%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX158^1 : 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 : n017.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 1.38s 0.55s
% Output : Refutation 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX158^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n017.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:04:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.25 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
% 0.64/0.38 % (518331)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.64/0.38 % (518341)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2173054909:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.64/0.38 % (518342)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.64/0.38 % (518342)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
% 0.64/0.38 % (518336)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=8589220:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.64/0.38 % (518342)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=2510571952:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.64/0.38 % (518337)lrs+10_16_si=on:nwc=1.5:random_seed=2372023909:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.64/0.38 % (518338)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=319354872:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.64/0.38 % (518340)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1843061956:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.64/0.38 % (518339)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=1188141680: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)
% 0.64/0.38 % (518338)Instruction limit reached!
% 0.64/0.38 % (518338)------------------------------
% 0.64/0.38 % (518338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (518338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (518338)CaDiCaL version: 2.1.3
% 0.64/0.38 % (518338)Termination reason: Instruction limit
% 0.64/0.38 % (518338)Termination phase: shuffling
% 0.64/0.38 % (518338)Time elapsed: 0.002 s
% 0.64/0.38 % (518338)Peak memory usage: 9 MB
% 0.64/0.38 % (518338)Instructions burned: 4 (million)
% 0.64/0.38 % (518337)Instruction limit reached!
% 0.64/0.38 % (518337)------------------------------
% 0.64/0.38 % (518337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (518337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (518337)CaDiCaL version: 2.1.3
% 0.64/0.38 % (518337)Termination reason: Instruction limit
% 0.64/0.38 % (518337)Termination phase: shuffling
% 0.64/0.38 % (518337)Time elapsed: 0.008 s
% 0.64/0.38 % (518337)Peak memory usage: 10 MB
% 0.64/0.38 % (518337)Instructions burned: 19 (million)
% 0.64/0.38 % (518340)Instruction limit reached!
% 0.64/0.38 % (518340)------------------------------
% 0.64/0.38 % (518340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (518340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (518340)CaDiCaL version: 2.1.3
% 0.64/0.38 % (518340)Termination reason: Instruction limit
% 0.64/0.38 % (518340)Termination phase: shuffling
% 0.64/0.38 % (518340)Time elapsed: 0.010 s
% 0.64/0.38 % (518340)Peak memory usage: 10 MB
% 0.64/0.38 % (518340)Instructions burned: 24 (million)
% 0.64/0.38 % (518341)Instruction limit reached!
% 0.64/0.38 % (518341)------------------------------
% 0.64/0.38 % (518341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.38 % (518341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.38 % (518341)CaDiCaL version: 2.1.3
% 0.64/0.38 % (518341)Termination reason: Instruction limit
% 0.64/0.38 % (518341)Termination phase: Preprocessing 3
% 0.64/0.38 % (518341)Time elapsed: 0.019 s
% 0.64/0.38 % (518341)Peak memory usage: 12 MB
% 0.64/0.38 % (518341)Instructions burned: 78 (million)
% 0.64/0.38 % (518350)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3269601625:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.38 % (518353)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2914427989:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.64/0.38 % (518350)Instruction limit reached!
% 0.64/0.41 % (518350)------------------------------
% 0.64/0.41 % (518350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (518350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (518350)CaDiCaL version: 2.1.3
% 0.64/0.41 % (518350)Termination reason: Instruction limit
% 0.64/0.41 % (518350)Termination phase: shuffling
% 0.64/0.41 % (518350)Time elapsed: 0.002 s
% 0.64/0.41 % (518350)Peak memory usage: 10 MB
% 0.64/0.41 % (518350)Instructions burned: 3 (million)
% 0.64/0.41 % (518353)Instruction limit reached!
% 0.64/0.41 % (518353)------------------------------
% 0.64/0.41 % (518353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (518353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (518353)CaDiCaL version: 2.1.3
% 0.64/0.41 % (518353)Termination reason: Instruction limit
% 0.64/0.41 % (518353)Termination phase: shuffling
% 0.64/0.41 % (518353)Time elapsed: 0.003 s
% 0.64/0.41 % (518353)Peak memory usage: 10 MB
% 0.64/0.41 % (518353)Instructions burned: 13 (million)
% 0.64/0.41 % (518352)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.41 % (518351)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2156562271:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.64/0.41 % (518352)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=490750838:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.64/0.41 % (518351)Instruction limit reached!
% 0.64/0.41 % (518351)------------------------------
% 0.64/0.41 % (518351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (518351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (518351)CaDiCaL version: 2.1.3
% 0.64/0.41 % (518351)Termination reason: Instruction limit
% 0.64/0.41 % (518351)Termination phase: shuffling
% 0.64/0.41 % (518351)Time elapsed: 0.003 s
% 0.64/0.41 % (518351)Peak memory usage: 9 MB
% 0.64/0.41 % (518351)Instructions burned: 7 (million)
% 0.64/0.41 % (518352)Instruction limit reached!
% 0.64/0.41 % (518352)------------------------------
% 0.64/0.41 % (518352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (518352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (518352)CaDiCaL version: 2.1.3
% 0.64/0.41 % (518352)Termination reason: Instruction limit
% 0.64/0.41 % (518352)Termination phase: shuffling
% 0.64/0.41 % (518352)Time elapsed: 0.003 s
% 0.64/0.41 % (518352)Peak memory usage: 10 MB
% 0.64/0.41 % (518352)Instructions burned: 7 (million)
% 0.64/0.41 % (518357)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=602518518:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.64/0.41 % (518336)Instruction limit reached!
% 0.64/0.41 % (518336)------------------------------
% 0.64/0.41 % (518336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.41 % (518336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.41 % (518336)CaDiCaL version: 2.1.3
% 0.64/0.41 % (518336)Termination reason: Instruction limit
% 0.64/0.41 % (518336)Termination phase: Preprocessing 3
% 0.64/0.41 % (518336)Time elapsed: 0.040 s
% 0.64/0.41 % (518336)Peak memory usage: 13 MB
% 0.64/0.41 % (518336)Instructions burned: 88 (million)
% 0.64/0.41 % (518356)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
% 0.64/0.41 % (518356)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.64/0.41 % (518356)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=179770166:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.64/0.41 % (518361)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.64/0.41 % (518360)lrs+10_1_si=on:cs=on:random_seed=2708195422:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.64/0.44 % (518361)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=50241908:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.64/0.44 % (518361)Instruction limit reached!
% 0.64/0.44 % (518361)------------------------------
% 0.64/0.44 % (518361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (518361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (518361)CaDiCaL version: 2.1.3
% 0.64/0.44 % (518361)Termination reason: Instruction limit
% 0.64/0.44 % (518361)Termination phase: shuffling
% 0.64/0.44 % (518361)Time elapsed: 0.001 s
% 0.64/0.44 % (518361)Peak memory usage: 10 MB
% 0.64/0.44 % (518361)Instructions burned: 2 (million)
% 0.64/0.44 % (518360)Instruction limit reached!
% 0.64/0.44 % (518360)------------------------------
% 0.64/0.44 % (518360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (518360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (518360)CaDiCaL version: 2.1.3
% 0.64/0.44 % (518360)Termination reason: Instruction limit
% 0.64/0.44 % (518360)Termination phase: shuffling
% 0.64/0.44 % (518360)Time elapsed: 0.004 s
% 0.64/0.44 % (518360)Peak memory usage: 10 MB
% 0.64/0.44 % (518360)Instructions burned: 9 (million)
% 0.64/0.44 % (518357)Instruction limit reached!
% 0.64/0.44 % (518357)------------------------------
% 0.64/0.44 % (518357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (518357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (518357)CaDiCaL version: 2.1.3
% 0.64/0.44 % (518357)Termination reason: Instruction limit
% 0.64/0.44 % (518357)Termination phase: Saturation
% 0.64/0.44 % (518357)Time elapsed: 0.019 s
% 0.64/0.44 % (518357)Peak memory usage: 12 MB
% 0.64/0.44 % (518357)Instructions burned: 87 (million)
% 0.64/0.44 % (518363)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3588353293:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.64/0.44 % (518356)Instruction limit reached!
% 0.64/0.44 % (518356)------------------------------
% 0.64/0.44 % (518356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.45 % (518356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.45 % (518356)CaDiCaL version: 2.1.3
% 0.64/0.45 % (518356)Termination reason: Instruction limit
% 0.64/0.45 % (518356)Termination phase: shuffling
% 0.64/0.45 % (518356)Time elapsed: 0.014 s
% 0.64/0.45 % (518356)Peak memory usage: 10 MB
% 0.64/0.45 % (518356)Instructions burned: 30 (million)
% 0.64/0.45 % (518369)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2159138333:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.64/0.45 % (518342)Instruction limit reached!
% 0.64/0.45 % (518342)------------------------------
% 0.64/0.45 % (518342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.45 % (518342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.45 % (518342)CaDiCaL version: 2.1.3
% 0.64/0.45 % (518342)Termination reason: Instruction limit
% 0.64/0.45 % (518342)Termination phase: Property scanning
% 0.64/0.45 % (518342)Time elapsed: 0.069 s
% 0.64/0.45 % (518342)Peak memory usage: 13 MB
% 0.64/0.45 % (518342)Instructions burned: 158 (million)
% 0.64/0.45 % (518369)Instruction limit reached!
% 0.64/0.45 % (518369)------------------------------
% 0.64/0.45 % (518369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.45 % (518369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.45 % (518369)CaDiCaL version: 2.1.3
% 0.64/0.45 % (518369)Termination reason: Instruction limit
% 0.64/0.45 % (518369)Termination phase: shuffling
% 0.64/0.45 % (518369)Time elapsed: 0.004 s
% 0.64/0.45 % (518369)Peak memory usage: 10 MB
% 0.64/0.45 % (518369)Instructions burned: 17 (million)
% 0.64/0.45 % (518367)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3162145231:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.64/0.45 % (518368)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=566627192:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.64/0.45 % (518363)Instruction limit reached!
% 0.64/0.45 % (518363)------------------------------
% 1.38/0.51 % (518363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518363)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518363)Termination reason: Instruction limit
% 1.38/0.51 % (518363)Termination phase: Saturation
% 1.38/0.51 % (518363)Time elapsed: 0.018 s
% 1.38/0.51 % (518363)Peak memory usage: 12 MB
% 1.38/0.51 % (518363)Instructions burned: 39 (million)
% 1.38/0.51 % (518371)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1809828518:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.38/0.51 % (518374)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1983297287: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)
% 1.38/0.51 % (518374)Instruction limit reached!
% 1.38/0.51 % (518374)------------------------------
% 1.38/0.51 % (518374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518374)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518374)Termination reason: Instruction limit
% 1.38/0.51 % (518374)Termination phase: shuffling
% 1.38/0.51 % (518374)Time elapsed: 0.001 s
% 1.38/0.51 % (518374)Peak memory usage: 10 MB
% 1.38/0.51 % (518374)Instructions burned: 4 (million)
% 1.38/0.51 % (518368)Instruction limit reached!
% 1.38/0.51 % (518368)------------------------------
% 1.38/0.51 % (518368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518368)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518368)Termination reason: Instruction limit
% 1.38/0.51 % (518368)Termination phase: Property scanning
% 1.38/0.51 % (518368)Time elapsed: 0.012 s
% 1.38/0.51 % (518368)Peak memory usage: 10 MB
% 1.38/0.51 % (518368)Instructions burned: 27 (million)
% 1.38/0.51 % (518373)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3928581053:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.38/0.51 % (518380)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2311493719:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.38/0.51 % (518373)Instruction limit reached!
% 1.38/0.51 % (518373)------------------------------
% 1.38/0.51 % (518373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518373)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518373)Termination reason: Instruction limit
% 1.38/0.51 % (518373)Termination phase: shuffling
% 1.38/0.51 % (518373)Time elapsed: 0.007 s
% 1.38/0.51 % (518373)Peak memory usage: 10 MB
% 1.38/0.51 % (518373)Instructions burned: 16 (million)
% 1.38/0.51 % (518377)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2968307784:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.38/0.51 % (518380)Instruction limit reached!
% 1.38/0.51 % (518380)------------------------------
% 1.38/0.51 % (518380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518380)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518380)Termination reason: Instruction limit
% 1.38/0.51 % (518380)Termination phase: shuffling
% 1.38/0.51 % (518380)Time elapsed: 0.005 s
% 1.38/0.51 % (518380)Peak memory usage: 10 MB
% 1.38/0.51 % (518380)Instructions burned: 24 (million)
% 1.38/0.51 % (518382)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3808655706:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.38/0.51 % (518386)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.38/0.51 % (518377)Instruction limit reached!
% 1.38/0.51 % (518377)------------------------------
% 1.38/0.51 % (518377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.51 % (518377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.51 % (518377)CaDiCaL version: 2.1.3
% 1.38/0.51 % (518377)Termination reason: Instruction limit
% 1.38/0.51 % (518377)Termination phase: shuffling
% 1.38/0.51 % (518377)Time elapsed: 0.012 s
% 1.38/0.51 % (518377)Peak memory usage: 10 MB
% 1.38/0.55 % (518377)Instructions burned: 27 (million)
% 1.38/0.55 % (518384)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
% 1.38/0.55 % (518384)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.38/0.55 % (518386)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=1857079266:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.38/0.55 % (518386)Instruction limit reached!
% 1.38/0.55 % (518386)------------------------------
% 1.38/0.55 % (518386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518386)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518386)Termination reason: Instruction limit
% 1.38/0.55 % (518386)Termination phase: shuffling
% 1.38/0.55 % (518386)Time elapsed: 0.002 s
% 1.38/0.55 % (518386)Peak memory usage: 10 MB
% 1.38/0.55 % (518386)Instructions burned: 8 (million)
% 1.38/0.55 % (518384)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=845706094:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.38/0.55 % (518384)Instruction limit reached!
% 1.38/0.55 % (518384)------------------------------
% 1.38/0.55 % (518384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518384)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518384)Termination reason: Instruction limit
% 1.38/0.55 % (518384)Termination phase: shuffling
% 1.38/0.55 % (518384)Time elapsed: 0.006 s
% 1.38/0.55 % (518384)Peak memory usage: 10 MB
% 1.38/0.55 % (518384)Instructions burned: 14 (million)
% 1.38/0.55 % (518390)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1443715436:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.38/0.55 % (518388)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=2975477:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.38/0.55 % (518390)Instruction limit reached!
% 1.38/0.55 % (518390)------------------------------
% 1.38/0.55 % (518390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518390)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518390)Termination reason: Instruction limit
% 1.38/0.55 % (518390)Termination phase: shuffling
% 1.38/0.55 % (518390)Time elapsed: 0.004 s
% 1.38/0.55 % (518390)Peak memory usage: 10 MB
% 1.38/0.55 % (518390)Instructions burned: 21 (million)
% 1.38/0.55 % (518382)Instruction limit reached!
% 1.38/0.55 % (518382)------------------------------
% 1.38/0.55 % (518382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518382)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518382)Termination reason: Instruction limit
% 1.38/0.55 % (518382)Termination phase: Preprocessing 3
% 1.38/0.55 % (518382)Time elapsed: 0.027 s
% 1.38/0.55 % (518382)Peak memory usage: 11 MB
% 1.38/0.55 % (518382)Instructions burned: 61 (million)
% 1.38/0.55 % (518395)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3666896756:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.38/0.55 % (518392)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3039087397:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.38/0.55 % (518388)Instruction limit reached!
% 1.38/0.55 % (518388)------------------------------
% 1.38/0.55 % (518388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518388)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518388)Termination reason: Instruction limit
% 1.38/0.55 % (518388)Termination phase: Property scanning
% 1.38/0.55 % (518388)Time elapsed: 0.013 s
% 1.38/0.55 % (518388)Peak memory usage: 10 MB
% 1.38/0.55 % (518388)Instructions burned: 31 (million)
% 1.38/0.55 % (518395)Instruction limit reached!
% 1.38/0.55 % (518395)------------------------------
% 1.38/0.55 % (518395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518395)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518395)Termination reason: Instruction limit
% 1.38/0.55 % (518395)Termination phase: shuffling
% 1.38/0.55 % (518395)Time elapsed: 0.005 s
% 1.38/0.55 % (518395)Peak memory usage: 10 MB
% 1.38/0.55 % (518395)Instructions burned: 20 (million)
% 1.38/0.55 % (518392)Instruction limit reached!
% 1.38/0.55 % (518392)------------------------------
% 1.38/0.55 % (518392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518392)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518392)Termination reason: Instruction limit
% 1.38/0.55 % (518392)Termination phase: shuffling
% 1.38/0.55 % (518392)Time elapsed: 0.010 s
% 1.38/0.55 % (518392)Peak memory usage: 10 MB
% 1.38/0.55 % (518392)Instructions burned: 24 (million)
% 1.38/0.55 % (518396)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3124502892:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.38/0.55 % (518400)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=350632218:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.38/0.55 % (518399)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2802617210:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.38/0.55 % (518401)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1424602972:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.38/0.55 % (518339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-518331-518339"...
% 1.38/0.55 % (518367)Instruction limit reached!
% 1.38/0.55 % (518367)------------------------------
% 1.38/0.55 % (518367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518367)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518367)Termination reason: Instruction limit
% 1.38/0.55 % (518367)Termination phase: Saturation
% 1.38/0.55 % (518367)Time elapsed: 0.110 s
% 1.38/0.55 % (518367)Peak memory usage: 15 MB
% 1.38/0.55 % (518367)Instructions burned: 249 (million)
% 1.38/0.55 % (518401)Instruction limit reached!
% 1.38/0.55 % (518401)------------------------------
% 1.38/0.55 % (518401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518401)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518401)Termination reason: Instruction limit
% 1.38/0.55 % (518401)Termination phase: Naming
% 1.38/0.55 % (518401)Time elapsed: 0.019 s
% 1.38/0.55 % (518401)Peak memory usage: 11 MB
% 1.38/0.55 % (518401)Instructions burned: 44 (million)
% 1.38/0.55 % (518400)Instruction limit reached!
% 1.38/0.55 % (518400)------------------------------
% 1.38/0.55 % (518400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518400)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518400)Termination reason: Instruction limit
% 1.38/0.55 % (518400)Termination phase: Property scanning
% 1.38/0.55 % (518400)Time elapsed: 0.044 s
% 1.38/0.55 % (518400)Peak memory usage: 13 MB
% 1.38/0.55 % (518400)Instructions burned: 194 (million)
% 1.38/0.55 % (518406)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.38/0.55 % (518406)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3030051918:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.38/0.55 % (518407)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2840380224:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.38/0.55 % (518406)Instruction limit reached!
% 1.38/0.55 % (518406)------------------------------
% 1.38/0.55 % (518406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518406)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518406)Termination reason: Instruction limit
% 1.38/0.55 % (518406)Termination phase: shuffling
% 1.38/0.55 % (518406)Time elapsed: 0.004 s
% 1.38/0.55 % (518406)Peak memory usage: 10 MB
% 1.38/0.55 % (518406)Instructions burned: 9 (million)
% 1.38/0.55 % (518408)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=2652497012: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)
% 1.38/0.55 % (518371) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-518331-518371"...
% 1.38/0.55 % (518411)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.38/0.55 % (518399)Instruction limit reached!
% 1.38/0.55 % (518399)------------------------------
% 1.38/0.55 % (518399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518399)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518399)Termination reason: Instruction limit
% 1.38/0.55 % (518399)Termination phase: Property scanning
% 1.38/0.55 % (518399)Time elapsed: 0.062 s
% 1.38/0.55 % (518399)Peak memory usage: 13 MB
% 1.38/0.55 % (518399)Instructions burned: 144 (million)
% 1.38/0.55 % (518411)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3398537959:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.38/0.55 % (518411)Instruction limit reached!
% 1.38/0.55 % (518411)------------------------------
% 1.38/0.55 % (518411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.55 % (518411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.55 % (518411)CaDiCaL version: 2.1.3
% 1.38/0.55 % (518411)Termination reason: Instruction limit
% 1.38/0.55 % (518411)Termination phase: shuffling
% 1.38/0.55 % (518411)Time elapsed: 0.003 s
% 1.38/0.55 % (518411)Peak memory usage: 10 MB
% 1.38/0.55 % (518411)Instructions burned: 6 (million)
% 1.38/0.55 % (518339)...printing done.
% 1.38/0.55 % (518413)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3393536629:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.38/0.55 % (518339)Refutation found. Thanks to Tanya!
% 1.38/0.55 % SZS status Theorem for theBenchmark
% 1.38/0.55 % SZS output start Proof for theBenchmark
% 1.38/0.55 thf(type_def_5, type, term: $tType).
% 1.38/0.55 thf(type_def_6, type, subst: $tType).
% 1.38/0.55 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 1.38/0.55 thf(type_def_8, type, d_term: $tType).
% 1.38/0.55 thf(type_def_9, type, d_subst: $tType).
% 1.38/0.55 thf(func_def_0, type, one: term).
% 1.38/0.55 thf(func_def_1, type, ap: (term > term > term)).
% 1.38/0.55 thf(func_def_2, type, lam: (term > term)).
% 1.38/0.55 thf(func_def_3, type, sub: (term > subst > term)).
% 1.38/0.55 thf(func_def_4, type, id: subst).
% 1.38/0.55 thf(func_def_5, type, sh: subst).
% 1.38/0.55 thf(func_def_6, type, push: (term > subst > subst)).
% 1.38/0.55 thf(func_def_7, type, comp: (subst > subst > subst)).
% 1.38/0.55 thf(func_def_8, type, var: (term > $o)).
% 1.38/0.55 thf(func_def_9, type, pushprop_lem1v2: $o).
% 1.38/0.55 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 1.38/0.55 thf(func_def_11, type, axmap: $o).
% 1.38/0.55 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 1.38/0.55 thf(func_def_13, type, shinj: $o).
% 1.38/0.55 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 1.38/0.55 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 1.38/0.55 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 1.38/0.55 thf(func_def_17, type, induction2lem: $o).
% 1.38/0.55 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 1.38/0.55 thf(func_def_19, type, axvarshift: $o).
% 1.38/0.55 thf(func_def_20, type, hoasapinj2: $o).
% 1.38/0.55 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 1.38/0.55 thf(func_def_22, type, hoasapinj1: $o).
% 1.38/0.55 thf(func_def_23, type, ulamvar1: $o).
% 1.38/0.55 thf(func_def_24, type, induction2lem_lthm: $o).
% 1.38/0.55 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 1.38/0.55 thf(func_def_26, type, apnotvar: $o).
% 1.38/0.55 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 1.38/0.55 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 1.38/0.55 thf(func_def_29, type, hoasinduction_lthm: $o).
% 1.38/0.55 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 1.38/0.55 thf(func_def_31, type, hoaslaminj: $o).
% 1.38/0.55 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 1.38/0.55 thf(func_def_33, type, induction2lem_gthm: $o).
% 1.38/0.55 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 1.38/0.55 thf(func_def_35, type, hoasinduction_lem3: $o).
% 1.38/0.55 thf(func_def_36, type, hoasinduction_lem2: $o).
% 1.38/0.55 thf(func_def_37, type, termmset_lthm: $o).
% 1.38/0.55 thf(func_def_38, type, hoasinduction_lem1: $o).
% 1.38/0.55 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 1.38/0.55 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 1.38/0.55 thf(func_def_41, type, hoasapnotvar: $o).
% 1.38/0.55 thf(func_def_42, type, hoasinduction_lem0: $o).
% 1.38/0.55 thf(func_def_43, type, hoasinduction: $o).
% 1.38/0.55 thf(func_def_44, type, hoasinduction_gthm: $o).
% 1.38/0.55 thf(func_def_45, type, axapp: $o).
% 1.38/0.55 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 1.38/0.55 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 1.38/0.55 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 1.38/0.55 thf(func_def_49, type, ulamvarind: $o).
% 1.38/0.55 thf(func_def_50, type, induction: $o).
% 1.38/0.55 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 1.38/0.55 thf(func_def_52, type, termmset_gthm: $o).
% 1.38/0.55 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 1.38/0.55 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 1.38/0.55 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 1.38/0.55 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 1.38/0.55 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 1.38/0.55 thf(func_def_58, type, pushprop_lem2v2: $o).
% 1.38/0.55 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 1.38/0.55 thf(func_def_60, type, axclos: $o).
% 1.38/0.55 thf(func_def_61, type, axassoc: $o).
% 1.38/0.55 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 1.38/0.55 thf(func_def_63, type, pushprop_lthm: $o).
% 1.38/0.55 thf(func_def_64, type, apinj2: $o).
% 1.38/0.55 thf(func_def_65, type, apinj1: $o).
% 1.38/0.55 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 1.38/0.55 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 1.38/0.55 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 1.38/0.55 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 1.38/0.55 thf(func_def_70, type, axvarcons: $o).
% 1.38/0.55 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 1.38/0.55 thf(func_def_72, type, axscons: $o).
% 1.38/0.55 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 1.38/0.55 thf(func_def_74, type, axidr: $o).
% 1.38/0.55 thf(func_def_75, type, pushprop_lem1: $o).
% 1.38/0.55 thf(func_def_76, type, laminj: $o).
% 1.38/0.55 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 1.38/0.55 thf(func_def_78, type, pushprop_lem0: $o).
% 1.38/0.55 thf(func_def_79, type, pushprop_gthm: $o).
% 1.38/0.55 thf(func_def_80, type, axabs: $o).
% 1.38/0.55 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 1.38/0.55 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 1.38/0.55 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 1.38/0.55 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 1.38/0.55 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 1.38/0.55 thf(func_def_86, type, lamnotap: $o).
% 1.38/0.55 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 1.38/0.55 thf(func_def_88, type, hoaslamnotvar: $o).
% 1.38/0.55 thf(func_def_89, type, axidl: $o).
% 1.38/0.55 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 1.38/0.55 thf(func_def_91, type, induction2_lthm: $o).
% 1.38/0.55 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 1.38/0.55 thf(func_def_93, type, substmonoid_lthm: $o).
% 1.38/0.55 thf(func_def_94, type, pushprop: $o).
% 1.38/0.55 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 1.38/0.55 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 1.38/0.55 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 1.38/0.55 thf(func_def_98, type, substmonoid: $o).
% 1.38/0.55 thf(func_def_99, type, lamnotvar: $o).
% 1.38/0.55 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 1.38/0.55 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 1.38/0.55 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 1.38/0.55 thf(func_def_103, type, induction2_gthm: $o).
% 1.38/0.55 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 1.38/0.55 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_106, type, hoaslamnotap: $o).
% 1.38/0.55 thf(func_def_107, type, substmonoid_gthm: $o).
% 1.38/0.55 thf(func_def_108, type, ulamvarsh: $o).
% 1.38/0.55 thf(func_def_109, type, induction2: $o).
% 1.38/0.55 thf(func_def_110, type, pushprop_lem3v2: $o).
% 1.38/0.55 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 1.38/0.55 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 1.38/0.55 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 1.38/0.55 thf(func_def_114, type, axshiftcons: $o).
% 1.38/0.55 thf(func_def_115, type, termmset: $o).
% 1.38/0.55 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 1.38/0.55 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 1.38/0.55 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 1.38/0.55 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 1.38/0.55 thf(func_def_120, type, axvarid: $o).
% 1.38/0.55 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 1.38/0.55 thf(func_def_122, type, d2term: (d_term > term)).
% 1.38/0.55 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 1.38/0.55 thf(func_def_124, type, d_one: d_term).
% 1.38/0.55 thf(func_def_125, type, d_id: d_subst).
% 1.38/0.55 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.38/0.55 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 1.38/0.55 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 1.38/0.55 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 1.38/0.55 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.38/0.55 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.38/0.55 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 1.38/0.55 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 1.38/0.55 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_138, type, sP1: $o).
% 1.38/0.55 thf(func_def_139, type, sP2: $o).
% 1.38/0.55 thf(func_def_140, type, sP3: $o).
% 1.38/0.55 thf(func_def_141, type, sP4: $o).
% 1.38/0.55 thf(func_def_142, type, sP5: $o).
% 1.38/0.55 thf(func_def_143, type, sP6: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_144, type, sP7: $o).
% 1.38/0.55 thf(func_def_145, type, sP8: $o).
% 1.38/0.55 thf(func_def_146, type, sP9: $o).
% 1.38/0.55 thf(func_def_147, type, sP10: $o).
% 1.38/0.55 thf(func_def_148, type, sP11: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_149, type, sP12: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_150, type, sP13: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_151, type, sP14: $o).
% 1.38/0.55 thf(func_def_152, type, sP15: $o).
% 1.38/0.55 thf(func_def_153, type, sP16: $o).
% 1.38/0.55 thf(func_def_154, type, sP17: $o).
% 1.38/0.55 thf(func_def_155, type, sP18: $o).
% 1.38/0.55 thf(func_def_156, type, sP19: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_157, type, sP20: $o).
% 1.38/0.55 thf(func_def_158, type, sP21: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_159, type, sP22: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_160, type, sP23: $o).
% 1.38/0.55 thf(func_def_161, type, sP24: $o).
% 1.38/0.55 thf(func_def_162, type, sP25: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_163, type, sP26: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_164, type, sP27: ((subst > term > subst > $o) > $o)).
% 1.38/0.55 thf(func_def_165, type, sK28: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_166, type, sK29: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_167, type, sK30: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_168, type, sK31: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_169, type, sK32: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_170, type, sK33: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_171, type, sK34: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_172, type, sK35: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_173, type, sK36: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_174, type, sK37: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_175, type, sK38: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_176, type, sK39: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_177, type, sK40: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_178, type, sK41: term).
% 1.38/0.55 thf(func_def_179, type, sK42: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_180, type, sK43: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_181, type, sK44: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_182, type, sK45: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_183, type, sK46: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_184, type, sK47: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_185, type, sK48: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_186, type, sK49: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_187, type, sK50: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_188, type, sK51: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_189, type, sK52: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_190, type, sK53: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_191, type, sK54: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_192, type, sK55: (term > $o)).
% 1.38/0.55 thf(func_def_193, type, sK56: term).
% 1.38/0.55 thf(func_def_194, type, sK57: (term > term)).
% 1.38/0.55 thf(func_def_195, type, sK58: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_196, type, sK59: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_197, type, sK60: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_198, type, sK61: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_199, type, sK62: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_200, type, sK63: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_202, type, sK65: term).
% 1.38/0.55 thf(func_def_203, type, sK66: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_204, type, sK67: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_205, type, sK68: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_206, type, sK69: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_207, type, sK70: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_208, type, sK71: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_209, type, sK72: ((subst > term > subst > $o) > term > term)).
% 1.38/0.55 thf(func_def_210, type, sK73: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_211, type, sK74: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_212, type, sK75: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_213, type, sK76: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_214, type, sK77: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_215, type, sK78: term).
% 1.38/0.55 thf(func_def_216, type, sK79: (term > $o)).
% 1.38/0.55 thf(func_def_217, type, sK80: subst).
% 1.38/0.55 thf(func_def_218, type, sK81: (term > term)).
% 1.38/0.55 thf(func_def_219, type, sK82: subst).
% 1.38/0.55 thf(func_def_220, type, sK83: term).
% 1.38/0.55 thf(func_def_221, type, sK84: term).
% 1.38/0.55 thf(func_def_222, type, sK85: subst).
% 1.38/0.55 thf(func_def_223, type, sK86: (subst > (term > $o) > term)).
% 1.38/0.55 thf(func_def_224, type, sK87: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_225, type, sK88: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_226, type, sK89: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_227, type, sK90: subst).
% 1.38/0.55 thf(func_def_228, type, sK91: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_229, type, sK92: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_230, type, sK93: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_231, type, sK94: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_232, type, sK95: term).
% 1.38/0.55 thf(func_def_233, type, sK96: (term > $o)).
% 1.38/0.55 thf(func_def_234, type, sK97: term).
% 1.38/0.55 thf(func_def_235, type, sK98: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_236, type, sK99: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_237, type, sK100: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_238, type, sK101: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_239, type, sK102: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_240, type, sK103: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_241, type, sK104: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_242, type, sK105: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_243, type, sK106: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_244, type, sK107: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_245, type, sK108: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_246, type, sK109: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_247, type, sK110: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_248, type, sK111: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_249, type, sK112: term).
% 1.38/0.55 thf(func_def_250, type, sK113: (term > $o)).
% 1.38/0.55 thf(func_def_251, type, sK114: (term > term)).
% 1.38/0.55 thf(func_def_252, type, sK115: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_253, type, sK116: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_256, type, sK119: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_259, type, sK122: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_260, type, sK123: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_261, type, sK124: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_262, type, sK125: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_263, type, sK126: term).
% 1.38/0.55 thf(func_def_264, type, sK127: term).
% 1.38/0.55 thf(func_def_265, type, sK128: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_266, type, sK129: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_267, type, sK130: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_268, type, sK131: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_269, type, sK132: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_270, type, sK133: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_271, type, sK134: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_272, type, sK135: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_273, type, sK136: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_274, type, sK137: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_275, type, sK138: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_276, type, sK139: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_277, type, sK140: subst).
% 1.38/0.55 thf(func_def_278, type, sK141: term).
% 1.38/0.55 thf(func_def_279, type, sK142: (term > $o)).
% 1.38/0.55 thf(func_def_280, type, sK143: (term > term)).
% 1.38/0.55 thf(func_def_281, type, sK144: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_282, type, sK145: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_283, type, sK146: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_284, type, sK147: ((term > $o) > subst > term)).
% 1.38/0.55 thf(func_def_285, type, sK148: term).
% 1.38/0.55 thf(func_def_286, type, sK149: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_287, type, sK150: term).
% 1.38/0.55 thf(func_def_288, type, sK151: (term > $o)).
% 1.38/0.55 thf(func_def_289, type, sK152: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_290, type, sK153: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_291, type, sK154: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_292, type, sK155: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_293, type, sK156: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_294, type, sK157: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_295, type, sK158: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_296, type, sK159: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_297, type, sK160: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_298, type, sK161: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_299, type, sK162: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_300, type, sK163: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_301, type, sK164: term).
% 1.38/0.55 thf(func_def_302, type, sK165: term).
% 1.38/0.55 thf(func_def_303, type, sK166: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_304, type, sK167: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_305, type, sK168: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_306, type, sK169: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_307, type, sK170: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_308, type, sK171: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_309, type, sK172: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_310, type, sK173: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_311, type, sK174: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_312, type, sK175: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_313, type, sK176: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_314, type, sK177: term).
% 1.38/0.55 thf(func_def_315, type, sK178: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_318, type, sK181: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_319, type, sK182: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_320, type, sK183: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_321, type, sK184: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_322, type, sK185: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_323, type, sK186: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_324, type, sK187: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_325, type, sK188: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_326, type, sK189: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_327, type, sK190: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_328, type, sK191: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_329, type, sK192: (term > $o)).
% 1.38/0.55 thf(func_def_330, type, sK193: term).
% 1.38/0.55 thf(func_def_331, type, sK194: (term > term)).
% 1.38/0.55 thf(func_def_332, type, sK195: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_333, type, sK196: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_334, type, sK197: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_335, type, sK198: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_336, type, sK199: term).
% 1.38/0.55 thf(func_def_337, type, sK200: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_338, type, sK201: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_339, type, sK202: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_340, type, sK203: ((term > $o) > subst > term)).
% 1.38/0.55 thf(func_def_341, type, sK204: subst).
% 1.38/0.55 thf(func_def_342, type, sK205: term).
% 1.38/0.55 thf(func_def_343, type, sK206: (term > $o)).
% 1.38/0.55 thf(func_def_344, type, sK207: (term > term)).
% 1.38/0.55 thf(func_def_345, type, sK208: term).
% 1.38/0.55 thf(func_def_346, type, sK209: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_347, type, sK210: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_348, type, sK211: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_349, type, sK212: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_350, type, sK213: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_351, type, sK214: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_352, type, sK215: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_353, type, sK216: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_354, type, sK217: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_355, type, sK218: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_356, type, sK219: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_357, type, sK220: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_358, type, sK221: (term > $o)).
% 1.38/0.55 thf(func_def_359, type, sK222: term).
% 1.38/0.55 thf(func_def_360, type, sK223: (term > term)).
% 1.38/0.55 thf(func_def_361, type, sK224: term).
% 1.38/0.55 thf(func_def_362, type, sK225: (term > $o)).
% 1.38/0.55 thf(func_def_363, type, sK226: (term > term)).
% 1.38/0.55 thf(func_def_364, type, sK227: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_365, type, sK228: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_366, type, sK229: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_367, type, sK230: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_368, type, sK231: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_369, type, sK232: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_370, type, sK233: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_371, type, sK234: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_372, type, sK235: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_373, type, sK236: subst).
% 1.38/0.55 thf(func_def_374, type, sK237: term).
% 1.38/0.55 thf(func_def_375, type, sK238: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_376, type, sK239: (term > $o)).
% 1.38/0.55 thf(func_def_377, type, sK240: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_378, type, sK241: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_379, type, sK242: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_380, type, sK243: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_381, type, sK244: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_382, type, sK245: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_383, type, sK246: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_384, type, sK247: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_385, type, sK248: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_386, type, sK249: ((term > $o) > term > term)).
