% 3.80/0.84 thf(func_def_597, type, sK459: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_598, type, sK460: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_599, type, sK461: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_600, type, sK462: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_601, type, sK463: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_602, type, sK464: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_603, type, sK465: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_604, type, sK466: ((subst > term > subst > $o) > subst)).
% 3.80/0.84 thf(func_def_605, type, sK467: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_606, type, sK468: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_607, type, sK469: ((subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_608, type, sK470: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.80/0.84 thf(func_def_609, type, sK471: ((subst > term > term) > term)).
% 3.80/0.84 thf(func_def_610, type, sK472: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_611, type, sK473: ((subst > term > term) > subst)).
% 3.80/0.84 thf(func_def_612, type, sK474: ((subst > term > subst > $o) > subst > term > term)).
% 3.80/0.84 thf(func_def_613, type, sK475: subst).
% 3.80/0.84 thf(func_def_614, type, sK476: subst).
% 3.80/0.84 thf(func_def_615, type, sK477: subst).
% 3.80/0.84 thf(func_def_616, type, sK478: subst).
% 3.80/0.84 thf(func_def_617, type, sK479: term).
% 3.80/0.84 thf(func_def_618, type, sK480: subst).
% 3.80/0.84 thf(func_def_619, type, sK481: (term > $o)).
% 3.80/0.84 thf(func_def_620, type, sK482: term).
% 3.80/0.84 thf(func_def_621, type, sK483: (term > $o)).
% 3.80/0.84 thf(func_def_622, type, sK484: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_623, type, sK485: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_624, type, sK486: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_625, type, sK487: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_626, type, sK488: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_627, type, sK489: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_628, type, sK490: (term > (term > $o) > term)).
% 3.80/0.84 thf(func_def_629, type, sK491: ((term > $o) > subst > term)).
% 3.80/0.84 thf(func_def_630, type, sK492: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_631, type, sK493: ((term > $o) > term)).
% 3.80/0.84 thf(func_def_632, type, sK494: term).
% 3.80/0.84 thf(func_def_633, type, sK495: term).
% 3.80/0.85 thf(func_def_634, type, sK496: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_635, type, sK497: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_636, type, sK498: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_637, type, sK499: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_638, type, sK500: ((subst > term > subst > $o) > term)).
% 3.80/0.85 thf(func_def_639, type, sK501: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_640, type, sK502: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_641, type, sK503: ((subst > term > subst > $o) > term)).
% 3.80/0.85 thf(func_def_642, type, sK504: ((subst > term > subst > $o) > subst)).
% 3.80/0.85 thf(func_def_643, type, sK505: ((subst > term > subst > $o) > term)).
% 3.80/0.85 thf(func_def_644, type, sK506: ((subst > term > subst > $o) > term)).
% 3.80/0.85 thf(func_def_645, type, sK507: term).
% 3.80/0.85 thf(func_def_646, type, sK508: (term > $o)).
% 3.80/0.85 thf(func_def_647, type, sK509: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_648, type, sK510: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_649, type, sK511: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_650, type, sK512: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_651, type, sK513: subst).
% 3.80/0.85 thf(func_def_652, type, sK514: term).
% 3.80/0.85 thf(func_def_653, type, sK515: subst).
% 3.80/0.85 thf(func_def_654, type, sK516: term).
% 3.80/0.85 thf(func_def_655, type, sK517: (term > $o)).
% 3.80/0.85 thf(func_def_656, type, sK518: (term > $o)).
% 3.80/0.85 thf(func_def_657, type, sK519: term).
% 3.80/0.85 thf(func_def_658, type, sK520: subst).
% 3.80/0.85 thf(func_def_659, type, sK521: term).
% 3.80/0.85 thf(func_def_660, type, sK522: subst).
% 3.80/0.85 thf(func_def_661, type, sK523: term).
% 3.80/0.85 thf(func_def_662, type, sK524: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_663, type, sK525: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_664, type, sK526: term).
% 3.80/0.85 thf(func_def_665, type, sK527: (term > subst > term > term)).
% 3.80/0.85 thf(func_def_666, type, sK528: (term > $o)).
% 3.80/0.85 thf(func_def_667, type, sK529: term).
% 3.80/0.85 thf(func_def_668, type, sK530: subst).
% 3.80/0.85 thf(func_def_669, type, sK531: (term > $o)).
% 3.80/0.85 thf(func_def_670, type, sK532: ((term > $o) > subst > term > (term > $o) > term)).
% 3.80/0.85 thf(func_def_671, type, sK533: term).
% 3.80/0.85 thf(func_def_672, type, sK534: (subst > term > term)).
% 3.80/0.85 thf(func_def_673, type, sK535: (subst > term > term)).
% 3.80/0.85 thf(func_def_674, type, sK536: subst).
% 3.80/0.85 thf(func_def_675, type, sK537: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_676, type, sK538: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_677, type, sK539: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_678, type, sK540: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_679, type, sK541: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_680, type, sK542: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_681, type, sK543: (subst > term > term)).
% 3.80/0.85 thf(func_def_682, type, sK544: term).
% 3.80/0.85 thf(func_def_683, type, sK545: term).
% 3.80/0.85 thf(func_def_684, type, sK546: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_685, type, sK547: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_686, type, sK548: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_687, type, sK549: term).
% 3.80/0.85 thf(func_def_688, type, sK550: term).
% 3.80/0.85 thf(func_def_689, type, sK551: (term > $o)).
% 3.80/0.85 thf(func_def_690, type, sK552: term).
% 3.80/0.85 thf(func_def_691, type, sK553: subst).
% 3.80/0.85 thf(func_def_692, type, sK554: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_693, type, sK555: (subst > term > (term > $o) > term > $o)).
% 3.80/0.85 thf(func_def_694, type, sK556: term).
% 3.80/0.85 thf(func_def_695, type, sK557: subst).
% 3.80/0.85 thf(func_def_696, type, sK558: term).
% 3.80/0.85 thf(func_def_697, type, sK559: subst).
% 3.80/0.85 thf(func_def_698, type, sK560: subst).
% 3.80/0.85 thf(func_def_699, type, sK561: term).
% 3.80/0.85 thf(func_def_700, type, sK562: term).
% 3.80/0.85 thf(func_def_701, type, sK563: (term > d_term)).
% 3.80/0.85 thf(func_def_702, type, sK564: term).
% 3.80/0.85 thf(func_def_703, type, sK565: term).
% 3.80/0.85 thf(func_def_704, type, sK566: (term > subst > term > term)).
% 3.80/0.85 thf(func_def_705, type, sK567: term).
% 3.80/0.85 thf(func_def_706, type, sK568: term).
% 3.80/0.85 thf(func_def_707, type, sK569: (term > $o)).
% 3.80/0.85 thf(func_def_708, type, sK570: (term > $o)).
% 3.80/0.85 thf(func_def_709, type, sK571: subst).
% 3.80/0.85 thf(func_def_710, type, sK572: term).
% 3.80/0.85 thf(func_def_711, type, sK573: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_712, type, sK574: term).
% 3.80/0.85 thf(func_def_713, type, sK575: term).
% 3.80/0.85 thf(func_def_714, type, sK576: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_715, type, sK577: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_716, type, sK578: (term > subst > term > term)).
% 3.80/0.85 thf(func_def_717, type, sK579: ((subst > term > subst > $o) > term > $o)).
% 3.80/0.85 thf(func_def_718, type, sK580: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_719, type, sK581: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_720, type, sK582: (term > $o)).
% 3.80/0.85 thf(func_def_721, type, sK583: (term > $o)).
% 3.80/0.85 thf(func_def_722, type, sK584: term).
% 3.80/0.85 thf(func_def_723, type, sK585: subst).
% 3.80/0.85 thf(func_def_724, type, sK586: subst).
% 3.80/0.85 thf(func_def_725, type, sK587: term).
% 3.80/0.85 thf(func_def_726, type, sK588: (subst > term > (term > $o) > (term > $o) > term)).
% 3.80/0.85 thf(func_def_727, type, sK589: subst).
% 3.80/0.85 thf(func_def_728, type, sK590: term).
% 3.80/0.85 thf(func_def_729, type, sK591: subst).
% 3.80/0.85 thf(func_def_730, type, sK592: term).
% 3.80/0.85 thf(func_def_731, type, sK593: (term > $o)).
% 3.80/0.85 thf(func_def_732, type, sK594: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_733, type, sK595: ((term > $o) > term > subst > term > $o)).
% 3.80/0.85 thf(func_def_734, type, sK596: subst).
% 3.80/0.85 thf(func_def_735, type, sK597: subst).
% 3.80/0.85 thf(func_def_736, type, sK598: ((subst > term > subst > $o) > term > $o)).
% 3.80/0.85 thf(func_def_737, type, sK599: term).
% 3.80/0.85 thf(func_def_738, type, sK600: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_739, type, sK601: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_740, type, sK602: term).
% 3.80/0.85 thf(func_def_741, type, sK603: subst).
% 3.80/0.85 thf(func_def_742, type, sK604: term).
% 3.80/0.85 thf(func_def_743, type, sK605: term).
% 3.80/0.85 thf(func_def_744, type, sK606: term).
% 3.80/0.85 thf(func_def_745, type, sK607: (term > subst > term > term)).
% 3.80/0.85 thf(func_def_746, type, sK608: term).
% 3.80/0.85 thf(func_def_747, type, sK609: ((subst > term > term) > term)).
% 3.80/0.85 thf(func_def_748, type, sK610: ((subst > term > term) > subst)).
% 3.80/0.85 thf(func_def_749, type, sK611: ((subst > term > subst > $o) > term > $o)).
% 3.80/0.85 thf(func_def_750, type, sK612: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_751, type, sK613: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_752, type, sK614: term).
% 3.80/0.85 thf(func_def_753, type, sK615: subst).
% 3.80/0.85 thf(func_def_754, type, sK616: term).
% 3.80/0.85 thf(func_def_755, type, sK617: term).
% 3.80/0.85 thf(func_def_756, type, sK618: term).
% 3.80/0.85 thf(func_def_757, type, sK619: term).
% 3.80/0.85 thf(func_def_758, type, sK620: term).
% 3.80/0.85 thf(func_def_759, type, sK621: (term > subst > term > term)).
% 3.80/0.85 thf(func_def_760, type, sK622: term).
% 3.80/0.85 thf(func_def_761, type, sK623: term).
% 3.80/0.85 thf(func_def_762, type, sK624: term).
% 3.80/0.85 thf(func_def_763, type, sK625: term).
% 3.80/0.85 thf(func_def_764, type, sK626: ((subst > term > subst > $o) > term > $o)).
% 3.80/0.85 thf(func_def_765, type, sK627: term).
% 3.80/0.85 thf(func_def_766, type, sK628: (subst > term > subst > $o)).
% 3.80/0.85 thf(func_def_767, type, sK629: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_768, type, sK630: term).
% 3.80/0.85 thf(func_def_769, type, sK631: term).
% 3.80/0.85 thf(func_def_770, type, sK632: term).
% 3.80/0.85 thf(func_def_771, type, sK633: term).
% 3.80/0.85 thf(func_def_772, type, sK634: term).
% 3.80/0.85 thf(func_def_773, type, sK635: term).
% 3.80/0.85 thf(func_def_774, type, sK636: term).
% 3.80/0.85 thf(func_def_775, type, sK637: term).
% 3.80/0.85 thf(func_def_776, type, sK638: term).
% 3.80/0.85 thf(func_def_777, type, sK639: term).
% 3.80/0.85 thf(func_def_778, type, sK640: (subst > d_subst)).
% 3.80/0.85 thf(func_def_779, type, sK641: subst).
% 3.80/0.85 thf(func_def_780, type, sK642: (term > $o)).
% 3.80/0.85 thf(func_def_781, type, db5: !>[X0: $tType]:(X0)).
% 3.80/0.85 thf(func_def_782, type, sK643: subst).
% 3.80/0.85 thf(func_def_783, type, sK644: term).
% 3.80/0.85 thf(func_def_784, type, sK645: ((term > $o) > term)).
% 3.80/0.85 thf(func_def_785, type, sK646: (term > (term > $o) > subst > term > $o)).
% 3.80/0.85 thf(f1,axiom,(
% 3.80/0.85 ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1v2_gthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ 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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X15 : term,X13 : term,X20 : term,X19 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & pushprop_lem1_gthm & (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)))))))) & hoasapinj2_gthm & (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & pushprop_lem1v2_gthm & (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X21)) <=> induction) & hoasinduction_lem1v2 & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & pushprop_lem2v2 & (hoasinduction_lem3v2 <=> ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [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) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & hoaslamnotvar & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & induction2_gthm & hoasinduction_lem3v2_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapnotvar_lthm & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id))) & (! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & ~lamnotap & pushprop_lthm_orig & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem2_gthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X32 : subst,X31 : (subst > term > term),X33 : term,X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))))) <=> hoaslaminj_lthm) & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X11 : (term > $o),X14 : subst,X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X23 @ id)) => (! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [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))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id)))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lthm & (hoasinduction_lem3aa_lthm <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & hoasinduction_lem1_lthm & (hoasinduction_lem3v2a <=> ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))) & apnotvar & hoasapnotvar & (hoasinduction_no_psi_cond <=> ! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ 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)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))) & axvarshift & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & termmset_gthm & induction2lem_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoasinduction_lem1_gthm & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & hoasinduction_lem3b_gthm & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : (term > $o),X10 : (subst > term > subst > $o),X45 : term] : (~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X44) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X45) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))) & pushprop_lem2v2_gthm & (hoasapinj2_lthm <=> (! [X20 : term,X13 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)))) & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ 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)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & axassoc & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)))) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & ulamvarind & hoasapinj1_gthm & (hoaslaminj <=> ! [X18 : (subst > term > term),X31 : (subst > term > term),X33 : term,X32 : subst] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((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)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X26 : (term > $o),X14 : subst,X10 : (term > $o),X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & axmap & hoasinduction_gthm & hoasinduction_lem1 & pushprop_lem3v2_lthm & ! [X1 : d_term] : (X1 = d_one) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X21) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => ! [X17 : subst,X10 : (term > $o),X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))))))) <=> induction2lem_lthm) & hoasinduction_lem3_gthm & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & ~(var @ (d2term @ d_one)) & pushprop_gthm & hoasapnotvar_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [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))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id)))) <=> hoasinduction_lem3_lthm) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & (! [X13 : term,X26 : (term > $o),X10 : (term > $o),X14 : subst,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & lamnotvar & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)))) & ~ulamvar1 & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & hoaslamnotvar_gthm & pushprop & (! [X10 : (subst > term > subst > $o),X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X41 : subst,X40 : term,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aaa) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & pushprop_lem2v2_lthm & pushprop_lem0_gthm & hoaslamnotvar_lthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoasinduction_lem2_lthm & (! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X43) @ id)) <=> hoasinduction_lem3a) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) <=> substmonoid) & ! [X5 : d_subst] : (X5 = d_id) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [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] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48))))) & (! [X15 : term,X20 : term,X13 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & (! [X47 : term,X18 : (subst > term > term),X46 : 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) & (! [X20 : term,X13 : term,X19 : term,X15 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj2) & (id = ((d2subst @ d_id))) & hoaslamnotap_gthm & (one = ((d2term @ d_one))) & (shinj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction2lem <=> ! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))))) & (hoasapinj1 <=> ! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & axclos & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [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))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))))) <=> hoasinduction_lem3a_lthm) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & hoaslaminj_gthm & hoasinduction_lem2v2_gthm & (sh = ((d2subst @ d_id))) & ulamvarsh & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [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)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) <=> hoasinduction_lthm_3) & (! [X11 : (term > $o),X10 : (term > $o),X14 : subst,X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & axapp & hoasinduction_lem3a_gthm & pushprop_lem3v2 & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))))) & (pushprop_lem0 <=> ! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & substmonoid_gthm & axabs & (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) <=> laminj) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & hoaslamnotap_lthm),
% 3.80/0.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 3.80/0.85 thf(f2,conjecture,(
% 3.80/0.85 (pushprop_lem0 = ! [X1 : term,X2 : subst,X0 : (term > $o)] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X1 @ X2 @ X0 @ X3))),
% 3.80/0.85 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0)).
% 3.80/0.85 thf(f3,negated_conjecture,(
% 3.80/0.85 ~ (pushprop_lem0 = ! [X1 : term,X2 : subst,X0 : (term > $o)] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X1 @ X2 @ X0 @ X3))),
% 3.80/0.85 inference(negated_conjecture,[status(cth)],[f2])).
% 3.80/0.85 thf(f4,plain,(
% 3.80/0.85 ~ (pushprop_lem0 = ! [X0 : term,X1 : subst,X2 : (term > $o)] : ? [X3 : (term > $o)] : (pushprop_p_and_p_prime @ X0 @ X1 @ X2 @ X3))),
% 3.80/0.85 inference(rectify,[],[f3])).
% 3.80/0.85 thf(f5,plain,(
% 3.80/0.85 ~ (pushprop_lem0 = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3)))))))))))),
% 3.80/0.85 inference(fool_elimination,[],[f4])).
% 3.80/0.85 thf(f6,plain,(
% 3.80/0.85 ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & hoasinduction_lem1v2_gthm & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : (~(var @ X5) | (X4 @ X5)) | ~ ! [X6 : term,X7 : term] : ((X4 @ (ap @ X6 @ X7)) | ~(X4 @ X7) | ~(X4 @ X6)) | (X4 @ X3) | ~ ! [X8 : term] : (~ ! [X9 : term] : ((X4 @ (sub @ X8 @ (push @ X9 @ id))) | ~(X4 @ X9)) | (X4 @ (lam @ X8)))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : term,X13 : (term > $o)] : (~ ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))) | ~ ! [X15 : term] : ((X13 @ (sub @ X12 @ (push @ X15 @ id))) | ~(X13 @ X15)) | ~ ! [X16 : (subst > term > term)] : ((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id) | ~ ! [X17 : subst,X18 : subst,X19 : term] : (((sub @ (X16 @ X17 @ X19) @ X18)) = ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18)))) | ~ ! [X20 : term] : (~(X11 @ id @ X20 @ id) | (X11 @ id @ (X16 @ id @ X20) @ id))) | (X13 @ (lam @ X12))) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((X21 @ id @ X22 @ id) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : subst,X25 : term,X26 : subst] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24)))) | (X21 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X27 : term] : ((X21 @ id @ (X23 @ id @ X27) @ id) | ~(X21 @ id @ X27 @ id))) | ~ ! [X28 : term,X29 : term] : (~(X21 @ id @ X28 @ id) | ~(X21 @ id @ X29 @ id) | (X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X30 : term,X31 : term,X32 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33)))) <=> apinj2) & pushprop_lem1_gthm & (pushprop_p_and_p_prime = (^[X34 : term, X35 : subst, X36 : (term > $o), X37 : (term > $o)] : (! [X38 : term] : (((X36 @ (sub @ X38 @ (push @ X34 @ X35)))) = ((X37 @ X38)))))) & hoasapinj2_gthm & (! [X39 : (subst > term > subst > $o),X40 : term] : (~ ! [X41 : term] : (~(X39 @ id @ X41 @ id) | (X39 @ id @ (sub @ X40 @ (push @ X41 @ id)) @ id)) | ~ ! [X42 : (subst > term > term)] : (~ ! [X43 : term] : ((X39 @ id @ (X42 @ id @ X43) @ id) | ~(X39 @ id @ X43 @ id)) | (X39 @ id @ (lam @ (X42 @ sh @ one)) @ id) | ~ ! [X44 : subst,X45 : term,X46 : subst] : (((X42 @ (comp @ X44 @ X46) @ (sub @ X45 @ X46))) = ((sub @ (X42 @ X44 @ X45) @ X46)))) | (X39 @ id @ (lam @ X40) @ id) | ~ ! [X47 : term,X48 : subst,X49 : subst,X50 : subst] : (~(X39 @ X49 @ X47 @ (comp @ X48 @ X50)) | (X39 @ (comp @ X49 @ X48) @ (sub @ X47 @ X48) @ X50)) | ~ ! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : ((X39 @ X51 @ X54 @ (comp @ X53 @ X52)) | ~(X39 @ (comp @ X51 @ X53) @ (sub @ X54 @ X53) @ X52))) <=> hoasinduction_lem3) & pushprop_lem1v2_gthm & (! [X55 : (term > $o),X56 : term] : (~ ! [X57 : term] : ((X55 @ (lam @ X57)) | ~(X55 @ X57)) | ~ ! [X58 : term] : (~(var @ X58) | (X55 @ X58)) | ~ ! [X59 : term,X60 : term] : (~(X55 @ X59) | ~(X55 @ X60) | (X55 @ (ap @ X60 @ X59))) | (X55 @ X56)) <=> induction) & hoasinduction_lem1v2 & (hoasinduction_p_and_p_prime = (^[X61 : (subst > term > subst > $o), X62 : (term > $o)] : (! [X63 : term] : (((X61 @ id @ X63 @ id)) = ((X62 @ X63)))))) & pushprop_lem2v2 & (hoasinduction_lem3v2 <=> ! [X64 : term,X65 : (term > $o),X66 : (subst > term > subst > $o)] : (~ ! [X67 : term] : ((X65 @ (sub @ X64 @ (push @ X67 @ id))) | ~(X65 @ X67)) | ~ ! [X68 : term,X69 : subst,X70 : subst,X71 : subst] : (~(X66 @ X69 @ X68 @ (comp @ X70 @ X71)) | (X66 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X71)) | ~ ! [X72 : (subst > term > term)] : (~ ! [X73 : term,X74 : subst,X75 : subst] : (((X72 @ (comp @ X74 @ X75) @ (sub @ X73 @ X75))) = ((sub @ (X72 @ X74 @ X73) @ X75))) | (X66 @ id @ (lam @ (X72 @ sh @ one)) @ id) | ~ ! [X76 : term] : ((X66 @ id @ (X72 @ id @ X76) @ id) | ~(X66 @ id @ X76 @ id))) | (X65 @ (lam @ X64)) | ~ ! [X77 : term,X78 : subst,X79 : subst,X80 : subst] : ((X66 @ X78 @ X77 @ (comp @ X80 @ X79)) | ~(X66 @ (comp @ X78 @ X80) @ (sub @ X77 @ X80) @ X79)) | ~ ! [X81 : term] : (((X66 @ id @ X81 @ id)) = ((X65 @ X81))))) & hoaslamnotvar & (! [X82 : term] : (((sub @ X82 @ id)) = X82) <=> axvarid) & induction2_gthm & hoasinduction_lem3v2_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & hoasapnotvar_lthm & (hoasinduction_lem2 <=> ! [X83 : (subst > term > subst > $o),X84 : term,X85 : term] : ((X83 @ id @ (ap @ X84 @ X85) @ id) | ~(X83 @ id @ X84 @ id) | ~ ! [X86 : term,X87 : term] : (~(X83 @ id @ X86 @ id) | (X83 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id) | ~(X83 @ id @ X87 @ id)) | ~ ! [X88 : subst,X89 : term,X90 : subst,X91 : subst] : (~(X83 @ X88 @ X89 @ (comp @ X90 @ X91)) | (X83 @ (comp @ X88 @ X90) @ (sub @ X89 @ X90) @ X91)) | ~ ! [X92 : subst,X93 : subst,X94 : term,X95 : subst] : (~(X83 @ (comp @ X92 @ X95) @ (sub @ X94 @ X95) @ X93) | (X83 @ X92 @ X94 @ (comp @ X95 @ X93))) | ~(X83 @ id @ X85 @ id))) & (! [X96 : (term > $o),X97 : subst,X98 : term] : ~ ! [X99 : (term > $o)] : ~ ! [X100 : term] : (((X99 @ X100)) = ((X96 @ (sub @ X100 @ (push @ X98 @ X97))))) <=> pushprop_lem0_lthm) & ~lamnotap & pushprop_lthm_orig & (! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((X102 @ sh @ one)) != ((sub @ X101 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem2_gthm & ((! [X103 : subst,X104 : term] : (((sub @ one @ (push @ X104 @ X103))) = X104) => (! [X105 : subst,X106 : term] : (((comp @ sh @ (push @ X106 @ X105))) = X105) => (! [X107 : term,X108 : term] : ((((lam @ X107)) != ((lam @ X108))) | (X107 = X108)) => ! [X109 : subst,X110 : (subst > term > term),X111 : term,X112 : (subst > term > term)] : (~ ! [X113 : subst,X114 : subst,X115 : term] : (((sub @ (X112 @ X113 @ X115) @ X114)) = ((X112 @ (comp @ X113 @ X114) @ (sub @ X115 @ X114)))) | (((X112 @ X109 @ X111)) = ((X110 @ X109 @ X111))) | ~ ! [X116 : subst,X117 : term,X118 : subst] : (((sub @ (X110 @ X118 @ X117) @ X116)) = ((X110 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116)))) | (((lam @ (X112 @ sh @ one))) != ((lam @ (X110 @ sh @ one)))))))) <=> hoaslaminj_lthm) & (pushprop_lem1v2_lthm <=> (! [X119 : term,X120 : subst] : (((sub @ one @ (push @ X119 @ X120))) = X119) => ! [X121 : (term > $o),X122 : (term > $o),X123 : subst,X124 : term] : (~(X121 @ X124) | (X122 @ one) | ~ ! [X125 : term] : (((X121 @ (sub @ X125 @ (push @ X124 @ X123)))) = ((X122 @ X125)))))) & (hoasinduction_lthm <=> (! [X126 : (term > $o),X127 : term] : ((X126 @ X127) | ~ ! [X128 : term,X129 : term] : (~(X126 @ X128) | (X126 @ (ap @ X128 @ X129)) | ~(X126 @ X129)) | ~ ! [X130 : term] : ((X126 @ (lam @ X130)) | ~ ! [X131 : term] : ((X126 @ (sub @ X130 @ (push @ X131 @ id))) | ~(X126 @ X131))) | ~ ! [X132 : term] : (~(var @ X132) | (X126 @ X132))) => (! [X133 : term,X134 : term,X135 : (subst > term > subst > $o)] : (~ ! [X136 : subst,X137 : subst,X138 : subst,X139 : term] : ((X135 @ (comp @ X136 @ X137) @ (sub @ X139 @ X137) @ X138) | ~(X135 @ X136 @ X139 @ (comp @ X137 @ X138))) | (X135 @ id @ (ap @ X133 @ X134) @ id) | ~ ! [X140 : subst,X141 : subst,X142 : subst,X143 : term] : ((X135 @ X140 @ X143 @ (comp @ X141 @ X142)) | ~(X135 @ (comp @ X140 @ X141) @ (sub @ X143 @ X141) @ X142)) | ~(X135 @ id @ X134 @ id) | ~ ! [X144 : term,X145 : term] : (~(X135 @ id @ X144 @ id) | (X135 @ id @ (ap @ (sub @ X145 @ id) @ X144) @ id) | ~(X135 @ id @ X145 @ id)) | ~(X135 @ id @ X133 @ id)) => (! [X146 : term,X147 : (subst > term > subst > $o)] : ((X147 @ id @ (lam @ X146) @ id) | ~ ! [X148 : term,X149 : subst,X150 : subst,X151 : subst] : (~(X147 @ (comp @ X149 @ X151) @ (sub @ X148 @ X151) @ X150) | (X147 @ X149 @ X148 @ (comp @ X151 @ X150))) | ~ ! [X152 : term] : (~(X147 @ id @ X152 @ id) | (X147 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) | ~ ! [X153 : (subst > term > term)] : (~ ! [X154 : term] : (~(X147 @ id @ X154 @ id) | (X147 @ id @ (X153 @ id @ X154) @ id)) | (X147 @ id @ (lam @ (X153 @ sh @ one)) @ id) | ~ ! [X155 : subst,X156 : subst,X157 : term] : (((X153 @ (comp @ X155 @ X156) @ (sub @ X157 @ X156))) = ((sub @ (X153 @ X155 @ X157) @ X156)))) | ~ ! [X158 : subst,X159 : subst,X160 : term,X161 : subst] : ((X147 @ (comp @ X158 @ X159) @ (sub @ X160 @ X159) @ X161) | ~(X147 @ X158 @ X160 @ (comp @ X159 @ X161)))) => ! [X162 : (subst > term > subst > $o),X163 : term] : (~ ! [X164 : term] : ((X162 @ id @ X164 @ id) | ~(var @ (sub @ X164 @ id))) | ~ ! [X165 : subst,X166 : subst,X167 : subst,X168 : term] : (~(X162 @ (comp @ X165 @ X166) @ (sub @ X168 @ X166) @ X167) | (X162 @ X165 @ X168 @ (comp @ X166 @ X167))) | ~ ! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : ((X162 @ (comp @ X169 @ X172) @ (sub @ X170 @ X172) @ X171) | ~(X162 @ X169 @ X170 @ (comp @ X172 @ X171))) | ~ ! [X173 : (subst > term > term)] : (~ ! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X176 @ X174) @ X175)) = ((X173 @ (comp @ X176 @ X175) @ (sub @ X174 @ X175)))) | (X162 @ id @ (lam @ (X173 @ sh @ one)) @ id) | ~ ! [X177 : term] : ((X162 @ id @ (X173 @ id @ X177) @ id) | ~(X162 @ id @ X177 @ id))) | ~ ! [X178 : term,X179 : term] : (~(X162 @ id @ X179 @ id) | (X162 @ id @ (ap @ (sub @ X179 @ id) @ X178) @ id) | ~(X162 @ id @ X178 @ id)) | (X162 @ id @ X163 @ id)))))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop_lthm & (hoasinduction_lem3aa_lthm <=> ! [X180 : term,X181 : (subst > term > subst > $o)] : ((X181 @ id @ (lam @ (sub @ X180 @ (push @ one @ sh))) @ id) | ~ ! [X182 : term] : ((X181 @ id @ (sub @ X180 @ (push @ X182 @ id)) @ id) | ~(X181 @ id @ X182 @ id)) | ~ ! [X183 : (subst > term > term)] : (~ ! [X184 : term] : (~(X181 @ id @ X184 @ id) | (X181 @ id @ (X183 @ id @ X184) @ id)) | (X181 @ id @ (lam @ (X183 @ sh @ one)) @ id) | ~ ! [X185 : subst,X186 : term,X187 : subst] : (((sub @ (X183 @ X185 @ X186) @ X187)) = ((X183 @ (comp @ X185 @ X187) @ (sub @ X186 @ X187))))))) & hoasinduction_lem1_lthm & (hoasinduction_lem3v2a <=> ! [X188 : term,X189 : (subst > term > subst > $o),X190 : (term > $o)] : (~ ! [X191 : (subst > term > term)] : (~ ! [X192 : term,X193 : subst,X194 : subst] : (((X191 @ (comp @ X193 @ X194) @ (sub @ X192 @ X194))) = ((sub @ (X191 @ X193 @ X192) @ X194))) | ~ ! [X195 : term] : (~(X189 @ id @ X195 @ id) | (X189 @ id @ (X191 @ id @ X195) @ id)) | (X189 @ id @ (lam @ (X191 @ sh @ one)) @ id)) | (X190 @ (lam @ X188)) | ~ ! [X196 : term] : (((X189 @ id @ X196 @ id)) = ((X190 @ X196))) | ~ ! [X197 : term] : ((X190 @ (sub @ X188 @ (push @ X197 @ id))) | ~(X190 @ X197)))) & apnotvar & hoasapnotvar & (hoasinduction_no_psi_cond <=> ! [X198 : term,X199 : (subst > term > subst > $o)] : ((X199 @ id @ X198 @ id) | ~ ! [X200 : (subst > term > term)] : (~ ! [X201 : term] : (~(X199 @ id @ X201 @ id) | (X199 @ id @ (X200 @ id @ X201) @ id)) | ~ ! [X202 : term,X203 : subst,X204 : subst] : (((X200 @ (comp @ X203 @ X204) @ (sub @ X202 @ X204))) = ((sub @ (X200 @ X203 @ X202) @ X204))) | (X199 @ id @ (lam @ (X200 @ sh @ one)) @ id)) | ~ ! [X205 : term,X206 : term] : (~(X199 @ id @ X205 @ id) | ~(X199 @ id @ X206 @ id) | (X199 @ id @ (ap @ (sub @ X206 @ id) @ X205) @ id)))) & axvarshift & (! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) <=> hoasinduction_lem0) & termmset_gthm & induction2lem_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem0_lthm <=> ! [X210 : (subst > term > subst > $o)] : ~ ! [X211 : (term > $o)] : ~ ! [X212 : term] : (((X211 @ X212)) = ((X210 @ id @ X212 @ id)))) & hoasinduction_lem1_gthm & (axvarcons <=> ! [X213 : term,X214 : subst] : (((sub @ one @ (push @ X213 @ X214))) = X213)) & hoasinduction_lem3b_gthm & (hoasinduction_lem2v2 <=> ! [X215 : term,X216 : (term > $o),X217 : (subst > term > subst > $o),X218 : term] : (~ ! [X219 : subst,X220 : term,X221 : subst,X222 : subst] : ((X217 @ X221 @ X220 @ (comp @ X219 @ X222)) | ~(X217 @ (comp @ X221 @ X219) @ (sub @ X220 @ X219) @ X222)) | ~(X216 @ X215) | ~ ! [X223 : term] : (((X217 @ id @ X223 @ id)) = ((X216 @ X223))) | (X216 @ (ap @ X215 @ X218)) | ~ ! [X224 : term,X225 : subst,X226 : subst,X227 : subst] : (~(X217 @ X226 @ X224 @ (comp @ X225 @ X227)) | (X217 @ (comp @ X226 @ X225) @ (sub @ X224 @ X225) @ X227)) | ~(X216 @ X218) | ~ ! [X228 : term,X229 : term] : (~(X217 @ id @ X229 @ id) | ~(X217 @ id @ X228 @ id) | (X217 @ id @ (ap @ (sub @ X228 @ id) @ X229) @ id)))) & pushprop_lem2v2_gthm & (hoasapinj2_lthm <=> (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ X232 @ X230)) != ((ap @ X231 @ X233))) | (X230 = X233)) => ! [X234 : term,X235 : term,X236 : term,X237 : term] : ((((ap @ (sub @ X234 @ id) @ X235)) != ((ap @ (sub @ X237 @ id) @ X236))) | (X235 = X236)))) & (hoasinduction_lem3aa <=> ! [X238 : term,X239 : (subst > term > subst > $o)] : ((X239 @ id @ (lam @ (sub @ X238 @ (push @ one @ sh))) @ id) | ~ ! [X240 : term] : ((X239 @ id @ (sub @ X238 @ (push @ X240 @ id)) @ id) | ~(X239 @ id @ X240 @ id)) | ~ ! [X241 : (subst > term > term)] : ((X239 @ id @ (lam @ (X241 @ sh @ one)) @ id) | ~ ! [X242 : subst,X243 : subst,X244 : term] : (((sub @ (X241 @ X242 @ X244) @ X243)) = ((X241 @ (comp @ X242 @ X243) @ (sub @ X244 @ X243)))) | ~ ! [X245 : term] : (~(X239 @ id @ X245 @ id) | (X239 @ id @ (X241 @ id @ X245) @ id))))) & (hoasinduction_lem3v2a_lthm <=> (! [X246 : term] : ~ ! [X247 : (subst > term > term)] : ~ ! [X248 : term,X249 : subst] : (((sub @ X246 @ (push @ X248 @ X249))) = ((X247 @ X249 @ X248))) => (! [X250 : term] : (((sub @ X250 @ id)) = X250) => ! [X251 : (subst > term > subst > $o),X252 : term,X253 : (term > $o)] : (~ ! [X254 : term] : (((X251 @ id @ X254 @ id)) = ((X253 @ X254))) | (X253 @ (lam @ X252)) | ~ ! [X255 : term] : (~(X253 @ X255) | (X253 @ (sub @ X252 @ (push @ X255 @ id)))) | ~ ! [X256 : (subst > term > term)] : ((X251 @ id @ (lam @ (X256 @ sh @ one)) @ id) | ~ ! [X257 : term] : ((X251 @ id @ (X256 @ id @ X257) @ id) | ~(X251 @ id @ X257 @ id)) | ~ ! [X258 : term,X259 : subst,X260 : subst] : (((X256 @ (comp @ X260 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X260 @ X258) @ X259)))))))) & axassoc & (hoasinduction <=> ! [X261 : term,X262 : (subst > term > subst > $o)] : (~ ! [X263 : subst,X264 : subst,X265 : term,X266 : subst] : ((X262 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264) @ X263) | ~(X262 @ X266 @ X265 @ (comp @ X264 @ X263))) | ~ ! [X267 : (subst > term > term)] : (~ ! [X268 : subst,X269 : term,X270 : subst] : (((X267 @ (comp @ X268 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X268 @ X269) @ X270))) | ~ ! [X271 : term] : (~(X262 @ id @ X271 @ id) | (X262 @ id @ (X267 @ id @ X271) @ id)) | (X262 @ id @ (lam @ (X267 @ sh @ one)) @ id)) | ~ ! [X272 : term] : (~(var @ (sub @ X272 @ id)) | (X262 @ id @ X272 @ id)) | ~ ! [X273 : subst,X274 : subst,X275 : subst,X276 : term] : (~(X262 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274) | (X262 @ X275 @ X276 @ (comp @ X273 @ X274))) | (X262 @ id @ X261 @ id) | ~ ! [X277 : term,X278 : term] : ((X262 @ id @ (ap @ (sub @ X277 @ id) @ X278) @ id) | ~(X262 @ id @ X278 @ id) | ~(X262 @ id @ X277 @ id)))) & ((^[X279 : subst, X280 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & ulamvarind & hoasapinj1_gthm & (hoaslaminj <=> ! [X281 : (subst > term > term),X282 : (subst > term > term),X283 : term,X284 : subst] : (~ ! [X285 : subst,X286 : term,X287 : subst] : (((sub @ (X281 @ X285 @ X286) @ X287)) = ((X281 @ (comp @ X285 @ X287) @ (sub @ X286 @ X287)))) | (((lam @ (X282 @ sh @ one))) != ((lam @ (X281 @ sh @ one)))) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((X282 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))) = ((sub @ (X282 @ X290 @ X289) @ X288))) | (((X282 @ X284 @ X283)) = ((X281 @ X284 @ X283))))) & (pushprop_lem1_lthm <=> (! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291) => (! [X293 : subst,X294 : term] : (((comp @ sh @ (push @ X294 @ X293))) = X293) => ! [X295 : term,X296 : (term > $o),X297 : subst,X298 : (term > $o),X299 : term] : (~(X298 @ X295) | (X296 @ (sub @ X295 @ (push @ X299 @ X297))))))) & ! [X300 : term] : ? [X301 : d_term] : (((d2term @ X301)) = X300) & axmap & hoasinduction_gthm & hoasinduction_lem1 & pushprop_lem3v2_lthm & ! [X302 : d_term] : (d_one = X302) & ((! [X303 : subst,X304 : term] : (((sub @ one @ (push @ X304 @ X303))) = X304) => (! [X305 : term,X306 : subst] : (((comp @ sh @ (push @ X305 @ X306))) = X306) => (! [X307 : subst] : (((comp @ X307 @ id)) = X307) => (! [X308 : (term > $o),X309 : term] : (~ ! [X310 : term] : (~(X308 @ X310) | (X308 @ (lam @ X310))) | ~ ! [X311 : term] : ((X308 @ X311) | ~(var @ X311)) | (X308 @ X309) | ~ ! [X312 : term,X313 : term] : ((X308 @ (ap @ X312 @ X313)) | ~(X308 @ X312) | ~(X308 @ X313))) => ! [X314 : subst,X315 : (term > $o),X316 : term] : ((X315 @ (sub @ X316 @ X314)) | ~ ! [X317 : term] : (~ ! [X318 : term] : ((X315 @ (sub @ X317 @ (push @ X318 @ id))) | ~(X315 @ X318)) | (X315 @ (lam @ X317))) | ~ ! [X319 : term] : (~(var @ X319) | (X315 @ (sub @ X319 @ X314))) | ~ ! [X320 : term,X321 : term] : ((X315 @ (ap @ X320 @ X321)) | ~(X315 @ X320) | ~(X315 @ X321))))))) <=> induction2lem_lthm) & hoasinduction_lem3_gthm & (! [X322 : subst] : (((push @ (sub @ one @ X322) @ (comp @ sh @ X322))) = X322) <=> axscons) & (termmset <=> ! [X323 : term] : (((sub @ X323 @ id)) = X323)) & ~(var @ (d2term @ d_one)) & pushprop_gthm & hoasapnotvar_gthm & ((! [X324 : term] : (((sub @ X324 @ id)) = X324) => (! [X325 : (subst > term > subst > $o),X326 : term] : (~ ! [X327 : (subst > term > term)] : ((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id) | ~ ! [X328 : term] : (~(X325 @ id @ X328 @ id) | (X325 @ id @ (X327 @ id @ X328) @ id)) | ~ ! [X329 : subst,X330 : term,X331 : subst] : (((sub @ (X327 @ X329 @ X330) @ X331)) = ((X327 @ (comp @ X329 @ X331) @ (sub @ X330 @ X331))))) | (X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id) | ~ ! [X332 : term] : ((X325 @ id @ (sub @ X326 @ (push @ X332 @ id)) @ id) | ~(X325 @ id @ X332 @ id))) => ! [X333 : (subst > term > subst > $o),X334 : term] : (~ ! [X335 : term] : (~(X333 @ id @ X335 @ id) | (X333 @ id @ (sub @ X334 @ (push @ X335 @ id)) @ id)) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : ((X333 @ X338 @ X339 @ (comp @ X337 @ X336)) | ~(X333 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : subst,X342 : subst,X343 : term] : (((X340 @ (comp @ X341 @ X342) @ (sub @ X343 @ X342))) = ((sub @ (X340 @ X341 @ X343) @ X342))) | ~ ! [X344 : term] : ((X333 @ id @ (X340 @ id @ X344) @ id) | ~(X333 @ id @ X344 @ id)) | (X333 @ id @ (lam @ (X340 @ sh @ one)) @ id)) | ~ ! [X345 : subst,X346 : term,X347 : subst,X348 : subst] : (~(X333 @ X348 @ X346 @ (comp @ X347 @ X345)) | (X333 @ (comp @ X348 @ X347) @ (sub @ X346 @ X347) @ X345)) | (X333 @ id @ (lam @ X334) @ id)))) <=> hoasinduction_lem3_lthm) & (axidr <=> ! [X349 : subst] : (((comp @ X349 @ id)) = X349)) & (! [X350 : term,X351 : (term > $o),X352 : (term > $o),X353 : subst,X354 : term] : ((X351 @ (sub @ X350 @ (push @ X354 @ X353))) | ~(X352 @ X350)) <=> pushprop_lem1) & (termmset_lthm <=> (! [X355 : term] : (((sub @ X355 @ id)) = X355) => ! [X356 : term] : (((sub @ X356 @ id)) = X356))) & lamnotvar & (! [X357 : term] : ~ ! [X358 : (subst > term > term)] : ~ ! [X359 : term,X360 : subst] : (((X358 @ X360 @ X359)) = ((sub @ X357 @ (push @ X359 @ X360)))) <=> hoasinduction_lem3v2_f_lthm) & (induction2 <=> ! [X361 : term,X362 : (term > $o)] : (~ ! [X363 : term] : ((X362 @ X363) | ~(var @ X363)) | (X362 @ X361) | ~ ! [X364 : term] : ((X362 @ (lam @ X364)) | ~ ! [X365 : term] : ((X362 @ (sub @ X364 @ (push @ X365 @ id))) | ~(X362 @ X365))) | ~ ! [X366 : term,X367 : term] : ((X362 @ (ap @ X367 @ X366)) | ~(X362 @ X367) | ~(X362 @ X366)))) & ~ulamvar1 & (hoasinduction_lem3b <=> ! [X368 : term] : ~ ! [X369 : (subst > term > term)] : (((X369 @ sh @ one)) != ((sub @ X368 @ (push @ one @ sh))))) & hoaslamnotvar_gthm & pushprop & (! [X370 : (subst > term > subst > $o),X371 : term] : ((X370 @ id @ (lam @ (sub @ X371 @ (push @ one @ sh))) @ id) | ~ ! [X372 : (subst > term > term),X373 : term] : (~ ! [X374 : term,X375 : subst,X376 : subst] : (((sub @ (X372 @ X376 @ X374) @ X375)) = ((sub @ (sub @ X373 @ (push @ X374 @ X376)) @ X375))) | (X370 @ id @ (lam @ (X372 @ sh @ one)) @ id) | ~ ! [X377 : subst,X378 : term,X379 : subst] : (((X372 @ (comp @ X379 @ X377) @ (sub @ X378 @ X377))) = ((sub @ X373 @ (push @ (sub @ X378 @ X377) @ (comp @ X379 @ X377))))) | ~ ! [X380 : term] : ((X370 @ id @ (X372 @ id @ X380) @ id) | ~(X370 @ id @ X380 @ id))) | ~ ! [X381 : term] : ((X370 @ id @ (sub @ X371 @ (push @ X381 @ id)) @ id) | ~(X370 @ id @ X381 @ id))) <=> hoasinduction_lem3aaa) & (axidl <=> ! [X382 : subst] : (((comp @ id @ X382)) = X382)) & pushprop_lem2v2_lthm & pushprop_lem0_gthm & hoaslamnotvar_lthm & ! [X383 : subst] : ? [X384 : d_subst] : (((d2subst @ X384)) = X383) & hoasinduction_lem2_lthm & (! [X385 : (subst > term > subst > $o),X386 : term] : (~ ! [X387 : (subst > term > term)] : (~ ! [X388 : subst,X389 : subst,X390 : term] : (((X387 @ (comp @ X389 @ X388) @ (sub @ X390 @ X388))) = ((sub @ (X387 @ X389 @ X390) @ X388))) | ~ ! [X391 : term] : (~(X385 @ id @ X391 @ id) | (X385 @ id @ (X387 @ id @ X391) @ id)) | (X385 @ id @ (lam @ (X387 @ sh @ one)) @ id)) | ~ ! [X392 : term] : (~(X385 @ id @ X392 @ id) | (X385 @ id @ (sub @ X386 @ (push @ X392 @ id)) @ id)) | (X385 @ id @ (lam @ X386) @ id)) <=> hoasinduction_lem3a) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X393 : subst] : (((comp @ X393 @ id)) = X393) & ! [X394 : subst] : (((comp @ id @ X394)) = X394)) <=> substmonoid) & ! [X395 : d_subst] : (d_id = X395) & (hoasinduction_lem3v2_lthm <=> (! [X396 : term] : (((sub @ X396 @ id)) = X396) => ! [X397 : (term > $o),X398 : (subst > term > subst > $o),X399 : term] : (~ ! [X400 : (subst > term > term)] : ((X398 @ id @ (lam @ (X400 @ sh @ one)) @ id) | ~ ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X403 @ X401) @ (sub @ X402 @ X401))) = ((sub @ (X400 @ X403 @ X402) @ X401))) | ~ ! [X404 : term] : ((X398 @ id @ (X400 @ id @ X404) @ id) | ~(X398 @ id @ X404 @ id))) | ~ ! [X405 : term] : ((X397 @ (sub @ X399 @ (push @ X405 @ id))) | ~(X397 @ X405)) | ~ ! [X406 : subst,X407 : subst,X408 : subst,X409 : term] : (~(X398 @ (comp @ X407 @ X406) @ (sub @ X409 @ X406) @ X408) | (X398 @ X407 @ X409 @ (comp @ X406 @ X408))) | ~ ! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : ((X398 @ (comp @ X413 @ X412) @ (sub @ X410 @ X412) @ X411) | ~(X398 @ X413 @ X410 @ (comp @ X412 @ X411))) | ~ ! [X414 : term] : (((X397 @ X414)) = ((X398 @ id @ X414 @ id))) | (X397 @ (lam @ X399))))) & (! [X415 : term,X416 : term,X417 : term,X418 : term] : ((((ap @ X415 @ X416)) != ((ap @ X417 @ X418))) | (X415 = X417)) <=> apinj1) & (! [X419 : term,X420 : (subst > term > term),X421 : term] : (~ ! [X422 : term,X423 : subst,X424 : subst] : (((sub @ (X420 @ X424 @ X422) @ X423)) = ((X420 @ (comp @ X424 @ X423) @ (sub @ X422 @ X423)))) | (((lam @ (X420 @ sh @ one))) != ((ap @ (sub @ X421 @ id) @ X419)))) <=> hoaslamnotap) & (! [X425 : term,X426 : term,X427 : term,X428 : term] : ((X425 = X427) | (((ap @ (sub @ X428 @ id) @ X425)) != ((ap @ (sub @ X426 @ id) @ X427)))) <=> hoasapinj2) & (id = ((d2subst @ d_id))) & hoaslamnotap_gthm & (one = ((d2term @ d_one))) & (shinj <=> ! [X429 : term,X430 : term] : ((X429 = X430) | (((sub @ X430 @ sh)) != ((sub @ X429 @ sh))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (induction2lem <=> ! [X431 : subst,X432 : (term > $o),X433 : term] : (~ ! [X434 : term] : ((X432 @ (lam @ X434)) | ~ ! [X435 : term] : (~(X432 @ X435) | (X432 @ (sub @ X434 @ (push @ X435 @ id))))) | (X432 @ (sub @ X433 @ X431)) | ~ ! [X436 : term] : (~(var @ X436) | (X432 @ (sub @ X436 @ X431))) | ~ ! [X437 : term,X438 : term] : (~(X432 @ X438) | ~(X432 @ X437) | (X432 @ (ap @ X437 @ X438))))) & (hoasapinj1 <=> ! [X439 : term,X440 : term,X441 : term,X442 : term] : ((X439 = X441) | (((ap @ (sub @ X441 @ id) @ X442)) != ((ap @ (sub @ X439 @ id) @ X440))))) & axclos & ((! [X443 : term] : (((sub @ X443 @ id)) = X443) => (! [X444 : (subst > term > subst > $o),X445 : term] : (~ ! [X446 : (subst > term > term)] : ((X444 @ id @ (lam @ (X446 @ sh @ one)) @ id) | ~ ! [X447 : term] : (~(X444 @ id @ X447 @ id) | (X444 @ id @ (X446 @ id @ X447) @ id)) | ~ ! [X448 : subst,X449 : subst,X450 : term] : (((sub @ (X446 @ X448 @ X450) @ X449)) = ((X446 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449))))) | ~ ! [X451 : term] : (~(X444 @ id @ X451 @ id) | (X444 @ id @ (sub @ X445 @ (push @ X451 @ id)) @ id)) | (X444 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) => ! [X452 : (subst > term > subst > $o),X453 : term] : (~ ! [X454 : term] : ((X452 @ id @ (sub @ X453 @ (push @ X454 @ id)) @ id) | ~(X452 @ id @ X454 @ id)) | (X452 @ id @ (lam @ X453) @ id) | ~ ! [X455 : (subst > term > term)] : (~ ! [X456 : term] : ((X452 @ id @ (X455 @ id @ X456) @ id) | ~(X452 @ id @ X456 @ id)) | ~ ! [X457 : term,X458 : subst,X459 : subst] : (((sub @ (X455 @ X458 @ X457) @ X459)) = ((X455 @ (comp @ X458 @ X459) @ (sub @ X457 @ X459)))) | (X452 @ id @ (lam @ (X455 @ sh @ one)) @ id))))) <=> hoasinduction_lem3a_lthm) & ((! [X460 : subst] : (((comp @ id @ X460)) = X460) => (! [X461 : subst] : (((comp @ X461 @ id)) = X461) => (! [X462 : subst] : (((comp @ X462 @ id)) = X462) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)))) <=> substmonoid_lthm) & hoaslaminj_gthm & hoasinduction_lem2v2_gthm & (sh = ((d2subst @ d_id))) & ulamvarsh & ((! [X464 : (subst > term > subst > $o)] : ~ ! [X465 : (term > $o)] : ~ ! [X466 : term] : (((X465 @ X466)) = ((X464 @ id @ X466 @ id))) => (! [X467 : (term > $o),X468 : term] : ((X467 @ X468) | ~ ! [X469 : term] : (~(var @ X469) | (X467 @ X469)) | ~ ! [X470 : term] : (~ ! [X471 : term] : (~(X467 @ X471) | (X467 @ (sub @ X470 @ (push @ X471 @ id)))) | (X467 @ (lam @ X470))) | ~ ! [X472 : term,X473 : term] : (~(X467 @ X473) | (X467 @ (ap @ X472 @ X473)) | ~(X467 @ X472))) => (! [X474 : term] : (((sub @ X474 @ id)) = X474) => (! [X475 : (subst > term > subst > $o),X476 : term,X477 : (term > $o)] : (~ ! [X478 : (subst > term > term)] : (~ ! [X479 : subst,X480 : subst,X481 : term] : (((sub @ (X478 @ X480 @ X481) @ X479)) = ((X478 @ (comp @ X480 @ X479) @ (sub @ X481 @ X479)))) | ~ ! [X482 : term] : (~(X475 @ id @ X482 @ id) | (X475 @ id @ (X478 @ id @ X482) @ id)) | (X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) | (X477 @ (lam @ X476)) | ~ ! [X483 : term] : ((X477 @ (sub @ X476 @ (push @ X483 @ id))) | ~(X477 @ X483)) | ~ ! [X484 : term] : (((X477 @ X484)) = ((X475 @ id @ X484 @ id)))) => ! [X485 : (subst > term > subst > $o),X486 : term] : (~ ! [X487 : (subst > term > term)] : (~ ! [X488 : subst,X489 : subst,X490 : term] : (((X487 @ (comp @ X489 @ X488) @ (sub @ X490 @ X488))) = ((sub @ (X487 @ X489 @ X490) @ X488))) | ~ ! [X491 : term] : ((X485 @ id @ (X487 @ id @ X491) @ id) | ~(X485 @ id @ X491 @ id)) | (X485 @ id @ (lam @ (X487 @ sh @ one)) @ id)) | ~ ! [X492 : term,X493 : term] : ((X485 @ id @ (ap @ (sub @ X493 @ id) @ X492) @ id) | ~(X485 @ id @ X492 @ id) | ~(X485 @ id @ X493 @ id)) | ~ ! [X494 : term] : (~(var @ (sub @ X494 @ id)) | (X485 @ id @ X494 @ id)) | (X485 @ id @ X486 @ id) | ~ ! [X495 : term,X496 : subst,X497 : subst,X498 : subst] : (~(X485 @ (comp @ X498 @ X496) @ (sub @ X495 @ X496) @ X497) | (X485 @ X498 @ X495 @ (comp @ X496 @ X497))) | ~ ! [X499 : term,X500 : subst,X501 : subst,X502 : subst] : (~(X485 @ X502 @ X499 @ (comp @ X500 @ X501)) | (X485 @ (comp @ X502 @ X500) @ (sub @ X499 @ X500) @ X501))))))) <=> hoasinduction_lthm_3) & (! [X503 : (term > $o),X504 : (term > $o),X505 : subst,X506 : term] : (~(X504 @ X506) | (X503 @ one) | ~ ! [X507 : term] : (((X503 @ X507)) = ((X504 @ (sub @ X507 @ (push @ X506 @ X505)))))) <=> pushprop_lem1v2) & (axshiftcons <=> ! [X508 : term,X509 : subst] : (((comp @ sh @ (push @ X508 @ X509))) = X509)) & ! [X510 : d_term,X511 : d_term] : ((((d2term @ X511)) = ((d2term @ X510))) => (X510 = X511)) & (hoasinduction_lem3v2_f <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : ~ ! [X514 : term,X515 : subst] : (((sub @ X512 @ (push @ X514 @ X515))) = ((X513 @ X515 @ X514)))) & axapp & hoasinduction_lem3a_gthm & pushprop_lem3v2 & (induction2_lthm <=> (! [X516 : term] : (((sub @ X516 @ id)) = X516) => (! [X517 : (term > $o),X518 : subst,X519 : term] : (~ ! [X520 : term] : (~ ! [X521 : term] : ((X517 @ (sub @ X520 @ (push @ X521 @ id))) | ~(X517 @ X521)) | (X517 @ (lam @ X520))) | ~ ! [X522 : term,X523 : term] : (~(X517 @ X522) | ~(X517 @ X523) | (X517 @ (ap @ X523 @ X522))) | ~ ! [X524 : term] : ((X517 @ (sub @ X524 @ X518)) | ~(var @ X524)) | (X517 @ (sub @ X519 @ X518))) => ! [X525 : term,X526 : (term > $o)] : ((X526 @ X525) | ~ ! [X527 : term,X528 : term] : ((X526 @ (ap @ X527 @ X528)) | ~(X526 @ X527) | ~(X526 @ X528)) | ~ ! [X529 : term] : (~ ! [X530 : term] : (~(X526 @ X530) | (X526 @ (sub @ X529 @ (push @ X530 @ id)))) | (X526 @ (lam @ X529))) | ~ ! [X531 : term] : (~(var @ X531) | (X526 @ X531)))))) & (pushprop_lem0 <=> ! [X532 : (term > $o),X533 : subst,X534 : term] : ~ ! [X535 : (term > $o)] : ~ ! [X536 : term] : (((X532 @ (sub @ X536 @ (push @ X534 @ X533)))) = ((X535 @ X536)))) & ! [X537 : d_subst,X538 : d_subst] : ((((d2subst @ X538)) = ((d2subst @ X537))) => (X537 = X538)) & substmonoid_gthm & axabs & (! [X539 : term,X540 : term] : ((((lam @ X539)) != ((lam @ X540))) | (X539 = X540)) <=> laminj) & (hoasapinj1_lthm <=> (! [X541 : term] : (((sub @ X541 @ id)) = X541) => (! [X542 : term,X543 : term,X544 : term,X545 : term] : ((((ap @ X544 @ X542)) != ((ap @ X545 @ X543))) | (X544 = X545)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((((ap @ (sub @ X547 @ id) @ X549)) != ((ap @ (sub @ X546 @ id) @ X548))) | (X546 = X547))))) & hoaslamnotap_lthm),
% 3.80/0.85 inference(rectify,[],[f1])).