% 1.38/0.55 thf(func_def_387, type, sK250: term).
% 1.38/0.55 thf(func_def_388, type, sK251: term).
% 1.38/0.55 thf(func_def_389, type, sK252: term).
% 1.38/0.55 thf(func_def_390, type, sK253: term).
% 1.38/0.55 thf(func_def_391, type, sK254: term).
% 1.38/0.55 thf(func_def_392, type, sK255: term).
% 1.38/0.55 thf(func_def_393, type, sK256: term).
% 1.38/0.55 thf(func_def_394, type, sK257: term).
% 1.38/0.55 thf(func_def_395, type, sK258: term).
% 1.38/0.55 thf(func_def_396, type, sK259: term).
% 1.38/0.55 thf(func_def_397, type, sK260: term).
% 1.38/0.55 thf(func_def_398, type, sK261: subst).
% 1.38/0.55 thf(func_def_399, type, sK262: (subst > term > term)).
% 1.38/0.55 thf(func_def_400, type, sK263: (subst > term > term)).
% 1.38/0.55 thf(func_def_401, type, sK264: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_402, type, sK265: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_403, type, sK266: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_404, type, sK267: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_405, type, sK268: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_406, type, sK269: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_407, type, sK270: subst).
% 1.38/0.55 thf(func_def_408, type, sK271: (subst > d_subst)).
% 1.38/0.55 thf(func_def_409, type, sK272: term).
% 1.38/0.55 thf(func_def_410, type, sK273: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_413, type, sK276: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_414, type, sK277: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_415, type, sK278: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_416, type, sK279: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_417, type, sK280: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_418, type, sK281: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_419, type, sK282: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_420, type, sK283: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_421, type, sK284: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_422, type, sK285: (term > $o)).
% 1.38/0.55 thf(func_def_423, type, sK286: term).
% 1.38/0.55 thf(func_def_424, type, sK287: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_425, type, sK288: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_426, type, sK289: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_427, type, sK290: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_428, type, sK291: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_429, type, sK292: term).
% 1.38/0.55 thf(func_def_430, type, sK293: ((subst > term > subst > $o) > term > $o)).
% 1.38/0.55 thf(func_def_431, type, sK294: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_432, type, sK295: (term > (term > $o) > term)).
% 1.38/0.55 thf(func_def_433, type, sK296: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.38/0.55 thf(func_def_434, type, sK297: subst).
% 1.38/0.55 thf(func_def_435, type, sK298: (term > $o)).
% 1.38/0.55 thf(func_def_436, type, sK299: term).
% 1.38/0.55 thf(func_def_437, type, sK300: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_438, type, sK301: (term > (term > $o) > subst > term > $o)).
% 1.38/0.55 thf(func_def_439, type, sK302: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_440, type, sK303: term).
% 1.38/0.55 thf(func_def_441, type, sK304: (term > (subst > term > term) > term)).
% 1.38/0.55 thf(func_def_442, type, sK305: (term > (subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_443, type, sK306: (term > (subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_444, type, sK307: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_445, type, sK308: (term > (subst > term > term) > term)).
% 1.38/0.55 thf(func_def_446, type, sK309: (term > (subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_447, type, sK310: (term > (subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_448, type, sK311: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_449, type, sK312: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_450, type, sK313: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_451, type, sK314: term).
% 1.38/0.55 thf(func_def_452, type, sK315: term).
% 1.38/0.55 thf(func_def_453, type, sK316: term).
% 1.38/0.55 thf(func_def_454, type, sK317: term).
% 1.38/0.55 thf(func_def_455, type, sK318: term).
% 1.38/0.55 thf(func_def_456, type, sK319: term).
% 1.38/0.55 thf(func_def_457, type, sK320: term).
% 1.38/0.55 thf(func_def_458, type, sK321: term).
% 1.38/0.55 thf(func_def_459, type, sK322: term).
% 1.38/0.55 thf(func_def_460, type, sK323: term).
% 1.38/0.55 thf(func_def_461, type, sK324: term).
% 1.38/0.55 thf(func_def_462, type, sK325: term).
% 1.38/0.55 thf(func_def_463, type, sK326: term).
% 1.38/0.55 thf(func_def_464, type, sK327: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_465, type, sK328: term).
% 1.38/0.55 thf(func_def_466, type, sK329: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_467, type, sK330: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_468, type, sK331: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_469, type, sK332: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_470, type, sK333: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_471, type, sK334: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_472, type, sK335: (term > subst > term > term)).
% 1.38/0.55 thf(func_def_473, type, sK336: term).
% 1.38/0.55 thf(func_def_474, type, sK337: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_475, type, sK338: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_476, type, sK339: subst).
% 1.38/0.55 thf(func_def_477, type, sK340: term).
% 1.38/0.55 thf(func_def_478, type, sK341: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_479, type, sK342: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_480, type, sK343: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_481, type, sK344: term).
% 1.38/0.55 thf(func_def_482, type, sK345: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_483, type, sK346: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_484, type, sK347: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_485, type, sK348: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_486, type, sK349: term).
% 1.38/0.55 thf(func_def_487, type, sK350: term).
% 1.38/0.55 thf(func_def_488, type, sK351: term).
% 1.38/0.55 thf(func_def_489, type, sK352: term).
% 1.38/0.55 thf(func_def_490, type, sK353: term).
% 1.38/0.55 thf(func_def_491, type, sK354: (term > $o)).
% 1.38/0.55 thf(func_def_492, type, sK355: (term > $o)).
% 1.38/0.55 thf(func_def_493, type, sK356: subst).
% 1.38/0.55 thf(func_def_494, type, sK357: term).
% 1.38/0.55 thf(func_def_495, type, sK358: subst).
% 1.38/0.55 thf(func_def_496, type, sK359: term).
% 1.38/0.55 thf(func_def_497, type, sK360: subst).
% 1.38/0.55 thf(func_def_498, type, sK361: term).
% 1.38/0.55 thf(func_def_499, type, sK362: term).
% 1.38/0.55 thf(func_def_500, type, sK363: (term > $o)).
% 1.38/0.55 thf(func_def_501, type, sK364: subst).
% 1.38/0.55 thf(func_def_502, type, sK365: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_503, type, sK366: (subst > (term > $o) > term > term > $o)).
% 1.38/0.55 thf(func_def_504, type, sK367: (term > d_term)).
% 1.38/0.55 thf(func_def_505, type, sK368: term).
% 1.38/0.55 thf(func_def_506, type, sK369: term).
% 1.38/0.55 thf(func_def_507, type, sK370: term).
% 1.38/0.55 thf(func_def_508, type, sK371: term).
% 1.38/0.55 thf(func_def_509, type, sK372: term).
% 1.38/0.55 thf(func_def_510, type, sK373: term).
% 1.38/0.55 thf(func_def_511, type, sK374: term).
% 1.38/0.55 thf(func_def_512, type, sK375: term).
% 1.38/0.55 thf(func_def_513, type, sK376: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_514, type, sK377: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_515, type, sK378: ((subst > term > subst > $o) > term > $o)).
% 1.38/0.55 thf(func_def_516, type, sK379: ((term > $o) > term > term)).
% 1.38/0.55 thf(func_def_517, type, sK380: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_518, type, sK381: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.38/0.55 thf(func_def_519, type, sK382: term).
% 1.38/0.55 thf(func_def_520, type, sK383: (term > $o)).
% 1.38/0.55 thf(func_def_521, type, sK384: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_522, type, sK385: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_523, type, sK386: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_524, type, sK387: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_525, type, sK388: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_526, type, sK389: subst).
% 1.38/0.55 thf(func_def_527, type, sK390: (subst > term > term)).
% 1.38/0.55 thf(func_def_528, type, sK391: term).
% 1.38/0.55 thf(func_def_529, type, sK392: (subst > term > term)).
% 1.38/0.55 thf(func_def_530, type, sK393: term).
% 1.38/0.55 thf(func_def_531, type, sK394: term).
% 1.38/0.55 thf(func_def_532, type, sK395: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_533, type, sK396: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_534, type, sK397: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_535, type, sK398: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_536, type, sK399: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_537, type, sK400: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_538, type, sK401: term).
% 1.38/0.55 thf(func_def_539, type, sK402: subst).
% 1.38/0.55 thf(func_def_540, type, sK403: term).
% 1.38/0.55 thf(func_def_541, type, sK404: subst).
% 1.38/0.55 thf(func_def_542, type, sK405: term).
% 1.38/0.55 thf(func_def_543, type, sK406: term).
% 1.38/0.55 thf(func_def_544, type, sK407: (term > subst > term > term)).
% 1.38/0.55 thf(func_def_545, type, sK408: term).
% 1.38/0.55 thf(func_def_546, type, sK409: (term > subst > (term > $o) > (term > $o) > term)).
% 1.38/0.55 thf(func_def_547, type, sK410: term).
% 1.38/0.55 thf(func_def_548, type, sK411: subst).
% 1.38/0.55 thf(func_def_549, type, sK412: (term > $o)).
% 1.38/0.55 thf(func_def_550, type, sK413: (term > $o)).
% 1.38/0.55 thf(func_def_551, type, sK414: subst).
% 1.38/0.55 thf(func_def_552, type, sK415: term).
% 1.38/0.55 thf(func_def_553, type, sK416: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_554, type, sK417: term).
% 1.38/0.55 thf(func_def_555, type, sK418: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_556, type, sK419: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_557, type, sK420: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_558, type, sK421: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_559, type, sK422: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_560, type, sK423: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_561, type, sK424: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_562, type, sK425: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_563, type, sK426: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_564, type, sK427: subst).
% 1.38/0.55 thf(func_def_565, type, sK428: subst).
% 1.38/0.55 thf(func_def_566, type, sK429: subst).
% 1.38/0.55 thf(func_def_567, type, sK430: subst).
% 1.38/0.55 thf(func_def_568, type, sK431: (term > subst > term > term)).
% 1.38/0.55 thf(func_def_569, type, sK432: term).
% 1.38/0.55 thf(func_def_570, type, sK433: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_571, type, sK434: (term > $o)).
% 1.38/0.55 thf(func_def_572, type, sK435: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_573, type, sK436: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_574, type, sK437: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_575, type, sK438: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_576, type, sK439: term).
% 1.38/0.55 thf(func_def_577, type, sK440: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_578, type, sK441: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_579, type, sK442: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_580, type, sK443: ((term > $o) > term > term)).
% 1.38/0.55 thf(func_def_581, type, sK444: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_582, type, sK445: term).
% 1.38/0.55 thf(func_def_583, type, sK446: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_584, type, sK447: term).
% 1.38/0.55 thf(func_def_585, type, sK448: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_586, type, sK449: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_587, type, sK450: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_588, type, sK451: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_589, type, sK452: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_590, type, sK453: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_591, type, sK454: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_592, type, sK455: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_593, type, sK456: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_594, type, sK457: (term > $o)).
% 1.38/0.55 thf(func_def_595, type, sK458: subst).
% 1.38/0.55 thf(func_def_596, type, sK459: (term > $o)).
% 1.38/0.55 thf(func_def_597, type, sK460: term).
% 1.38/0.55 thf(func_def_598, type, sK461: term).
% 1.38/0.55 thf(func_def_599, type, sK462: subst).
% 1.38/0.55 thf(func_def_600, type, sK463: ((subst > term > subst > $o) > term > $o)).
% 1.38/0.55 thf(func_def_601, type, sK464: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_602, type, sK465: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_603, type, sK466: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_604, type, sK467: ((subst > term > subst > $o) > term > term)).
% 1.38/0.55 thf(func_def_605, type, sK468: term).
% 1.38/0.55 thf(func_def_606, type, sK469: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_607, type, sK470: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_608, type, sK471: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_609, type, sK472: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_610, type, sK473: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_611, type, sK474: term).
% 1.38/0.55 thf(func_def_612, type, sK475: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_613, type, sK476: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_614, type, sK477: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_615, type, sK478: term).
% 1.38/0.55 thf(func_def_616, type, sK479: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_617, type, sK480: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_618, type, sK481: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_619, type, sK482: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_620, type, sK483: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_621, type, sK484: (term > subst > term > term)).
% 1.38/0.55 thf(func_def_622, type, sK485: term).
% 1.38/0.55 thf(func_def_623, type, sK486: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_624, type, sK487: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_625, type, sK488: term).
% 1.38/0.55 thf(func_def_626, type, sK489: (subst > term > term)).
% 1.38/0.55 thf(func_def_627, type, sK490: term).
% 1.38/0.55 thf(func_def_628, type, sK491: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_629, type, sK492: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_630, type, sK493: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_631, type, sK494: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_632, type, sK495: term).
% 1.38/0.55 thf(func_def_633, type, sK496: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_634, type, sK497: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_635, type, sK498: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_636, type, sK499: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_637, type, sK500: (term > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_638, type, sK501: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_639, type, sK502: (term > subst > term > term)).
% 1.38/0.55 thf(func_def_640, type, sK503: term).
% 1.38/0.55 thf(func_def_641, type, sK504: ((subst > term > subst > $o) > term > term)).
% 1.38/0.55 thf(func_def_642, type, sK505: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_643, type, sK506: term).
% 1.38/0.55 thf(func_def_644, type, sK507: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_645, type, sK508: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_646, type, sK509: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_647, type, sK510: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_648, type, sK511: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_649, type, sK512: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_650, type, sK513: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_651, type, sK514: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_652, type, sK515: (term > $o)).
% 1.38/0.55 thf(func_def_653, type, sK516: term).
% 1.38/0.55 thf(func_def_654, type, sK517: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_655, type, sK518: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_656, type, sK519: ((subst > term > term) > term)).
% 1.38/0.55 thf(func_def_657, type, sK520: ((subst > term > term) > subst)).
% 1.38/0.55 thf(func_def_658, type, sK521: term).
% 1.38/0.55 thf(func_def_659, type, sK522: ((subst > term > subst > $o) > term > $o)).
% 1.38/0.55 thf(func_def_660, type, sK523: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_661, type, sK524: ((subst > term > subst > $o) > subst > term > term)).
% 1.38/0.55 thf(func_def_662, type, sK525: (term > (term > $o) > term)).
% 1.38/0.55 thf(func_def_663, type, sK526: term).
% 1.38/0.55 thf(func_def_664, type, sK527: term).
% 1.38/0.55 thf(func_def_665, type, sK528: term).
% 1.38/0.55 thf(func_def_666, type, sK529: (term > $o)).
% 1.38/0.55 thf(func_def_667, type, sK530: term).
% 1.38/0.55 thf(func_def_668, type, sK531: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_669, type, sK532: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_670, type, sK533: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_671, type, sK534: ((term > $o) > term)).
% 1.38/0.55 thf(func_def_672, type, sK535: term).
% 1.38/0.55 thf(func_def_673, type, sK536: term).
% 1.38/0.55 thf(func_def_674, type, sK537: subst).
% 1.38/0.55 thf(func_def_675, type, sK538: subst).
% 1.38/0.55 thf(func_def_676, type, sK539: (term > (term > $o) > subst > (term > $o) > term)).
% 1.38/0.55 thf(func_def_677, type, sK540: (term > $o)).
% 1.38/0.55 thf(func_def_678, type, sK541: subst).
% 1.38/0.55 thf(func_def_679, type, sK542: (term > $o)).
% 1.38/0.55 thf(func_def_680, type, sK543: term).
% 1.38/0.55 thf(func_def_681, type, sK544: subst).
% 1.38/0.55 thf(func_def_682, type, sK545: term).
% 1.38/0.55 thf(func_def_683, type, sK546: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_684, type, sK547: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_685, type, sK548: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_686, type, sK549: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_687, type, sK550: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_688, type, sK551: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_689, type, sK552: ((subst > term > subst > $o) > subst)).
% 1.38/0.55 thf(func_def_690, type, sK553: ((subst > term > subst > $o) > term)).
% 1.38/0.55 thf(func_def_691, type, sK554: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.38/0.55 thf(func_def_692, type, sK555: (term > (term > $o) > term)).
% 1.38/0.55 thf(func_def_693, type, sK556: (term > $o)).
% 1.38/0.55 thf(func_def_694, type, sK557: term).
% 1.38/0.55 thf(func_def_695, type, sK558: (subst > term > subst > $o)).
% 1.38/0.55 thf(func_def_696, type, sK559: term).
% 1.38/0.55 thf(func_def_697, type, sK560: term).
% 1.38/0.55 thf(func_def_698, type, sK561: (term > $o)).
% 1.38/0.55 thf(func_def_699, type, sK562: (term > $o)).
% 1.38/0.55 thf(func_def_700, type, sK563: subst).
% 1.38/0.55 thf(func_def_701, type, sK564: term).
% 1.38/0.55 thf(func_def_702, type, sK565: (subst > (term > $o) > term)).
% 1.38/0.55 thf(func_def_703, type, vNOT: ($o > $o)).
% 1.38/0.55 thf(func_def_705, type, inv_lam_567: (term > term)).
% 1.38/0.55 thf(f1,axiom,(
% 1.38/0.55 (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ 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 @ X28 @ id))))))) & hoaslaminj_gthm & (! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X38 : subst,X37 : term,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & ! [X5 : d_subst] : (X5 = d_id) & hoasinduction_lem1v2_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : 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)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoasinduction_lem3_lthm) & axmap & hoasinduction_lem3a_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axassoc & (! [X15 : term,X13 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj2) & pushprop_lem3v2 & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21)) => ! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))))))) <=> induction2lem_lthm) & (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)))))))) & pushprop_lem2v2_lthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & induction2lem_gthm & hoaslamnotap_lthm & ~ulamvar1 & (sh = ((d2subst @ d_id))) & pushprop_lem2v2_gthm & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X14 : subst,X26 : (term > $o),X13 : term,X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & hoasinduction_lem3_gthm & ((! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) <=> substmonoid) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & ~(var @ (d2term @ d_one)) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & substmonoid_gthm & (laminj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & apnotvar & (hoasapinj2_lthm <=> (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X20 : term,X15 : term,X13 : term,X19 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)))) & (! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & axvarshift & (hoaslaminj_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X18 : (subst > term > term),X31 : (subst > term > term),X33 : term,X32 : subst] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))))))) & (apinj2 <=> ! [X20 : term,X15 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & ulamvarsh & pushprop_lem0_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & (! [X13 : term,X26 : (term > $o),X14 : subst,X15 : term,X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & hoasinduction_lem1_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & hoasapnotvar & axclos & hoasinduction_lem3v2_gthm & hoasapnotvar_gthm & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & (one = ((d2term @ d_one))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & ~lamnotap & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (substmonoid_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))))))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [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)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1v2 & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X28 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) <=> hoasinduction) & (id = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & hoasapnotvar_lthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X13 : term,X11 : (term > $o),X14 : subst] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) <=> pushprop_lem1v2_lthm) & termmset_gthm & ! [X1 : d_term] : (X1 = d_one) & induction2_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22)) => (! [X10 : (subst > term > subst > $o),X24 : term,X23 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id)) => (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))))))) <=> hoasinduction_lthm) & hoasapinj2_gthm & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & (! [X10 : (term > $o),X14 : subst,X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & hoasinduction_lem1_lthm & (! [X10 : (subst > term > subst > $o),X45 : term,X44 : term,X11 : (term > $o)] : (~ ! [X14 : subst,X13 : term,X26 : 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 @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X44)) <=> hoasinduction_lem2v2) & pushprop_lem1_gthm & pushprop_lem1v2_gthm & (hoasapinj1 <=> ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))) & ulamvarind & (hoasinduction_lem3v2 <=> ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X48)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(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))))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ X30 @ id))))))) & hoasinduction_lem3b_gthm & (pushprop_lem1v2 <=> ! [X13 : term,X14 : subst,X10 : (term > $o),X11 : (term > $o)] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & hoasinduction_gthm & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~(X10 @ id @ X24 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id))) & pushprop_lem3v2_lthm & hoasinduction_lem2_lthm & pushprop & (pushprop_lem0_lthm <=> ! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $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 @ 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)))))))) <=> hoasinduction_lem3v2a_lthm) & lamnotvar & (hoaslaminj <=> ! [X18 : (subst > term > term),X31 : (subst > term > term),X33 : term,X32 : subst] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & (hoasinduction_lem3v2a <=> ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X21) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) <=> induction) & pushprop_lthm & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & pushprop_lthm_orig & hoaslamnotvar_lthm & (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj1) & (hoaslamnotap <=> ! [X18 : (subst > term > term),X46 : term,X47 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & hoasinduction_lem1 & hoasinduction_lem2_gthm & (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ 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))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & hoaslamnotvar & hoaslamnotvar_gthm & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotap_gthm & (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) <=> induction2) & (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) <=> induction2lem) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))))) & pushprop_gthm & hoasapinj1_gthm & axapp & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X19 : term,X15 : term,X20 : term,X13 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & pushprop_lem2v2 & axabs),
% 1.38/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 1.38/0.55 thf(f2,conjecture,(
% 1.38/0.55 (! [X1 : (term > $o),X0 : (term > $o),X3 : subst,X2 : term] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X4 : term] : ((var @ X4) => (X0 @ (sub @ X4 @ X3))) => ! [X5 : term] : ((var @ X5) => ((X1 @ X5) => (X1 @ (sub @ X5 @ sh)))))) = pushprop_lem2v2)),
% 1.38/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2)).
% 1.38/0.55 thf(f3,negated_conjecture,(
% 1.38/0.55 ~ (! [X1 : (term > $o),X0 : (term > $o),X3 : subst,X2 : term] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X4 : term] : ((var @ X4) => (X0 @ (sub @ X4 @ X3))) => ! [X5 : term] : ((var @ X5) => ((X1 @ X5) => (X1 @ (sub @ X5 @ sh)))))) = pushprop_lem2v2)),
% 1.38/0.55 inference(negated_conjecture,[status(cth)],[f2])).
% 1.38/0.55 thf(f4,plain,(
% 1.38/0.55 ~ (! [X0 : (term > $o),X1 : (term > $o),X2 : subst,X3 : term] : ((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0) => (! [X4 : term] : ((var @ X4) => (X1 @ (sub @ X4 @ X2))) => ! [X5 : term] : ((var @ X5) => ((X0 @ X5) => (X0 @ (sub @ X5 @ sh)))))) = pushprop_lem2v2)),
% 1.38/0.55 inference(rectify,[],[f3])).
% 1.38/0.55 thf(f5,plain,(
% 1.38/0.55 ~(! [X2 : subst,X3 : term,X0 : (term > $o),X1 : (term > $o)] : ((((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0)) = $true) => (! [X4 : term] : ((((var @ X4)) = $true) => ($true = ((X1 @ (sub @ X4 @ X2))))) => ! [X5 : term] : ((((var @ X5)) = $true) => ((((X0 @ X5)) = $true) => (((X0 @ (sub @ X5 @ sh))) = $true))))) <=> (pushprop_lem2v2 = $true))),
% 1.38/0.55 inference(fool_elimination,[],[f4])).
% 1.38/0.55 thf(f6,plain,(
% 1.38/0.55 (hoasinduction_lthm_3 <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : ((X4 @ (lam @ X5)) | ~ ! [X6 : term] : ((X4 @ (sub @ X5 @ (push @ X6 @ id))) | ~(X4 @ X6))) | (X4 @ X3) | ~ ! [X7 : term,X8 : term] : (~(X4 @ X8) | ~(X4 @ X7) | (X4 @ (ap @ X7 @ X8))) | ~ ! [X9 : term] : (~(var @ X9) | (X4 @ X9))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : ((X11 @ id @ (X14 @ id @ X15) @ id) | ~(X11 @ id @ X15 @ id)) | ~ ! [X16 : term,X17 : subst,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) | (X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)) | ~ ! [X19 : term] : ((X12 @ (sub @ X13 @ (push @ X19 @ id))) | ~(X12 @ X19)) | (X12 @ (lam @ X13)) | ~ ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : term] : (~(var @ (sub @ X23 @ id)) | (X21 @ id @ X23 @ id)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X25 : subst,X26 : term,X27 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) | (X21 @ id @ (lam @ (X24 @ sh @ one)) @ id) | ~ ! [X28 : term] : ((X21 @ id @ (X24 @ id @ X28) @ id) | ~(X21 @ id @ X28 @ id))) | ~ ! [X29 : term,X30 : term] : ((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id) | ~(X21 @ id @ X30 @ id) | ~(X21 @ id @ X29 @ id)) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~(X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32) | (X21 @ X34 @ X31 @ (comp @ X33 @ X32))) | ~ ! [X35 : subst,X36 : subst,X37 : term,X38 : subst] : ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36) | ~(X21 @ X35 @ X37 @ (comp @ X38 @ X36))) | (X21 @ id @ X22 @ id))))))) & hoaslaminj_gthm & (! [X39 : term,X40 : (subst > term > subst > $o)] : (~ ! [X41 : (subst > term > term),X42 : term] : (~ ! [X43 : term,X44 : subst,X45 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | ~ ! [X46 : subst,X47 : term,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46))) | ~ ! [X49 : term] : ((X40 @ id @ (X41 @ id @ X49) @ id) | ~(X40 @ id @ X49 @ id)) | (X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) | ~ ! [X50 : term] : (~(X40 @ id @ X50 @ id) | (X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) | (X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & ! [X51 : d_subst] : (d_id = X51) & hoasinduction_lem1v2_gthm & ((! [X52 : term] : (((sub @ X52 @ id)) = X52) => (! [X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term] : (~(X53 @ id @ X55 @ id) | (X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) | (X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id) | ~ ! [X56 : (subst > term > term)] : (~ ! [X57 : term,X58 : subst,X59 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | (X53 @ id @ (lam @ (X56 @ sh @ one)) @ id) | ~ ! [X60 : term] : ((X53 @ id @ (X56 @ id @ X60) @ id) | ~(X53 @ id @ X60 @ id)))) => ! [X61 : term,X62 : (subst > term > subst > $o)] : (~ ! [X63 : subst,X64 : subst,X65 : subst,X66 : term] : (~(X62 @ X65 @ X66 @ (comp @ X64 @ X63)) | (X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)) | ~ ! [X67 : subst,X68 : subst,X69 : term,X70 : subst] : (~(X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70) | (X62 @ X67 @ X69 @ (comp @ X68 @ X70))) | ~ ! [X71 : term] : (~(X62 @ id @ X71 @ id) | (X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id)) | (X62 @ id @ (lam @ X61) @ id) | ~ ! [X72 : (subst > term > term)] : (~ ! [X73 : term] : (~(X62 @ id @ X73 @ id) | (X62 @ id @ (X72 @ id @ X73) @ id)) | (X62 @ id @ (lam @ (X72 @ sh @ one)) @ id) | ~ ! [X74 : subst,X75 : term,X76 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))))))) <=> hoasinduction_lem3_lthm) & axmap & hoasinduction_lem3a_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & axassoc & (! [X77 : term,X78 : term,X79 : term,X80 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> hoasapinj2) & pushprop_lem3v2 & ((! [X81 : term,X82 : subst] : (((sub @ one @ (push @ X81 @ X82))) = X81) => (! [X83 : subst,X84 : term] : (((comp @ sh @ (push @ X84 @ X83))) = X83) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : term,X87 : (term > $o)] : (~ ! [X88 : term] : (~(var @ X88) | (X87 @ X88)) | ~ ! [X89 : term,X90 : term] : (~(X87 @ X89) | ~(X87 @ X90) | (X87 @ (ap @ X90 @ X89))) | ~ ! [X91 : term] : ((X87 @ (lam @ X91)) | ~(X87 @ X91)) | (X87 @ X86)) => ! [X92 : (term > $o),X93 : term,X94 : subst] : (~ ! [X95 : term] : (~(var @ X95) | (X92 @ (sub @ X95 @ X94))) | ~ ! [X96 : term] : (~ ! [X97 : term] : (~(X92 @ X97) | (X92 @ (sub @ X96 @ (push @ X97 @ id)))) | (X92 @ (lam @ X96))) | (X92 @ (sub @ X93 @ X94)) | ~ ! [X98 : term,X99 : term] : (~(X92 @ X99) | (X92 @ (ap @ X98 @ X99)) | ~(X92 @ X98))))))) <=> induction2lem_lthm) & (pushprop_p_and_p_prime = (^[X100 : term, X101 : subst, X102 : (term > $o), X103 : (term > $o)] : (! [X104 : term] : (((X102 @ (sub @ X104 @ (push @ X100 @ X101)))) = ((X103 @ X104)))))) & pushprop_lem2v2_lthm & (! [X105 : (subst > term > subst > $o)] : ~ ! [X106 : (term > $o)] : ~ ! [X107 : term] : (((X105 @ id @ X107 @ id)) = ((X106 @ X107))) <=> hoasinduction_lem0_lthm) & induction2lem_gthm & hoaslamnotap_lthm & ~ulamvar1 & (sh = ((d2subst @ d_id))) & pushprop_lem2v2_gthm & (hoasinduction_lem3a <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (~ ! [X110 : (subst > term > term)] : (~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X110 @ X113 @ X112) @ X111)) = ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)))) | ~ ! [X114 : term] : (~(X108 @ id @ X114 @ id) | (X108 @ id @ (X110 @ id @ X114) @ id)) | (X108 @ id @ (lam @ (X110 @ sh @ one)) @ id)) | (X108 @ id @ (lam @ X109) @ id) | ~ ! [X115 : term] : (~(X108 @ id @ X115 @ id) | (X108 @ id @ (sub @ X109 @ (push @ X115 @ id)) @ id)))) & (pushprop_lem1_lthm <=> (! [X116 : term,X117 : subst] : (((sub @ one @ (push @ X116 @ X117))) = X116) => (! [X118 : term,X119 : subst] : (((comp @ sh @ (push @ X118 @ X119))) = X119) => ! [X120 : term,X121 : subst,X122 : (term > $o),X123 : term,X124 : (term > $o)] : (~(X124 @ X123) | (X122 @ (sub @ X123 @ (push @ X120 @ X121))))))) & (axshiftcons <=> ! [X125 : term,X126 : subst] : (((comp @ sh @ (push @ X125 @ X126))) = X126)) & hoasinduction_lem3_gthm & ((! [X127 : subst] : (((comp @ X127 @ id)) = X127) & ! [X128 : subst] : (((comp @ id @ X128)) = X128)) <=> substmonoid) & (axvarid <=> ! [X129 : term] : (((sub @ X129 @ id)) = X129)) & (hoasinduction_lem0 <=> ! [X130 : (subst > term > subst > $o)] : ~ ! [X131 : (term > $o)] : ~ ! [X132 : term] : (((X131 @ X132)) = ((X130 @ id @ X132 @ id)))) & ~(var @ (d2term @ d_one)) & (! [X133 : term] : (((sub @ X133 @ id)) = X133) <=> termmset) & (hoasinduction_lem3b <=> ! [X134 : term] : ~ ! [X135 : (subst > term > term)] : (((sub @ X134 @ (push @ one @ sh))) != ((X135 @ sh @ one)))) & substmonoid_gthm & (laminj <=> ! [X136 : term,X137 : term] : ((X136 = X137) | (((lam @ X137)) != ((lam @ X136))))) & apnotvar & (hoasapinj2_lthm <=> (! [X138 : term,X139 : term,X140 : term,X141 : term] : ((((ap @ X140 @ X139)) != ((ap @ X138 @ X141))) | (X139 = X141)) => ! [X142 : term,X143 : term,X144 : term,X145 : term] : ((((ap @ (sub @ X144 @ id) @ X145)) != ((ap @ (sub @ X143 @ id) @ X142))) | (X142 = X145)))) & (! [X146 : term,X147 : term] : ((X146 = X147) | (((sub @ X147 @ sh)) != ((sub @ X146 @ sh)))) <=> shinj) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ((^[X148 : subst, X149 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & axvarshift & (hoaslaminj_lthm <=> (! [X150 : subst,X151 : term] : (((sub @ one @ (push @ X151 @ X150))) = X151) => (! [X152 : subst,X153 : term] : (((comp @ sh @ (push @ X153 @ X152))) = X152) => (! [X154 : term,X155 : term] : ((((lam @ X154)) != ((lam @ X155))) | (X154 = X155)) => ! [X156 : (subst > term > term),X157 : (subst > term > term),X158 : term,X159 : subst] : ((((X156 @ X159 @ X158)) = ((X157 @ X159 @ X158))) | ~ ! [X160 : subst,X161 : subst,X162 : term] : (((sub @ (X156 @ X161 @ X162) @ X160)) = ((X156 @ (comp @ X161 @ X160) @ (sub @ X162 @ X160)))) | ~ ! [X163 : subst,X164 : subst,X165 : term] : (((sub @ (X157 @ X164 @ X165) @ X163)) = ((X157 @ (comp @ X164 @ X163) @ (sub @ X165 @ X163)))) | (((lam @ (X156 @ sh @ one))) != ((lam @ (X157 @ sh @ one))))))))) & (apinj2 <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X166 = X168) | (((ap @ X167 @ X166)) != ((ap @ X169 @ X168))))) & ulamvarsh & pushprop_lem0_gthm & (! [X170 : term] : ~ ! [X171 : (subst > term > term)] : ~ ! [X172 : term,X173 : subst] : (((X171 @ X173 @ X172)) = ((sub @ X170 @ (push @ X172 @ X173)))) <=> hoasinduction_lem3v2_f) & (! [X174 : term,X175 : (term > $o),X176 : subst,X177 : term,X178 : (term > $o)] : ((X175 @ (sub @ X174 @ (push @ X177 @ X176))) | ~(X178 @ X174)) <=> pushprop_lem1) & hoasinduction_lem1_gthm & ! [X179 : term] : ? [X180 : d_term] : (((d2term @ X180)) = X179) & hoasapnotvar & axclos & hoasinduction_lem3v2_gthm & hoasapnotvar_gthm & (hoasinduction_no_psi_cond <=> ! [X181 : (subst > term > subst > $o),X182 : term] : ((X181 @ id @ X182 @ id) | ~ ! [X183 : (subst > term > term)] : (~ ! [X184 : term] : (~(X181 @ id @ X184 @ id) | (X181 @ id @ (X183 @ id @ X184) @ id)) | ~ ! [X185 : subst,X186 : subst,X187 : term] : (((sub @ (X183 @ X186 @ X187) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X187 @ X185)))) | (X181 @ id @ (lam @ (X183 @ sh @ one)) @ id)) | ~ ! [X188 : term,X189 : term] : (~(X181 @ id @ X188 @ id) | (X181 @ id @ (ap @ (sub @ X188 @ id) @ X189) @ id) | ~(X181 @ id @ X189 @ id)))) & (one = ((d2term @ d_one))) & ! [X190 : d_term,X191 : d_term] : ((((d2term @ X191)) = ((d2term @ X190))) => (X190 = X191)) & (hoasinduction_lem3v2_f_lthm <=> ! [X192 : term] : ~ ! [X193 : (subst > term > term)] : ~ ! [X194 : term,X195 : subst] : (((sub @ X192 @ (push @ X194 @ X195))) = ((X193 @ X195 @ X194)))) & ~lamnotap & (axscons <=> ! [X196 : subst] : (((push @ (sub @ one @ X196) @ (comp @ sh @ X196))) = X196)) & (substmonoid_lthm <=> (! [X197 : subst] : (((comp @ id @ X197)) = X197) => (! [X198 : subst] : (((comp @ X198 @ id)) = X198) => (! [X199 : subst] : (((comp @ X199 @ id)) = X199) & ! [X200 : subst] : (((comp @ id @ X200)) = X200))))) & (axidr <=> ! [X201 : subst] : (((comp @ X201 @ id)) = X201)) & (hoasinduction_lem3v2_lthm <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : ((X203 @ (comp @ X208 @ X206) @ (sub @ X209 @ X206) @ X207) | ~(X203 @ X208 @ X209 @ (comp @ X206 @ X207))) | ~ ! [X210 : term] : (((X203 @ id @ X210 @ id)) = ((X205 @ X210))) | (X205 @ (lam @ X204)) | ~ ! [X211 : term] : (~(X205 @ X211) | (X205 @ (sub @ X204 @ (push @ X211 @ id)))) | ~ ! [X212 : subst,X213 : term,X214 : subst,X215 : subst] : ((X203 @ X215 @ X213 @ (comp @ X214 @ X212)) | ~(X203 @ (comp @ X215 @ X214) @ (sub @ X213 @ X214) @ X212)) | ~ ! [X216 : (subst > term > term)] : (~ ! [X217 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X219 @ X217) @ (sub @ X218 @ X217))) = ((sub @ (X216 @ X219 @ X218) @ X217))) | (X203 @ id @ (lam @ (X216 @ sh @ one)) @ id) | ~ ! [X220 : term] : ((X203 @ id @ (X216 @ id @ X220) @ id) | ~(X203 @ id @ X220 @ id)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1v2 & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X221 : term,X222 : (subst > term > subst > $o)] : ((X222 @ id @ X221 @ id) | ~ ! [X223 : term] : (~(var @ (sub @ X223 @ id)) | (X222 @ id @ X223 @ id)) | ~ ! [X224 : subst,X225 : term,X226 : subst,X227 : subst] : (~(X222 @ (comp @ X227 @ X226) @ (sub @ X225 @ X226) @ X224) | (X222 @ X227 @ X225 @ (comp @ X226 @ X224))) | ~ ! [X228 : term,X229 : term] : ((X222 @ id @ (ap @ (sub @ X229 @ id) @ X228) @ id) | ~(X222 @ id @ X228 @ id) | ~(X222 @ id @ X229 @ id)) | ~ ! [X230 : term,X231 : subst,X232 : subst,X233 : subst] : (~(X222 @ X231 @ X230 @ (comp @ X233 @ X232)) | (X222 @ (comp @ X231 @ X233) @ (sub @ X230 @ X233) @ X232)) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : subst,X236 : term,X237 : subst] : (((X234 @ (comp @ X235 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X234 @ X235 @ X236) @ X237))) | (X222 @ id @ (lam @ (X234 @ sh @ one)) @ id) | ~ ! [X238 : term] : ((X222 @ id @ (X234 @ id @ X238) @ id) | ~(X222 @ id @ X238 @ id)))) <=> hoasinduction) & (id = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & (hoasinduction_p_and_p_prime = (^[X239 : (subst > term > subst > $o), X240 : (term > $o)] : (! [X241 : term] : (((X239 @ id @ X241 @ id)) = ((X240 @ X241)))))) & hoasapnotvar_lthm & ((! [X242 : subst,X243 : term] : (((sub @ one @ (push @ X243 @ X242))) = X243) => ! [X244 : (term > $o),X245 : term,X246 : (term > $o),X247 : subst] : ((X246 @ one) | ~ ! [X248 : term] : (((X246 @ X248)) = ((X244 @ (sub @ X248 @ (push @ X245 @ X247))))) | ~(X244 @ X245))) <=> pushprop_lem1v2_lthm) & termmset_gthm & ! [X249 : d_term] : (d_one = X249) & induction2_gthm & (! [X250 : subst] : (((comp @ id @ X250)) = X250) <=> axidl) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X251 : (term > $o),X252 : term] : (~ ! [X253 : term,X254 : term] : ((X251 @ (ap @ X253 @ X254)) | ~(X251 @ X254) | ~(X251 @ X253)) | ~ ! [X255 : term] : (~(var @ X255) | (X251 @ X255)) | ~ ! [X256 : term] : ((X251 @ (lam @ X256)) | ~ ! [X257 : term] : (~(X251 @ X257) | (X251 @ (sub @ X256 @ (push @ X257 @ id))))) | (X251 @ X252)) => (! [X258 : (subst > term > subst > $o),X259 : term,X260 : term] : (~ ! [X261 : term,X262 : term] : (~(X258 @ id @ X261 @ id) | (X258 @ id @ (ap @ (sub @ X262 @ id) @ X261) @ id) | ~(X258 @ id @ X262 @ id)) | (X258 @ id @ (ap @ X260 @ X259) @ id) | ~ ! [X263 : subst,X264 : term,X265 : subst,X266 : subst] : ((X258 @ X263 @ X264 @ (comp @ X265 @ X266)) | ~(X258 @ (comp @ X263 @ X265) @ (sub @ X264 @ X265) @ X266)) | ~ ! [X267 : subst,X268 : subst,X269 : term,X270 : subst] : ((X258 @ (comp @ X268 @ X270) @ (sub @ X269 @ X270) @ X267) | ~(X258 @ X268 @ X269 @ (comp @ X270 @ X267))) | ~(X258 @ id @ X260 @ id) | ~(X258 @ id @ X259 @ id)) => (! [X271 : term,X272 : (subst > term > subst > $o)] : (~ ! [X273 : subst,X274 : term,X275 : subst,X276 : subst] : ((X272 @ (comp @ X275 @ X276) @ (sub @ X274 @ X276) @ X273) | ~(X272 @ X275 @ X274 @ (comp @ X276 @ X273))) | (X272 @ id @ (lam @ X271) @ id) | ~ ! [X277 : (subst > term > term)] : ((X272 @ id @ (lam @ (X277 @ sh @ one)) @ id) | ~ ! [X278 : term] : (~(X272 @ id @ X278 @ id) | (X272 @ id @ (X277 @ id @ X278) @ id)) | ~ ! [X279 : subst,X280 : subst,X281 : term] : (((sub @ (X277 @ X280 @ X281) @ X279)) = ((X277 @ (comp @ X280 @ X279) @ (sub @ X281 @ X279))))) | ~ ! [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (~(X272 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284) | (X272 @ X285 @ X283 @ (comp @ X282 @ X284))) | ~ ! [X286 : term] : ((X272 @ id @ (sub @ X271 @ (push @ X286 @ id)) @ id) | ~(X272 @ id @ X286 @ id))) => ! [X287 : (subst > term > subst > $o),X288 : term] : (~ ! [X289 : term,X290 : term] : ((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id) | ~(X287 @ id @ X290 @ id) | ~(X287 @ id @ X289 @ id)) | ~ ! [X291 : (subst > term > term)] : ((X287 @ id @ (lam @ (X291 @ sh @ one)) @ id) | ~ ! [X292 : subst,X293 : subst,X294 : term] : (((X291 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292))) = ((sub @ (X291 @ X293 @ X294) @ X292))) | ~ ! [X295 : term] : (~(X287 @ id @ X295 @ id) | (X287 @ id @ (X291 @ id @ X295) @ id))) | ~ ! [X296 : subst,X297 : term,X298 : subst,X299 : subst] : ((X287 @ X298 @ X297 @ (comp @ X299 @ X296)) | ~(X287 @ (comp @ X298 @ X299) @ (sub @ X297 @ X299) @ X296)) | ~ ! [X300 : subst,X301 : subst,X302 : term,X303 : subst] : (~(X287 @ X301 @ X302 @ (comp @ X303 @ X300)) | (X287 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303) @ X300)) | (X287 @ id @ X288 @ id) | ~ ! [X304 : term] : ((X287 @ id @ X304 @ id) | ~(var @ (sub @ X304 @ id))))))) <=> hoasinduction_lthm) & hoasapinj2_gthm & (! [X305 : term,X306 : (subst > term > subst > $o)] : (~ ! [X307 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((sub @ (X307 @ X308 @ X309) @ X310)) = ((X307 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310)))) | ~ ! [X311 : term] : ((X306 @ id @ (X307 @ id @ X311) @ id) | ~(X306 @ id @ X311 @ id)) | (X306 @ id @ (lam @ (X307 @ sh @ one)) @ id)) | ~ ! [X312 : term] : ((X306 @ id @ (sub @ X305 @ (push @ X312 @ id)) @ id) | ~(X306 @ id @ X312 @ id)) | (X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm) & ((! [X313 : term] : (((sub @ X313 @ id)) = X313) => ! [X314 : term] : (((sub @ X314 @ id)) = X314)) <=> termmset_lthm) & (hoasinduction_lem3aa <=> ! [X315 : term,X316 : (subst > term > subst > $o)] : (~ ! [X317 : term] : (~(X316 @ id @ X317 @ id) | (X316 @ id @ (sub @ X315 @ (push @ X317 @ id)) @ id)) | ~ ! [X318 : (subst > term > term)] : (~ ! [X319 : term,X320 : subst,X321 : subst] : (((sub @ (X318 @ X321 @ X319) @ X320)) = ((X318 @ (comp @ X321 @ X320) @ (sub @ X319 @ X320)))) | (X316 @ id @ (lam @ (X318 @ sh @ one)) @ id) | ~ ! [X322 : term] : ((X316 @ id @ (X318 @ id @ X322) @ id) | ~(X316 @ id @ X322 @ id))) | (X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id))) & (! [X323 : (term > $o),X324 : subst,X325 : term] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X323 @ (sub @ X327 @ (push @ X325 @ X324))))) <=> pushprop_lem0) & hoasinduction_lem1_lthm & (! [X328 : (subst > term > subst > $o),X329 : term,X330 : term,X331 : (term > $o)] : (~ ! [X332 : subst,X333 : term,X334 : subst,X335 : subst] : (~(X328 @ X332 @ X333 @ (comp @ X334 @ X335)) | (X328 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334) @ X335)) | ~(X331 @ X329) | ~ ! [X336 : term,X337 : term] : (~(X328 @ id @ X337 @ id) | (X328 @ id @ (ap @ (sub @ X336 @ id) @ X337) @ id) | ~(X328 @ id @ X336 @ id)) | ~ ! [X338 : subst,X339 : term,X340 : subst,X341 : subst] : (~(X328 @ (comp @ X340 @ X341) @ (sub @ X339 @ X341) @ X338) | (X328 @ X340 @ X339 @ (comp @ X341 @ X338))) | ~ ! [X342 : term] : (((X328 @ id @ X342 @ id)) = ((X331 @ X342))) | (X331 @ (ap @ X330 @ X329)) | ~(X331 @ X330)) <=> hoasinduction_lem2v2) & pushprop_lem1_gthm & pushprop_lem1v2_gthm & (hoasapinj1 <=> ! [X343 : term,X344 : term,X345 : term,X346 : term] : ((((ap @ (sub @ X343 @ id) @ X344)) != ((ap @ (sub @ X346 @ id) @ X345))) | (X343 = X346))) & ulamvarind & (hoasinduction_lem3v2 <=> ! [X347 : (term > $o),X348 : (subst > term > subst > $o),X349 : term] : (~ ! [X350 : subst,X351 : subst,X352 : term,X353 : subst] : (~(X348 @ X351 @ X352 @ (comp @ X353 @ X350)) | (X348 @ (comp @ X351 @ X353) @ (sub @ X352 @ X353) @ X350)) | ~ ! [X354 : term] : ((X347 @ (sub @ X349 @ (push @ X354 @ id))) | ~(X347 @ X354)) | (X347 @ (lam @ X349)) | ~ ! [X355 : (subst > term > term)] : (~ ! [X356 : term] : (~(X348 @ id @ X356 @ id) | (X348 @ id @ (X355 @ id @ X356) @ id)) | ~ ! [X357 : subst,X358 : subst,X359 : term] : (((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357))) = ((sub @ (X355 @ X358 @ X359) @ X357))) | (X348 @ id @ (lam @ (X355 @ sh @ one)) @ id)) | ~ ! [X360 : subst,X361 : subst,X362 : term,X363 : subst] : (~(X348 @ (comp @ X360 @ X361) @ (sub @ X362 @ X361) @ X363) | (X348 @ X360 @ X362 @ (comp @ X361 @ X363))) | ~ ! [X364 : term] : (((X348 @ id @ X364 @ id)) = ((X347 @ X364))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & ! [X365 : subst] : ? [X366 : d_subst] : (((d2subst @ X366)) = X365) & (hoasinduction_no_psi_cond_lthm <=> (! [X367 : (subst > term > subst > $o)] : ~ ! [X368 : (term > $o)] : ~ ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) => (! [X370 : term,X371 : (term > $o)] : (~ ! [X372 : term] : (~(var @ X372) | (X371 @ X372)) | ~ ! [X373 : term] : (~ ! [X374 : term] : (~(X371 @ X374) | (X371 @ (sub @ X373 @ (push @ X374 @ id)))) | (X371 @ (lam @ X373))) | (X371 @ X370) | ~ ! [X375 : term,X376 : term] : ((X371 @ (ap @ X375 @ X376)) | ~(X371 @ X375) | ~(X371 @ X376))) => (! [X377 : term] : (((sub @ X377 @ id)) = X377) => (! [X378 : (subst > term > subst > $o),X379 : term,X380 : (term > $o)] : (~ ! [X381 : (subst > term > term)] : ((X378 @ id @ (lam @ (X381 @ sh @ one)) @ id) | ~ ! [X382 : term] : (~(X378 @ id @ X382 @ id) | (X378 @ id @ (X381 @ id @ X382) @ id)) | ~ ! [X383 : term,X384 : subst,X385 : subst] : (((sub @ (X381 @ X384 @ X383) @ X385)) = ((X381 @ (comp @ X384 @ X385) @ (sub @ X383 @ X385))))) | ~ ! [X386 : term] : (((X380 @ X386)) = ((X378 @ id @ X386 @ id))) | ~ ! [X387 : term] : (~(X380 @ X387) | (X380 @ (sub @ X379 @ (push @ X387 @ id)))) | (X380 @ (lam @ X379))) => ! [X388 : term,X389 : (subst > term > subst > $o)] : (~ ! [X390 : term,X391 : term] : (~(X389 @ id @ X390 @ id) | ~(X389 @ id @ X391 @ id) | (X389 @ id @ (ap @ (sub @ X390 @ id) @ X391) @ id)) | ~ ! [X392 : (subst > term > term)] : (~ ! [X393 : subst,X394 : subst,X395 : term] : (((sub @ (X392 @ X393 @ X395) @ X394)) = ((X392 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394)))) | (X389 @ id @ (lam @ (X392 @ sh @ one)) @ id) | ~ ! [X396 : term] : ((X389 @ id @ (X392 @ id @ X396) @ id) | ~(X389 @ id @ X396 @ id))) | (X389 @ id @ X388 @ id))))))) & hoasinduction_lem3b_gthm & (pushprop_lem1v2 <=> ! [X397 : term,X398 : subst,X399 : (term > $o),X400 : (term > $o)] : (~(X399 @ X397) | (X400 @ one) | ~ ! [X401 : term] : (((X400 @ X401)) = ((X399 @ (sub @ X401 @ (push @ X397 @ X398))))))) & ! [X402 : d_subst,X403 : d_subst] : ((((d2subst @ X403)) = ((d2subst @ X402))) => (X402 = X403)) & hoasinduction_gthm & (hoasinduction_lem3b_lthm <=> ! [X404 : term] : ~ ! [X405 : (subst > term > term)] : (((sub @ X404 @ (push @ one @ sh))) != ((X405 @ sh @ one)))) & (hoasinduction_lem2 <=> ! [X406 : (subst > term > subst > $o),X407 : term,X408 : term] : (~ ! [X409 : term,X410 : subst,X411 : subst,X412 : subst] : ((X406 @ (comp @ X411 @ X412) @ (sub @ X409 @ X412) @ X410) | ~(X406 @ X411 @ X409 @ (comp @ X412 @ X410))) | ~ ! [X413 : term,X414 : term] : (~(X406 @ id @ X413 @ id) | (X406 @ id @ (ap @ (sub @ X413 @ id) @ X414) @ id) | ~(X406 @ id @ X414 @ id)) | ~(X406 @ id @ X408 @ id) | (X406 @ id @ (ap @ X407 @ X408) @ id) | ~ ! [X415 : subst,X416 : subst,X417 : term,X418 : subst] : ((X406 @ X416 @ X417 @ (comp @ X415 @ X418)) | ~(X406 @ (comp @ X416 @ X415) @ (sub @ X417 @ X415) @ X418)) | ~(X406 @ id @ X407 @ id))) & pushprop_lem3v2_lthm & hoasinduction_lem2_lthm & pushprop & (pushprop_lem0_lthm <=> ! [X419 : subst,X420 : term,X421 : (term > $o)] : ~ ! [X422 : (term > $o)] : ~ ! [X423 : term] : (((X422 @ X423)) = ((X421 @ (sub @ X423 @ (push @ X420 @ X419)))))) & ((! [X424 : term] : ~ ! [X425 : (subst > term > term)] : ~ ! [X426 : term,X427 : subst] : (((sub @ X424 @ (push @ X426 @ X427))) = ((X425 @ X427 @ X426))) => (! [X428 : term] : (((sub @ X428 @ id)) = X428) => ! [X429 : (term > $o),X430 : term,X431 : (subst > term > subst > $o)] : (~ ! [X432 : term] : (((X431 @ id @ X432 @ id)) = ((X429 @ X432))) | (X429 @ (lam @ X430)) | ~ ! [X433 : term] : (~(X429 @ X433) | (X429 @ (sub @ X430 @ (push @ X433 @ id)))) | ~ ! [X434 : (subst > term > term)] : ((X431 @ id @ (lam @ (X434 @ sh @ one)) @ id) | ~ ! [X435 : term] : (~(X431 @ id @ X435 @ id) | (X431 @ id @ (X434 @ id @ X435) @ id)) | ~ ! [X436 : subst,X437 : subst,X438 : term] : (((X434 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437))) = ((sub @ (X434 @ X436 @ X438) @ X437))))))) <=> hoasinduction_lem3v2a_lthm) & lamnotvar & (hoaslaminj <=> ! [X439 : (subst > term > term),X440 : (subst > term > term),X441 : term,X442 : subst] : (~ ! [X443 : subst,X444 : subst,X445 : term] : (((X439 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444))) = ((sub @ (X439 @ X443 @ X445) @ X444))) | (((lam @ (X440 @ sh @ one))) != ((lam @ (X439 @ sh @ one)))) | ~ ! [X446 : subst,X447 : subst,X448 : term] : (((sub @ (X440 @ X446 @ X448) @ X447)) = ((X440 @ (comp @ X446 @ X447) @ (sub @ X448 @ X447)))) | (((X439 @ X442 @ X441)) = ((X440 @ X442 @ X441))))) & (hoasinduction_lem3v2a <=> ! [X449 : (term > $o),X450 : (subst > term > subst > $o),X451 : term] : (~ ! [X452 : (subst > term > term)] : ((X450 @ id @ (lam @ (X452 @ sh @ one)) @ id) | ~ ! [X453 : term] : (~(X450 @ id @ X453 @ id) | (X450 @ id @ (X452 @ id @ X453) @ id)) | ~ ! [X454 : subst,X455 : term,X456 : subst] : (((sub @ (X452 @ X456 @ X455) @ X454)) = ((X452 @ (comp @ X456 @ X454) @ (sub @ X455 @ X454))))) | ~ ! [X457 : term] : (~(X449 @ X457) | (X449 @ (sub @ X451 @ (push @ X457 @ id)))) | (X449 @ (lam @ X451)) | ~ ! [X458 : term] : (((X449 @ X458)) = ((X450 @ id @ X458 @ id))))) & (! [X459 : term,X460 : (term > $o)] : (~ ! [X461 : term,X462 : term] : (~(X460 @ X461) | ~(X460 @ X462) | (X460 @ (ap @ X461 @ X462))) | (X460 @ X459) | ~ ! [X463 : term] : (~(var @ X463) | (X460 @ X463)) | ~ ! [X464 : term] : ((X460 @ (lam @ X464)) | ~(X460 @ X464))) <=> induction) & pushprop_lthm & (axvarcons <=> ! [X465 : term,X466 : subst] : (((sub @ one @ (push @ X465 @ X466))) = X465)) & pushprop_lthm_orig & hoaslamnotvar_lthm & (! [X467 : term,X468 : term,X469 : term,X470 : term] : ((X469 = X470) | (((ap @ X469 @ X468)) != ((ap @ X470 @ X467)))) <=> apinj1) & (hoaslamnotap <=> ! [X471 : (subst > term > term),X472 : term,X473 : term] : ((((lam @ (X471 @ sh @ one))) != ((ap @ (sub @ X472 @ id) @ X473))) | ~ ! [X474 : subst,X475 : term,X476 : subst] : (((sub @ (X471 @ X474 @ X475) @ X476)) = ((X471 @ (comp @ X474 @ X476) @ (sub @ X475 @ X476)))))) & hoasinduction_lem1 & hoasinduction_lem2_gthm & (! [X477 : term,X478 : (subst > term > subst > $o)] : (~ ! [X479 : subst,X480 : subst,X481 : subst,X482 : term] : (~(X478 @ (comp @ X480 @ X479) @ (sub @ X482 @ X479) @ X481) | (X478 @ X480 @ X482 @ (comp @ X479 @ X481))) | (X478 @ id @ (lam @ X477) @ id) | ~ ! [X483 : (subst > term > term)] : ((X478 @ id @ (lam @ (X483 @ sh @ one)) @ id) | ~ ! [X484 : subst,X485 : subst,X486 : term] : (((sub @ (X483 @ X484 @ X486) @ X485)) = ((X483 @ (comp @ X484 @ X485) @ (sub @ X486 @ X485)))) | ~ ! [X487 : term] : (~(X478 @ id @ X487 @ id) | (X478 @ id @ (X483 @ id @ X487) @ id))) | ~ ! [X488 : term] : ((X478 @ id @ (sub @ X477 @ (push @ X488 @ id)) @ id) | ~(X478 @ id @ X488 @ id)) | ~ ! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (~(X478 @ X492 @ X490 @ (comp @ X489 @ X491)) | (X478 @ (comp @ X492 @ X489) @ (sub @ X490 @ X489) @ X491))) <=> hoasinduction_lem3) & hoaslamnotvar & hoaslamnotvar_gthm & (induction2_lthm <=> (! [X493 : term] : (((sub @ X493 @ id)) = X493) => (! [X494 : term,X495 : (term > $o),X496 : subst] : (~ ! [X497 : term] : (~ ! [X498 : term] : ((X495 @ (sub @ X497 @ (push @ X498 @ id))) | ~(X495 @ X498)) | (X495 @ (lam @ X497))) | (X495 @ (sub @ X494 @ X496)) | ~ ! [X499 : term,X500 : term] : (~(X495 @ X500) | (X495 @ (ap @ X500 @ X499)) | ~(X495 @ X499)) | ~ ! [X501 : term] : ((X495 @ (sub @ X501 @ X496)) | ~(var @ X501))) => ! [X502 : (term > $o),X503 : term] : (~ ! [X504 : term] : (~ ! [X505 : term] : ((X502 @ (sub @ X504 @ (push @ X505 @ id))) | ~(X502 @ X505)) | (X502 @ (lam @ X504))) | (X502 @ X503) | ~ ! [X506 : term,X507 : term] : ((X502 @ (ap @ X506 @ X507)) | ~(X502 @ X506) | ~(X502 @ X507)) | ~ ! [X508 : term] : (~(var @ X508) | (X502 @ X508)))))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoaslamnotap_gthm & (! [X509 : term,X510 : (term > $o)] : ((X510 @ X509) | ~ ! [X511 : term] : (~(var @ X511) | (X510 @ X511)) | ~ ! [X512 : term,X513 : term] : (~(X510 @ X512) | (X510 @ (ap @ X513 @ X512)) | ~(X510 @ X513)) | ~ ! [X514 : term] : (~ ! [X515 : term] : ((X510 @ (sub @ X514 @ (push @ X515 @ id))) | ~(X510 @ X515)) | (X510 @ (lam @ X514)))) <=> induction2) & (! [X516 : (term > $o),X517 : subst,X518 : term] : (~ ! [X519 : term,X520 : term] : (~(X516 @ X519) | ~(X516 @ X520) | (X516 @ (ap @ X520 @ X519))) | (X516 @ (sub @ X518 @ X517)) | ~ ! [X521 : term] : ((X516 @ (sub @ X521 @ X517)) | ~(var @ X521)) | ~ ! [X522 : term] : (~ ! [X523 : term] : (~(X516 @ X523) | (X516 @ (sub @ X522 @ (push @ X523 @ id)))) | (X516 @ (lam @ X522)))) <=> induction2lem) & (hoasinduction_lem3a_lthm <=> (! [X524 : term] : (((sub @ X524 @ id)) = X524) => (! [X525 : term,X526 : (subst > term > subst > $o)] : (~ ! [X527 : term] : (~(X526 @ id @ X527 @ id) | (X526 @ id @ (sub @ X525 @ (push @ X527 @ id)) @ id)) | ~ ! [X528 : (subst > term > term)] : (~ ! [X529 : subst,X530 : term,X531 : subst] : (((sub @ (X528 @ X529 @ X530) @ X531)) = ((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531)))) | ~ ! [X532 : term] : (~(X526 @ id @ X532 @ id) | (X526 @ id @ (X528 @ id @ X532) @ id)) | (X526 @ id @ (lam @ (X528 @ sh @ one)) @ id)) | (X526 @ id @ (lam @ (sub @ X525 @ (push @ one @ sh))) @ id)) => ! [X533 : (subst > term > subst > $o),X534 : term] : (~ ! [X535 : (subst > term > term)] : ((X533 @ id @ (lam @ (X535 @ sh @ one)) @ id) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((X535 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537))) = ((sub @ (X535 @ X536 @ X538) @ X537))) | ~ ! [X539 : term] : ((X533 @ id @ (X535 @ id @ X539) @ id) | ~(X533 @ id @ X539 @ id))) | (X533 @ id @ (lam @ X534) @ id) | ~ ! [X540 : term] : (~(X533 @ id @ X540 @ id) | (X533 @ id @ (sub @ X534 @ (push @ X540 @ id)) @ id)))))) & pushprop_gthm & hoasapinj1_gthm & axapp & (hoasapinj1_lthm <=> (! [X541 : term] : (((sub @ X541 @ id)) = X541) => (! [X542 : term,X543 : term,X544 : term,X545 : term] : ((X544 = X545) | (((ap @ X545 @ X542)) != ((ap @ X544 @ X543)))) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X547 = X549) | (((ap @ (sub @ X549 @ id) @ X546)) != ((ap @ (sub @ X547 @ id) @ X548))))))) & pushprop_lem2v2 & axabs),
% 1.38/0.55 inference(rectify,[],[f1])).
% 1.38/0.55 thf(f7,plain,(