% 3.80/0.85 thf(f7,plain,(
% 3.80/0.85 ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : (~ (((var @ X5)) = $true) | (((X4 @ X5)) = $true)) | ~ ! [X6 : term,X7 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | ~ (((X4 @ X7)) = $true) | ~ (((X4 @ X6)) = $true)) | (((X4 @ X3)) = $true) | ~ ! [X8 : term] : (~ ! [X9 : term] : ((((X4 @ (sub @ X8 @ (push @ X9 @ id)))) = $true) | ~ (((X4 @ X9)) = $true)) | (((X4 @ (lam @ X8))) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : term,X13 : (term > $o)] : (~ ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))) | ~ ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | ~ (((X13 @ X15)) = $true)) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X18 : subst,X19 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X19) @ X18)) = ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18)))) | ~ ! [X20 : term] : (~ (((X11 @ id @ X20 @ id)) = $true) | (((X11 @ id @ (X16 @ id @ X20) @ id)) = $true))) | (((X13 @ (lam @ X12))) = $true)) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : (~ ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24)))) | ($true = ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) | ~ ! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | ~ (((X21 @ id @ X27 @ id)) = $true))) | ~ ! [X28 : term,X29 : term] : (~ (((X21 @ id @ X28 @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & (pushprop_lem1_gthm = $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)))))))))))) & (hoasapinj2_gthm = $true) & (! [X39 : (subst > term > subst > $o),X40 : term] : (~ ! [X41 : term] : (~ (((X39 @ id @ X41 @ id)) = $true) | ($true = ((X39 @ id @ (sub @ X40 @ (push @ X41 @ id)) @ id)))) | ~ ! [X42 : (subst > term > term)] : (~ ! [X43 : term] : (($true = ((X39 @ id @ (X42 @ id @ X43) @ id))) | ~ ($true = ((X39 @ id @ X43 @ id)))) | (((X39 @ id @ (lam @ (X42 @ sh @ one)) @ id)) = $true) | ~ ! [X44 : subst,X45 : term,X46 : subst] : (((X42 @ (comp @ X44 @ X46) @ (sub @ X45 @ X46))) = ((sub @ (X42 @ X44 @ X45) @ X46)))) | (((X39 @ id @ (lam @ X40) @ id)) = $true) | ~ ! [X47 : term,X48 : subst,X49 : subst,X50 : subst] : (~ (((X39 @ X49 @ X47 @ (comp @ X48 @ X50))) = $true) | (((X39 @ (comp @ X49 @ X48) @ (sub @ X47 @ X48) @ X50)) = $true)) | ~ ! [X51 : subst,X52 : subst,X53 : subst,X54 : term] : (($true = ((X39 @ X51 @ X54 @ (comp @ X53 @ X52)))) | ~ (((X39 @ (comp @ X51 @ X53) @ (sub @ X54 @ X53) @ X52)) = $true))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem1v2_gthm = $true) & (! [X55 : (term > $o),X56 : term] : (~ ! [X57 : term] : ((((X55 @ (lam @ X57))) = $true) | ~ (((X55 @ X57)) = $true)) | ~ ! [X58 : term] : (~ (((var @ X58)) = $true) | ($true = ((X55 @ X58)))) | ~ ! [X59 : term,X60 : term] : (~ ($true = ((X55 @ X59))) | ~ (((X55 @ X60)) = $true) | (((X55 @ (ap @ X60 @ X59))) = $true)) | ($true = ((X55 @ X56)))) <=> (induction = $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X64 : term,X65 : (term > $o),X66 : (subst > term > subst > $o)] : (~ ! [X67 : term] : ((((X65 @ (sub @ X64 @ (push @ X67 @ id)))) = $true) | ~ ($true = ((X65 @ X67)))) | ~ ! [X68 : term,X69 : subst,X70 : subst,X71 : subst] : (~ (((X66 @ X69 @ X68 @ (comp @ X70 @ X71))) = $true) | ($true = ((X66 @ (comp @ X69 @ X70) @ (sub @ X68 @ X70) @ X71)))) | ~ ! [X72 : (subst > term > term)] : (~ ! [X73 : term,X74 : subst,X75 : subst] : (((X72 @ (comp @ X74 @ X75) @ (sub @ X73 @ X75))) = ((sub @ (X72 @ X74 @ X73) @ X75))) | (((X66 @ id @ (lam @ (X72 @ sh @ one)) @ id)) = $true) | ~ ! [X76 : term] : (($true = ((X66 @ id @ (X72 @ id @ X76) @ id))) | ~ ($true = ((X66 @ id @ X76 @ id))))) | (((X65 @ (lam @ X64))) = $true) | ~ ! [X77 : term,X78 : subst,X79 : subst,X80 : subst] : ((((X66 @ X78 @ X77 @ (comp @ X80 @ X79))) = $true) | ~ (((X66 @ (comp @ X78 @ X80) @ (sub @ X77 @ X80) @ X79)) = $true)) | ~ ! [X81 : term] : (((X66 @ id @ X81 @ id)) = ((X65 @ X81))))) & (hoaslamnotvar = $true) & (! [X82 : term] : (((sub @ X82 @ id)) = X82) <=> (axvarid = $true)) & (induction2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X83 : (subst > term > subst > $o),X84 : term,X85 : term] : ((((X83 @ id @ (ap @ X84 @ X85) @ id)) = $true) | ~ ($true = ((X83 @ id @ X84 @ id))) | ~ ! [X86 : term,X87 : term] : (~ (((X83 @ id @ X86 @ id)) = $true) | ($true = ((X83 @ id @ (ap @ (sub @ X87 @ id) @ X86) @ id))) | ~ (((X83 @ id @ X87 @ id)) = $true)) | ~ ! [X88 : subst,X89 : term,X90 : subst,X91 : subst] : (~ (((X83 @ X88 @ X89 @ (comp @ X90 @ X91))) = $true) | (((X83 @ (comp @ X88 @ X90) @ (sub @ X89 @ X90) @ X91)) = $true)) | ~ ! [X92 : subst,X93 : subst,X94 : term,X95 : subst] : (~ (((X83 @ (comp @ X92 @ X95) @ (sub @ X94 @ X95) @ X93)) = $true) | ($true = ((X83 @ X92 @ X94 @ (comp @ X95 @ X93))))) | ~ ($true = ((X83 @ id @ X85 @ id))))) & (! [X96 : (term > $o),X97 : subst,X98 : term] : ~ ! [X99 : (term > $o)] : ~ ! [X100 : term] : (((X99 @ X100)) = ((X96 @ (sub @ X100 @ (push @ X98 @ X97))))) <=> (pushprop_lem0_lthm = $true)) & ~ (lamnotap = $true) & (pushprop_lthm_orig = $true) & (! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((X102 @ sh @ one)) != ((sub @ X101 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & ((! [X103 : subst,X104 : term] : (((sub @ one @ (push @ X104 @ X103))) = X104) => (! [X105 : subst,X106 : term] : (((comp @ sh @ (push @ X106 @ X105))) = X105) => (! [X107 : term,X108 : term] : ((((lam @ X107)) != ((lam @ X108))) | (X107 = X108)) => ! [X109 : subst,X110 : (subst > term > term),X111 : term,X112 : (subst > term > term)] : (~ ! [X113 : subst,X114 : subst,X115 : term] : (((sub @ (X112 @ X113 @ X115) @ X114)) = ((X112 @ (comp @ X113 @ X114) @ (sub @ X115 @ X114)))) | (((X112 @ X109 @ X111)) = ((X110 @ X109 @ X111))) | ~ ! [X116 : subst,X117 : term,X118 : subst] : (((sub @ (X110 @ X118 @ X117) @ X116)) = ((X110 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116)))) | (((lam @ (X112 @ sh @ one))) != ((lam @ (X110 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X119 : term,X120 : subst] : (((sub @ one @ (push @ X119 @ X120))) = X119) => ! [X121 : (term > $o),X122 : (term > $o),X123 : subst,X124 : term] : (~ (((X121 @ X124)) = $true) | (((X122 @ one)) = $true) | ~ ! [X125 : term] : (((X121 @ (sub @ X125 @ (push @ X124 @ X123)))) = ((X122 @ X125)))))) & ((hoasinduction_lthm = $true) <=> (! [X126 : (term > $o),X127 : term] : ((((X126 @ X127)) = $true) | ~ ! [X128 : term,X129 : term] : (~ (((X126 @ X128)) = $true) | (((X126 @ (ap @ X128 @ X129))) = $true) | ~ (((X126 @ X129)) = $true)) | ~ ! [X130 : term] : ((((X126 @ (lam @ X130))) = $true) | ~ ! [X131 : term] : ((((X126 @ (sub @ X130 @ (push @ X131 @ id)))) = $true) | ~ (((X126 @ X131)) = $true))) | ~ ! [X132 : term] : (~ ($true = ((var @ X132))) | (((X126 @ X132)) = $true))) => (! [X133 : term,X134 : term,X135 : (subst > term > subst > $o)] : (~ ! [X136 : subst,X137 : subst,X138 : subst,X139 : term] : ((((X135 @ (comp @ X136 @ X137) @ (sub @ X139 @ X137) @ X138)) = $true) | ~ ($true = ((X135 @ X136 @ X139 @ (comp @ X137 @ X138))))) | (((X135 @ id @ (ap @ X133 @ X134) @ id)) = $true) | ~ ! [X140 : subst,X141 : subst,X142 : subst,X143 : term] : (($true = ((X135 @ X140 @ X143 @ (comp @ X141 @ X142)))) | ~ (((X135 @ (comp @ X140 @ X141) @ (sub @ X143 @ X141) @ X142)) = $true)) | ~ (((X135 @ id @ X134 @ id)) = $true) | ~ ! [X144 : term,X145 : term] : (~ (((X135 @ id @ X144 @ id)) = $true) | ($true = ((X135 @ id @ (ap @ (sub @ X145 @ id) @ X144) @ id))) | ~ (((X135 @ id @ X145 @ id)) = $true)) | ~ (((X135 @ id @ X133 @ id)) = $true)) => (! [X146 : term,X147 : (subst > term > subst > $o)] : ((((X147 @ id @ (lam @ X146) @ id)) = $true) | ~ ! [X148 : term,X149 : subst,X150 : subst,X151 : subst] : (~ (((X147 @ (comp @ X149 @ X151) @ (sub @ X148 @ X151) @ X150)) = $true) | (((X147 @ X149 @ X148 @ (comp @ X151 @ X150))) = $true)) | ~ ! [X152 : term] : (~ (((X147 @ id @ X152 @ id)) = $true) | ($true = ((X147 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)))) | ~ ! [X153 : (subst > term > term)] : (~ ! [X154 : term] : (~ (((X147 @ id @ X154 @ id)) = $true) | ($true = ((X147 @ id @ (X153 @ id @ X154) @ id)))) | (((X147 @ id @ (lam @ (X153 @ sh @ one)) @ id)) = $true) | ~ ! [X155 : subst,X156 : subst,X157 : term] : (((X153 @ (comp @ X155 @ X156) @ (sub @ X157 @ X156))) = ((sub @ (X153 @ X155 @ X157) @ X156)))) | ~ ! [X158 : subst,X159 : subst,X160 : term,X161 : subst] : ((((X147 @ (comp @ X158 @ X159) @ (sub @ X160 @ X159) @ X161)) = $true) | ~ ($true = ((X147 @ X158 @ X160 @ (comp @ X159 @ X161)))))) => ! [X162 : (subst > term > subst > $o),X163 : term] : (~ ! [X164 : term] : ((((X162 @ id @ X164 @ id)) = $true) | ~ (((var @ (sub @ X164 @ id))) = $true)) | ~ ! [X165 : subst,X166 : subst,X167 : subst,X168 : term] : (~ (((X162 @ (comp @ X165 @ X166) @ (sub @ X168 @ X166) @ X167)) = $true) | (((X162 @ X165 @ X168 @ (comp @ X166 @ X167))) = $true)) | ~ ! [X169 : subst,X170 : term,X171 : subst,X172 : subst] : ((((X162 @ (comp @ X169 @ X172) @ (sub @ X170 @ X172) @ X171)) = $true) | ~ (((X162 @ X169 @ X170 @ (comp @ X172 @ X171))) = $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X176 @ X174) @ X175)) = ((X173 @ (comp @ X176 @ X175) @ (sub @ X174 @ X175)))) | (((X162 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : ((((X162 @ id @ (X173 @ id @ X177) @ id)) = $true) | ~ (((X162 @ id @ X177 @ id)) = $true))) | ~ ! [X178 : term,X179 : term] : (~ (((X162 @ id @ X179 @ id)) = $true) | (((X162 @ id @ (ap @ (sub @ X179 @ id) @ X178) @ id)) = $true) | ~ (((X162 @ id @ X178 @ id)) = $true)) | (((X162 @ id @ X163 @ id)) = $true)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X180 : term,X181 : (subst > term > subst > $o)] : ((((X181 @ id @ (lam @ (sub @ X180 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X182 : term] : (($true = ((X181 @ id @ (sub @ X180 @ (push @ X182 @ id)) @ id))) | ~ (((X181 @ id @ X182 @ id)) = $true)) | ~ ! [X183 : (subst > term > term)] : (~ ! [X184 : term] : (~ (((X181 @ id @ X184 @ id)) = $true) | ($true = ((X181 @ id @ (X183 @ id @ X184) @ id)))) | ($true = ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) | ~ ! [X185 : subst,X186 : term,X187 : subst] : (((sub @ (X183 @ X185 @ X186) @ X187)) = ((X183 @ (comp @ X185 @ X187) @ (sub @ X186 @ X187))))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X188 : term,X189 : (subst > term > subst > $o),X190 : (term > $o)] : (~ ! [X191 : (subst > term > term)] : (~ ! [X192 : term,X193 : subst,X194 : subst] : (((X191 @ (comp @ X193 @ X194) @ (sub @ X192 @ X194))) = ((sub @ (X191 @ X193 @ X192) @ X194))) | ~ ! [X195 : term] : (~ (((X189 @ id @ X195 @ id)) = $true) | (((X189 @ id @ (X191 @ id @ X195) @ id)) = $true)) | (((X189 @ id @ (lam @ (X191 @ sh @ one)) @ id)) = $true)) | (((X190 @ (lam @ X188))) = $true) | ~ ! [X196 : term] : (((X189 @ id @ X196 @ id)) = ((X190 @ X196))) | ~ ! [X197 : term] : ((((X190 @ (sub @ X188 @ (push @ X197 @ id)))) = $true) | ~ (((X190 @ X197)) = $true)))) & (apnotvar = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X198 : term,X199 : (subst > term > subst > $o)] : (($true = ((X199 @ id @ X198 @ id))) | ~ ! [X200 : (subst > term > term)] : (~ ! [X201 : term] : (~ ($true = ((X199 @ id @ X201 @ id))) | (((X199 @ id @ (X200 @ id @ X201) @ id)) = $true)) | ~ ! [X202 : term,X203 : subst,X204 : subst] : (((X200 @ (comp @ X203 @ X204) @ (sub @ X202 @ X204))) = ((sub @ (X200 @ X203 @ X202) @ X204))) | (((X199 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true)) | ~ ! [X205 : term,X206 : term] : (~ (((X199 @ id @ X205 @ id)) = $true) | ~ ($true = ((X199 @ id @ X206 @ id))) | (((X199 @ id @ (ap @ (sub @ X206 @ id) @ X205) @ id)) = $true)))) & (axvarshift = $true) & (! [X207 : (subst > term > subst > $o)] : ~ ! [X208 : (term > $o)] : ~ ! [X209 : term] : (((X208 @ X209)) = ((X207 @ id @ X209 @ id))) <=> (hoasinduction_lem0 = $true)) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X210 : (subst > term > subst > $o)] : ~ ! [X211 : (term > $o)] : ~ ! [X212 : term] : (((X211 @ X212)) = ((X210 @ id @ X212 @ id)))) & (hoasinduction_lem1_gthm = $true) & ((axvarcons = $true) <=> ! [X213 : term,X214 : subst] : (((sub @ one @ (push @ X213 @ X214))) = X213)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X215 : term,X216 : (term > $o),X217 : (subst > term > subst > $o),X218 : term] : (~ ! [X219 : subst,X220 : term,X221 : subst,X222 : subst] : ((((X217 @ X221 @ X220 @ (comp @ X219 @ X222))) = $true) | ~ (((X217 @ (comp @ X221 @ X219) @ (sub @ X220 @ X219) @ X222)) = $true)) | ~ (((X216 @ X215)) = $true) | ~ ! [X223 : term] : (((X217 @ id @ X223 @ id)) = ((X216 @ X223))) | (((X216 @ (ap @ X215 @ X218))) = $true) | ~ ! [X224 : term,X225 : subst,X226 : subst,X227 : subst] : (~ (((X217 @ X226 @ X224 @ (comp @ X225 @ X227))) = $true) | (((X217 @ (comp @ X226 @ X225) @ (sub @ X224 @ X225) @ X227)) = $true)) | ~ (((X216 @ X218)) = $true) | ~ ! [X228 : term,X229 : term] : (~ ($true = ((X217 @ id @ X229 @ id))) | ~ (((X217 @ id @ X228 @ id)) = $true) | (((X217 @ id @ (ap @ (sub @ X228 @ id) @ X229) @ id)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ X232 @ X230)) != ((ap @ X231 @ X233))) | (X230 = X233)) => ! [X234 : term,X235 : term,X236 : term,X237 : term] : ((((ap @ (sub @ X234 @ id) @ X235)) != ((ap @ (sub @ X237 @ id) @ X236))) | (X235 = X236)))) & ((hoasinduction_lem3aa = $true) <=> ! [X238 : term,X239 : (subst > term > subst > $o)] : ((((X239 @ id @ (lam @ (sub @ X238 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X240 : term] : (($true = ((X239 @ id @ (sub @ X238 @ (push @ X240 @ id)) @ id))) | ~ (((X239 @ id @ X240 @ id)) = $true)) | ~ ! [X241 : (subst > term > term)] : ((((X239 @ id @ (lam @ (X241 @ sh @ one)) @ id)) = $true) | ~ ! [X242 : subst,X243 : subst,X244 : term] : (((sub @ (X241 @ X242 @ X244) @ X243)) = ((X241 @ (comp @ X242 @ X243) @ (sub @ X244 @ X243)))) | ~ ! [X245 : term] : (~ (((X239 @ id @ X245 @ id)) = $true) | (((X239 @ id @ (X241 @ id @ X245) @ id)) = $true))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X246 : term] : ~ ! [X247 : (subst > term > term)] : ~ ! [X248 : term,X249 : subst] : (((sub @ X246 @ (push @ X248 @ X249))) = ((X247 @ X249 @ X248))) => (! [X250 : term] : (((sub @ X250 @ id)) = X250) => ! [X251 : (subst > term > subst > $o),X252 : term,X253 : (term > $o)] : (~ ! [X254 : term] : (((X251 @ id @ X254 @ id)) = ((X253 @ X254))) | (((X253 @ (lam @ X252))) = $true) | ~ ! [X255 : term] : (~ (((X253 @ X255)) = $true) | (((X253 @ (sub @ X252 @ (push @ X255 @ id)))) = $true)) | ~ ! [X256 : (subst > term > term)] : (($true = ((X251 @ id @ (lam @ (X256 @ sh @ one)) @ id))) | ~ ! [X257 : term] : ((((X251 @ id @ (X256 @ id @ X257) @ id)) = $true) | ~ (((X251 @ id @ X257 @ id)) = $true)) | ~ ! [X258 : term,X259 : subst,X260 : subst] : (((X256 @ (comp @ X260 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X260 @ X258) @ X259)))))))) & (axassoc = $true) & ((hoasinduction = $true) <=> ! [X261 : term,X262 : (subst > term > subst > $o)] : (~ ! [X263 : subst,X264 : subst,X265 : term,X266 : subst] : ((((X262 @ (comp @ X266 @ X264) @ (sub @ X265 @ X264) @ X263)) = $true) | ~ (((X262 @ X266 @ X265 @ (comp @ X264 @ X263))) = $true)) | ~ ! [X267 : (subst > term > term)] : (~ ! [X268 : subst,X269 : term,X270 : subst] : (((X267 @ (comp @ X268 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X268 @ X269) @ X270))) | ~ ! [X271 : term] : (~ ($true = ((X262 @ id @ X271 @ id))) | ($true = ((X262 @ id @ (X267 @ id @ X271) @ id)))) | ($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id)))) | ~ ! [X272 : term] : (~ (((var @ (sub @ X272 @ id))) = $true) | (((X262 @ id @ X272 @ id)) = $true)) | ~ ! [X273 : subst,X274 : subst,X275 : subst,X276 : term] : (~ ($true = ((X262 @ (comp @ X275 @ X273) @ (sub @ X276 @ X273) @ X274))) | ($true = ((X262 @ X275 @ X276 @ (comp @ X273 @ X274))))) | (((X262 @ id @ X261 @ id)) = $true) | ~ ! [X277 : term,X278 : term] : ((((X262 @ id @ (ap @ (sub @ X277 @ id) @ X278) @ id)) = $true) | ~ (((X262 @ id @ X278 @ id)) = $true) | ~ (((X262 @ id @ X277 @ id)) = $true)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvarind = $true) & (hoasapinj1_gthm = $true) & ((hoaslaminj = $true) <=> ! [X281 : (subst > term > term),X282 : (subst > term > term),X283 : term,X284 : subst] : (~ ! [X285 : subst,X286 : term,X287 : subst] : (((sub @ (X281 @ X285 @ X286) @ X287)) = ((X281 @ (comp @ X285 @ X287) @ (sub @ X286 @ X287)))) | (((lam @ (X282 @ sh @ one))) != ((lam @ (X281 @ sh @ one)))) | ~ ! [X288 : subst,X289 : term,X290 : subst] : (((X282 @ (comp @ X290 @ X288) @ (sub @ X289 @ X288))) = ((sub @ (X282 @ X290 @ X289) @ X288))) | (((X282 @ X284 @ X283)) = ((X281 @ X284 @ X283))))) & ((pushprop_lem1_lthm = $true) <=> (! [X291 : term,X292 : subst] : (((sub @ one @ (push @ X291 @ X292))) = X291) => (! [X293 : subst,X294 : term] : (((comp @ sh @ (push @ X294 @ X293))) = X293) => ! [X295 : term,X296 : (term > $o),X297 : subst,X298 : (term > $o),X299 : term] : (~ (((X298 @ X295)) = $true) | (((X296 @ (sub @ X295 @ (push @ X299 @ X297)))) = $true))))) & ! [X300 : term] : ? [X301 : d_term] : (((d2term @ X301)) = X300) & (axmap = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & ! [X302 : d_term] : (d_one = X302) & ((! [X303 : subst,X304 : term] : (((sub @ one @ (push @ X304 @ X303))) = X304) => (! [X305 : term,X306 : subst] : (((comp @ sh @ (push @ X305 @ X306))) = X306) => (! [X307 : subst] : (((comp @ X307 @ id)) = X307) => (! [X308 : (term > $o),X309 : term] : (~ ! [X310 : term] : (~ ($true = ((X308 @ X310))) | (((X308 @ (lam @ X310))) = $true)) | ~ ! [X311 : term] : (($true = ((X308 @ X311))) | ~ ($true = ((var @ X311)))) | (((X308 @ X309)) = $true) | ~ ! [X312 : term,X313 : term] : ((((X308 @ (ap @ X312 @ X313))) = $true) | ~ (((X308 @ X312)) = $true) | ~ (((X308 @ X313)) = $true))) => ! [X314 : subst,X315 : (term > $o),X316 : term] : ((((X315 @ (sub @ X316 @ X314))) = $true) | ~ ! [X317 : term] : (~ ! [X318 : term] : (($true = ((X315 @ (sub @ X317 @ (push @ X318 @ id))))) | ~ (((X315 @ X318)) = $true)) | ($true = ((X315 @ (lam @ X317))))) | ~ ! [X319 : term] : (~ (((var @ X319)) = $true) | ($true = ((X315 @ (sub @ X319 @ X314))))) | ~ ! [X320 : term,X321 : term] : ((((X315 @ (ap @ X320 @ X321))) = $true) | ~ (((X315 @ X320)) = $true) | ~ (((X315 @ X321)) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X322 : subst] : (((push @ (sub @ one @ X322) @ (comp @ sh @ X322))) = X322) <=> (axscons = $true)) & ((termmset = $true) <=> ! [X323 : term] : (((sub @ X323 @ id)) = X323)) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_gthm = $true) & (hoasapnotvar_gthm = $true) & ((! [X324 : term] : (((sub @ X324 @ id)) = X324) => (! [X325 : (subst > term > subst > $o),X326 : term] : (~ ! [X327 : (subst > term > term)] : (($true = ((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id))) | ~ ! [X328 : term] : (~ (((X325 @ id @ X328 @ id)) = $true) | (((X325 @ id @ (X327 @ id @ X328) @ id)) = $true)) | ~ ! [X329 : subst,X330 : term,X331 : subst] : (((sub @ (X327 @ X329 @ X330) @ X331)) = ((X327 @ (comp @ X329 @ X331) @ (sub @ X330 @ X331))))) | ($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id))) | ~ ! [X332 : term] : ((((X325 @ id @ (sub @ X326 @ (push @ X332 @ id)) @ id)) = $true) | ~ (((X325 @ id @ X332 @ id)) = $true))) => ! [X333 : (subst > term > subst > $o),X334 : term] : (~ ! [X335 : term] : (~ (((X333 @ id @ X335 @ id)) = $true) | (((X333 @ id @ (sub @ X334 @ (push @ X335 @ id)) @ id)) = $true)) | ~ ! [X336 : subst,X337 : subst,X338 : subst,X339 : term] : ((((X333 @ X338 @ X339 @ (comp @ X337 @ X336))) = $true) | ~ ($true = ((X333 @ (comp @ X338 @ X337) @ (sub @ X339 @ X337) @ X336)))) | ~ ! [X340 : (subst > term > term)] : (~ ! [X341 : subst,X342 : subst,X343 : term] : (((X340 @ (comp @ X341 @ X342) @ (sub @ X343 @ X342))) = ((sub @ (X340 @ X341 @ X343) @ X342))) | ~ ! [X344 : term] : ((((X333 @ id @ (X340 @ id @ X344) @ id)) = $true) | ~ (((X333 @ id @ X344 @ id)) = $true)) | (((X333 @ id @ (lam @ (X340 @ sh @ one)) @ id)) = $true)) | ~ ! [X345 : subst,X346 : term,X347 : subst,X348 : subst] : (~ (((X333 @ X348 @ X346 @ (comp @ X347 @ X345))) = $true) | ($true = ((X333 @ (comp @ X348 @ X347) @ (sub @ X346 @ X347) @ X345)))) | (((X333 @ id @ (lam @ X334) @ id)) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & ((axidr = $true) <=> ! [X349 : subst] : (((comp @ X349 @ id)) = X349)) & (! [X350 : term,X351 : (term > $o),X352 : (term > $o),X353 : subst,X354 : term] : (($true = ((X351 @ (sub @ X350 @ (push @ X354 @ X353))))) | ~ ($true = ((X352 @ X350)))) <=> (pushprop_lem1 = $true)) & ((termmset_lthm = $true) <=> (! [X355 : term] : (((sub @ X355 @ id)) = X355) => ! [X356 : term] : (((sub @ X356 @ id)) = X356))) & (lamnotvar = $true) & (! [X357 : term] : ~ ! [X358 : (subst > term > term)] : ~ ! [X359 : term,X360 : subst] : (((X358 @ X360 @ X359)) = ((sub @ X357 @ (push @ X359 @ X360)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((induction2 = $true) <=> ! [X361 : term,X362 : (term > $o)] : (~ ! [X363 : term] : (($true = ((X362 @ X363))) | ~ (((var @ X363)) = $true)) | (((X362 @ X361)) = $true) | ~ ! [X364 : term] : (($true = ((X362 @ (lam @ X364)))) | ~ ! [X365 : term] : ((((X362 @ (sub @ X364 @ (push @ X365 @ id)))) = $true) | ~ (((X362 @ X365)) = $true))) | ~ ! [X366 : term,X367 : term] : ((((X362 @ (ap @ X367 @ X366))) = $true) | ~ (((X362 @ X367)) = $true) | ~ ($true = ((X362 @ X366)))))) & ~ (ulamvar1 = $true) & ((hoasinduction_lem3b = $true) <=> ! [X368 : term] : ~ ! [X369 : (subst > term > term)] : (((X369 @ sh @ one)) != ((sub @ X368 @ (push @ one @ sh))))) & (hoaslamnotvar_gthm = $true) & (pushprop = $true) & (! [X370 : (subst > term > subst > $o),X371 : term] : ((((X370 @ id @ (lam @ (sub @ X371 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X372 : (subst > term > term),X373 : term] : (~ ! [X374 : term,X375 : subst,X376 : subst] : (((sub @ (X372 @ X376 @ X374) @ X375)) = ((sub @ (sub @ X373 @ (push @ X374 @ X376)) @ X375))) | ($true = ((X370 @ id @ (lam @ (X372 @ sh @ one)) @ id))) | ~ ! [X377 : subst,X378 : term,X379 : subst] : (((X372 @ (comp @ X379 @ X377) @ (sub @ X378 @ X377))) = ((sub @ X373 @ (push @ (sub @ X378 @ X377) @ (comp @ X379 @ X377))))) | ~ ! [X380 : term] : (($true = ((X370 @ id @ (X372 @ id @ X380) @ id))) | ~ (((X370 @ id @ X380 @ id)) = $true))) | ~ ! [X381 : term] : (($true = ((X370 @ id @ (sub @ X371 @ (push @ X381 @ id)) @ id))) | ~ (((X370 @ id @ X381 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ((axidl = $true) <=> ! [X382 : subst] : (((comp @ id @ X382)) = X382)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar_lthm = $true) & ! [X383 : subst] : ? [X384 : d_subst] : (((d2subst @ X384)) = X383) & (hoasinduction_lem2_lthm = $true) & (! [X385 : (subst > term > subst > $o),X386 : term] : (~ ! [X387 : (subst > term > term)] : (~ ! [X388 : subst,X389 : subst,X390 : term] : (((X387 @ (comp @ X389 @ X388) @ (sub @ X390 @ X388))) = ((sub @ (X387 @ X389 @ X390) @ X388))) | ~ ! [X391 : term] : (~ (((X385 @ id @ X391 @ id)) = $true) | (((X385 @ id @ (X387 @ id @ X391) @ id)) = $true)) | (((X385 @ id @ (lam @ (X387 @ sh @ one)) @ id)) = $true)) | ~ ! [X392 : term] : (~ (((X385 @ id @ X392 @ id)) = $true) | (((X385 @ id @ (sub @ X386 @ (push @ X392 @ id)) @ id)) = $true)) | (((X385 @ id @ (lam @ X386) @ id)) = $true)) <=> (hoasinduction_lem3a = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((! [X393 : subst] : (((comp @ X393 @ id)) = X393) & ! [X394 : subst] : (((comp @ id @ X394)) = X394)) <=> (substmonoid = $true)) & ! [X395 : d_subst] : (d_id = X395) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X396 : term] : (((sub @ X396 @ id)) = X396) => ! [X397 : (term > $o),X398 : (subst > term > subst > $o),X399 : term] : (~ ! [X400 : (subst > term > term)] : ((((X398 @ id @ (lam @ (X400 @ sh @ one)) @ id)) = $true) | ~ ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X403 @ X401) @ (sub @ X402 @ X401))) = ((sub @ (X400 @ X403 @ X402) @ X401))) | ~ ! [X404 : term] : ((((X398 @ id @ (X400 @ id @ X404) @ id)) = $true) | ~ (((X398 @ id @ X404 @ id)) = $true))) | ~ ! [X405 : term] : ((((X397 @ (sub @ X399 @ (push @ X405 @ id)))) = $true) | ~ (((X397 @ X405)) = $true)) | ~ ! [X406 : subst,X407 : subst,X408 : subst,X409 : term] : (~ (((X398 @ (comp @ X407 @ X406) @ (sub @ X409 @ X406) @ X408)) = $true) | (((X398 @ X407 @ X409 @ (comp @ X406 @ X408))) = $true)) | ~ ! [X410 : term,X411 : subst,X412 : subst,X413 : subst] : (($true = ((X398 @ (comp @ X413 @ X412) @ (sub @ X410 @ X412) @ X411))) | ~ (((X398 @ X413 @ X410 @ (comp @ X412 @ X411))) = $true)) | ~ ! [X414 : term] : (((X397 @ X414)) = ((X398 @ id @ X414 @ id))) | ($true = ((X397 @ (lam @ X399))))))) & (! [X415 : term,X416 : term,X417 : term,X418 : term] : ((((ap @ X415 @ X416)) != ((ap @ X417 @ X418))) | (X415 = X417)) <=> (apinj1 = $true)) & (! [X419 : term,X420 : (subst > term > term),X421 : term] : (~ ! [X422 : term,X423 : subst,X424 : subst] : (((sub @ (X420 @ X424 @ X422) @ X423)) = ((X420 @ (comp @ X424 @ X423) @ (sub @ X422 @ X423)))) | (((lam @ (X420 @ sh @ one))) != ((ap @ (sub @ X421 @ id) @ X419)))) <=> (hoaslamnotap = $true)) & (! [X425 : term,X426 : term,X427 : term,X428 : term] : ((X425 = X427) | (((ap @ (sub @ X428 @ id) @ X425)) != ((ap @ (sub @ X426 @ id) @ X427)))) <=> (hoasapinj2 = $true)) & (((d2subst @ d_id)) = id) & (hoaslamnotap_gthm = $true) & (one = ((d2term @ d_one))) & ((shinj = $true) <=> ! [X429 : term,X430 : term] : ((X429 = X430) | (((sub @ X430 @ sh)) != ((sub @ X429 @ sh))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((induction2lem = $true) <=> ! [X431 : subst,X432 : (term > $o),X433 : term] : (~ ! [X434 : term] : (($true = ((X432 @ (lam @ X434)))) | ~ ! [X435 : term] : (~ (((X432 @ X435)) = $true) | (((X432 @ (sub @ X434 @ (push @ X435 @ id)))) = $true))) | (((X432 @ (sub @ X433 @ X431))) = $true) | ~ ! [X436 : term] : (~ (((var @ X436)) = $true) | ($true = ((X432 @ (sub @ X436 @ X431))))) | ~ ! [X437 : term,X438 : term] : (~ ($true = ((X432 @ X438))) | ~ ($true = ((X432 @ X437))) | (((X432 @ (ap @ X437 @ X438))) = $true)))) & ((hoasapinj1 = $true) <=> ! [X439 : term,X440 : term,X441 : term,X442 : term] : ((X439 = X441) | (((ap @ (sub @ X441 @ id) @ X442)) != ((ap @ (sub @ X439 @ id) @ X440))))) & (axclos = $true) & ((! [X443 : term] : (((sub @ X443 @ id)) = X443) => (! [X444 : (subst > term > subst > $o),X445 : term] : (~ ! [X446 : (subst > term > term)] : (($true = ((X444 @ id @ (lam @ (X446 @ sh @ one)) @ id))) | ~ ! [X447 : term] : (~ (((X444 @ id @ X447 @ id)) = $true) | (((X444 @ id @ (X446 @ id @ X447) @ id)) = $true)) | ~ ! [X448 : subst,X449 : subst,X450 : term] : (((sub @ (X446 @ X448 @ X450) @ X449)) = ((X446 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449))))) | ~ ! [X451 : term] : (~ (((X444 @ id @ X451 @ id)) = $true) | ($true = ((X444 @ id @ (sub @ X445 @ (push @ X451 @ id)) @ id)))) | (((X444 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) = $true)) => ! [X452 : (subst > term > subst > $o),X453 : term] : (~ ! [X454 : term] : ((((X452 @ id @ (sub @ X453 @ (push @ X454 @ id)) @ id)) = $true) | ~ (((X452 @ id @ X454 @ id)) = $true)) | (((X452 @ id @ (lam @ X453) @ id)) = $true) | ~ ! [X455 : (subst > term > term)] : (~ ! [X456 : term] : ((((X452 @ id @ (X455 @ id @ X456) @ id)) = $true) | ~ (((X452 @ id @ X456 @ id)) = $true)) | ~ ! [X457 : term,X458 : subst,X459 : subst] : (((sub @ (X455 @ X458 @ X457) @ X459)) = ((X455 @ (comp @ X458 @ X459) @ (sub @ X457 @ X459)))) | (((X452 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((! [X460 : subst] : (((comp @ id @ X460)) = X460) => (! [X461 : subst] : (((comp @ X461 @ id)) = X461) => (! [X462 : subst] : (((comp @ X462 @ id)) = X462) & ! [X463 : subst] : (((comp @ id @ X463)) = X463)))) <=> (substmonoid_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (ulamvarsh = $true) & ((! [X464 : (subst > term > subst > $o)] : ~ ! [X465 : (term > $o)] : ~ ! [X466 : term] : (((X465 @ X466)) = ((X464 @ id @ X466 @ id))) => (! [X467 : (term > $o),X468 : term] : ((((X467 @ X468)) = $true) | ~ ! [X469 : term] : (~ (((var @ X469)) = $true) | (((X467 @ X469)) = $true)) | ~ ! [X470 : term] : (~ ! [X471 : term] : (~ ($true = ((X467 @ X471))) | (((X467 @ (sub @ X470 @ (push @ X471 @ id)))) = $true)) | (((X467 @ (lam @ X470))) = $true)) | ~ ! [X472 : term,X473 : term] : (~ (((X467 @ X473)) = $true) | (((X467 @ (ap @ X472 @ X473))) = $true) | ~ ($true = ((X467 @ X472))))) => (! [X474 : term] : (((sub @ X474 @ id)) = X474) => (! [X475 : (subst > term > subst > $o),X476 : term,X477 : (term > $o)] : (~ ! [X478 : (subst > term > term)] : (~ ! [X479 : subst,X480 : subst,X481 : term] : (((sub @ (X478 @ X480 @ X481) @ X479)) = ((X478 @ (comp @ X480 @ X479) @ (sub @ X481 @ X479)))) | ~ ! [X482 : term] : (~ ($true = ((X475 @ id @ X482 @ id))) | (((X475 @ id @ (X478 @ id @ X482) @ id)) = $true)) | (((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id)) = $true)) | (((X477 @ (lam @ X476))) = $true) | ~ ! [X483 : term] : (($true = ((X477 @ (sub @ X476 @ (push @ X483 @ id))))) | ~ (((X477 @ X483)) = $true)) | ~ ! [X484 : term] : (((X477 @ X484)) = ((X475 @ id @ X484 @ id)))) => ! [X485 : (subst > term > subst > $o),X486 : term] : (~ ! [X487 : (subst > term > term)] : (~ ! [X488 : subst,X489 : subst,X490 : term] : (((X487 @ (comp @ X489 @ X488) @ (sub @ X490 @ X488))) = ((sub @ (X487 @ X489 @ X490) @ X488))) | ~ ! [X491 : term] : (($true = ((X485 @ id @ (X487 @ id @ X491) @ id))) | ~ ($true = ((X485 @ id @ X491 @ id)))) | (((X485 @ id @ (lam @ (X487 @ sh @ one)) @ id)) = $true)) | ~ ! [X492 : term,X493 : term] : ((((X485 @ id @ (ap @ (sub @ X493 @ id) @ X492) @ id)) = $true) | ~ (((X485 @ id @ X492 @ id)) = $true) | ~ (((X485 @ id @ X493 @ id)) = $true)) | ~ ! [X494 : term] : (~ (((var @ (sub @ X494 @ id))) = $true) | (((X485 @ id @ X494 @ id)) = $true)) | (((X485 @ id @ X486 @ id)) = $true) | ~ ! [X495 : term,X496 : subst,X497 : subst,X498 : subst] : (~ (((X485 @ (comp @ X498 @ X496) @ (sub @ X495 @ X496) @ X497)) = $true) | (((X485 @ X498 @ X495 @ (comp @ X496 @ X497))) = $true)) | ~ ! [X499 : term,X500 : subst,X501 : subst,X502 : subst] : (~ ($true = ((X485 @ X502 @ X499 @ (comp @ X500 @ X501)))) | (((X485 @ (comp @ X502 @ X500) @ (sub @ X499 @ X500) @ X501)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X503 : (term > $o),X504 : (term > $o),X505 : subst,X506 : term] : (~ (((X504 @ X506)) = $true) | ($true = ((X503 @ one))) | ~ ! [X507 : term] : (((X503 @ X507)) = ((X504 @ (sub @ X507 @ (push @ X506 @ X505)))))) <=> (pushprop_lem1v2 = $true)) & ((axshiftcons = $true) <=> ! [X508 : term,X509 : subst] : (((comp @ sh @ (push @ X508 @ X509))) = X509)) & ! [X510 : d_term,X511 : d_term] : ((((d2term @ X511)) = ((d2term @ X510))) => (X510 = X511)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X512 : term] : ~ ! [X513 : (subst > term > term)] : ~ ! [X514 : term,X515 : subst] : (((sub @ X512 @ (push @ X514 @ X515))) = ((X513 @ X515 @ X514)))) & (axapp = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> (! [X516 : term] : (((sub @ X516 @ id)) = X516) => (! [X517 : (term > $o),X518 : subst,X519 : term] : (~ ! [X520 : term] : (~ ! [X521 : term] : ((((X517 @ (sub @ X520 @ (push @ X521 @ id)))) = $true) | ~ ($true = ((X517 @ X521)))) | (((X517 @ (lam @ X520))) = $true)) | ~ ! [X522 : term,X523 : term] : (~ (((X517 @ X522)) = $true) | ~ (((X517 @ X523)) = $true) | ($true = ((X517 @ (ap @ X523 @ X522))))) | ~ ! [X524 : term] : ((((X517 @ (sub @ X524 @ X518))) = $true) | ~ ($true = ((var @ X524)))) | (((X517 @ (sub @ X519 @ X518))) = $true)) => ! [X525 : term,X526 : (term > $o)] : ((((X526 @ X525)) = $true) | ~ ! [X527 : term,X528 : term] : ((((X526 @ (ap @ X527 @ X528))) = $true) | ~ (((X526 @ X527)) = $true) | ~ ($true = ((X526 @ X528)))) | ~ ! [X529 : term] : (~ ! [X530 : term] : (~ (((X526 @ X530)) = $true) | (((X526 @ (sub @ X529 @ (push @ X530 @ id)))) = $true)) | (((X526 @ (lam @ X529))) = $true)) | ~ ! [X531 : term] : (~ (((var @ X531)) = $true) | ($true = ((X526 @ X531)))))))) & ((pushprop_lem0 = $true) <=> ! [X532 : (term > $o),X533 : subst,X534 : term] : ~ ! [X535 : (term > $o)] : ~ ! [X536 : term] : (((X532 @ (sub @ X536 @ (push @ X534 @ X533)))) = ((X535 @ X536)))) & ! [X537 : d_subst,X538 : d_subst] : ((((d2subst @ X538)) = ((d2subst @ X537))) => (X537 = X538)) & (substmonoid_gthm = $true) & (axabs = $true) & (! [X539 : term,X540 : term] : ((((lam @ X539)) != ((lam @ X540))) | (X539 = X540)) <=> (laminj = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X541 : term] : (((sub @ X541 @ id)) = X541) => (! [X542 : term,X543 : term,X544 : term,X545 : term] : ((((ap @ X544 @ X542)) != ((ap @ X545 @ X543))) | (X544 = X545)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((((ap @ (sub @ X547 @ id) @ X549)) != ((ap @ (sub @ X546 @ id) @ X548))) | (X546 = X547))))) & (hoaslamnotap_lthm = $true)),
% 3.80/0.85 inference(fool_elimination,[],[f6])).
% 3.80/0.85 thf(f8,plain,(
% 3.80/0.85 (pushprop_lem0 != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3)))))))))))),
% 3.80/0.85 inference(flattening,[],[f5])).
% 3.80/0.85 thf(f9,plain,(
% 3.80/0.85 ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : (~ (((var @ X5)) = $true) | (((X4 @ X5)) = $true)) | ~ ! [X6 : term,X7 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | ~ (((X4 @ X7)) = $true) | ~ (((X4 @ X6)) = $true)) | (((X4 @ X3)) = $true) | ~ ! [X8 : term] : (~ ! [X9 : term] : ((((X4 @ (sub @ X8 @ (push @ X9 @ id)))) = $true) | ~ (((X4 @ X9)) = $true)) | (((X4 @ (lam @ X8))) = $true))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : term,X13 : (term > $o)] : (~ ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))) | ~ ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | ~ (((X13 @ X15)) = $true)) | ~ ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X18 : subst,X19 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X19) @ X18)) = ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18)))) | ~ ! [X20 : term] : (~ (((X11 @ id @ X20 @ id)) = $true) | (((X11 @ id @ (X16 @ id @ X20) @ id)) = $true))) | (((X13 @ (lam @ X12))) = $true)) => ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ~ ! [X23 : (subst > term > term)] : (~ ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24)))) | ($true = ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) | ~ ! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | ~ (((X21 @ id @ X27 @ id)) = $true))) | ~ ! [X28 : term,X29 : term] : (~ (((X21 @ id @ X28 @ id)) = $true) | ~ (((X21 @ id @ X29 @ id)) = $true) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & (pushprop_lem1_gthm = $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)))))))))))) & (hoasapinj2_gthm = $true) & (! [X34 : (subst > term > subst > $o),X35 : term] : (~ ! [X36 : term] : (~ (((X34 @ id @ X36 @ id)) = $true) | (((X34 @ id @ (sub @ X35 @ (push @ X36 @ id)) @ id)) = $true)) | ~ ! [X37 : (subst > term > term)] : (~ ! [X38 : term] : ((((X34 @ id @ (X37 @ id @ X38) @ id)) = $true) | ~ ($true = ((X34 @ id @ X38 @ id)))) | (((X34 @ id @ (lam @ (X37 @ sh @ one)) @ id)) = $true) | ~ ! [X41 : subst,X39 : subst,X40 : term] : (((X37 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ (X37 @ X39 @ X40) @ X41)))) | (((X34 @ id @ (lam @ X35) @ id)) = $true) | ~ ! [X42 : term,X43 : subst,X44 : subst,X45 : subst] : (~ (((X34 @ X44 @ X42 @ (comp @ X43 @ X45))) = $true) | (((X34 @ (comp @ X44 @ X43) @ (sub @ X42 @ X43) @ X45)) = $true)) | ~ ! [X46 : subst,X47 : subst,X48 : subst,X49 : term] : ((((X34 @ X46 @ X49 @ (comp @ X48 @ X47))) = $true) | ~ (((X34 @ (comp @ X46 @ X48) @ (sub @ X49 @ X48) @ X47)) = $true))) <=> (hoasinduction_lem3 = $true)) & (pushprop_lem1v2_gthm = $true) & (! [X50 : (term > $o),X51 : term] : (~ ! [X52 : term] : ((((X50 @ (lam @ X52))) = $true) | ~ (((X50 @ X52)) = $true)) | ~ ! [X53 : term] : (~ (((var @ X53)) = $true) | (((X50 @ X53)) = $true)) | ~ ! [X54 : term,X55 : term] : (~ (((X50 @ X54)) = $true) | ~ (((X50 @ X55)) = $true) | (((X50 @ (ap @ X55 @ X54))) = $true)) | (((X50 @ X51)) = $true)) <=> (induction = $true)) & (hoasinduction_lem1v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X56 : term,X57 : (term > $o),X58 : (subst > term > subst > $o)] : (~ ! [X59 : term] : ((((X57 @ (sub @ X56 @ (push @ X59 @ id)))) = $true) | ~ (((X57 @ X59)) = $true)) | ~ ! [X60 : term,X61 : subst,X62 : subst,X63 : subst] : (~ (((X58 @ X61 @ X60 @ (comp @ X62 @ X63))) = $true) | ($true = ((X58 @ (comp @ X61 @ X62) @ (sub @ X60 @ X62) @ X63)))) | ~ ! [X64 : (subst > term > term)] : (~ ! [X66 : subst,X65 : term,X67 : subst] : (((sub @ (X64 @ X66 @ X65) @ X67)) = ((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) | (((X58 @ id @ (lam @ (X64 @ sh @ one)) @ id)) = $true) | ~ ! [X68 : term] : ((((X58 @ id @ (X64 @ id @ X68) @ id)) = $true) | ~ (((X58 @ id @ X68 @ id)) = $true))) | ($true = ((X57 @ (lam @ X56)))) | ~ ! [X69 : term,X70 : subst,X71 : subst,X72 : subst] : ((((X58 @ X70 @ X69 @ (comp @ X72 @ X71))) = $true) | ~ (((X58 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) = $true)) | ~ ! [X73 : term] : (((X58 @ id @ X73 @ id)) = ((X57 @ X73))))) & (hoaslamnotvar = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (induction2_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X75 : (subst > term > subst > $o),X76 : term,X77 : term] : ((((X75 @ id @ (ap @ X76 @ X77) @ id)) = $true) | ~ ($true = ((X75 @ id @ X76 @ id))) | ~ ! [X78 : term,X79 : term] : (~ (((X75 @ id @ X78 @ id)) = $true) | (((X75 @ id @ (ap @ (sub @ X79 @ id) @ X78) @ id)) = $true) | ~ (((X75 @ id @ X79 @ id)) = $true)) | ~ ! [X80 : subst,X81 : term,X82 : subst,X83 : subst] : (~ (((X75 @ X80 @ X81 @ (comp @ X82 @ X83))) = $true) | ($true = ((X75 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82) @ X83)))) | ~ ! [X84 : subst,X85 : subst,X86 : term,X87 : subst] : (~ (((X75 @ (comp @ X84 @ X87) @ (sub @ X86 @ X87) @ X85)) = $true) | ($true = ((X75 @ X84 @ X86 @ (comp @ X87 @ X85))))) | ~ ($true = ((X75 @ id @ X77 @ id))))) & (! [X90 : term,X88 : (term > $o),X89 : subst] : ~ ! [X91 : (term > $o)] : ~ ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92))) <=> (pushprop_lem0_lthm = $true)) & ~ (lamnotap = $true) & (pushprop_lthm_orig = $true) & (! [X93 : term] : ~ ! [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) != ((X94 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (! [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) = X96) => (! [X98 : term,X97 : subst] : (((comp @ sh @ (push @ X98 @ X97))) = X97) => (! [X100 : term,X99 : term] : ((((lam @ X99)) != ((lam @ X100))) | (X99 = X100)) => ! [X103 : term,X104 : (subst > term > term),X102 : (subst > term > term),X101 : subst] : ((((X104 @ X101 @ X103)) = ((X102 @ X101 @ X103))) | ~ ! [X107 : term,X105 : subst,X106 : subst] : (((X104 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) = ((sub @ (X104 @ X105 @ X107) @ X106))) | ~ ! [X110 : subst,X108 : subst,X109 : term] : (((X102 @ (comp @ X110 @ X108) @ (sub @ X109 @ X108))) = ((sub @ (X102 @ X110 @ X109) @ X108))) | (((lam @ (X104 @ sh @ one))) != ((lam @ (X102 @ sh @ one))))))))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) => ! [X113 : (term > $o),X114 : (term > $o),X115 : subst,X116 : term] : (~ (((X113 @ X116)) = $true) | (((X114 @ one)) = $true) | ~ ! [X117 : term] : (((X114 @ X117)) = ((X113 @ (sub @ X117 @ (push @ X116 @ X115)))))))) & ((hoasinduction_lthm = $true) <=> (! [X118 : (term > $o),X119 : term] : (($true = ((X118 @ X119))) | ~ ! [X120 : term,X121 : term] : (~ (((X118 @ X120)) = $true) | (((X118 @ (ap @ X120 @ X121))) = $true) | ~ ($true = ((X118 @ X121)))) | ~ ! [X122 : term] : ((((X118 @ (lam @ X122))) = $true) | ~ ! [X123 : term] : ((((X118 @ (sub @ X122 @ (push @ X123 @ id)))) = $true) | ~ ($true = ((X118 @ X123))))) | ~ ! [X124 : term] : (~ ($true = ((var @ X124))) | (((X118 @ X124)) = $true))) => (! [X125 : term,X126 : term,X127 : (subst > term > subst > $o)] : (~ ! [X128 : subst,X129 : subst,X130 : subst,X131 : term] : (($true = ((X127 @ (comp @ X128 @ X129) @ (sub @ X131 @ X129) @ X130))) | ~ (((X127 @ X128 @ X131 @ (comp @ X129 @ X130))) = $true)) | ($true = ((X127 @ id @ (ap @ X125 @ X126) @ id))) | ~ ! [X132 : subst,X133 : subst,X134 : subst,X135 : term] : (($true = ((X127 @ X132 @ X135 @ (comp @ X133 @ X134)))) | ~ (((X127 @ (comp @ X132 @ X133) @ (sub @ X135 @ X133) @ X134)) = $true)) | ~ (((X127 @ id @ X126 @ id)) = $true) | ~ ! [X136 : term,X137 : term] : (~ (((X127 @ id @ X136 @ id)) = $true) | (((X127 @ id @ (ap @ (sub @ X137 @ id) @ X136) @ id)) = $true) | ~ ($true = ((X127 @ id @ X137 @ id)))) | ~ (((X127 @ id @ X125 @ id)) = $true)) => (! [X138 : term,X139 : (subst > term > subst > $o)] : ((((X139 @ id @ (lam @ X138) @ id)) = $true) | ~ ! [X140 : term,X141 : subst,X142 : subst,X143 : subst] : (~ ($true = ((X139 @ (comp @ X141 @ X143) @ (sub @ X140 @ X143) @ X142))) | (((X139 @ X141 @ X140 @ (comp @ X143 @ X142))) = $true)) | ~ ! [X144 : term] : (~ (((X139 @ id @ X144 @ id)) = $true) | (((X139 @ id @ (sub @ X138 @ (push @ X144 @ id)) @ id)) = $true)) | ~ ! [X145 : (subst > term > term)] : (~ ! [X146 : term] : (~ (((X139 @ id @ X146 @ id)) = $true) | (((X139 @ id @ (X145 @ id @ X146) @ id)) = $true)) | ($true = ((X139 @ id @ (lam @ (X145 @ sh @ one)) @ id))) | ~ ! [X147 : subst,X149 : term,X148 : subst] : (((sub @ (X145 @ X147 @ X149) @ X148)) = ((X145 @ (comp @ X147 @ X148) @ (sub @ X149 @ X148))))) | ~ ! [X150 : subst,X151 : subst,X152 : term,X153 : subst] : ((((X139 @ (comp @ X150 @ X151) @ (sub @ X152 @ X151) @ X153)) = $true) | ~ (((X139 @ X150 @ X152 @ (comp @ X151 @ X153))) = $true))) => ! [X154 : (subst > term > subst > $o),X155 : term] : (~ ! [X156 : term] : (($true = ((X154 @ id @ X156 @ id))) | ~ ($true = ((var @ (sub @ X156 @ id))))) | ~ ! [X157 : subst,X158 : subst,X159 : subst,X160 : term] : (~ ($true = ((X154 @ (comp @ X157 @ X158) @ (sub @ X160 @ X158) @ X159))) | (((X154 @ X157 @ X160 @ (comp @ X158 @ X159))) = $true)) | ~ ! [X161 : subst,X162 : term,X163 : subst,X164 : subst] : ((((X154 @ (comp @ X161 @ X164) @ (sub @ X162 @ X164) @ X163)) = $true) | ~ (((X154 @ X161 @ X162 @ (comp @ X164 @ X163))) = $true)) | ~ ! [X165 : (subst > term > term)] : (~ ! [X167 : subst,X166 : term,X168 : subst] : (((X165 @ (comp @ X168 @ X167) @ (sub @ X166 @ X167))) = ((sub @ (X165 @ X168 @ X166) @ X167))) | (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) = $true) | ~ ! [X169 : term] : ((((X154 @ id @ (X165 @ id @ X169) @ id)) = $true) | ~ (((X154 @ id @ X169 @ id)) = $true))) | ~ ! [X170 : term,X171 : term] : (~ (((X154 @ id @ X171 @ id)) = $true) | (((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)) = $true) | ~ (((X154 @ id @ X170 @ id)) = $true)) | (((X154 @ id @ X155 @ id)) = $true)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X172 : term,X173 : (subst > term > subst > $o)] : ((((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X174 : term] : (($true = ((X173 @ id @ (sub @ X172 @ (push @ X174 @ id)) @ id))) | ~ ($true = ((X173 @ id @ X174 @ id)))) | ~ ! [X175 : (subst > term > term)] : (~ ! [X176 : term] : (~ (((X173 @ id @ X176 @ id)) = $true) | (((X173 @ id @ (X175 @ id @ X176) @ id)) = $true)) | (((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id)) = $true) | ~ ! [X179 : subst,X177 : subst,X178 : term] : (((X175 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179))) = ((sub @ (X175 @ X177 @ X178) @ X179)))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X180 : term,X181 : (subst > term > subst > $o),X182 : (term > $o)] : (~ ! [X183 : (subst > term > term)] : (~ ! [X186 : subst,X185 : subst,X184 : term] : (((sub @ (X183 @ X185 @ X184) @ X186)) = ((X183 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)))) | ~ ! [X187 : term] : (~ (((X181 @ id @ X187 @ id)) = $true) | (((X181 @ id @ (X183 @ id @ X187) @ id)) = $true)) | ($true = ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id)))) | (((X182 @ (lam @ X180))) = $true) | ~ ! [X188 : term] : (((X181 @ id @ X188 @ id)) = ((X182 @ X188))) | ~ ! [X189 : term] : ((((X182 @ (sub @ X180 @ (push @ X189 @ id)))) = $true) | ~ (((X182 @ X189)) = $true)))) & (apnotvar = $true) & (hoasapnotvar = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X190 : term,X191 : (subst > term > subst > $o)] : (($true = ((X191 @ id @ X190 @ id))) | ~ ! [X192 : (subst > term > term)] : (~ ! [X193 : term] : (~ (((X191 @ id @ X193 @ id)) = $true) | (((X191 @ id @ (X192 @ id @ X193) @ id)) = $true)) | ~ ! [X196 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X196) @ (sub @ X194 @ X196))) = ((sub @ (X192 @ X195 @ X194) @ X196))) | (((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id)) = $true)) | ~ ! [X197 : term,X198 : term] : (~ (((X191 @ id @ X197 @ id)) = $true) | ~ (((X191 @ id @ X198 @ id)) = $true) | (((X191 @ id @ (ap @ (sub @ X198 @ id) @ X197) @ id)) = $true)))) & (axvarshift = $true) & ((hoasinduction_lem0 = $true) <=> ! [X199 : (subst > term > subst > $o)] : ~ ! [X200 : (term > $o)] : ~ ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id)))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X202 : (subst > term > subst > $o)] : ~ ! [X203 : (term > $o)] : ~ ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) <=> (axvarcons = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X207 : term,X208 : (term > $o),X209 : (subst > term > subst > $o),X210 : term] : (~ ! [X211 : subst,X212 : term,X213 : subst,X214 : subst] : ((((X209 @ X213 @ X212 @ (comp @ X211 @ X214))) = $true) | ~ (((X209 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211) @ X214)) = $true)) | ~ (((X208 @ X207)) = $true) | ~ ! [X215 : term] : (((X209 @ id @ X215 @ id)) = ((X208 @ X215))) | ($true = ((X208 @ (ap @ X207 @ X210)))) | ~ ! [X216 : term,X217 : subst,X218 : subst,X219 : subst] : (~ (((X209 @ X218 @ X216 @ (comp @ X217 @ X219))) = $true) | (((X209 @ (comp @ X218 @ X217) @ (sub @ X216 @ X217) @ X219)) = $true)) | ~ (((X208 @ X210)) = $true) | ~ ! [X220 : term,X221 : term] : (~ (((X209 @ id @ X221 @ id)) = $true) | ~ ($true = ((X209 @ id @ X220 @ id))) | (((X209 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) = $true)))) & (pushprop_lem2v2_gthm = $true) & ((! [X222 : term,X224 : term,X223 : term,X225 : term] : ((X222 = X225) | (((ap @ X224 @ X222)) != ((ap @ X223 @ X225)))) => ! [X229 : term,X227 : term,X228 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X227)) != ((ap @ (sub @ X229 @ id) @ X228))) | (X227 = X228))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X230 : term,X231 : (subst > term > subst > $o)] : ((((X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X232 : term] : ((((X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) = $true) | ~ (((X231 @ id @ X232 @ id)) = $true)) | ~ ! [X233 : (subst > term > term)] : ((((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) = $true) | ~ ! [X234 : subst,X235 : subst,X236 : term] : (((X233 @ (comp @ X234 @ X235) @ (sub @ X236 @ X235))) = ((sub @ (X233 @ X234 @ X236) @ X235))) | ~ ! [X237 : term] : (~ (((X231 @ id @ X237 @ id)) = $true) | (((X231 @ id @ (X233 @ id @ X237) @ id)) = $true))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X238 : term] : ~ ! [X239 : (subst > term > term)] : ~ ! [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) = ((X239 @ X241 @ X240))) => (! [X242 : term] : (((sub @ X242 @ id)) = X242) => ! [X243 : (subst > term > subst > $o),X244 : term,X245 : (term > $o)] : (~ ! [X246 : term] : (((X245 @ X246)) = ((X243 @ id @ X246 @ id))) | (((X245 @ (lam @ X244))) = $true) | ~ ! [X247 : term] : (~ (((X245 @ X247)) = $true) | (((X245 @ (sub @ X244 @ (push @ X247 @ id)))) = $true)) | ~ ! [X248 : (subst > term > term)] : ((((X243 @ id @ (lam @ (X248 @ sh @ one)) @ id)) = $true) | ~ ! [X249 : term] : ((((X243 @ id @ (X248 @ id @ X249) @ id)) = $true) | ~ (((X243 @ id @ X249 @ id)) = $true)) | ~ ! [X251 : subst,X250 : term,X252 : subst] : (((sub @ (X248 @ X252 @ X250) @ X251)) = ((X248 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251))))))))) & (axassoc = $true) & ((hoasinduction = $true) <=> ! [X253 : term,X254 : (subst > term > subst > $o)] : (~ ! [X255 : subst,X256 : subst,X257 : term,X258 : subst] : ((((X254 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) = $true) | ~ ($true = ((X254 @ X258 @ X257 @ (comp @ X256 @ X255))))) | ~ ! [X259 : (subst > term > term)] : (~ ! [X261 : term,X260 : subst,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) | ~ ! [X263 : term] : (~ (((X254 @ id @ X263 @ id)) = $true) | ($true = ((X254 @ id @ (X259 @ id @ X263) @ id)))) | (((X254 @ id @ (lam @ (X259 @ sh @ one)) @ id)) = $true)) | ~ ! [X264 : term] : (~ (((var @ (sub @ X264 @ id))) = $true) | (((X254 @ id @ X264 @ id)) = $true)) | ~ ! [X265 : subst,X266 : subst,X267 : subst,X268 : term] : (~ (((X254 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true) | (((X254 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true)) | (((X254 @ id @ X253 @ id)) = $true) | ~ ! [X269 : term,X270 : term] : ((((X254 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)) = $true) | ~ (((X254 @ id @ X270 @ id)) = $true) | ~ ($true = ((X254 @ id @ X269 @ id)))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvarind = $true) & (hoasapinj1_gthm = $true) & ((hoaslaminj = $true) <=> ! [X271 : (subst > term > term),X274 : subst,X272 : (subst > term > term),X273 : term] : (~ ! [X276 : term,X277 : subst,X275 : subst] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) = ((sub @ (X271 @ X275 @ X276) @ X277))) | (((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ~ ! [X278 : subst,X279 : term,X280 : subst] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) = ((sub @ (X272 @ X280 @ X279) @ X278))))) & ((pushprop_lem1_lthm = $true) <=> (! [X281 : term,X282 : subst] : (((sub @ one @ (push @ X281 @ X282))) = X281) => (! [X284 : term,X283 : subst] : (((comp @ sh @ (push @ X284 @ X283))) = X283) => ! [X285 : term,X286 : (term > $o),X287 : subst,X288 : (term > $o),X289 : term] : (~ ($true = ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true))))) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (axmap = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & ! [X292 : d_term] : (d_one = X292) & ((! [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) = X294) => (! [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) = X296) => (! [X297 : subst] : (((comp @ X297 @ id)) = X297) => (! [X298 : (term > $o),X299 : term] : (~ ! [X300 : term] : (~ (((X298 @ X300)) = $true) | (((X298 @ (lam @ X300))) = $true)) | ~ ! [X301 : term] : (($true = ((X298 @ X301))) | ~ ($true = ((var @ X301)))) | ($true = ((X298 @ X299))) | ~ ! [X302 : term,X303 : term] : (($true = ((X298 @ (ap @ X302 @ X303)))) | ~ (((X298 @ X302)) = $true) | ~ (((X298 @ X303)) = $true))) => ! [X304 : subst,X305 : (term > $o),X306 : term] : ((((X305 @ (sub @ X306 @ X304))) = $true) | ~ ! [X307 : term] : (~ ! [X308 : term] : ((((X305 @ (sub @ X307 @ (push @ X308 @ id)))) = $true) | ~ (((X305 @ X308)) = $true)) | (((X305 @ (lam @ X307))) = $true)) | ~ ! [X309 : term] : (~ ($true = ((var @ X309))) | (((X305 @ (sub @ X309 @ X304))) = $true)) | ~ ! [X310 : term,X311 : term] : ((((X305 @ (ap @ X310 @ X311))) = $true) | ~ (((X305 @ X310)) = $true) | ~ ($true = ((X305 @ X311))))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & ((termmset = $true) <=> ! [X313 : term] : (((sub @ X313 @ id)) = X313)) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_gthm = $true) & (hoasapnotvar_gthm = $true) & ((! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X315 : (subst > term > subst > $o),X316 : term] : (~ ! [X317 : (subst > term > term)] : (($true = ((X315 @ id @ (lam @ (X317 @ sh @ one)) @ id))) | ~ ! [X318 : term] : (~ ($true = ((X315 @ id @ X318 @ id))) | ($true = ((X315 @ id @ (X317 @ id @ X318) @ id)))) | ~ ! [X321 : subst,X319 : subst,X320 : term] : (((X317 @ (comp @ X319 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X317 @ X319 @ X320) @ X321)))) | ($true = ((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id))) | ~ ! [X322 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X322 @ id)) @ id)) = $true) | ~ ($true = ((X315 @ id @ X322 @ id))))) => ! [X323 : (subst > term > subst > $o),X324 : term] : (~ ! [X325 : term] : (~ ($true = ((X323 @ id @ X325 @ id))) | (((X323 @ id @ (sub @ X324 @ (push @ X325 @ id)) @ id)) = $true)) | ~ ! [X326 : subst,X327 : subst,X328 : subst,X329 : term] : (($true = ((X323 @ X328 @ X329 @ (comp @ X327 @ X326)))) | ~ (((X323 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327) @ X326)) = $true)) | ~ ! [X330 : (subst > term > term)] : (~ ! [X331 : subst,X332 : subst,X333 : term] : (((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))) = ((sub @ (X330 @ X331 @ X333) @ X332))) | ~ ! [X334 : term] : ((((X323 @ id @ (X330 @ id @ X334) @ id)) = $true) | ~ (((X323 @ id @ X334 @ id)) = $true)) | (((X323 @ id @ (lam @ (X330 @ sh @ one)) @ id)) = $true)) | ~ ! [X335 : subst,X336 : term,X337 : subst,X338 : subst] : (~ (((X323 @ X338 @ X336 @ (comp @ X337 @ X335))) = $true) | (((X323 @ (comp @ X338 @ X337) @ (sub @ X336 @ X337) @ X335)) = $true)) | (((X323 @ id @ (lam @ X324) @ id)) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) <=> (axidr = $true)) & (! [X340 : term,X341 : (term > $o),X342 : (term > $o),X343 : subst,X344 : term] : ((((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true) | ~ ($true = ((X342 @ X340)))) <=> (pushprop_lem1 = $true)) & ((! [X345 : term] : (((sub @ X345 @ id)) = X345) => ! [X346 : term] : (((sub @ X346 @ id)) = X346)) <=> (termmset_lthm = $true)) & (lamnotvar = $true) & (! [X347 : term] : ~ ! [X348 : (subst > term > term)] : ~ ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((induction2 = $true) <=> ! [X351 : term,X352 : (term > $o)] : (~ ! [X353 : term] : ((((X352 @ X353)) = $true) | ~ (((var @ X353)) = $true)) | ($true = ((X352 @ X351))) | ~ ! [X354 : term] : ((((X352 @ (lam @ X354))) = $true) | ~ ! [X355 : term] : ((((X352 @ (sub @ X354 @ (push @ X355 @ id)))) = $true) | ~ (((X352 @ X355)) = $true))) | ~ ! [X356 : term,X357 : term] : (($true = ((X352 @ (ap @ X357 @ X356)))) | ~ (((X352 @ X357)) = $true) | ~ ($true = ((X352 @ X356)))))) & ~ (ulamvar1 = $true) & (! [X358 : term] : ~ ! [X359 : (subst > term > term)] : (((X359 @ sh @ one)) != ((sub @ X358 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop = $true) & (! [X360 : (subst > term > subst > $o),X361 : term] : ((((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X362 : (subst > term > term),X363 : term] : (~ ! [X366 : subst,X365 : subst,X364 : term] : (((sub @ (sub @ X363 @ (push @ X364 @ X366)) @ X365)) = ((sub @ (X362 @ X366 @ X364) @ X365))) | (((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) = $true) | ~ ! [X368 : term,X369 : subst,X367 : subst] : (((sub @ X363 @ (push @ (sub @ X368 @ X367) @ (comp @ X369 @ X367)))) = ((X362 @ (comp @ X369 @ X367) @ (sub @ X368 @ X367)))) | ~ ! [X370 : term] : ((((X360 @ id @ (X362 @ id @ X370) @ id)) = $true) | ~ (((X360 @ id @ X370 @ id)) = $true))) | ~ ! [X371 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X371 @ id)) @ id)) = $true) | ~ ($true = ((X360 @ id @ X371 @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((axidl = $true) <=> ! [X372 : subst] : (((comp @ id @ X372)) = X372)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar_lthm = $true) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & (hoasinduction_lem2_lthm = $true) & (! [X375 : (subst > term > subst > $o),X376 : term] : (~ ! [X377 : (subst > term > term)] : (~ ! [X379 : subst,X380 : term,X378 : subst] : (((X377 @ (comp @ X379 @ X378) @ (sub @ X380 @ X378))) = ((sub @ (X377 @ X379 @ X380) @ X378))) | ~ ! [X381 : term] : (~ ($true = ((X375 @ id @ X381 @ id))) | (((X375 @ id @ (X377 @ id @ X381) @ id)) = $true)) | ($true = ((X375 @ id @ (lam @ (X377 @ sh @ one)) @ id)))) | ~ ! [X382 : term] : (~ (((X375 @ id @ X382 @ id)) = $true) | (((X375 @ id @ (sub @ X376 @ (push @ X382 @ id)) @ id)) = $true)) | ($true = ((X375 @ id @ (lam @ X376) @ id)))) <=> (hoasinduction_lem3a = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((substmonoid = $true) <=> (! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384))) & ! [X385 : d_subst] : (d_id = X385) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X386 : term] : (((sub @ X386 @ id)) = X386) => ! [X387 : (term > $o),X388 : (subst > term > subst > $o),X389 : term] : (~ ! [X390 : (subst > term > term)] : ((((X388 @ id @ (lam @ (X390 @ sh @ one)) @ id)) = $true) | ~ ! [X393 : subst,X391 : subst,X392 : term] : (((X390 @ (comp @ X393 @ X391) @ (sub @ X392 @ X391))) = ((sub @ (X390 @ X393 @ X392) @ X391))) | ~ ! [X394 : term] : (($true = ((X388 @ id @ (X390 @ id @ X394) @ id))) | ~ ($true = ((X388 @ id @ X394 @ id))))) | ~ ! [X395 : term] : ((((X387 @ (sub @ X389 @ (push @ X395 @ id)))) = $true) | ~ (((X387 @ X395)) = $true)) | ~ ! [X396 : subst,X397 : subst,X398 : subst,X399 : term] : (~ (((X388 @ (comp @ X397 @ X396) @ (sub @ X399 @ X396) @ X398)) = $true) | (((X388 @ X397 @ X399 @ (comp @ X396 @ X398))) = $true)) | ~ ! [X400 : term,X401 : subst,X402 : subst,X403 : subst] : (($true = ((X388 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))) | ~ (((X388 @ X403 @ X400 @ (comp @ X402 @ X401))) = $true)) | ~ ! [X404 : term] : (((X388 @ id @ X404 @ id)) = ((X387 @ X404))) | (((X387 @ (lam @ X389))) = $true)))) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) <=> (apinj1 = $true)) & (! [X411 : term,X409 : term,X410 : (subst > term > term)] : (~ ! [X413 : subst,X414 : subst,X412 : term] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409)))) <=> (hoaslamnotap = $true)) & ((hoasapinj2 = $true) <=> ! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417))) & (((d2subst @ d_id)) = id) & (hoaslamnotap_gthm = $true) & (one = ((d2term @ d_one))) & ((shinj = $true) <=> ! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((induction2lem = $true) <=> ! [X421 : subst,X422 : (term > $o),X423 : term] : (~ ! [X424 : term] : ((((X422 @ (lam @ X424))) = $true) | ~ ! [X425 : term] : (~ (((X422 @ X425)) = $true) | (((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true))) | ($true = ((X422 @ (sub @ X423 @ X421)))) | ~ ! [X426 : term] : (~ (((var @ X426)) = $true) | (((X422 @ (sub @ X426 @ X421))) = $true)) | ~ ! [X427 : term,X428 : term] : (~ ($true = ((X422 @ X428))) | ~ ($true = ((X422 @ X427))) | (((X422 @ (ap @ X427 @ X428))) = $true)))) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) <=> (hoasapinj1 = $true)) & (axclos = $true) & ((! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X434 : (subst > term > subst > $o),X435 : term] : (~ ! [X436 : (subst > term > term)] : ((((X434 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ~ ! [X437 : term] : (~ ($true = ((X434 @ id @ X437 @ id))) | ($true = ((X434 @ id @ (X436 @ id @ X437) @ id)))) | ~ ! [X440 : term,X439 : subst,X438 : subst] : (((sub @ (X436 @ X438 @ X440) @ X439)) = ((X436 @ (comp @ X438 @ X439) @ (sub @ X440 @ X439))))) | ~ ! [X441 : term] : (~ ($true = ((X434 @ id @ X441 @ id))) | ($true = ((X434 @ id @ (sub @ X435 @ (push @ X441 @ id)) @ id)))) | (((X434 @ id @ (lam @ (sub @ X435 @ (push @ one @ sh))) @ id)) = $true)) => ! [X442 : (subst > term > subst > $o),X443 : term] : (~ ! [X444 : term] : (($true = ((X442 @ id @ (sub @ X443 @ (push @ X444 @ id)) @ id))) | ~ ($true = ((X442 @ id @ X444 @ id)))) | (((X442 @ id @ (lam @ X443) @ id)) = $true) | ~ ! [X445 : (subst > term > term)] : (~ ! [X446 : term] : ((((X442 @ id @ (X445 @ id @ X446) @ id)) = $true) | ~ (((X442 @ id @ X446 @ id)) = $true)) | ~ ! [X447 : term,X449 : subst,X448 : subst] : (((sub @ (X445 @ X448 @ X447) @ X449)) = ((X445 @ (comp @ X448 @ X449) @ (sub @ X447 @ X449)))) | ($true = ((X442 @ id @ (lam @ (X445 @ sh @ one)) @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((substmonoid_lthm = $true) <=> (! [X450 : subst] : (((comp @ id @ X450)) = X450) => (! [X451 : subst] : (((comp @ X451 @ id)) = X451) => (! [X452 : subst] : (((comp @ X452 @ id)) = X452) & ! [X453 : subst] : (((comp @ id @ X453)) = X453))))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (ulamvarsh = $true) & ((! [X454 : (subst > term > subst > $o)] : ~ ! [X455 : (term > $o)] : ~ ! [X456 : term] : (((X455 @ X456)) = ((X454 @ id @ X456 @ id))) => (! [X457 : (term > $o),X458 : term] : ((((X457 @ X458)) = $true) | ~ ! [X459 : term] : (~ ($true = ((var @ X459))) | (((X457 @ X459)) = $true)) | ~ ! [X460 : term] : (~ ! [X461 : term] : (~ (((X457 @ X461)) = $true) | ($true = ((X457 @ (sub @ X460 @ (push @ X461 @ id)))))) | (((X457 @ (lam @ X460))) = $true)) | ~ ! [X462 : term,X463 : term] : (~ ($true = ((X457 @ X463))) | ($true = ((X457 @ (ap @ X462 @ X463)))) | ~ ($true = ((X457 @ X462))))) => (! [X464 : term] : (((sub @ X464 @ id)) = X464) => (! [X465 : (subst > term > subst > $o),X466 : term,X467 : (term > $o)] : (~ ! [X468 : (subst > term > term)] : (~ ! [X470 : subst,X469 : subst,X471 : term] : (((sub @ (X468 @ X470 @ X471) @ X469)) = ((X468 @ (comp @ X470 @ X469) @ (sub @ X471 @ X469)))) | ~ ! [X472 : term] : (~ (((X465 @ id @ X472 @ id)) = $true) | (((X465 @ id @ (X468 @ id @ X472) @ id)) = $true)) | (((X465 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true)) | (((X467 @ (lam @ X466))) = $true) | ~ ! [X473 : term] : ((((X467 @ (sub @ X466 @ (push @ X473 @ id)))) = $true) | ~ (((X467 @ X473)) = $true)) | ~ ! [X474 : term] : (((X467 @ X474)) = ((X465 @ id @ X474 @ id)))) => ! [X475 : (subst > term > subst > $o),X476 : term] : (~ ! [X477 : (subst > term > term)] : (~ ! [X478 : subst,X479 : subst,X480 : term] : (((X477 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478))) = ((sub @ (X477 @ X479 @ X480) @ X478))) | ~ ! [X481 : term] : ((((X475 @ id @ (X477 @ id @ X481) @ id)) = $true) | ~ ($true = ((X475 @ id @ X481 @ id)))) | (((X475 @ id @ (lam @ (X477 @ sh @ one)) @ id)) = $true)) | ~ ! [X482 : term,X483 : term] : ((((X475 @ id @ (ap @ (sub @ X483 @ id) @ X482) @ id)) = $true) | ~ ($true = ((X475 @ id @ X482 @ id))) | ~ (((X475 @ id @ X483 @ id)) = $true)) | ~ ! [X484 : term] : (~ (((var @ (sub @ X484 @ id))) = $true) | ($true = ((X475 @ id @ X484 @ id)))) | (((X475 @ id @ X476 @ id)) = $true) | ~ ! [X485 : term,X486 : subst,X487 : subst,X488 : subst] : (~ (((X475 @ (comp @ X488 @ X486) @ (sub @ X485 @ X486) @ X487)) = $true) | (((X475 @ X488 @ X485 @ (comp @ X486 @ X487))) = $true)) | ~ ! [X489 : term,X490 : subst,X491 : subst,X492 : subst] : (~ (((X475 @ X492 @ X489 @ (comp @ X490 @ X491))) = $true) | (((X475 @ (comp @ X492 @ X490) @ (sub @ X489 @ X490) @ X491)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X493 : (term > $o),X494 : (term > $o),X495 : subst,X496 : term] : (~ (((X494 @ X496)) = $true) | ($true = ((X493 @ one))) | ~ ! [X497 : term] : (((X493 @ X497)) = ((X494 @ (sub @ X497 @ (push @ X496 @ X495)))))) <=> (pushprop_lem1v2 = $true)) & ((axshiftcons = $true) <=> ! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499)) & ! [X500 : d_term,X501 : d_term] : ((((d2term @ X500)) = ((d2term @ X501))) => (X500 = X501)) & (! [X502 : term] : ~ ! [X503 : (subst > term > term)] : ~ ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) <=> (hoasinduction_lem3v2_f = $true)) & (axapp = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & ((induction2_lthm = $true) <=> (! [X506 : term] : (((sub @ X506 @ id)) = X506) => (! [X507 : (term > $o),X508 : subst,X509 : term] : (~ ! [X510 : term] : (~ ! [X511 : term] : ((((X507 @ (sub @ X510 @ (push @ X511 @ id)))) = $true) | ~ (((X507 @ X511)) = $true)) | (((X507 @ (lam @ X510))) = $true)) | ~ ! [X512 : term,X513 : term] : (~ (((X507 @ X512)) = $true) | ~ ($true = ((X507 @ X513))) | ($true = ((X507 @ (ap @ X513 @ X512))))) | ~ ! [X514 : term] : (($true = ((X507 @ (sub @ X514 @ X508)))) | ~ ($true = ((var @ X514)))) | (((X507 @ (sub @ X509 @ X508))) = $true)) => ! [X515 : term,X516 : (term > $o)] : ((((X516 @ X515)) = $true) | ~ ! [X517 : term,X518 : term] : ((((X516 @ (ap @ X517 @ X518))) = $true) | ~ (((X516 @ X517)) = $true) | ~ (((X516 @ X518)) = $true)) | ~ ! [X519 : term] : (~ ! [X520 : term] : (~ (((X516 @ X520)) = $true) | (((X516 @ (sub @ X519 @ (push @ X520 @ id)))) = $true)) | (((X516 @ (lam @ X519))) = $true)) | ~ ! [X521 : term] : (~ (((var @ X521)) = $true) | (((X516 @ X521)) = $true)))))) & (! [X522 : (term > $o),X523 : subst,X524 : term] : ~ ! [X525 : (term > $o)] : ~ ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523))))) <=> (pushprop_lem0 = $true)) & ! [X527 : d_subst,X528 : d_subst] : ((((d2subst @ X528)) = ((d2subst @ X527))) => (X527 = X528)) & (substmonoid_gthm = $true) & (axabs = $true) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) <=> (laminj = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X533 : term,X534 : term,X532 : term,X535 : term] : ((X534 = X535) | (((ap @ X535 @ X533)) != ((ap @ X534 @ X532)))) => ! [X537 : term,X536 : term,X539 : term,X538 : term] : ((((ap @ (sub @ X537 @ id) @ X539)) != ((ap @ (sub @ X536 @ id) @ X538))) | (X536 = X537))))) & (hoaslamnotap_lthm = $true)),
% 3.80/0.85 inference(rectify,[],[f7])).