% 1.38/0.55 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : ((((X4 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X4 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X4 @ X6)) = $true))) | ($true = ((X4 @ X3))) | ~ ! [X7 : term,X8 : term] : (~ (((X4 @ X8)) = $true) | ~ (((X4 @ X7)) = $true) | ($true = ((X4 @ (ap @ X7 @ X8))))) | ~ ! [X9 : term] : (~ ($true = ((var @ X9))) | ($true = ((X4 @ X9))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : (($true = ((X11 @ id @ (X14 @ id @ X15) @ id))) | ~ ($true = ((X11 @ id @ X15 @ id)))) | ~ ! [X18 : subst,X17 : subst,X16 : term] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) | ~ ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ~ ($true = ((X12 @ X19)))) | ($true = ((X12 @ (lam @ X13)))) | ~ ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : term] : (~ (((var @ (sub @ X23 @ id))) = $true) | ($true = ((X21 @ id @ X23 @ id)))) | ~ ! [X24 : (subst > term > term)] : (~ ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) | (((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true) | ~ ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ~ ($true = ((X21 @ id @ X28 @ id))))) | ~ ! [X29 : term,X30 : term] : ((((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) = $true) | ~ (((X21 @ id @ X30 @ id)) = $true) | ~ ($true = ((X21 @ id @ X29 @ id)))) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~ ($true = ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32))) | ($true = ((X21 @ X34 @ X31 @ (comp @ X33 @ X32))))) | ~ ! [X35 : subst,X36 : subst,X37 : term,X38 : subst] : (($true = ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36))) | ~ ($true = ((X21 @ X35 @ X37 @ (comp @ X38 @ X36))))) | (((X21 @ id @ X22 @ id)) = $true))))))) & (hoaslaminj_gthm = $true) & (! [X39 : term,X40 : (subst > term > subst > $o)] : (~ ! [X41 : (subst > term > term),X42 : term] : (~ ! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | ~ ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46))) | ~ ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ~ ($true = ((X40 @ id @ X49 @ id)))) | (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) = $true)) | ~ ! [X50 : term] : (~ (((X40 @ id @ X50 @ id)) = $true) | (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) = $true)) | ($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ! [X51 : d_subst] : (d_id = X51) & (hoasinduction_lem1v2_gthm = $true) & ((! [X52 : term] : (((sub @ X52 @ id)) = X52) => (! [X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term] : (~ ($true = ((X53 @ id @ X55 @ id))) | (((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true)) | ($true = ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) | ~ ! [X56 : (subst > term > term)] : (~ ! [X58 : subst,X57 : term,X59 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ~ ! [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) = $true) | ~ ($true = ((X53 @ id @ X60 @ id)))))) => ! [X61 : term,X62 : (subst > term > subst > $o)] : (~ ! [X63 : subst,X64 : subst,X65 : subst,X66 : term] : (~ (((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) = $true) | ($true = ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)))) | ~ ! [X67 : subst,X68 : subst,X69 : term,X70 : subst] : (~ ($true = ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70))) | ($true = ((X62 @ X67 @ X69 @ (comp @ X68 @ X70))))) | ~ ! [X71 : term] : (~ ($true = ((X62 @ id @ X71 @ id))) | ($true = ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | ~ ! [X72 : (subst > term > term)] : (~ ! [X73 : term] : (~ (((X62 @ id @ X73 @ id)) = $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id)))) | ($true = ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) | ~ ! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))))))) <=> (hoasinduction_lem3_lthm = $true)) & (axmap = $true) & (hoasinduction_lem3a_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axassoc = $true) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2 = $true) & ((! [X81 : term,X82 : subst] : (((sub @ one @ (push @ X81 @ X82))) = X81) => (! [X83 : subst,X84 : term] : (((comp @ sh @ (push @ X84 @ X83))) = X83) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : term,X87 : (term > $o)] : (~ ! [X88 : term] : (~ (((var @ X88)) = $true) | ($true = ((X87 @ X88)))) | ~ ! [X89 : term,X90 : term] : (~ ($true = ((X87 @ X89))) | ~ ($true = ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) | ~ ! [X91 : term] : (($true = ((X87 @ (lam @ X91)))) | ~ (((X87 @ X91)) = $true)) | ($true = ((X87 @ X86)))) => ! [X92 : (term > $o),X93 : term,X94 : subst] : (~ ! [X95 : term] : (~ (((var @ X95)) = $true) | ($true = ((X92 @ (sub @ X95 @ X94))))) | ~ ! [X96 : term] : (~ ! [X97 : term] : (~ ($true = ((X92 @ X97))) | ($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id)))))) | ($true = ((X92 @ (lam @ X96))))) | (((X92 @ (sub @ X93 @ X94))) = $true) | ~ ! [X98 : term,X99 : term] : (~ ($true = ((X92 @ X99))) | ($true = ((X92 @ (ap @ X98 @ X99)))) | ~ (((X92 @ X98)) = $true))))))) <=> (induction2lem_lthm = $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)))))))))))) & (pushprop_lem2v2_lthm = $true) & (! [X105 : (subst > term > subst > $o)] : ~ ! [X106 : (term > $o)] : ~ ! [X107 : term] : (((X105 @ id @ X107 @ id)) = ((X106 @ X107))) <=> (hoasinduction_lem0_lthm = $true)) & (induction2lem_gthm = $true) & (hoaslamnotap_lthm = $true) & ~ (ulamvar1 = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X108 : (subst > term > subst > $o),X109 : term] : (~ ! [X110 : (subst > term > term)] : (~ ! [X111 : subst,X112 : term,X113 : subst] : (((sub @ (X110 @ X113 @ X112) @ X111)) = ((X110 @ (comp @ X113 @ X111) @ (sub @ X112 @ X111)))) | ~ ! [X114 : term] : (~ ($true = ((X108 @ id @ X114 @ id))) | ($true = ((X108 @ id @ (X110 @ id @ X114) @ id)))) | (((X108 @ id @ (lam @ (X110 @ sh @ one)) @ id)) = $true)) | ($true = ((X108 @ id @ (lam @ X109) @ id))) | ~ ! [X115 : term] : (~ (((X108 @ id @ X115 @ id)) = $true) | (((X108 @ id @ (sub @ X109 @ (push @ X115 @ id)) @ id)) = $true)))) & ((pushprop_lem1_lthm = $true) <=> (! [X116 : term,X117 : subst] : (((sub @ one @ (push @ X116 @ X117))) = X116) => (! [X118 : term,X119 : subst] : (((comp @ sh @ (push @ X118 @ X119))) = X119) => ! [X120 : term,X121 : subst,X122 : (term > $o),X123 : term,X124 : (term > $o)] : (~ ($true = ((X124 @ X123))) | ($true = ((X122 @ (sub @ X123 @ (push @ X120 @ X121))))))))) & ((axshiftcons = $true) <=> ! [X125 : term,X126 : subst] : (((comp @ sh @ (push @ X125 @ X126))) = X126)) & (hoasinduction_lem3_gthm = $true) & ((! [X127 : subst] : (((comp @ X127 @ id)) = X127) & ! [X128 : subst] : (((comp @ id @ X128)) = X128)) <=> (substmonoid = $true)) & ((axvarid = $true) <=> ! [X129 : term] : (((sub @ X129 @ id)) = X129)) & ((hoasinduction_lem0 = $true) <=> ! [X130 : (subst > term > subst > $o)] : ~ ! [X131 : (term > $o)] : ~ ! [X132 : term] : (((X131 @ X132)) = ((X130 @ id @ X132 @ id)))) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X133 : term] : (((sub @ X133 @ id)) = X133) <=> (termmset = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X134 : term] : ~ ! [X135 : (subst > term > term)] : (((sub @ X134 @ (push @ one @ sh))) != ((X135 @ sh @ one)))) & (substmonoid_gthm = $true) & ((laminj = $true) <=> ! [X136 : term,X137 : term] : ((X136 = X137) | (((lam @ X137)) != ((lam @ X136))))) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (! [X138 : term,X139 : term,X140 : term,X141 : term] : ((((ap @ X140 @ X139)) != ((ap @ X138 @ X141))) | (X139 = X141)) => ! [X142 : term,X143 : term,X144 : term,X145 : term] : ((((ap @ (sub @ X144 @ id) @ X145)) != ((ap @ (sub @ X143 @ id) @ X142))) | (X142 = X145)))) & (! [X146 : term,X147 : term] : ((X146 = X147) | (((sub @ X147 @ sh)) != ((sub @ X146 @ sh)))) <=> (shinj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) <=> (! [X150 : subst,X151 : term] : (((sub @ one @ (push @ X151 @ X150))) = X151) => (! [X152 : subst,X153 : term] : (((comp @ sh @ (push @ X153 @ X152))) = X152) => (! [X154 : term,X155 : term] : ((((lam @ X154)) != ((lam @ X155))) | (X154 = X155)) => ! [X156 : (subst > term > term),X157 : (subst > term > term),X158 : term,X159 : subst] : ((((X156 @ X159 @ X158)) = ((X157 @ X159 @ X158))) | ~ ! [X160 : subst,X161 : subst,X162 : term] : (((sub @ (X156 @ X161 @ X162) @ X160)) = ((X156 @ (comp @ X161 @ X160) @ (sub @ X162 @ X160)))) | ~ ! [X163 : subst,X164 : subst,X165 : term] : (((sub @ (X157 @ X164 @ X165) @ X163)) = ((X157 @ (comp @ X164 @ X163) @ (sub @ X165 @ X163)))) | (((lam @ (X156 @ sh @ one))) != ((lam @ (X157 @ sh @ one))))))))) & ((apinj2 = $true) <=> ! [X166 : term,X167 : term,X168 : term,X169 : term] : ((X166 = X168) | (((ap @ X167 @ X166)) != ((ap @ X169 @ X168))))) & (ulamvarsh = $true) & (pushprop_lem0_gthm = $true) & (! [X170 : term] : ~ ! [X171 : (subst > term > term)] : ~ ! [X172 : term,X173 : subst] : (((X171 @ X173 @ X172)) = ((sub @ X170 @ (push @ X172 @ X173)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X174 : term,X175 : (term > $o),X176 : subst,X177 : term,X178 : (term > $o)] : ((((X175 @ (sub @ X174 @ (push @ X177 @ X176)))) = $true) | ~ ($true = ((X178 @ X174)))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X179 : term] : ? [X180 : d_term] : (((d2term @ X180)) = X179) & (hoasapnotvar = $true) & (axclos = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X181 : (subst > term > subst > $o),X182 : term] : ((((X181 @ id @ X182 @ id)) = $true) | ~ ! [X183 : (subst > term > term)] : (~ ! [X184 : term] : (~ (((X181 @ id @ X184 @ id)) = $true) | ($true = ((X181 @ id @ (X183 @ id @ X184) @ id)))) | ~ ! [X185 : subst,X186 : subst,X187 : term] : (((sub @ (X183 @ X186 @ X187) @ X185)) = ((X183 @ (comp @ X186 @ X185) @ (sub @ X187 @ X185)))) | ($true = ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id)))) | ~ ! [X188 : term,X189 : term] : (~ ($true = ((X181 @ id @ X188 @ id))) | ($true = ((X181 @ id @ (ap @ (sub @ X188 @ id) @ X189) @ id))) | ~ ($true = ((X181 @ id @ X189 @ id)))))) & (one = ((d2term @ d_one))) & ! [X190 : d_term,X191 : d_term] : ((((d2term @ X191)) = ((d2term @ X190))) => (X190 = X191)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X192 : term] : ~ ! [X193 : (subst > term > term)] : ~ ! [X194 : term,X195 : subst] : (((sub @ X192 @ (push @ X194 @ X195))) = ((X193 @ X195 @ X194)))) & ~ (lamnotap = $true) & ((axscons = $true) <=> ! [X196 : subst] : (((push @ (sub @ one @ X196) @ (comp @ sh @ X196))) = X196)) & ((substmonoid_lthm = $true) <=> (! [X197 : subst] : (((comp @ id @ X197)) = X197) => (! [X198 : subst] : (((comp @ X198 @ id)) = X198) => (! [X199 : subst] : (((comp @ X199 @ id)) = X199) & ! [X200 : subst] : (((comp @ id @ X200)) = X200))))) & ((axidr = $true) <=> ! [X201 : subst] : (((comp @ X201 @ id)) = X201)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => ! [X203 : (subst > term > subst > $o),X204 : term,X205 : (term > $o)] : (~ ! [X206 : subst,X207 : subst,X208 : subst,X209 : term] : ((((X203 @ (comp @ X208 @ X206) @ (sub @ X209 @ X206) @ X207)) = $true) | ~ (((X203 @ X208 @ X209 @ (comp @ X206 @ X207))) = $true)) | ~ ! [X210 : term] : (((X203 @ id @ X210 @ id)) = ((X205 @ X210))) | ($true = ((X205 @ (lam @ X204)))) | ~ ! [X211 : term] : (~ ($true = ((X205 @ X211))) | ($true = ((X205 @ (sub @ X204 @ (push @ X211 @ id)))))) | ~ ! [X212 : subst,X213 : term,X214 : subst,X215 : subst] : (($true = ((X203 @ X215 @ X213 @ (comp @ X214 @ X212)))) | ~ ($true = ((X203 @ (comp @ X215 @ X214) @ (sub @ X213 @ X214) @ X212)))) | ~ ! [X216 : (subst > term > term)] : (~ ! [X217 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X219 @ X217) @ (sub @ X218 @ X217))) = ((sub @ (X216 @ X219 @ X218) @ X217))) | ($true = ((X203 @ id @ (lam @ (X216 @ sh @ one)) @ id))) | ~ ! [X220 : term] : (($true = ((X203 @ id @ (X216 @ id @ X220) @ id))) | ~ ($true = ((X203 @ id @ X220 @ id)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X221 : term,X222 : (subst > term > subst > $o)] : ((((X222 @ id @ X221 @ id)) = $true) | ~ ! [X223 : term] : (~ (((var @ (sub @ X223 @ id))) = $true) | (((X222 @ id @ X223 @ id)) = $true)) | ~ ! [X224 : subst,X225 : term,X226 : subst,X227 : subst] : (~ ($true = ((X222 @ (comp @ X227 @ X226) @ (sub @ X225 @ X226) @ X224))) | ($true = ((X222 @ X227 @ X225 @ (comp @ X226 @ X224))))) | ~ ! [X228 : term,X229 : term] : ((((X222 @ id @ (ap @ (sub @ X229 @ id) @ X228) @ id)) = $true) | ~ ($true = ((X222 @ id @ X228 @ id))) | ~ ($true = ((X222 @ id @ X229 @ id)))) | ~ ! [X230 : term,X231 : subst,X232 : subst,X233 : subst] : (~ ($true = ((X222 @ X231 @ X230 @ (comp @ X233 @ X232)))) | ($true = ((X222 @ (comp @ X231 @ X233) @ (sub @ X230 @ X233) @ X232)))) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : subst,X236 : term,X237 : subst] : (((X234 @ (comp @ X235 @ X237) @ (sub @ X236 @ X237))) = ((sub @ (X234 @ X235 @ X236) @ X237))) | ($true = ((X222 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X238 : term] : ((((X222 @ id @ (X234 @ id @ X238) @ id)) = $true) | ~ ($true = ((X222 @ id @ X238 @ id)))))) <=> (hoasinduction = $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapnotvar_lthm = $true) & ((! [X242 : subst,X243 : term] : (((sub @ one @ (push @ X243 @ X242))) = X243) => ! [X244 : (term > $o),X245 : term,X246 : (term > $o),X247 : subst] : (($true = ((X246 @ one))) | ~ ! [X248 : term] : (((X246 @ X248)) = ((X244 @ (sub @ X248 @ (push @ X245 @ X247))))) | ~ ($true = ((X244 @ X245))))) <=> (pushprop_lem1v2_lthm = $true)) & (termmset_gthm = $true) & ! [X249 : d_term] : (d_one = X249) & (induction2_gthm = $true) & (! [X250 : subst] : (((comp @ id @ X250)) = X250) <=> (axidl = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X251 : (term > $o),X252 : term] : (~ ! [X253 : term,X254 : term] : (($true = ((X251 @ (ap @ X253 @ X254)))) | ~ (((X251 @ X254)) = $true) | ~ (((X251 @ X253)) = $true)) | ~ ! [X255 : term] : (~ ($true = ((var @ X255))) | (((X251 @ X255)) = $true)) | ~ ! [X256 : term] : ((((X251 @ (lam @ X256))) = $true) | ~ ! [X257 : term] : (~ ($true = ((X251 @ X257))) | (((X251 @ (sub @ X256 @ (push @ X257 @ id)))) = $true))) | ($true = ((X251 @ X252)))) => (! [X258 : (subst > term > subst > $o),X259 : term,X260 : term] : (~ ! [X261 : term,X262 : term] : (~ ($true = ((X258 @ id @ X261 @ id))) | (((X258 @ id @ (ap @ (sub @ X262 @ id) @ X261) @ id)) = $true) | ~ (((X258 @ id @ X262 @ id)) = $true)) | ($true = ((X258 @ id @ (ap @ X260 @ X259) @ id))) | ~ ! [X263 : subst,X264 : term,X265 : subst,X266 : subst] : (($true = ((X258 @ X263 @ X264 @ (comp @ X265 @ X266)))) | ~ ($true = ((X258 @ (comp @ X263 @ X265) @ (sub @ X264 @ X265) @ X266)))) | ~ ! [X267 : subst,X268 : subst,X269 : term,X270 : subst] : ((((X258 @ (comp @ X268 @ X270) @ (sub @ X269 @ X270) @ X267)) = $true) | ~ (((X258 @ X268 @ X269 @ (comp @ X270 @ X267))) = $true)) | ~ ($true = ((X258 @ id @ X260 @ id))) | ~ (((X258 @ id @ X259 @ id)) = $true)) => (! [X271 : term,X272 : (subst > term > subst > $o)] : (~ ! [X273 : subst,X274 : term,X275 : subst,X276 : subst] : (($true = ((X272 @ (comp @ X275 @ X276) @ (sub @ X274 @ X276) @ X273))) | ~ ($true = ((X272 @ X275 @ X274 @ (comp @ X276 @ X273))))) | ($true = ((X272 @ id @ (lam @ X271) @ id))) | ~ ! [X277 : (subst > term > term)] : (($true = ((X272 @ id @ (lam @ (X277 @ sh @ one)) @ id))) | ~ ! [X278 : term] : (~ ($true = ((X272 @ id @ X278 @ id))) | ($true = ((X272 @ id @ (X277 @ id @ X278) @ id)))) | ~ ! [X279 : subst,X280 : subst,X281 : term] : (((sub @ (X277 @ X280 @ X281) @ X279)) = ((X277 @ (comp @ X280 @ X279) @ (sub @ X281 @ X279))))) | ~ ! [X282 : subst,X283 : term,X284 : subst,X285 : subst] : (~ (((X272 @ (comp @ X285 @ X282) @ (sub @ X283 @ X282) @ X284)) = $true) | ($true = ((X272 @ X285 @ X283 @ (comp @ X282 @ X284))))) | ~ ! [X286 : term] : (($true = ((X272 @ id @ (sub @ X271 @ (push @ X286 @ id)) @ id))) | ~ (((X272 @ id @ X286 @ id)) = $true))) => ! [X287 : (subst > term > subst > $o),X288 : term] : (~ ! [X289 : term,X290 : term] : ((((X287 @ id @ (ap @ (sub @ X290 @ id) @ X289) @ id)) = $true) | ~ (((X287 @ id @ X290 @ id)) = $true) | ~ ($true = ((X287 @ id @ X289 @ id)))) | ~ ! [X291 : (subst > term > term)] : ((((X287 @ id @ (lam @ (X291 @ sh @ one)) @ id)) = $true) | ~ ! [X292 : subst,X293 : subst,X294 : term] : (((X291 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292))) = ((sub @ (X291 @ X293 @ X294) @ X292))) | ~ ! [X295 : term] : (~ (((X287 @ id @ X295 @ id)) = $true) | ($true = ((X287 @ id @ (X291 @ id @ X295) @ id))))) | ~ ! [X296 : subst,X297 : term,X298 : subst,X299 : subst] : ((((X287 @ X298 @ X297 @ (comp @ X299 @ X296))) = $true) | ~ (((X287 @ (comp @ X298 @ X299) @ (sub @ X297 @ X299) @ X296)) = $true)) | ~ ! [X300 : subst,X301 : subst,X302 : term,X303 : subst] : (~ (((X287 @ X301 @ X302 @ (comp @ X303 @ X300))) = $true) | (((X287 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303) @ X300)) = $true)) | (((X287 @ id @ X288 @ id)) = $true) | ~ ! [X304 : term] : (($true = ((X287 @ id @ X304 @ id))) | ~ ($true = ((var @ (sub @ X304 @ id))))))))) <=> (hoasinduction_lthm = $true)) & (hoasapinj2_gthm = $true) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (~ ! [X307 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((sub @ (X307 @ X308 @ X309) @ X310)) = ((X307 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310)))) | ~ ! [X311 : term] : (($true = ((X306 @ id @ (X307 @ id @ X311) @ id))) | ~ ($true = ((X306 @ id @ X311 @ id)))) | ($true = ((X306 @ id @ (lam @ (X307 @ sh @ one)) @ id)))) | ~ ! [X312 : term] : ((((X306 @ id @ (sub @ X305 @ (push @ X312 @ id)) @ id)) = $true) | ~ ($true = ((X306 @ id @ X312 @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((! [X313 : term] : (((sub @ X313 @ id)) = X313) => ! [X314 : term] : (((sub @ X314 @ id)) = X314)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X315 : term,X316 : (subst > term > subst > $o)] : (~ ! [X317 : term] : (~ ($true = ((X316 @ id @ X317 @ id))) | ($true = ((X316 @ id @ (sub @ X315 @ (push @ X317 @ id)) @ id)))) | ~ ! [X318 : (subst > term > term)] : (~ ! [X319 : term,X320 : subst,X321 : subst] : (((sub @ (X318 @ X321 @ X319) @ X320)) = ((X318 @ (comp @ X321 @ X320) @ (sub @ X319 @ X320)))) | (((X316 @ id @ (lam @ (X318 @ sh @ one)) @ id)) = $true) | ~ ! [X322 : term] : (($true = ((X316 @ id @ (X318 @ id @ X322) @ id))) | ~ (((X316 @ id @ X322 @ id)) = $true))) | (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) = $true))) & (! [X323 : (term > $o),X324 : subst,X325 : term] : ~ ! [X326 : (term > $o)] : ~ ! [X327 : term] : (((X326 @ X327)) = ((X323 @ (sub @ X327 @ (push @ X325 @ X324))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X328 : (subst > term > subst > $o),X329 : term,X330 : term,X331 : (term > $o)] : (~ ! [X332 : subst,X333 : term,X334 : subst,X335 : subst] : (~ (((X328 @ X332 @ X333 @ (comp @ X334 @ X335))) = $true) | ($true = ((X328 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334) @ X335)))) | ~ (((X331 @ X329)) = $true) | ~ ! [X336 : term,X337 : term] : (~ (((X328 @ id @ X337 @ id)) = $true) | ($true = ((X328 @ id @ (ap @ (sub @ X336 @ id) @ X337) @ id))) | ~ ($true = ((X328 @ id @ X336 @ id)))) | ~ ! [X338 : subst,X339 : term,X340 : subst,X341 : subst] : (~ ($true = ((X328 @ (comp @ X340 @ X341) @ (sub @ X339 @ X341) @ X338))) | ($true = ((X328 @ X340 @ X339 @ (comp @ X341 @ X338))))) | ~ ! [X342 : term] : (((X328 @ id @ X342 @ id)) = ((X331 @ X342))) | (((X331 @ (ap @ X330 @ X329))) = $true) | ~ ($true = ((X331 @ X330)))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X343 : term,X344 : term,X345 : term,X346 : term] : ((((ap @ (sub @ X343 @ id) @ X344)) != ((ap @ (sub @ X346 @ id) @ X345))) | (X343 = X346))) & (ulamvarind = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X347 : (term > $o),X348 : (subst > term > subst > $o),X349 : term] : (~ ! [X350 : subst,X351 : subst,X352 : term,X353 : subst] : (~ ($true = ((X348 @ X351 @ X352 @ (comp @ X353 @ X350)))) | (((X348 @ (comp @ X351 @ X353) @ (sub @ X352 @ X353) @ X350)) = $true)) | ~ ! [X354 : term] : (($true = ((X347 @ (sub @ X349 @ (push @ X354 @ id))))) | ~ ($true = ((X347 @ X354)))) | (((X347 @ (lam @ X349))) = $true) | ~ ! [X355 : (subst > term > term)] : (~ ! [X356 : term] : (~ ($true = ((X348 @ id @ X356 @ id))) | ($true = ((X348 @ id @ (X355 @ id @ X356) @ id)))) | ~ ! [X357 : subst,X358 : subst,X359 : term] : (((X355 @ (comp @ X358 @ X357) @ (sub @ X359 @ X357))) = ((sub @ (X355 @ X358 @ X359) @ X357))) | ($true = ((X348 @ id @ (lam @ (X355 @ sh @ one)) @ id)))) | ~ ! [X360 : subst,X361 : subst,X362 : term,X363 : subst] : (~ (((X348 @ (comp @ X360 @ X361) @ (sub @ X362 @ X361) @ X363)) = $true) | ($true = ((X348 @ X360 @ X362 @ (comp @ X361 @ X363))))) | ~ ! [X364 : term] : (((X348 @ id @ X364 @ id)) = ((X347 @ X364))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X365 : subst] : ? [X366 : d_subst] : (((d2subst @ X366)) = X365) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X367 : (subst > term > subst > $o)] : ~ ! [X368 : (term > $o)] : ~ ! [X369 : term] : (((X367 @ id @ X369 @ id)) = ((X368 @ X369))) => (! [X370 : term,X371 : (term > $o)] : (~ ! [X372 : term] : (~ ($true = ((var @ X372))) | (((X371 @ X372)) = $true)) | ~ ! [X373 : term] : (~ ! [X374 : term] : (~ ($true = ((X371 @ X374))) | ($true = ((X371 @ (sub @ X373 @ (push @ X374 @ id)))))) | ($true = ((X371 @ (lam @ X373))))) | ($true = ((X371 @ X370))) | ~ ! [X375 : term,X376 : term] : ((((X371 @ (ap @ X375 @ X376))) = $true) | ~ ($true = ((X371 @ X375))) | ~ (((X371 @ X376)) = $true))) => (! [X377 : term] : (((sub @ X377 @ id)) = X377) => (! [X378 : (subst > term > subst > $o),X379 : term,X380 : (term > $o)] : (~ ! [X381 : (subst > term > term)] : (($true = ((X378 @ id @ (lam @ (X381 @ sh @ one)) @ id))) | ~ ! [X382 : term] : (~ ($true = ((X378 @ id @ X382 @ id))) | (((X378 @ id @ (X381 @ id @ X382) @ id)) = $true)) | ~ ! [X383 : term,X384 : subst,X385 : subst] : (((sub @ (X381 @ X384 @ X383) @ X385)) = ((X381 @ (comp @ X384 @ X385) @ (sub @ X383 @ X385))))) | ~ ! [X386 : term] : (((X380 @ X386)) = ((X378 @ id @ X386 @ id))) | ~ ! [X387 : term] : (~ ($true = ((X380 @ X387))) | ($true = ((X380 @ (sub @ X379 @ (push @ X387 @ id)))))) | (((X380 @ (lam @ X379))) = $true)) => ! [X388 : term,X389 : (subst > term > subst > $o)] : (~ ! [X390 : term,X391 : term] : (~ ($true = ((X389 @ id @ X390 @ id))) | ~ ($true = ((X389 @ id @ X391 @ id))) | ($true = ((X389 @ id @ (ap @ (sub @ X390 @ id) @ X391) @ id)))) | ~ ! [X392 : (subst > term > term)] : (~ ! [X393 : subst,X394 : subst,X395 : term] : (((sub @ (X392 @ X393 @ X395) @ X394)) = ((X392 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394)))) | ($true = ((X389 @ id @ (lam @ (X392 @ sh @ one)) @ id))) | ~ ! [X396 : term] : (($true = ((X389 @ id @ (X392 @ id @ X396) @ id))) | ~ ($true = ((X389 @ id @ X396 @ id))))) | ($true = ((X389 @ id @ X388 @ id))))))))) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X397 : term,X398 : subst,X399 : (term > $o),X400 : (term > $o)] : (~ (((X399 @ X397)) = $true) | (((X400 @ one)) = $true) | ~ ! [X401 : term] : (((X400 @ X401)) = ((X399 @ (sub @ X401 @ (push @ X397 @ X398))))))) & ! [X402 : d_subst,X403 : d_subst] : ((((d2subst @ X403)) = ((d2subst @ X402))) => (X402 = X403)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X404 : term] : ~ ! [X405 : (subst > term > term)] : (((sub @ X404 @ (push @ one @ sh))) != ((X405 @ sh @ one)))) & ((hoasinduction_lem2 = $true) <=> ! [X406 : (subst > term > subst > $o),X407 : term,X408 : term] : (~ ! [X409 : term,X410 : subst,X411 : subst,X412 : subst] : (($true = ((X406 @ (comp @ X411 @ X412) @ (sub @ X409 @ X412) @ X410))) | ~ ($true = ((X406 @ X411 @ X409 @ (comp @ X412 @ X410))))) | ~ ! [X413 : term,X414 : term] : (~ (((X406 @ id @ X413 @ id)) = $true) | ($true = ((X406 @ id @ (ap @ (sub @ X413 @ id) @ X414) @ id))) | ~ (((X406 @ id @ X414 @ id)) = $true)) | ~ (((X406 @ id @ X408 @ id)) = $true) | (((X406 @ id @ (ap @ X407 @ X408) @ id)) = $true) | ~ ! [X415 : subst,X416 : subst,X417 : term,X418 : subst] : (($true = ((X406 @ X416 @ X417 @ (comp @ X415 @ X418)))) | ~ ($true = ((X406 @ (comp @ X416 @ X415) @ (sub @ X417 @ X415) @ X418)))) | ~ ($true = ((X406 @ id @ X407 @ id))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X419 : subst,X420 : term,X421 : (term > $o)] : ~ ! [X422 : (term > $o)] : ~ ! [X423 : term] : (((X422 @ X423)) = ((X421 @ (sub @ X423 @ (push @ X420 @ X419)))))) & ((! [X424 : term] : ~ ! [X425 : (subst > term > term)] : ~ ! [X426 : term,X427 : subst] : (((sub @ X424 @ (push @ X426 @ X427))) = ((X425 @ X427 @ X426))) => (! [X428 : term] : (((sub @ X428 @ id)) = X428) => ! [X429 : (term > $o),X430 : term,X431 : (subst > term > subst > $o)] : (~ ! [X432 : term] : (((X431 @ id @ X432 @ id)) = ((X429 @ X432))) | ($true = ((X429 @ (lam @ X430)))) | ~ ! [X433 : term] : (~ ($true = ((X429 @ X433))) | (((X429 @ (sub @ X430 @ (push @ X433 @ id)))) = $true)) | ~ ! [X434 : (subst > term > term)] : ((((X431 @ id @ (lam @ (X434 @ sh @ one)) @ id)) = $true) | ~ ! [X435 : term] : (~ ($true = ((X431 @ id @ X435 @ id))) | ($true = ((X431 @ id @ (X434 @ id @ X435) @ id)))) | ~ ! [X436 : subst,X437 : subst,X438 : term] : (((X434 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437))) = ((sub @ (X434 @ X436 @ X438) @ X437))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (lamnotvar = $true) & ((hoaslaminj = $true) <=> ! [X439 : (subst > term > term),X440 : (subst > term > term),X441 : term,X442 : subst] : (~ ! [X443 : subst,X444 : subst,X445 : term] : (((X439 @ (comp @ X443 @ X444) @ (sub @ X445 @ X444))) = ((sub @ (X439 @ X443 @ X445) @ X444))) | (((lam @ (X440 @ sh @ one))) != ((lam @ (X439 @ sh @ one)))) | ~ ! [X446 : subst,X447 : subst,X448 : term] : (((sub @ (X440 @ X446 @ X448) @ X447)) = ((X440 @ (comp @ X446 @ X447) @ (sub @ X448 @ X447)))) | (((X439 @ X442 @ X441)) = ((X440 @ X442 @ X441))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X449 : (term > $o),X450 : (subst > term > subst > $o),X451 : term] : (~ ! [X452 : (subst > term > term)] : (($true = ((X450 @ id @ (lam @ (X452 @ sh @ one)) @ id))) | ~ ! [X453 : term] : (~ (((X450 @ id @ X453 @ id)) = $true) | ($true = ((X450 @ id @ (X452 @ id @ X453) @ id)))) | ~ ! [X454 : subst,X455 : term,X456 : subst] : (((sub @ (X452 @ X456 @ X455) @ X454)) = ((X452 @ (comp @ X456 @ X454) @ (sub @ X455 @ X454))))) | ~ ! [X457 : term] : (~ (((X449 @ X457)) = $true) | ($true = ((X449 @ (sub @ X451 @ (push @ X457 @ id)))))) | ($true = ((X449 @ (lam @ X451)))) | ~ ! [X458 : term] : (((X449 @ X458)) = ((X450 @ id @ X458 @ id))))) & (! [X459 : term,X460 : (term > $o)] : (~ ! [X461 : term,X462 : term] : (~ ($true = ((X460 @ X461))) | ~ ($true = ((X460 @ X462))) | ($true = ((X460 @ (ap @ X461 @ X462))))) | ($true = ((X460 @ X459))) | ~ ! [X463 : term] : (~ ($true = ((var @ X463))) | (((X460 @ X463)) = $true)) | ~ ! [X464 : term] : (($true = ((X460 @ (lam @ X464)))) | ~ ($true = ((X460 @ X464))))) <=> (induction = $true)) & (pushprop_lthm = $true) & ((axvarcons = $true) <=> ! [X465 : term,X466 : subst] : (((sub @ one @ (push @ X465 @ X466))) = X465)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (! [X467 : term,X468 : term,X469 : term,X470 : term] : ((X469 = X470) | (((ap @ X469 @ X468)) != ((ap @ X470 @ X467)))) <=> (apinj1 = $true)) & ((hoaslamnotap = $true) <=> ! [X471 : (subst > term > term),X472 : term,X473 : term] : ((((lam @ (X471 @ sh @ one))) != ((ap @ (sub @ X472 @ id) @ X473))) | ~ ! [X474 : subst,X475 : term,X476 : subst] : (((sub @ (X471 @ X474 @ X475) @ X476)) = ((X471 @ (comp @ X474 @ X476) @ (sub @ X475 @ X476)))))) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_gthm = $true) & (! [X477 : term,X478 : (subst > term > subst > $o)] : (~ ! [X479 : subst,X480 : subst,X481 : subst,X482 : term] : (~ ($true = ((X478 @ (comp @ X480 @ X479) @ (sub @ X482 @ X479) @ X481))) | ($true = ((X478 @ X480 @ X482 @ (comp @ X479 @ X481))))) | ($true = ((X478 @ id @ (lam @ X477) @ id))) | ~ ! [X483 : (subst > term > term)] : (($true = ((X478 @ id @ (lam @ (X483 @ sh @ one)) @ id))) | ~ ! [X484 : subst,X485 : subst,X486 : term] : (((sub @ (X483 @ X484 @ X486) @ X485)) = ((X483 @ (comp @ X484 @ X485) @ (sub @ X486 @ X485)))) | ~ ! [X487 : term] : (~ ($true = ((X478 @ id @ X487 @ id))) | ($true = ((X478 @ id @ (X483 @ id @ X487) @ id))))) | ~ ! [X488 : term] : (($true = ((X478 @ id @ (sub @ X477 @ (push @ X488 @ id)) @ id))) | ~ ($true = ((X478 @ id @ X488 @ id)))) | ~ ! [X489 : subst,X490 : term,X491 : subst,X492 : subst] : (~ ($true = ((X478 @ X492 @ X490 @ (comp @ X489 @ X491)))) | ($true = ((X478 @ (comp @ X492 @ X489) @ (sub @ X490 @ X489) @ X491))))) <=> (hoasinduction_lem3 = $true)) & (hoaslamnotvar = $true) & (hoaslamnotvar_gthm = $true) & ((induction2_lthm = $true) <=> (! [X493 : term] : (((sub @ X493 @ id)) = X493) => (! [X494 : term,X495 : (term > $o),X496 : subst] : (~ ! [X497 : term] : (~ ! [X498 : term] : (($true = ((X495 @ (sub @ X497 @ (push @ X498 @ id))))) | ~ (((X495 @ X498)) = $true)) | ($true = ((X495 @ (lam @ X497))))) | ($true = ((X495 @ (sub @ X494 @ X496)))) | ~ ! [X499 : term,X500 : term] : (~ ($true = ((X495 @ X500))) | (((X495 @ (ap @ X500 @ X499))) = $true) | ~ (((X495 @ X499)) = $true)) | ~ ! [X501 : term] : ((((X495 @ (sub @ X501 @ X496))) = $true) | ~ ($true = ((var @ X501))))) => ! [X502 : (term > $o),X503 : term] : (~ ! [X504 : term] : (~ ! [X505 : term] : (($true = ((X502 @ (sub @ X504 @ (push @ X505 @ id))))) | ~ (((X502 @ X505)) = $true)) | ($true = ((X502 @ (lam @ X504))))) | (((X502 @ X503)) = $true) | ~ ! [X506 : term,X507 : term] : ((((X502 @ (ap @ X506 @ X507))) = $true) | ~ (((X502 @ X506)) = $true) | ~ ($true = ((X502 @ X507)))) | ~ ! [X508 : term] : (~ (((var @ X508)) = $true) | ($true = ((X502 @ X508)))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoaslamnotap_gthm = $true) & (! [X509 : term,X510 : (term > $o)] : ((((X510 @ X509)) = $true) | ~ ! [X511 : term] : (~ ($true = ((var @ X511))) | ($true = ((X510 @ X511)))) | ~ ! [X512 : term,X513 : term] : (~ (((X510 @ X512)) = $true) | (((X510 @ (ap @ X513 @ X512))) = $true) | ~ ($true = ((X510 @ X513)))) | ~ ! [X514 : term] : (~ ! [X515 : term] : ((((X510 @ (sub @ X514 @ (push @ X515 @ id)))) = $true) | ~ ($true = ((X510 @ X515)))) | (((X510 @ (lam @ X514))) = $true))) <=> (induction2 = $true)) & (! [X516 : (term > $o),X517 : subst,X518 : term] : (~ ! [X519 : term,X520 : term] : (~ (((X516 @ X519)) = $true) | ~ ($true = ((X516 @ X520))) | (((X516 @ (ap @ X520 @ X519))) = $true)) | (((X516 @ (sub @ X518 @ X517))) = $true) | ~ ! [X521 : term] : (($true = ((X516 @ (sub @ X521 @ X517)))) | ~ ($true = ((var @ X521)))) | ~ ! [X522 : term] : (~ ! [X523 : term] : (~ (((X516 @ X523)) = $true) | ($true = ((X516 @ (sub @ X522 @ (push @ X523 @ id)))))) | ($true = ((X516 @ (lam @ X522)))))) <=> (induction2lem = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X524 : term] : (((sub @ X524 @ id)) = X524) => (! [X525 : term,X526 : (subst > term > subst > $o)] : (~ ! [X527 : term] : (~ (((X526 @ id @ X527 @ id)) = $true) | ($true = ((X526 @ id @ (sub @ X525 @ (push @ X527 @ id)) @ id)))) | ~ ! [X528 : (subst > term > term)] : (~ ! [X529 : subst,X530 : term,X531 : subst] : (((sub @ (X528 @ X529 @ X530) @ X531)) = ((X528 @ (comp @ X529 @ X531) @ (sub @ X530 @ X531)))) | ~ ! [X532 : term] : (~ (((X526 @ id @ X532 @ id)) = $true) | (((X526 @ id @ (X528 @ id @ X532) @ id)) = $true)) | ($true = ((X526 @ id @ (lam @ (X528 @ sh @ one)) @ id)))) | ($true = ((X526 @ id @ (lam @ (sub @ X525 @ (push @ one @ sh))) @ id)))) => ! [X533 : (subst > term > subst > $o),X534 : term] : (~ ! [X535 : (subst > term > term)] : ((((X533 @ id @ (lam @ (X535 @ sh @ one)) @ id)) = $true) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((X535 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537))) = ((sub @ (X535 @ X536 @ X538) @ X537))) | ~ ! [X539 : term] : (($true = ((X533 @ id @ (X535 @ id @ X539) @ id))) | ~ (((X533 @ id @ X539 @ id)) = $true))) | ($true = ((X533 @ id @ (lam @ X534) @ id))) | ~ ! [X540 : term] : (~ (((X533 @ id @ X540 @ id)) = $true) | (((X533 @ id @ (sub @ X534 @ (push @ X540 @ id)) @ id)) = $true)))))) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (axapp = $true) & ((hoasapinj1_lthm = $true) <=> (! [X541 : term] : (((sub @ X541 @ id)) = X541) => (! [X542 : term,X543 : term,X544 : term,X545 : term] : ((X544 = X545) | (((ap @ X545 @ X542)) != ((ap @ X544 @ X543)))) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : ((X547 = X549) | (((ap @ (sub @ X549 @ id) @ X546)) != ((ap @ (sub @ X547 @ id) @ X548))))))) & (pushprop_lem2v2 = $true) & (axabs = $true)),
% 1.38/0.55 inference(fool_elimination,[],[f6])).
% 1.38/0.55 thf(f8,plain,(
% 1.38/0.55 ((hoasinduction_lthm_3 = $true) <=> (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : ((((X4 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X4 @ (sub @ X5 @ (push @ X6 @ id)))) = $true) | ~ (((X4 @ X6)) = $true))) | ($true = ((X4 @ X3))) | ~ ! [X7 : term,X8 : term] : (~ (((X4 @ X8)) = $true) | ~ (((X4 @ X7)) = $true) | ($true = ((X4 @ (ap @ X7 @ X8))))) | ~ ! [X9 : term] : (~ ($true = ((var @ X9))) | ($true = ((X4 @ X9))))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X11 : (subst > term > subst > $o),X12 : (term > $o),X13 : term] : (~ ! [X14 : (subst > term > term)] : (~ ! [X15 : term] : (($true = ((X11 @ id @ (X14 @ id @ X15) @ id))) | ~ ($true = ((X11 @ id @ X15 @ id)))) | ~ ! [X18 : subst,X17 : subst,X16 : term] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) | ~ ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ~ ($true = ((X12 @ X19)))) | ($true = ((X12 @ (lam @ X13)))) | ~ ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : term] : (~ (((var @ (sub @ X23 @ id))) = $true) | ($true = ((X21 @ id @ X23 @ id)))) | ~ ! [X24 : (subst > term > term)] : (~ ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) | (((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true) | ~ ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ~ ($true = ((X21 @ id @ X28 @ id))))) | ~ ! [X29 : term,X30 : term] : ((((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) = $true) | ~ (((X21 @ id @ X30 @ id)) = $true) | ~ ($true = ((X21 @ id @ X29 @ id)))) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~ ($true = ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32))) | ($true = ((X21 @ X34 @ X31 @ (comp @ X33 @ X32))))) | ~ ! [X35 : subst,X36 : subst,X37 : term,X38 : subst] : (($true = ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36))) | ~ ($true = ((X21 @ X35 @ X37 @ (comp @ X38 @ X36))))) | (((X21 @ id @ X22 @ id)) = $true))))))) & (hoaslaminj_gthm = $true) & (! [X39 : term,X40 : (subst > term > subst > $o)] : (~ ! [X41 : (subst > term > term),X42 : term] : (~ ! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | ~ ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46))) | ~ ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ~ ($true = ((X40 @ id @ X49 @ id)))) | (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) = $true)) | ~ ! [X50 : term] : (~ (((X40 @ id @ X50 @ id)) = $true) | (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) = $true)) | ($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ! [X51 : d_subst] : (d_id = X51) & (hoasinduction_lem1v2_gthm = $true) & ((! [X52 : term] : (((sub @ X52 @ id)) = X52) => (! [X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term] : (~ ($true = ((X53 @ id @ X55 @ id))) | (((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true)) | ($true = ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) | ~ ! [X56 : (subst > term > term)] : (~ ! [X58 : subst,X57 : term,X59 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ~ ! [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) = $true) | ~ ($true = ((X53 @ id @ X60 @ id)))))) => ! [X61 : term,X62 : (subst > term > subst > $o)] : (~ ! [X63 : subst,X64 : subst,X65 : subst,X66 : term] : (~ (((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) = $true) | ($true = ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)))) | ~ ! [X67 : subst,X68 : subst,X69 : term,X70 : subst] : (~ ($true = ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70))) | ($true = ((X62 @ X67 @ X69 @ (comp @ X68 @ X70))))) | ~ ! [X71 : term] : (~ ($true = ((X62 @ id @ X71 @ id))) | ($true = ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | ~ ! [X72 : (subst > term > term)] : (~ ! [X73 : term] : (~ (((X62 @ id @ X73 @ id)) = $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id)))) | ($true = ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) | ~ ! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))))))) <=> (hoasinduction_lem3_lthm = $true)) & (axmap = $true) & (hoasinduction_lem3a_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (axassoc = $true) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & (pushprop_lem3v2 = $true) & ((! [X81 : term,X82 : subst] : (((sub @ one @ (push @ X81 @ X82))) = X81) => (! [X83 : subst,X84 : term] : (((comp @ sh @ (push @ X84 @ X83))) = X83) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : term,X87 : (term > $o)] : (~ ! [X88 : term] : (~ (((var @ X88)) = $true) | ($true = ((X87 @ X88)))) | ~ ! [X89 : term,X90 : term] : (~ ($true = ((X87 @ X89))) | ~ ($true = ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) | ~ ! [X91 : term] : (($true = ((X87 @ (lam @ X91)))) | ~ (((X87 @ X91)) = $true)) | ($true = ((X87 @ X86)))) => ! [X92 : (term > $o),X93 : term,X94 : subst] : (~ ! [X95 : term] : (~ (((var @ X95)) = $true) | ($true = ((X92 @ (sub @ X95 @ X94))))) | ~ ! [X96 : term] : (~ ! [X97 : term] : (~ ($true = ((X92 @ X97))) | ($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id)))))) | ($true = ((X92 @ (lam @ X96))))) | (((X92 @ (sub @ X93 @ X94))) = $true) | ~ ! [X98 : term,X99 : term] : (~ ($true = ((X92 @ X99))) | ($true = ((X92 @ (ap @ X98 @ X99)))) | ~ (((X92 @ X98)) = $true))))))) <=> (induction2lem_lthm = $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)))))))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X100 : (subst > term > subst > $o)] : ~ ! [X101 : (term > $o)] : ~ ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102)))) & (induction2lem_gthm = $true) & (hoaslamnotap_lthm = $true) & ~ (ulamvar1 = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X103 : (subst > term > subst > $o),X104 : term] : (~ ! [X105 : (subst > term > term)] : (~ ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106)))) | ~ ! [X109 : term] : (~ ($true = ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) | (((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) = $true)) | ($true = ((X103 @ id @ (lam @ X104) @ id))) | ~ ! [X110 : term] : (~ ($true = ((X103 @ id @ X110 @ id))) | ($true = ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id)))))) & ((pushprop_lem1_lthm = $true) <=> (! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) => (! [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) = X114) => ! [X115 : term,X116 : subst,X117 : (term > $o),X118 : term,X119 : (term > $o)] : (~ (((X119 @ X118)) = $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true))))) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) <=> (axshiftcons = $true)) & (hoasinduction_lem3_gthm = $true) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) <=> (substmonoid = $true)) & ((axvarid = $true) <=> ! [X124 : term] : (((sub @ X124 @ id)) = X124)) & ((hoasinduction_lem0 = $true) <=> ! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) <=> (termmset = $true)) & (! [X129 : term] : ~ ! [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) != ((X130 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (substmonoid_gthm = $true) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) <=> (laminj = $true)) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (! [X133 : term,X136 : term,X134 : term,X135 : term] : ((X134 = X136) | (((ap @ X135 @ X134)) != ((ap @ X133 @ X136)))) => ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))))) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) <=> (shinj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) <=> (! [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) = X145) => (! [X148 : term,X147 : term] : ((((lam @ X148)) != ((lam @ X147))) | (X147 = X148)) => ! [X150 : (subst > term > term),X152 : subst,X149 : (subst > term > term),X151 : term] : (~ ! [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X149 @ X154 @ X155) @ X153)) = ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | ~ ! [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) = ((sub @ (X150 @ X157 @ X158) @ X156))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))))))) & ((apinj2 = $true) <=> ! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159))))) & (ulamvarsh = $true) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X163 : term] : ~ ! [X164 : (subst > term > term)] : ~ ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166))))) & (! [X167 : term,X168 : (term > $o),X169 : subst,X170 : term,X171 : (term > $o)] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | ~ (((X171 @ X167)) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (hoasapnotvar = $true) & (axclos = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X174 : (subst > term > subst > $o),X175 : term] : (($true = ((X174 @ id @ X175 @ id))) | ~ ! [X176 : (subst > term > term)] : (~ ! [X177 : term] : (~ ($true = ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) | ~ ! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) | (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true)) | ~ ! [X181 : term,X182 : term] : (~ (((X174 @ id @ X181 @ id)) = $true) | (((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) = $true) | ~ ($true = ((X174 @ id @ X182 @ id)))))) & (one = ((d2term @ d_one))) & ! [X183 : d_term,X184 : d_term] : ((((d2term @ X184)) = ((d2term @ X183))) => (X183 = X184)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X185 : term] : ~ ! [X186 : (subst > term > term)] : ~ ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188))))) & ~ (lamnotap = $true) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) <=> (axscons = $true)) & ((substmonoid_lthm = $true) <=> (! [X190 : subst] : (((comp @ id @ X190)) = X190) => (! [X191 : subst] : (((comp @ X191 @ id)) = X191) => (! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192))))) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) <=> (axidr = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X195 : term] : (((sub @ X195 @ id)) = X195) => ! [X196 : (subst > term > subst > $o),X197 : term,X198 : (term > $o)] : (~ ! [X199 : subst,X200 : subst,X201 : subst,X202 : term] : ((((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) = $true) | ~ (((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true)) | ~ ! [X203 : term] : (((X196 @ id @ X203 @ id)) = ((X198 @ X203))) | ($true = ((X198 @ (lam @ X197)))) | ~ ! [X204 : term] : (~ ($true = ((X198 @ X204))) | (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) = $true)) | ~ ! [X205 : subst,X206 : term,X207 : subst,X208 : subst] : (($true = ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) | ~ (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ~ ! [X209 : (subst > term > term)] : (~ ! [X211 : term,X212 : subst,X210 : subst] : (((X209 @ (comp @ X212 @ X210) @ (sub @ X211 @ X210))) = ((sub @ (X209 @ X212 @ X211) @ X210))) | (((X196 @ id @ (lam @ (X209 @ sh @ one)) @ id)) = $true) | ~ ! [X213 : term] : ((((X196 @ id @ (X209 @ id @ X213) @ id)) = $true) | ~ (((X196 @ id @ X213 @ id)) = $true)))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X214 : term,X215 : (subst > term > subst > $o)] : ((((X215 @ id @ X214 @ id)) = $true) | ~ ! [X216 : term] : (~ ($true = ((var @ (sub @ X216 @ id)))) | ($true = ((X215 @ id @ X216 @ id)))) | ~ ! [X217 : subst,X218 : term,X219 : subst,X220 : subst] : (~ (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true) | ($true = ((X215 @ X220 @ X218 @ (comp @ X219 @ X217))))) | ~ ! [X221 : term,X222 : term] : ((((X215 @ id @ (ap @ (sub @ X222 @ id) @ X221) @ id)) = $true) | ~ (((X215 @ id @ X221 @ id)) = $true) | ~ (((X215 @ id @ X222 @ id)) = $true)) | ~ ! [X223 : term,X224 : subst,X225 : subst,X226 : subst] : (~ ($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) | ($true = ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | ~ ! [X227 : (subst > term > term)] : (~ ! [X230 : subst,X228 : subst,X229 : term] : (((sub @ (X227 @ X228 @ X229) @ X230)) = ((X227 @ (comp @ X228 @ X230) @ (sub @ X229 @ X230)))) | (((X215 @ id @ (lam @ (X227 @ sh @ one)) @ id)) = $true) | ~ ! [X231 : term] : (($true = ((X215 @ id @ (X227 @ id @ X231) @ id))) | ~ (((X215 @ id @ X231 @ id)) = $true)))) <=> (hoasinduction = $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasapnotvar_lthm = $true) & ((! [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) = X233) => ! [X234 : (term > $o),X235 : term,X236 : (term > $o),X237 : subst] : (($true = ((X236 @ one))) | ~ ! [X238 : term] : (((X236 @ X238)) = ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ~ (((X234 @ X235)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (termmset_gthm = $true) & ! [X239 : d_term] : (d_one = X239) & (induction2_gthm = $true) & ((axidl = $true) <=> ! [X240 : subst] : (((comp @ id @ X240)) = X240)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X241 : (term > $o),X242 : term] : (~ ! [X243 : term,X244 : term] : (($true = ((X241 @ (ap @ X243 @ X244)))) | ~ ($true = ((X241 @ X244))) | ~ ($true = ((X241 @ X243)))) | ~ ! [X245 : term] : (~ (((var @ X245)) = $true) | ($true = ((X241 @ X245)))) | ~ ! [X246 : term] : (($true = ((X241 @ (lam @ X246)))) | ~ ! [X247 : term] : (~ ($true = ((X241 @ X247))) | (((X241 @ (sub @ X246 @ (push @ X247 @ id)))) = $true))) | ($true = ((X241 @ X242)))) => (! [X248 : (subst > term > subst > $o),X249 : term,X250 : term] : (~ ! [X251 : term,X252 : term] : (~ ($true = ((X248 @ id @ X251 @ id))) | ($true = ((X248 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id))) | ~ (((X248 @ id @ X252 @ id)) = $true)) | (((X248 @ id @ (ap @ X250 @ X249) @ id)) = $true) | ~ ! [X253 : subst,X254 : term,X255 : subst,X256 : subst] : (($true = ((X248 @ X253 @ X254 @ (comp @ X255 @ X256)))) | ~ (((X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255) @ X256)) = $true)) | ~ ! [X257 : subst,X258 : subst,X259 : term,X260 : subst] : (($true = ((X248 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260) @ X257))) | ~ ($true = ((X248 @ X258 @ X259 @ (comp @ X260 @ X257))))) | ~ ($true = ((X248 @ id @ X250 @ id))) | ~ ($true = ((X248 @ id @ X249 @ id)))) => (! [X261 : term,X262 : (subst > term > subst > $o)] : (~ ! [X263 : subst,X264 : term,X265 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ~ ($true = ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) | (((X262 @ id @ (lam @ X261) @ id)) = $true) | ~ ! [X267 : (subst > term > term)] : (($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | ~ ! [X268 : term] : (~ ($true = ((X262 @ id @ X268 @ id))) | (((X262 @ id @ (X267 @ id @ X268) @ id)) = $true)) | ~ ! [X269 : subst,X270 : subst,X271 : term] : (((X267 @ (comp @ X270 @ X269) @ (sub @ X271 @ X269))) = ((sub @ (X267 @ X270 @ X271) @ X269)))) | ~ ! [X272 : subst,X273 : term,X274 : subst,X275 : subst] : (~ (((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) = $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) | ~ ! [X276 : term] : (($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))) | ~ ($true = ((X262 @ id @ X276 @ id))))) => ! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X279 : term,X280 : term] : ((((X277 @ id @ (ap @ (sub @ X280 @ id) @ X279) @ id)) = $true) | ~ ($true = ((X277 @ id @ X280 @ id))) | ~ (((X277 @ id @ X279 @ id)) = $true)) | ~ ! [X281 : (subst > term > term)] : ((((X277 @ id @ (lam @ (X281 @ sh @ one)) @ id)) = $true) | ~ ! [X283 : subst,X284 : term,X282 : subst] : (((sub @ (X281 @ X283 @ X284) @ X282)) = ((X281 @ (comp @ X283 @ X282) @ (sub @ X284 @ X282)))) | ~ ! [X285 : term] : (~ ($true = ((X277 @ id @ X285 @ id))) | ($true = ((X277 @ id @ (X281 @ id @ X285) @ id))))) | ~ ! [X286 : subst,X287 : term,X288 : subst,X289 : subst] : ((((X277 @ X288 @ X287 @ (comp @ X289 @ X286))) = $true) | ~ ($true = ((X277 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289) @ X286)))) | ~ ! [X290 : subst,X291 : subst,X292 : term,X293 : subst] : (~ ($true = ((X277 @ X291 @ X292 @ (comp @ X293 @ X290)))) | ($true = ((X277 @ (comp @ X291 @ X293) @ (sub @ X292 @ X293) @ X290)))) | ($true = ((X277 @ id @ X278 @ id))) | ~ ! [X294 : term] : ((((X277 @ id @ X294 @ id)) = $true) | ~ ($true = ((var @ (sub @ X294 @ id))))))))) <=> (hoasinduction_lthm = $true)) & (hoasapinj2_gthm = $true) & (! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X297 : (subst > term > term)] : (~ ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300))) | ~ ! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ~ ($true = ((X296 @ id @ X301 @ id)))) | (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)) | ~ ! [X302 : term] : (($true = ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id))) | ~ (((X296 @ id @ X302 @ id)) = $true)) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X303 : term] : (((sub @ X303 @ id)) = X303) => ! [X304 : term] : (((sub @ X304 @ id)) = X304))) & ((hoasinduction_lem3aa = $true) <=> ! [X305 : term,X306 : (subst > term > subst > $o)] : (~ ! [X307 : term] : (~ ($true = ((X306 @ id @ X307 @ id))) | ($true = ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ~ ! [X308 : (subst > term > term)] : (~ ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) | ($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X312 : term] : ((((X306 @ id @ (X308 @ id @ X312) @ id)) = $true) | ~ ($true = ((X306 @ id @ X312 @ id))))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id))))) & (! [X313 : (term > $o),X315 : term,X314 : subst] : ~ ! [X316 : (term > $o)] : ~ ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314))))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X318 : (subst > term > subst > $o),X319 : term,X320 : term,X321 : (term > $o)] : (~ ! [X322 : subst,X323 : term,X324 : subst,X325 : subst] : (~ (((X318 @ X322 @ X323 @ (comp @ X324 @ X325))) = $true) | ($true = ((X318 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324) @ X325)))) | ~ ($true = ((X321 @ X319))) | ~ ! [X326 : term,X327 : term] : (~ ($true = ((X318 @ id @ X327 @ id))) | (((X318 @ id @ (ap @ (sub @ X326 @ id) @ X327) @ id)) = $true) | ~ (((X318 @ id @ X326 @ id)) = $true)) | ~ ! [X328 : subst,X329 : term,X330 : subst,X331 : subst] : (~ ($true = ((X318 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328))) | ($true = ((X318 @ X330 @ X329 @ (comp @ X331 @ X328))))) | ~ ! [X332 : term] : (((X318 @ id @ X332 @ id)) = ((X321 @ X332))) | ($true = ((X321 @ (ap @ X320 @ X319)))) | ~ ($true = ((X321 @ X320)))) <=> (hoasinduction_lem2v2 = $true)) & (pushprop_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336))) & (ulamvarind = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X337 : (term > $o),X338 : (subst > term > subst > $o),X339 : term] : (~ ! [X340 : subst,X341 : subst,X342 : term,X343 : subst] : (~ ($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) | (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) = $true)) | ~ ! [X344 : term] : (($true = ((X337 @ (sub @ X339 @ (push @ X344 @ id))))) | ~ ($true = ((X337 @ X344)))) | ($true = ((X337 @ (lam @ X339)))) | ~ ! [X345 : (subst > term > term)] : (~ ! [X346 : term] : (~ ($true = ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (X345 @ id @ X346) @ id)))) | ~ ! [X348 : subst,X349 : term,X347 : subst] : (((sub @ (X345 @ X348 @ X349) @ X347)) = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347)))) | (((X338 @ id @ (lam @ (X345 @ sh @ one)) @ id)) = $true)) | ~ ! [X350 : subst,X351 : subst,X352 : term,X353 : subst] : (~ (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true) | ($true = ((X338 @ X350 @ X352 @ (comp @ X351 @ X353))))) | ~ ! [X354 : term] : (((X338 @ id @ X354 @ id)) = ((X337 @ X354))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X357 : (subst > term > subst > $o)] : ~ ! [X358 : (term > $o)] : ~ ! [X359 : term] : (((X357 @ id @ X359 @ id)) = ((X358 @ X359))) => (! [X360 : term,X361 : (term > $o)] : (~ ! [X362 : term] : (~ ($true = ((var @ X362))) | (((X361 @ X362)) = $true)) | ~ ! [X363 : term] : (~ ! [X364 : term] : (~ ($true = ((X361 @ X364))) | ($true = ((X361 @ (sub @ X363 @ (push @ X364 @ id)))))) | ($true = ((X361 @ (lam @ X363))))) | (((X361 @ X360)) = $true) | ~ ! [X365 : term,X366 : term] : ((((X361 @ (ap @ X365 @ X366))) = $true) | ~ ($true = ((X361 @ X365))) | ~ (((X361 @ X366)) = $true))) => (! [X367 : term] : (((sub @ X367 @ id)) = X367) => (! [X368 : (subst > term > subst > $o),X369 : term,X370 : (term > $o)] : (~ ! [X371 : (subst > term > term)] : (($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ~ ! [X372 : term] : (~ ($true = ((X368 @ id @ X372 @ id))) | ($true = ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ~ ! [X375 : subst,X374 : subst,X373 : term] : (((sub @ (X371 @ X374 @ X373) @ X375)) = ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) | ~ ! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) | ~ ! [X377 : term] : (~ (((X370 @ X377)) = $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true)) | ($true = ((X370 @ (lam @ X369))))) => ! [X378 : term,X379 : (subst > term > subst > $o)] : (~ ! [X380 : term,X381 : term] : (~ ($true = ((X379 @ id @ X380 @ id))) | ~ ($true = ((X379 @ id @ X381 @ id))) | ($true = ((X379 @ id @ (ap @ (sub @ X380 @ id) @ X381) @ id)))) | ~ ! [X382 : (subst > term > term)] : (~ ! [X383 : subst,X385 : term,X384 : subst] : (((sub @ (X382 @ X383 @ X385) @ X384)) = ((X382 @ (comp @ X383 @ X384) @ (sub @ X385 @ X384)))) | (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ~ ! [X386 : term] : ((((X379 @ id @ (X382 @ id @ X386) @ id)) = $true) | ~ (((X379 @ id @ X386 @ id)) = $true))) | (((X379 @ id @ X378 @ id)) = $true))))))) & (hoasinduction_lem3b_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X387 : term,X388 : subst,X389 : (term > $o),X390 : (term > $o)] : (~ ($true = ((X389 @ X387))) | (((X390 @ one)) = $true) | ~ ! [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) = ((X390 @ X391))))) & ! [X392 : d_subst,X393 : d_subst] : ((((d2subst @ X392)) = ((d2subst @ X393))) => (X392 = X393)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X394 : term] : ~ ! [X395 : (subst > term > term)] : (((X395 @ sh @ one)) != ((sub @ X394 @ (push @ one @ sh))))) & ((hoasinduction_lem2 = $true) <=> ! [X396 : (subst > term > subst > $o),X397 : term,X398 : term] : (~ ! [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (($true = ((X396 @ (comp @ X401 @ X402) @ (sub @ X399 @ X402) @ X400))) | ~ ($true = ((X396 @ X401 @ X399 @ (comp @ X402 @ X400))))) | ~ ! [X403 : term,X404 : term] : (~ ($true = ((X396 @ id @ X403 @ id))) | (((X396 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id)) = $true) | ~ ($true = ((X396 @ id @ X404 @ id)))) | ~ ($true = ((X396 @ id @ X398 @ id))) | (((X396 @ id @ (ap @ X397 @ X398) @ id)) = $true) | ~ ! [X405 : subst,X406 : subst,X407 : term,X408 : subst] : ((((X396 @ X406 @ X407 @ (comp @ X405 @ X408))) = $true) | ~ ($true = ((X396 @ (comp @ X406 @ X405) @ (sub @ X407 @ X405) @ X408)))) | ~ ($true = ((X396 @ id @ X397 @ id))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X411 : (term > $o),X409 : subst,X410 : term] : ~ ! [X412 : (term > $o)] : ~ ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & ((! [X414 : term] : ~ ! [X415 : (subst > term > term)] : ~ ! [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) = ((sub @ X414 @ (push @ X416 @ X417)))) => (! [X418 : term] : (((sub @ X418 @ id)) = X418) => ! [X419 : (term > $o),X420 : term,X421 : (subst > term > subst > $o)] : (~ ! [X422 : term] : (((X421 @ id @ X422 @ id)) = ((X419 @ X422))) | ($true = ((X419 @ (lam @ X420)))) | ~ ! [X423 : term] : (~ ($true = ((X419 @ X423))) | (((X419 @ (sub @ X420 @ (push @ X423 @ id)))) = $true)) | ~ ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ~ ! [X425 : term] : (~ (((X421 @ id @ X425 @ id)) = $true) | ($true = ((X421 @ id @ (X424 @ id @ X425) @ id)))) | ~ ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (lamnotvar = $true) & (! [X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term),X431 : term] : ((((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one)))) | ~ ! [X435 : term,X434 : subst,X433 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) = ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ~ ! [X436 : subst,X438 : term,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) = ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X439 : (term > $o),X440 : (subst > term > subst > $o),X441 : term] : (~ ! [X442 : (subst > term > term)] : ((((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) = $true) | ~ ! [X443 : term] : (~ ($true = ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id)))) | ~ ! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444))))) | ~ ! [X447 : term] : (~ ($true = ((X439 @ X447))) | (((X439 @ (sub @ X441 @ (push @ X447 @ id)))) = $true)) | (((X439 @ (lam @ X441))) = $true) | ~ ! [X448 : term] : (((X439 @ X448)) = ((X440 @ id @ X448 @ id))))) & (! [X449 : term,X450 : (term > $o)] : (~ ! [X451 : term,X452 : term] : (~ ($true = ((X450 @ X451))) | ~ ($true = ((X450 @ X452))) | (((X450 @ (ap @ X451 @ X452))) = $true)) | (((X450 @ X449)) = $true) | ~ ! [X453 : term] : (~ (((var @ X453)) = $true) | (((X450 @ X453)) = $true)) | ~ ! [X454 : term] : ((((X450 @ (lam @ X454))) = $true) | ~ ($true = ((X450 @ X454))))) <=> (induction = $true)) & (pushprop_lthm = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) <=> (axvarcons = $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((apinj1 = $true) <=> ! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460))) & (! [X461 : (subst > term > term),X462 : term,X463 : term] : ((((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463))) | ~ ! [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) = ((sub @ (X461 @ X464 @ X465) @ X466)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_gthm = $true) & (! [X467 : term,X468 : (subst > term > subst > $o)] : (~ ! [X469 : subst,X470 : subst,X471 : subst,X472 : term] : (~ ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471))) | ($true = ((X468 @ X470 @ X472 @ (comp @ X469 @ X471))))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ~ ! [X473 : (subst > term > term)] : (($true = ((X468 @ id @ (lam @ (X473 @ sh @ one)) @ id))) | ~ ! [X476 : term,X474 : subst,X475 : subst] : (((X473 @ (comp @ X474 @ X475) @ (sub @ X476 @ X475))) = ((sub @ (X473 @ X474 @ X476) @ X475))) | ~ ! [X477 : term] : (~ ($true = ((X468 @ id @ X477 @ id))) | ($true = ((X468 @ id @ (X473 @ id @ X477) @ id))))) | ~ ! [X478 : term] : (($true = ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) | ~ ($true = ((X468 @ id @ X478 @ id)))) | ~ ! [X479 : subst,X480 : term,X481 : subst,X482 : subst] : (~ ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481)))) | ($true = ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))))) <=> (hoasinduction_lem3 = $true)) & (hoaslamnotvar = $true) & (hoaslamnotvar_gthm = $true) & ((induction2_lthm = $true) <=> (! [X483 : term] : (((sub @ X483 @ id)) = X483) => (! [X484 : term,X485 : (term > $o),X486 : subst] : (~ ! [X487 : term] : (~ ! [X488 : term] : (($true = ((X485 @ (sub @ X487 @ (push @ X488 @ id))))) | ~ ($true = ((X485 @ X488)))) | (((X485 @ (lam @ X487))) = $true)) | (((X485 @ (sub @ X484 @ X486))) = $true) | ~ ! [X489 : term,X490 : term] : (~ ($true = ((X485 @ X490))) | ($true = ((X485 @ (ap @ X490 @ X489)))) | ~ (((X485 @ X489)) = $true)) | ~ ! [X491 : term] : (($true = ((X485 @ (sub @ X491 @ X486)))) | ~ ($true = ((var @ X491))))) => ! [X492 : (term > $o),X493 : term] : (~ ! [X494 : term] : (~ ! [X495 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X495 @ id))))) | ~ ($true = ((X492 @ X495)))) | ($true = ((X492 @ (lam @ X494))))) | (((X492 @ X493)) = $true) | ~ ! [X496 : term,X497 : term] : (($true = ((X492 @ (ap @ X496 @ X497)))) | ~ ($true = ((X492 @ X496))) | ~ ($true = ((X492 @ X497)))) | ~ ! [X498 : term] : (~ (((var @ X498)) = $true) | (((X492 @ X498)) = $true)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoaslamnotap_gthm = $true) & (! [X499 : term,X500 : (term > $o)] : ((((X500 @ X499)) = $true) | ~ ! [X501 : term] : (~ ($true = ((var @ X501))) | ($true = ((X500 @ X501)))) | ~ ! [X502 : term,X503 : term] : (~ (((X500 @ X502)) = $true) | ($true = ((X500 @ (ap @ X503 @ X502)))) | ~ ($true = ((X500 @ X503)))) | ~ ! [X504 : term] : (~ ! [X505 : term] : ((((X500 @ (sub @ X504 @ (push @ X505 @ id)))) = $true) | ~ ($true = ((X500 @ X505)))) | ($true = ((X500 @ (lam @ X504)))))) <=> (induction2 = $true)) & (! [X506 : (term > $o),X507 : subst,X508 : term] : (~ ! [X509 : term,X510 : term] : (~ ($true = ((X506 @ X509))) | ~ ($true = ((X506 @ X510))) | ($true = ((X506 @ (ap @ X510 @ X509))))) | ($true = ((X506 @ (sub @ X508 @ X507)))) | ~ ! [X511 : term] : ((((X506 @ (sub @ X511 @ X507))) = $true) | ~ ($true = ((var @ X511)))) | ~ ! [X512 : term] : (~ ! [X513 : term] : (~ ($true = ((X506 @ X513))) | ($true = ((X506 @ (sub @ X512 @ (push @ X513 @ id)))))) | ($true = ((X506 @ (lam @ X512)))))) <=> (induction2lem = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X514 : term] : (((sub @ X514 @ id)) = X514) => (! [X515 : term,X516 : (subst > term > subst > $o)] : (~ ! [X517 : term] : (~ (((X516 @ id @ X517 @ id)) = $true) | ($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)))) | ~ ! [X518 : (subst > term > term)] : (~ ! [X519 : subst,X521 : subst,X520 : term] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) = ((sub @ (X518 @ X519 @ X520) @ X521))) | ~ ! [X522 : term] : (~ (((X516 @ id @ X522 @ id)) = $true) | (((X516 @ id @ (X518 @ id @ X522) @ id)) = $true)) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id)))) | (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) = $true)) => ! [X523 : (subst > term > subst > $o),X524 : term] : (~ ! [X525 : (subst > term > term)] : ((((X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) = $true) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X525 @ X526 @ X528) @ X527))) | ~ ! [X529 : term] : (($true = ((X523 @ id @ (X525 @ id @ X529) @ id))) | ~ ($true = ((X523 @ id @ X529 @ id))))) | (((X523 @ id @ (lam @ X524) @ id)) = $true) | ~ ! [X530 : term] : (~ (((X523 @ id @ X530 @ id)) = $true) | (((X523 @ id @ (sub @ X524 @ (push @ X530 @ id)) @ id)) = $true)))))) & (pushprop_gthm = $true) & (hoasapinj1_gthm = $true) & (axapp = $true) & ((! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X535 : term,X532 : term,X534 : term,X533 : term] : ((X534 = X535) | (((ap @ X535 @ X532)) != ((ap @ X534 @ X533)))) => ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem2v2 = $true) & (axabs = $true)),
% 1.38/0.56 inference(rectify,[],[f7])).
% 1.38/0.56 thf(f9,plain,(
% 1.38/0.56 ((hoasinduction_lem3aa_lthm = $true) <=> ! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X302 : term] : ((((X296 @ id @ X302 @ id)) != $true) | ($true = ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X297 : (subst > term > term)] : (~ ! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) | ~ ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300))) | (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)))) & (hoasapnotvar_lthm = $true) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) <=> (substmonoid = $true)) & (apnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axabs = $true) & (! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) <=> (pushprop_lem1 = $true)) & (! [X440 : (subst > term > subst > $o),X439 : (term > $o),X441 : term] : ((((X439 @ (lam @ X441))) = $true) | ~ ! [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) = $true) | ($true != ((X439 @ X447)))) | ~ ! [X442 : (subst > term > term)] : ((((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) = $true) | ~ ! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) | ~ ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ~ ! [X448 : term] : (((X439 @ X448)) = ((X440 @ id @ X448 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem2v2_lthm = $true) & ((axvarid = $true) <=> ! [X124 : term] : (((sub @ X124 @ id)) = X124)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3 = $true) <=> ! [X467 : term,X468 : (subst > term > subst > $o)] : (~ ! [X480 : term,X481 : subst,X479 : subst,X482 : subst] : (($true != ((X468 @ X482 @ X480 @ (comp @ X479 @ X481)))) | ($true = ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481)))) | ~ ! [X470 : subst,X469 : subst,X472 : term,X471 : subst] : (($true != ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471))) | ($true = ((X468 @ X470 @ X472 @ (comp @ X469 @ X471))))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ~ ! [X478 : term] : (($true != ((X468 @ id @ X478 @ id))) | ($true = ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id)))) | ~ ! [X473 : (subst > term > term)] : (~ ! [X477 : term] : (($true != ((X468 @ id @ X477 @ id))) | ($true = ((X468 @ id @ (X473 @ id @ X477) @ id)))) | ($true = ((X468 @ id @ (lam @ (X473 @ sh @ one)) @ id))) | ~ ! [X476 : term,X474 : subst,X475 : subst] : (((X473 @ (comp @ X474 @ X475) @ (sub @ X476 @ X475))) = ((sub @ (X473 @ X474 @ X476) @ X475)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X357 : (subst > term > subst > $o)] : ~ ! [X358 : (term > $o)] : ~ ! [X359 : term] : (((X357 @ id @ X359 @ id)) = ((X358 @ X359))) => (! [X360 : term,X361 : (term > $o)] : (~ ! [X366 : term,X365 : term] : ((((X361 @ X366)) != $true) | (((X361 @ (ap @ X365 @ X366))) = $true) | ($true != ((X361 @ X365)))) | ~ ! [X362 : term] : ((((X361 @ X362)) = $true) | ($true != ((var @ X362)))) | (((X361 @ X360)) = $true) | ~ ! [X363 : term] : (($true = ((X361 @ (lam @ X363)))) | ~ ! [X364 : term] : (($true = ((X361 @ (sub @ X363 @ (push @ X364 @ id))))) | ($true != ((X361 @ X364)))))) => (! [X367 : term] : (((sub @ X367 @ id)) = X367) => (! [X369 : term,X370 : (term > $o),X368 : (subst > term > subst > $o)] : (~ ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true)) | ($true = ((X370 @ (lam @ X369)))) | ~ ! [X371 : (subst > term > term)] : (($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ~ ! [X372 : term] : (($true = ((X368 @ id @ (X371 @ id @ X372) @ id))) | ($true != ((X368 @ id @ X372 @ id)))) | ~ ! [X375 : subst,X374 : subst,X373 : term] : (((sub @ (X371 @ X374 @ X373) @ X375)) = ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) | ~ ! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id)))) => ! [X378 : term,X379 : (subst > term > subst > $o)] : (~ ! [X382 : (subst > term > term)] : ((((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ~ ! [X383 : subst,X385 : term,X384 : subst] : (((sub @ (X382 @ X383 @ X385) @ X384)) = ((X382 @ (comp @ X383 @ X384) @ (sub @ X385 @ X384)))) | ~ ! [X386 : term] : ((((X379 @ id @ X386 @ id)) != $true) | (((X379 @ id @ (X382 @ id @ X386) @ id)) = $true))) | ~ ! [X380 : term,X381 : term] : (($true != ((X379 @ id @ X381 @ id))) | ($true = ((X379 @ id @ (ap @ (sub @ X380 @ id) @ X381) @ id))) | ($true != ((X379 @ id @ X380 @ id)))) | (((X379 @ id @ X378 @ id)) = $true))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasapinj1 = $true) <=> ! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336))) & (termmset_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X414 : term] : ~ ! [X415 : (subst > term > term)] : ~ ! [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) = ((sub @ X414 @ (push @ X416 @ X417)))) => (! [X418 : term] : (((sub @ X418 @ id)) = X418) => ! [X419 : (term > $o),X421 : (subst > term > subst > $o),X420 : term] : (~ ! [X423 : term] : (($true != ((X419 @ X423))) | (((X419 @ (sub @ X420 @ (push @ X423 @ id)))) = $true)) | ~ ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ~ ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) | ~ ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ($true = ((X419 @ (lam @ X420)))) | ~ ! [X422 : term] : (((X421 @ id @ X422 @ id)) = ((X419 @ X422))))))) & (hoaslamnotvar = $true) & ((substmonoid_lthm = $true) <=> (! [X190 : subst] : (((comp @ id @ X190)) = X190) => (! [X191 : subst] : (((comp @ X191 @ id)) = X191) => (! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192))))) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) <=> (shinj = $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X103 : (subst > term > subst > $o),X104 : term] : (~ ! [X110 : term] : (($true = ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))) | ($true != ((X103 @ id @ X110 @ id)))) | ($true = ((X103 @ id @ (lam @ X104) @ id))) | ~ ! [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) = $true) | ~ ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) | ~ ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))))) & (hoasinduction_lem3v2_gthm = $true) & (induction2_gthm = $true) & ! [X392 : d_subst,X393 : d_subst] : ((((d2subst @ X392)) = ((d2subst @ X393))) => (X392 = X393)) & (hoasinduction_lem3b_gthm = $true) & (! [X174 : (subst > term > subst > $o),X175 : term] : (~ ! [X176 : (subst > term > term)] : (~ ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) | (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true) | ~ ! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178))))) | ($true = ((X174 @ id @ X175 @ id))) | ~ ! [X182 : term,X181 : term] : (($true != ((X174 @ id @ X182 @ id))) | (((X174 @ id @ X181 @ id)) != $true) | (((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) <=> (laminj = $true)) & ! [X183 : d_term,X184 : d_term] : ((((d2term @ X184)) = ((d2term @ X183))) => (X183 = X184)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & ((termmset_lthm = $true) <=> (! [X303 : term] : (((sub @ X303 @ id)) = X303) => ! [X304 : term] : (((sub @ X304 @ id)) = X304))) & ((axidl = $true) <=> ! [X240 : subst] : (((comp @ id @ X240)) = X240)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X40 : (subst > term > subst > $o),X39 : term] : (~ ! [X50 : term] : ((((X40 @ id @ X50 @ id)) != $true) | (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) = $true)) | ~ ! [X42 : term,X41 : (subst > term > term)] : (~ ! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) = $true) | ~ ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46))) | ~ ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id))))) | ($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2_lthm = $true) & (! [X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term),X431 : term] : ((((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one)))) | ~ ! [X435 : term,X434 : subst,X433 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) = ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ~ ! [X436 : subst,X438 : term,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) = ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437))))) <=> (hoaslaminj = $true)) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) <=> (axidr = $true)) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (! [X318 : (subst > term > subst > $o),X321 : (term > $o),X319 : term,X320 : term] : (($true != ((X321 @ X320))) | ~ ! [X322 : subst,X323 : term,X324 : subst,X325 : subst] : ((((X318 @ X322 @ X323 @ (comp @ X324 @ X325))) != $true) | ($true = ((X318 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324) @ X325)))) | ($true != ((X321 @ X319))) | ($true = ((X321 @ (ap @ X320 @ X319)))) | ~ ! [X327 : term,X326 : term] : ((((X318 @ id @ X326 @ id)) != $true) | ($true != ((X318 @ id @ X327 @ id))) | (((X318 @ id @ (ap @ (sub @ X326 @ id) @ X327) @ id)) = $true)) | ~ ! [X331 : subst,X328 : subst,X330 : subst,X329 : term] : (($true != ((X318 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328))) | ($true = ((X318 @ X330 @ X329 @ (comp @ X331 @ X328))))) | ~ ! [X332 : term] : (((X318 @ id @ X332 @ id)) = ((X321 @ X332)))) <=> (hoasinduction_lem2v2 = $true)) & ((! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) => (! [X3 : term,X4 : (term > $o)] : (~ ! [X5 : term] : ((((X4 @ (lam @ X5))) = $true) | ~ ! [X6 : term] : ((((X4 @ X6)) != $true) | (((X4 @ (sub @ X5 @ (push @ X6 @ id)))) = $true))) | ~ ! [X9 : term] : (($true = ((X4 @ X9))) | ($true != ((var @ X9)))) | ~ ! [X7 : term,X8 : term] : (($true = ((X4 @ (ap @ X7 @ X8)))) | (((X4 @ X7)) != $true) | (((X4 @ X8)) != $true)) | ($true = ((X4 @ X3)))) => (! [X10 : term] : (((sub @ X10 @ id)) = X10) => (! [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true = ((X12 @ (lam @ X13)))) | ~ ! [X14 : (subst > term > term)] : (~ ! [X18 : subst,X17 : subst,X16 : term] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) | ~ ! [X15 : term] : (($true = ((X11 @ id @ (X14 @ id @ X15) @ id))) | ($true != ((X11 @ id @ X15 @ id)))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) | ~ ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) | ~ ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) => ! [X21 : (subst > term > subst > $o),X22 : term] : (~ ! [X23 : term] : (($true = ((X21 @ id @ X23 @ id))) | (((var @ (sub @ X23 @ id))) != $true)) | ~ ! [X29 : term,X30 : term] : (($true != ((X21 @ id @ X29 @ id))) | (((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) = $true) | (((X21 @ id @ X30 @ id)) != $true)) | ~ ! [X24 : (subst > term > term)] : (~ ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id)))) | ~ ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) | (((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)) | (((X21 @ id @ X22 @ id)) = $true) | ~ ! [X34 : subst,X33 : subst,X32 : subst,X31 : term] : (($true = ((X21 @ X34 @ X31 @ (comp @ X33 @ X32)))) | ($true != ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32)))) | ~ ! [X38 : subst,X37 : term,X36 : subst,X35 : subst] : (($true = ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36))) | ($true != ((X21 @ X35 @ X37 @ (comp @ X38 @ X36)))))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2_gthm = $true) & ! [X239 : d_term] : (d_one = X239) & (hoaslamnotvar_lthm = $true) & ((induction2_lthm = $true) <=> (! [X483 : term] : (((sub @ X483 @ id)) = X483) => (! [X485 : (term > $o),X484 : term,X486 : subst] : (~ ! [X491 : term] : (($true != ((var @ X491))) | ($true = ((X485 @ (sub @ X491 @ X486))))) | ~ ! [X487 : term] : (~ ! [X488 : term] : (($true != ((X485 @ X488))) | ($true = ((X485 @ (sub @ X487 @ (push @ X488 @ id)))))) | (((X485 @ (lam @ X487))) = $true)) | ~ ! [X490 : term,X489 : term] : (($true != ((X485 @ X490))) | (((X485 @ X489)) != $true) | ($true = ((X485 @ (ap @ X490 @ X489))))) | (((X485 @ (sub @ X484 @ X486))) = $true)) => ! [X493 : term,X492 : (term > $o)] : ((((X492 @ X493)) = $true) | ~ ! [X498 : term] : ((((X492 @ X498)) = $true) | (((var @ X498)) != $true)) | ~ ! [X497 : term,X496 : term] : (($true = ((X492 @ (ap @ X496 @ X497)))) | ($true != ((X492 @ X496))) | ($true != ((X492 @ X497)))) | ~ ! [X494 : term] : (~ ! [X495 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X495 @ id))))) | ($true != ((X492 @ X495)))) | ($true = ((X492 @ (lam @ X494))))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X129 : term] : ~ ! [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) != ((X130 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X143 : subst,X144 : term] : (((sub @ one @ (push @ X144 @ X143))) = X144) => (! [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) = X145) => (! [X148 : term,X147 : term] : ((((lam @ X148)) != ((lam @ X147))) | (X147 = X148)) => ! [X150 : (subst > term > term),X152 : subst,X149 : (subst > term > term),X151 : term] : (~ ! [X155 : term,X153 : subst,X154 : subst] : (((sub @ (X149 @ X154 @ X155) @ X153)) = ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | ~ ! [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) = ((sub @ (X150 @ X157 @ X158) @ X156))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))))))) & (hoasapnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X394 : term] : ~ ! [X395 : (subst > term > term)] : (((X395 @ sh @ one)) != ((sub @ X394 @ (push @ one @ sh))))) & ((hoasapinj2_lthm = $true) <=> (! [X133 : term,X136 : term,X134 : term,X135 : term] : ((X134 = X136) | (((ap @ X135 @ X134)) != ((ap @ X133 @ X136)))) => ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))))) & ((! [X195 : term] : (((sub @ X195 @ id)) = X195) => ! [X196 : (subst > term > subst > $o),X198 : (term > $o),X197 : term] : (~ ! [X204 : term] : (($true != ((X198 @ X204))) | (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) = $true)) | ~ ! [X202 : term,X200 : subst,X201 : subst,X199 : subst] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) != $true) | (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ~ ! [X206 : term,X207 : subst,X205 : subst,X208 : subst] : (($true = ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) | (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) != $true)) | ~ ! [X209 : (subst > term > term)] : ((((X196 @ id @ (lam @ (X209 @ sh @ one)) @ id)) = $true) | ~ ! [X213 : term] : ((((X196 @ id @ (X209 @ id @ X213) @ id)) = $true) | (((X196 @ id @ X213 @ id)) != $true)) | ~ ! [X211 : term,X212 : subst,X210 : subst] : (((X209 @ (comp @ X212 @ X210) @ (sub @ X211 @ X210))) = ((sub @ (X209 @ X212 @ X211) @ X210)))) | ~ ! [X203 : term] : (((X196 @ id @ X203 @ id)) = ((X198 @ X203))))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X185 : term] : ~ ! [X186 : (subst > term > term)] : ~ ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188))))) & ((pushprop_lem1_lthm = $true) <=> (! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111) => (! [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) = X114) => ! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true))))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (! [X461 : (subst > term > term),X462 : term,X463 : term] : ((((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463))) | ~ ! [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) = ((sub @ (X461 @ X464 @ X465) @ X466)))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X52 : term] : (((sub @ X52 @ id)) = X52) => (! [X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X56 : (subst > term > term)] : (($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ~ ! [X60 : term] : (($true != ((X53 @ id @ X60 @ id))) | (((X53 @ id @ (X56 @ id @ X60) @ id)) = $true)) | ~ ! [X58 : subst,X57 : term,X59 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59))))) | ~ ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id)))) | ($true = ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id)))) => ! [X61 : term,X62 : (subst > term > subst > $o)] : (~ ! [X72 : (subst > term > term)] : (~ ! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))) | ($true = ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) | ~ ! [X73 : term] : ((((X62 @ id @ X73 @ id)) != $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id))))) | ~ ! [X70 : subst,X68 : subst,X67 : subst,X69 : term] : (($true = ((X62 @ X67 @ X69 @ (comp @ X68 @ X70)))) | ($true != ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | ~ ! [X64 : subst,X65 : subst,X63 : subst,X66 : term] : (($true = ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63))) | (((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) != $true)) | ~ ! [X71 : term] : (($true != ((X62 @ id @ X71 @ id))) | ($true = ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id)))))))) & ((induction2lem_lthm = $true) <=> (! [X81 : term,X82 : subst] : (((sub @ one @ (push @ X81 @ X82))) = X81) => (! [X83 : subst,X84 : term] : (((comp @ sh @ (push @ X84 @ X83))) = X83) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X87 : (term > $o),X86 : term] : (~ ! [X88 : term] : ((((var @ X88)) != $true) | ($true = ((X87 @ X88)))) | ~ ! [X91 : term] : ((((X87 @ X91)) != $true) | ($true = ((X87 @ (lam @ X91))))) | ~ ! [X90 : term,X89 : term] : (($true != ((X87 @ X89))) | ($true != ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) | ($true = ((X87 @ X86)))) => ! [X93 : term,X92 : (term > $o),X94 : subst] : (~ ! [X95 : term] : ((((var @ X95)) != $true) | ($true = ((X92 @ (sub @ X95 @ X94))))) | (((X92 @ (sub @ X93 @ X94))) = $true) | ~ ! [X99 : term,X98 : term] : (($true != ((X92 @ X99))) | ($true = ((X92 @ (ap @ X98 @ X99)))) | (((X92 @ X98)) != $true)) | ~ ! [X96 : term] : (~ ! [X97 : term] : (($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id))))) | ($true != ((X92 @ X97)))) | ($true = ((X92 @ (lam @ X96))))))))))) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) <=> (axscons = $true)) & (hoasapinj2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (! [X313 : (term > $o),X315 : term,X314 : subst] : ~ ! [X316 : (term > $o)] : ~ ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314))))) <=> (pushprop_lem0 = $true)) & ((! [X242 : term,X241 : (term > $o)] : (($true = ((X241 @ X242))) | ~ ! [X244 : term,X243 : term] : (($true != ((X241 @ X244))) | ($true != ((X241 @ X243))) | ($true = ((X241 @ (ap @ X243 @ X244))))) | ~ ! [X246 : term] : (~ ! [X247 : term] : ((((X241 @ (sub @ X246 @ (push @ X247 @ id)))) = $true) | ($true != ((X241 @ X247)))) | ($true = ((X241 @ (lam @ X246))))) | ~ ! [X245 : term] : ((((var @ X245)) != $true) | ($true = ((X241 @ X245))))) => (! [X249 : term,X250 : term,X248 : (subst > term > subst > $o)] : (($true != ((X248 @ id @ X250 @ id))) | (((X248 @ id @ (ap @ X250 @ X249) @ id)) = $true) | ~ ! [X251 : term,X252 : term] : ((((X248 @ id @ X252 @ id)) != $true) | ($true != ((X248 @ id @ X251 @ id))) | ($true = ((X248 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id)))) | ~ ! [X257 : subst,X260 : subst,X258 : subst,X259 : term] : (($true = ((X248 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260) @ X257))) | ($true != ((X248 @ X258 @ X259 @ (comp @ X260 @ X257))))) | ($true != ((X248 @ id @ X249 @ id))) | ~ ! [X256 : subst,X253 : subst,X255 : subst,X254 : term] : ((((X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255) @ X256)) != $true) | ($true = ((X248 @ X253 @ X254 @ (comp @ X255 @ X256)))))) => (! [X262 : (subst > term > subst > $o),X261 : term] : (~ ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id)))) | ~ ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) | ~ ! [X267 : (subst > term > term)] : (~ ! [X268 : term] : ((((X262 @ id @ (X267 @ id @ X268) @ id)) = $true) | ($true != ((X262 @ id @ X268 @ id)))) | ($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | ~ ! [X269 : subst,X270 : subst,X271 : term] : (((X267 @ (comp @ X270 @ X269) @ (sub @ X271 @ X269))) = ((sub @ (X267 @ X270 @ X271) @ X269)))) | (((X262 @ id @ (lam @ X261) @ id)) = $true) | ~ ! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274)))))) => ! [X277 : (subst > term > subst > $o),X278 : term] : (~ ! [X294 : term] : (($true != ((var @ (sub @ X294 @ id)))) | (((X277 @ id @ X294 @ id)) = $true)) | ~ ! [X288 : subst,X286 : subst,X289 : subst,X287 : term] : ((((X277 @ X288 @ X287 @ (comp @ X289 @ X286))) = $true) | ($true != ((X277 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289) @ X286)))) | ~ ! [X290 : subst,X291 : subst,X293 : subst,X292 : term] : (($true = ((X277 @ (comp @ X291 @ X293) @ (sub @ X292 @ X293) @ X290))) | ($true != ((X277 @ X291 @ X292 @ (comp @ X293 @ X290))))) | ~ ! [X281 : (subst > term > term)] : ((((X277 @ id @ (lam @ (X281 @ sh @ one)) @ id)) = $true) | ~ ! [X283 : subst,X284 : term,X282 : subst] : (((sub @ (X281 @ X283 @ X284) @ X282)) = ((X281 @ (comp @ X283 @ X282) @ (sub @ X284 @ X282)))) | ~ ! [X285 : term] : (($true = ((X277 @ id @ (X281 @ id @ X285) @ id))) | ($true != ((X277 @ id @ X285 @ id))))) | ($true = ((X277 @ id @ X278 @ id))) | ~ ! [X279 : term,X280 : term] : (($true != ((X277 @ id @ X280 @ id))) | (((X277 @ id @ X279 @ id)) != $true) | (((X277 @ id @ (ap @ (sub @ X280 @ id) @ X279) @ id)) = $true)))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X125 : (subst > term > subst > $o)] : ~ ! [X126 : (term > $o)] : ~ ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id)))) & ((induction2lem = $true) <=> ! [X508 : term,X507 : subst,X506 : (term > $o)] : (~ ! [X512 : term] : (($true = ((X506 @ (lam @ X512)))) | ~ ! [X513 : term] : (($true = ((X506 @ (sub @ X512 @ (push @ X513 @ id))))) | ($true != ((X506 @ X513))))) | ($true = ((X506 @ (sub @ X508 @ X507)))) | ~ ! [X511 : term] : ((((X506 @ (sub @ X511 @ X507))) = $true) | ($true != ((var @ X511)))) | ~ ! [X510 : term,X509 : term] : (($true = ((X506 @ (ap @ X510 @ X509)))) | ($true != ((X506 @ X509))) | ($true != ((X506 @ X510)))))) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) = X233) => ! [X235 : term,X237 : subst,X234 : (term > $o),X236 : (term > $o)] : ((((X234 @ X235)) != $true) | ($true = ((X236 @ one))) | ~ ! [X238 : term] : (((X236 @ X238)) = ((X234 @ (sub @ X238 @ (push @ X235 @ X237)))))))) & ((hoasinduction_lem2 = $true) <=> ! [X398 : term,X396 : (subst > term > subst > $o),X397 : term] : (($true != ((X396 @ id @ X397 @ id))) | ~ ! [X408 : subst,X406 : subst,X407 : term,X405 : subst] : ((((X396 @ X406 @ X407 @ (comp @ X405 @ X408))) = $true) | ($true != ((X396 @ (comp @ X406 @ X405) @ (sub @ X407 @ X405) @ X408)))) | ~ ! [X399 : term,X401 : subst,X402 : subst,X400 : subst] : (($true = ((X396 @ (comp @ X401 @ X402) @ (sub @ X399 @ X402) @ X400))) | ($true != ((X396 @ X401 @ X399 @ (comp @ X402 @ X400))))) | (((X396 @ id @ (ap @ X397 @ X398) @ id)) = $true) | ($true != ((X396 @ id @ X398 @ id))) | ~ ! [X404 : term,X403 : term] : (($true != ((X396 @ id @ X404 @ id))) | (((X396 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id)) = $true) | ($true != ((X396 @ id @ X403 @ id)))))) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (ulamvar1 != $true) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (((d2subst @ d_id)) = sh) & ((induction2 = $true) <=> ! [X499 : term,X500 : (term > $o)] : (~ ! [X502 : term,X503 : term] : ((((X500 @ X502)) != $true) | ($true = ((X500 @ (ap @ X503 @ X502)))) | ($true != ((X500 @ X503)))) | ~ ! [X501 : term] : (($true = ((X500 @ X501))) | ($true != ((var @ X501)))) | ~ ! [X504 : term] : (($true = ((X500 @ (lam @ X504)))) | ~ ! [X505 : term] : (($true != ((X500 @ X505))) | (((X500 @ (sub @ X504 @ (push @ X505 @ id)))) = $true))) | (((X500 @ X499)) = $true))) & ((! [X531 : term] : (((sub @ X531 @ id)) = X531) => (! [X535 : term,X532 : term,X534 : term,X533 : term] : ((X534 = X535) | (((ap @ X535 @ X532)) != ((ap @ X534 @ X533)))) => ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)))) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (~ ! [X308 : (subst > term > term)] : (($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id))) | ~ ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) | ~ ! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id))) | ~ ! [X307 : term] : (($true = ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id))) | ($true != ((X306 @ id @ X307 @ id))))) <=> (hoasinduction_lem3aa = $true)) & (axmap = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) <=> (axshiftcons = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (axapp = $true) & (lamnotvar = $true) & ((hoasinduction = $true) <=> ! [X215 : (subst > term > subst > $o),X214 : term] : (~ ! [X220 : subst,X219 : subst,X217 : subst,X218 : term] : ((((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) != $true) | ($true = ((X215 @ X220 @ X218 @ (comp @ X219 @ X217))))) | (((X215 @ id @ X214 @ id)) = $true) | ~ ! [X216 : term] : (($true != ((var @ (sub @ X216 @ id)))) | ($true = ((X215 @ id @ X216 @ id)))) | ~ ! [X222 : term,X221 : term] : ((((X215 @ id @ X221 @ id)) != $true) | (((X215 @ id @ X222 @ id)) != $true) | (((X215 @ id @ (ap @ (sub @ X222 @ id) @ X221) @ id)) = $true)) | ~ ! [X223 : term,X225 : subst,X226 : subst,X224 : subst] : (($true = ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225))) | ($true != ((X215 @ X224 @ X223 @ (comp @ X226 @ X225))))) | ~ ! [X227 : (subst > term > term)] : (~ ! [X231 : term] : (($true = ((X215 @ id @ (X227 @ id @ X231) @ id))) | (((X215 @ id @ X231 @ id)) != $true)) | (((X215 @ id @ (lam @ (X227 @ sh @ one)) @ id)) = $true) | ~ ! [X230 : subst,X228 : subst,X229 : term] : (((sub @ (X227 @ X228 @ X229) @ X230)) = ((X227 @ (comp @ X228 @ X230) @ (sub @ X229 @ X230))))))) & (hoaslaminj_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X100 : (subst > term > subst > $o)] : ~ ! [X101 : (term > $o)] : ~ ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102)))) & (! [X449 : term,X450 : (term > $o)] : (~ ! [X453 : term] : ((((var @ X453)) != $true) | (((X450 @ X453)) = $true)) | ~ ! [X454 : term] : ((((X450 @ (lam @ X454))) = $true) | ($true != ((X450 @ X454)))) | ~ ! [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) = $true) | ($true != ((X450 @ X451))) | ($true != ((X450 @ X452)))) | (((X450 @ X449)) = $true)) <=> (induction = $true)) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X411 : (term > $o),X409 : subst,X410 : term] : ~ ! [X412 : (term > $o)] : ~ ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (hoaslamnotap_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X387 : term,X389 : (term > $o),X390 : (term > $o),X388 : subst] : ((((X390 @ one)) = $true) | ~ ! [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) = ((X390 @ X391))) | ($true != ((X389 @ X387))))) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) <=> (termmset = $true)) & (induction2lem_gthm = $true) & ((apinj1 = $true) <=> ! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460))) & ! [X51 : d_subst] : (d_id = X51) & (! [X338 : (subst > term > subst > $o),X337 : (term > $o),X339 : term] : (($true = ((X337 @ (lam @ X339)))) | ~ ! [X344 : term] : (($true != ((X337 @ X344))) | ($true = ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ~ ! [X354 : term] : (((X338 @ id @ X354 @ id)) = ((X337 @ X354))) | ~ ! [X340 : subst,X341 : subst,X342 : term,X343 : subst] : (($true != ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) | (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) = $true)) | ~ ! [X345 : (subst > term > term)] : ((((X338 @ id @ (lam @ (X345 @ sh @ one)) @ id)) = $true) | ~ ! [X348 : subst,X349 : term,X347 : subst] : (((sub @ (X345 @ X348 @ X349) @ X347)) = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347)))) | ~ ! [X346 : term] : (($true != ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (X345 @ id @ X346) @ id))))) | ~ ! [X352 : term,X350 : subst,X353 : subst,X351 : subst] : (($true = ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) | (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = ((push @ (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)))))))))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & ((! [X514 : term] : (((sub @ X514 @ id)) = X514) => (! [X515 : term,X516 : (subst > term > subst > $o)] : (~ ! [X518 : (subst > term > term)] : (($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ~ ! [X519 : subst,X521 : subst,X520 : term] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) = ((sub @ (X518 @ X519 @ X520) @ X521))) | ~ ! [X522 : term] : ((((X516 @ id @ X522 @ id)) != $true) | (((X516 @ id @ (X518 @ id @ X522) @ id)) = $true))) | (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true))) => ! [X523 : (subst > term > subst > $o),X524 : term] : ((((X523 @ id @ (lam @ X524) @ id)) = $true) | ~ ! [X530 : term] : ((((X523 @ id @ X530 @ id)) != $true) | (((X523 @ id @ (sub @ X524 @ (push @ X530 @ id)) @ id)) = $true)) | ~ ! [X525 : (subst > term > term)] : ((((X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) = $true) | ~ ! [X529 : term] : (($true != ((X523 @ id @ X529 @ id))) | ($true = ((X523 @ id @ (X525 @ id @ X529) @ id)))) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X525 @ X526 @ X528) @ X527))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X163 : term] : ~ ! [X164 : (subst > term > term)] : ~ ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166))))) & ((apinj2 = $true) <=> ! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159))))) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) <=> (axvarcons = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true)),
% 1.38/0.56 inference(flattening,[],[f8])).
% 1.38/0.56 thf(f10,plain,(
% 1.38/0.56 ((hoasinduction_lem3aa_lthm = $true) <=> ! [X296 : (subst > term > subst > $o),X295 : term] : (? [X302 : term] : ((((X296 @ id @ X302 @ id)) = $true) & ($true != ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ? [X297 : (subst > term > term)] : (! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) & (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true) & ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300)))))) & (hoasapnotvar_lthm = $true) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) <=> (substmonoid = $true)) & (apnotvar = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axabs = $true) & (! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) <=> (pushprop_lem1 = $true)) & (! [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) = $true) | ? [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) != $true) & ($true = ((X439 @ X447)))) | ? [X442 : (subst > term > term)] : (! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) & (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) != $true) & ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ? [X448 : term] : (((X439 @ X448)) != ((X440 @ id @ X448 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem2v2_lthm = $true) & ((axvarid = $true) <=> ! [X124 : term] : (((sub @ X124 @ id)) = X124)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3 = $true) <=> ! [X468 : (subst > term > subst > $o),X467 : term] : (? [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true != ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) & ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) | ? [X473 : (subst > term > term)] : (! [X476 : term,X474 : subst,X475 : subst] : (((X473 @ (comp @ X474 @ X475) @ (sub @ X476 @ X475))) = ((sub @ (X473 @ X474 @ X476) @ X475))) & ($true != ((X468 @ id @ (lam @ (X473 @ sh @ one)) @ id))) & ! [X477 : term] : (($true != ((X468 @ id @ X477 @ id))) | ($true = ((X468 @ id @ (X473 @ id @ X477) @ id))))) | ? [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true != ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) & ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ? [X478 : term] : (($true != ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) & ($true = ((X468 @ id @ X478 @ id)))))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X378 : term,X379 : (subst > term > subst > $o)] : (? [X382 : (subst > term > term)] : (! [X386 : term] : ((((X379 @ id @ X386 @ id)) != $true) | (((X379 @ id @ (X382 @ id @ X386) @ id)) = $true)) & (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) != $true) & ! [X383 : subst,X385 : term,X384 : subst] : (((sub @ (X382 @ X383 @ X385) @ X384)) = ((X382 @ (comp @ X383 @ X384) @ (sub @ X385 @ X384))))) | ? [X380 : term,X381 : term] : (($true = ((X379 @ id @ X380 @ id))) & ($true = ((X379 @ id @ X381 @ id))) & ($true != ((X379 @ id @ (ap @ (sub @ X380 @ id) @ X381) @ id)))) | (((X379 @ id @ X378 @ id)) = $true)) | ? [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) & ($true != ((X370 @ (lam @ X369)))) & ! [X371 : (subst > term > term)] : (? [X372 : term] : (($true = ((X368 @ id @ X372 @ id))) & ($true != ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ? [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) != ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) & ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true)))) | ? [X367 : term] : (((sub @ X367 @ id)) != X367)) | ? [X361 : (term > $o),X360 : term] : (! [X363 : term] : (($true = ((X361 @ (lam @ X363)))) | ? [X364 : term] : (($true != ((X361 @ (sub @ X363 @ (push @ X364 @ id))))) & ($true = ((X361 @ X364))))) & ! [X362 : term] : ((((X361 @ X362)) = $true) | ($true != ((var @ X362)))) & ! [X366 : term,X365 : term] : ((((X361 @ X366)) != $true) | (((X361 @ (ap @ X365 @ X366))) = $true) | ($true != ((X361 @ X365)))) & (((X361 @ X360)) != $true))) | ? [X357 : (subst > term > subst > $o)] : ! [X358 : (term > $o)] : ? [X359 : term] : (((X357 @ id @ X359 @ id)) != ((X358 @ X359))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasapinj1 = $true) <=> ! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336))) & (termmset_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true = ((X419 @ (lam @ X420)))) | ? [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) != $true) & ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) & ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ? [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) != $true) & ($true = ((X419 @ X423)))) | ? [X422 : term] : (((X421 @ id @ X422 @ id)) != ((X419 @ X422)))) | ? [X418 : term] : (((sub @ X418 @ id)) != X418)) | ? [X414 : term] : ! [X415 : (subst > term > term)] : ? [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) != ((sub @ X414 @ (push @ X416 @ X417)))))) & (hoaslamnotvar = $true) & ((substmonoid_lthm = $true) <=> (((! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | ? [X191 : subst] : (((comp @ X191 @ id)) != X191)) | ? [X190 : subst] : (((comp @ id @ X190)) != X190))) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) <=> (shinj = $true)) & (hoasinduction_gthm = $true) & (! [X103 : (subst > term > subst > $o),X104 : term] : (($true = ((X103 @ id @ (lam @ X104) @ id))) | ? [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) != $true) & ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) & ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) | ? [X110 : term] : (($true = ((X103 @ id @ X110 @ id))) & ($true != ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem3v2_gthm = $true) & (induction2_gthm = $true) & ! [X393 : d_subst,X392 : d_subst] : ((((d2subst @ X392)) != ((d2subst @ X393))) | (X392 = X393)) & (hoasinduction_lem3b_gthm = $true) & (! [X175 : term,X174 : (subst > term > subst > $o)] : (($true = ((X174 @ id @ X175 @ id))) | ? [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) != $true) & ($true = ((X174 @ id @ X182 @ id))) & (((X174 @ id @ X181 @ id)) = $true)) | ? [X176 : (subst > term > term)] : (! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) & (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) <=> (laminj = $true)) & ! [X183 : d_term,X184 : d_term] : ((X183 = X184) | (((d2term @ X184)) != ((d2term @ X183)))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm = $true) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = id) & ((! [X304 : term] : (((sub @ X304 @ id)) = X304) | ? [X303 : term] : (((sub @ X303 @ id)) != X303)) <=> (termmset_lthm = $true)) & ((axidl = $true) <=> ! [X240 : subst] : (((comp @ id @ X240)) = X240)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X40 : (subst > term > subst > $o),X39 : term] : (($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) | ? [X41 : (subst > term > term),X42 : term] : (! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) & ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id)))) & (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) != $true) & ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) | ? [X50 : term] : ((((X40 @ id @ X50 @ id)) = $true) & (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) != $true)))) & (hoasinduction_lem1_lthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2_lthm = $true) & ((hoaslaminj = $true) <=> ! [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (? [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) != ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ? [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) != ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one)))))) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) <=> (axidr = $true)) & (hoasapinj1_gthm = $true) & (ulamvarsh = $true) & (! [X320 : term,X318 : (subst > term > subst > $o),X319 : term,X321 : (term > $o)] : (? [X332 : term] : (((X318 @ id @ X332 @ id)) != ((X321 @ X332))) | ($true != ((X321 @ X319))) | ? [X327 : term,X326 : term] : ((((X318 @ id @ (ap @ (sub @ X326 @ id) @ X327) @ id)) != $true) & (((X318 @ id @ X326 @ id)) = $true) & ($true = ((X318 @ id @ X327 @ id)))) | ($true = ((X321 @ (ap @ X320 @ X319)))) | ? [X323 : term,X322 : subst,X325 : subst,X324 : subst] : ((((X318 @ X322 @ X323 @ (comp @ X324 @ X325))) = $true) & ($true != ((X318 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324) @ X325)))) | ? [X328 : subst,X330 : subst,X331 : subst,X329 : term] : (($true != ((X318 @ X330 @ X329 @ (comp @ X331 @ X328)))) & ($true = ((X318 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328)))) | ($true != ((X321 @ X320)))) <=> (hoasinduction_lem2v2 = $true)) & (((((! [X21 : (subst > term > subst > $o),X22 : term] : (? [X36 : subst,X35 : subst,X38 : subst,X37 : term] : (($true = ((X21 @ X35 @ X37 @ (comp @ X38 @ X36)))) & ($true != ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36)))) | ? [X32 : subst,X33 : subst,X31 : term,X34 : subst] : (($true = ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32))) & ($true != ((X21 @ X34 @ X31 @ (comp @ X33 @ X32))))) | ? [X24 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true) & ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) & ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id))))) | (((X21 @ id @ X22 @ id)) = $true) | ? [X30 : term,X29 : term] : ((((X21 @ id @ X30 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) != $true)) | ? [X23 : term] : ((((var @ (sub @ X23 @ id))) = $true) & ($true != ((X21 @ id @ X23 @ id))))) | ? [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true != ((X12 @ (lam @ X13)))) & ! [X14 : (subst > term > term)] : (? [X15 : term] : (($true = ((X11 @ id @ X15 @ id))) & ($true != ((X11 @ id @ (X14 @ id @ X15) @ id)))) | ? [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) != ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) & ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10)) | ? [X4 : (term > $o),X3 : term] : (($true != ((X4 @ X3))) & ! [X7 : term,X8 : term] : (($true = ((X4 @ (ap @ X7 @ X8)))) | (((X4 @ X7)) != $true) | (((X4 @ X8)) != $true)) & ! [X9 : term] : (($true = ((X4 @ X9))) | ($true != ((var @ X9)))) & ! [X5 : term] : (? [X6 : term] : ((((X4 @ X6)) = $true) & (((X4 @ (sub @ X5 @ (push @ X6 @ id)))) != $true)) | (((X4 @ (lam @ X5))) = $true)))) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2)))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem2v2_gthm = $true) & ! [X239 : d_term] : (d_one = X239) & (hoaslamnotvar_lthm = $true) & ((induction2_lthm = $true) <=> ((! [X492 : (term > $o),X493 : term] : (? [X498 : term] : ((((X492 @ X498)) != $true) & (((var @ X498)) = $true)) | (((X492 @ X493)) = $true) | ? [X494 : term] : (($true != ((X492 @ (lam @ X494)))) & ! [X495 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X495 @ id))))) | ($true != ((X492 @ X495))))) | ? [X496 : term,X497 : term] : (($true = ((X492 @ X497))) & ($true != ((X492 @ (ap @ X496 @ X497)))) & ($true = ((X492 @ X496))))) | ? [X486 : subst,X484 : term,X485 : (term > $o)] : ((((X485 @ (sub @ X484 @ X486))) != $true) & ! [X487 : term] : ((((X485 @ (lam @ X487))) = $true) | ? [X488 : term] : (($true = ((X485 @ X488))) & ($true != ((X485 @ (sub @ X487 @ (push @ X488 @ id))))))) & ! [X490 : term,X489 : term] : (($true != ((X485 @ X490))) | (((X485 @ X489)) != $true) | ($true = ((X485 @ (ap @ X490 @ X489))))) & ! [X491 : term] : (($true != ((var @ X491))) | ($true = ((X485 @ (sub @ X491 @ X486))))))) | ? [X483 : term] : (((sub @ X483 @ id)) != X483))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X129 : term] : ? [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) = ((X130 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((hoaslaminj_lthm = $true) <=> (((! [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (? [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) != ((sub @ (X150 @ X157 @ X158) @ X156))) | ? [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) != ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))) | ? [X147 : term,X148 : term] : ((X147 != X148) & (((lam @ X148)) = ((lam @ X147))))) | ? [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) != X145)) | ? [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) != X144))) & (hoasapnotvar = $true) & (! [X394 : term] : ? [X395 : (subst > term > term)] : (((X395 @ sh @ one)) = ((sub @ X394 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((hoasapinj2_lthm = $true) <=> (? [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) = ((ap @ X133 @ X136))) & (X134 != X136)) | ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (? [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true != ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) & (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ? [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true) & (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) != $true)) | ? [X203 : term] : (((X196 @ id @ X203 @ id)) != ((X198 @ X203))) | ? [X204 : term] : (($true = ((X198 @ X204))) & (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) != $true)) | ? [X209 : (subst > term > term)] : (! [X213 : term] : ((((X196 @ id @ (X209 @ id @ X213) @ id)) = $true) | (((X196 @ id @ X213 @ id)) != $true)) & (((X196 @ id @ (lam @ (X209 @ sh @ one)) @ id)) != $true) & ! [X211 : term,X212 : subst,X210 : subst] : (((X209 @ (comp @ X212 @ X210) @ (sub @ X211 @ X210))) = ((sub @ (X209 @ X212 @ X211) @ X210))))) | ? [X195 : term] : (((sub @ X195 @ id)) != X195))) & (! [X185 : term] : ? [X186 : (subst > term > term)] : ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true)) | ? [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) != X114)) | ? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X463 : term,X461 : (subst > term > term),X462 : term] : (? [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) != ((sub @ (X461 @ X464 @ X465) @ X466))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463))))) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X62 : (subst > term > subst > $o),X61 : term] : (? [X71 : term] : (($true != ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id))) & ($true = ((X62 @ id @ X71 @ id)))) | ? [X63 : subst,X66 : term,X65 : subst,X64 : subst] : ((((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) = $true) & ($true != ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | ? [X72 : (subst > term > term)] : (! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))) & ($true != ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) & ! [X73 : term] : ((((X62 @ id @ X73 @ id)) != $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id))))) | ? [X69 : term,X68 : subst,X67 : subst,X70 : subst] : (($true != ((X62 @ X67 @ X69 @ (comp @ X68 @ X70)))) & ($true = ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70))))) | ? [X54 : term,X53 : (subst > term > subst > $o)] : (($true != ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) & ! [X56 : (subst > term > term)] : (? [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) != ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ? [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) != $true) & ($true = ((X53 @ id @ X60 @ id))))) & ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id)))))) | ? [X52 : term] : (((sub @ X52 @ id)) != X52))) & ((induction2lem_lthm = $true) <=> ((((! [X93 : term,X92 : (term > $o),X94 : subst] : ((((X92 @ (sub @ X93 @ X94))) = $true) | ? [X95 : term] : (($true != ((X92 @ (sub @ X95 @ X94)))) & (((var @ X95)) = $true)) | ? [X98 : term,X99 : term] : ((((X92 @ X98)) = $true) & ($true != ((X92 @ (ap @ X98 @ X99)))) & ($true = ((X92 @ X99)))) | ? [X96 : term] : (! [X97 : term] : (($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id))))) | ($true != ((X92 @ X97)))) & ($true != ((X92 @ (lam @ X96)))))) | ? [X86 : term,X87 : (term > $o)] : (! [X90 : term,X89 : term] : (($true != ((X87 @ X89))) | ($true != ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) & ! [X91 : term] : ((((X87 @ X91)) != $true) | ($true = ((X87 @ (lam @ X91))))) & ! [X88 : term] : ((((var @ X88)) != $true) | ($true = ((X87 @ X88)))) & ($true != ((X87 @ X86))))) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85)) | ? [X84 : term,X83 : subst] : (((comp @ sh @ (push @ X84 @ X83))) != X83)) | ? [X82 : subst,X81 : term] : (((sub @ one @ (push @ X81 @ X82))) != X81))) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) <=> (axscons = $true)) & (hoasapinj2_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0 = $true) <=> ! [X314 : subst,X313 : (term > $o),X315 : term] : ? [X316 : (term > $o)] : ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314)))))) & ((((! [X278 : term,X277 : (subst > term > subst > $o)] : (($true = ((X277 @ id @ X278 @ id))) | ? [X290 : subst,X292 : term,X291 : subst,X293 : subst] : (($true != ((X277 @ (comp @ X291 @ X293) @ (sub @ X292 @ X293) @ X290))) & ($true = ((X277 @ X291 @ X292 @ (comp @ X293 @ X290))))) | ? [X289 : subst,X286 : subst,X287 : term,X288 : subst] : (($true = ((X277 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289) @ X286))) & (((X277 @ X288 @ X287 @ (comp @ X289 @ X286))) != $true)) | ? [X279 : term,X280 : term] : ((((X277 @ id @ (ap @ (sub @ X280 @ id) @ X279) @ id)) != $true) & (((X277 @ id @ X279 @ id)) = $true) & ($true = ((X277 @ id @ X280 @ id)))) | ? [X294 : term] : (($true = ((var @ (sub @ X294 @ id)))) & (((X277 @ id @ X294 @ id)) != $true)) | ? [X281 : (subst > term > term)] : (! [X283 : subst,X284 : term,X282 : subst] : (((sub @ (X281 @ X283 @ X284) @ X282)) = ((X281 @ (comp @ X283 @ X282) @ (sub @ X284 @ X282)))) & (((X277 @ id @ (lam @ (X281 @ sh @ one)) @ id)) != $true) & ! [X285 : term] : (($true = ((X277 @ id @ (X281 @ id @ X285) @ id))) | ($true != ((X277 @ id @ X285 @ id)))))) | ? [X262 : (subst > term > subst > $o),X261 : term] : (! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) & ! [X267 : (subst > term > term)] : (? [X270 : subst,X271 : term,X269 : subst] : (((X267 @ (comp @ X270 @ X269) @ (sub @ X271 @ X269))) != ((sub @ (X267 @ X270 @ X271) @ X269))) | ($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | ? [X268 : term] : (($true = ((X262 @ id @ X268 @ id))) & (((X262 @ id @ (X267 @ id @ X268) @ id)) != $true))) & ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) & (((X262 @ id @ (lam @ X261) @ id)) != $true) & ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id)))))) | ? [X248 : (subst > term > subst > $o),X250 : term,X249 : term] : (! [X257 : subst,X260 : subst,X258 : subst,X259 : term] : (($true = ((X248 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260) @ X257))) | ($true != ((X248 @ X258 @ X259 @ (comp @ X260 @ X257))))) & ! [X256 : subst,X253 : subst,X255 : subst,X254 : term] : ((((X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255) @ X256)) != $true) | ($true = ((X248 @ X253 @ X254 @ (comp @ X255 @ X256))))) & ($true = ((X248 @ id @ X249 @ id))) & ($true = ((X248 @ id @ X250 @ id))) & (((X248 @ id @ (ap @ X250 @ X249) @ id)) != $true) & ! [X251 : term,X252 : term] : ((((X248 @ id @ X252 @ id)) != $true) | ($true != ((X248 @ id @ X251 @ id))) | ($true = ((X248 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id)))))) | ? [X242 : term,X241 : (term > $o)] : (! [X245 : term] : ((((var @ X245)) != $true) | ($true = ((X241 @ X245)))) & ! [X246 : term] : (($true = ((X241 @ (lam @ X246)))) | ? [X247 : term] : ((((X241 @ (sub @ X246 @ (push @ X247 @ id)))) != $true) & ($true = ((X241 @ X247))))) & ! [X244 : term,X243 : term] : (($true != ((X241 @ X244))) | ($true != ((X241 @ X243))) | ($true = ((X241 @ (ap @ X243 @ X244))))) & ($true != ((X241 @ X242))))) <=> (hoasinduction_lthm = $true)) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0 = $true)) & (! [X507 : subst,X508 : term,X506 : (term > $o)] : (? [X509 : term,X510 : term] : (($true = ((X506 @ X510))) & ($true = ((X506 @ X509))) & ($true != ((X506 @ (ap @ X510 @ X509))))) | ? [X512 : term] : (! [X513 : term] : (($true = ((X506 @ (sub @ X512 @ (push @ X513 @ id))))) | ($true != ((X506 @ X513)))) & ($true != ((X506 @ (lam @ X512))))) | ($true = ((X506 @ (sub @ X508 @ X507)))) | ? [X511 : term] : ((((X506 @ (sub @ X511 @ X507))) != $true) & ($true = ((var @ X511))))) <=> (induction2lem = $true)) & (hoasinduction_lem2_lthm = $true) & ((! [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) != $true) | ? [X238 : term] : (((X236 @ X238)) != ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ($true = ((X236 @ one)))) | ? [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) != X233)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X396 : (subst > term > subst > $o),X397 : term,X398 : term] : (($true != ((X396 @ id @ X397 @ id))) | ? [X400 : subst,X401 : subst,X399 : term,X402 : subst] : (($true != ((X396 @ (comp @ X401 @ X402) @ (sub @ X399 @ X402) @ X400))) & ($true = ((X396 @ X401 @ X399 @ (comp @ X402 @ X400))))) | ? [X405 : subst,X408 : subst,X407 : term,X406 : subst] : (($true = ((X396 @ (comp @ X406 @ X405) @ (sub @ X407 @ X405) @ X408))) & (((X396 @ X406 @ X407 @ (comp @ X405 @ X408))) != $true)) | ? [X403 : term,X404 : term] : (($true = ((X396 @ id @ X404 @ id))) & (((X396 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id)) != $true) & ($true = ((X396 @ id @ X403 @ id)))) | ($true != ((X396 @ id @ X398 @ id))) | (((X396 @ id @ (ap @ X397 @ X398) @ id)) = $true))) & (axclos = $true) & (hoasapnotvar_gthm = $true) & (ulamvar1 != $true) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (((d2subst @ d_id)) = sh) & (! [X499 : term,X500 : (term > $o)] : ((((X500 @ X499)) = $true) | ? [X504 : term] : (! [X505 : term] : (($true != ((X500 @ X505))) | (((X500 @ (sub @ X504 @ (push @ X505 @ id)))) = $true)) & ($true != ((X500 @ (lam @ X504))))) | ? [X501 : term] : (($true = ((var @ X501))) & ($true != ((X500 @ X501)))) | ? [X503 : term,X502 : term] : (($true = ((X500 @ X503))) & (((X500 @ X502)) = $true) & ($true != ((X500 @ (ap @ X503 @ X502)))))) <=> (induction2 = $true)) & (((! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)) | ? [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) = ((ap @ X534 @ X533))) & (X534 != X535))) | ? [X531 : term] : (((sub @ X531 @ id)) != X531)) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (? [X307 : term] : (($true = ((X306 @ id @ X307 @ id))) & ($true != ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ? [X308 : (subst > term > term)] : (! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true)) & ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (axmap = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) <=> (axshiftcons = $true)) & (hoasinduction_lem3a_gthm = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (axapp = $true) & (lamnotvar = $true) & ((hoasinduction = $true) <=> ! [X214 : term,X215 : (subst > term > subst > $o)] : (? [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) & ($true != ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | ? [X222 : term,X221 : term] : ((((X215 @ id @ X221 @ id)) = $true) & (((X215 @ id @ (ap @ (sub @ X222 @ id) @ X221) @ id)) != $true) & (((X215 @ id @ X222 @ id)) = $true)) | (((X215 @ id @ X214 @ id)) = $true) | ? [X227 : (subst > term > term)] : (! [X231 : term] : (($true = ((X215 @ id @ (X227 @ id @ X231) @ id))) | (((X215 @ id @ X231 @ id)) != $true)) & (((X215 @ id @ (lam @ (X227 @ sh @ one)) @ id)) != $true) & ! [X230 : subst,X228 : subst,X229 : term] : (((sub @ (X227 @ X228 @ X229) @ X230)) = ((X227 @ (comp @ X228 @ X230) @ (sub @ X229 @ X230))))) | ? [X216 : term] : (($true = ((var @ (sub @ X216 @ id)))) & ($true != ((X215 @ id @ X216 @ id)))) | ? [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true != ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) & (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true)))) & (hoaslaminj_gthm = $true) & (axvarshift = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X100 : (subst > term > subst > $o)] : ? [X101 : (term > $o)] : ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102)))) & ((induction = $true) <=> ! [X450 : (term > $o),X449 : term] : (? [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) != $true) & ($true = ((X450 @ X452))) & ($true = ((X450 @ X451)))) | ? [X454 : term] : (($true = ((X450 @ X454))) & (((X450 @ (lam @ X454))) != $true)) | (((X450 @ X449)) = $true) | ? [X453 : term] : ((((X450 @ X453)) != $true) & (((var @ X453)) = $true)))) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X410 : term,X411 : (term > $o),X409 : subst] : ? [X412 : (term > $o)] : ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (hoaslamnotap_gthm = $true) & (! [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true != ((X389 @ X387))) | (((X390 @ one)) = $true) | ? [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) != ((X390 @ X391)))) <=> (pushprop_lem1v2 = $true)) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) <=> (termmset = $true)) & (induction2lem_gthm = $true) & ((apinj1 = $true) <=> ! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460))) & ! [X51 : d_subst] : (d_id = X51) & (! [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (? [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) & (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) != $true)) | ? [X345 : (subst > term > term)] : ((((X338 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true) & ! [X346 : term] : (($true != ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (X345 @ id @ X346) @ id)))) & ! [X348 : subst,X349 : term,X347 : subst] : (((sub @ (X345 @ X348 @ X349) @ X347)) = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347))))) | ? [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true != ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) & (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true)) | ? [X354 : term] : (((X338 @ id @ X354 @ id)) != ((X337 @ X354))) | ? [X344 : term] : (($true = ((X337 @ X344))) & ($true != ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ($true = ((X337 @ (lam @ X339))))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1_gthm = $true) & (one = ((d2term @ d_one))) & (((d2subst @ d_id)) = ((push @ (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)))))))))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (lamnotap != $true) & (((! [X524 : term,X523 : (subst > term > subst > $o)] : ((((X523 @ id @ (lam @ X524) @ id)) = $true) | ? [X525 : (subst > term > term)] : ((((X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) != $true) & ! [X529 : term] : (($true != ((X523 @ id @ X529 @ id))) | ($true = ((X523 @ id @ (X525 @ id @ X529) @ id)))) & ! [X528 : term,X527 : subst,X526 : subst] : (((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X525 @ X526 @ X528) @ X527)))) | ? [X530 : term] : ((((X523 @ id @ X530 @ id)) = $true) & (((X523 @ id @ (sub @ X524 @ (push @ X530 @ id)) @ id)) != $true))) | ? [X516 : (subst > term > subst > $o),X515 : term] : (! [X518 : (subst > term > term)] : (? [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) != ((sub @ (X518 @ X519 @ X520) @ X521))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ? [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) != $true) & (((X516 @ id @ X522 @ id)) = $true))) & ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true)) & (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) != $true))) | ? [X514 : term] : (((sub @ X514 @ id)) != X514)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1 = $true) & (! [X163 : term] : ? [X164 : (subst > term > term)] : ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166)))) <=> (hoasinduction_lem3v2_f = $true)) & ((apinj2 = $true) <=> ! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159))))) & (hoasinduction_lem2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) <=> (axvarcons = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true)),
% 1.38/0.56 inference(ennf_transformation,[],[f9])).