% 3.80/0.85 thf(f10,plain,(
% 3.80/0.85 (! [X502 : term] : ~ ! [X503 : (subst > term > term)] : ~ ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem1v2_gthm = $true) & (! [X347 : term] : ~ ! [X348 : (subst > term > term)] : ~ ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X202 : (subst > term > subst > $o)] : ~ ! [X203 : (term > $o)] : ~ ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((substmonoid = $true) <=> (! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384))) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X386 : term] : (((sub @ X386 @ id)) = X386) => ! [X389 : term,X388 : (subst > term > subst > $o),X387 : (term > $o)] : (~ ! [X390 : (subst > term > term)] : (~ ! [X394 : term] : (($true != ((X388 @ id @ X394 @ id))) | ($true = ((X388 @ id @ (X390 @ id @ X394) @ id)))) | ~ ! [X393 : subst,X391 : subst,X392 : term] : (((X390 @ (comp @ X393 @ X391) @ (sub @ X392 @ X391))) = ((sub @ (X390 @ X393 @ X392) @ X391))) | (((X388 @ id @ (lam @ (X390 @ sh @ one)) @ id)) = $true)) | ~ ! [X404 : term] : (((X388 @ id @ X404 @ id)) = ((X387 @ X404))) | ~ ! [X395 : term] : ((((X387 @ (sub @ X389 @ (push @ X395 @ id)))) = $true) | (((X387 @ X395)) != $true)) | ~ ! [X400 : term,X401 : subst,X402 : subst,X403 : subst] : (($true = ((X388 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))) | (((X388 @ X403 @ X400 @ (comp @ X402 @ X401))) != $true)) | ~ ! [X399 : term,X397 : subst,X398 : subst,X396 : subst] : ((((X388 @ (comp @ X397 @ X396) @ (sub @ X399 @ X396) @ X398)) != $true) | (((X388 @ X397 @ X399 @ (comp @ X396 @ X398))) = $true)) | (((X387 @ (lam @ X389))) = $true)))) & (hoasinduction_lem2v2_gthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X35 : term,X34 : (subst > term > subst > $o)] : ((((X34 @ id @ (lam @ X35) @ id)) = $true) | ~ ! [X46 : subst,X47 : subst,X49 : term,X48 : subst] : ((((X34 @ (comp @ X46 @ X48) @ (sub @ X49 @ X48) @ X47)) != $true) | (((X34 @ X46 @ X49 @ (comp @ X48 @ X47))) = $true)) | ~ ! [X37 : (subst > term > term)] : (~ ! [X41 : subst,X39 : subst,X40 : term] : (((X37 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ (X37 @ X39 @ X40) @ X41))) | ~ ! [X38 : term] : ((((X34 @ id @ (X37 @ id @ X38) @ id)) = $true) | ($true != ((X34 @ id @ X38 @ id)))) | (((X34 @ id @ (lam @ (X37 @ sh @ one)) @ id)) = $true)) | ~ ! [X45 : subst,X42 : term,X43 : subst,X44 : subst] : ((((X34 @ X44 @ X42 @ (comp @ X43 @ X45))) != $true) | (((X34 @ (comp @ X44 @ X43) @ (sub @ X42 @ X43) @ X45)) = $true)) | ~ ! [X36 : term] : ((((X34 @ id @ (sub @ X35 @ (push @ X36 @ id)) @ id)) = $true) | (((X34 @ id @ X36 @ id)) != $true))) <=> (hoasinduction_lem3 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X495 : subst,X496 : term,X494 : (term > $o),X493 : (term > $o)] : (~ ! [X497 : term] : (((X493 @ X497)) = ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | (((X494 @ X496)) != $true) | ($true = ((X493 @ one))))) & (pushprop_lthm = $true) & (apnotvar = $true) & (! [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ X253 @ id)) = $true) | ~ ! [X258 : subst,X257 : term,X255 : subst,X256 : subst] : (($true != ((X254 @ X258 @ X257 @ (comp @ X256 @ X255)))) | (((X254 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) = $true)) | ~ ! [X259 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X259 @ sh @ one)) @ id)) = $true) | ~ ! [X263 : term] : (($true = ((X254 @ id @ (X259 @ id @ X263) @ id))) | (((X254 @ id @ X263 @ id)) != $true)) | ~ ! [X261 : term,X260 : subst,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262)))) | ~ ! [X270 : term,X269 : term] : ((((X254 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)) = $true) | (((X254 @ id @ X270 @ id)) != $true) | ($true != ((X254 @ id @ X269 @ id)))) | ~ ! [X264 : term] : ((((var @ (sub @ X264 @ id))) != $true) | (((X254 @ id @ X264 @ id)) = $true)) | ~ ! [X265 : subst,X267 : subst,X266 : subst,X268 : term] : ((((X254 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true) | (((X254 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) != $true))) <=> (hoasinduction = $true)) & (induction2lem_gthm = $true) & (pushprop_lem3v2 = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X281 : term,X282 : subst] : (((sub @ one @ (push @ X281 @ X282))) = X281) => (! [X284 : term,X283 : subst] : (((comp @ sh @ (push @ X284 @ X283))) = X283) => ! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true))))) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & ((hoaslaminj_lthm = $true) <=> (! [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) = X96) => (! [X98 : term,X97 : subst] : (((comp @ sh @ (push @ X98 @ X97))) = X97) => (! [X100 : term,X99 : term] : ((((lam @ X99)) != ((lam @ X100))) | (X99 = X100)) => ! [X103 : term,X104 : (subst > term > term),X102 : (subst > term > term),X101 : subst] : ((((X104 @ X101 @ X103)) = ((X102 @ X101 @ X103))) | ~ ! [X107 : term,X105 : subst,X106 : subst] : (((X104 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) = ((sub @ (X104 @ X105 @ X107) @ X106))) | ~ ! [X110 : subst,X108 : subst,X109 : term] : (((X102 @ (comp @ X110 @ X108) @ (sub @ X109 @ X108))) = ((sub @ (X102 @ X110 @ X109) @ X108))) | (((lam @ (X104 @ sh @ one))) != ((lam @ (X102 @ sh @ one))))))))) & ((hoasapinj1_lthm = $true) <=> (! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X533 : term,X534 : term,X532 : term,X535 : term] : ((X534 = X535) | (((ap @ X535 @ X533)) != ((ap @ X534 @ X532)))) => ! [X537 : term,X536 : term,X539 : term,X538 : term] : ((((ap @ (sub @ X537 @ id) @ X539)) != ((ap @ (sub @ X536 @ id) @ X538))) | (X536 = X537))))) & (axapp = $true) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) <=> (axvarcons = $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X199 : (subst > term > subst > $o)] : ~ ! [X200 : (term > $o)] : ~ ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id)))) & ((hoaslaminj = $true) <=> ! [X271 : (subst > term > term),X274 : subst,X272 : (subst > term > term),X273 : term] : (~ ! [X276 : term,X277 : subst,X275 : subst] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) = ((sub @ (X271 @ X275 @ X276) @ X277))) | (((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ~ ! [X278 : subst,X279 : term,X280 : subst] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) = ((sub @ (X272 @ X280 @ X279) @ X278))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X207 : term,X210 : term,X208 : (term > $o),X209 : (subst > term > subst > $o)] : ((((X208 @ X210)) != $true) | ~ ! [X215 : term] : (((X209 @ id @ X215 @ id)) = ((X208 @ X215))) | (((X208 @ X207)) != $true) | ~ ! [X218 : subst,X216 : term,X219 : subst,X217 : subst] : ((((X209 @ X218 @ X216 @ (comp @ X217 @ X219))) != $true) | (((X209 @ (comp @ X218 @ X217) @ (sub @ X216 @ X217) @ X219)) = $true)) | ~ ! [X212 : term,X213 : subst,X214 : subst,X211 : subst] : ((((X209 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211) @ X214)) != $true) | (((X209 @ X213 @ X212 @ (comp @ X211 @ X214))) = $true)) | ~ ! [X220 : term,X221 : term] : ((((X209 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) = $true) | (((X209 @ id @ X221 @ id)) != $true) | ($true != ((X209 @ id @ X220 @ id)))) | ($true = ((X208 @ (ap @ X207 @ X210)))))) & (ulamvarind = $true) & (axvarshift = $true) & ((! [X222 : term,X224 : term,X223 : term,X225 : term] : ((X222 = X225) | (((ap @ X224 @ X222)) != ((ap @ X223 @ X225)))) => ! [X229 : term,X227 : term,X228 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X227)) != ((ap @ (sub @ X229 @ id) @ X228))) | (X227 = X228))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X75 : (subst > term > subst > $o),X76 : term,X77 : term] : (($true != ((X75 @ id @ X76 @ id))) | ~ ! [X82 : subst,X80 : subst,X83 : subst,X81 : term] : (($true = ((X75 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82) @ X83))) | (((X75 @ X80 @ X81 @ (comp @ X82 @ X83))) != $true)) | ~ ! [X85 : subst,X84 : subst,X86 : term,X87 : subst] : ((((X75 @ (comp @ X84 @ X87) @ (sub @ X86 @ X87) @ X85)) != $true) | ($true = ((X75 @ X84 @ X86 @ (comp @ X87 @ X85))))) | (((X75 @ id @ (ap @ X76 @ X77) @ id)) = $true) | ~ ! [X78 : term,X79 : term] : ((((X75 @ id @ X79 @ id)) != $true) | (((X75 @ id @ X78 @ id)) != $true) | (((X75 @ id @ (ap @ (sub @ X79 @ id) @ X78) @ id)) = $true)) | ($true != ((X75 @ id @ X77 @ id))))) & (axmap = $true) & (termmset_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (! [X90 : term,X88 : (term > $o),X89 : subst] : ~ ! [X91 : (term > $o)] : ~ ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92))) <=> (pushprop_lem0_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499)) & (lamnotap != $true) & (hoasapnotvar_lthm = $true) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & ((hoasinduction_lem3v2a = $true) <=> ! [X180 : term,X181 : (subst > term > subst > $o),X182 : (term > $o)] : ((((X182 @ (lam @ X180))) = $true) | ~ ! [X189 : term] : ((((X182 @ (sub @ X180 @ (push @ X189 @ id)))) = $true) | (((X182 @ X189)) != $true)) | ~ ! [X188 : term] : (((X181 @ id @ X188 @ id)) = ((X182 @ X188))) | ~ ! [X183 : (subst > term > term)] : (($true = ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) | ~ ! [X187 : term] : ((((X181 @ id @ (X183 @ id @ X187) @ id)) = $true) | (((X181 @ id @ X187 @ id)) != $true)) | ~ ! [X186 : subst,X185 : subst,X184 : term] : (((sub @ (X183 @ X185 @ X184) @ X186)) = ((X183 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186))))))) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X7 : term,X6 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | (((X4 @ X7)) != $true) | (((X4 @ X6)) != $true)) | (((X4 @ X3)) = $true) | ~ ! [X5 : term] : ((((X4 @ X5)) = $true) | (((var @ X5)) != $true)) | ~ ! [X8 : term] : ((((X4 @ (lam @ X8))) = $true) | ~ ! [X9 : term] : ((((X4 @ X9)) != $true) | (((X4 @ (sub @ X8 @ (push @ X9 @ id)))) = $true)))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X13 : (term > $o),X12 : term,X11 : (subst > term > subst > $o)] : (~ ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))) | (((X13 @ (lam @ X12))) = $true) | ~ ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | (((X13 @ X15)) != $true)) | ~ ! [X16 : (subst > term > term)] : (~ ! [X18 : subst,X19 : term,X17 : subst] : (((sub @ (X16 @ X17 @ X19) @ X18)) = ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18)))) | (((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ~ ! [X20 : term] : ((((X11 @ id @ (X16 @ id @ X20) @ id)) = $true) | (((X11 @ id @ X20 @ id)) != $true)))) => ! [X22 : term,X21 : (subst > term > subst > $o)] : (~ ! [X23 : (subst > term > term)] : (~ ! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | (((X21 @ id @ X27 @ id)) != $true)) | ($true = ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) | ~ ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))))) | (((X21 @ id @ X22 @ id)) = $true) | ~ ! [X29 : term,X28 : term] : ((((X21 @ id @ X28 @ id)) != $true) | (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) = $true) | (((X21 @ id @ X29 @ id)) != $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X372 : subst] : (((comp @ id @ X372)) = X372)) & (induction2_gthm = $true) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) <=> (laminj = $true)) & (! [X351 : term,X352 : (term > $o)] : (~ ! [X357 : term,X356 : term] : ((((X352 @ X357)) != $true) | ($true = ((X352 @ (ap @ X357 @ X356)))) | ($true != ((X352 @ X356)))) | ~ ! [X353 : term] : ((((X352 @ X353)) = $true) | (((var @ X353)) != $true)) | ($true = ((X352 @ X351))) | ~ ! [X354 : term] : (~ ! [X355 : term] : ((((X352 @ X355)) != $true) | (((X352 @ (sub @ X354 @ (push @ X355 @ id)))) = $true)) | (((X352 @ (lam @ X354))) = $true))) <=> (induction2 = $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)))))))))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X172 : term,X173 : (subst > term > subst > $o)] : ((((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X175 : (subst > term > term)] : (~ ! [X176 : term] : ((((X173 @ id @ X176 @ id)) != $true) | (((X173 @ id @ (X175 @ id @ X176) @ id)) = $true)) | ~ ! [X179 : subst,X177 : subst,X178 : term] : (((X175 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179))) = ((sub @ (X175 @ X177 @ X178) @ X179))) | (((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id)) = $true)) | ~ ! [X174 : term] : (($true = ((X173 @ id @ (sub @ X172 @ (push @ X174 @ id)) @ id))) | ($true != ((X173 @ id @ X174 @ id)))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X190 : term,X191 : (subst > term > subst > $o)] : (($true = ((X191 @ id @ X190 @ id))) | ~ ! [X197 : term,X198 : term] : ((((X191 @ id @ X198 @ id)) != $true) | (((X191 @ id @ X197 @ id)) != $true) | (((X191 @ id @ (ap @ (sub @ X198 @ id) @ X197) @ id)) = $true)) | ~ ! [X192 : (subst > term > term)] : (~ ! [X196 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X196) @ (sub @ X194 @ X196))) = ((sub @ (X192 @ X195 @ X194) @ X196))) | ~ ! [X193 : term] : ((((X191 @ id @ X193 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X193) @ id)) = $true)) | (((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id)) = $true)))) & (hoasinduction_lem3a_gthm = $true) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) <=> (apinj1 = $true)) & (hoasinduction_lem1 = $true) & ((hoasapinj2 = $true) <=> ! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417))) & ((! [X433 : term] : (((sub @ X433 @ id)) = X433) => (! [X435 : term,X434 : (subst > term > subst > $o)] : ((((X434 @ id @ (lam @ (sub @ X435 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X441 : term] : (($true != ((X434 @ id @ X441 @ id))) | ($true = ((X434 @ id @ (sub @ X435 @ (push @ X441 @ id)) @ id)))) | ~ ! [X436 : (subst > term > term)] : (~ ! [X440 : term,X439 : subst,X438 : subst] : (((sub @ (X436 @ X438 @ X440) @ X439)) = ((X436 @ (comp @ X438 @ X439) @ (sub @ X440 @ X439)))) | (((X434 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ~ ! [X437 : term] : (($true = ((X434 @ id @ (X436 @ id @ X437) @ id))) | ($true != ((X434 @ id @ X437 @ id)))))) => ! [X442 : (subst > term > subst > $o),X443 : term] : (~ ! [X444 : term] : (($true != ((X442 @ id @ X444 @ id))) | ($true = ((X442 @ id @ (sub @ X443 @ (push @ X444 @ id)) @ id)))) | ~ ! [X445 : (subst > term > term)] : (~ ! [X447 : term,X449 : subst,X448 : subst] : (((sub @ (X445 @ X448 @ X447) @ X449)) = ((X445 @ (comp @ X448 @ X449) @ (sub @ X447 @ X449)))) | ($true = ((X442 @ id @ (lam @ (X445 @ sh @ one)) @ id))) | ~ ! [X446 : term] : ((((X442 @ id @ X446 @ id)) != $true) | (((X442 @ id @ (X445 @ id @ X446) @ id)) = $true))) | (((X442 @ id @ (lam @ X443) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X411 : term,X409 : term,X410 : (subst > term > term)] : (~ ! [X413 : subst,X414 : subst,X412 : term] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409)))) <=> (hoaslamnotap = $true)) & (! [X58 : (subst > term > subst > $o),X57 : (term > $o),X56 : term] : (~ ! [X72 : subst,X69 : term,X70 : subst,X71 : subst] : ((((X58 @ X70 @ X69 @ (comp @ X72 @ X71))) = $true) | (((X58 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) != $true)) | ~ ! [X64 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X64 @ sh @ one)) @ id)) = $true) | ~ ! [X66 : subst,X65 : term,X67 : subst] : (((sub @ (X64 @ X66 @ X65) @ X67)) = ((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) | ~ ! [X68 : term] : ((((X58 @ id @ (X64 @ id @ X68) @ id)) = $true) | (((X58 @ id @ X68 @ id)) != $true))) | ~ ! [X59 : term] : ((((X57 @ (sub @ X56 @ (push @ X59 @ id)))) = $true) | (((X57 @ X59)) != $true)) | ($true = ((X57 @ (lam @ X56)))) | ~ ! [X73 : term] : (((X58 @ id @ X73 @ id)) = ((X57 @ X73))) | ~ ! [X63 : subst,X62 : subst,X60 : term,X61 : subst] : ((((X58 @ X61 @ X60 @ (comp @ X62 @ X63))) != $true) | ($true = ((X58 @ (comp @ X61 @ X62) @ (sub @ X60 @ X62) @ X63))))) <=> (hoasinduction_lem3v2 = $true)) & (! [X93 : term] : ~ ! [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) != ((X94 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (! [X358 : term] : ~ ! [X359 : (subst > term > term)] : (((X359 @ sh @ one)) != ((sub @ X358 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X522 : (term > $o),X523 : subst,X524 : term] : ~ ! [X525 : (term > $o)] : ~ ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523))))) <=> (pushprop_lem0 = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X231 : (subst > term > subst > $o),X230 : term] : (~ ! [X233 : (subst > term > term)] : (~ ! [X237 : term] : ((((X231 @ id @ X237 @ id)) != $true) | (((X231 @ id @ (X233 @ id @ X237) @ id)) = $true)) | (((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) = $true) | ~ ! [X234 : subst,X235 : subst,X236 : term] : (((X233 @ (comp @ X234 @ X235) @ (sub @ X236 @ X235))) = ((sub @ (X233 @ X234 @ X236) @ X235)))) | (((X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X232 : term] : ((((X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) = $true) | (((X231 @ id @ X232 @ id)) != $true)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_gthm = $true) & ((induction2_lthm = $true) <=> (! [X506 : term] : (((sub @ X506 @ id)) = X506) => (! [X509 : term,X507 : (term > $o),X508 : subst] : (~ ! [X513 : term,X512 : term] : ((((X507 @ X512)) != $true) | ($true != ((X507 @ X513))) | ($true = ((X507 @ (ap @ X513 @ X512))))) | (((X507 @ (sub @ X509 @ X508))) = $true) | ~ ! [X514 : term] : (($true != ((var @ X514))) | ($true = ((X507 @ (sub @ X514 @ X508))))) | ~ ! [X510 : term] : ((((X507 @ (lam @ X510))) = $true) | ~ ! [X511 : term] : ((((X507 @ X511)) != $true) | (((X507 @ (sub @ X510 @ (push @ X511 @ id)))) = $true)))) => ! [X515 : term,X516 : (term > $o)] : (~ ! [X521 : term] : ((((var @ X521)) != $true) | (((X516 @ X521)) = $true)) | ~ ! [X519 : term] : ((((X516 @ (lam @ X519))) = $true) | ~ ! [X520 : term] : ((((X516 @ X520)) != $true) | (((X516 @ (sub @ X519 @ (push @ X520 @ id)))) = $true))) | (((X516 @ X515)) = $true) | ~ ! [X517 : term,X518 : term] : ((((X516 @ X517)) != $true) | (((X516 @ X518)) != $true) | (((X516 @ (ap @ X517 @ X518))) = $true)))))) & ((hoasinduction_lthm_3 = $true) <=> (! [X454 : (subst > term > subst > $o)] : ~ ! [X455 : (term > $o)] : ~ ! [X456 : term] : (((X455 @ X456)) = ((X454 @ id @ X456 @ id))) => (! [X458 : term,X457 : (term > $o)] : ((((X457 @ X458)) = $true) | ~ ! [X460 : term] : (~ ! [X461 : term] : ((((X457 @ X461)) != $true) | ($true = ((X457 @ (sub @ X460 @ (push @ X461 @ id)))))) | (((X457 @ (lam @ X460))) = $true)) | ~ ! [X459 : term] : ((((X457 @ X459)) = $true) | ($true != ((var @ X459)))) | ~ ! [X463 : term,X462 : term] : (($true != ((X457 @ X462))) | ($true != ((X457 @ X463))) | ($true = ((X457 @ (ap @ X462 @ X463)))))) => (! [X464 : term] : (((sub @ X464 @ id)) = X464) => (! [X465 : (subst > term > subst > $o),X467 : (term > $o),X466 : term] : (~ ! [X468 : (subst > term > term)] : (~ ! [X472 : term] : ((((X465 @ id @ (X468 @ id @ X472) @ id)) = $true) | (((X465 @ id @ X472 @ id)) != $true)) | (((X465 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true) | ~ ! [X470 : subst,X469 : subst,X471 : term] : (((sub @ (X468 @ X470 @ X471) @ X469)) = ((X468 @ (comp @ X470 @ X469) @ (sub @ X471 @ X469))))) | ~ ! [X473 : term] : ((((X467 @ X473)) != $true) | (((X467 @ (sub @ X466 @ (push @ X473 @ id)))) = $true)) | (((X467 @ (lam @ X466))) = $true) | ~ ! [X474 : term] : (((X467 @ X474)) = ((X465 @ id @ X474 @ id)))) => ! [X476 : term,X475 : (subst > term > subst > $o)] : (~ ! [X484 : term] : (($true = ((X475 @ id @ X484 @ id))) | (((var @ (sub @ X484 @ id))) != $true)) | ~ ! [X482 : term,X483 : term] : ((((X475 @ id @ X483 @ id)) != $true) | (((X475 @ id @ (ap @ (sub @ X483 @ id) @ X482) @ id)) = $true) | ($true != ((X475 @ id @ X482 @ id)))) | ~ ! [X492 : subst,X491 : subst,X490 : subst,X489 : term] : ((((X475 @ X492 @ X489 @ (comp @ X490 @ X491))) != $true) | (((X475 @ (comp @ X492 @ X490) @ (sub @ X489 @ X490) @ X491)) = $true)) | (((X475 @ id @ X476 @ id)) = $true) | ~ ! [X477 : (subst > term > term)] : (~ ! [X478 : subst,X479 : subst,X480 : term] : (((X477 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478))) = ((sub @ (X477 @ X479 @ X480) @ X478))) | ~ ! [X481 : term] : ((((X475 @ id @ (X477 @ id @ X481) @ id)) = $true) | ($true != ((X475 @ id @ X481 @ id)))) | (((X475 @ id @ (lam @ (X477 @ sh @ one)) @ id)) = $true)) | ~ ! [X488 : subst,X486 : subst,X487 : subst,X485 : term] : ((((X475 @ X488 @ X485 @ (comp @ X486 @ X487))) = $true) | (((X475 @ (comp @ X488 @ X486) @ (sub @ X485 @ X486) @ X487)) != $true)))))))) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((shinj = $true) <=> ! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh))))) & ! [X527 : d_subst,X528 : d_subst] : ((((d2subst @ X528)) = ((d2subst @ X527))) => (X527 = X528)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((induction = $true) <=> ! [X50 : (term > $o),X51 : term] : (~ ! [X55 : term,X54 : term] : ((((X50 @ X54)) != $true) | (((X50 @ X55)) != $true) | (((X50 @ (ap @ X55 @ X54))) = $true)) | ~ ! [X52 : term] : ((((X50 @ X52)) != $true) | (((X50 @ (lam @ X52))) = $true)) | ~ ! [X53 : term] : ((((X50 @ X53)) = $true) | (((var @ X53)) != $true)) | (((X50 @ X51)) = $true))) & (hoasinduction_lem3_gthm = $true) & ((! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X316 : term,X315 : (subst > term > subst > $o)] : (~ ! [X322 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X322 @ id)) @ id)) = $true) | ($true != ((X315 @ id @ X322 @ id)))) | ~ ! [X317 : (subst > term > term)] : (~ ! [X321 : subst,X319 : subst,X320 : term] : (((X317 @ (comp @ X319 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X317 @ X319 @ X320) @ X321))) | ($true = ((X315 @ id @ (lam @ (X317 @ sh @ one)) @ id))) | ~ ! [X318 : term] : (($true = ((X315 @ id @ (X317 @ id @ X318) @ id))) | ($true != ((X315 @ id @ X318 @ id))))) | ($true = ((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id)))) => ! [X323 : (subst > term > subst > $o),X324 : term] : ((((X323 @ id @ (lam @ X324) @ id)) = $true) | ~ ! [X330 : (subst > term > term)] : (~ ! [X331 : subst,X332 : subst,X333 : term] : (((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))) = ((sub @ (X330 @ X331 @ X333) @ X332))) | ~ ! [X334 : term] : ((((X323 @ id @ X334 @ id)) != $true) | (((X323 @ id @ (X330 @ id @ X334) @ id)) = $true)) | (((X323 @ id @ (lam @ (X330 @ sh @ one)) @ id)) = $true)) | ~ ! [X338 : subst,X336 : term,X335 : subst,X337 : subst] : ((((X323 @ (comp @ X338 @ X337) @ (sub @ X336 @ X337) @ X335)) = $true) | (((X323 @ X338 @ X336 @ (comp @ X337 @ X335))) != $true)) | ~ ! [X329 : term,X326 : subst,X327 : subst,X328 : subst] : (($true = ((X323 @ X328 @ X329 @ (comp @ X327 @ X326)))) | (((X323 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327) @ X326)) != $true)) | ~ ! [X325 : term] : ((((X323 @ id @ (sub @ X324 @ (push @ X325 @ id)) @ id)) = $true) | ($true != ((X323 @ id @ X325 @ id))))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) <=> (hoasapinj1 = $true)) & ((substmonoid_lthm = $true) <=> (! [X450 : subst] : (((comp @ id @ X450)) = X450) => (! [X451 : subst] : (((comp @ X451 @ id)) = X451) => (! [X452 : subst] : (((comp @ X452 @ id)) = X452) & ! [X453 : subst] : (((comp @ id @ X453)) = X453))))) & ((! [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) = X294) => (! [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) = X296) => (! [X297 : subst] : (((comp @ X297 @ id)) = X297) => (! [X298 : (term > $o),X299 : term] : (($true = ((X298 @ X299))) | ~ ! [X302 : term,X303 : term] : ((((X298 @ X303)) != $true) | (((X298 @ X302)) != $true) | ($true = ((X298 @ (ap @ X302 @ X303))))) | ~ ! [X300 : term] : ((((X298 @ X300)) != $true) | (((X298 @ (lam @ X300))) = $true)) | ~ ! [X301 : term] : (($true != ((var @ X301))) | ($true = ((X298 @ X301))))) => ! [X306 : term,X304 : subst,X305 : (term > $o)] : (~ ! [X311 : term,X310 : term] : (($true != ((X305 @ X311))) | (((X305 @ (ap @ X310 @ X311))) = $true) | (((X305 @ X310)) != $true)) | ~ ! [X307 : term] : (~ ! [X308 : term] : ((((X305 @ (sub @ X307 @ (push @ X308 @ id)))) = $true) | (((X305 @ X308)) != $true)) | (((X305 @ (lam @ X307))) = $true)) | ~ ! [X309 : term] : ((((X305 @ (sub @ X309 @ X304))) = $true) | ($true != ((var @ X309)))) | (((X305 @ (sub @ X306 @ X304))) = $true)))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X361 : term,X360 : (subst > term > subst > $o)] : ((((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X371 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X371 @ id)) @ id)) = $true) | ($true != ((X360 @ id @ X371 @ id)))) | ~ ! [X363 : term,X362 : (subst > term > term)] : (~ ! [X366 : subst,X365 : subst,X364 : term] : (((sub @ (sub @ X363 @ (push @ X364 @ X366)) @ X365)) = ((sub @ (X362 @ X366 @ X364) @ X365))) | ~ ! [X368 : term,X369 : subst,X367 : subst] : (((sub @ X363 @ (push @ (sub @ X368 @ X367) @ (comp @ X369 @ X367)))) = ((X362 @ (comp @ X369 @ X367) @ (sub @ X368 @ X367)))) | (((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) = $true) | ~ ! [X370 : term] : ((((X360 @ id @ (X362 @ id @ X370) @ id)) = $true) | (((X360 @ id @ X370 @ id)) != $true))))) & (axassoc = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & ! [X385 : d_subst] : (d_id = X385) & (ulamvarsh = $true) & ! [X292 : d_term] : (d_one = X292) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & ((! [X345 : term] : (((sub @ X345 @ id)) = X345) => ! [X346 : term] : (((sub @ X346 @ id)) = X346)) <=> (termmset_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (((d2subst @ d_id)) = sh) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) <=> (axidr = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem2v2 = $true) & ((termmset = $true) <=> ! [X313 : term] : (((sub @ X313 @ id)) = X313)) & (axclos = $true) & (hoaslaminj_gthm = $true) & (! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X500 : d_term,X501 : d_term] : ((((d2term @ X500)) = ((d2term @ X501))) => (X500 = X501)) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lthm = $true) <=> (! [X118 : (term > $o),X119 : term] : (~ ! [X122 : term] : (~ ! [X123 : term] : ((((X118 @ (sub @ X122 @ (push @ X123 @ id)))) = $true) | ($true != ((X118 @ X123)))) | (((X118 @ (lam @ X122))) = $true)) | ~ ! [X120 : term,X121 : term] : (($true != ((X118 @ X121))) | (((X118 @ (ap @ X120 @ X121))) = $true) | (((X118 @ X120)) != $true)) | ($true = ((X118 @ X119))) | ~ ! [X124 : term] : (($true != ((var @ X124))) | (((X118 @ X124)) = $true))) => (! [X125 : term,X126 : term,X127 : (subst > term > subst > $o)] : (~ ! [X128 : subst,X129 : subst,X130 : subst,X131 : term] : (($true = ((X127 @ (comp @ X128 @ X129) @ (sub @ X131 @ X129) @ X130))) | (((X127 @ X128 @ X131 @ (comp @ X129 @ X130))) != $true)) | ~ ! [X133 : subst,X135 : term,X132 : subst,X134 : subst] : ((((X127 @ (comp @ X132 @ X133) @ (sub @ X135 @ X133) @ X134)) != $true) | ($true = ((X127 @ X132 @ X135 @ (comp @ X133 @ X134))))) | (((X127 @ id @ X126 @ id)) != $true) | (((X127 @ id @ X125 @ id)) != $true) | ($true = ((X127 @ id @ (ap @ X125 @ X126) @ id))) | ~ ! [X137 : term,X136 : term] : ((((X127 @ id @ X136 @ id)) != $true) | ($true != ((X127 @ id @ X137 @ id))) | (((X127 @ id @ (ap @ (sub @ X137 @ id) @ X136) @ id)) = $true))) => (! [X139 : (subst > term > subst > $o),X138 : term] : ((((X139 @ id @ (lam @ X138) @ id)) = $true) | ~ ! [X153 : subst,X151 : subst,X152 : term,X150 : subst] : ((((X139 @ (comp @ X150 @ X151) @ (sub @ X152 @ X151) @ X153)) = $true) | (((X139 @ X150 @ X152 @ (comp @ X151 @ X153))) != $true)) | ~ ! [X142 : subst,X143 : subst,X141 : subst,X140 : term] : (($true != ((X139 @ (comp @ X141 @ X143) @ (sub @ X140 @ X143) @ X142))) | (((X139 @ X141 @ X140 @ (comp @ X143 @ X142))) = $true)) | ~ ! [X145 : (subst > term > term)] : (($true = ((X139 @ id @ (lam @ (X145 @ sh @ one)) @ id))) | ~ ! [X146 : term] : ((((X139 @ id @ X146 @ id)) != $true) | (((X139 @ id @ (X145 @ id @ X146) @ id)) = $true)) | ~ ! [X147 : subst,X149 : term,X148 : subst] : (((sub @ (X145 @ X147 @ X149) @ X148)) = ((X145 @ (comp @ X147 @ X148) @ (sub @ X149 @ X148))))) | ~ ! [X144 : term] : ((((X139 @ id @ (sub @ X138 @ (push @ X144 @ id)) @ id)) = $true) | (((X139 @ id @ X144 @ id)) != $true))) => ! [X155 : term,X154 : (subst > term > subst > $o)] : (~ ! [X156 : term] : (($true = ((X154 @ id @ X156 @ id))) | ($true != ((var @ (sub @ X156 @ id))))) | (((X154 @ id @ X155 @ id)) = $true) | ~ ! [X171 : term,X170 : term] : ((((X154 @ id @ X170 @ id)) != $true) | (((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)) = $true) | (((X154 @ id @ X171 @ id)) != $true)) | ~ ! [X165 : (subst > term > term)] : (~ ! [X169 : term] : ((((X154 @ id @ X169 @ id)) != $true) | (((X154 @ id @ (X165 @ id @ X169) @ id)) = $true)) | (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) = $true) | ~ ! [X167 : subst,X166 : term,X168 : subst] : (((X165 @ (comp @ X168 @ X167) @ (sub @ X166 @ X167))) = ((sub @ (X165 @ X168 @ X166) @ X167)))) | ~ ! [X157 : subst,X159 : subst,X158 : subst,X160 : term] : (($true != ((X154 @ (comp @ X157 @ X158) @ (sub @ X160 @ X158) @ X159))) | (((X154 @ X157 @ X160 @ (comp @ X158 @ X159))) = $true)) | ~ ! [X163 : subst,X164 : subst,X162 : term,X161 : subst] : ((((X154 @ (comp @ X161 @ X164) @ (sub @ X162 @ X164) @ X163)) = $true) | (((X154 @ X161 @ X162 @ (comp @ X164 @ X163))) != $true))))))) & ((! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) => ! [X115 : subst,X116 : term,X113 : (term > $o),X114 : (term > $o)] : ((((X113 @ X116)) != $true) | (((X114 @ one)) = $true) | ~ ! [X117 : term] : (((X114 @ X117)) = ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X376 : term,X375 : (subst > term > subst > $o)] : (~ ! [X377 : (subst > term > term)] : (~ ! [X381 : term] : (($true != ((X375 @ id @ X381 @ id))) | (((X375 @ id @ (X377 @ id @ X381) @ id)) = $true)) | ~ ! [X379 : subst,X380 : term,X378 : subst] : (((X377 @ (comp @ X379 @ X378) @ (sub @ X380 @ X378))) = ((sub @ (X377 @ X379 @ X380) @ X378))) | ($true = ((X375 @ id @ (lam @ (X377 @ sh @ one)) @ id)))) | ($true = ((X375 @ id @ (lam @ X376) @ id))) | ~ ! [X382 : term] : ((((X375 @ id @ X382 @ id)) != $true) | (((X375 @ id @ (sub @ X376 @ (push @ X382 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3a = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X238 : term] : ~ ! [X239 : (subst > term > term)] : ~ ! [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) = ((X239 @ X241 @ X240))) => (! [X242 : term] : (((sub @ X242 @ id)) = X242) => ! [X243 : (subst > term > subst > $o),X244 : term,X245 : (term > $o)] : (~ ! [X248 : (subst > term > term)] : (~ ! [X251 : subst,X250 : term,X252 : subst] : (((sub @ (X248 @ X252 @ X250) @ X251)) = ((X248 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)))) | ~ ! [X249 : term] : ((((X243 @ id @ X249 @ id)) != $true) | (((X243 @ id @ (X248 @ id @ X249) @ id)) = $true)) | (((X243 @ id @ (lam @ (X248 @ sh @ one)) @ id)) = $true)) | ~ ! [X246 : term] : (((X245 @ X246)) = ((X243 @ id @ X246 @ id))) | ~ ! [X247 : term] : ((((X245 @ X247)) != $true) | (((X245 @ (sub @ X244 @ (push @ X247 @ id)))) = $true)) | (((X245 @ (lam @ X244))) = $true))))) & (axabs = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (ulamvar1 != $true) & ((induction2lem = $true) <=> ! [X422 : (term > $o),X423 : term,X421 : subst] : (~ ! [X424 : term] : ((((X422 @ (lam @ X424))) = $true) | ~ ! [X425 : term] : ((((X422 @ X425)) != $true) | (((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true))) | ~ ! [X426 : term] : ((((var @ X426)) != $true) | (((X422 @ (sub @ X426 @ X421))) = $true)) | ($true = ((X422 @ (sub @ X423 @ X421)))) | ~ ! [X427 : term,X428 : term] : (($true != ((X422 @ X428))) | (((X422 @ (ap @ X427 @ X428))) = $true) | ($true != ((X422 @ X427))))))),
% 3.80/0.85 inference(flattening,[],[f9])).
% 3.80/0.85 thf(f11,plain,(
% 3.80/0.85 (! [X502 : term] : ? [X503 : (subst > term > term)] : ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X347 : term] : ? [X348 : (subst > term > term)] : ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350))))) & (! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((substmonoid = $true) <=> (! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384))) & (hoasapinj1_gthm = $true) & ((! [X388 : (subst > term > subst > $o),X389 : term,X387 : (term > $o)] : ((((X387 @ (lam @ X389))) = $true) | ? [X395 : term] : ((((X387 @ (sub @ X389 @ (push @ X395 @ id)))) != $true) & (((X387 @ X395)) = $true)) | ? [X401 : subst,X403 : subst,X400 : term,X402 : subst] : (($true != ((X388 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))) & (((X388 @ X403 @ X400 @ (comp @ X402 @ X401))) = $true)) | ? [X404 : term] : (((X388 @ id @ X404 @ id)) != ((X387 @ X404))) | ? [X390 : (subst > term > term)] : (! [X394 : term] : (($true != ((X388 @ id @ X394 @ id))) | ($true = ((X388 @ id @ (X390 @ id @ X394) @ id)))) & (((X388 @ id @ (lam @ (X390 @ sh @ one)) @ id)) != $true) & ! [X393 : subst,X391 : subst,X392 : term] : (((X390 @ (comp @ X393 @ X391) @ (sub @ X392 @ X391))) = ((sub @ (X390 @ X393 @ X392) @ X391)))) | ? [X396 : subst,X398 : subst,X397 : subst,X399 : term] : ((((X388 @ X397 @ X399 @ (comp @ X396 @ X398))) != $true) & (((X388 @ (comp @ X397 @ X396) @ (sub @ X399 @ X396) @ X398)) = $true))) | ? [X386 : term] : (((sub @ X386 @ id)) != X386)) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3 = $true) <=> ! [X34 : (subst > term > subst > $o),X35 : term] : (? [X36 : term] : ((((X34 @ id @ (sub @ X35 @ (push @ X36 @ id)) @ id)) != $true) & (((X34 @ id @ X36 @ id)) = $true)) | ? [X47 : subst,X49 : term,X48 : subst,X46 : subst] : ((((X34 @ X46 @ X49 @ (comp @ X48 @ X47))) != $true) & (((X34 @ (comp @ X46 @ X48) @ (sub @ X49 @ X48) @ X47)) = $true)) | (((X34 @ id @ (lam @ X35) @ id)) = $true) | ? [X37 : (subst > term > term)] : (! [X41 : subst,X39 : subst,X40 : term] : (((X37 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ (X37 @ X39 @ X40) @ X41))) & ! [X38 : term] : ((((X34 @ id @ (X37 @ id @ X38) @ id)) = $true) | ($true != ((X34 @ id @ X38 @ id)))) & (((X34 @ id @ (lam @ (X37 @ sh @ one)) @ id)) != $true)) | ? [X45 : subst,X42 : term,X43 : subst,X44 : subst] : ((((X34 @ X44 @ X42 @ (comp @ X43 @ X45))) = $true) & (((X34 @ (comp @ X44 @ X43) @ (sub @ X42 @ X43) @ X45)) != $true)))) & ((pushprop_lem1v2 = $true) <=> ! [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (? [X497 : term] : (((X493 @ X497)) != ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | ($true = ((X493 @ one))) | (((X494 @ X496)) != $true))) & (pushprop_lthm = $true) & (apnotvar = $true) & ((hoasinduction = $true) <=> ! [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ X253 @ id)) = $true) | ? [X269 : term,X270 : term] : ((((X254 @ id @ X270 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)) != $true) & ($true = ((X254 @ id @ X269 @ id)))) | ? [X259 : (subst > term > term)] : (! [X263 : term] : (($true = ((X254 @ id @ (X259 @ id @ X263) @ id))) | (((X254 @ id @ X263 @ id)) != $true)) & ! [X261 : term,X260 : subst,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) & (((X254 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true)) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X254 @ id @ X264 @ id)) != $true)) | ? [X265 : subst,X268 : term,X267 : subst,X266 : subst] : ((((X254 @ X267 @ X268 @ (comp @ X265 @ X266))) != $true) & (((X254 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true)) | ? [X256 : subst,X258 : subst,X255 : subst,X257 : term] : (($true = ((X254 @ X258 @ X257 @ (comp @ X256 @ X255)))) & (((X254 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) != $true)))) & (induction2lem_gthm = $true) & (pushprop_lem3v2 = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true)) | ? [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) != X283)) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281))) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & ((hoaslaminj_lthm = $true) <=> (((! [X104 : (subst > term > term),X103 : term,X102 : (subst > term > term),X101 : subst] : (? [X107 : term,X106 : subst,X105 : subst] : (((X104 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X104 @ X105 @ X107) @ X106))) | ? [X109 : term,X108 : subst,X110 : subst] : (((X102 @ (comp @ X110 @ X108) @ (sub @ X109 @ X108))) != ((sub @ (X102 @ X110 @ X109) @ X108))) | (((lam @ (X104 @ sh @ one))) != ((lam @ (X102 @ sh @ one)))) | (((X104 @ X101 @ X103)) = ((X102 @ X101 @ X103)))) | ? [X100 : term,X99 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100))))) | ? [X97 : subst,X98 : term] : (((comp @ sh @ (push @ X98 @ X97))) != X97)) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96))) & ((hoasapinj1_lthm = $true) <=> ((! [X537 : term,X536 : term,X539 : term,X538 : term] : ((((ap @ (sub @ X537 @ id) @ X539)) != ((ap @ (sub @ X536 @ id) @ X538))) | (X536 = X537)) | ? [X533 : term,X532 : term,X534 : term,X535 : term] : ((((ap @ X535 @ X533)) = ((ap @ X534 @ X532))) & (X534 != X535))) | ? [X531 : term] : (((sub @ X531 @ id)) != X531))) & (axapp = $true) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) <=> (axvarcons = $true)) & (pushprop_lem0_gthm = $true) & (! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) <=> (hoasinduction_lem0 = $true)) & ((hoaslaminj = $true) <=> ! [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ? [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) != ((sub @ (X271 @ X275 @ X276) @ X277))) | ? [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) != ((sub @ (X272 @ X280 @ X279) @ X278))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X207 : term,X209 : (subst > term > subst > $o),X210 : term,X208 : (term > $o)] : ((((X208 @ X207)) != $true) | ? [X216 : term,X218 : subst,X217 : subst,X219 : subst] : ((((X209 @ (comp @ X218 @ X217) @ (sub @ X216 @ X217) @ X219)) != $true) & (((X209 @ X218 @ X216 @ (comp @ X217 @ X219))) = $true)) | ? [X212 : term,X211 : subst,X214 : subst,X213 : subst] : ((((X209 @ X213 @ X212 @ (comp @ X211 @ X214))) != $true) & (((X209 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211) @ X214)) = $true)) | ? [X221 : term,X220 : term] : ((((X209 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) != $true) & ($true = ((X209 @ id @ X220 @ id))) & (((X209 @ id @ X221 @ id)) = $true)) | (((X208 @ X210)) != $true) | ? [X215 : term] : (((X209 @ id @ X215 @ id)) != ((X208 @ X215))) | ($true = ((X208 @ (ap @ X207 @ X210)))))) & (ulamvarind = $true) & (axvarshift = $true) & ((! [X229 : term,X227 : term,X228 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X227)) != ((ap @ (sub @ X229 @ id) @ X228))) | (X227 = X228)) | ? [X225 : term,X223 : term,X222 : term,X224 : term] : ((((ap @ X224 @ X222)) = ((ap @ X223 @ X225))) & (X222 != X225))) <=> (hoasapinj2_lthm = $true)) & (! [X77 : term,X76 : term,X75 : (subst > term > subst > $o)] : (? [X79 : term,X78 : term] : ((((X75 @ id @ X78 @ id)) = $true) & (((X75 @ id @ X79 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X79 @ id) @ X78) @ id)) != $true)) | ($true != ((X75 @ id @ X77 @ id))) | (((X75 @ id @ (ap @ X76 @ X77) @ id)) = $true) | ? [X83 : subst,X80 : subst,X82 : subst,X81 : term] : ((((X75 @ X80 @ X81 @ (comp @ X82 @ X83))) = $true) & ($true != ((X75 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82) @ X83)))) | ? [X85 : subst,X84 : subst,X86 : term,X87 : subst] : ((((X75 @ (comp @ X84 @ X87) @ (sub @ X86 @ X87) @ X85)) = $true) & ($true != ((X75 @ X84 @ X86 @ (comp @ X87 @ X85))))) | ($true != ((X75 @ id @ X76 @ id)))) <=> (hoasinduction_lem2 = $true)) & (axmap = $true) & (termmset_gthm = $true) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X89 : subst,X90 : term,X88 : (term > $o)] : ? [X91 : (term > $o)] : ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & ((axshiftcons = $true) <=> ! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499)) & (lamnotap != $true) & (hoasapnotvar_lthm = $true) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & ((hoasinduction_lem3v2a = $true) <=> ! [X180 : term,X181 : (subst > term > subst > $o),X182 : (term > $o)] : (? [X188 : term] : (((X181 @ id @ X188 @ id)) != ((X182 @ X188))) | ? [X189 : term] : ((((X182 @ (sub @ X180 @ (push @ X189 @ id)))) != $true) & (((X182 @ X189)) = $true)) | ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : subst,X184 : term] : (((sub @ (X183 @ X185 @ X184) @ X186)) = ((X183 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)))) & ($true != ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) & ! [X187 : term] : ((((X181 @ id @ (X183 @ id @ X187) @ id)) = $true) | (((X181 @ id @ X187 @ id)) != $true))) | (((X182 @ (lam @ X180))) = $true))) & (((((! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X29 : term,X28 : term] : ((((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X23 : (subst > term > term)] : (! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | (((X21 @ id @ X27 @ id)) != $true)) & ($true != ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) & ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24)))))) | ? [X11 : (subst > term > subst > $o),X13 : (term > $o),X12 : term] : ((((X13 @ (lam @ X12))) != $true) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X20 : term] : ((((X11 @ id @ (X16 @ id @ X20) @ id)) != $true) & (((X11 @ id @ X20 @ id)) = $true)) | ? [X17 : subst,X18 : subst,X19 : term] : (((sub @ (X16 @ X17 @ X19) @ X18)) != ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18))))) & ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | (((X13 @ X15)) != $true)) & ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X3 : term,X4 : (term > $o)] : (! [X5 : term] : ((((X4 @ X5)) = $true) | (((var @ X5)) != $true)) & ! [X7 : term,X6 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | (((X4 @ X7)) != $true) | (((X4 @ X6)) != $true)) & (((X4 @ X3)) != $true) & ! [X8 : term] : (? [X9 : term] : ((((X4 @ X9)) = $true) & (((X4 @ (sub @ X8 @ (push @ X9 @ id)))) != $true)) | (((X4 @ (lam @ X8))) = $true)))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X372 : subst] : (((comp @ id @ X372)) = X372)) & (induction2_gthm = $true) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) <=> (laminj = $true)) & (! [X352 : (term > $o),X351 : term] : (? [X354 : term] : (! [X355 : term] : ((((X352 @ X355)) != $true) | (((X352 @ (sub @ X354 @ (push @ X355 @ id)))) = $true)) & (((X352 @ (lam @ X354))) != $true)) | ($true = ((X352 @ X351))) | ? [X353 : term] : ((((X352 @ X353)) != $true) & (((var @ X353)) = $true)) | ? [X357 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true != ((X352 @ (ap @ X357 @ X356)))) & (((X352 @ X357)) = $true))) <=> (induction2 = $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)))))))))))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X172 : term,X173 : (subst > term > subst > $o)] : ((((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) = $true) | ? [X175 : (subst > term > term)] : (! [X179 : subst,X177 : subst,X178 : term] : (((X175 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179))) = ((sub @ (X175 @ X177 @ X178) @ X179))) & (((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id)) != $true) & ! [X176 : term] : ((((X173 @ id @ X176 @ id)) != $true) | (((X173 @ id @ (X175 @ id @ X176) @ id)) = $true))) | ? [X174 : term] : (($true != ((X173 @ id @ (sub @ X172 @ (push @ X174 @ id)) @ id))) & ($true = ((X173 @ id @ X174 @ id)))))) & (! [X191 : (subst > term > subst > $o),X190 : term] : (($true = ((X191 @ id @ X190 @ id))) | ? [X192 : (subst > term > term)] : (! [X196 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X196) @ (sub @ X194 @ X196))) = ((sub @ (X192 @ X195 @ X194) @ X196))) & (((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id)) != $true) & ! [X193 : term] : ((((X191 @ id @ X193 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X193) @ id)) = $true))) | ? [X198 : term,X197 : term] : ((((X191 @ id @ (ap @ (sub @ X198 @ id) @ X197) @ id)) != $true) & (((X191 @ id @ X198 @ id)) = $true) & (((X191 @ id @ X197 @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) <=> (apinj1 = $true)) & (hoasinduction_lem1 = $true) & ((hoasapinj2 = $true) <=> ! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417))) & (((! [X443 : term,X442 : (subst > term > subst > $o)] : ((((X442 @ id @ (lam @ X443) @ id)) = $true) | ? [X444 : term] : (($true = ((X442 @ id @ X444 @ id))) & ($true != ((X442 @ id @ (sub @ X443 @ (push @ X444 @ id)) @ id)))) | ? [X445 : (subst > term > term)] : (! [X447 : term,X449 : subst,X448 : subst] : (((sub @ (X445 @ X448 @ X447) @ X449)) = ((X445 @ (comp @ X448 @ X449) @ (sub @ X447 @ X449)))) & ! [X446 : term] : ((((X442 @ id @ X446 @ id)) != $true) | (((X442 @ id @ (X445 @ id @ X446) @ id)) = $true)) & ($true != ((X442 @ id @ (lam @ (X445 @ sh @ one)) @ id))))) | ? [X434 : (subst > term > subst > $o),X435 : term] : (! [X436 : (subst > term > term)] : ((((X434 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X439 : subst,X438 : subst,X440 : term] : (((sub @ (X436 @ X438 @ X440) @ X439)) != ((X436 @ (comp @ X438 @ X439) @ (sub @ X440 @ X439)))) | ? [X437 : term] : (($true = ((X434 @ id @ X437 @ id))) & ($true != ((X434 @ id @ (X436 @ id @ X437) @ id))))) & ! [X441 : term] : (($true != ((X434 @ id @ X441 @ id))) | ($true = ((X434 @ id @ (sub @ X435 @ (push @ X441 @ id)) @ id)))) & (((X434 @ id @ (lam @ (sub @ X435 @ (push @ one @ sh))) @ id)) != $true))) | ? [X433 : term] : (((sub @ X433 @ id)) != X433)) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X410 : (subst > term > term),X411 : term,X409 : term] : (? [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) != ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409))))) & (! [X57 : (term > $o),X58 : (subst > term > subst > $o),X56 : term] : (? [X64 : (subst > term > term)] : (! [X68 : term] : ((((X58 @ id @ (X64 @ id @ X68) @ id)) = $true) | (((X58 @ id @ X68 @ id)) != $true)) & ! [X66 : subst,X65 : term,X67 : subst] : (((sub @ (X64 @ X66 @ X65) @ X67)) = ((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & (((X58 @ id @ (lam @ (X64 @ sh @ one)) @ id)) != $true)) | ($true = ((X57 @ (lam @ X56)))) | ? [X69 : term,X72 : subst,X71 : subst,X70 : subst] : ((((X58 @ X70 @ X69 @ (comp @ X72 @ X71))) != $true) & (((X58 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) = $true)) | ? [X63 : subst,X61 : subst,X62 : subst,X60 : term] : (($true != ((X58 @ (comp @ X61 @ X62) @ (sub @ X60 @ X62) @ X63))) & (((X58 @ X61 @ X60 @ (comp @ X62 @ X63))) = $true)) | ? [X59 : term] : ((((X57 @ X59)) = $true) & (((X57 @ (sub @ X56 @ (push @ X59 @ id)))) != $true)) | ? [X73 : term] : (((X58 @ id @ X73 @ id)) != ((X57 @ X73)))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X93 : term] : ? [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) = ((X94 @ sh @ one)))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X358 : term] : ? [X359 : (subst > term > term)] : (((X359 @ sh @ one)) = ((sub @ X358 @ (push @ one @ sh))))) & ((pushprop_lem0 = $true) <=> ! [X522 : (term > $o),X524 : term,X523 : subst] : ? [X525 : (term > $o)] : ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523)))))) & (! [X231 : (subst > term > subst > $o),X230 : term] : (? [X232 : term] : ((((X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) != $true) & (((X231 @ id @ X232 @ id)) = $true)) | (((X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) = $true) | ? [X233 : (subst > term > term)] : ((((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true) & ! [X234 : subst,X235 : subst,X236 : term] : (((X233 @ (comp @ X234 @ X235) @ (sub @ X236 @ X235))) = ((sub @ (X233 @ X234 @ X236) @ X235))) & ! [X237 : term] : ((((X231 @ id @ X237 @ id)) != $true) | (((X231 @ id @ (X233 @ id @ X237) @ id)) = $true)))) <=> (hoasinduction_lem3aa = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_gthm = $true) & ((induction2_lthm = $true) <=> ((! [X515 : term,X516 : (term > $o)] : (? [X518 : term,X517 : term] : ((((X516 @ X518)) = $true) & (((X516 @ (ap @ X517 @ X518))) != $true) & (((X516 @ X517)) = $true)) | ? [X519 : term] : ((((X516 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X516 @ X520)) != $true) | (((X516 @ (sub @ X519 @ (push @ X520 @ id)))) = $true))) | ? [X521 : term] : ((((var @ X521)) = $true) & (((X516 @ X521)) != $true)) | (((X516 @ X515)) = $true)) | ? [X509 : term,X508 : subst,X507 : (term > $o)] : (! [X513 : term,X512 : term] : ((((X507 @ X512)) != $true) | ($true != ((X507 @ X513))) | ($true = ((X507 @ (ap @ X513 @ X512))))) & ! [X510 : term] : ((((X507 @ (lam @ X510))) = $true) | ? [X511 : term] : ((((X507 @ X511)) = $true) & (((X507 @ (sub @ X510 @ (push @ X511 @ id)))) != $true))) & ! [X514 : term] : (($true != ((var @ X514))) | ($true = ((X507 @ (sub @ X514 @ X508))))) & (((X507 @ (sub @ X509 @ X508))) != $true))) | ? [X506 : term] : (((sub @ X506 @ id)) != X506))) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X475 : (subst > term > subst > $o),X476 : term] : (? [X492 : subst,X491 : subst,X490 : subst,X489 : term] : ((((X475 @ X492 @ X489 @ (comp @ X490 @ X491))) = $true) & (((X475 @ (comp @ X492 @ X490) @ (sub @ X489 @ X490) @ X491)) != $true)) | (((X475 @ id @ X476 @ id)) = $true) | ? [X484 : term] : (($true != ((X475 @ id @ X484 @ id))) & (((var @ (sub @ X484 @ id))) = $true)) | ? [X477 : (subst > term > term)] : (! [X481 : term] : ((((X475 @ id @ (X477 @ id @ X481) @ id)) = $true) | ($true != ((X475 @ id @ X481 @ id)))) & ! [X478 : subst,X479 : subst,X480 : term] : (((X477 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478))) = ((sub @ (X477 @ X479 @ X480) @ X478))) & (((X475 @ id @ (lam @ (X477 @ sh @ one)) @ id)) != $true)) | ? [X482 : term,X483 : term] : (($true = ((X475 @ id @ X482 @ id))) & (((X475 @ id @ X483 @ id)) = $true) & (((X475 @ id @ (ap @ (sub @ X483 @ id) @ X482) @ id)) != $true)) | ? [X485 : term,X488 : subst,X486 : subst,X487 : subst] : ((((X475 @ (comp @ X488 @ X486) @ (sub @ X485 @ X486) @ X487)) = $true) & (((X475 @ X488 @ X485 @ (comp @ X486 @ X487))) != $true))) | ? [X465 : (subst > term > subst > $o),X466 : term,X467 : (term > $o)] : (! [X474 : term] : (((X467 @ X474)) = ((X465 @ id @ X474 @ id))) & ! [X468 : (subst > term > term)] : (? [X469 : subst,X471 : term,X470 : subst] : (((sub @ (X468 @ X470 @ X471) @ X469)) != ((X468 @ (comp @ X470 @ X469) @ (sub @ X471 @ X469)))) | (((X465 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true) | ? [X472 : term] : ((((X465 @ id @ (X468 @ id @ X472) @ id)) != $true) & (((X465 @ id @ X472 @ id)) = $true))) & ! [X473 : term] : ((((X467 @ X473)) != $true) | (((X467 @ (sub @ X466 @ (push @ X473 @ id)))) = $true)) & (((X467 @ (lam @ X466))) != $true))) | ? [X464 : term] : (((sub @ X464 @ id)) != X464)) | ? [X458 : term,X457 : (term > $o)] : (! [X463 : term,X462 : term] : (($true != ((X457 @ X462))) | ($true != ((X457 @ X463))) | ($true = ((X457 @ (ap @ X462 @ X463))))) & ! [X459 : term] : ((((X457 @ X459)) = $true) | ($true != ((var @ X459)))) & (((X457 @ X458)) != $true) & ! [X460 : term] : ((((X457 @ (lam @ X460))) = $true) | ? [X461 : term] : (($true != ((X457 @ (sub @ X460 @ (push @ X461 @ id))))) & (((X457 @ X461)) = $true))))) | ? [X454 : (subst > term > subst > $o)] : ! [X455 : (term > $o)] : ? [X456 : term] : (((X455 @ X456)) != ((X454 @ id @ X456 @ id))))) & (hoaslamnotvar = $true) & (pushprop_gthm = $true) & ((shinj = $true) <=> ! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh))))) & ! [X528 : d_subst,X527 : d_subst] : ((X527 = X528) | (((d2subst @ X528)) != ((d2subst @ X527)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((induction = $true) <=> ! [X51 : term,X50 : (term > $o)] : (? [X52 : term] : ((((X50 @ X52)) = $true) & (((X50 @ (lam @ X52))) != $true)) | ? [X54 : term,X55 : term] : ((((X50 @ X54)) = $true) & (((X50 @ (ap @ X55 @ X54))) != $true) & (((X50 @ X55)) = $true)) | ? [X53 : term] : ((((var @ X53)) = $true) & (((X50 @ X53)) != $true)) | (((X50 @ X51)) = $true))) & (hoasinduction_lem3_gthm = $true) & (((! [X324 : term,X323 : (subst > term > subst > $o)] : (? [X330 : (subst > term > term)] : ((((X323 @ id @ (lam @ (X330 @ sh @ one)) @ id)) != $true) & ! [X331 : subst,X332 : subst,X333 : term] : (((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))) = ((sub @ (X330 @ X331 @ X333) @ X332))) & ! [X334 : term] : ((((X323 @ id @ X334 @ id)) != $true) | (((X323 @ id @ (X330 @ id @ X334) @ id)) = $true))) | (((X323 @ id @ (lam @ X324) @ id)) = $true) | ? [X338 : subst,X337 : subst,X335 : subst,X336 : term] : ((((X323 @ X338 @ X336 @ (comp @ X337 @ X335))) = $true) & (((X323 @ (comp @ X338 @ X337) @ (sub @ X336 @ X337) @ X335)) != $true)) | ? [X325 : term] : (($true = ((X323 @ id @ X325 @ id))) & (((X323 @ id @ (sub @ X324 @ (push @ X325 @ id)) @ id)) != $true)) | ? [X328 : subst,X326 : subst,X327 : subst,X329 : term] : (($true != ((X323 @ X328 @ X329 @ (comp @ X327 @ X326)))) & (((X323 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327) @ X326)) = $true))) | ? [X316 : term,X315 : (subst > term > subst > $o)] : (($true != ((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id))) & ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true != ((X315 @ id @ (X317 @ id @ X318) @ id))) & ($true = ((X315 @ id @ X318 @ id)))) | ? [X319 : subst,X320 : term,X321 : subst] : (((X317 @ (comp @ X319 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X317 @ X319 @ X320) @ X321))) | ($true = ((X315 @ id @ (lam @ (X317 @ sh @ one)) @ id)))) & ! [X322 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X322 @ id)) @ id)) = $true) | ($true != ((X315 @ id @ X322 @ id)))))) | ? [X314 : term] : (((sub @ X314 @ id)) != X314)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) <=> (hoasapinj1 = $true)) & ((substmonoid_lthm = $true) <=> (((! [X452 : subst] : (((comp @ X452 @ id)) = X452) & ! [X453 : subst] : (((comp @ id @ X453)) = X453)) | ? [X451 : subst] : (((comp @ X451 @ id)) != X451)) | ? [X450 : subst] : (((comp @ id @ X450)) != X450))) & (((((! [X304 : subst,X306 : term,X305 : (term > $o)] : ((((X305 @ (sub @ X306 @ X304))) = $true) | ? [X307 : term] : (! [X308 : term] : ((((X305 @ (sub @ X307 @ (push @ X308 @ id)))) = $true) | (((X305 @ X308)) != $true)) & (((X305 @ (lam @ X307))) != $true)) | ? [X310 : term,X311 : term] : ((((X305 @ X310)) = $true) & ($true = ((X305 @ X311))) & (((X305 @ (ap @ X310 @ X311))) != $true)) | ? [X309 : term] : ((((X305 @ (sub @ X309 @ X304))) != $true) & ($true = ((var @ X309))))) | ? [X298 : (term > $o),X299 : term] : (! [X301 : term] : (($true != ((var @ X301))) | ($true = ((X298 @ X301)))) & ($true != ((X298 @ X299))) & ! [X302 : term,X303 : term] : ((((X298 @ X303)) != $true) | (((X298 @ X302)) != $true) | ($true = ((X298 @ (ap @ X302 @ X303))))) & ! [X300 : term] : ((((X298 @ X300)) != $true) | (((X298 @ (lam @ X300))) = $true)))) | ? [X297 : subst] : (((comp @ X297 @ id)) != X297)) | ? [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) != X296)) | ? [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) != X294)) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X360 : (subst > term > subst > $o),X361 : term] : (? [X363 : term,X362 : (subst > term > term)] : ((((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X360 @ id @ (X362 @ id @ X370) @ id)) = $true) | (((X360 @ id @ X370 @ id)) != $true)) & ! [X366 : subst,X365 : subst,X364 : term] : (((sub @ (sub @ X363 @ (push @ X364 @ X366)) @ X365)) = ((sub @ (X362 @ X366 @ X364) @ X365))) & ! [X368 : term,X369 : subst,X367 : subst] : (((sub @ X363 @ (push @ (sub @ X368 @ X367) @ (comp @ X369 @ X367)))) = ((X362 @ (comp @ X369 @ X367) @ (sub @ X368 @ X367))))) | ? [X371 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X371 @ id)) @ id)) != $true) & ($true = ((X360 @ id @ X371 @ id)))) | (((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true))) & (axassoc = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & ! [X385 : d_subst] : (d_id = X385) & (ulamvarsh = $true) & ! [X292 : d_term] : (d_one = X292) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & ((termmset_lthm = $true) <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) | ? [X345 : term] : (((sub @ X345 @ id)) != X345))) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (((d2subst @ d_id)) = sh) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) <=> (axidr = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem2v2 = $true) & ((termmset = $true) <=> ! [X313 : term] : (((sub @ X313 @ id)) = X313)) & (axclos = $true) & (hoaslaminj_gthm = $true) & (! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoaslamnotap_lthm = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ! [X501 : d_term,X500 : d_term] : ((X500 = X501) | (((d2term @ X500)) != ((d2term @ X501)))) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm_orig = $true) & ((hoasinduction_lthm = $true) <=> (((! [X154 : (subst > term > subst > $o),X155 : term] : ((((X154 @ id @ X155 @ id)) = $true) | ? [X158 : subst,X157 : subst,X159 : subst,X160 : term] : ((((X154 @ X157 @ X160 @ (comp @ X158 @ X159))) != $true) & ($true = ((X154 @ (comp @ X157 @ X158) @ (sub @ X160 @ X158) @ X159)))) | ? [X170 : term,X171 : term] : ((((X154 @ id @ X170 @ id)) = $true) & (((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)) != $true) & (((X154 @ id @ X171 @ id)) = $true)) | ? [X165 : (subst > term > term)] : (! [X167 : subst,X166 : term,X168 : subst] : (((X165 @ (comp @ X168 @ X167) @ (sub @ X166 @ X167))) = ((sub @ (X165 @ X168 @ X166) @ X167))) & ! [X169 : term] : ((((X154 @ id @ X169 @ id)) != $true) | (((X154 @ id @ (X165 @ id @ X169) @ id)) = $true)) & (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) != $true)) | ? [X164 : subst,X161 : subst,X162 : term,X163 : subst] : ((((X154 @ (comp @ X161 @ X164) @ (sub @ X162 @ X164) @ X163)) != $true) & (((X154 @ X161 @ X162 @ (comp @ X164 @ X163))) = $true)) | ? [X156 : term] : (($true != ((X154 @ id @ X156 @ id))) & ($true = ((var @ (sub @ X156 @ id)))))) | ? [X139 : (subst > term > subst > $o),X138 : term] : ((((X139 @ id @ (lam @ X138) @ id)) != $true) & ! [X144 : term] : ((((X139 @ id @ (sub @ X138 @ (push @ X144 @ id)) @ id)) = $true) | (((X139 @ id @ X144 @ id)) != $true)) & ! [X145 : (subst > term > term)] : (? [X146 : term] : ((((X139 @ id @ X146 @ id)) = $true) & (((X139 @ id @ (X145 @ id @ X146) @ id)) != $true)) | ($true = ((X139 @ id @ (lam @ (X145 @ sh @ one)) @ id))) | ? [X149 : term,X147 : subst,X148 : subst] : (((sub @ (X145 @ X147 @ X149) @ X148)) != ((X145 @ (comp @ X147 @ X148) @ (sub @ X149 @ X148))))) & ! [X153 : subst,X151 : subst,X152 : term,X150 : subst] : ((((X139 @ (comp @ X150 @ X151) @ (sub @ X152 @ X151) @ X153)) = $true) | (((X139 @ X150 @ X152 @ (comp @ X151 @ X153))) != $true)) & ! [X142 : subst,X143 : subst,X141 : subst,X140 : term] : (($true != ((X139 @ (comp @ X141 @ X143) @ (sub @ X140 @ X143) @ X142))) | (((X139 @ X141 @ X140 @ (comp @ X143 @ X142))) = $true)))) | ? [X127 : (subst > term > subst > $o),X126 : term,X125 : term] : (! [X128 : subst,X129 : subst,X130 : subst,X131 : term] : (($true = ((X127 @ (comp @ X128 @ X129) @ (sub @ X131 @ X129) @ X130))) | (((X127 @ X128 @ X131 @ (comp @ X129 @ X130))) != $true)) & (((X127 @ id @ X125 @ id)) = $true) & (((X127 @ id @ X126 @ id)) = $true) & ! [X137 : term,X136 : term] : ((((X127 @ id @ X136 @ id)) != $true) | ($true != ((X127 @ id @ X137 @ id))) | (((X127 @ id @ (ap @ (sub @ X137 @ id) @ X136) @ id)) = $true)) & ($true != ((X127 @ id @ (ap @ X125 @ X126) @ id))) & ! [X133 : subst,X135 : term,X132 : subst,X134 : subst] : ((((X127 @ (comp @ X132 @ X133) @ (sub @ X135 @ X133) @ X134)) != $true) | ($true = ((X127 @ X132 @ X135 @ (comp @ X133 @ X134))))))) | ? [X119 : term,X118 : (term > $o)] : (! [X122 : term] : ((((X118 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X118 @ (sub @ X122 @ (push @ X123 @ id)))) != $true) & ($true = ((X118 @ X123))))) & ($true != ((X118 @ X119))) & ! [X124 : term] : (($true != ((var @ X124))) | (((X118 @ X124)) = $true)) & ! [X120 : term,X121 : term] : (($true != ((X118 @ X121))) | (((X118 @ (ap @ X120 @ X121))) = $true) | (((X118 @ X120)) != $true))))) & ((pushprop_lem1v2_lthm = $true) <=> (? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ! [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (? [X117 : term] : (((X114 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) | (((X114 @ one)) = $true) | (((X113 @ X116)) != $true)))) & ((hoasinduction_lem3a = $true) <=> ! [X376 : term,X375 : (subst > term > subst > $o)] : (($true = ((X375 @ id @ (lam @ X376) @ id))) | ? [X382 : term] : ((((X375 @ id @ X382 @ id)) = $true) & (((X375 @ id @ (sub @ X376 @ (push @ X382 @ id)) @ id)) != $true)) | ? [X377 : (subst > term > term)] : (($true != ((X375 @ id @ (lam @ (X377 @ sh @ one)) @ id))) & ! [X381 : term] : (($true != ((X375 @ id @ X381 @ id))) | (((X375 @ id @ (X377 @ id @ X381) @ id)) = $true)) & ! [X379 : subst,X380 : term,X378 : subst] : (((X377 @ (comp @ X379 @ X378) @ (sub @ X380 @ X378))) = ((sub @ (X377 @ X379 @ X380) @ X378)))))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X244 : term,X245 : (term > $o),X243 : (subst > term > subst > $o)] : (? [X247 : term] : ((((X245 @ (sub @ X244 @ (push @ X247 @ id)))) != $true) & (((X245 @ X247)) = $true)) | ? [X246 : term] : (((X245 @ X246)) != ((X243 @ id @ X246 @ id))) | ? [X248 : (subst > term > term)] : (! [X249 : term] : ((((X243 @ id @ X249 @ id)) != $true) | (((X243 @ id @ (X248 @ id @ X249) @ id)) = $true)) & ! [X251 : subst,X250 : term,X252 : subst] : (((sub @ (X248 @ X252 @ X250) @ X251)) = ((X248 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)))) & (((X243 @ id @ (lam @ (X248 @ sh @ one)) @ id)) != $true)) | (((X245 @ (lam @ X244))) = $true)) | ? [X242 : term] : (((sub @ X242 @ id)) != X242)) | ? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) != ((X239 @ X241 @ X240))))) & (axabs = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (ulamvar1 != $true) & (! [X422 : (term > $o),X423 : term,X421 : subst] : (? [X426 : term] : ((((var @ X426)) = $true) & (((X422 @ (sub @ X426 @ X421))) != $true)) | ? [X428 : term,X427 : term] : ((((X422 @ (ap @ X427 @ X428))) != $true) & ($true = ((X422 @ X427))) & ($true = ((X422 @ X428)))) | ? [X424 : term] : (! [X425 : term] : ((((X422 @ X425)) != $true) | (((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true)) & (((X422 @ (lam @ X424))) != $true)) | ($true = ((X422 @ (sub @ X423 @ X421))))) <=> (induction2lem = $true))),
% 3.80/0.85 inference(ennf_transformation,[],[f10])).
% 3.80/0.85 thf(f12,plain,(
% 3.80/0.85 ((? [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) != X283) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281) | ! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true))) <=> (pushprop_lem1_lthm = $true)) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (pushprop_lem2v2_lthm = $true) & ((? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) != ((X239 @ X241 @ X240))) | ! [X244 : term,X245 : (term > $o),X243 : (subst > term > subst > $o)] : (? [X247 : term] : ((((X245 @ (sub @ X244 @ (push @ X247 @ id)))) != $true) & (((X245 @ X247)) = $true)) | ? [X246 : term] : (((X245 @ X246)) != ((X243 @ id @ X246 @ id))) | ? [X248 : (subst > term > term)] : (! [X249 : term] : ((((X243 @ id @ X249 @ id)) != $true) | (((X243 @ id @ (X248 @ id @ X249) @ id)) = $true)) & ! [X251 : subst,X250 : term,X252 : subst] : (((sub @ (X248 @ X252 @ X250) @ X251)) = ((X248 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)))) & (((X243 @ id @ (lam @ (X248 @ sh @ one)) @ id)) != $true)) | (((X245 @ (lam @ X244))) = $true)) | ? [X242 : term] : (((sub @ X242 @ id)) != X242)) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (? [X497 : term] : (((X493 @ X497)) != ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | ($true = ((X493 @ one))) | (((X494 @ X496)) != $true))) & (lamnotvar = $true) & ((hoaslaminj = $true) <=> ! [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ? [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) != ((sub @ (X271 @ X275 @ X276) @ X277))) | ? [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) != ((sub @ (X272 @ X280 @ X279) @ X278))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X410 : (subst > term > term),X411 : term,X409 : term] : (? [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) != ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409))))) & (hoasinduction_lem2_lthm = $true) & (! [X352 : (term > $o),X351 : term] : (? [X354 : term] : (! [X355 : term] : ((((X352 @ X355)) != $true) | (((X352 @ (sub @ X354 @ (push @ X355 @ id)))) = $true)) & (((X352 @ (lam @ X354))) != $true)) | ($true = ((X352 @ X351))) | ? [X353 : term] : ((((X352 @ X353)) != $true) & (((var @ X353)) = $true)) | ? [X357 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true != ((X352 @ (ap @ X357 @ X356)))) & (((X352 @ X357)) = $true))) <=> (induction2 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X528 : d_subst,X527 : d_subst] : ((X527 = X528) | (((d2subst @ X528)) != ((d2subst @ X527)))) & ((hoaslaminj_lthm = $true) <=> (? [X100 : term,X99 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100)))) | ? [X97 : subst,X98 : term] : (((comp @ sh @ (push @ X98 @ X97))) != X97) | ! [X104 : (subst > term > term),X103 : term,X102 : (subst > term > term),X101 : subst] : (? [X107 : term,X106 : subst,X105 : subst] : (((X104 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X104 @ X105 @ X107) @ X106))) | ? [X109 : term,X108 : subst,X110 : subst] : (((X102 @ (comp @ X110 @ X108) @ (sub @ X109 @ X108))) != ((sub @ (X102 @ X110 @ X109) @ X108))) | (((lam @ (X104 @ sh @ one))) != ((lam @ (X102 @ sh @ one)))) | (((X104 @ X101 @ X103)) = ((X102 @ X101 @ X103)))) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96))) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) | ? [X345 : term] : (((sub @ X345 @ id)) != X345))) & ((pushprop_lem0 = $true) <=> ! [X522 : (term > $o),X524 : term,X523 : subst] : ? [X525 : (term > $o)] : ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523)))))) & ((? [X298 : (term > $o),X299 : term] : (! [X301 : term] : (($true != ((var @ X301))) | ($true = ((X298 @ X301)))) & ($true != ((X298 @ X299))) & ! [X302 : term,X303 : term] : ((((X298 @ X303)) != $true) | (((X298 @ X302)) != $true) | ($true = ((X298 @ (ap @ X302 @ X303))))) & ! [X300 : term] : ((((X298 @ X300)) != $true) | (((X298 @ (lam @ X300))) = $true))) | ! [X304 : subst,X306 : term,X305 : (term > $o)] : ((((X305 @ (sub @ X306 @ X304))) = $true) | ? [X307 : term] : (! [X308 : term] : ((((X305 @ (sub @ X307 @ (push @ X308 @ id)))) = $true) | (((X305 @ X308)) != $true)) & (((X305 @ (lam @ X307))) != $true)) | ? [X310 : term,X311 : term] : ((((X305 @ X310)) = $true) & ($true = ((X305 @ X311))) & (((X305 @ (ap @ X310 @ X311))) != $true)) | ? [X309 : term] : ((((X305 @ (sub @ X309 @ X304))) != $true) & ($true = ((var @ X309))))) | ? [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) != X294) | ? [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) != X296) | ? [X297 : subst] : (((comp @ X297 @ id)) != X297)) <=> (induction2lem_lthm = $true)) & (axabs = $true) & (pushprop_lem3v2 = $true) & ((shinj = $true) <=> ! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh))))) & (hoasinduction_lem1_lthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (hoasinduction_lem3b_gthm = $true) & ((! [X229 : term,X227 : term,X228 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X227)) != ((ap @ (sub @ X229 @ id) @ X228))) | (X227 = X228)) | ? [X225 : term,X223 : term,X222 : term,X224 : term] : ((((ap @ X224 @ X222)) = ((ap @ X223 @ X225))) & (X222 != X225))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X376 : term,X375 : (subst > term > subst > $o)] : (($true = ((X375 @ id @ (lam @ X376) @ id))) | ? [X382 : term] : ((((X375 @ id @ X382 @ id)) = $true) & (((X375 @ id @ (sub @ X376 @ (push @ X382 @ id)) @ id)) != $true)) | ? [X377 : (subst > term > term)] : (($true != ((X375 @ id @ (lam @ (X377 @ sh @ one)) @ id))) & ! [X381 : term] : (($true != ((X375 @ id @ X381 @ id))) | (((X375 @ id @ (X377 @ id @ X381) @ id)) = $true)) & ! [X379 : subst,X380 : term,X378 : subst] : (((X377 @ (comp @ X379 @ X378) @ (sub @ X380 @ X378))) = ((sub @ (X377 @ X379 @ X380) @ X378)))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X172 : term,X173 : (subst > term > subst > $o)] : ((((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) = $true) | ? [X175 : (subst > term > term)] : (! [X179 : subst,X177 : subst,X178 : term] : (((X175 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179))) = ((sub @ (X175 @ X177 @ X178) @ X179))) & (((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id)) != $true) & ! [X176 : term] : ((((X173 @ id @ X176 @ id)) != $true) | (((X173 @ id @ (X175 @ id @ X176) @ id)) = $true))) | ? [X174 : term] : (($true != ((X173 @ id @ (sub @ X172 @ (push @ X174 @ id)) @ id))) & ($true = ((X173 @ id @ X174 @ id)))))) & ((termmset = $true) <=> ! [X313 : term] : (((sub @ X313 @ id)) = X313)) & ((hoasinduction_lem3b = $true) <=> ! [X358 : term] : ? [X359 : (subst > term > term)] : (((X359 @ sh @ one)) = ((sub @ X358 @ (push @ one @ sh))))) & (! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X180 : term,X181 : (subst > term > subst > $o),X182 : (term > $o)] : (? [X188 : term] : (((X181 @ id @ X188 @ id)) != ((X182 @ X188))) | ? [X189 : term] : ((((X182 @ (sub @ X180 @ (push @ X189 @ id)))) != $true) & (((X182 @ X189)) = $true)) | ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : subst,X184 : term] : (((sub @ (X183 @ X185 @ X184) @ X186)) = ((X183 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)))) & ($true != ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) & ! [X187 : term] : ((((X181 @ id @ (X183 @ id @ X187) @ id)) = $true) | (((X181 @ id @ X187 @ id)) != $true))) | (((X182 @ (lam @ X180))) = $true))) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X443 : term,X442 : (subst > term > subst > $o)] : ((((X442 @ id @ (lam @ X443) @ id)) = $true) | ? [X444 : term] : (($true = ((X442 @ id @ X444 @ id))) & ($true != ((X442 @ id @ (sub @ X443 @ (push @ X444 @ id)) @ id)))) | ? [X445 : (subst > term > term)] : (! [X447 : term,X449 : subst,X448 : subst] : (((sub @ (X445 @ X448 @ X447) @ X449)) = ((X445 @ (comp @ X448 @ X449) @ (sub @ X447 @ X449)))) & ! [X446 : term] : ((((X442 @ id @ X446 @ id)) != $true) | (((X442 @ id @ (X445 @ id @ X446) @ id)) = $true)) & ($true != ((X442 @ id @ (lam @ (X445 @ sh @ one)) @ id))))) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | ? [X434 : (subst > term > subst > $o),X435 : term] : (! [X436 : (subst > term > term)] : ((((X434 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X439 : subst,X438 : subst,X440 : term] : (((sub @ (X436 @ X438 @ X440) @ X439)) != ((X436 @ (comp @ X438 @ X439) @ (sub @ X440 @ X439)))) | ? [X437 : term] : (($true = ((X434 @ id @ X437 @ id))) & ($true != ((X434 @ id @ (X436 @ id @ X437) @ id))))) & ! [X441 : term] : (($true != ((X434 @ id @ X441 @ id))) | ($true = ((X434 @ id @ (sub @ X435 @ (push @ X441 @ id)) @ id)))) & (((X434 @ id @ (lam @ (sub @ X435 @ (push @ one @ sh))) @ id)) != $true)))) & ! [X501 : d_term,X500 : d_term] : ((X500 = X501) | (((d2term @ X500)) != ((d2term @ X501)))) & (! [X191 : (subst > term > subst > $o),X190 : term] : (($true = ((X191 @ id @ X190 @ id))) | ? [X192 : (subst > term > term)] : (! [X196 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X196) @ (sub @ X194 @ X196))) = ((sub @ (X192 @ X195 @ X194) @ X196))) & (((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id)) != $true) & ! [X193 : term] : ((((X191 @ id @ X193 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X193) @ id)) = $true))) | ? [X198 : term,X197 : term] : ((((X191 @ id @ (ap @ (sub @ X198 @ id) @ X197) @ id)) != $true) & (((X191 @ id @ X198 @ id)) = $true) & (((X191 @ id @ X197 @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X347 : term] : ? [X348 : (subst > term > term)] : ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350))))) & (! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = id) & ((? [X533 : term,X532 : term,X534 : term,X535 : term] : ((((ap @ X535 @ X533)) = ((ap @ X534 @ X532))) & (X534 != X535)) | ! [X537 : term,X536 : term,X539 : term,X538 : term] : ((((ap @ (sub @ X537 @ id) @ X539)) != ((ap @ (sub @ X536 @ id) @ X538))) | (X536 = X537)) | ? [X531 : term] : (((sub @ X531 @ id)) != X531)) <=> (hoasapinj1_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X231 : (subst > term > subst > $o),X230 : term] : (? [X232 : term] : ((((X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) != $true) & (((X231 @ id @ X232 @ id)) = $true)) | (((X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) = $true) | ? [X233 : (subst > term > term)] : ((((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true) & ! [X234 : subst,X235 : subst,X236 : term] : (((X233 @ (comp @ X234 @ X235) @ (sub @ X236 @ X235))) = ((sub @ (X233 @ X234 @ X236) @ X235))) & ! [X237 : term] : ((((X231 @ id @ X237 @ id)) != $true) | (((X231 @ id @ (X233 @ id @ X237) @ id)) = $true)))) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ! [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (? [X117 : term] : (((X114 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) | (((X114 @ one)) = $true) | (((X113 @ X116)) != $true)))) & ((? [X139 : (subst > term > subst > $o),X138 : term] : ((((X139 @ id @ (lam @ X138) @ id)) != $true) & ! [X144 : term] : ((((X139 @ id @ (sub @ X138 @ (push @ X144 @ id)) @ id)) = $true) | (((X139 @ id @ X144 @ id)) != $true)) & ! [X145 : (subst > term > term)] : (? [X146 : term] : ((((X139 @ id @ X146 @ id)) = $true) & (((X139 @ id @ (X145 @ id @ X146) @ id)) != $true)) | ($true = ((X139 @ id @ (lam @ (X145 @ sh @ one)) @ id))) | ? [X149 : term,X147 : subst,X148 : subst] : (((sub @ (X145 @ X147 @ X149) @ X148)) != ((X145 @ (comp @ X147 @ X148) @ (sub @ X149 @ X148))))) & ! [X153 : subst,X151 : subst,X152 : term,X150 : subst] : ((((X139 @ (comp @ X150 @ X151) @ (sub @ X152 @ X151) @ X153)) = $true) | (((X139 @ X150 @ X152 @ (comp @ X151 @ X153))) != $true)) & ! [X142 : subst,X143 : subst,X141 : subst,X140 : term] : (($true != ((X139 @ (comp @ X141 @ X143) @ (sub @ X140 @ X143) @ X142))) | (((X139 @ X141 @ X140 @ (comp @ X143 @ X142))) = $true))) | ! [X154 : (subst > term > subst > $o),X155 : term] : ((((X154 @ id @ X155 @ id)) = $true) | ? [X158 : subst,X157 : subst,X159 : subst,X160 : term] : ((((X154 @ X157 @ X160 @ (comp @ X158 @ X159))) != $true) & ($true = ((X154 @ (comp @ X157 @ X158) @ (sub @ X160 @ X158) @ X159)))) | ? [X170 : term,X171 : term] : ((((X154 @ id @ X170 @ id)) = $true) & (((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)) != $true) & (((X154 @ id @ X171 @ id)) = $true)) | ? [X165 : (subst > term > term)] : (! [X167 : subst,X166 : term,X168 : subst] : (((X165 @ (comp @ X168 @ X167) @ (sub @ X166 @ X167))) = ((sub @ (X165 @ X168 @ X166) @ X167))) & ! [X169 : term] : ((((X154 @ id @ X169 @ id)) != $true) | (((X154 @ id @ (X165 @ id @ X169) @ id)) = $true)) & (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) != $true)) | ? [X164 : subst,X161 : subst,X162 : term,X163 : subst] : ((((X154 @ (comp @ X161 @ X164) @ (sub @ X162 @ X164) @ X163)) != $true) & (((X154 @ X161 @ X162 @ (comp @ X164 @ X163))) = $true)) | ? [X156 : term] : (($true != ((X154 @ id @ X156 @ id))) & ($true = ((var @ (sub @ X156 @ id)))))) | ? [X119 : term,X118 : (term > $o)] : (! [X122 : term] : ((((X118 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X118 @ (sub @ X122 @ (push @ X123 @ id)))) != $true) & ($true = ((X118 @ X123))))) & ($true != ((X118 @ X119))) & ! [X124 : term] : (($true != ((var @ X124))) | (((X118 @ X124)) = $true)) & ! [X120 : term,X121 : term] : (($true != ((X118 @ X121))) | (((X118 @ (ap @ X120 @ X121))) = $true) | (((X118 @ X120)) != $true))) | ? [X127 : (subst > term > subst > $o),X126 : term,X125 : term] : (! [X128 : subst,X129 : subst,X130 : subst,X131 : term] : (($true = ((X127 @ (comp @ X128 @ X129) @ (sub @ X131 @ X129) @ X130))) | (((X127 @ X128 @ X131 @ (comp @ X129 @ X130))) != $true)) & (((X127 @ id @ X125 @ id)) = $true) & (((X127 @ id @ X126 @ id)) = $true) & ! [X137 : term,X136 : term] : ((((X127 @ id @ X136 @ id)) != $true) | ($true != ((X127 @ id @ X137 @ id))) | (((X127 @ id @ (ap @ (sub @ X137 @ id) @ X136) @ id)) = $true)) & ($true != ((X127 @ id @ (ap @ X125 @ X126) @ id))) & ! [X133 : subst,X135 : term,X132 : subst,X134 : subst] : ((((X127 @ (comp @ X132 @ X133) @ (sub @ X135 @ X133) @ X134)) != $true) | ($true = ((X127 @ X132 @ X135 @ (comp @ X133 @ X134))))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X422 : (term > $o),X423 : term,X421 : subst] : (? [X426 : term] : ((((var @ X426)) = $true) & (((X422 @ (sub @ X426 @ X421))) != $true)) | ? [X428 : term,X427 : term] : ((((X422 @ (ap @ X427 @ X428))) != $true) & ($true = ((X422 @ X427))) & ($true = ((X422 @ X428)))) | ? [X424 : term] : (! [X425 : term] : ((((X422 @ X425)) != $true) | (((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true)) & (((X422 @ (lam @ X424))) != $true)) | ($true = ((X422 @ (sub @ X423 @ X421))))) <=> (induction2lem = $true)) & (ulamvarsh = $true) & (axvarshift = $true) & (! [X57 : (term > $o),X58 : (subst > term > subst > $o),X56 : term] : (? [X64 : (subst > term > term)] : (! [X68 : term] : ((((X58 @ id @ (X64 @ id @ X68) @ id)) = $true) | (((X58 @ id @ X68 @ id)) != $true)) & ! [X66 : subst,X65 : term,X67 : subst] : (((sub @ (X64 @ X66 @ X65) @ X67)) = ((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & (((X58 @ id @ (lam @ (X64 @ sh @ one)) @ id)) != $true)) | ($true = ((X57 @ (lam @ X56)))) | ? [X69 : term,X72 : subst,X71 : subst,X70 : subst] : ((((X58 @ X70 @ X69 @ (comp @ X72 @ X71))) != $true) & (((X58 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) = $true)) | ? [X63 : subst,X61 : subst,X62 : subst,X60 : term] : (($true != ((X58 @ (comp @ X61 @ X62) @ (sub @ X60 @ X62) @ X63))) & (((X58 @ X61 @ X60 @ (comp @ X62 @ X63))) = $true)) | ? [X59 : term] : ((((X57 @ X59)) = $true) & (((X57 @ (sub @ X56 @ (push @ X59 @ id)))) != $true)) | ? [X73 : term] : (((X58 @ id @ X73 @ id)) != ((X57 @ X73)))) <=> (hoasinduction_lem3v2 = $true)) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) <=> (axidr = $true)) & (pushprop = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X360 : (subst > term > subst > $o),X361 : term] : (? [X363 : term,X362 : (subst > term > term)] : ((((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X360 @ id @ (X362 @ id @ X370) @ id)) = $true) | (((X360 @ id @ X370 @ id)) != $true)) & ! [X366 : subst,X365 : subst,X364 : term] : (((sub @ (sub @ X363 @ (push @ X364 @ X366)) @ X365)) = ((sub @ (X362 @ X366 @ X364) @ X365))) & ! [X368 : term,X369 : subst,X367 : subst] : (((sub @ X363 @ (push @ (sub @ X368 @ X367) @ (comp @ X369 @ X367)))) = ((X362 @ (comp @ X369 @ X367) @ (sub @ X368 @ X367))))) | ? [X371 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X371 @ id)) @ id)) != $true) & ($true = ((X360 @ id @ X371 @ id)))) | (((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem0_lthm = $true) <=> ! [X89 : subst,X90 : term,X88 : (term > $o)] : ? [X91 : (term > $o)] : ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92)))) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) <=> (! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384))) & ((hoasinduction_lthm_3 = $true) <=> (? [X458 : term,X457 : (term > $o)] : (! [X463 : term,X462 : term] : (($true != ((X457 @ X462))) | ($true != ((X457 @ X463))) | ($true = ((X457 @ (ap @ X462 @ X463))))) & ! [X459 : term] : ((((X457 @ X459)) = $true) | ($true != ((var @ X459)))) & (((X457 @ X458)) != $true) & ! [X460 : term] : ((((X457 @ (lam @ X460))) = $true) | ? [X461 : term] : (($true != ((X457 @ (sub @ X460 @ (push @ X461 @ id))))) & (((X457 @ X461)) = $true)))) | ! [X475 : (subst > term > subst > $o),X476 : term] : (? [X492 : subst,X491 : subst,X490 : subst,X489 : term] : ((((X475 @ X492 @ X489 @ (comp @ X490 @ X491))) = $true) & (((X475 @ (comp @ X492 @ X490) @ (sub @ X489 @ X490) @ X491)) != $true)) | (((X475 @ id @ X476 @ id)) = $true) | ? [X484 : term] : (($true != ((X475 @ id @ X484 @ id))) & (((var @ (sub @ X484 @ id))) = $true)) | ? [X477 : (subst > term > term)] : (! [X481 : term] : ((((X475 @ id @ (X477 @ id @ X481) @ id)) = $true) | ($true != ((X475 @ id @ X481 @ id)))) & ! [X478 : subst,X479 : subst,X480 : term] : (((X477 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478))) = ((sub @ (X477 @ X479 @ X480) @ X478))) & (((X475 @ id @ (lam @ (X477 @ sh @ one)) @ id)) != $true)) | ? [X482 : term,X483 : term] : (($true = ((X475 @ id @ X482 @ id))) & (((X475 @ id @ X483 @ id)) = $true) & (((X475 @ id @ (ap @ (sub @ X483 @ id) @ X482) @ id)) != $true)) | ? [X485 : term,X488 : subst,X486 : subst,X487 : subst] : ((((X475 @ (comp @ X488 @ X486) @ (sub @ X485 @ X486) @ X487)) = $true) & (((X475 @ X488 @ X485 @ (comp @ X486 @ X487))) != $true))) | ? [X465 : (subst > term > subst > $o),X466 : term,X467 : (term > $o)] : (! [X474 : term] : (((X467 @ X474)) = ((X465 @ id @ X474 @ id))) & ! [X468 : (subst > term > term)] : (? [X469 : subst,X471 : term,X470 : subst] : (((sub @ (X468 @ X470 @ X471) @ X469)) != ((X468 @ (comp @ X470 @ X469) @ (sub @ X471 @ X469)))) | (((X465 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true) | ? [X472 : term] : ((((X465 @ id @ (X468 @ id @ X472) @ id)) != $true) & (((X465 @ id @ X472 @ id)) = $true))) & ! [X473 : term] : ((((X467 @ X473)) != $true) | (((X467 @ (sub @ X466 @ (push @ X473 @ id)))) = $true)) & (((X467 @ (lam @ X466))) != $true)) | ? [X464 : term] : (((sub @ X464 @ id)) != X464) | ? [X454 : (subst > term > subst > $o)] : ! [X455 : (term > $o)] : ? [X456 : term] : (((X455 @ X456)) != ((X454 @ id @ X456 @ id))))) & ((hoasinduction_lem3 = $true) <=> ! [X34 : (subst > term > subst > $o),X35 : term] : (? [X36 : term] : ((((X34 @ id @ (sub @ X35 @ (push @ X36 @ id)) @ id)) != $true) & (((X34 @ id @ X36 @ id)) = $true)) | ? [X47 : subst,X49 : term,X48 : subst,X46 : subst] : ((((X34 @ X46 @ X49 @ (comp @ X48 @ X47))) != $true) & (((X34 @ (comp @ X46 @ X48) @ (sub @ X49 @ X48) @ X47)) = $true)) | (((X34 @ id @ (lam @ X35) @ id)) = $true) | ? [X37 : (subst > term > term)] : (! [X41 : subst,X39 : subst,X40 : term] : (((X37 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ (X37 @ X39 @ X40) @ X41))) & ! [X38 : term] : ((((X34 @ id @ (X37 @ id @ X38) @ id)) = $true) | ($true != ((X34 @ id @ X38 @ id)))) & (((X34 @ id @ (lam @ (X37 @ sh @ one)) @ id)) != $true)) | ? [X45 : subst,X42 : term,X43 : subst,X44 : subst] : ((((X34 @ X44 @ X42 @ (comp @ X43 @ X45))) = $true) & (((X34 @ (comp @ X44 @ X43) @ (sub @ X42 @ X43) @ X45)) != $true)))) & ! [X385 : d_subst] : (d_id = X385) & ((? [X316 : term,X315 : (subst > term > subst > $o)] : (($true != ((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id))) & ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true != ((X315 @ id @ (X317 @ id @ X318) @ id))) & ($true = ((X315 @ id @ X318 @ id)))) | ? [X319 : subst,X320 : term,X321 : subst] : (((X317 @ (comp @ X319 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X317 @ X319 @ X320) @ X321))) | ($true = ((X315 @ id @ (lam @ (X317 @ sh @ one)) @ id)))) & ! [X322 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X322 @ id)) @ id)) = $true) | ($true != ((X315 @ id @ X322 @ id))))) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ! [X324 : term,X323 : (subst > term > subst > $o)] : (? [X330 : (subst > term > term)] : ((((X323 @ id @ (lam @ (X330 @ sh @ one)) @ id)) != $true) & ! [X331 : subst,X332 : subst,X333 : term] : (((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))) = ((sub @ (X330 @ X331 @ X333) @ X332))) & ! [X334 : term] : ((((X323 @ id @ X334 @ id)) != $true) | (((X323 @ id @ (X330 @ id @ X334) @ id)) = $true))) | (((X323 @ id @ (lam @ X324) @ id)) = $true) | ? [X338 : subst,X337 : subst,X335 : subst,X336 : term] : ((((X323 @ X338 @ X336 @ (comp @ X337 @ X335))) = $true) & (((X323 @ (comp @ X338 @ X337) @ (sub @ X336 @ X337) @ X335)) != $true)) | ? [X325 : term] : (($true = ((X323 @ id @ X325 @ id))) & (((X323 @ id @ (sub @ X324 @ (push @ X325 @ id)) @ id)) != $true)) | ? [X328 : subst,X326 : subst,X327 : subst,X329 : term] : (($true != ((X323 @ X328 @ X329 @ (comp @ X327 @ X326)))) & (((X323 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327) @ X326)) = $true)))) <=> (hoasinduction_lem3_lthm = $true)) & ! [X292 : d_term] : (d_one = X292) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) <=> (axvarcons = $true)) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) <=> (laminj = $true)) & (((d2subst @ d_id)) = sh) & (! [X502 : term] : ? [X503 : (subst > term > term)] : ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X207 : term,X209 : (subst > term > subst > $o),X210 : term,X208 : (term > $o)] : ((((X208 @ X207)) != $true) | ? [X216 : term,X218 : subst,X217 : subst,X219 : subst] : ((((X209 @ (comp @ X218 @ X217) @ (sub @ X216 @ X217) @ X219)) != $true) & (((X209 @ X218 @ X216 @ (comp @ X217 @ X219))) = $true)) | ? [X212 : term,X211 : subst,X214 : subst,X213 : subst] : ((((X209 @ X213 @ X212 @ (comp @ X211 @ X214))) != $true) & (((X209 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211) @ X214)) = $true)) | ? [X221 : term,X220 : term] : ((((X209 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) != $true) & ($true = ((X209 @ id @ X220 @ id))) & (((X209 @ id @ X221 @ id)) = $true)) | (((X208 @ X210)) != $true) | ? [X215 : term] : (((X209 @ id @ X215 @ id)) != ((X208 @ X215))) | ($true = ((X208 @ (ap @ X207 @ X210)))))) & ((axshiftcons = $true) <=> ! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499)) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X93 : term] : ? [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) = ((X94 @ sh @ one)))) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) <=> (apinj1 = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X11 : (subst > term > subst > $o),X13 : (term > $o),X12 : term] : ((((X13 @ (lam @ X12))) != $true) & ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X20 : term] : ((((X11 @ id @ (X16 @ id @ X20) @ id)) != $true) & (((X11 @ id @ X20 @ id)) = $true)) | ? [X17 : subst,X18 : subst,X19 : term] : (((sub @ (X16 @ X17 @ X19) @ X18)) != ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18))))) & ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | (((X13 @ X15)) != $true)) & ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id)))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | ? [X3 : term,X4 : (term > $o)] : (! [X5 : term] : ((((X4 @ X5)) = $true) | (((var @ X5)) != $true)) & ! [X7 : term,X6 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | (((X4 @ X7)) != $true) | (((X4 @ X6)) != $true)) & (((X4 @ X3)) != $true) & ! [X8 : term] : (? [X9 : term] : ((((X4 @ X9)) = $true) & (((X4 @ (sub @ X8 @ (push @ X9 @ id)))) != $true)) | (((X4 @ (lam @ X8))) = $true))) | ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | ? [X29 : term,X28 : term] : ((((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X28 @ id)) = $true)) | ? [X23 : (subst > term > term)] : (! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | (((X21 @ id @ X27 @ id)) != $true)) & ($true != ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) & ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24)))))))) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) <=> (hoasapinj1 = $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417))) & ((! [X388 : (subst > term > subst > $o),X389 : term,X387 : (term > $o)] : ((((X387 @ (lam @ X389))) = $true) | ? [X395 : term] : ((((X387 @ (sub @ X389 @ (push @ X395 @ id)))) != $true) & (((X387 @ X395)) = $true)) | ? [X401 : subst,X403 : subst,X400 : term,X402 : subst] : (($true != ((X388 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))) & (((X388 @ X403 @ X400 @ (comp @ X402 @ X401))) = $true)) | ? [X404 : term] : (((X388 @ id @ X404 @ id)) != ((X387 @ X404))) | ? [X390 : (subst > term > term)] : (! [X394 : term] : (($true != ((X388 @ id @ X394 @ id))) | ($true = ((X388 @ id @ (X390 @ id @ X394) @ id)))) & (((X388 @ id @ (lam @ (X390 @ sh @ one)) @ id)) != $true) & ! [X393 : subst,X391 : subst,X392 : term] : (((X390 @ (comp @ X393 @ X391) @ (sub @ X392 @ X391))) = ((sub @ (X390 @ X393 @ X392) @ X391)))) | ? [X396 : subst,X398 : subst,X397 : subst,X399 : term] : ((((X388 @ X397 @ X399 @ (comp @ X396 @ X398))) != $true) & (((X388 @ (comp @ X397 @ X396) @ (sub @ X399 @ X396) @ X398)) = $true))) | ? [X386 : term] : (((sub @ X386 @ id)) != X386)) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) <=> ! [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ X253 @ id)) = $true) | ? [X269 : term,X270 : term] : ((((X254 @ id @ X270 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)) != $true) & ($true = ((X254 @ id @ X269 @ id)))) | ? [X259 : (subst > term > term)] : (! [X263 : term] : (($true = ((X254 @ id @ (X259 @ id @ X263) @ id))) | (((X254 @ id @ X263 @ id)) != $true)) & ! [X261 : term,X260 : subst,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) & (((X254 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true)) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X254 @ id @ X264 @ id)) != $true)) | ? [X265 : subst,X268 : term,X267 : subst,X266 : subst] : ((((X254 @ X267 @ X268 @ (comp @ X265 @ X266))) != $true) & (((X254 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true)) | ? [X256 : subst,X258 : subst,X255 : subst,X257 : term] : (($true = ((X254 @ X258 @ X257 @ (comp @ X256 @ X255)))) & (((X254 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) != $true)))) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((substmonoid_lthm = $true) <=> (? [X450 : subst] : (((comp @ id @ X450)) != X450) | (! [X452 : subst] : (((comp @ X452 @ id)) = X452) & ! [X453 : subst] : (((comp @ id @ X453)) = X453)) | ? [X451 : subst] : (((comp @ X451 @ id)) != X451))) & ((! [X515 : term,X516 : (term > $o)] : (? [X518 : term,X517 : term] : ((((X516 @ X518)) = $true) & (((X516 @ (ap @ X517 @ X518))) != $true) & (((X516 @ X517)) = $true)) | ? [X519 : term] : ((((X516 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X516 @ X520)) != $true) | (((X516 @ (sub @ X519 @ (push @ X520 @ id)))) = $true))) | ? [X521 : term] : ((((var @ X521)) = $true) & (((X516 @ X521)) != $true)) | (((X516 @ X515)) = $true)) | ? [X509 : term,X508 : subst,X507 : (term > $o)] : (! [X513 : term,X512 : term] : ((((X507 @ X512)) != $true) | ($true != ((X507 @ X513))) | ($true = ((X507 @ (ap @ X513 @ X512))))) & ! [X510 : term] : ((((X507 @ (lam @ X510))) = $true) | ? [X511 : term] : ((((X507 @ X511)) = $true) & (((X507 @ (sub @ X510 @ (push @ X511 @ id)))) != $true))) & ! [X514 : term] : (($true != ((var @ X514))) | ($true = ((X507 @ (sub @ X514 @ X508))))) & (((X507 @ (sub @ X509 @ X508))) != $true)) | ? [X506 : term] : (((sub @ X506 @ id)) != X506)) <=> (induction2_lthm = $true)) & (! [X77 : term,X76 : term,X75 : (subst > term > subst > $o)] : (? [X79 : term,X78 : term] : ((((X75 @ id @ X78 @ id)) = $true) & (((X75 @ id @ X79 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X79 @ id) @ X78) @ id)) != $true)) | ($true != ((X75 @ id @ X77 @ id))) | (((X75 @ id @ (ap @ X76 @ X77) @ id)) = $true) | ? [X83 : subst,X80 : subst,X82 : subst,X81 : term] : ((((X75 @ X80 @ X81 @ (comp @ X82 @ X83))) = $true) & ($true != ((X75 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82) @ X83)))) | ? [X85 : subst,X84 : subst,X86 : term,X87 : subst] : ((((X75 @ (comp @ X84 @ X87) @ (sub @ X86 @ X87) @ X85)) = $true) & ($true != ((X75 @ X84 @ X86 @ (comp @ X87 @ X85))))) | ($true != ((X75 @ id @ X76 @ id)))) <=> (hoasinduction_lem2 = $true)) & (hoasapnotvar = $true) & ((induction = $true) <=> ! [X51 : term,X50 : (term > $o)] : (? [X52 : term] : ((((X50 @ X52)) = $true) & (((X50 @ (lam @ X52))) != $true)) | ? [X54 : term,X55 : term] : ((((X50 @ X54)) = $true) & (((X50 @ (ap @ X55 @ X54))) != $true) & (((X50 @ X55)) = $true)) | ? [X53 : term] : ((((var @ X53)) = $true) & (((X50 @ X53)) != $true)) | (((X50 @ X51)) = $true))) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & (lamnotap != $true) & ((axidl = $true) <=> ! [X372 : subst] : (((comp @ id @ X372)) = X372)) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(flattening,[],[f11])).
% 3.80/0.85 thf(f13,definition,(
% 3.80/0.85 ! [X50 : (term > $o)] : (($true = ((sP0 @ X50))) <=> ? [X54 : term,X55 : term] : ((((X50 @ X54)) = $true) & (((X50 @ (ap @ X55 @ X54))) != $true) & (((X50 @ X55)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f14,definition,(
% 3.80/0.85 ! [X50 : (term > $o)] : (($true = ((sP1 @ X50))) <=> ? [X53 : term] : ((((var @ X53)) = $true) & (((X50 @ X53)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f15,definition,(
% 3.80/0.85 ($true = sP2) <=> ! [X51 : term,X50 : (term > $o)] : (? [X52 : term] : ((((X50 @ X52)) = $true) & (((X50 @ (lam @ X52))) != $true)) | ($true = ((sP0 @ X50))) | ($true = ((sP1 @ X50))) | (((X50 @ X51)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f16,definition,(
% 3.80/0.85 ! [X75 : (subst > term > subst > $o)] : ((((sP3 @ X75)) = $true) <=> ? [X79 : term,X78 : term] : ((((X75 @ id @ X78 @ id)) = $true) & (((X75 @ id @ X79 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X79 @ id) @ X78) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f17,definition,(
% 3.80/0.85 ! [X75 : (subst > term > subst > $o)] : ((((sP4 @ X75)) = $true) <=> ? [X85 : subst,X84 : subst,X86 : term,X87 : subst] : ((((X75 @ (comp @ X84 @ X87) @ (sub @ X86 @ X87) @ X85)) = $true) & ($true != ((X75 @ X84 @ X86 @ (comp @ X87 @ X85))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f18,definition,(
% 3.80/0.85 (sP5 = $true) <=> ! [X77 : term,X76 : term,X75 : (subst > term > subst > $o)] : ((((sP3 @ X75)) = $true) | ($true != ((X75 @ id @ X77 @ id))) | (((X75 @ id @ (ap @ X76 @ X77) @ id)) = $true) | ? [X83 : subst,X80 : subst,X82 : subst,X81 : term] : ((((X75 @ X80 @ X81 @ (comp @ X82 @ X83))) = $true) & ($true != ((X75 @ (comp @ X80 @ X82) @ (sub @ X81 @ X82) @ X83)))) | (((sP4 @ X75)) = $true) | ($true != ((X75 @ id @ X76 @ id))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f19,definition,(
% 3.80/0.85 ! [X507 : (term > $o)] : ((((sP6 @ X507)) = $true) <=> ! [X513 : term,X512 : term] : ((((X507 @ X512)) != $true) | ($true != ((X507 @ X513))) | ($true = ((X507 @ (ap @ X513 @ X512))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f20,definition,(
% 3.80/0.85 ! [X508 : subst,X507 : (term > $o)] : ((((sP7 @ X507 @ X508)) = $true) <=> ! [X514 : term] : (($true != ((var @ X514))) | ($true = ((X507 @ (sub @ X514 @ X508))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f21,definition,(
% 3.80/0.85 ! [X507 : (term > $o)] : ((((sP8 @ X507)) = $true) <=> ! [X510 : term] : ((((X507 @ (lam @ X510))) = $true) | ? [X511 : term] : ((((X507 @ X511)) = $true) & (((X507 @ (sub @ X510 @ (push @ X511 @ id)))) != $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f22,definition,(
% 3.80/0.85 ! [X516 : (term > $o)] : (($true = ((sP9 @ X516))) <=> ? [X519 : term] : ((((X516 @ (lam @ X519))) != $true) & ! [X520 : term] : ((((X516 @ X520)) != $true) | (((X516 @ (sub @ X519 @ (push @ X520 @ id)))) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f23,definition,(
% 3.80/0.85 ! [X516 : (term > $o)] : ((((sP10 @ X516)) = $true) <=> ? [X518 : term,X517 : term] : ((((X516 @ X518)) = $true) & (((X516 @ (ap @ X517 @ X518))) != $true) & (((X516 @ X517)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f24,definition,(
% 3.80/0.85 ($true = sP11) <=> ! [X515 : term,X516 : (term > $o)] : ((((sP10 @ X516)) = $true) | ($true = ((sP9 @ X516))) | ? [X521 : term] : ((((var @ X521)) = $true) & (((X516 @ X521)) != $true)) | (((X516 @ X515)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f25,definition,(
% 3.80/0.85 (sP12 = $true) <=> ? [X509 : term,X508 : subst,X507 : (term > $o)] : ((((sP6 @ X507)) = $true) & (((sP8 @ X507)) = $true) & (((sP7 @ X507 @ X508)) = $true) & (((X507 @ (sub @ X509 @ X508))) != $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f26,definition,(
% 3.80/0.85 (sP13 = $true) <=> (? [X450 : subst] : (((comp @ id @ X450)) != X450) | (! [X452 : subst] : (((comp @ X452 @ id)) = X452) & ! [X453 : subst] : (((comp @ id @ X453)) = X453)) | ? [X451 : subst] : (((comp @ X451 @ id)) != X451))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f27,definition,(
% 3.80/0.85 ! [X254 : (subst > term > subst > $o)] : ((((sP14 @ X254)) = $true) <=> ? [X259 : (subst > term > term)] : (! [X263 : term] : (($true = ((X254 @ id @ (X259 @ id @ X263) @ id))) | (((X254 @ id @ X263 @ id)) != $true)) & ! [X261 : term,X260 : subst,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) & (((X254 @ id @ (lam @ (X259 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f28,definition,(
% 3.80/0.85 ! [X254 : (subst > term > subst > $o)] : ((((sP15 @ X254)) = $true) <=> ? [X269 : term,X270 : term] : ((((X254 @ id @ X270 @ id)) = $true) & (((X254 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)) != $true) & ($true = ((X254 @ id @ X269 @ id)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f29,definition,(
% 3.80/0.85 ! [X254 : (subst > term > subst > $o)] : ((((sP16 @ X254)) = $true) <=> ? [X256 : subst,X258 : subst,X255 : subst,X257 : term] : (($true = ((X254 @ X258 @ X257 @ (comp @ X256 @ X255)))) & (((X254 @ (comp @ X258 @ X256) @ (sub @ X257 @ X256) @ X255)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f30,definition,(
% 3.80/0.85 ! [X254 : (subst > term > subst > $o)] : ((((sP17 @ X254)) = $true) <=> ? [X265 : subst,X268 : term,X267 : subst,X266 : subst] : ((((X254 @ X267 @ X268 @ (comp @ X265 @ X266))) != $true) & (((X254 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f31,definition,(
% 3.80/0.85 (sP18 = $true) <=> ! [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ X253 @ id)) = $true) | (((sP15 @ X254)) = $true) | (((sP14 @ X254)) = $true) | ? [X264 : term] : ((((var @ (sub @ X264 @ id))) = $true) & (((X254 @ id @ X264 @ id)) != $true)) | (((sP17 @ X254)) = $true) | (((sP16 @ X254)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f32,definition,(
% 3.80/0.85 ! [X388 : (subst > term > subst > $o)] : ((((sP19 @ X388)) = $true) <=> ? [X390 : (subst > term > term)] : (! [X394 : term] : (($true != ((X388 @ id @ X394 @ id))) | ($true = ((X388 @ id @ (X390 @ id @ X394) @ id)))) & (((X388 @ id @ (lam @ (X390 @ sh @ one)) @ id)) != $true) & ! [X393 : subst,X391 : subst,X392 : term] : (((X390 @ (comp @ X393 @ X391) @ (sub @ X392 @ X391))) = ((sub @ (X390 @ X393 @ X392) @ X391)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f33,definition,(
% 3.80/0.85 ! [X388 : (subst > term > subst > $o)] : ((((sP20 @ X388)) = $true) <=> ? [X396 : subst,X398 : subst,X397 : subst,X399 : term] : ((((X388 @ X397 @ X399 @ (comp @ X396 @ X398))) != $true) & (((X388 @ (comp @ X397 @ X396) @ (sub @ X399 @ X396) @ X398)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f34,definition,(
% 3.80/0.85 ! [X388 : (subst > term > subst > $o)] : (($true = ((sP21 @ X388))) <=> ? [X401 : subst,X403 : subst,X400 : term,X402 : subst] : (($true != ((X388 @ (comp @ X403 @ X402) @ (sub @ X400 @ X402) @ X401))) & (((X388 @ X403 @ X400 @ (comp @ X402 @ X401))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f35,definition,(
% 3.80/0.85 (sP22 = $true) <=> ! [X388 : (subst > term > subst > $o),X389 : term,X387 : (term > $o)] : ((((X387 @ (lam @ X389))) = $true) | ? [X395 : term] : ((((X387 @ (sub @ X389 @ (push @ X395 @ id)))) != $true) & (((X387 @ X395)) = $true)) | ($true = ((sP21 @ X388))) | ? [X404 : term] : (((X388 @ id @ X404 @ id)) != ((X387 @ X404))) | (((sP19 @ X388)) = $true) | (((sP20 @ X388)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f36,definition,(
% 3.80/0.85 ! [X21 : (subst > term > subst > $o)] : ((((sP23 @ X21)) = $true) <=> ? [X23 : (subst > term > term)] : (! [X27 : term] : (($true = ((X21 @ id @ (X23 @ id @ X27) @ id))) | (((X21 @ id @ X27 @ id)) != $true)) & ($true != ((X21 @ id @ (lam @ (X23 @ sh @ one)) @ id))) & ! [X26 : subst,X24 : subst,X25 : term] : (((sub @ (X23 @ X26 @ X25) @ X24)) = ((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f37,definition,(
% 3.80/0.85 ! [X21 : (subst > term > subst > $o)] : ((((sP24 @ X21)) = $true) <=> ? [X29 : term,X28 : term] : ((((X21 @ id @ X29 @ id)) = $true) & (((X21 @ id @ (ap @ (sub @ X28 @ id) @ X29) @ id)) != $true) & (((X21 @ id @ X28 @ id)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f38,definition,(
% 3.80/0.85 ! [X4 : (term > $o)] : (($true = ((sP25 @ X4))) <=> ! [X7 : term,X6 : term] : (($true = ((X4 @ (ap @ X6 @ X7)))) | (((X4 @ X7)) != $true) | (((X4 @ X6)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f39,definition,(
% 3.80/0.85 ! [X4 : (term > $o)] : (($true = ((sP26 @ X4))) <=> ! [X8 : term] : (? [X9 : term] : ((((X4 @ X9)) = $true) & (((X4 @ (sub @ X8 @ (push @ X9 @ id)))) != $true)) | (((X4 @ (lam @ X8))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f40,definition,(
% 3.80/0.85 ! [X11 : (subst > term > subst > $o)] : ((((sP27 @ X11)) = $true) <=> ! [X16 : (subst > term > term)] : ((((X11 @ id @ (lam @ (X16 @ sh @ one)) @ id)) = $true) | ? [X20 : term] : ((((X11 @ id @ (X16 @ id @ X20) @ id)) != $true) & (((X11 @ id @ X20 @ id)) = $true)) | ? [X17 : subst,X18 : subst,X19 : term] : (((sub @ (X16 @ X17 @ X19) @ X18)) != ((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f41,definition,(
% 3.80/0.85 (sP28 = $true) <=> ! [X21 : (subst > term > subst > $o),X22 : term] : ((((X21 @ id @ X22 @ id)) = $true) | (((sP24 @ X21)) = $true) | (((sP23 @ X21)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f42,definition,(
% 3.80/0.85 (sP29 = $true) <=> ? [X3 : term,X4 : (term > $o)] : (! [X5 : term] : ((((X4 @ X5)) = $true) | (((var @ X5)) != $true)) & ($true = ((sP25 @ X4))) & (((X4 @ X3)) != $true) & ($true = ((sP26 @ X4))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f43,definition,(
% 3.80/0.85 (sP30 = $true) <=> ? [X11 : (subst > term > subst > $o),X13 : (term > $o),X12 : term] : ((((X13 @ (lam @ X12))) != $true) & (((sP27 @ X11)) = $true) & ! [X15 : term] : (($true = ((X13 @ (sub @ X12 @ (push @ X15 @ id))))) | (((X13 @ X15)) != $true)) & ! [X14 : term] : (((X13 @ X14)) = ((X11 @ id @ X14 @ id))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f44,definition,(
% 3.80/0.85 ! [X209 : (subst > term > subst > $o)] : ((((sP31 @ X209)) = $true) <=> ? [X221 : term,X220 : term] : ((((X209 @ id @ (ap @ (sub @ X220 @ id) @ X221) @ id)) != $true) & ($true = ((X209 @ id @ X220 @ id))) & (((X209 @ id @ X221 @ id)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f45,definition,(
% 3.80/0.85 ! [X209 : (subst > term > subst > $o)] : ((((sP32 @ X209)) = $true) <=> ? [X212 : term,X211 : subst,X214 : subst,X213 : subst] : ((((X209 @ X213 @ X212 @ (comp @ X211 @ X214))) != $true) & (((X209 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211) @ X214)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f46,definition,(
% 3.80/0.85 ($true = sP33) <=> ! [X207 : term,X209 : (subst > term > subst > $o),X210 : term,X208 : (term > $o)] : ((((X208 @ X207)) != $true) | ? [X216 : term,X218 : subst,X217 : subst,X219 : subst] : ((((X209 @ (comp @ X218 @ X217) @ (sub @ X216 @ X217) @ X219)) != $true) & (((X209 @ X218 @ X216 @ (comp @ X217 @ X219))) = $true)) | (((sP32 @ X209)) = $true) | (((sP31 @ X209)) = $true) | (((X208 @ X210)) != $true) | ? [X215 : term] : (((X209 @ id @ X215 @ id)) != ((X208 @ X215))) | ($true = ((X208 @ (ap @ X207 @ X210)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f47,definition,(
% 3.80/0.85 ! [X323 : (subst > term > subst > $o)] : ((((sP34 @ X323)) = $true) <=> ? [X330 : (subst > term > term)] : ((((X323 @ id @ (lam @ (X330 @ sh @ one)) @ id)) != $true) & ! [X331 : subst,X332 : subst,X333 : term] : (((X330 @ (comp @ X331 @ X332) @ (sub @ X333 @ X332))) = ((sub @ (X330 @ X331 @ X333) @ X332))) & ! [X334 : term] : ((((X323 @ id @ X334 @ id)) != $true) | (((X323 @ id @ (X330 @ id @ X334) @ id)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f48,definition,(
% 3.80/0.85 ! [X323 : (subst > term > subst > $o)] : ((((sP35 @ X323)) = $true) <=> ? [X328 : subst,X326 : subst,X327 : subst,X329 : term] : (($true != ((X323 @ X328 @ X329 @ (comp @ X327 @ X326)))) & (((X323 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327) @ X326)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f49,definition,(
% 3.80/0.85 ! [X323 : (subst > term > subst > $o),X324 : term] : ((((sP36 @ X324 @ X323)) = $true) <=> ? [X325 : term] : (($true = ((X323 @ id @ X325 @ id))) & (((X323 @ id @ (sub @ X324 @ (push @ X325 @ id)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f50,definition,(
% 3.80/0.85 ! [X315 : (subst > term > subst > $o)] : ((((sP37 @ X315)) = $true) <=> ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true != ((X315 @ id @ (X317 @ id @ X318) @ id))) & ($true = ((X315 @ id @ X318 @ id)))) | ? [X319 : subst,X320 : term,X321 : subst] : (((X317 @ (comp @ X319 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X317 @ X319 @ X320) @ X321))) | ($true = ((X315 @ id @ (lam @ (X317 @ sh @ one)) @ id)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f51,definition,(
% 3.80/0.85 ($true = sP38) <=> ! [X324 : term,X323 : (subst > term > subst > $o)] : ((((sP34 @ X323)) = $true) | (((X323 @ id @ (lam @ X324) @ id)) = $true) | ? [X338 : subst,X337 : subst,X335 : subst,X336 : term] : ((((X323 @ X338 @ X336 @ (comp @ X337 @ X335))) = $true) & (((X323 @ (comp @ X338 @ X337) @ (sub @ X336 @ X337) @ X335)) != $true)) | (((sP36 @ X324 @ X323)) = $true) | (((sP35 @ X323)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f52,definition,(
% 3.80/0.85 (sP39 = $true) <=> ? [X316 : term,X315 : (subst > term > subst > $o)] : (($true != ((X315 @ id @ (lam @ (sub @ X316 @ (push @ one @ sh))) @ id))) & (((sP37 @ X315)) = $true) & ! [X322 : term] : ((((X315 @ id @ (sub @ X316 @ (push @ X322 @ id)) @ id)) = $true) | ($true != ((X315 @ id @ X322 @ id)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f53,definition,(
% 3.80/0.85 ! [X34 : (subst > term > subst > $o)] : ((((sP40 @ X34)) = $true) <=> ? [X37 : (subst > term > term)] : (! [X41 : subst,X39 : subst,X40 : term] : (((X37 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ (X37 @ X39 @ X40) @ X41))) & ! [X38 : term] : ((((X34 @ id @ (X37 @ id @ X38) @ id)) = $true) | ($true != ((X34 @ id @ X38 @ id)))) & (((X34 @ id @ (lam @ (X37 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f54,definition,(
% 3.80/0.85 ! [X34 : (subst > term > subst > $o)] : (($true = ((sP41 @ X34))) <=> ? [X45 : subst,X42 : term,X43 : subst,X44 : subst] : ((((X34 @ X44 @ X42 @ (comp @ X43 @ X45))) = $true) & (((X34 @ (comp @ X44 @ X43) @ (sub @ X42 @ X43) @ X45)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f55,definition,(
% 3.80/0.85 ! [X34 : (subst > term > subst > $o)] : ((((sP42 @ X34)) = $true) <=> ? [X47 : subst,X49 : term,X48 : subst,X46 : subst] : ((((X34 @ X46 @ X49 @ (comp @ X48 @ X47))) != $true) & (((X34 @ (comp @ X46 @ X48) @ (sub @ X49 @ X48) @ X47)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f56,definition,(
% 3.80/0.85 ($true = sP43) <=> ! [X34 : (subst > term > subst > $o),X35 : term] : (? [X36 : term] : ((((X34 @ id @ (sub @ X35 @ (push @ X36 @ id)) @ id)) != $true) & (((X34 @ id @ X36 @ id)) = $true)) | (((sP42 @ X34)) = $true) | (((X34 @ id @ (lam @ X35) @ id)) = $true) | (((sP40 @ X34)) = $true) | ($true = ((sP41 @ X34))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f57,definition,(
% 3.80/0.85 ! [X465 : (subst > term > subst > $o)] : ((((sP44 @ X465)) = $true) <=> ! [X468 : (subst > term > term)] : (? [X469 : subst,X471 : term,X470 : subst] : (((sub @ (X468 @ X470 @ X471) @ X469)) != ((X468 @ (comp @ X470 @ X469) @ (sub @ X471 @ X469)))) | (((X465 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true) | ? [X472 : term] : ((((X465 @ id @ (X468 @ id @ X472) @ id)) != $true) & (((X465 @ id @ X472 @ id)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f58,definition,(
% 3.80/0.85 ! [X475 : (subst > term > subst > $o)] : ((((sP45 @ X475)) = $true) <=> ? [X477 : (subst > term > term)] : (! [X481 : term] : ((((X475 @ id @ (X477 @ id @ X481) @ id)) = $true) | ($true != ((X475 @ id @ X481 @ id)))) & ! [X478 : subst,X479 : subst,X480 : term] : (((X477 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478))) = ((sub @ (X477 @ X479 @ X480) @ X478))) & (((X475 @ id @ (lam @ (X477 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f59,definition,(
% 3.80/0.85 ! [X475 : (subst > term > subst > $o)] : ((((sP46 @ X475)) = $true) <=> ? [X482 : term,X483 : term] : (($true = ((X475 @ id @ X482 @ id))) & (((X475 @ id @ X483 @ id)) = $true) & (((X475 @ id @ (ap @ (sub @ X483 @ id) @ X482) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f60,definition,(
% 3.80/0.85 ! [X475 : (subst > term > subst > $o)] : ((((sP47 @ X475)) = $true) <=> ? [X485 : term,X488 : subst,X486 : subst,X487 : subst] : ((((X475 @ (comp @ X488 @ X486) @ (sub @ X485 @ X486) @ X487)) = $true) & (((X475 @ X488 @ X485 @ (comp @ X486 @ X487))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f61,definition,(
% 3.80/0.85 ! [X475 : (subst > term > subst > $o)] : ((((sP48 @ X475)) = $true) <=> ? [X484 : term] : (($true != ((X475 @ id @ X484 @ id))) & (((var @ (sub @ X484 @ id))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f62,definition,(
% 3.80/0.85 ! [X457 : (term > $o)] : ((((sP49 @ X457)) = $true) <=> ! [X463 : term,X462 : term] : (($true != ((X457 @ X462))) | ($true != ((X457 @ X463))) | ($true = ((X457 @ (ap @ X462 @ X463))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f63,definition,(
% 3.80/0.85 ! [X457 : (term > $o)] : (($true = ((sP50 @ X457))) <=> ! [X460 : term] : ((((X457 @ (lam @ X460))) = $true) | ? [X461 : term] : (($true != ((X457 @ (sub @ X460 @ (push @ X461 @ id))))) & (((X457 @ X461)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f64,definition,(
% 3.80/0.85 (sP51 = $true) <=> ! [X475 : (subst > term > subst > $o),X476 : term] : (? [X492 : subst,X491 : subst,X490 : subst,X489 : term] : ((((X475 @ X492 @ X489 @ (comp @ X490 @ X491))) = $true) & (((X475 @ (comp @ X492 @ X490) @ (sub @ X489 @ X490) @ X491)) != $true)) | (((X475 @ id @ X476 @ id)) = $true) | (((sP48 @ X475)) = $true) | (((sP45 @ X475)) = $true) | (((sP46 @ X475)) = $true) | (((sP47 @ X475)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f65,definition,(
% 3.80/0.85 ($true = sP52) <=> ? [X465 : (subst > term > subst > $o),X466 : term,X467 : (term > $o)] : (! [X474 : term] : (((X467 @ X474)) = ((X465 @ id @ X474 @ id))) & (((sP44 @ X465)) = $true) & ! [X473 : term] : ((((X467 @ X473)) != $true) | (((X467 @ (sub @ X466 @ (push @ X473 @ id)))) = $true)) & (((X467 @ (lam @ X466))) != $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f66,definition,(
% 3.80/0.85 ($true = sP53) <=> ? [X458 : term,X457 : (term > $o)] : ((((sP49 @ X457)) = $true) & ! [X459 : term] : ((((X457 @ X459)) = $true) | ($true != ((var @ X459)))) & (((X457 @ X458)) != $true) & ($true = ((sP50 @ X457))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f67,definition,(
% 3.80/0.85 ! [X360 : (subst > term > subst > $o)] : ((((sP54 @ X360)) = $true) <=> ? [X363 : term,X362 : (subst > term > term)] : ((((X360 @ id @ (lam @ (X362 @ sh @ one)) @ id)) != $true) & ! [X370 : term] : ((((X360 @ id @ (X362 @ id @ X370) @ id)) = $true) | (((X360 @ id @ X370 @ id)) != $true)) & ! [X366 : subst,X365 : subst,X364 : term] : (((sub @ (sub @ X363 @ (push @ X364 @ X366)) @ X365)) = ((sub @ (X362 @ X366 @ X364) @ X365))) & ! [X368 : term,X369 : subst,X367 : subst] : (((sub @ X363 @ (push @ (sub @ X368 @ X367) @ (comp @ X369 @ X367)))) = ((X362 @ (comp @ X369 @ X367) @ (sub @ X368 @ X367))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f68,definition,(
% 3.80/0.85 ($true = sP55) <=> ! [X360 : (subst > term > subst > $o),X361 : term] : ((((sP54 @ X360)) = $true) | ? [X371 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X371 @ id)) @ id)) != $true) & ($true = ((X360 @ id @ X371 @ id)))) | (((X360 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f69,definition,(
% 3.80/0.85 ! [X58 : (subst > term > subst > $o)] : (($true = ((sP56 @ X58))) <=> ? [X64 : (subst > term > term)] : (! [X68 : term] : ((((X58 @ id @ (X64 @ id @ X68) @ id)) = $true) | (((X58 @ id @ X68 @ id)) != $true)) & ! [X66 : subst,X65 : term,X67 : subst] : (((sub @ (X64 @ X66 @ X65) @ X67)) = ((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & (((X58 @ id @ (lam @ (X64 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f70,definition,(
% 3.80/0.85 ! [X57 : (term > $o),X56 : term] : ((((sP57 @ X56 @ X57)) = $true) <=> ? [X59 : term] : ((((X57 @ X59)) = $true) & (((X57 @ (sub @ X56 @ (push @ X59 @ id)))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f71,definition,(
% 3.80/0.85 ! [X58 : (subst > term > subst > $o)] : (($true = ((sP58 @ X58))) <=> ? [X63 : subst,X61 : subst,X62 : subst,X60 : term] : (($true != ((X58 @ (comp @ X61 @ X62) @ (sub @ X60 @ X62) @ X63))) & (((X58 @ X61 @ X60 @ (comp @ X62 @ X63))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f72,definition,(
% 3.80/0.85 (sP59 = $true) <=> ! [X57 : (term > $o),X58 : (subst > term > subst > $o),X56 : term] : (($true = ((sP56 @ X58))) | ($true = ((X57 @ (lam @ X56)))) | ? [X69 : term,X72 : subst,X71 : subst,X70 : subst] : ((((X58 @ X70 @ X69 @ (comp @ X72 @ X71))) != $true) & (((X58 @ (comp @ X70 @ X72) @ (sub @ X69 @ X72) @ X71)) = $true)) | ($true = ((sP58 @ X58))) | (((sP57 @ X56 @ X57)) = $true) | ? [X73 : term] : (((X58 @ id @ X73 @ id)) != ((X57 @ X73))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f73,definition,(
% 3.80/0.85 ! [X422 : (term > $o)] : (($true = ((sP60 @ X422))) <=> ? [X424 : term] : (! [X425 : term] : ((((X422 @ X425)) != $true) | (((X422 @ (sub @ X424 @ (push @ X425 @ id)))) = $true)) & (((X422 @ (lam @ X424))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f74,definition,(
% 3.80/0.85 ! [X422 : (term > $o)] : ((((sP61 @ X422)) = $true) <=> ? [X428 : term,X427 : term] : ((((X422 @ (ap @ X427 @ X428))) != $true) & ($true = ((X422 @ X427))) & ($true = ((X422 @ X428)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f75,definition,(
% 3.80/0.85 (sP62 = $true) <=> ! [X422 : (term > $o),X423 : term,X421 : subst] : (? [X426 : term] : ((((var @ X426)) = $true) & (((X422 @ (sub @ X426 @ X421))) != $true)) | (((sP61 @ X422)) = $true) | ($true = ((sP60 @ X422))) | ($true = ((X422 @ (sub @ X423 @ X421)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f76,definition,(
% 3.80/0.85 ! [X127 : (subst > term > subst > $o)] : (($true = ((sP63 @ X127))) <=> ! [X137 : term,X136 : term] : ((((X127 @ id @ X136 @ id)) != $true) | ($true != ((X127 @ id @ X137 @ id))) | (((X127 @ id @ (ap @ (sub @ X137 @ id) @ X136) @ id)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f77,definition,(
% 3.80/0.85 ! [X127 : (subst > term > subst > $o)] : ((((sP64 @ X127)) = $true) <=> ! [X133 : subst,X135 : term,X132 : subst,X134 : subst] : ((((X127 @ (comp @ X132 @ X133) @ (sub @ X135 @ X133) @ X134)) != $true) | ($true = ((X127 @ X132 @ X135 @ (comp @ X133 @ X134))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f78,definition,(
% 3.80/0.85 ! [X118 : (term > $o)] : ((((sP65 @ X118)) = $true) <=> ! [X120 : term,X121 : term] : (($true != ((X118 @ X121))) | (((X118 @ (ap @ X120 @ X121))) = $true) | (((X118 @ X120)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f79,definition,(
% 3.80/0.85 ! [X118 : (term > $o)] : ((((sP66 @ X118)) = $true) <=> ! [X124 : term] : (($true != ((var @ X124))) | (((X118 @ X124)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f80,definition,(
% 3.80/0.85 ! [X118 : (term > $o)] : ((((sP67 @ X118)) = $true) <=> ! [X122 : term] : ((((X118 @ (lam @ X122))) = $true) | ? [X123 : term] : ((((X118 @ (sub @ X122 @ (push @ X123 @ id)))) != $true) & ($true = ((X118 @ X123))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f81,definition,(
% 3.80/0.85 ! [X154 : (subst > term > subst > $o)] : ((((sP68 @ X154)) = $true) <=> ? [X165 : (subst > term > term)] : (! [X167 : subst,X166 : term,X168 : subst] : (((X165 @ (comp @ X168 @ X167) @ (sub @ X166 @ X167))) = ((sub @ (X165 @ X168 @ X166) @ X167))) & ! [X169 : term] : ((((X154 @ id @ X169 @ id)) != $true) | (((X154 @ id @ (X165 @ id @ X169) @ id)) = $true)) & (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f82,definition,(
% 3.80/0.85 ! [X154 : (subst > term > subst > $o)] : (($true = ((sP69 @ X154))) <=> ? [X170 : term,X171 : term] : ((((X154 @ id @ X170 @ id)) = $true) & (((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)) != $true) & (((X154 @ id @ X171 @ id)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f83,definition,(
% 3.80/0.85 ! [X154 : (subst > term > subst > $o)] : ((((sP70 @ X154)) = $true) <=> ? [X156 : term] : (($true != ((X154 @ id @ X156 @ id))) & ($true = ((var @ (sub @ X156 @ id))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f84,definition,(
% 3.80/0.85 ! [X154 : (subst > term > subst > $o)] : ((((sP71 @ X154)) = $true) <=> ? [X164 : subst,X161 : subst,X162 : term,X163 : subst] : ((((X154 @ (comp @ X161 @ X164) @ (sub @ X162 @ X164) @ X163)) != $true) & (((X154 @ X161 @ X162 @ (comp @ X164 @ X163))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f85,definition,(
% 3.80/0.85 ! [X139 : (subst > term > subst > $o)] : ((((sP72 @ X139)) = $true) <=> ! [X145 : (subst > term > term)] : (? [X146 : term] : ((((X139 @ id @ X146 @ id)) = $true) & (((X139 @ id @ (X145 @ id @ X146) @ id)) != $true)) | ($true = ((X139 @ id @ (lam @ (X145 @ sh @ one)) @ id))) | ? [X149 : term,X147 : subst,X148 : subst] : (((sub @ (X145 @ X147 @ X149) @ X148)) != ((X145 @ (comp @ X147 @ X148) @ (sub @ X149 @ X148))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f86,definition,(
% 3.80/0.85 ! [X139 : (subst > term > subst > $o)] : ((((sP73 @ X139)) = $true) <=> ! [X142 : subst,X143 : subst,X141 : subst,X140 : term] : (($true != ((X139 @ (comp @ X141 @ X143) @ (sub @ X140 @ X143) @ X142))) | (((X139 @ X141 @ X140 @ (comp @ X143 @ X142))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f87,definition,(
% 3.80/0.85 ! [X139 : (subst > term > subst > $o)] : ((((sP74 @ X139)) = $true) <=> ! [X153 : subst,X151 : subst,X152 : term,X150 : subst] : ((((X139 @ (comp @ X150 @ X151) @ (sub @ X152 @ X151) @ X153)) = $true) | (((X139 @ X150 @ X152 @ (comp @ X151 @ X153))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f88,definition,(
% 3.80/0.85 (sP75 = $true) <=> ! [X154 : (subst > term > subst > $o),X155 : term] : ((((X154 @ id @ X155 @ id)) = $true) | ? [X158 : subst,X157 : subst,X159 : subst,X160 : term] : ((((X154 @ X157 @ X160 @ (comp @ X158 @ X159))) != $true) & ($true = ((X154 @ (comp @ X157 @ X158) @ (sub @ X160 @ X158) @ X159)))) | ($true = ((sP69 @ X154))) | (((sP68 @ X154)) = $true) | (((sP71 @ X154)) = $true) | (((sP70 @ X154)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f89,definition,(
% 3.80/0.85 ($true = sP76) <=> ? [X127 : (subst > term > subst > $o),X126 : term,X125 : term] : (! [X128 : subst,X129 : subst,X130 : subst,X131 : term] : (($true = ((X127 @ (comp @ X128 @ X129) @ (sub @ X131 @ X129) @ X130))) | (((X127 @ X128 @ X131 @ (comp @ X129 @ X130))) != $true)) & (((X127 @ id @ X125 @ id)) = $true) & (((X127 @ id @ X126 @ id)) = $true) & ($true = ((sP63 @ X127))) & ($true != ((X127 @ id @ (ap @ X125 @ X126) @ id))) & (((sP64 @ X127)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f90,definition,(
% 3.80/0.85 (sP77 = $true) <=> ? [X139 : (subst > term > subst > $o),X138 : term] : ((((X139 @ id @ (lam @ X138) @ id)) != $true) & ! [X144 : term] : ((((X139 @ id @ (sub @ X138 @ (push @ X144 @ id)) @ id)) = $true) | (((X139 @ id @ X144 @ id)) != $true)) & (((sP72 @ X139)) = $true) & (((sP74 @ X139)) = $true) & (((sP73 @ X139)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f91,definition,(
% 3.80/0.85 (sP78 = $true) <=> ? [X119 : term,X118 : (term > $o)] : ((((sP67 @ X118)) = $true) & ($true != ((X118 @ X119))) & (((sP66 @ X118)) = $true) & (((sP65 @ X118)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f92,definition,(
% 3.80/0.85 ! [X231 : (subst > term > subst > $o)] : (($true = ((sP79 @ X231))) <=> ? [X233 : (subst > term > term)] : ((((X231 @ id @ (lam @ (X233 @ sh @ one)) @ id)) != $true) & ! [X234 : subst,X235 : subst,X236 : term] : (((X233 @ (comp @ X234 @ X235) @ (sub @ X236 @ X235))) = ((sub @ (X233 @ X234 @ X236) @ X235))) & ! [X237 : term] : ((((X231 @ id @ X237 @ id)) != $true) | (((X231 @ id @ (X233 @ id @ X237) @ id)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f93,definition,(
% 3.80/0.85 ($true = sP80) <=> ! [X231 : (subst > term > subst > $o),X230 : term] : (? [X232 : term] : ((((X231 @ id @ (sub @ X230 @ (push @ X232 @ id)) @ id)) != $true) & (((X231 @ id @ X232 @ id)) = $true)) | (((X231 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id)) = $true) | ($true = ((sP79 @ X231))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f94,definition,(
% 3.80/0.85 ($true = sP81) <=> ! [X537 : term,X536 : term,X539 : term,X538 : term] : ((((ap @ (sub @ X537 @ id) @ X539)) != ((ap @ (sub @ X536 @ id) @ X538))) | (X536 = X537))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f95,definition,(
% 3.80/0.85 ($true = sP82) <=> (? [X533 : term,X532 : term,X534 : term,X535 : term] : ((((ap @ X535 @ X533)) = ((ap @ X534 @ X532))) & (X534 != X535)) | ($true = sP81) | ? [X531 : term] : (((sub @ X531 @ id)) != X531))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f96,definition,(
% 3.80/0.85 ! [X191 : (subst > term > subst > $o)] : ((((sP83 @ X191)) = $true) <=> ? [X192 : (subst > term > term)] : (! [X196 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X196) @ (sub @ X194 @ X196))) = ((sub @ (X192 @ X195 @ X194) @ X196))) & (((X191 @ id @ (lam @ (X192 @ sh @ one)) @ id)) != $true) & ! [X193 : term] : ((((X191 @ id @ X193 @ id)) != $true) | (((X191 @ id @ (X192 @ id @ X193) @ id)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f97,definition,(
% 3.80/0.85 ! [X191 : (subst > term > subst > $o)] : (($true = ((sP84 @ X191))) <=> ? [X198 : term,X197 : term] : ((((X191 @ id @ (ap @ (sub @ X198 @ id) @ X197) @ id)) != $true) & (((X191 @ id @ X198 @ id)) = $true) & (((X191 @ id @ X197 @ id)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f98,definition,(
% 3.80/0.85 ! [X434 : (subst > term > subst > $o)] : (($true = ((sP85 @ X434))) <=> ! [X436 : (subst > term > term)] : ((((X434 @ id @ (lam @ (X436 @ sh @ one)) @ id)) = $true) | ? [X439 : subst,X438 : subst,X440 : term] : (((sub @ (X436 @ X438 @ X440) @ X439)) != ((X436 @ (comp @ X438 @ X439) @ (sub @ X440 @ X439)))) | ? [X437 : term] : (($true = ((X434 @ id @ X437 @ id))) & ($true != ((X434 @ id @ (X436 @ id @ X437) @ id))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f99,definition,(
% 3.80/0.85 ! [X442 : (subst > term > subst > $o)] : ((((sP86 @ X442)) = $true) <=> ? [X445 : (subst > term > term)] : (! [X447 : term,X449 : subst,X448 : subst] : (((sub @ (X445 @ X448 @ X447) @ X449)) = ((X445 @ (comp @ X448 @ X449) @ (sub @ X447 @ X449)))) & ! [X446 : term] : ((((X442 @ id @ X446 @ id)) != $true) | (((X442 @ id @ (X445 @ id @ X446) @ id)) = $true)) & ($true != ((X442 @ id @ (lam @ (X445 @ sh @ one)) @ id)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f100,definition,(
% 3.80/0.85 (sP87 = $true) <=> ! [X443 : term,X442 : (subst > term > subst > $o)] : ((((X442 @ id @ (lam @ X443) @ id)) = $true) | ? [X444 : term] : (($true = ((X442 @ id @ X444 @ id))) & ($true != ((X442 @ id @ (sub @ X443 @ (push @ X444 @ id)) @ id)))) | (((sP86 @ X442)) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f101,definition,(
% 3.80/0.85 (sP88 = $true) <=> ? [X434 : (subst > term > subst > $o),X435 : term] : (($true = ((sP85 @ X434))) & ! [X441 : term] : (($true != ((X434 @ id @ X441 @ id))) | ($true = ((X434 @ id @ (sub @ X435 @ (push @ X441 @ id)) @ id)))) & (((X434 @ id @ (lam @ (sub @ X435 @ (push @ one @ sh))) @ id)) != $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f102,definition,(
% 3.80/0.85 ! [X181 : (subst > term > subst > $o)] : ((((sP89 @ X181)) = $true) <=> ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : subst,X184 : term] : (((sub @ (X183 @ X185 @ X184) @ X186)) = ((X183 @ (comp @ X185 @ X186) @ (sub @ X184 @ X186)))) & ($true != ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) & ! [X187 : term] : ((((X181 @ id @ (X183 @ id @ X187) @ id)) = $true) | (((X181 @ id @ X187 @ id)) != $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f103,definition,(
% 3.80/0.85 ($true = sP90) <=> ! [X180 : term,X181 : (subst > term > subst > $o),X182 : (term > $o)] : (? [X188 : term] : (((X181 @ id @ X188 @ id)) != ((X182 @ X188))) | ? [X189 : term] : ((((X182 @ (sub @ X180 @ (push @ X189 @ id)))) != $true) & (((X182 @ X189)) = $true)) | (((sP89 @ X181)) = $true) | (((X182 @ (lam @ X180))) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f104,definition,(
% 3.80/0.85 ! [X173 : (subst > term > subst > $o)] : (($true = ((sP91 @ X173))) <=> ? [X175 : (subst > term > term)] : (! [X179 : subst,X177 : subst,X178 : term] : (((X175 @ (comp @ X177 @ X179) @ (sub @ X178 @ X179))) = ((sub @ (X175 @ X177 @ X178) @ X179))) & (((X173 @ id @ (lam @ (X175 @ sh @ one)) @ id)) != $true) & ! [X176 : term] : ((((X173 @ id @ X176 @ id)) != $true) | (((X173 @ id @ (X175 @ id @ X176) @ id)) = $true))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f105,definition,(
% 3.80/0.85 ($true = sP92) <=> ! [X172 : term,X173 : (subst > term > subst > $o)] : ((((X173 @ id @ (lam @ (sub @ X172 @ (push @ one @ sh))) @ id)) = $true) | ($true = ((sP91 @ X173))) | ? [X174 : term] : (($true != ((X173 @ id @ (sub @ X172 @ (push @ X174 @ id)) @ id))) & ($true = ((X173 @ id @ X174 @ id)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f106,definition,(
% 3.80/0.85 ! [X375 : (subst > term > subst > $o)] : (($true = ((sP93 @ X375))) <=> ? [X377 : (subst > term > term)] : (($true != ((X375 @ id @ (lam @ (X377 @ sh @ one)) @ id))) & ! [X381 : term] : (($true != ((X375 @ id @ X381 @ id))) | (((X375 @ id @ (X377 @ id @ X381) @ id)) = $true)) & ! [X379 : subst,X380 : term,X378 : subst] : (((X377 @ (comp @ X379 @ X378) @ (sub @ X380 @ X378))) = ((sub @ (X377 @ X379 @ X380) @ X378)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f107,definition,(
% 3.80/0.85 (sP94 = $true) <=> ! [X376 : term,X375 : (subst > term > subst > $o)] : (($true = ((X375 @ id @ (lam @ X376) @ id))) | ? [X382 : term] : ((((X375 @ id @ X382 @ id)) = $true) & (((X375 @ id @ (sub @ X376 @ (push @ X382 @ id)) @ id)) != $true)) | ($true = ((sP93 @ X375))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f108,definition,(
% 3.80/0.85 (sP95 = $true) <=> ! [X229 : term,X227 : term,X228 : term,X226 : term] : ((((ap @ (sub @ X226 @ id) @ X227)) != ((ap @ (sub @ X229 @ id) @ X228))) | (X227 = X228))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f109,definition,(
% 3.80/0.85 ($true = sP96) <=> ((sP95 = $true) | ? [X225 : term,X223 : term,X222 : term,X224 : term] : ((((ap @ X224 @ X222)) = ((ap @ X223 @ X225))) & (X222 != X225)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f110,definition,(
% 3.80/0.85 ! [X305 : (term > $o)] : (($true = ((sP97 @ X305))) <=> ? [X307 : term] : (! [X308 : term] : ((((X305 @ (sub @ X307 @ (push @ X308 @ id)))) = $true) | (((X305 @ X308)) != $true)) & (((X305 @ (lam @ X307))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f111,definition,(
% 3.80/0.85 ! [X305 : (term > $o)] : ((((sP98 @ X305)) = $true) <=> ? [X310 : term,X311 : term] : ((((X305 @ X310)) = $true) & ($true = ((X305 @ X311))) & (((X305 @ (ap @ X310 @ X311))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f112,definition,(
% 3.80/0.85 ! [X298 : (term > $o)] : (($true = ((sP99 @ X298))) <=> ! [X302 : term,X303 : term] : ((((X298 @ X303)) != $true) | (((X298 @ X302)) != $true) | ($true = ((X298 @ (ap @ X302 @ X303))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f113,definition,(
% 3.80/0.85 ! [X298 : (term > $o)] : (($true = ((sP100 @ X298))) <=> ! [X300 : term] : ((((X298 @ X300)) != $true) | (((X298 @ (lam @ X300))) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f114,definition,(
% 3.80/0.85 (sP101 = $true) <=> ! [X304 : subst,X306 : term,X305 : (term > $o)] : ((((X305 @ (sub @ X306 @ X304))) = $true) | ($true = ((sP97 @ X305))) | (((sP98 @ X305)) = $true) | ? [X309 : term] : ((((X305 @ (sub @ X309 @ X304))) != $true) & ($true = ((var @ X309)))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f115,definition,(
% 3.80/0.85 (sP102 = $true) <=> ? [X298 : (term > $o),X299 : term] : (! [X301 : term] : (($true != ((var @ X301))) | ($true = ((X298 @ X301)))) & ($true != ((X298 @ X299))) & ($true = ((sP99 @ X298))) & ($true = ((sP100 @ X298))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f116,definition,(
% 3.80/0.85 (sP103 = $true) <=> ! [X104 : (subst > term > term),X103 : term,X102 : (subst > term > term),X101 : subst] : (? [X107 : term,X106 : subst,X105 : subst] : (((X104 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X104 @ X105 @ X107) @ X106))) | ? [X109 : term,X108 : subst,X110 : subst] : (((X102 @ (comp @ X110 @ X108) @ (sub @ X109 @ X108))) != ((sub @ (X102 @ X110 @ X109) @ X108))) | (((lam @ (X104 @ sh @ one))) != ((lam @ (X102 @ sh @ one)))) | (((X104 @ X101 @ X103)) = ((X102 @ X101 @ X103))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f117,definition,(
% 3.80/0.85 ($true = sP104) <=> (? [X100 : term,X99 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100)))) | ? [X97 : subst,X98 : term] : (((comp @ sh @ (push @ X98 @ X97))) != X97) | (sP103 = $true) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f118,definition,(
% 3.80/0.85 ! [X352 : (term > $o)] : ((((sP105 @ X352)) = $true) <=> ? [X354 : term] : (! [X355 : term] : ((((X352 @ X355)) != $true) | (((X352 @ (sub @ X354 @ (push @ X355 @ id)))) = $true)) & (((X352 @ (lam @ X354))) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f119,definition,(
% 3.80/0.85 ! [X352 : (term > $o)] : (($true = ((sP106 @ X352))) <=> ? [X357 : term,X356 : term] : (($true = ((X352 @ X356))) & ($true != ((X352 @ (ap @ X357 @ X356)))) & (((X352 @ X357)) = $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f120,definition,(
% 3.80/0.85 (sP107 = $true) <=> ! [X352 : (term > $o),X351 : term] : ((((sP105 @ X352)) = $true) | ($true = ((X352 @ X351))) | ? [X353 : term] : ((((X352 @ X353)) != $true) & (((var @ X353)) = $true)) | ($true = ((sP106 @ X352))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f121,definition,(
% 3.80/0.85 ! [X243 : (subst > term > subst > $o)] : ((((sP108 @ X243)) = $true) <=> ? [X248 : (subst > term > term)] : (! [X249 : term] : ((((X243 @ id @ X249 @ id)) != $true) | (((X243 @ id @ (X248 @ id @ X249) @ id)) = $true)) & ! [X251 : subst,X250 : term,X252 : subst] : (((sub @ (X248 @ X252 @ X250) @ X251)) = ((X248 @ (comp @ X252 @ X251) @ (sub @ X250 @ X251)))) & (((X243 @ id @ (lam @ (X248 @ sh @ one)) @ id)) != $true)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f122,definition,(
% 3.80/0.85 ($true = sP109) <=> ! [X244 : term,X245 : (term > $o),X243 : (subst > term > subst > $o)] : (? [X247 : term] : ((((X245 @ (sub @ X244 @ (push @ X247 @ id)))) != $true) & (((X245 @ X247)) = $true)) | ? [X246 : term] : (((X245 @ X246)) != ((X243 @ id @ X246 @ id))) | (((sP108 @ X243)) = $true) | (((X245 @ (lam @ X244))) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.80/0.85 thf(f123,plain,(
% 3.80/0.85 ((? [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) != X283) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281) | ! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true))) <=> (pushprop_lem1_lthm = $true)) & ((axscons = $true) <=> ! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312)) & (pushprop_lem2v2_lthm = $true) & ((? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) != ((X239 @ X241 @ X240))) | ($true = sP109) | ? [X242 : term] : (((sub @ X242 @ id)) != X242)) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (? [X497 : term] : (((X493 @ X497)) != ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | ($true = ((X493 @ one))) | (((X494 @ X496)) != $true))) & (lamnotvar = $true) & ((hoaslaminj = $true) <=> ! [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ? [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) != ((sub @ (X271 @ X275 @ X276) @ X277))) | ? [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) != ((sub @ (X272 @ X280 @ X279) @ X278))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X410 : (subst > term > term),X411 : term,X409 : term] : (? [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) != ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409))))) & (hoasinduction_lem2_lthm = $true) & ((sP107 = $true) <=> (induction2 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X528 : d_subst,X527 : d_subst] : ((X527 = X528) | (((d2subst @ X528)) != ((d2subst @ X527)))) & ((hoaslaminj_lthm = $true) <=> ($true = sP104)) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) | ? [X345 : term] : (((sub @ X345 @ id)) != X345))) & ((pushprop_lem0 = $true) <=> ! [X522 : (term > $o),X524 : term,X523 : subst] : ? [X525 : (term > $o)] : ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523)))))) & (((sP102 = $true) | (sP101 = $true) | ? [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) != X294) | ? [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) != X296) | ? [X297 : subst] : (((comp @ X297 @ id)) != X297)) <=> (induction2lem_lthm = $true)) & (axabs = $true) & (pushprop_lem3v2 = $true) & ((shinj = $true) <=> ! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh))))) & (hoasinduction_lem1_lthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (hoasinduction_lem3b_gthm = $true) & (($true = sP96) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> (sP94 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP92)) & ((termmset = $true) <=> ! [X313 : term] : (((sub @ X313 @ id)) = X313)) & ((hoasinduction_lem3b = $true) <=> ! [X358 : term] : ? [X359 : (subst > term > term)] : (((X359 @ sh @ one)) = ((sub @ X358 @ (push @ one @ sh))))) & (! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ($true = sP90)) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((sP87 = $true) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | (sP88 = $true))) & ! [X501 : d_term,X500 : d_term] : ((X500 = X501) | (((d2term @ X500)) != ((d2term @ X501)))) & (! [X191 : (subst > term > subst > $o),X190 : term] : (($true = ((X191 @ id @ X190 @ id))) | (((sP83 @ X191)) = $true) | ($true = ((sP84 @ X191)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X347 : term] : ? [X348 : (subst > term > term)] : ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350))))) & (! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = id) & (($true = sP82) <=> (hoasapinj1_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP80) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ! [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (? [X117 : term] : (((X114 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) | (((X114 @ one)) = $true) | (((X113 @ X116)) != $true)))) & (((sP77 = $true) | (sP75 = $true) | (sP78 = $true) | ($true = sP76)) <=> (hoasinduction_lthm = $true)) & (hoaslamnotap_gthm = $true) & ((sP62 = $true) <=> (induction2lem = $true)) & (ulamvarsh = $true) & (axvarshift = $true) & ((sP59 = $true) <=> (hoasinduction_lem3v2 = $true)) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) <=> (axidr = $true)) & (pushprop = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP55)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem0_lthm = $true) <=> ! [X89 : subst,X90 : term,X88 : (term > $o)] : ? [X91 : (term > $o)] : ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92)))) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) <=> (! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384))) & ((hoasinduction_lthm_3 = $true) <=> (($true = sP53) | (sP51 = $true) | ($true = sP52) | ? [X464 : term] : (((sub @ X464 @ id)) != X464) | ? [X454 : (subst > term > subst > $o)] : ! [X455 : (term > $o)] : ? [X456 : term] : (((X455 @ X456)) != ((X454 @ id @ X456 @ id))))) & ((hoasinduction_lem3 = $true) <=> ($true = sP43)) & ! [X385 : d_subst] : (d_id = X385) & (((sP39 = $true) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ($true = sP38)) <=> (hoasinduction_lem3_lthm = $true)) & ! [X292 : d_term] : (d_one = X292) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) <=> (axvarcons = $true)) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) <=> (laminj = $true)) & (((d2subst @ d_id)) = sh) & (! [X502 : term] : ? [X503 : (subst > term > term)] : ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP33)) & ((axshiftcons = $true) <=> ! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499)) & ((apinj2 = $true) <=> ! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33))))) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X93 : term] : ? [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) = ((X94 @ sh @ one)))) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) <=> (apinj1 = $true)) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((sP30 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | (sP29 = $true) | (sP28 = $true))) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) <=> (hoasapinj1 = $true)) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417))) & (((sP22 = $true) | ? [X386 : term] : (((sub @ X386 @ id)) != X386)) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) <=> (sP18 = $true)) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((substmonoid_lthm = $true) <=> (sP13 = $true)) & ((($true = sP11) | (sP12 = $true) | ? [X506 : term] : (((sub @ X506 @ id)) != X506)) <=> (induction2_lthm = $true)) & ((sP5 = $true) <=> (hoasinduction_lem2 = $true)) & (hoasapnotvar = $true) & ((induction = $true) <=> ($true = sP2)) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & (lamnotap != $true) & ((axidl = $true) <=> ! [X372 : subst] : (((comp @ id @ X372)) = X372)) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(definition_folding,[],[f12,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 3.80/0.85 thf(f458,plain,(