% 1.38/0.56 thf(f11,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & ((axidl = $true) <=> ! [X240 : subst] : (((comp @ id @ X240)) = X240)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (? [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true != ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) & (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ? [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true) & (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) != $true)) | ? [X203 : term] : (((X196 @ id @ X203 @ id)) != ((X198 @ X203))) | ? [X204 : term] : (($true = ((X198 @ X204))) & (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) != $true)) | ? [X209 : (subst > term > term)] : (! [X213 : term] : ((((X196 @ id @ (X209 @ id @ X213) @ id)) = $true) | (((X196 @ id @ X213 @ id)) != $true)) & (((X196 @ id @ (lam @ (X209 @ sh @ one)) @ id)) != $true) & ! [X211 : term,X212 : subst,X210 : subst] : (((X209 @ (comp @ X212 @ X210) @ (sub @ X211 @ X210))) = ((sub @ (X209 @ X212 @ X211) @ X210))))) | ? [X195 : term] : (((sub @ X195 @ id)) != X195))) & (hoaslamnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X531 : term] : (((sub @ X531 @ id)) != X531) | ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)) | ? [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) = ((ap @ X534 @ X533))) & (X534 != X535)))) & ((hoaslaminj = $true) <=> ! [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (? [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) != ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ? [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) != ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) <=> (axidr = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> ! [X214 : term,X215 : (subst > term > subst > $o)] : (? [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) & ($true != ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | ? [X222 : term,X221 : term] : ((((X215 @ id @ X221 @ id)) = $true) & (((X215 @ id @ (ap @ (sub @ X222 @ id) @ X221) @ id)) != $true) & (((X215 @ id @ X222 @ id)) = $true)) | (((X215 @ id @ X214 @ id)) = $true) | ? [X227 : (subst > term > term)] : (! [X231 : term] : (($true = ((X215 @ id @ (X227 @ id @ X231) @ id))) | (((X215 @ id @ X231 @ id)) != $true)) & (((X215 @ id @ (lam @ (X227 @ sh @ one)) @ id)) != $true) & ! [X230 : subst,X228 : subst,X229 : term] : (((sub @ (X227 @ X228 @ X229) @ X230)) = ((X227 @ (comp @ X228 @ X230) @ (sub @ X229 @ X230))))) | ? [X216 : term] : (($true = ((var @ (sub @ X216 @ id)))) & ($true != ((X215 @ id @ X216 @ id)))) | ? [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true != ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) & (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true)))) & ((? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true != ((X12 @ (lam @ X13)))) & ! [X14 : (subst > term > term)] : (? [X15 : term] : (($true = ((X11 @ id @ X15 @ id))) & ($true != ((X11 @ id @ (X14 @ id @ X15) @ id)))) | ? [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) != ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) & ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) | ! [X21 : (subst > term > subst > $o),X22 : term] : (? [X36 : subst,X35 : subst,X38 : subst,X37 : term] : (($true = ((X21 @ X35 @ X37 @ (comp @ X38 @ X36)))) & ($true != ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36)))) | ? [X32 : subst,X33 : subst,X31 : term,X34 : subst] : (($true = ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32))) & ($true != ((X21 @ X34 @ X31 @ (comp @ X33 @ X32))))) | ? [X24 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true) & ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) & ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id))))) | (((X21 @ id @ X22 @ id)) = $true) | ? [X30 : term,X29 : term] : ((((X21 @ id @ X30 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) != $true)) | ? [X23 : term] : ((((var @ (sub @ X23 @ id))) = $true) & ($true != ((X21 @ id @ X23 @ id))))) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | ? [X4 : (term > $o),X3 : term] : (($true != ((X4 @ X3))) & ! [X7 : term,X8 : term] : (($true = ((X4 @ (ap @ X7 @ X8)))) | (((X4 @ X7)) != $true) | (((X4 @ X8)) != $true)) & ! [X9 : term] : (($true = ((X4 @ X9))) | ($true != ((var @ X9)))) & ! [X5 : term] : (? [X6 : term] : ((((X4 @ X6)) = $true) & (((X4 @ (sub @ X5 @ (push @ X6 @ id)))) != $true)) | (((X4 @ (lam @ X5))) = $true)))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X314 : subst,X313 : (term > $o),X315 : term] : ? [X316 : (term > $o)] : ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314)))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X40 : (subst > term > subst > $o),X39 : term] : (($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) | ? [X41 : (subst > term > term),X42 : term] : (! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) & ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id)))) & (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) != $true) & ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) | ? [X50 : term] : ((((X40 @ id @ X50 @ id)) = $true) & (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) != $true)))) & (pushprop_lem0_gthm = $true) & ((apinj2 = $true) <=> ! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159))))) & (hoasinduction_lem3a_gthm = $true) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & ((apinj1 = $true) <=> ! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460))) & ((! [X524 : term,X523 : (subst > term > subst > $o)] : ((((X523 @ id @ (lam @ X524) @ id)) = $true) | ? [X525 : (subst > term > term)] : ((((X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) != $true) & ! [X529 : term] : (($true != ((X523 @ id @ X529 @ id))) | ($true = ((X523 @ id @ (X525 @ id @ X529) @ id)))) & ! [X528 : term,X527 : subst,X526 : subst] : (((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X525 @ X526 @ X528) @ X527)))) | ? [X530 : term] : ((((X523 @ id @ X530 @ id)) = $true) & (((X523 @ id @ (sub @ X524 @ (push @ X530 @ id)) @ id)) != $true))) | ? [X514 : term] : (((sub @ X514 @ id)) != X514) | ? [X516 : (subst > term > subst > $o),X515 : term] : (! [X518 : (subst > term > term)] : (? [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) != ((sub @ (X518 @ X519 @ X520) @ X521))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ? [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) != $true) & (((X516 @ id @ X522 @ id)) = $true))) & ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true)) & (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) != $true))) <=> (hoasinduction_lem3a_lthm = $true)) & (ulamvarind = $true) & (! [X163 : term] : ? [X164 : (subst > term > term)] : ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) <=> (axvarcons = $true)) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & (! [X103 : (subst > term > subst > $o),X104 : term] : (($true = ((X103 @ id @ (lam @ X104) @ id))) | ? [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) != $true) & ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) & ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) | ? [X110 : term] : (($true = ((X103 @ id @ X110 @ id))) & ($true != ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & ((hoasapinj1 = $true) <=> ! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336))) & ((pushprop_lem1_lthm = $true) <=> (? [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) != X114) | ! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true)) | ? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111))) & ((pushprop_lem0_lthm = $true) <=> ! [X410 : term,X411 : (term > $o),X409 : subst] : ? [X412 : (term > $o)] : ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (apnotvar = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) <=> (? [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) = ((ap @ X133 @ X136))) & (X134 != X136)) | ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X100 : (subst > term > subst > $o)] : ? [X101 : (term > $o)] : ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102)))) & (axclos = $true) & (hoasapinj2_gthm = $true) & (! [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) = $true) | ? [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) != $true) & ($true = ((X439 @ X447)))) | ? [X442 : (subst > term > term)] : (! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) & (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) != $true) & ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ? [X448 : term] : (((X439 @ X448)) != ((X440 @ id @ X448 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) <=> (? [X147 : term,X148 : term] : ((X147 != X148) & (((lam @ X148)) = ((lam @ X147)))) | ! [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (? [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) != ((sub @ (X150 @ X157 @ X158) @ X156))) | ? [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) != ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))) | ? [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) != X145) | ? [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) != X144))) & ((! [X304 : term] : (((sub @ X304 @ id)) = X304) | ? [X303 : term] : (((sub @ X303 @ id)) != X303)) <=> (termmset_lthm = $true)) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X394 : term] : ? [X395 : (subst > term > term)] : (((X395 @ sh @ one)) = ((sub @ X394 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) != $true) | ? [X238 : term] : (((X236 @ X238)) != ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ($true = ((X236 @ one)))) | ? [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) != X233)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X468 : (subst > term > subst > $o),X467 : term] : (? [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true != ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) & ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) | ? [X473 : (subst > term > term)] : (! [X476 : term,X474 : subst,X475 : subst] : (((X473 @ (comp @ X474 @ X475) @ (sub @ X476 @ X475))) = ((sub @ (X473 @ X474 @ X476) @ X475))) & ($true != ((X468 @ id @ (lam @ (X473 @ sh @ one)) @ id))) & ! [X477 : term] : (($true != ((X468 @ id @ X477 @ id))) | ($true = ((X468 @ id @ (X473 @ id @ X477) @ id))))) | ? [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true != ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) & ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ? [X478 : term] : (($true != ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) & ($true = ((X468 @ id @ X478 @ id)))))) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | ? [X191 : subst] : (((comp @ X191 @ id)) != X191) | ? [X190 : subst] : (((comp @ id @ X190)) != X190)) <=> (substmonoid_lthm = $true)) & ((induction2lem_lthm = $true) <=> (? [X82 : subst,X81 : term] : (((sub @ one @ (push @ X81 @ X82))) != X81) | ? [X84 : term,X83 : subst] : (((comp @ sh @ (push @ X84 @ X83))) != X83) | ! [X93 : term,X92 : (term > $o),X94 : subst] : ((((X92 @ (sub @ X93 @ X94))) = $true) | ? [X95 : term] : (($true != ((X92 @ (sub @ X95 @ X94)))) & (((var @ X95)) = $true)) | ? [X98 : term,X99 : term] : ((((X92 @ X98)) = $true) & ($true != ((X92 @ (ap @ X98 @ X99)))) & ($true = ((X92 @ X99)))) | ? [X96 : term] : (! [X97 : term] : (($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id))))) | ($true != ((X92 @ X97)))) & ($true != ((X92 @ (lam @ X96)))))) | ? [X86 : term,X87 : (term > $o)] : (! [X90 : term,X89 : term] : (($true != ((X87 @ X89))) | ($true != ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) & ! [X91 : term] : ((((X87 @ X91)) != $true) | ($true = ((X87 @ (lam @ X91))))) & ! [X88 : term] : ((((var @ X88)) != $true) | ($true = ((X87 @ X88)))) & ($true != ((X87 @ X86)))) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85))) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X414 : term] : ! [X415 : (subst > term > term)] : ? [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) != ((sub @ X414 @ (push @ X416 @ X417)))) | ! [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true = ((X419 @ (lam @ X420)))) | ? [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) != $true) & ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) & ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ? [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) != $true) & ($true = ((X419 @ X423)))) | ? [X422 : term] : (((X421 @ id @ X422 @ id)) != ((X419 @ X422)))) | ? [X418 : term] : (((sub @ X418 @ id)) != X418))) & ((? [X262 : (subst > term > subst > $o),X261 : term] : (! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) & ! [X267 : (subst > term > term)] : (? [X270 : subst,X271 : term,X269 : subst] : (((X267 @ (comp @ X270 @ X269) @ (sub @ X271 @ X269))) != ((sub @ (X267 @ X270 @ X271) @ X269))) | ($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | ? [X268 : term] : (($true = ((X262 @ id @ X268 @ id))) & (((X262 @ id @ (X267 @ id @ X268) @ id)) != $true))) & ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) & (((X262 @ id @ (lam @ X261) @ id)) != $true) & ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) | ? [X242 : term,X241 : (term > $o)] : (! [X245 : term] : ((((var @ X245)) != $true) | ($true = ((X241 @ X245)))) & ! [X246 : term] : (($true = ((X241 @ (lam @ X246)))) | ? [X247 : term] : ((((X241 @ (sub @ X246 @ (push @ X247 @ id)))) != $true) & ($true = ((X241 @ X247))))) & ! [X244 : term,X243 : term] : (($true != ((X241 @ X244))) | ($true != ((X241 @ X243))) | ($true = ((X241 @ (ap @ X243 @ X244))))) & ($true != ((X241 @ X242)))) | ? [X248 : (subst > term > subst > $o),X250 : term,X249 : term] : (! [X257 : subst,X260 : subst,X258 : subst,X259 : term] : (($true = ((X248 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260) @ X257))) | ($true != ((X248 @ X258 @ X259 @ (comp @ X260 @ X257))))) & ! [X256 : subst,X253 : subst,X255 : subst,X254 : term] : ((((X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255) @ X256)) != $true) | ($true = ((X248 @ X253 @ X254 @ (comp @ X255 @ X256))))) & ($true = ((X248 @ id @ X249 @ id))) & ($true = ((X248 @ id @ X250 @ id))) & (((X248 @ id @ (ap @ X250 @ X249) @ id)) != $true) & ! [X251 : term,X252 : term] : ((((X248 @ id @ X252 @ id)) != $true) | ($true != ((X248 @ id @ X251 @ id))) | ($true = ((X248 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id))))) | ! [X278 : term,X277 : (subst > term > subst > $o)] : (($true = ((X277 @ id @ X278 @ id))) | ? [X290 : subst,X292 : term,X291 : subst,X293 : subst] : (($true != ((X277 @ (comp @ X291 @ X293) @ (sub @ X292 @ X293) @ X290))) & ($true = ((X277 @ X291 @ X292 @ (comp @ X293 @ X290))))) | ? [X289 : subst,X286 : subst,X287 : term,X288 : subst] : (($true = ((X277 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289) @ X286))) & (((X277 @ X288 @ X287 @ (comp @ X289 @ X286))) != $true)) | ? [X279 : term,X280 : term] : ((((X277 @ id @ (ap @ (sub @ X280 @ id) @ X279) @ id)) != $true) & (((X277 @ id @ X279 @ id)) = $true) & ($true = ((X277 @ id @ X280 @ id)))) | ? [X294 : term] : (($true = ((var @ (sub @ X294 @ id)))) & (((X277 @ id @ X294 @ id)) != $true)) | ? [X281 : (subst > term > term)] : (! [X283 : subst,X284 : term,X282 : subst] : (((sub @ (X281 @ X283 @ X284) @ X282)) = ((X281 @ (comp @ X283 @ X282) @ (sub @ X284 @ X282)))) & (((X277 @ id @ (lam @ (X281 @ sh @ one)) @ id)) != $true) & ! [X285 : term] : (($true = ((X277 @ id @ (X281 @ id @ X285) @ id))) | ($true != ((X277 @ id @ X285 @ id))))))) <=> (hoasinduction_lthm = $true)) & (! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) <=> (pushprop_lem1 = $true)) & (! [X507 : subst,X508 : term,X506 : (term > $o)] : (? [X509 : term,X510 : term] : (($true = ((X506 @ X510))) & ($true = ((X506 @ X509))) & ($true != ((X506 @ (ap @ X510 @ X509))))) | ? [X512 : term] : (! [X513 : term] : (($true = ((X506 @ (sub @ X512 @ (push @ X513 @ id))))) | ($true != ((X506 @ X513)))) & ($true != ((X506 @ (lam @ X512))))) | ($true = ((X506 @ (sub @ X508 @ X507)))) | ? [X511 : term] : ((((X506 @ (sub @ X511 @ X507))) != $true) & ($true = ((var @ X511))))) <=> (induction2lem = $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)))))))))))) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) <=> (axscons = $true)) & (! [X320 : term,X318 : (subst > term > subst > $o),X319 : term,X321 : (term > $o)] : (? [X332 : term] : (((X318 @ id @ X332 @ id)) != ((X321 @ X332))) | ($true != ((X321 @ X319))) | ? [X327 : term,X326 : term] : ((((X318 @ id @ (ap @ (sub @ X326 @ id) @ X327) @ id)) != $true) & (((X318 @ id @ X326 @ id)) = $true) & ($true = ((X318 @ id @ X327 @ id)))) | ($true = ((X321 @ (ap @ X320 @ X319)))) | ? [X323 : term,X322 : subst,X325 : subst,X324 : subst] : ((((X318 @ X322 @ X323 @ (comp @ X324 @ X325))) = $true) & ($true != ((X318 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324) @ X325)))) | ? [X328 : subst,X330 : subst,X331 : subst,X329 : term] : (($true != ((X318 @ X330 @ X329 @ (comp @ X331 @ X328)))) & ($true = ((X318 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328)))) | ($true != ((X321 @ X320)))) <=> (hoasinduction_lem2v2 = $true)) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0 = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X396 : (subst > term > subst > $o),X397 : term,X398 : term] : (($true != ((X396 @ id @ X397 @ id))) | ? [X400 : subst,X401 : subst,X399 : term,X402 : subst] : (($true != ((X396 @ (comp @ X401 @ X402) @ (sub @ X399 @ X402) @ X400))) & ($true = ((X396 @ X401 @ X399 @ (comp @ X402 @ X400))))) | ? [X405 : subst,X408 : subst,X407 : term,X406 : subst] : (($true = ((X396 @ (comp @ X406 @ X405) @ (sub @ X407 @ X405) @ X408))) & (((X396 @ X406 @ X407 @ (comp @ X405 @ X408))) != $true)) | ? [X403 : term,X404 : term] : (($true = ((X396 @ id @ X404 @ id))) & (((X396 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id)) != $true) & ($true = ((X396 @ id @ X403 @ id)))) | ($true != ((X396 @ id @ X398 @ id))) | (((X396 @ id @ (ap @ X397 @ X398) @ id)) = $true))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X54 : term,X53 : (subst > term > subst > $o)] : (($true != ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) & ! [X56 : (subst > term > term)] : (? [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) != ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ? [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) != $true) & ($true = ((X53 @ id @ X60 @ id))))) & ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id))))) | ? [X52 : term] : (((sub @ X52 @ id)) != X52) | ! [X62 : (subst > term > subst > $o),X61 : term] : (? [X71 : term] : (($true != ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id))) & ($true = ((X62 @ id @ X71 @ id)))) | ? [X63 : subst,X66 : term,X65 : subst,X64 : subst] : ((((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) = $true) & ($true != ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | ? [X72 : (subst > term > term)] : (! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))) & ($true != ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) & ! [X73 : term] : ((((X62 @ id @ X73 @ id)) != $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id))))) | ? [X69 : term,X68 : subst,X67 : subst,X70 : subst] : (($true != ((X62 @ X67 @ X69 @ (comp @ X68 @ X70)))) & ($true = ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70))))))) & (! [X175 : term,X174 : (subst > term > subst > $o)] : (($true = ((X174 @ id @ X175 @ id))) | ? [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) != $true) & ($true = ((X174 @ id @ X182 @ id))) & (((X174 @ id @ X181 @ id)) = $true)) | ? [X176 : (subst > term > term)] : (! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) & (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X185 : term] : ? [X186 : (subst > term > term)] : ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoaslamnotap = $true) <=> ! [X463 : term,X461 : (subst > term > term),X462 : term] : (? [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) != ((sub @ (X461 @ X464 @ X465) @ X466))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463))))) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X296 : (subst > term > subst > $o),X295 : term] : (? [X302 : term] : ((((X296 @ id @ X302 @ id)) = $true) & ($true != ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ? [X297 : (subst > term > term)] : (! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) & (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true) & ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300)))))) & (! [X129 : term] : ? [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) = ((X130 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (((d2subst @ d_id)) = id) & ! [X393 : d_subst,X392 : d_subst] : ((((d2subst @ X392)) != ((d2subst @ X393))) | (X392 = X393)) & ((? [X486 : subst,X484 : term,X485 : (term > $o)] : ((((X485 @ (sub @ X484 @ X486))) != $true) & ! [X487 : term] : ((((X485 @ (lam @ X487))) = $true) | ? [X488 : term] : (($true = ((X485 @ X488))) & ($true != ((X485 @ (sub @ X487 @ (push @ X488 @ id))))))) & ! [X490 : term,X489 : term] : (($true != ((X485 @ X490))) | (((X485 @ X489)) != $true) | ($true = ((X485 @ (ap @ X490 @ X489))))) & ! [X491 : term] : (($true != ((var @ X491))) | ($true = ((X485 @ (sub @ X491 @ X486)))))) | ! [X492 : (term > $o),X493 : term] : (? [X498 : term] : ((((X492 @ X498)) != $true) & (((var @ X498)) = $true)) | (((X492 @ X493)) = $true) | ? [X494 : term] : (($true != ((X492 @ (lam @ X494)))) & ! [X495 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X495 @ id))))) | ($true != ((X492 @ X495))))) | ? [X496 : term,X497 : term] : (($true = ((X492 @ X497))) & ($true != ((X492 @ (ap @ X496 @ X497)))) & ($true = ((X492 @ X496))))) | ? [X483 : term] : (((sub @ X483 @ id)) != X483)) <=> (induction2_lthm = $true)) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (? [X307 : term] : (($true = ((X306 @ id @ X307 @ id))) & ($true != ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ? [X308 : (subst > term > term)] : (! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true)) & ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X378 : term,X379 : (subst > term > subst > $o)] : (? [X382 : (subst > term > term)] : (! [X386 : term] : ((((X379 @ id @ X386 @ id)) != $true) | (((X379 @ id @ (X382 @ id @ X386) @ id)) = $true)) & (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) != $true) & ! [X383 : subst,X385 : term,X384 : subst] : (((sub @ (X382 @ X383 @ X385) @ X384)) = ((X382 @ (comp @ X383 @ X384) @ (sub @ X385 @ X384))))) | ? [X380 : term,X381 : term] : (($true = ((X379 @ id @ X380 @ id))) & ($true = ((X379 @ id @ X381 @ id))) & ($true != ((X379 @ id @ (ap @ (sub @ X380 @ id) @ X381) @ id)))) | (((X379 @ id @ X378 @ id)) = $true)) | ? [X357 : (subst > term > subst > $o)] : ! [X358 : (term > $o)] : ? [X359 : term] : (((X357 @ id @ X359 @ id)) != ((X358 @ X359))) | ? [X361 : (term > $o),X360 : term] : (! [X363 : term] : (($true = ((X361 @ (lam @ X363)))) | ? [X364 : term] : (($true != ((X361 @ (sub @ X363 @ (push @ X364 @ id))))) & ($true = ((X361 @ X364))))) & ! [X362 : term] : ((((X361 @ X362)) = $true) | ($true != ((var @ X362)))) & ! [X366 : term,X365 : term] : ((((X361 @ X366)) != $true) | (((X361 @ (ap @ X365 @ X366))) = $true) | ($true != ((X361 @ X365)))) & (((X361 @ X360)) != $true)) | ? [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) & ($true != ((X370 @ (lam @ X369)))) & ! [X371 : (subst > term > term)] : (? [X372 : term] : (($true = ((X368 @ id @ X372 @ id))) & ($true != ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ? [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) != ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) & ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true))) | ? [X367 : term] : (((sub @ X367 @ id)) != X367)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axvarid = $true) <=> ! [X124 : term] : (((sub @ X124 @ id)) = X124)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) <=> (shinj = $true)) & ((induction = $true) <=> ! [X450 : (term > $o),X449 : term] : (? [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) != $true) & ($true = ((X450 @ X452))) & ($true = ((X450 @ X451)))) | ? [X454 : term] : (($true = ((X450 @ X454))) & (((X450 @ (lam @ X454))) != $true)) | (((X450 @ X449)) = $true) | ? [X453 : term] : ((((X450 @ X453)) != $true) & (((var @ X453)) = $true)))) & (pushprop_lem3v2 = $true) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) <=> (laminj = $true)) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) <=> (substmonoid = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X51 : d_subst] : (d_id = X51) & ! [X239 : d_term] : (d_one = X239) & (hoasinduction_lem2v2_gthm = $true) & (! [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true != ((X389 @ X387))) | (((X390 @ one)) = $true) | ? [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) != ((X390 @ X391)))) <=> (pushprop_lem1v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & (! [X499 : term,X500 : (term > $o)] : ((((X500 @ X499)) = $true) | ? [X504 : term] : (! [X505 : term] : (($true != ((X500 @ X505))) | (((X500 @ (sub @ X504 @ (push @ X505 @ id)))) = $true)) & ($true != ((X500 @ (lam @ X504))))) | ? [X501 : term] : (($true = ((var @ X501))) & ($true != ((X500 @ X501)))) | ? [X503 : term,X502 : term] : (($true = ((X500 @ X503))) & (((X500 @ X502)) = $true) & ($true != ((X500 @ (ap @ X503 @ X502)))))) <=> (induction2 = $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) <=> (axshiftcons = $true)) & (! [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (? [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) & (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) != $true)) | ? [X345 : (subst > term > term)] : ((((X338 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true) & ! [X346 : term] : (($true != ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (X345 @ id @ X346) @ id)))) & ! [X348 : subst,X349 : term,X347 : subst] : (((sub @ (X345 @ X348 @ X349) @ X347)) = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347))))) | ? [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true != ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) & (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true)) | ? [X354 : term] : (((X338 @ id @ X354 @ id)) != ((X337 @ X354))) | ? [X344 : term] : (($true = ((X337 @ X344))) & ($true != ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ($true = ((X337 @ (lam @ X339))))) <=> (hoasinduction_lem3v2 = $true)) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) <=> (termmset = $true)) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X183 : d_term,X184 : d_term] : ((X183 = X184) | (((d2term @ X184)) != ((d2term @ X183)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(flattening,[],[f10])).
% 1.38/0.56 thf(f12,plain,(
% 1.38/0.56 ! [X2 : subst,X3 : term,X0 : (term > $o),X1 : (term > $o)] : ((! [X5 : term] : (((((X0 @ (sub @ X5 @ sh))) = $true) | (((X0 @ X5)) != $true)) | (((var @ X5)) != $true)) | ? [X4 : term] : (($true != ((X1 @ (sub @ X4 @ X2)))) & (((var @ X4)) = $true))) | (((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0)) != $true)) <~> (pushprop_lem2v2 = $true)),
% 1.38/0.56 inference(ennf_transformation,[],[f5])).
% 1.38/0.56 thf(f13,plain,(
% 1.38/0.56 ! [X3 : term,X0 : (term > $o),X1 : (term > $o),X2 : subst] : (! [X5 : term] : ((((X0 @ (sub @ X5 @ sh))) = $true) | (((var @ X5)) != $true) | (((X0 @ X5)) != $true)) | ? [X4 : term] : (($true != ((X1 @ (sub @ X4 @ X2)))) & (((var @ X4)) = $true)) | (((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0)) != $true)) <~> (pushprop_lem2v2 = $true)),
% 1.38/0.56 inference(flattening,[],[f12])).