% 3.80/0.85 (((? [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) != X283) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281) | ! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) = X283) & ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281) & ? [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true = ((X288 @ X285))) & (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) != $true))))) & (((axscons = $true) | ? [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) != X312)) & (! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312) | (axscons != $true))) & (pushprop_lem2v2_lthm = $true) & (((? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) != ((X239 @ X241 @ X240))) | ($true = sP109) | ? [X242 : term] : (((sub @ X242 @ id)) != X242)) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X238 : term] : ? [X239 : (subst > term > term)] : ! [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) = ((X239 @ X241 @ X240))) & ($true != sP109) & ! [X242 : term] : (((sub @ X242 @ id)) = X242)))) & (((pushprop_lem1v2 = $true) | ? [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (! [X497 : term] : (((X493 @ X497)) = ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) & ($true != ((X493 @ one))) & (((X494 @ X496)) = $true))) & (! [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (? [X497 : term] : (((X493 @ X497)) != ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | ($true = ((X493 @ one))) | (((X494 @ X496)) != $true)) | (pushprop_lem1v2 != $true))) & (lamnotvar = $true) & (((hoaslaminj = $true) | ? [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) = ((lam @ (X271 @ sh @ one)))) & (((X271 @ X274 @ X273)) != ((X272 @ X274 @ X273))) & ! [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) = ((sub @ (X271 @ X275 @ X276) @ X277))) & ! [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) = ((sub @ (X272 @ X280 @ X279) @ X278))))) & (! [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ? [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) != ((sub @ (X271 @ X275 @ X276) @ X277))) | ? [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) != ((sub @ (X272 @ X280 @ X279) @ X278)))) | (hoaslaminj != $true))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (((hoaslamnotap = $true) | ? [X410 : (subst > term > term),X411 : term,X409 : term] : (! [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X414 @ X412) @ X413))) & (((lam @ (X410 @ sh @ one))) = ((ap @ (sub @ X411 @ id) @ X409))))) & (! [X410 : (subst > term > term),X411 : term,X409 : term] : (? [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) != ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409)))) | (hoaslamnotap != $true))) & (hoasinduction_lem2_lthm = $true) & (((sP107 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP107 != $true))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X528 : d_subst,X527 : d_subst] : ((X527 = X528) | (((d2subst @ X528)) != ((d2subst @ X527)))) & (((hoaslaminj_lthm = $true) | ($true != sP104)) & (($true = sP104) | (hoaslaminj_lthm != $true))) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & (((termmset_lthm = $true) | (? [X346 : term] : (((sub @ X346 @ id)) != X346) & ! [X345 : term] : (((sub @ X345 @ id)) = X345))) & ((! [X346 : term] : (((sub @ X346 @ id)) = X346) | ? [X345 : term] : (((sub @ X345 @ id)) != X345)) | (termmset_lthm != $true))) & (((pushprop_lem0 = $true) | ? [X522 : (term > $o),X524 : term,X523 : subst] : ! [X525 : (term > $o)] : ? [X526 : term] : (((X525 @ X526)) != ((X522 @ (sub @ X526 @ (push @ X524 @ X523)))))) & (! [X522 : (term > $o),X524 : term,X523 : subst] : ? [X525 : (term > $o)] : ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523))))) | (pushprop_lem0 != $true))) & ((((sP102 = $true) | (sP101 = $true) | ? [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) != X294) | ? [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) != X296) | ? [X297 : subst] : (((comp @ X297 @ id)) != X297)) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP102 != $true) & (sP101 != $true) & ! [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) = X294) & ! [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) = X296) & ! [X297 : subst] : (((comp @ X297 @ id)) = X297)))) & (axabs = $true) & (pushprop_lem3v2 = $true) & (((shinj = $true) | ? [X419 : term,X420 : term] : ((X419 != X420) & (((sub @ X420 @ sh)) = ((sub @ X419 @ sh))))) & (! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh)))) | (shinj != $true))) & (hoasinduction_lem1_lthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (hoasinduction_lem3b_gthm = $true) & ((($true = sP96) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP96))) & (((hoasinduction_lem3a = $true) | (sP94 != $true)) & ((sP94 = $true) | (hoasinduction_lem3a != $true))) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP92)) & (($true = sP92) | (hoasinduction_lem3aa_lthm != $true))) & (((termmset = $true) | ? [X313 : term] : (((sub @ X313 @ id)) != X313)) & (! [X313 : term] : (((sub @ X313 @ id)) = X313) | (termmset != $true))) & (((hoasinduction_lem3b = $true) | ? [X358 : term] : ! [X359 : (subst > term > term)] : (((X359 @ sh @ one)) != ((sub @ X358 @ (push @ one @ sh))))) & (! [X358 : term] : ? [X359 : (subst > term > term)] : (((X359 @ sh @ one)) = ((sub @ X358 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & ((! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true = ((X342 @ X340))) & (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) != $true)))) & (((hoasinduction_lem3v2a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3v2a != $true))) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & (((hoasinduction_lem3a_lthm = $true) | ((sP87 != $true) & ! [X433 : term] : (((sub @ X433 @ id)) = X433) & (sP88 != $true))) & (((sP87 = $true) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | (sP88 = $true)) | (hoasinduction_lem3a_lthm != $true))) & ! [X501 : d_term,X500 : d_term] : ((X500 = X501) | (((d2term @ X500)) != ((d2term @ X501)))) & ((! [X191 : (subst > term > subst > $o),X190 : term] : (($true = ((X191 @ id @ X190 @ id))) | (((sP83 @ X191)) = $true) | ($true = ((sP84 @ X191)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X191 : (subst > term > subst > $o),X190 : term] : (($true != ((X191 @ id @ X190 @ id))) & (((sP83 @ X191)) != $true) & ($true != ((sP84 @ X191)))))) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X347 : term] : ! [X348 : (subst > term > term)] : ? [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) != ((sub @ X347 @ (push @ X349 @ X350))))) & (! [X347 : term] : ? [X348 : (subst > term > term)] : ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350)))) | (hoasinduction_lem3v2_f_lthm != $true))) & ((! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X199 : (subst > term > subst > $o)] : ! [X200 : (term > $o)] : ? [X201 : term] : (((X200 @ X201)) != ((X199 @ id @ X201 @ id))))) & (((d2subst @ d_id)) = id) & ((($true = sP82) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP82))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((($true = sP80) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP80))) & (((pushprop_lem1v2_lthm = $true) | (! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) & ? [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (! [X117 : term] : (((X114 @ X117)) = ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) & (((X114 @ one)) != $true) & (((X113 @ X116)) = $true)))) & ((? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ! [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (? [X117 : term] : (((X114 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) | (((X114 @ one)) = $true) | (((X113 @ X116)) != $true))) | (pushprop_lem1v2_lthm != $true))) & ((((sP77 = $true) | (sP75 = $true) | (sP78 = $true) | ($true = sP76)) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP77 != $true) & (sP75 != $true) & (sP78 != $true) & ($true != sP76)))) & (hoaslamnotap_gthm = $true) & (((sP62 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP62 != $true))) & (ulamvarsh = $true) & (axvarshift = $true) & (((sP59 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP59 != $true))) & ((! [X339 : subst] : (((comp @ X339 @ id)) = X339) | (axidr != $true)) & ((axidr = $true) | ? [X339 : subst] : (((comp @ X339 @ id)) != X339))) & (pushprop = $true) & ((! [X74 : term] : (((sub @ X74 @ id)) = X74) | (axvarid != $true)) & ((axvarid = $true) | ? [X74 : term] : (((sub @ X74 @ id)) != X74))) & (((var @ (d2term @ d_one))) != $true) & (((hoasinduction_lem3aaa = $true) | ($true != sP55)) & (($true = sP55) | (hoasinduction_lem3aaa != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((pushprop_lem0_lthm = $true) | ? [X89 : subst,X90 : term,X88 : (term > $o)] : ! [X91 : (term > $o)] : ? [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) != ((X91 @ X92)))) & (! [X89 : subst,X90 : term,X88 : (term > $o)] : ? [X91 : (term > $o)] : ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92))) | (pushprop_lem0_lthm != $true))) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & (((substmonoid = $true) | (? [X383 : subst] : (((comp @ X383 @ id)) != X383) | ? [X384 : subst] : (((comp @ id @ X384)) != X384))) & ((! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384)) | (substmonoid != $true))) & (((hoasinduction_lthm_3 = $true) | (($true != sP53) & (sP51 != $true) & ($true != sP52) & ! [X464 : term] : (((sub @ X464 @ id)) = X464) & ! [X454 : (subst > term > subst > $o)] : ? [X455 : (term > $o)] : ! [X456 : term] : (((X455 @ X456)) = ((X454 @ id @ X456 @ id))))) & ((($true = sP53) | (sP51 = $true) | ($true = sP52) | ? [X464 : term] : (((sub @ X464 @ id)) != X464) | ? [X454 : (subst > term > subst > $o)] : ! [X455 : (term > $o)] : ? [X456 : term] : (((X455 @ X456)) != ((X454 @ id @ X456 @ id)))) | (hoasinduction_lthm_3 != $true))) & (((hoasinduction_lem3 = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3 != $true))) & ! [X385 : d_subst] : (d_id = X385) & ((((sP39 = $true) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ($true = sP38)) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ((sP39 != $true) & ! [X314 : term] : (((sub @ X314 @ id)) = X314) & ($true != sP38)))) & ! [X292 : d_term] : (d_one = X292) & ((! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) != X205))) & ((! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) | (laminj != $true)) & ((laminj = $true) | ? [X530 : term,X529 : term] : ((((lam @ X530)) = ((lam @ X529))) & (X529 != X530)))) & (((d2subst @ d_id)) = sh) & ((! [X502 : term] : ? [X503 : (subst > term > term)] : ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X502 : term] : ! [X503 : (subst > term > term)] : ? [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) != ((sub @ X502 @ (push @ X504 @ X505)))))) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X202 : (subst > term > subst > $o)] : ! [X203 : (term > $o)] : ? [X204 : term] : (((X203 @ X204)) != ((X202 @ id @ X204 @ id))))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem2v2 != $true))) & (((axshiftcons = $true) | ? [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) != X499)) & (! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499) | (axshiftcons != $true))) & (((apinj2 = $true) | ? [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 != X33) & (((ap @ X30 @ X32)) = ((ap @ X31 @ X33))))) & (! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33)))) | (apinj2 != $true))) & (hoaslamnotvar_lthm = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X93 : term] : ! [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) != ((X94 @ sh @ one)))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) = ((X94 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & ((! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) = ((ap @ X407 @ X408))) & (X405 != X407)))) & (pushprop_lem1v2_gthm = $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ((sP30 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) & (sP29 != $true) & (sP28 != $true))) & (((sP30 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | (sP29 = $true) | (sP28 = $true)) | (hoasinduction_no_psi_cond_lthm != $true))) & ((! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 != X431) & (((ap @ (sub @ X431 @ id) @ X432)) = ((ap @ (sub @ X429 @ id) @ X430)))))) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((hoasapinj2 = $true) | ? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) = ((ap @ (sub @ X416 @ id) @ X417))) & (X415 != X417))) & (! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417)) | (hoasapinj2 != $true))) & ((((sP22 = $true) | ? [X386 : term] : (((sub @ X386 @ id)) != X386)) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((sP22 != $true) & ! [X386 : term] : (((sub @ X386 @ id)) = X386)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & (((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true))) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((substmonoid_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (substmonoid_lthm != $true))) & (((($true = sP11) | (sP12 = $true) | ? [X506 : term] : (((sub @ X506 @ id)) != X506)) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP11) & (sP12 != $true) & ! [X506 : term] : (((sub @ X506 @ id)) = X506)))) & (((sP5 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP5 != $true))) & (hoasapnotvar = $true) & (((induction = $true) | ($true != sP2)) & (($true = sP2) | (induction != $true))) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & (lamnotap != $true) & (((axidl = $true) | ? [X372 : subst] : (((comp @ id @ X372)) != X372)) & (! [X372 : subst] : (((comp @ id @ X372)) = X372) | (axidl != $true))) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(nnf_transformation,[],[f123])).
% 3.80/0.85 thf(f459,plain,(
% 3.80/0.85 (? [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) != X283) | ? [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) != X281) | ! [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true != ((X288 @ X285))) | (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) = $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X283 : subst,X284 : term] : (((comp @ sh @ (push @ X284 @ X283))) = X283) & ! [X282 : subst,X281 : term] : (((sub @ one @ (push @ X281 @ X282))) = X281) & ? [X288 : (term > $o),X286 : (term > $o),X285 : term,X287 : subst,X289 : term] : (($true = ((X288 @ X285))) & (((X286 @ (sub @ X285 @ (push @ X289 @ X287)))) != $true)))) & ((axscons = $true) | ? [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) != X312)) & (! [X312 : subst] : (((push @ (sub @ one @ X312) @ (comp @ sh @ X312))) = X312) | (axscons != $true)) & (pushprop_lem2v2_lthm = $true) & (? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) != ((X239 @ X241 @ X240))) | ($true = sP109) | ? [X242 : term] : (((sub @ X242 @ id)) != X242) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X238 : term] : ? [X239 : (subst > term > term)] : ! [X241 : subst,X240 : term] : (((sub @ X238 @ (push @ X240 @ X241))) = ((X239 @ X241 @ X240))) & ($true != sP109) & ! [X242 : term] : (((sub @ X242 @ id)) = X242))) & ((pushprop_lem1v2 = $true) | ? [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (! [X497 : term] : (((X493 @ X497)) = ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) & ($true != ((X493 @ one))) & (((X494 @ X496)) = $true))) & (! [X494 : (term > $o),X496 : term,X495 : subst,X493 : (term > $o)] : (? [X497 : term] : (((X493 @ X497)) != ((X494 @ (sub @ X497 @ (push @ X496 @ X495))))) | ($true = ((X493 @ one))) | (((X494 @ X496)) != $true)) | (pushprop_lem1v2 != $true)) & (lamnotvar = $true) & ((hoaslaminj = $true) | ? [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) = ((lam @ (X271 @ sh @ one)))) & (((X271 @ X274 @ X273)) != ((X272 @ X274 @ X273))) & ! [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) = ((sub @ (X271 @ X275 @ X276) @ X277))) & ! [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) = ((sub @ (X272 @ X280 @ X279) @ X278))))) & (! [X273 : term,X272 : (subst > term > term),X271 : (subst > term > term),X274 : subst] : ((((lam @ (X272 @ sh @ one))) != ((lam @ (X271 @ sh @ one)))) | (((X271 @ X274 @ X273)) = ((X272 @ X274 @ X273))) | ? [X275 : subst,X277 : subst,X276 : term] : (((X271 @ (comp @ X275 @ X277) @ (sub @ X276 @ X277))) != ((sub @ (X271 @ X275 @ X276) @ X277))) | ? [X280 : subst,X278 : subst,X279 : term] : (((X272 @ (comp @ X280 @ X278) @ (sub @ X279 @ X278))) != ((sub @ (X272 @ X280 @ X279) @ X278)))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X410 : (subst > term > term),X411 : term,X409 : term] : (! [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X414 @ X412) @ X413))) & (((lam @ (X410 @ sh @ one))) = ((ap @ (sub @ X411 @ id) @ X409))))) & (! [X410 : (subst > term > term),X411 : term,X409 : term] : (? [X412 : term,X413 : subst,X414 : subst] : (((X410 @ (comp @ X414 @ X413) @ (sub @ X412 @ X413))) != ((sub @ (X410 @ X414 @ X412) @ X413))) | (((lam @ (X410 @ sh @ one))) != ((ap @ (sub @ X411 @ id) @ X409)))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_lthm = $true) & ((sP107 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP107 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X528 : d_subst,X527 : d_subst] : ((X527 = X528) | (((d2subst @ X528)) != ((d2subst @ X527)))) & ((hoaslaminj_lthm = $true) | ($true != sP104)) & (($true = sP104) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) | (? [X346 : term] : (((sub @ X346 @ id)) != X346) & ! [X345 : term] : (((sub @ X345 @ id)) = X345))) & (! [X346 : term] : (((sub @ X346 @ id)) = X346) | ? [X345 : term] : (((sub @ X345 @ id)) != X345) | (termmset_lthm != $true)) & ((pushprop_lem0 = $true) | ? [X522 : (term > $o),X524 : term,X523 : subst] : ! [X525 : (term > $o)] : ? [X526 : term] : (((X525 @ X526)) != ((X522 @ (sub @ X526 @ (push @ X524 @ X523)))))) & (! [X522 : (term > $o),X524 : term,X523 : subst] : ? [X525 : (term > $o)] : ! [X526 : term] : (((X525 @ X526)) = ((X522 @ (sub @ X526 @ (push @ X524 @ X523))))) | (pushprop_lem0 != $true)) & ((sP102 = $true) | (sP101 = $true) | ? [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) != X294) | ? [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) != X296) | ? [X297 : subst] : (((comp @ X297 @ id)) != X297) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP102 != $true) & (sP101 != $true) & ! [X294 : term,X293 : subst] : (((sub @ one @ (push @ X294 @ X293))) = X294) & ! [X295 : term,X296 : subst] : (((comp @ sh @ (push @ X295 @ X296))) = X296) & ! [X297 : subst] : (((comp @ X297 @ id)) = X297))) & (axabs = $true) & (pushprop_lem3v2 = $true) & ((shinj = $true) | ? [X419 : term,X420 : term] : ((X419 != X420) & (((sub @ X420 @ sh)) = ((sub @ X419 @ sh))))) & (! [X419 : term,X420 : term] : ((X419 = X420) | (((sub @ X420 @ sh)) != ((sub @ X419 @ sh)))) | (shinj != $true)) & (hoasinduction_lem1_lthm = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (hoasinduction_lem3b_gthm = $true) & (($true = sP96) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP96)) & ((hoasinduction_lem3a = $true) | (sP94 != $true)) & ((sP94 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP92)) & (($true = sP92) | (hoasinduction_lem3aa_lthm != $true)) & ((termmset = $true) | ? [X313 : term] : (((sub @ X313 @ id)) != X313)) & (! [X313 : term] : (((sub @ X313 @ id)) = X313) | (termmset != $true)) & ((hoasinduction_lem3b = $true) | ? [X358 : term] : ! [X359 : (subst > term > term)] : (((X359 @ sh @ one)) != ((sub @ X358 @ (push @ one @ sh))))) & (! [X358 : term] : ? [X359 : (subst > term > term)] : (((X359 @ sh @ one)) = ((sub @ X358 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true != ((X342 @ X340))) | (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X340 : term,X344 : term,X342 : (term > $o),X341 : (term > $o),X343 : subst] : (($true = ((X342 @ X340))) & (((X341 @ (sub @ X340 @ (push @ X344 @ X343)))) != $true))) & ((hoasinduction_lem3v2a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3v2a != $true)) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ((hoasinduction_lem3a_lthm = $true) | ((sP87 != $true) & ! [X433 : term] : (((sub @ X433 @ id)) = X433) & (sP88 != $true))) & ((sP87 = $true) | ? [X433 : term] : (((sub @ X433 @ id)) != X433) | (sP88 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X501 : d_term,X500 : d_term] : ((X500 = X501) | (((d2term @ X500)) != ((d2term @ X501)))) & (! [X191 : (subst > term > subst > $o),X190 : term] : (($true = ((X191 @ id @ X190 @ id))) | (((sP83 @ X191)) = $true) | ($true = ((sP84 @ X191)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X191 : (subst > term > subst > $o),X190 : term] : (($true != ((X191 @ id @ X190 @ id))) & (((sP83 @ X191)) != $true) & ($true != ((sP84 @ X191))))) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X347 : term] : ! [X348 : (subst > term > term)] : ? [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) != ((sub @ X347 @ (push @ X349 @ X350))))) & (! [X347 : term] : ? [X348 : (subst > term > term)] : ! [X349 : term,X350 : subst] : (((X348 @ X350 @ X349)) = ((sub @ X347 @ (push @ X349 @ X350)))) | (hoasinduction_lem3v2_f_lthm != $true)) & (! [X199 : (subst > term > subst > $o)] : ? [X200 : (term > $o)] : ! [X201 : term] : (((X200 @ X201)) = ((X199 @ id @ X201 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X199 : (subst > term > subst > $o)] : ! [X200 : (term > $o)] : ? [X201 : term] : (((X200 @ X201)) != ((X199 @ id @ X201 @ id)))) & (((d2subst @ d_id)) = id) & (($true = sP82) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP82)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP80) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP80)) & ((pushprop_lem1v2_lthm = $true) | (! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) & ? [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (! [X117 : term] : (((X114 @ X117)) = ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) & (((X114 @ one)) != $true) & (((X113 @ X116)) = $true)))) & (? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | ! [X114 : (term > $o),X113 : (term > $o),X116 : term,X115 : subst] : (? [X117 : term] : (((X114 @ X117)) != ((X113 @ (sub @ X117 @ (push @ X116 @ X115))))) | (((X114 @ one)) = $true) | (((X113 @ X116)) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((sP77 = $true) | (sP75 = $true) | (sP78 = $true) | ($true = sP76) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP77 != $true) & (sP75 != $true) & (sP78 != $true) & ($true != sP76))) & (hoaslamnotap_gthm = $true) & ((sP62 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP62 != $true)) & (ulamvarsh = $true) & (axvarshift = $true) & ((sP59 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP59 != $true)) & (! [X339 : subst] : (((comp @ X339 @ id)) = X339) | (axidr != $true)) & ((axidr = $true) | ? [X339 : subst] : (((comp @ X339 @ id)) != X339)) & (pushprop = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) | (axvarid != $true)) & ((axvarid = $true) | ? [X74 : term] : (((sub @ X74 @ id)) != X74)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP55)) & (($true = sP55) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem0_lthm = $true) | ? [X89 : subst,X90 : term,X88 : (term > $o)] : ! [X91 : (term > $o)] : ? [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) != ((X91 @ X92)))) & (! [X89 : subst,X90 : term,X88 : (term > $o)] : ? [X91 : (term > $o)] : ! [X92 : term] : (((X88 @ (sub @ X92 @ (push @ X90 @ X89)))) = ((X91 @ X92))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | ? [X383 : subst] : (((comp @ X383 @ id)) != X383) | ? [X384 : subst] : (((comp @ id @ X384)) != X384)) & ((! [X383 : subst] : (((comp @ X383 @ id)) = X383) & ! [X384 : subst] : (((comp @ id @ X384)) = X384)) | (substmonoid != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP53) & (sP51 != $true) & ($true != sP52) & ! [X464 : term] : (((sub @ X464 @ id)) = X464) & ! [X454 : (subst > term > subst > $o)] : ? [X455 : (term > $o)] : ! [X456 : term] : (((X455 @ X456)) = ((X454 @ id @ X456 @ id))))) & (($true = sP53) | (sP51 = $true) | ($true = sP52) | ? [X464 : term] : (((sub @ X464 @ id)) != X464) | ? [X454 : (subst > term > subst > $o)] : ! [X455 : (term > $o)] : ? [X456 : term] : (((X455 @ X456)) != ((X454 @ id @ X456 @ id))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3 != $true)) & ! [X385 : d_subst] : (d_id = X385) & ((sP39 = $true) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ($true = sP38) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ((sP39 != $true) & ! [X314 : term] : (((sub @ X314 @ id)) = X314) & ($true != sP38))) & ! [X292 : d_term] : (d_one = X292) & (! [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) = X205) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X206 : subst,X205 : term] : (((sub @ one @ (push @ X205 @ X206))) != X205)) & (! [X530 : term,X529 : term] : ((((lam @ X530)) != ((lam @ X529))) | (X529 = X530)) | (laminj != $true)) & ((laminj = $true) | ? [X530 : term,X529 : term] : ((((lam @ X530)) = ((lam @ X529))) & (X529 != X530))) & (((d2subst @ d_id)) = sh) & (! [X502 : term] : ? [X503 : (subst > term > term)] : ! [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) = ((sub @ X502 @ (push @ X504 @ X505)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X502 : term] : ! [X503 : (subst > term > term)] : ? [X504 : term,X505 : subst] : (((X503 @ X505 @ X504)) != ((sub @ X502 @ (push @ X504 @ X505))))) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X202 : (subst > term > subst > $o)] : ! [X203 : (term > $o)] : ? [X204 : term] : (((X203 @ X204)) != ((X202 @ id @ X204 @ id)))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem2v2 != $true)) & ((axshiftcons = $true) | ? [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) != X499)) & (! [X498 : term,X499 : subst] : (((comp @ sh @ (push @ X498 @ X499))) = X499) | (axshiftcons != $true)) & ((apinj2 = $true) | ? [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 != X33) & (((ap @ X30 @ X32)) = ((ap @ X31 @ X33))))) & (! [X32 : term,X31 : term,X30 : term,X33 : term] : ((X32 = X33) | (((ap @ X30 @ X32)) != ((ap @ X31 @ X33)))) | (apinj2 != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X93 : term] : ! [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) != ((X94 @ sh @ one)))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : (((sub @ X93 @ (push @ one @ sh))) = ((X94 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) != ((ap @ X407 @ X408))) | (X405 = X407)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X407 : term,X405 : term,X406 : term,X408 : term] : ((((ap @ X405 @ X406)) = ((ap @ X407 @ X408))) & (X405 != X407))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP30 != $true) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) & (sP29 != $true) & (sP28 != $true))) & ((sP30 = $true) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id))) | (sP29 = $true) | (sP28 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 = X431) | (((ap @ (sub @ X431 @ id) @ X432)) != ((ap @ (sub @ X429 @ id) @ X430)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X429 != X431) & (((ap @ (sub @ X431 @ id) @ X432)) = ((ap @ (sub @ X429 @ id) @ X430))))) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) | ? [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) = ((ap @ (sub @ X416 @ id) @ X417))) & (X415 != X417))) & (! [X418 : term,X416 : term,X417 : term,X415 : term] : ((((ap @ (sub @ X418 @ id) @ X415)) != ((ap @ (sub @ X416 @ id) @ X417))) | (X415 = X417)) | (hoasapinj2 != $true)) & ((sP22 = $true) | ? [X386 : term] : (((sub @ X386 @ id)) != X386) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((sP22 != $true) & ! [X386 : term] : (((sub @ X386 @ id)) = X386))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((substmonoid_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (substmonoid_lthm != $true)) & (($true = sP11) | (sP12 = $true) | ? [X506 : term] : (((sub @ X506 @ id)) != X506) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP11) & (sP12 != $true) & ! [X506 : term] : (((sub @ X506 @ id)) = X506))) & ((sP5 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP5 != $true)) & (hoasapnotvar = $true) & ((induction = $true) | ($true != sP2)) & (($true = sP2) | (induction != $true)) & ! [X373 : subst] : ? [X374 : d_subst] : (((d2subst @ X374)) = X373) & (lamnotap != $true) & ((axidl = $true) | ? [X372 : subst] : (((comp @ id @ X372)) != X372)) & (! [X372 : subst] : (((comp @ id @ X372)) = X372) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(flattening,[],[f458])).
% 3.80/0.85 thf(f460,plain,(
% 3.80/0.85 (? [X0 : subst,X1 : term] : (((comp @ sh @ (push @ X1 @ X0))) != X0) | ? [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) != X3) | ! [X4 : (term > $o),X5 : (term > $o),X6 : term,X7 : subst,X8 : term] : ((((X4 @ X6)) != $true) | (((X5 @ (sub @ X6 @ (push @ X8 @ X7)))) = $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X9 : subst,X10 : term] : (((comp @ sh @ (push @ X10 @ X9))) = X9) & ! [X11 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X11))) = X12) & ? [X13 : (term > $o),X14 : (term > $o),X15 : term,X16 : subst,X17 : term] : ((((X13 @ X15)) = $true) & (((X14 @ (sub @ X15 @ (push @ X17 @ X16)))) != $true)))) & ((axscons = $true) | ? [X18 : subst] : (((push @ (sub @ one @ X18) @ (comp @ sh @ X18))) != X18)) & (! [X19 : subst] : (((push @ (sub @ one @ X19) @ (comp @ sh @ X19))) = X19) | (axscons != $true)) & (pushprop_lem2v2_lthm = $true) & (? [X20 : term] : ! [X21 : (subst > term > term)] : ? [X22 : subst,X23 : term] : (((X21 @ X22 @ X23)) != ((sub @ X20 @ (push @ X23 @ X22)))) | ($true = sP109) | ? [X24 : term] : (((sub @ X24 @ id)) != X24) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X25 : term] : ? [X26 : (subst > term > term)] : ! [X27 : subst,X28 : term] : (((sub @ X25 @ (push @ X28 @ X27))) = ((X26 @ X27 @ X28))) & ($true != sP109) & ! [X29 : term] : (((sub @ X29 @ id)) = X29))) & ((pushprop_lem1v2 = $true) | ? [X30 : (term > $o),X31 : term,X32 : subst,X33 : (term > $o)] : (! [X34 : term] : (((X30 @ (sub @ X34 @ (push @ X31 @ X32)))) = ((X33 @ X34))) & (((X33 @ one)) != $true) & (((X30 @ X31)) = $true))) & (! [X35 : (term > $o),X36 : term,X37 : subst,X38 : (term > $o)] : (? [X39 : term] : (((X38 @ X39)) != ((X35 @ (sub @ X39 @ (push @ X36 @ X37))))) | (((X38 @ one)) = $true) | (((X35 @ X36)) != $true)) | (pushprop_lem1v2 != $true)) & (lamnotvar = $true) & ((hoaslaminj = $true) | ? [X40 : term,X41 : (subst > term > term),X42 : (subst > term > term),X43 : subst] : ((((lam @ (X41 @ sh @ one))) = ((lam @ (X42 @ sh @ one)))) & (((X41 @ X43 @ X40)) != ((X42 @ X43 @ X40))) & ! [X44 : subst,X45 : subst,X46 : term] : (((X42 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45))) = ((sub @ (X42 @ X44 @ X46) @ X45))) & ! [X47 : subst,X48 : subst,X49 : term] : (((sub @ (X41 @ X47 @ X49) @ X48)) = ((X41 @ (comp @ X47 @ X48) @ (sub @ X49 @ X48)))))) & (! [X50 : term,X51 : (subst > term > term),X52 : (subst > term > term),X53 : subst] : ((((lam @ (X52 @ sh @ one))) != ((lam @ (X51 @ sh @ one)))) | (((X51 @ X53 @ X50)) = ((X52 @ X53 @ X50))) | ? [X54 : subst,X55 : subst,X56 : term] : (((sub @ (X52 @ X54 @ X56) @ X55)) != ((X52 @ (comp @ X54 @ X55) @ (sub @ X56 @ X55)))) | ? [X57 : subst,X58 : subst,X59 : term] : (((X51 @ (comp @ X57 @ X58) @ (sub @ X59 @ X58))) != ((sub @ (X51 @ X57 @ X59) @ X58)))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | ? [X60 : (subst > term > term),X61 : term,X62 : term] : (! [X63 : term,X64 : subst,X65 : subst] : (((sub @ (X60 @ X65 @ X63) @ X64)) = ((X60 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) & (((ap @ (sub @ X61 @ id) @ X62)) = ((lam @ (X60 @ sh @ one)))))) & (! [X66 : (subst > term > term),X67 : term,X68 : term] : (? [X69 : term,X70 : subst,X71 : subst] : (((X66 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70))) != ((sub @ (X66 @ X71 @ X69) @ X70))) | (((lam @ (X66 @ sh @ one))) != ((ap @ (sub @ X67 @ id) @ X68)))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_lthm = $true) & ((sP107 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP107 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X72 : d_subst,X73 : d_subst] : ((X72 = X73) | (((d2subst @ X73)) != ((d2subst @ X72)))) & ((hoaslaminj_lthm = $true) | ($true != sP104)) & (($true = sP104) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) | (? [X74 : term] : (((sub @ X74 @ id)) != X74) & ! [X75 : term] : (((sub @ X75 @ id)) = X75))) & (! [X76 : term] : (((sub @ X76 @ id)) = X76) | ? [X77 : term] : (((sub @ X77 @ id)) != X77) | (termmset_lthm != $true)) & ((pushprop_lem0 = $true) | ? [X78 : (term > $o),X79 : term,X80 : subst] : ! [X81 : (term > $o)] : ? [X82 : term] : (((X81 @ X82)) != ((X78 @ (sub @ X82 @ (push @ X79 @ X80)))))) & (! [X83 : (term > $o),X84 : term,X85 : subst] : ? [X86 : (term > $o)] : ! [X87 : term] : (((X83 @ (sub @ X87 @ (push @ X84 @ X85)))) = ((X86 @ X87))) | (pushprop_lem0 != $true)) & ((sP102 = $true) | (sP101 = $true) | ? [X88 : term,X89 : subst] : (((sub @ one @ (push @ X88 @ X89))) != X88) | ? [X90 : term,X91 : subst] : (((comp @ sh @ (push @ X90 @ X91))) != X91) | ? [X92 : subst] : (((comp @ X92 @ id)) != X92) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP102 != $true) & (sP101 != $true) & ! [X93 : term,X94 : subst] : (((sub @ one @ (push @ X93 @ X94))) = X93) & ! [X95 : term,X96 : subst] : (((comp @ sh @ (push @ X95 @ X96))) = X96) & ! [X97 : subst] : (((comp @ X97 @ id)) = X97))) & (axabs = $true) & (pushprop_lem3v2 = $true) & ((shinj = $true) | ? [X98 : term,X99 : term] : ((X98 != X99) & (((sub @ X99 @ sh)) = ((sub @ X98 @ sh))))) & (! [X100 : term,X101 : term] : ((X100 = X101) | (((sub @ X101 @ sh)) != ((sub @ X100 @ sh)))) | (shinj != $true)) & (hoasinduction_lem1_lthm = $true) & ! [X102 : term] : ? [X103 : d_term] : (((d2term @ X103)) = X102) & (hoasinduction_lem3b_gthm = $true) & (($true = sP96) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP96)) & ((hoasinduction_lem3a = $true) | (sP94 != $true)) & ((sP94 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP92)) & (($true = sP92) | (hoasinduction_lem3aa_lthm != $true)) & ((termmset = $true) | ? [X104 : term] : (((sub @ X104 @ id)) != X104)) & (! [X105 : term] : (((sub @ X105 @ id)) = X105) | (termmset != $true)) & ((hoasinduction_lem3b = $true) | ? [X106 : term] : ! [X107 : (subst > term > term)] : (((X107 @ sh @ one)) != ((sub @ X106 @ (push @ one @ sh))))) & (! [X108 : term] : ? [X109 : (subst > term > term)] : (((X109 @ sh @ one)) = ((sub @ X108 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X110 : term,X111 : term,X112 : (term > $o),X113 : (term > $o),X114 : subst] : ((((X112 @ X110)) != $true) | ($true = ((X113 @ (sub @ X110 @ (push @ X111 @ X114)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X115 : term,X116 : term,X117 : (term > $o),X118 : (term > $o),X119 : subst] : ((((X117 @ X115)) = $true) & (((X118 @ (sub @ X115 @ (push @ X116 @ X119)))) != $true))) & ((hoasinduction_lem3v2a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3v2a != $true)) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ((hoasinduction_lem3a_lthm = $true) | ((sP87 != $true) & ! [X120 : term] : (((sub @ X120 @ id)) = X120) & (sP88 != $true))) & ((sP87 = $true) | ? [X121 : term] : (((sub @ X121 @ id)) != X121) | (sP88 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X122 : d_term,X123 : d_term] : ((X122 = X123) | (((d2term @ X122)) != ((d2term @ X123)))) & (! [X124 : (subst > term > subst > $o),X125 : term] : ((((X124 @ id @ X125 @ id)) = $true) | (((sP83 @ X124)) = $true) | (((sP84 @ X124)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X126 : (subst > term > subst > $o),X127 : term] : (($true != ((X126 @ id @ X127 @ id))) & ($true != ((sP83 @ X126))) & (((sP84 @ X126)) != $true))) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X128 : term] : ! [X129 : (subst > term > term)] : ? [X130 : term,X131 : subst] : (((sub @ X128 @ (push @ X130 @ X131))) != ((X129 @ X131 @ X130)))) & (! [X132 : term] : ? [X133 : (subst > term > term)] : ! [X134 : term,X135 : subst] : (((sub @ X132 @ (push @ X134 @ X135))) = ((X133 @ X135 @ X134))) | (hoasinduction_lem3v2_f_lthm != $true)) & (! [X136 : (subst > term > subst > $o)] : ? [X137 : (term > $o)] : ! [X138 : term] : (((X136 @ id @ X138 @ id)) = ((X137 @ X138))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X139 : (subst > term > subst > $o)] : ! [X140 : (term > $o)] : ? [X141 : term] : (((X140 @ X141)) != ((X139 @ id @ X141 @ id)))) & (((d2subst @ d_id)) = id) & (($true = sP82) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP82)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP80) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP80)) & ((pushprop_lem1v2_lthm = $true) | (! [X142 : subst,X143 : term] : (((sub @ one @ (push @ X143 @ X142))) = X143) & ? [X144 : (term > $o),X145 : (term > $o),X146 : term,X147 : subst] : (! [X148 : term] : (((X144 @ X148)) = ((X145 @ (sub @ X148 @ (push @ X146 @ X147))))) & ($true != ((X144 @ one))) & (((X145 @ X146)) = $true)))) & (? [X149 : subst,X150 : term] : (((sub @ one @ (push @ X150 @ X149))) != X150) | ! [X151 : (term > $o),X152 : (term > $o),X153 : term,X154 : subst] : (? [X155 : term] : (((X152 @ (sub @ X155 @ (push @ X153 @ X154)))) != ((X151 @ X155))) | (((X151 @ one)) = $true) | (((X152 @ X153)) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((sP77 = $true) | (sP75 = $true) | (sP78 = $true) | ($true = sP76) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP77 != $true) & (sP75 != $true) & (sP78 != $true) & ($true != sP76))) & (hoaslamnotap_gthm = $true) & ((sP62 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP62 != $true)) & (ulamvarsh = $true) & (axvarshift = $true) & ((sP59 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP59 != $true)) & (! [X156 : subst] : (((comp @ X156 @ id)) = X156) | (axidr != $true)) & ((axidr = $true) | ? [X157 : subst] : (((comp @ X157 @ id)) != X157)) & (pushprop = $true) & (! [X158 : term] : (((sub @ X158 @ id)) = X158) | (axvarid != $true)) & ((axvarid = $true) | ? [X159 : term] : (((sub @ X159 @ id)) != X159)) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP55)) & (($true = sP55) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem0_lthm = $true) | ? [X160 : subst,X161 : term,X162 : (term > $o)] : ! [X163 : (term > $o)] : ? [X164 : term] : (((X162 @ (sub @ X164 @ (push @ X161 @ X160)))) != ((X163 @ X164)))) & (! [X165 : subst,X166 : term,X167 : (term > $o)] : ? [X168 : (term > $o)] : ! [X169 : term] : (((X168 @ X169)) = ((X167 @ (sub @ X169 @ (push @ X166 @ X165))))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | ? [X170 : subst] : (((comp @ X170 @ id)) != X170) | ? [X171 : subst] : (((comp @ id @ X171)) != X171)) & ((! [X172 : subst] : (((comp @ X172 @ id)) = X172) & ! [X173 : subst] : (((comp @ id @ X173)) = X173)) | (substmonoid != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP53) & (sP51 != $true) & ($true != sP52) & ! [X174 : term] : (((sub @ X174 @ id)) = X174) & ! [X175 : (subst > term > subst > $o)] : ? [X176 : (term > $o)] : ! [X177 : term] : (((X176 @ X177)) = ((X175 @ id @ X177 @ id))))) & (($true = sP53) | (sP51 = $true) | ($true = sP52) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ? [X179 : (subst > term > subst > $o)] : ! [X180 : (term > $o)] : ? [X181 : term] : (((X179 @ id @ X181 @ id)) != ((X180 @ X181))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3 != $true)) & ! [X182 : d_subst] : (d_id = X182) & ((sP39 = $true) | ? [X183 : term] : (((sub @ X183 @ id)) != X183) | ($true = sP38) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ((sP39 != $true) & ! [X184 : term] : (((sub @ X184 @ id)) = X184) & ($true != sP38))) & ! [X185 : d_term] : (d_one = X185) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X188 : subst,X189 : term] : (((sub @ one @ (push @ X189 @ X188))) != X189)) & (! [X190 : term,X191 : term] : ((((lam @ X191)) != ((lam @ X190))) | (X190 = X191)) | (laminj != $true)) & ((laminj = $true) | ? [X192 : term,X193 : term] : ((((lam @ X192)) = ((lam @ X193))) & (X192 != X193))) & (((d2subst @ d_id)) = sh) & (! [X194 : term] : ? [X195 : (subst > term > term)] : ! [X196 : term,X197 : subst] : (((sub @ X194 @ (push @ X196 @ X197))) = ((X195 @ X197 @ X196))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X198 : term] : ! [X199 : (subst > term > term)] : ? [X200 : term,X201 : subst] : (((X199 @ X201 @ X200)) != ((sub @ X198 @ (push @ X200 @ X201))))) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X202 : (subst > term > subst > $o)] : ? [X203 : (term > $o)] : ! [X204 : term] : (((X203 @ X204)) = ((X202 @ id @ X204 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X205 : (subst > term > subst > $o)] : ! [X206 : (term > $o)] : ? [X207 : term] : (((X206 @ X207)) != ((X205 @ id @ X207 @ id)))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem2v2 != $true)) & ((axshiftcons = $true) | ? [X208 : term,X209 : subst] : (((comp @ sh @ (push @ X208 @ X209))) != X209)) & (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) | (axshiftcons != $true)) & ((apinj2 = $true) | ? [X212 : term,X213 : term,X214 : term,X215 : term] : ((X212 != X215) & (((ap @ X214 @ X212)) = ((ap @ X213 @ X215))))) & (! [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 = X219) | (((ap @ X218 @ X216)) != ((ap @ X217 @ X219)))) | (apinj2 != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X220 : term] : ! [X221 : (subst > term > term)] : (((sub @ X220 @ (push @ one @ sh))) != ((X221 @ sh @ one)))) & (! [X222 : term] : ? [X223 : (subst > term > term)] : (((sub @ X222 @ (push @ one @ sh))) = ((X223 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X224 : term,X225 : term,X226 : term,X227 : term] : ((((ap @ X225 @ X226)) != ((ap @ X224 @ X227))) | (X224 = X225)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X228 : term,X229 : term,X230 : term,X231 : term] : ((((ap @ X229 @ X230)) = ((ap @ X228 @ X231))) & (X228 != X229))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP30 != $true) & ! [X232 : term] : (((sub @ X232 @ id)) = X232) & ! [X233 : (subst > term > subst > $o)] : ? [X234 : (term > $o)] : ! [X235 : term] : (((X234 @ X235)) = ((X233 @ id @ X235 @ id))) & (sP29 != $true) & (sP28 != $true))) & ((sP30 = $true) | ? [X236 : term] : (((sub @ X236 @ id)) != X236) | ? [X237 : (subst > term > subst > $o)] : ! [X238 : (term > $o)] : ? [X239 : term] : (((X238 @ X239)) != ((X237 @ id @ X239 @ id))) | (sP29 = $true) | (sP28 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X240 : term,X241 : term,X242 : term,X243 : term] : ((X240 = X242) | (((ap @ (sub @ X240 @ id) @ X243)) != ((ap @ (sub @ X242 @ id) @ X241)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X244 : term,X245 : term,X246 : term,X247 : term] : ((X244 != X246) & (((ap @ (sub @ X244 @ id) @ X247)) = ((ap @ (sub @ X246 @ id) @ X245))))) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) | ? [X248 : term,X249 : term,X250 : term,X251 : term] : ((((ap @ (sub @ X249 @ id) @ X250)) = ((ap @ (sub @ X248 @ id) @ X251))) & (X250 != X251))) & (! [X252 : term,X253 : term,X254 : term,X255 : term] : ((((ap @ (sub @ X253 @ id) @ X254)) != ((ap @ (sub @ X252 @ id) @ X255))) | (X254 = X255)) | (hoasapinj2 != $true)) & ((sP22 = $true) | ? [X256 : term] : (((sub @ X256 @ id)) != X256) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((sP22 != $true) & ! [X257 : term] : (((sub @ X257 @ id)) = X257))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((substmonoid_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (substmonoid_lthm != $true)) & (($true = sP11) | (sP12 = $true) | ? [X258 : term] : (((sub @ X258 @ id)) != X258) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP11) & (sP12 != $true) & ! [X259 : term] : (((sub @ X259 @ id)) = X259))) & ((sP5 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP5 != $true)) & (hoasapnotvar = $true) & ((induction = $true) | ($true != sP2)) & (($true = sP2) | (induction != $true)) & ! [X260 : subst] : ? [X261 : d_subst] : (((d2subst @ X261)) = X260) & (lamnotap != $true) & ((axidl = $true) | ? [X262 : subst] : (((comp @ id @ X262)) != X262)) & (! [X263 : subst] : (((comp @ id @ X263)) = X263) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(rectify,[],[f459])).
% 3.80/0.85 thf(f461,plain,(
% 3.80/0.85 ((sK513 != ((comp @ sh @ (push @ sK514 @ sK513)))) | (((sub @ one @ (push @ sK516 @ sK515))) != sK516) | ! [X4 : (term > $o),X5 : (term > $o),X6 : term,X7 : subst,X8 : term] : ((((X4 @ X6)) != $true) | (((X5 @ (sub @ X6 @ (push @ X8 @ X7)))) = $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X9 : subst,X10 : term] : (((comp @ sh @ (push @ X10 @ X9))) = X9) & ! [X11 : subst,X12 : term] : (((sub @ one @ (push @ X12 @ X11))) = X12) & (($true = ((sK517 @ sK519))) & (((sK518 @ (sub @ sK519 @ (push @ sK521 @ sK520)))) != $true)))) & ((axscons = $true) | (((push @ (sub @ one @ sK522) @ (comp @ sh @ sK522))) != sK522)) & (! [X19 : subst] : (((push @ (sub @ one @ X19) @ (comp @ sh @ X19))) = X19) | (axscons != $true)) & (pushprop_lem2v2_lthm = $true) & (! [X21 : (subst > term > term)] : (((X21 @ (sK524 @ X21) @ (sK525 @ X21))) != ((sub @ sK523 @ (push @ (sK525 @ X21) @ (sK524 @ X21))))) | ($true = sP109) | (sK526 != ((sub @ sK526 @ id))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X25 : term] : ! [X27 : subst,X28 : term] : (((sub @ X25 @ (push @ X28 @ X27))) = ((sK527 @ X25 @ X27 @ X28))) & ($true != sP109) & ! [X29 : term] : (((sub @ X29 @ id)) = X29))) & ((pushprop_lem1v2 = $true) | (! [X34 : term] : (((sK528 @ (sub @ X34 @ (push @ sK529 @ sK530)))) = ((sK531 @ X34))) & (((sK531 @ one)) != $true) & ($true = ((sK528 @ sK529))))) & (! [X35 : (term > $o),X36 : term,X37 : subst,X38 : (term > $o)] : ((((X35 @ (sub @ (sK532 @ X38 @ X37 @ X36 @ X35) @ (push @ X36 @ X37)))) != ((X38 @ (sK532 @ X38 @ X37 @ X36 @ X35)))) | (((X38 @ one)) = $true) | (((X35 @ X36)) != $true)) | (pushprop_lem1v2 != $true)) & (lamnotvar = $true) & ((hoaslaminj = $true) | ((((lam @ (sK535 @ sh @ one))) = ((lam @ (sK534 @ sh @ one)))) & (((sK535 @ sK536 @ sK533)) != ((sK534 @ sK536 @ sK533))) & ! [X44 : subst,X45 : subst,X46 : term] : (((sK535 @ (comp @ X44 @ X45) @ (sub @ X46 @ X45))) = ((sub @ (sK535 @ X44 @ X46) @ X45))) & ! [X47 : subst,X48 : subst,X49 : term] : (((sK534 @ (comp @ X47 @ X48) @ (sub @ X49 @ X48))) = ((sub @ (sK534 @ X47 @ X49) @ X48))))) & (! [X50 : term,X51 : (subst > term > term),X52 : (subst > term > term),X53 : subst] : ((((lam @ (X52 @ sh @ one))) != ((lam @ (X51 @ sh @ one)))) | (((X51 @ X53 @ X50)) = ((X52 @ X53 @ X50))) | (((sub @ (X52 @ (sK537 @ X52) @ (sK539 @ X52)) @ (sK538 @ X52))) != ((X52 @ (comp @ (sK537 @ X52) @ (sK538 @ X52)) @ (sub @ (sK539 @ X52) @ (sK538 @ X52))))) | (((sub @ (X51 @ (sK540 @ X51) @ (sK542 @ X51)) @ (sK541 @ X51))) != ((X51 @ (comp @ (sK540 @ X51) @ (sK541 @ X51)) @ (sub @ (sK542 @ X51) @ (sK541 @ X51)))))) | (hoaslaminj != $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoaslamnotap = $true) | (! [X63 : term,X64 : subst,X65 : subst] : (((sub @ (sK543 @ X65 @ X63) @ X64)) = ((sK543 @ (comp @ X65 @ X64) @ (sub @ X63 @ X64)))) & (((ap @ (sub @ sK544 @ id) @ sK545)) = ((lam @ (sK543 @ sh @ one)))))) & (! [X66 : (subst > term > term),X67 : term,X68 : term] : ((((sub @ (X66 @ (sK548 @ X66) @ (sK546 @ X66)) @ (sK547 @ X66))) != ((X66 @ (comp @ (sK548 @ X66) @ (sK547 @ X66)) @ (sub @ (sK546 @ X66) @ (sK547 @ X66))))) | (((lam @ (X66 @ sh @ one))) != ((ap @ (sub @ X67 @ id) @ X68)))) | (hoaslamnotap != $true)) & (hoasinduction_lem2_lthm = $true) & ((sP107 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP107 != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_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)))))))))))) & ! [X72 : d_subst,X73 : d_subst] : ((X72 = X73) | (((d2subst @ X73)) != ((d2subst @ X72)))) & ((hoaslaminj_lthm = $true) | ($true != sP104)) & (($true = sP104) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & (induction2_gthm = $true) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) | ((((sub @ sK549 @ id)) != sK549) & ! [X75 : term] : (((sub @ X75 @ id)) = X75))) & (! [X76 : term] : (((sub @ X76 @ id)) = X76) | (((sub @ sK550 @ id)) != sK550) | (termmset_lthm != $true)) & ((pushprop_lem0 = $true) | ! [X81 : (term > $o)] : (((X81 @ (sK554 @ X81))) != ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))))) & (! [X83 : (term > $o),X84 : term,X85 : subst] : ! [X87 : term] : (((X83 @ (sub @ X87 @ (push @ X84 @ X85)))) = ((sK555 @ X85 @ X84 @ X83 @ X87))) | (pushprop_lem0 != $true)) & ((sP102 = $true) | (sP101 = $true) | (((sub @ one @ (push @ sK556 @ sK557))) != sK556) | (sK559 != ((comp @ sh @ (push @ sK558 @ sK559)))) | (sK560 != ((comp @ sK560 @ id))) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ((sP102 != $true) & (sP101 != $true) & ! [X93 : term,X94 : subst] : (((sub @ one @ (push @ X93 @ X94))) = X93) & ! [X95 : term,X96 : subst] : (((comp @ sh @ (push @ X95 @ X96))) = X96) & ! [X97 : subst] : (((comp @ X97 @ id)) = X97))) & (axabs = $true) & (pushprop_lem3v2 = $true) & ((shinj = $true) | ((sK561 != sK562) & (((sub @ sK561 @ sh)) = ((sub @ sK562 @ sh))))) & (! [X100 : term,X101 : term] : ((X100 = X101) | (((sub @ X101 @ sh)) != ((sub @ X100 @ sh)))) | (shinj != $true)) & (hoasinduction_lem1_lthm = $true) & ! [X102 : term] : (((d2term @ (sK563 @ X102))) = X102) & (hoasinduction_lem3b_gthm = $true) & (($true = sP96) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP96)) & ((hoasinduction_lem3a = $true) | (sP94 != $true)) & ((sP94 = $true) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP92)) & (($true = sP92) | (hoasinduction_lem3aa_lthm != $true)) & ((termmset = $true) | (((sub @ sK564 @ id)) != sK564)) & (! [X105 : term] : (((sub @ X105 @ id)) = X105) | (termmset != $true)) & ((hoasinduction_lem3b = $true) | ! [X107 : (subst > term > term)] : (((X107 @ sh @ one)) != ((sub @ sK565 @ (push @ one @ sh))))) & (! [X108 : term] : (((sK566 @ X108 @ sh @ one)) = ((sub @ X108 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (! [X110 : term,X111 : term,X112 : (term > $o),X113 : (term > $o),X114 : subst] : ((((X112 @ X110)) != $true) | ($true = ((X113 @ (sub @ X110 @ (push @ X111 @ X114)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true = ((sK569 @ sK567))) & (((sK570 @ (sub @ sK567 @ (push @ sK568 @ sK571)))) != $true))) & ((hoasinduction_lem3v2a = $true) | ($true != sP90)) & (($true = sP90) | (hoasinduction_lem3v2a != $true)) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ((hoasinduction_lem3a_lthm = $true) | ((sP87 != $true) & ! [X120 : term] : (((sub @ X120 @ id)) = X120) & (sP88 != $true))) & ((sP87 = $true) | (sK572 != ((sub @ sK572 @ id))) | (sP88 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X122 : d_term,X123 : d_term] : ((X122 = X123) | (((d2term @ X122)) != ((d2term @ X123)))) & (! [X124 : (subst > term > subst > $o),X125 : term] : ((((X124 @ id @ X125 @ id)) = $true) | (((sP83 @ X124)) = $true) | (((sP84 @ X124)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK573 @ id @ sK574 @ id)) != $true) & ($true != ((sP83 @ sK573))) & (((sP84 @ sK573)) != $true))) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X129 : (subst > term > term)] : (((sub @ sK575 @ (push @ (sK576 @ X129) @ (sK577 @ X129)))) != ((X129 @ (sK577 @ X129) @ (sK576 @ X129))))) & (! [X132 : term] : ! [X134 : term,X135 : subst] : (((sub @ X132 @ (push @ X134 @ X135))) = ((sK578 @ X132 @ X135 @ X134))) | (hoasinduction_lem3v2_f_lthm != $true)) & (! [X136 : (subst > term > subst > $o)] : ! [X138 : term] : (((X136 @ id @ X138 @ id)) = ((sK579 @ X136 @ X138))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X140 : (term > $o)] : (((X140 @ (sK581 @ X140))) != ((sK580 @ id @ (sK581 @ X140) @ id)))) & (((d2subst @ d_id)) = id) & (($true = sP82) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP82)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (($true = sP80) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP80)) & ((pushprop_lem1v2_lthm = $true) | (! [X142 : subst,X143 : term] : (((sub @ one @ (push @ X143 @ X142))) = X143) & (! [X148 : term] : (((sK582 @ X148)) = ((sK583 @ (sub @ X148 @ (push @ sK584 @ sK585))))) & ($true != ((sK582 @ one))) & ($true = ((sK583 @ sK584)))))) & ((sK587 != ((sub @ one @ (push @ sK587 @ sK586)))) | ! [X151 : (term > $o),X152 : (term > $o),X153 : term,X154 : subst] : ((((X151 @ (sK588 @ X154 @ X153 @ X152 @ X151))) != ((X152 @ (sub @ (sK588 @ X154 @ X153 @ X152 @ X151) @ (push @ X153 @ X154))))) | (((X151 @ one)) = $true) | (((X152 @ X153)) != $true)) | (pushprop_lem1v2_lthm != $true)) & ((sP77 = $true) | (sP75 = $true) | (sP78 = $true) | ($true = sP76) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP77 != $true) & (sP75 != $true) & (sP78 != $true) & ($true != sP76))) & (hoaslamnotap_gthm = $true) & ((sP62 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP62 != $true)) & (ulamvarsh = $true) & (axvarshift = $true) & ((sP59 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP59 != $true)) & (! [X156 : subst] : (((comp @ X156 @ id)) = X156) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK589 @ id)) != sK589)) & (pushprop = $true) & (! [X158 : term] : (((sub @ X158 @ id)) = X158) | (axvarid != $true)) & ((axvarid = $true) | (sK590 != ((sub @ sK590 @ id)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3aaa = $true) | ($true != sP55)) & (($true = sP55) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((pushprop_lem0_lthm = $true) | ! [X163 : (term > $o)] : (((X163 @ (sK594 @ X163))) != ((sK593 @ (sub @ (sK594 @ X163) @ (push @ sK592 @ sK591)))))) & (! [X165 : subst,X166 : term,X167 : (term > $o)] : ! [X169 : term] : (((sK595 @ X167 @ X166 @ X165 @ X169)) = ((X167 @ (sub @ X169 @ (push @ X166 @ X165))))) | (pushprop_lem0_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotvar = $true) & (pushprop_lem2v2 = $true) & ((substmonoid = $true) | (((comp @ sK596 @ id)) != sK596) | (sK597 != ((comp @ id @ sK597)))) & ((! [X172 : subst] : (((comp @ X172 @ id)) = X172) & ! [X173 : subst] : (((comp @ id @ X173)) = X173)) | (substmonoid != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP53) & (sP51 != $true) & ($true != sP52) & ! [X174 : term] : (((sub @ X174 @ id)) = X174) & ! [X175 : (subst > term > subst > $o)] : ! [X177 : term] : (((sK598 @ X175 @ X177)) = ((X175 @ id @ X177 @ id))))) & (($true = sP53) | (sP51 = $true) | ($true = sP52) | (sK599 != ((sub @ sK599 @ id))) | ! [X180 : (term > $o)] : (((sK600 @ id @ (sK601 @ X180) @ id)) != ((X180 @ (sK601 @ X180)))) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3 != $true)) & ! [X182 : d_subst] : (d_id = X182) & ((sP39 = $true) | (((sub @ sK602 @ id)) != sK602) | ($true = sP38) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | ((sP39 != $true) & ! [X184 : term] : (((sub @ X184 @ id)) = X184) & ($true != sP38))) & ! [X185 : d_term] : (d_one = X185) & (! [X186 : subst,X187 : term] : (((sub @ one @ (push @ X187 @ X186))) = X187) | (axvarcons != $true)) & ((axvarcons = $true) | (sK604 != ((sub @ one @ (push @ sK604 @ sK603))))) & (! [X190 : term,X191 : term] : ((((lam @ X191)) != ((lam @ X190))) | (X190 = X191)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK606)) = ((lam @ sK605))) & (sK605 != sK606))) & (((d2subst @ d_id)) = sh) & (! [X194 : term] : ! [X196 : term,X197 : subst] : (((sub @ X194 @ (push @ X196 @ X197))) = ((sK607 @ X194 @ X197 @ X196))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X199 : (subst > term > term)] : (((sub @ sK608 @ (push @ (sK609 @ X199) @ (sK610 @ X199)))) != ((X199 @ (sK610 @ X199) @ (sK609 @ X199))))) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X202 : (subst > term > subst > $o)] : ! [X204 : term] : (((sK611 @ X202 @ X204)) = ((X202 @ id @ X204 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X206 : (term > $o)] : (((X206 @ (sK613 @ X206))) != ((sK612 @ id @ (sK613 @ X206) @ id)))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem2v2 != $true)) & ((axshiftcons = $true) | (sK615 != ((comp @ sh @ (push @ sK614 @ sK615))))) & (! [X210 : term,X211 : subst] : (((comp @ sh @ (push @ X210 @ X211))) = X211) | (axshiftcons != $true)) & ((apinj2 = $true) | ((sK616 != sK619) & (((ap @ sK618 @ sK616)) = ((ap @ sK617 @ sK619))))) & (! [X216 : term,X217 : term,X218 : term,X219 : term] : ((X216 = X219) | (((ap @ X218 @ X216)) != ((ap @ X217 @ X219)))) | (apinj2 != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X221 : (subst > term > term)] : (((X221 @ sh @ one)) != ((sub @ sK620 @ (push @ one @ sh))))) & (! [X222 : term] : (((sub @ X222 @ (push @ one @ sh))) = ((sK621 @ X222 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (hoasinduction_gthm = $true) & (axapp = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X224 : term,X225 : term,X226 : term,X227 : term] : ((((ap @ X225 @ X226)) != ((ap @ X224 @ X227))) | (X224 = X225)) | (apinj1 != $true)) & ((apinj1 = $true) | ((((ap @ sK623 @ sK624)) = ((ap @ sK622 @ sK625))) & (sK623 != sK622))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP30 != $true) & ! [X232 : term] : (((sub @ X232 @ id)) = X232) & ! [X233 : (subst > term > subst > $o)] : ! [X235 : term] : (((sK626 @ X233 @ X235)) = ((X233 @ id @ X235 @ id))) & (sP29 != $true) & (sP28 != $true))) & ((sP30 = $true) | (((sub @ sK627 @ id)) != sK627) | ! [X238 : (term > $o)] : (((sK628 @ id @ (sK629 @ X238) @ id)) != ((X238 @ (sK629 @ X238)))) | (sP29 = $true) | (sP28 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & (! [X240 : term,X241 : term,X242 : term,X243 : term] : ((X240 = X242) | (((ap @ (sub @ X240 @ id) @ X243)) != ((ap @ (sub @ X242 @ id) @ X241)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((sK630 != sK632) & (((ap @ (sub @ sK632 @ id) @ sK631)) = ((ap @ (sub @ sK630 @ id) @ sK633))))) & (pushprop_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK635 @ id) @ sK636)) = ((ap @ (sub @ sK634 @ id) @ sK637))) & (sK637 != sK636))) & (! [X252 : term,X253 : term,X254 : term,X255 : term] : ((((ap @ (sub @ X253 @ id) @ X254)) != ((ap @ (sub @ X252 @ id) @ X255))) | (X254 = X255)) | (hoasapinj2 != $true)) & ((sP22 = $true) | (sK638 != ((sub @ sK638 @ id))) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((sP22 != $true) & ! [X257 : term] : (((sub @ X257 @ id)) = X257))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction != $true)) & (axassoc = $true) & (pushprop_lthm_orig = $true) & (axmap = $true) & (hoaslamnotap_lthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (termmset_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((substmonoid_lthm = $true) | (sP13 != $true)) & ((sP13 = $true) | (substmonoid_lthm != $true)) & (($true = sP11) | (sP12 = $true) | (((sub @ sK639 @ id)) != sK639) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | (($true != sP11) & (sP12 != $true) & ! [X259 : term] : (((sub @ X259 @ id)) = X259))) & ((sP5 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP5 != $true)) & (hoasapnotvar = $true) & ((induction = $true) | ($true != sP2)) & (($true = sP2) | (induction != $true)) & ! [X260 : subst] : (((d2subst @ (sK640 @ X260))) = X260) & (lamnotap != $true) & ((axidl = $true) | (((comp @ id @ sK641)) != sK641)) & (! [X263 : subst] : (((comp @ id @ X263)) = X263) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & (axclos = $true) & (ulamvar1 != $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem3v2_lthm = $true)),
% 3.80/0.85 inference(skolemize,[status(esa),new_symbols(skolem,[sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,vAPP,vAPP,sK526,vAPP,sK528,sK529,sK530,sK531,vAPP,sK533,sK534,sK535,sK536,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK543,sK544,sK545,vAPP,vAPP,vAPP,sK549,sK550,sK551,sK552,sK553,vAPP,vAPP,sK556,sK557,sK558,sK559,sK560,sK561,sK562,vAPP,sK564,sK565,vAPP,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,vAPP,vAPP,vAPP,vAPP,sK580,vAPP,sK582,sK583,sK584,sK585,sK586,sK587,vAPP,sK589,sK590,sK591,sK592,sK593,vAPP,vAPP,sK596,sK597,vAPP,sK599,sK600,vAPP,sK602,sK603,sK604,sK605,sK606,vAPP,sK608,vAPP,vAPP,vAPP,sK612,vAPP,sK614,sK615,sK616,sK617,sK618,sK619,sK620,vAPP,sK622,sK623,sK624,sK625,vAPP,sK627,sK628,vAPP,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,vAPP,sK641]),skolemize(X0,sK513),skolemize(X1,sK514),skolemize(X2,sK515),skolemize(X3,sK516),skolemize(X13,sK517),skolemize(X14,sK518),skolemize(X15,sK519),skolemize(X16,sK520),skolemize(X17,sK521),skolemize(X18,sK522),skolemize(X20,sK523),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X24,sK526),skolemize(X9,sK114 @ X7 @ X6),skolemize(X30,sK528),skolemize(X31,sK529),skolemize(X32,sK530),skolemize(X33,sK531),skolemize(X9,sK114 @ X7 @ X6),skolemize(X40,sK533),skolemize(X41,sK534),skolemize(X42,sK535),skolemize(X43,sK536),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X60,sK543),skolemize(X61,sK544),skolemize(X62,sK545),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X74,sK549),skolemize(X77,sK550),skolemize(X78,sK551),skolemize(X79,sK552),skolemize(X80,sK553),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X88,sK556),skolemize(X89,sK557),skolemize(X90,sK558),skolemize(X91,sK559),skolemize(X92,sK560),skolemize(X98,sK561),skolemize(X99,sK562),skolemize(X9,sK114 @ X7 @ X6),skolemize(X104,sK564),skolemize(X106,sK565),skolemize(X9,sK114 @ X7 @ X6),skolemize(X115,sK567),skolemize(X116,sK568),skolemize(X117,sK569),skolemize(X118,sK570),skolemize(X119,sK571),skolemize(X121,sK572),skolemize(X126,sK573),skolemize(X127,sK574),skolemize(X128,sK575),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X139,sK580),skolemize(X9,sK114 @ X7 @ X6),skolemize(X144,sK582),skolemize(X145,sK583),skolemize(X146,sK584),skolemize(X147,sK585),skolemize(X149,sK586),skolemize(X150,sK587),skolemize(X9,sK114 @ X7 @ X6),skolemize(X157,sK589),skolemize(X159,sK590),skolemize(X160,sK591),skolemize(X161,sK592),skolemize(X162,sK593),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X170,sK596),skolemize(X171,sK597),skolemize(X9,sK114 @ X7 @ X6),skolemize(X178,sK599),skolemize(X179,sK600),skolemize(X9,sK114 @ X7 @ X6),skolemize(X183,sK602),skolemize(X188,sK603),skolemize(X189,sK604),skolemize(X192,sK605),skolemize(X193,sK606),skolemize(X9,sK114 @ X7 @ X6),skolemize(X198,sK608),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X9,sK114 @ X7 @ X6),skolemize(X205,sK612),skolemize(X9,sK114 @ X7 @ X6),skolemize(X208,sK614),skolemize(X209,sK615),skolemize(X212,sK616),skolemize(X213,sK617),skolemize(X214,sK618),skolemize(X215,sK619),skolemize(X220,sK620),skolemize(X9,sK114 @ X7 @ X6),skolemize(X228,sK622),skolemize(X229,sK623),skolemize(X230,sK624),skolemize(X231,sK625),skolemize(X9,sK114 @ X7 @ X6),skolemize(X236,sK627),skolemize(X237,sK628),skolemize(X9,sK114 @ X7 @ X6),skolemize(X244,sK630),skolemize(X245,sK631),skolemize(X246,sK632),skolemize(X247,sK633),skolemize(X248,sK634),skolemize(X249,sK635),skolemize(X250,sK636),skolemize(X251,sK637),skolemize(X256,sK638),skolemize(X258,sK639),skolemize(X9,sK114 @ X7 @ X6),skolemize(X262,sK641)],[f460])).
% 3.80/0.85 thf(f462,plain,(
% 3.80/0.85 (pushprop_lem0 != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: (pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3)))))))))))),
% 3.80/0.85 inference(cnf_transformation,[],[f8])).
% 3.80/0.85 thf(f982,plain,(
% 3.80/0.85 (ulamvar1 != $true)),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f988,plain,(
% 3.80/0.85 ( ! [X260 : subst] : ((((d2subst @ (sK640 @ X260))) = X260)) )),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1066,plain,(
% 3.80/0.85 ( ! [X185 : d_term] : ((d_one = X185)) )),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1071,plain,(
% 3.80/0.85 ( ! [X182 : d_subst] : ((d_id = X182)) )),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1121,plain,(
% 3.80/0.85 (((d2subst @ d_id)) = id)),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1136,plain,(
% 3.80/0.85 (one = ((d2term @ d_one)))),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1153,plain,(
% 3.80/0.85 ( ! [X102 : term] : ((((d2term @ (sK563 @ X102))) = X102)) )),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1167,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ (sK554 @ X81))) != ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553))))) | (pushprop_lem0 = $true)) )),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1177,plain,(
% 3.80/0.85 (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4))))))))))))),
% 3.80/0.85 inference(cnf_transformation,[],[f461])).
% 3.80/0.85 thf(f1211,definition,(
% 3.80/0.85 ($false != $true)),
% 3.80/0.85 introduced(theory,[fool_distinctness_axiom])).
% 3.80/0.85 thf(f1212,definition,(
% 3.80/0.85 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.80/0.85 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.80/0.85 thf(f1213,plain,(
% 3.80/0.85 (pushprop_lem0 != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))) = (Y7 @ Y8))))))))))) @ Y2 @ Y1 @ Y0 @ Y3)))))))))))),
% 3.80/0.85 inference(definition_unfolding,[],[f462,f1177])).
% 3.80/0.85 thf(f1285,plain,(
% 3.80/0.85 ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))) = (Y7 @ Y8))))))))))) @ Y2 @ Y1 @ Y0 @ Y3))))))))))) | (pushprop_lem0 = $false)),
% 3.80/0.85 inference(xor_proxy_clausification,[],[f1213])).
% 3.80/0.85 thf(f1286,plain,(
% 3.80/0.85 (pushprop_lem0 = $false) | ($false = (((^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (?? @ (term > $o) @ (^[Y3 : term > $o]: ((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))) = (Y7 @ Y8))))))))))) @ Y2 @ Y1 @ Y0 @ Y3)))))))) @ sK642)))),
% 3.80/0.85 inference(sigma_proxy_clausification,[],[f1285])).
% 3.80/0.85 thf(f1287,plain,(
% 3.80/0.85 (pushprop_lem0 = $false) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (?? @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((sK642 @ (sub @ Y3 @ (push @ Y1 @ Y0))) = (Y2 @ Y3))))))))))))),
% 3.80/0.85 inference(beta-eta_normalization,[],[f1286])).
% 3.80/0.85 thf(f1288,plain,(
% 3.80/0.85 (pushprop_lem0 = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (?? @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((sK642 @ (sub @ Y3 @ (push @ Y1 @ Y0))) = (Y2 @ Y3))))))))) @ sK643)))),
% 3.80/0.85 inference(sigma_proxy_clausification,[],[f1287])).
% 3.80/0.85 thf(f1289,plain,(
% 3.80/0.85 (pushprop_lem0 = $false) | ($false = ((!! @ term @ (^[Y0 : term]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((sK642 @ (sub @ Y2 @ (push @ Y0 @ sK643))) = (Y1 @ Y2))))))))))),
% 3.80/0.85 inference(beta-eta_normalization,[],[f1288])).
% 3.80/0.85 thf(f1290,plain,(
% 3.80/0.85 ($false = (((^[Y0 : term]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((sK642 @ (sub @ Y2 @ (push @ Y0 @ sK643))) = (Y1 @ Y2))))))) @ sK644))) | (pushprop_lem0 = $false)),
% 3.80/0.85 inference(sigma_proxy_clausification,[],[f1289])).
% 3.80/0.85 thf(f1291,plain,(
% 3.80/0.85 ($false = ((?? @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK642 @ (sub @ Y1 @ (push @ sK644 @ sK643))) = (Y0 @ Y1)))))))) | (pushprop_lem0 = $false)),
% 3.80/0.85 inference(beta-eta_normalization,[],[f1290])).
% 3.80/0.85 thf(f1292,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = (((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK642 @ (sub @ Y1 @ (push @ sK644 @ sK643))) = (Y0 @ Y1))))) @ X1)))) )),
% 3.80/0.85 inference(pi_proxy_clausification,[],[f1291])).
% 3.80/0.85 thf(f1293,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : (($false = ((!! @ term @ (^[Y0 : term]: ((sK642 @ (sub @ Y0 @ (push @ sK644 @ sK643))) = (X1 @ Y0)))))) | (pushprop_lem0 = $false)) )),
% 3.80/0.85 inference(beta-eta_normalization,[],[f1292])).
% 3.80/0.85 thf(f1294,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ((((^[Y0 : term]: ((sK642 @ (sub @ Y0 @ (push @ sK644 @ sK643))) = (X1 @ Y0))) @ (sK645 @ X1))) = $false)) )),
% 3.80/0.85 inference(sigma_proxy_clausification,[],[f1293])).
% 3.80/0.85 thf(f1295,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : (($false = (((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643))) = (X1 @ (sK645 @ X1))))) | (pushprop_lem0 = $false)) )),
% 3.80/0.85 inference(beta-eta_normalization,[],[f1294])).
% 3.80/0.85 thf(f1296,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | (((X1 @ (sK645 @ X1))) != ((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643)))))) )),
% 3.80/0.85 inference(equality_proxy_clausification,[],[f1295])).
% 3.80/0.85 thf(f1297,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643)))) = $true) | (((X1 @ (sK645 @ X1))) = $true) | (pushprop_lem0 = $false)) )),
% 3.80/0.85 inference(xor_proxy_clausification,[],[f1296])).
% 3.80/0.85 thf(f1298,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((pushprop_lem0 = $false) | ($false = ((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643))))) | (((X1 @ (sK645 @ X1))) = $false)) )),
% 3.80/0.85 inference(xor_proxy_clausification,[],[f1296])).
% 3.80/0.85 thf(f1312,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))) = $true) | (pushprop_lem0 = $true) | (((X81 @ (sK554 @ X81))) = $true)) )),
% 3.80/0.85 inference(xor_proxy_clausification,[],[f1167])).
% 3.80/0.85 thf(f1313,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ (sK554 @ X81))) = $false) | ($false = ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553))))) | (pushprop_lem0 = $true)) )),
% 3.80/0.85 inference(xor_proxy_clausification,[],[f1167])).
% 3.80/0.85 thf(f2239,definition,(
% 3.80/0.85 spl647_212 <=> (pushprop_lem0 = $true)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_212])],[avatar_definition])).
% 3.80/0.85 thf(f2240,plain,(
% 3.80/0.85 (pushprop_lem0 = $true) | ~spl647_212),
% 3.80/0.85 inference(avatar_component_clause,[],[f2239])).
% 3.80/0.85 thf(f3205,definition,(
% 3.80/0.85 spl647_417 <=> (pushprop_lem0 = $false)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_417])],[avatar_definition])).
% 3.80/0.85 thf(f3207,plain,(
% 3.80/0.85 (pushprop_lem0 = $false) | ~spl647_417),
% 3.80/0.85 inference(avatar_component_clause,[],[f3205])).
% 3.80/0.85 thf(f3209,definition,(
% 3.80/0.85 spl647_418 <=> ! [X1 : (term > $o)] : (($false = ((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643))))) | (((X1 @ (sK645 @ X1))) = $false))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_418])],[avatar_definition])).
% 3.80/0.85 thf(f3210,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : (($false = ((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643))))) | (((X1 @ (sK645 @ X1))) = $false)) ) | ~spl647_418),
% 3.80/0.85 inference(avatar_component_clause,[],[f3209])).
% 3.80/0.85 thf(f3211,plain,(
% 3.80/0.85 spl647_417 | spl647_418),
% 3.80/0.85 inference(avatar_split_clause,[],[f1298,f3209,f3205])).
% 3.80/0.85 thf(f3213,definition,(
% 3.80/0.85 spl647_419 <=> ! [X1 : (term > $o)] : ((((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643)))) = $true) | (((X1 @ (sK645 @ X1))) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_419])],[avatar_definition])).
% 3.80/0.85 thf(f3214,plain,(
% 3.80/0.85 ( ! [X1 : (term > $o)] : ((((sK642 @ (sub @ (sK645 @ X1) @ (push @ sK644 @ sK643)))) = $true) | (((X1 @ (sK645 @ X1))) = $true)) ) | ~spl647_419),
% 3.80/0.85 inference(avatar_component_clause,[],[f3213])).
% 3.80/0.85 thf(f3215,plain,(
% 3.80/0.85 spl647_419 | spl647_417),
% 3.80/0.85 inference(avatar_split_clause,[],[f1297,f3205,f3213])).
% 3.80/0.85 thf(f3239,definition,(
% 3.80/0.85 spl647_425 <=> ! [X81 : (term > $o)] : ((((X81 @ (sK554 @ X81))) = $false) | ($false = ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553))))))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_425])],[avatar_definition])).
% 3.80/0.85 thf(f3240,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ (sK554 @ X81))) = $false) | ($false = ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))))) ) | ~spl647_425),
% 3.80/0.85 inference(avatar_component_clause,[],[f3239])).
% 3.80/0.85 thf(f3241,plain,(
% 3.80/0.85 spl647_425 | spl647_212),
% 3.80/0.85 inference(avatar_split_clause,[],[f1313,f2239,f3239])).
% 3.80/0.85 thf(f3243,definition,(
% 3.80/0.85 spl647_426 <=> ! [X81 : (term > $o)] : ((((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))) = $true) | (((X81 @ (sK554 @ X81))) = $true))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_426])],[avatar_definition])).
% 3.80/0.85 thf(f3244,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ (sK554 @ X81))) = $true) | (((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))) = $true)) ) | ~spl647_426),
% 3.80/0.85 inference(avatar_component_clause,[],[f3243])).
% 3.80/0.85 thf(f3245,plain,(
% 3.80/0.85 spl647_212 | spl647_426),
% 3.80/0.85 inference(avatar_split_clause,[],[f1312,f3243,f2239])).
% 3.80/0.85 thf(f3417,plain,(
% 3.80/0.85 ($true != $true) | (ulamvar1 = $false)),
% 3.80/0.85 inference(constrained_superposition,[],[f982,f1212])).
% 3.80/0.85 thf(f3425,plain,(
% 3.80/0.85 (ulamvar1 = $false)),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f3417])).
% 3.80/0.85 thf(f3429,plain,(
% 3.80/0.85 ($false = $true) | (~spl647_212 | ~spl647_417)),
% 3.80/0.85 inference(forward_demodulation,[],[f2240,f3207])).
% 3.80/0.85 thf(f3430,plain,(
% 3.80/0.85 $false | (~spl647_212 | ~spl647_417)),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f3429])).
% 3.80/0.85 thf(f3431,plain,(
% 3.80/0.85 ~spl647_212 | ~spl647_417),
% 3.80/0.85 inference(avatar_contradiction_clause,[],[f3430])).
% 3.80/0.85 thf(f3451,plain,(
% 3.80/0.85 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 3.80/0.85 inference(constrained_superposition,[],[f1121,f1071])).
% 3.80/0.85 thf(f3468,plain,(
% 3.80/0.85 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 3.80/0.85 inference(constrained_superposition,[],[f1136,f1066])).
% 3.80/0.85 thf(f3497,plain,(
% 3.80/0.85 ( ! [X260 : subst] : ((id = X260)) )),
% 3.80/0.85 inference(forward_demodulation,[],[f988,f3451])).
% 3.80/0.85 thf(f3500,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : ((((sK642 @ (sub @ (sK645 @ X0) @ id))) = $true) | (((X0 @ (sK645 @ X0))) = $true)) ) | ~spl647_419),
% 3.80/0.85 inference(constrained_superposition,[],[f3214,f3497])).
% 3.80/0.85 thf(f3501,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : (($false = ((sK642 @ (sub @ (sK645 @ X0) @ id)))) | ($false = ((X0 @ (sK645 @ X0))))) ) | ~spl647_418),
% 3.80/0.85 inference(constrained_superposition,[],[f3210,f3497])).
% 3.80/0.85 thf(f3507,plain,(
% 3.80/0.85 ( ! [X0 : subst,X1 : (term > $o)] : (($true = ((sK642 @ (sub @ (sK645 @ X1) @ X0)))) | (((X1 @ (sK645 @ X1))) = $true)) ) | ~spl647_419),
% 3.80/0.85 inference(constrained_superposition,[],[f3500,f3497])).
% 3.80/0.85 thf(f3514,plain,(
% 3.80/0.85 ( ! [X0 : subst,X1 : (term > $o)] : (($false = ((sK642 @ (sub @ (sK645 @ X1) @ X0)))) | (((X1 @ (sK645 @ X1))) = $false)) ) | ~spl647_418),
% 3.80/0.85 inference(constrained_superposition,[],[f3501,f3497])).
% 3.80/0.85 thf(f3588,plain,(
% 3.80/0.85 ( ! [X102 : term] : ((one = X102)) )),
% 3.80/0.85 inference(forward_demodulation,[],[f1153,f3468])).
% 3.80/0.85 thf(f3592,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o),X1 : subst] : (($false = ((X0 @ one))) | ($false = ((sK642 @ (sub @ one @ X1))))) ) | ~spl647_418),
% 3.80/0.85 inference(constrained_superposition,[],[f3514,f3588])).
% 3.80/0.85 thf(f3603,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : ((((sK642 @ one)) = $true) | (((X0 @ (sK645 @ X0))) = $true)) ) | ~spl647_419),
% 3.80/0.85 inference(constrained_superposition,[],[f3507,f3588])).
% 3.80/0.85 thf(f3624,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : (($false = ((X0 @ one))) | (((sK642 @ one)) = $false)) ) | ~spl647_418),
% 3.80/0.85 inference(forward_demodulation,[],[f3592,f3588])).
% 3.80/0.85 thf(f3625,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : ((((sK642 @ one)) = $true) | (((X0 @ one)) = $true)) ) | ~spl647_419),
% 3.80/0.85 inference(forward_demodulation,[],[f3603,f3588])).
% 3.80/0.85 thf(f3627,definition,(
% 3.80/0.85 spl647_463 <=> (((sK642 @ one)) = $true)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_463])],[avatar_definition])).
% 3.80/0.85 thf(f3629,plain,(
% 3.80/0.85 (((sK642 @ one)) = $true) | ~spl647_463),
% 3.80/0.85 inference(avatar_component_clause,[],[f3627])).
% 3.80/0.85 thf(f3631,definition,(
% 3.80/0.85 spl647_464 <=> ! [X0 : (term > $o)] : (((X0 @ one)) = $true)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_464])],[avatar_definition])).
% 3.80/0.85 thf(f3632,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : ((((X0 @ one)) = $true)) ) | ~spl647_464),
% 3.80/0.85 inference(avatar_component_clause,[],[f3631])).
% 3.80/0.85 thf(f3636,definition,(
% 3.80/0.85 spl647_465 <=> ! [X0 : (term > $o)] : ($false = ((X0 @ one)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_465])],[avatar_definition])).
% 3.80/0.85 thf(f3637,plain,(
% 3.80/0.85 ( ! [X0 : (term > $o)] : (($false = ((X0 @ one)))) ) | ~spl647_465),
% 3.80/0.85 inference(avatar_component_clause,[],[f3636])).
% 3.80/0.85 thf(f3639,definition,(
% 3.80/0.85 spl647_466 <=> (((sK642 @ one)) = $false)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_466])],[avatar_definition])).
% 3.80/0.85 thf(f3641,plain,(
% 3.80/0.85 (((sK642 @ one)) = $false) | ~spl647_466),
% 3.80/0.85 inference(avatar_component_clause,[],[f3639])).
% 3.80/0.85 thf(f3650,plain,(
% 3.80/0.85 spl647_466 | spl647_465 | ~spl647_418),
% 3.80/0.85 inference(avatar_split_clause,[],[f3624,f3209,f3636,f3639])).
% 3.80/0.85 thf(f3651,plain,(
% 3.80/0.85 spl647_464 | spl647_463 | ~spl647_419),
% 3.80/0.85 inference(avatar_split_clause,[],[f3625,f3213,f3627,f3631])).
% 3.80/0.85 thf(f3655,plain,(
% 3.80/0.85 ($false = $true) | (~spl647_463 | ~spl647_466)),
% 3.80/0.85 inference(constrained_superposition,[],[f3641,f3629])).
% 3.80/0.85 thf(f3657,plain,(
% 3.80/0.85 $false | (~spl647_463 | ~spl647_466)),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f3655])).
% 3.80/0.85 thf(f3658,plain,(
% 3.80/0.85 ~spl647_463 | ~spl647_466),
% 3.80/0.85 inference(avatar_contradiction_clause,[],[f3657])).
% 3.80/0.85 thf(f3859,plain,(
% 3.80/0.85 ($false != $false) | ~spl647_465),
% 3.80/0.85 inference(constrained_superposition,[],[f1211,f3637])).
% 3.80/0.85 thf(f3909,plain,(
% 3.80/0.85 $false | ~spl647_465),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f3859])).
% 3.80/0.85 thf(f3910,plain,(
% 3.80/0.85 ~spl647_465),
% 3.80/0.85 inference(avatar_contradiction_clause,[],[f3909])).
% 3.80/0.85 thf(f4370,plain,(
% 3.80/0.85 ($false = $true) | ~spl647_464),
% 3.80/0.85 inference(constrained_superposition,[],[f3632,f3425])).
% 3.80/0.85 thf(f4460,plain,(
% 3.80/0.85 $false | ~spl647_464),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f4370])).
% 3.80/0.85 thf(f4461,plain,(
% 3.80/0.85 ~spl647_464),
% 3.80/0.85 inference(avatar_contradiction_clause,[],[f4460])).
% 3.80/0.85 thf(f4529,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ one)) = $false) | ($false = ((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))))) ) | ~spl647_425),
% 3.80/0.85 inference(forward_demodulation,[],[f3240,f3588])).
% 3.80/0.85 thf(f4530,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((sK551 @ (sub @ (sK554 @ X81) @ (push @ sK552 @ sK553)))) = $true) | (((X81 @ one)) = $true)) ) | ~spl647_426),
% 3.80/0.85 inference(forward_demodulation,[],[f3244,f3588])).
% 3.80/0.85 thf(f4630,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((X81 @ one)) = $false) | ($false = ((sK551 @ one)))) ) | ~spl647_425),
% 3.80/0.85 inference(forward_demodulation,[],[f4529,f3588])).
% 3.80/0.85 thf(f4631,plain,(
% 3.80/0.85 ( ! [X81 : (term > $o)] : ((((sK551 @ one)) = $true) | (((X81 @ one)) = $true)) ) | ~spl647_426),
% 3.80/0.85 inference(forward_demodulation,[],[f4530,f3588])).
% 3.80/0.85 thf(f4710,definition,(
% 3.80/0.85 spl647_487 <=> ($false = ((sK551 @ one)))),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_487])],[avatar_definition])).
% 3.80/0.85 thf(f4712,plain,(
% 3.80/0.85 ($false = ((sK551 @ one))) | ~spl647_487),
% 3.80/0.85 inference(avatar_component_clause,[],[f4710])).
% 3.80/0.85 thf(f4713,plain,(
% 3.80/0.85 spl647_487 | spl647_465 | ~spl647_425),
% 3.80/0.85 inference(avatar_split_clause,[],[f4630,f3239,f3636,f4710])).
% 3.80/0.85 thf(f4715,definition,(
% 3.80/0.85 spl647_488 <=> (((sK551 @ one)) = $true)),
% 3.80/0.85 introduced(definition,[new_symbols(definition,[spl647_488])],[avatar_definition])).
% 3.80/0.85 thf(f4717,plain,(
% 3.80/0.85 (((sK551 @ one)) = $true) | ~spl647_488),
% 3.80/0.85 inference(avatar_component_clause,[],[f4715])).
% 3.80/0.85 thf(f4718,plain,(
% 3.80/0.85 spl647_464 | spl647_488 | ~spl647_426),
% 3.80/0.85 inference(avatar_split_clause,[],[f4631,f3243,f4715,f3631])).
% 3.80/0.85 thf(f5420,plain,(
% 3.80/0.85 ($false = $true) | (~spl647_487 | ~spl647_488)),
% 3.80/0.85 inference(forward_demodulation,[],[f4717,f4712])).
% 3.80/0.85 thf(f5421,plain,(
% 3.80/0.85 $false | (~spl647_487 | ~spl647_488)),
% 3.80/0.85 inference(trivial_inequality_removal,[],[f5420])).
% 3.80/0.85 thf(f5422,plain,(
% 3.80/0.85 ~spl647_487 | ~spl647_488),
% 3.80/0.85 inference(avatar_contradiction_clause,[],[f5421])).
% 3.80/0.85 cnf(s392, plain, spl647_417 | spl647_418, inference(sat_conversion,[],[f3211])).
% 3.80/0.85 cnf(s393, plain, spl647_417 | spl647_419, inference(sat_conversion,[],[f3215])).
% 3.80/0.85 cnf(s399, plain, spl647_212 | spl647_425, inference(sat_conversion,[],[f3241])).
% 3.80/0.85 cnf(s400, plain, spl647_212 | spl647_426, inference(sat_conversion,[],[f3245])).
% 3.80/0.85 cnf(s439, plain, ~spl647_212 | ~spl647_417, inference(sat_conversion,[],[f3431])).
% 3.80/0.85 cnf(s450, plain, ~spl647_418 | spl647_465 | spl647_466, inference(sat_conversion,[],[f3650])).
% 3.80/0.85 cnf(s451, plain, ~spl647_419 | spl647_463 | spl647_464, inference(sat_conversion,[],[f3651])).
% 3.80/0.85 cnf(s452, plain, ~spl647_463 | ~spl647_466, inference(sat_conversion,[],[f3658])).
% 3.80/0.85 cnf(s458, plain, ~spl647_465, inference(sat_conversion,[],[f3910])).
% 3.80/0.85 cnf(s682, plain, ~spl647_464, inference(sat_conversion,[],[f4461])).
% 3.80/0.85 cnf(s725, plain, ~spl647_425 | spl647_465 | spl647_487, inference(sat_conversion,[],[f4713])).
% 3.80/0.85 cnf(s726, plain, ~spl647_426 | spl647_464 | spl647_488, inference(sat_conversion,[],[f4718])).
% 3.80/0.85 cnf(s839, plain, ~spl647_487 | ~spl647_488, inference(sat_conversion,[],[f5422])).
% 3.80/0.85 cnf(s842, plain, ~spl647_419 | spl647_463, inference(rat,[],[s451,s682])).
% 3.80/0.85 cnf(s843, plain, ~spl647_418 | spl647_466, inference(rat,[],[s450,s458])).
% 3.80/0.85 cnf(s897, plain, spl647_212, inference(rat,[],[s839,s725,s726,s399,s400,s458,s682])).
% 3.80/0.85 cnf(s898, plain, ~spl647_417, inference(rat,[],[s439,s897])).
% 3.80/0.85 cnf(s901, plain, spl647_419, inference(rat,[],[s393,s898])).
% 3.80/0.85 cnf(s902, plain, spl647_418, inference(rat,[],[s392,s898])).
% 3.80/0.85 cnf(s903, plain, spl647_463, inference(rat,[],[s842,s901])).
% 3.80/0.85 cnf(s904, plain, spl647_466, inference(rat,[],[s843,s902])).
% 3.80/0.85 cnf(s905, plain, $false, inference(rat,[],[s452,s904,s903])).
% 3.80/0.85 thf(f5423,plain,(
% 3.80/0.85 $false),
% 3.80/0.85 inference(avatar_sat_refutation,[],[s905])).
% 3.80/0.85 % SZS output end Proof for theBenchmark
% 3.80/0.85 % (4189575)------------------------------
% 3.80/0.85 % (4189575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.85 % (4189575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.85 % (4189575)CaDiCaL version: 2.1.3
% 3.80/0.85 % (4189575)Termination reason: Refutation
% 3.80/0.85 % (4189575)Time elapsed: 0.116 s
% 3.80/0.85 % (4189575)Peak memory usage: 18 MB
% 3.80/0.85 % (4189575)Instructions burned: 477 (million)
% 3.80/0.85 % (4189454)Success in time 0.606 s
% 3.80/0.85 % Vampire exiting
%------------------------------------------------------------------------------