% 1.38/0.56 thf(f14,definition,(
% 1.38/0.56 ! [X338 : (subst > term > subst > $o)] : (($true = ((sP0 @ X338))) <=> ? [X345 : (subst > term > term)] : ((((X338 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true) & ! [X346 : term] : (($true != ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (X345 @ id @ X346) @ id)))) & ! [X348 : subst,X349 : term,X347 : subst] : (((sub @ (X345 @ X348 @ X349) @ X347)) = ((X345 @ (comp @ X348 @ X347) @ (sub @ X349 @ X347))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f15,definition,(
% 1.38/0.56 ($true = sP1) <=> ! [X499 : term,X500 : (term > $o)] : ((((X500 @ X499)) = $true) | ? [X504 : term] : (! [X505 : term] : (($true != ((X500 @ X505))) | (((X500 @ (sub @ X504 @ (push @ X505 @ id)))) = $true)) & ($true != ((X500 @ (lam @ X504))))) | ? [X501 : term] : (($true = ((var @ X501))) & ($true != ((X500 @ X501)))) | ? [X503 : term,X502 : term] : (($true = ((X500 @ X503))) & (((X500 @ X502)) = $true) & ($true != ((X500 @ (ap @ X503 @ X502))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f16,definition,(
% 1.38/0.56 ($true = sP2) <=> ? [X361 : (term > $o),X360 : term] : (! [X363 : term] : (($true = ((X361 @ (lam @ X363)))) | ? [X364 : term] : (($true != ((X361 @ (sub @ X363 @ (push @ X364 @ id))))) & ($true = ((X361 @ X364))))) & ! [X362 : term] : ((((X361 @ X362)) = $true) | ($true != ((var @ X362)))) & ! [X366 : term,X365 : term] : ((((X361 @ X366)) != $true) | (((X361 @ (ap @ X365 @ X366))) = $true) | ($true != ((X361 @ X365)))) & (((X361 @ X360)) != $true))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f17,definition,(
% 1.38/0.56 ($true = sP3) <=> ! [X378 : term,X379 : (subst > term > subst > $o)] : (? [X382 : (subst > term > term)] : (! [X386 : term] : ((((X379 @ id @ X386 @ id)) != $true) | (((X379 @ id @ (X382 @ id @ X386) @ id)) = $true)) & (((X379 @ id @ (lam @ (X382 @ sh @ one)) @ id)) != $true) & ! [X383 : subst,X385 : term,X384 : subst] : (((sub @ (X382 @ X383 @ X385) @ X384)) = ((X382 @ (comp @ X383 @ X384) @ (sub @ X385 @ X384))))) | ? [X380 : term,X381 : term] : (($true = ((X379 @ id @ X380 @ id))) & ($true = ((X379 @ id @ X381 @ id))) & ($true != ((X379 @ id @ (ap @ (sub @ X380 @ id) @ X381) @ id)))) | (((X379 @ id @ X378 @ id)) = $true))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f18,definition,(
% 1.38/0.56 ($true = sP4) <=> ? [X486 : subst,X484 : term,X485 : (term > $o)] : ((((X485 @ (sub @ X484 @ X486))) != $true) & ! [X487 : term] : ((((X485 @ (lam @ X487))) = $true) | ? [X488 : term] : (($true = ((X485 @ X488))) & ($true != ((X485 @ (sub @ X487 @ (push @ X488 @ id))))))) & ! [X490 : term,X489 : term] : (($true != ((X485 @ X490))) | (((X485 @ X489)) != $true) | ($true = ((X485 @ (ap @ X490 @ X489))))) & ! [X491 : term] : (($true != ((var @ X491))) | ($true = ((X485 @ (sub @ X491 @ X486))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f19,definition,(
% 1.38/0.56 ($true = sP5) <=> (($true = sP4) | ! [X492 : (term > $o),X493 : term] : (? [X498 : term] : ((((X492 @ X498)) != $true) & (((var @ X498)) = $true)) | (((X492 @ X493)) = $true) | ? [X494 : term] : (($true != ((X492 @ (lam @ X494)))) & ! [X495 : term] : (($true = ((X492 @ (sub @ X494 @ (push @ X495 @ id))))) | ($true != ((X492 @ X495))))) | ? [X496 : term,X497 : term] : (($true = ((X492 @ X497))) & ($true != ((X492 @ (ap @ X496 @ X497)))) & ($true = ((X492 @ X496))))) | ? [X483 : term] : (((sub @ X483 @ id)) != X483))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f20,definition,(
% 1.38/0.56 ! [X62 : (subst > term > subst > $o)] : ((((sP6 @ X62)) = $true) <=> ? [X72 : (subst > term > term)] : (! [X75 : term,X76 : subst,X74 : subst] : (((X72 @ (comp @ X76 @ X74) @ (sub @ X75 @ X74))) = ((sub @ (X72 @ X76 @ X75) @ X74))) & ($true != ((X62 @ id @ (lam @ (X72 @ sh @ one)) @ id))) & ! [X73 : term] : ((((X62 @ id @ X73 @ id)) != $true) | ($true = ((X62 @ id @ (X72 @ id @ X73) @ id))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f21,definition,(
% 1.38/0.56 (sP7 = $true) <=> ! [X62 : (subst > term > subst > $o),X61 : term] : (? [X71 : term] : (($true != ((X62 @ id @ (sub @ X61 @ (push @ X71 @ id)) @ id))) & ($true = ((X62 @ id @ X71 @ id)))) | ? [X63 : subst,X66 : term,X65 : subst,X64 : subst] : ((((X62 @ X65 @ X66 @ (comp @ X64 @ X63))) = $true) & ($true != ((X62 @ (comp @ X65 @ X64) @ (sub @ X66 @ X64) @ X63)))) | (((X62 @ id @ (lam @ X61) @ id)) = $true) | (((sP6 @ X62)) = $true) | ? [X69 : term,X68 : subst,X67 : subst,X70 : subst] : (($true != ((X62 @ X67 @ X69 @ (comp @ X68 @ X70)))) & ($true = ((X62 @ (comp @ X67 @ X68) @ (sub @ X69 @ X68) @ X70)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f22,definition,(
% 1.38/0.56 ($true = sP8) <=> ! [X396 : (subst > term > subst > $o),X397 : term,X398 : term] : (($true != ((X396 @ id @ X397 @ id))) | ? [X400 : subst,X401 : subst,X399 : term,X402 : subst] : (($true != ((X396 @ (comp @ X401 @ X402) @ (sub @ X399 @ X402) @ X400))) & ($true = ((X396 @ X401 @ X399 @ (comp @ X402 @ X400))))) | ? [X405 : subst,X408 : subst,X407 : term,X406 : subst] : (($true = ((X396 @ (comp @ X406 @ X405) @ (sub @ X407 @ X405) @ X408))) & (((X396 @ X406 @ X407 @ (comp @ X405 @ X408))) != $true)) | ? [X403 : term,X404 : term] : (($true = ((X396 @ id @ X404 @ id))) & (((X396 @ id @ (ap @ (sub @ X403 @ id) @ X404) @ id)) != $true) & ($true = ((X396 @ id @ X403 @ id)))) | ($true != ((X396 @ id @ X398 @ id))) | (((X396 @ id @ (ap @ X397 @ X398) @ id)) = $true))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f23,definition,(
% 1.38/0.56 ($true = sP9) <=> ! [X320 : term,X318 : (subst > term > subst > $o),X319 : term,X321 : (term > $o)] : (? [X332 : term] : (((X318 @ id @ X332 @ id)) != ((X321 @ X332))) | ($true != ((X321 @ X319))) | ? [X327 : term,X326 : term] : ((((X318 @ id @ (ap @ (sub @ X326 @ id) @ X327) @ id)) != $true) & (((X318 @ id @ X326 @ id)) = $true) & ($true = ((X318 @ id @ X327 @ id)))) | ($true = ((X321 @ (ap @ X320 @ X319)))) | ? [X323 : term,X322 : subst,X325 : subst,X324 : subst] : ((((X318 @ X322 @ X323 @ (comp @ X324 @ X325))) = $true) & ($true != ((X318 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324) @ X325)))) | ? [X328 : subst,X330 : subst,X331 : subst,X329 : term] : (($true != ((X318 @ X330 @ X329 @ (comp @ X331 @ X328)))) & ($true = ((X318 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331) @ X328)))) | ($true != ((X321 @ X320))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f24,definition,(
% 1.38/0.56 ($true = sP10) <=> ! [X507 : subst,X508 : term,X506 : (term > $o)] : (? [X509 : term,X510 : term] : (($true = ((X506 @ X510))) & ($true = ((X506 @ X509))) & ($true != ((X506 @ (ap @ X510 @ X509))))) | ? [X512 : term] : (! [X513 : term] : (($true = ((X506 @ (sub @ X512 @ (push @ X513 @ id))))) | ($true != ((X506 @ X513)))) & ($true != ((X506 @ (lam @ X512))))) | ($true = ((X506 @ (sub @ X508 @ X507)))) | ? [X511 : term] : ((((X506 @ (sub @ X511 @ X507))) != $true) & ($true = ((var @ X511)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f25,definition,(
% 1.38/0.56 ! [X277 : (subst > term > subst > $o)] : (($true = ((sP11 @ X277))) <=> ? [X281 : (subst > term > term)] : (! [X283 : subst,X284 : term,X282 : subst] : (((sub @ (X281 @ X283 @ X284) @ X282)) = ((X281 @ (comp @ X283 @ X282) @ (sub @ X284 @ X282)))) & (((X277 @ id @ (lam @ (X281 @ sh @ one)) @ id)) != $true) & ! [X285 : term] : (($true = ((X277 @ id @ (X281 @ id @ X285) @ id))) | ($true != ((X277 @ id @ X285 @ id))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f26,definition,(
% 1.38/0.56 ! [X277 : (subst > term > subst > $o)] : (($true = ((sP12 @ X277))) <=> ? [X279 : term,X280 : term] : ((((X277 @ id @ (ap @ (sub @ X280 @ id) @ X279) @ id)) != $true) & (((X277 @ id @ X279 @ id)) = $true) & ($true = ((X277 @ id @ X280 @ id)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f27,definition,(
% 1.38/0.56 ! [X262 : (subst > term > subst > $o)] : ((((sP13 @ X262)) = $true) <=> ! [X267 : (subst > term > term)] : (? [X270 : subst,X271 : term,X269 : subst] : (((X267 @ (comp @ X270 @ X269) @ (sub @ X271 @ X269))) != ((sub @ (X267 @ X270 @ X271) @ X269))) | ($true = ((X262 @ id @ (lam @ (X267 @ sh @ one)) @ id))) | ? [X268 : term] : (($true = ((X262 @ id @ X268 @ id))) & (((X262 @ id @ (X267 @ id @ X268) @ id)) != $true))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f28,definition,(
% 1.38/0.56 (sP14 = $true) <=> ? [X248 : (subst > term > subst > $o),X250 : term,X249 : term] : (! [X257 : subst,X260 : subst,X258 : subst,X259 : term] : (($true = ((X248 @ (comp @ X258 @ X260) @ (sub @ X259 @ X260) @ X257))) | ($true != ((X248 @ X258 @ X259 @ (comp @ X260 @ X257))))) & ! [X256 : subst,X253 : subst,X255 : subst,X254 : term] : ((((X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255) @ X256)) != $true) | ($true = ((X248 @ X253 @ X254 @ (comp @ X255 @ X256))))) & ($true = ((X248 @ id @ X249 @ id))) & ($true = ((X248 @ id @ X250 @ id))) & (((X248 @ id @ (ap @ X250 @ X249) @ id)) != $true) & ! [X251 : term,X252 : term] : ((((X248 @ id @ X252 @ id)) != $true) | ($true != ((X248 @ id @ X251 @ id))) | ($true = ((X248 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f29,definition,(
% 1.38/0.56 (sP15 = $true) <=> ? [X242 : term,X241 : (term > $o)] : (! [X245 : term] : ((((var @ X245)) != $true) | ($true = ((X241 @ X245)))) & ! [X246 : term] : (($true = ((X241 @ (lam @ X246)))) | ? [X247 : term] : ((((X241 @ (sub @ X246 @ (push @ X247 @ id)))) != $true) & ($true = ((X241 @ X247))))) & ! [X244 : term,X243 : term] : (($true != ((X241 @ X244))) | ($true != ((X241 @ X243))) | ($true = ((X241 @ (ap @ X243 @ X244))))) & ($true != ((X241 @ X242))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f30,definition,(
% 1.38/0.56 (sP16 = $true) <=> ! [X278 : term,X277 : (subst > term > subst > $o)] : (($true = ((X277 @ id @ X278 @ id))) | ? [X290 : subst,X292 : term,X291 : subst,X293 : subst] : (($true != ((X277 @ (comp @ X291 @ X293) @ (sub @ X292 @ X293) @ X290))) & ($true = ((X277 @ X291 @ X292 @ (comp @ X293 @ X290))))) | ? [X289 : subst,X286 : subst,X287 : term,X288 : subst] : (($true = ((X277 @ (comp @ X288 @ X289) @ (sub @ X287 @ X289) @ X286))) & (((X277 @ X288 @ X287 @ (comp @ X289 @ X286))) != $true)) | ($true = ((sP12 @ X277))) | ? [X294 : term] : (($true = ((var @ (sub @ X294 @ id)))) & (((X277 @ id @ X294 @ id)) != $true)) | ($true = ((sP11 @ X277))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f31,definition,(
% 1.38/0.56 ($true = sP17) <=> ? [X86 : term,X87 : (term > $o)] : (! [X90 : term,X89 : term] : (($true != ((X87 @ X89))) | ($true != ((X87 @ X90))) | ($true = ((X87 @ (ap @ X90 @ X89))))) & ! [X91 : term] : ((((X87 @ X91)) != $true) | ($true = ((X87 @ (lam @ X91))))) & ! [X88 : term] : ((((var @ X88)) != $true) | ($true = ((X87 @ X88)))) & ($true != ((X87 @ X86))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f32,definition,(
% 1.38/0.56 ($true = sP18) <=> (? [X82 : subst,X81 : term] : (((sub @ one @ (push @ X81 @ X82))) != X81) | ? [X84 : term,X83 : subst] : (((comp @ sh @ (push @ X84 @ X83))) != X83) | ! [X93 : term,X92 : (term > $o),X94 : subst] : ((((X92 @ (sub @ X93 @ X94))) = $true) | ? [X95 : term] : (($true != ((X92 @ (sub @ X95 @ X94)))) & (((var @ X95)) = $true)) | ? [X98 : term,X99 : term] : ((((X92 @ X98)) = $true) & ($true != ((X92 @ (ap @ X98 @ X99)))) & ($true = ((X92 @ X99)))) | ? [X96 : term] : (! [X97 : term] : (($true = ((X92 @ (sub @ X96 @ (push @ X97 @ id))))) | ($true != ((X92 @ X97)))) & ($true != ((X92 @ (lam @ X96)))))) | ($true = sP17) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f33,definition,(
% 1.38/0.56 ! [X468 : (subst > term > subst > $o)] : ((((sP19 @ X468)) = $true) <=> ? [X473 : (subst > term > term)] : (! [X476 : term,X474 : subst,X475 : subst] : (((X473 @ (comp @ X474 @ X475) @ (sub @ X476 @ X475))) = ((sub @ (X473 @ X474 @ X476) @ X475))) & ($true != ((X468 @ id @ (lam @ (X473 @ sh @ one)) @ id))) & ! [X477 : term] : (($true != ((X468 @ id @ X477 @ id))) | ($true = ((X468 @ id @ (X473 @ id @ X477) @ id))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f34,definition,(
% 1.38/0.56 ($true = sP20) <=> ! [X524 : term,X523 : (subst > term > subst > $o)] : ((((X523 @ id @ (lam @ X524) @ id)) = $true) | ? [X525 : (subst > term > term)] : ((((X523 @ id @ (lam @ (X525 @ sh @ one)) @ id)) != $true) & ! [X529 : term] : (($true != ((X523 @ id @ X529 @ id))) | ($true = ((X523 @ id @ (X525 @ id @ X529) @ id)))) & ! [X528 : term,X527 : subst,X526 : subst] : (((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X525 @ X526 @ X528) @ X527)))) | ? [X530 : term] : ((((X523 @ id @ X530 @ id)) = $true) & (((X523 @ id @ (sub @ X524 @ (push @ X530 @ id)) @ id)) != $true)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f35,definition,(
% 1.38/0.56 ! [X21 : (subst > term > subst > $o)] : ((((sP21 @ X21)) = $true) <=> ? [X30 : term,X29 : term] : ((((X21 @ id @ X30 @ id)) = $true) & ($true = ((X21 @ id @ X29 @ id))) & (((X21 @ id @ (ap @ (sub @ X29 @ id) @ X30) @ id)) != $true)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f36,definition,(
% 1.38/0.56 ! [X21 : (subst > term > subst > $o)] : (($true = ((sP22 @ X21))) <=> ? [X24 : (subst > term > term)] : ((((X21 @ id @ (lam @ (X24 @ sh @ one)) @ id)) != $true) & ! [X27 : subst,X26 : term,X25 : subst] : (((sub @ (X24 @ X25 @ X26) @ X27)) = ((X24 @ (comp @ X25 @ X27) @ (sub @ X26 @ X27)))) & ! [X28 : term] : ((((X21 @ id @ (X24 @ id @ X28) @ id)) = $true) | ($true != ((X21 @ id @ X28 @ id))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f37,definition,(
% 1.38/0.56 (sP23 = $true) <=> ? [X4 : (term > $o),X3 : term] : (($true != ((X4 @ X3))) & ! [X7 : term,X8 : term] : (($true = ((X4 @ (ap @ X7 @ X8)))) | (((X4 @ X7)) != $true) | (((X4 @ X8)) != $true)) & ! [X9 : term] : (($true = ((X4 @ X9))) | ($true != ((var @ X9)))) & ! [X5 : term] : (? [X6 : term] : ((((X4 @ X6)) = $true) & (((X4 @ (sub @ X5 @ (push @ X6 @ id)))) != $true)) | (((X4 @ (lam @ X5))) = $true)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f38,definition,(
% 1.38/0.56 ($true = sP24) <=> ! [X21 : (subst > term > subst > $o),X22 : term] : (? [X36 : subst,X35 : subst,X38 : subst,X37 : term] : (($true = ((X21 @ X35 @ X37 @ (comp @ X38 @ X36)))) & ($true != ((X21 @ (comp @ X35 @ X38) @ (sub @ X37 @ X38) @ X36)))) | ? [X32 : subst,X33 : subst,X31 : term,X34 : subst] : (($true = ((X21 @ (comp @ X34 @ X33) @ (sub @ X31 @ X33) @ X32))) & ($true != ((X21 @ X34 @ X31 @ (comp @ X33 @ X32))))) | ($true = ((sP22 @ X21))) | (((X21 @ id @ X22 @ id)) = $true) | (((sP21 @ X21)) = $true) | ? [X23 : term] : ((((var @ (sub @ X23 @ id))) = $true) & ($true != ((X21 @ id @ X23 @ id)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f39,definition,(
% 1.38/0.56 ! [X215 : (subst > term > subst > $o)] : ((((sP25 @ X215)) = $true) <=> ? [X227 : (subst > term > term)] : (! [X231 : term] : (($true = ((X215 @ id @ (X227 @ id @ X231) @ id))) | (((X215 @ id @ X231 @ id)) != $true)) & (((X215 @ id @ (lam @ (X227 @ sh @ one)) @ id)) != $true) & ! [X230 : subst,X228 : subst,X229 : term] : (((sub @ (X227 @ X228 @ X229) @ X230)) = ((X227 @ (comp @ X228 @ X230) @ (sub @ X229 @ X230))))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f40,definition,(
% 1.38/0.56 ! [X215 : (subst > term > subst > $o)] : ((((sP26 @ X215)) = $true) <=> ? [X222 : term,X221 : term] : ((((X215 @ id @ X221 @ id)) = $true) & (((X215 @ id @ (ap @ (sub @ X222 @ id) @ X221) @ id)) != $true) & (((X215 @ id @ X222 @ id)) = $true)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f41,definition,(
% 1.38/0.56 ! [X196 : (subst > term > subst > $o)] : ((((sP27 @ X196)) = $true) <=> ? [X209 : (subst > term > term)] : (! [X213 : term] : ((((X196 @ id @ (X209 @ id @ X213) @ id)) = $true) | (((X196 @ id @ X213 @ id)) != $true)) & (((X196 @ id @ (lam @ (X209 @ sh @ one)) @ id)) != $true) & ! [X211 : term,X212 : subst,X210 : subst] : (((X209 @ (comp @ X212 @ X210) @ (sub @ X211 @ X210))) = ((sub @ (X209 @ X212 @ X211) @ X210)))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.38/0.56 thf(f42,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & ((axidl = $true) <=> ! [X240 : subst] : (((comp @ id @ X240)) = X240)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (? [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true != ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) & (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ? [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true) & (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) != $true)) | ? [X203 : term] : (((X196 @ id @ X203 @ id)) != ((X198 @ X203))) | ? [X204 : term] : (($true = ((X198 @ X204))) & (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) != $true)) | (((sP27 @ X196)) = $true)) | ? [X195 : term] : (((sub @ X195 @ id)) != X195))) & (hoaslamnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) <=> (? [X531 : term] : (((sub @ X531 @ id)) != X531) | ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)) | ? [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) = ((ap @ X534 @ X533))) & (X534 != X535)))) & ((hoaslaminj = $true) <=> ! [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (? [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) != ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ? [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) != ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) <=> (axidr = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) <=> ! [X214 : term,X215 : (subst > term > subst > $o)] : (? [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) & ($true != ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | (((sP26 @ X215)) = $true) | (((X215 @ id @ X214 @ id)) = $true) | (((sP25 @ X215)) = $true) | ? [X216 : term] : (($true = ((var @ (sub @ X216 @ id)))) & ($true != ((X215 @ id @ X216 @ id)))) | ? [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true != ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) & (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true)))) & ((? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true != ((X12 @ (lam @ X13)))) & ! [X14 : (subst > term > term)] : (? [X15 : term] : (($true = ((X11 @ id @ X15 @ id))) & ($true != ((X11 @ id @ (X14 @ id @ X15) @ id)))) | ? [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) != ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) & ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) | ($true = sP24) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | (sP23 = $true)) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X314 : subst,X313 : (term > $o),X315 : term] : ? [X316 : (term > $o)] : ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314)))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X40 : (subst > term > subst > $o),X39 : term] : (($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) | ? [X41 : (subst > term > term),X42 : term] : (! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) & ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id)))) & (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) != $true) & ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) | ? [X50 : term] : ((((X40 @ id @ X50 @ id)) = $true) & (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) != $true)))) & (pushprop_lem0_gthm = $true) & ((apinj2 = $true) <=> ! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159))))) & (hoasinduction_lem3a_gthm = $true) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) <=> (hoasapinj2 = $true)) & ((apinj1 = $true) <=> ! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460))) & ((($true = sP20) | ? [X514 : term] : (((sub @ X514 @ id)) != X514) | ? [X516 : (subst > term > subst > $o),X515 : term] : (! [X518 : (subst > term > term)] : (? [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) != ((sub @ (X518 @ X519 @ X520) @ X521))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ? [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) != $true) & (((X516 @ id @ X522 @ id)) = $true))) & ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true)) & (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) != $true))) <=> (hoasinduction_lem3a_lthm = $true)) & (ulamvarind = $true) & (! [X163 : term] : ? [X164 : (subst > term > term)] : ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166)))) <=> (hoasinduction_lem3v2_f = $true)) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) <=> (axvarcons = $true)) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & (! [X103 : (subst > term > subst > $o),X104 : term] : (($true = ((X103 @ id @ (lam @ X104) @ id))) | ? [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) != $true) & ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) & ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) | ? [X110 : term] : (($true = ((X103 @ id @ X110 @ id))) & ($true != ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & ((hoasapinj1 = $true) <=> ! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336))) & ((pushprop_lem1_lthm = $true) <=> (? [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) != X114) | ! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true)) | ? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111))) & ((pushprop_lem0_lthm = $true) <=> ! [X410 : term,X411 : (term > $o),X409 : subst] : ? [X412 : (term > $o)] : ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (apnotvar = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) <=> (? [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) = ((ap @ X133 @ X136))) & (X134 != X136)) | ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X100 : (subst > term > subst > $o)] : ? [X101 : (term > $o)] : ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102)))) & (axclos = $true) & (hoasapinj2_gthm = $true) & (! [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) = $true) | ? [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) != $true) & ($true = ((X439 @ X447)))) | ? [X442 : (subst > term > term)] : (! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) & (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) != $true) & ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ? [X448 : term] : (((X439 @ X448)) != ((X440 @ id @ X448 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) <=> (? [X147 : term,X148 : term] : ((X147 != X148) & (((lam @ X148)) = ((lam @ X147)))) | ! [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (? [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) != ((sub @ (X150 @ X157 @ X158) @ X156))) | ? [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) != ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))) | ? [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) != X145) | ? [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) != X144))) & ((! [X304 : term] : (((sub @ X304 @ id)) = X304) | ? [X303 : term] : (((sub @ X303 @ id)) != X303)) <=> (termmset_lthm = $true)) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X394 : term] : ? [X395 : (subst > term > term)] : (((X395 @ sh @ one)) = ((sub @ X394 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & ((! [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) != $true) | ? [X238 : term] : (((X236 @ X238)) != ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ($true = ((X236 @ one)))) | ? [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) != X233)) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X468 : (subst > term > subst > $o),X467 : term] : (? [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true != ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) & ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) | (((sP19 @ X468)) = $true) | ? [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true != ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) & ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ? [X478 : term] : (($true != ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) & ($true = ((X468 @ id @ X478 @ id)))))) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | ? [X191 : subst] : (((comp @ X191 @ id)) != X191) | ? [X190 : subst] : (((comp @ id @ X190)) != X190)) <=> (substmonoid_lthm = $true)) & ((induction2lem_lthm = $true) <=> ($true = sP18)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X414 : term] : ! [X415 : (subst > term > term)] : ? [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) != ((sub @ X414 @ (push @ X416 @ X417)))) | ! [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true = ((X419 @ (lam @ X420)))) | ? [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) != $true) & ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) & ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ? [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) != $true) & ($true = ((X419 @ X423)))) | ? [X422 : term] : (((X421 @ id @ X422 @ id)) != ((X419 @ X422)))) | ? [X418 : term] : (((sub @ X418 @ id)) != X418))) & ((? [X262 : (subst > term > subst > $o),X261 : term] : (! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) & (((sP13 @ X262)) = $true) & ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) & (((X262 @ id @ (lam @ X261) @ id)) != $true) & ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) | (sP15 = $true) | (sP14 = $true) | (sP16 = $true)) <=> (hoasinduction_lthm = $true)) & (! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) <=> (pushprop_lem1 = $true)) & (($true = sP10) <=> (induction2lem = $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)))))))))))) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) <=> (axscons = $true)) & (($true = sP9) <=> (hoasinduction_lem2v2 = $true)) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) <=> (hoasinduction_lem0 = $true)) & ((hoasinduction_lem2 = $true) <=> ($true = sP8)) & ((hoasinduction_lem3_lthm = $true) <=> (? [X54 : term,X53 : (subst > term > subst > $o)] : (($true != ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) & ! [X56 : (subst > term > term)] : (? [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) != ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ? [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) != $true) & ($true = ((X53 @ id @ X60 @ id))))) & ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id))))) | ? [X52 : term] : (((sub @ X52 @ id)) != X52) | (sP7 = $true))) & (! [X175 : term,X174 : (subst > term > subst > $o)] : (($true = ((X174 @ id @ X175 @ id))) | ? [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) != $true) & ($true = ((X174 @ id @ X182 @ id))) & (((X174 @ id @ X181 @ id)) = $true)) | ? [X176 : (subst > term > term)] : (! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) & (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X185 : term] : ? [X186 : (subst > term > term)] : ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem2v2 = $true) & ((hoaslamnotap = $true) <=> ! [X463 : term,X461 : (subst > term > term),X462 : term] : (? [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) != ((sub @ (X461 @ X464 @ X465) @ X466))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463))))) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X296 : (subst > term > subst > $o),X295 : term] : (? [X302 : term] : ((((X296 @ id @ X302 @ id)) = $true) & ($true != ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ? [X297 : (subst > term > term)] : (! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) & (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true) & ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300)))))) & (! [X129 : term] : ? [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) = ((X130 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (((d2subst @ d_id)) = id) & ! [X393 : d_subst,X392 : d_subst] : ((((d2subst @ X392)) != ((d2subst @ X393))) | (X392 = X393)) & (($true = sP5) <=> (induction2_lthm = $true)) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (? [X307 : term] : (($true = ((X306 @ id @ X307 @ id))) & ($true != ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ? [X308 : (subst > term > term)] : (! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true)) & ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((($true = sP3) | ? [X357 : (subst > term > subst > $o)] : ! [X358 : (term > $o)] : ? [X359 : term] : (((X357 @ id @ X359 @ id)) != ((X358 @ X359))) | ($true = sP2) | ? [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) & ($true != ((X370 @ (lam @ X369)))) & ! [X371 : (subst > term > term)] : (? [X372 : term] : (($true = ((X368 @ id @ X372 @ id))) & ($true != ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ? [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) != ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) & ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true))) | ? [X367 : term] : (((sub @ X367 @ id)) != X367)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axvarid = $true) <=> ! [X124 : term] : (((sub @ X124 @ id)) = X124)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) <=> (shinj = $true)) & ((induction = $true) <=> ! [X450 : (term > $o),X449 : term] : (? [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) != $true) & ($true = ((X450 @ X452))) & ($true = ((X450 @ X451)))) | ? [X454 : term] : (($true = ((X450 @ X454))) & (((X450 @ (lam @ X454))) != $true)) | (((X450 @ X449)) = $true) | ? [X453 : term] : ((((X450 @ X453)) != $true) & (((var @ X453)) = $true)))) & (pushprop_lem3v2 = $true) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) <=> (laminj = $true)) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) <=> (substmonoid = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X51 : d_subst] : (d_id = X51) & ! [X239 : d_term] : (d_one = X239) & (hoasinduction_lem2v2_gthm = $true) & (! [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true != ((X389 @ X387))) | (((X390 @ one)) = $true) | ? [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) != ((X390 @ X391)))) <=> (pushprop_lem1v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & (($true = sP1) <=> (induction2 = $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) <=> (axshiftcons = $true)) & (! [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (? [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) & (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) != $true)) | ($true = ((sP0 @ X338))) | ? [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true != ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) & (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true)) | ? [X354 : term] : (((X338 @ id @ X354 @ id)) != ((X337 @ X354))) | ? [X344 : term] : (($true = ((X337 @ X344))) & ($true != ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ($true = ((X337 @ (lam @ X339))))) <=> (hoasinduction_lem3v2 = $true)) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) <=> (termmset = $true)) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X183 : d_term,X184 : d_term] : ((X183 = X184) | (((d2term @ X184)) != ((d2term @ X183)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(definition_folding,[],[f11,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])).
% 1.38/0.56 thf(f129,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & (((axidl = $true) | ? [X240 : subst] : (((comp @ id @ X240)) != X240)) & (! [X240 : subst] : (((comp @ id @ X240)) = X240) | (axidl != $true))) & (((hoasinduction_lem3v2_lthm = $true) | (? [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (! [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true = ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) | (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) != $true)) & ($true != ((X198 @ (lam @ X197)))) & ! [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) != $true) | (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) = $true)) & ! [X203 : term] : (((X196 @ id @ X203 @ id)) = ((X198 @ X203))) & ! [X204 : term] : (($true != ((X198 @ X204))) | (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) = $true)) & (((sP27 @ X196)) != $true)) & ! [X195 : term] : (((sub @ X195 @ id)) = X195))) & ((! [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (? [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true != ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) & (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ? [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true) & (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) != $true)) | ? [X203 : term] : (((X196 @ id @ X203 @ id)) != ((X198 @ X203))) | ? [X204 : term] : (($true = ((X198 @ X204))) & (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) != $true)) | (((sP27 @ X196)) = $true)) | ? [X195 : term] : (((sub @ X195 @ id)) != X195)) | (hoasinduction_lem3v2_lthm != $true))) & (hoaslamnotvar_lthm = $true) & (((hoasapinj1_lthm = $true) | (! [X531 : term] : (((sub @ X531 @ id)) = X531) & ? [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) = ((ap @ (sub @ X539 @ id) @ X536))) & (X537 != X539)) & ! [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) != ((ap @ X534 @ X533))) | (X534 = X535)))) & ((? [X531 : term] : (((sub @ X531 @ id)) != X531) | ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)) | ? [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) = ((ap @ X534 @ X533))) & (X534 != X535))) | (hoasapinj1_lthm != $true))) & (((hoaslaminj = $true) | ? [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (! [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) = ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) & (((X430 @ X432 @ X431)) != ((X429 @ X432 @ X431))) & ! [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) = ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) & (((lam @ (X429 @ sh @ one))) = ((lam @ (X430 @ sh @ one)))))) & (! [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (? [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) != ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ? [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) != ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one))))) | (hoaslaminj != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((! [X194 : subst] : (((comp @ X194 @ id)) = X194) | (axidr != $true)) & ((axidr = $true) | ? [X194 : subst] : (((comp @ X194 @ id)) != X194))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoasinduction = $true) | ? [X214 : term,X215 : (subst > term > subst > $o)] : (! [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true != ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) | ($true = ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) & (((sP26 @ X215)) != $true) & (((X215 @ id @ X214 @ id)) != $true) & (((sP25 @ X215)) != $true) & ! [X216 : term] : (($true != ((var @ (sub @ X216 @ id)))) | ($true = ((X215 @ id @ X216 @ id)))) & ! [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true = ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) | (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) != $true)))) & (! [X214 : term,X215 : (subst > term > subst > $o)] : (? [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) & ($true != ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | (((sP26 @ X215)) = $true) | (((X215 @ id @ X214 @ id)) = $true) | (((sP25 @ X215)) = $true) | ? [X216 : term] : (($true = ((var @ (sub @ X216 @ id)))) & ($true != ((X215 @ id @ X216 @ id)))) | ? [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true != ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) & (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true))) | (hoasinduction != $true))) & (((? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true != ((X12 @ (lam @ X13)))) & ! [X14 : (subst > term > term)] : (? [X15 : term] : (($true = ((X11 @ id @ X15 @ id))) & ($true != ((X11 @ id @ (X14 @ id @ X15) @ id)))) | ? [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) != ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) & ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) | ($true = sP24) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | (sP23 = $true)) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) & ! [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true = ((X12 @ (lam @ X13)))) | ? [X14 : (subst > term > term)] : (! [X15 : term] : (($true != ((X11 @ id @ X15 @ id))) | ($true = ((X11 @ id @ (X14 @ id @ X15) @ id)))) & ! [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) & ($true != ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) | ? [X19 : term] : (($true != ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) & ($true = ((X12 @ X19)))) | ? [X20 : term] : (((X12 @ X20)) != ((X11 @ id @ X20 @ id)))) & ($true != sP24) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & (sP23 != $true)))) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & (((pushprop_lem0 = $true) | ? [X314 : subst,X313 : (term > $o),X315 : term] : ! [X316 : (term > $o)] : ? [X317 : term] : (((X316 @ X317)) != ((X313 @ (sub @ X317 @ (push @ X315 @ X314)))))) & (! [X314 : subst,X313 : (term > $o),X315 : term] : ? [X316 : (term > $o)] : ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314))))) | (pushprop_lem0 != $true))) & (((hoasinduction_lem3aaa = $true) | ? [X40 : (subst > term > subst > $o),X39 : term] : (($true != ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) & ! [X41 : (subst > term > term),X42 : term] : (? [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) != ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | ? [X49 : term] : (($true != ((X40 @ id @ (X41 @ id @ X49) @ id))) & ($true = ((X40 @ id @ X49 @ id)))) | (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) = $true) | ? [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) != ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) & ! [X50 : term] : ((((X40 @ id @ X50 @ id)) != $true) | (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) = $true)))) & (! [X40 : (subst > term > subst > $o),X39 : term] : (($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) | ? [X41 : (subst > term > term),X42 : term] : (! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) & ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id)))) & (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) != $true) & ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) | ? [X50 : term] : ((((X40 @ id @ X50 @ id)) = $true) & (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) != $true))) | (hoasinduction_lem3aaa != $true))) & (pushprop_lem0_gthm = $true) & (((apinj2 = $true) | ? [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 != X161) & (((ap @ X162 @ X161)) = ((ap @ X160 @ X159))))) & (! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159)))) | (apinj2 != $true))) & (hoasinduction_lem3a_gthm = $true) & ((! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 != X80) & (((ap @ (sub @ X77 @ id) @ X80)) = ((ap @ (sub @ X78 @ id) @ X79)))))) & (((apinj1 = $true) | ? [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) = ((ap @ X459 @ X458))) & (X459 != X460))) & (! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460)) | (apinj1 != $true))) & (((($true = sP20) | ? [X514 : term] : (((sub @ X514 @ id)) != X514) | ? [X516 : (subst > term > subst > $o),X515 : term] : (! [X518 : (subst > term > term)] : (? [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) != ((sub @ (X518 @ X519 @ X520) @ X521))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ? [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) != $true) & (((X516 @ id @ X522 @ id)) = $true))) & ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true)) & (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) != $true))) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP20) & ! [X514 : term] : (((sub @ X514 @ id)) = X514) & ! [X516 : (subst > term > subst > $o),X515 : term] : (? [X518 : (subst > term > term)] : (! [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) = ((sub @ (X518 @ X519 @ X520) @ X521))) & ($true != ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) & ! [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) = $true) | (((X516 @ id @ X522 @ id)) != $true))) | ? [X517 : term] : (($true != ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) & (((X516 @ id @ X517 @ id)) = $true)) | (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) = $true))))) & (ulamvarind = $true) & ((! [X163 : term] : ? [X164 : (subst > term > term)] : ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X163 : term] : ! [X164 : (subst > term > term)] : ? [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) != ((sub @ X163 @ (push @ X165 @ X166)))))) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & ((! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) != X455))) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & ((! [X103 : (subst > term > subst > $o),X104 : term] : (($true = ((X103 @ id @ (lam @ X104) @ id))) | ? [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) != $true) & ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) & ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) | ? [X110 : term] : (($true = ((X103 @ id @ X110 @ id))) & ($true != ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X103 : (subst > term > subst > $o),X104 : term] : (($true != ((X103 @ id @ (lam @ X104) @ id))) & ! [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) = $true) | ? [X109 : term] : (($true = ((X103 @ id @ X109 @ id))) & ($true != ((X103 @ id @ (X105 @ id @ X109) @ id)))) | ? [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) != ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) & ! [X110 : term] : (($true != ((X103 @ id @ X110 @ id))) | ($true = ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))))) & (((hoasapinj1 = $true) | ? [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) = ((ap @ (sub @ X333 @ id) @ X334))) & (X333 != X336))) & (! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336)) | (hoasapinj1 != $true))) & (((pushprop_lem1_lthm = $true) | (! [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) = X114) & ? [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) = $true) & (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) != $true)) & ! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111))) & ((? [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) != X114) | ! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true)) | ? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111)) | (pushprop_lem1_lthm != $true))) & (((pushprop_lem0_lthm = $true) | ? [X410 : term,X411 : (term > $o),X409 : subst] : ! [X412 : (term > $o)] : ? [X413 : term] : (((X412 @ X413)) != ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (! [X410 : term,X411 : (term > $o),X409 : subst] : ? [X412 : (term > $o)] : ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409))))) | (pushprop_lem0_lthm != $true))) & (apnotvar = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (one = ((d2term @ d_one))) & (((hoasapinj2_lthm = $true) | (! [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) != ((ap @ X133 @ X136))) | (X134 = X136)) & ? [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 != X140) & (((ap @ (sub @ X138 @ id) @ X137)) = ((ap @ (sub @ X139 @ id) @ X140)))))) & ((? [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) = ((ap @ X133 @ X136))) & (X134 != X136)) | ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140))))) | (hoasapinj2_lthm != $true))) & (((hoasinduction_lem0_lthm = $true) | ? [X100 : (subst > term > subst > $o)] : ! [X101 : (term > $o)] : ? [X102 : term] : (((X100 @ id @ X102 @ id)) != ((X101 @ X102)))) & (! [X100 : (subst > term > subst > $o)] : ? [X101 : (term > $o)] : ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102))) | (hoasinduction_lem0_lthm != $true))) & (axclos = $true) & (hoasapinj2_gthm = $true) & ((! [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) = $true) | ? [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) != $true) & ($true = ((X439 @ X447)))) | ? [X442 : (subst > term > term)] : (! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) & (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) != $true) & ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ? [X448 : term] : (((X439 @ X448)) != ((X440 @ id @ X448 @ id)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) != $true) & ! [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) = $true) | ($true != ((X439 @ X447)))) & ! [X442 : (subst > term > term)] : (? [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) != ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) | (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) = $true) | ? [X443 : term] : (($true = ((X440 @ id @ X443 @ id))) & ($true != ((X440 @ id @ (X442 @ id @ X443) @ id))))) & ! [X448 : term] : (((X439 @ X448)) = ((X440 @ id @ X448 @ id)))))) & (axvarshift = $true) & (((hoaslaminj_lthm = $true) | (! [X147 : term,X148 : term] : ((X147 = X148) | (((lam @ X148)) != ((lam @ X147)))) & ? [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (! [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) = ((sub @ (X150 @ X157 @ X158) @ X156))) & ! [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) = ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) & (((X150 @ X152 @ X151)) != ((X149 @ X152 @ X151))) & (((lam @ (X149 @ sh @ one))) = ((lam @ (X150 @ sh @ one))))) & ! [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) = X145) & ! [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) = X144))) & ((? [X147 : term,X148 : term] : ((X147 != X148) & (((lam @ X148)) = ((lam @ X147)))) | ! [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (? [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) != ((sub @ (X150 @ X157 @ X158) @ X156))) | ? [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) != ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))) | ? [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) != X145) | ? [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) != X144)) | (hoaslaminj_lthm != $true))) & (((! [X304 : term] : (((sub @ X304 @ id)) = X304) | ? [X303 : term] : (((sub @ X303 @ id)) != X303)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X304 : term] : (((sub @ X304 @ id)) != X304) & ! [X303 : term] : (((sub @ X303 @ id)) = X303)))) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((! [X394 : term] : ? [X395 : (subst > term > term)] : (((X395 @ sh @ one)) = ((sub @ X394 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X394 : term] : ! [X395 : (subst > term > term)] : (((X395 @ sh @ one)) != ((sub @ X394 @ (push @ one @ sh)))))) & (((! [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) != $true) | ? [X238 : term] : (((X236 @ X238)) != ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ($true = ((X236 @ one)))) | ? [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) != X233)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) = $true) & ! [X238 : term] : (((X236 @ X238)) = ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) & ($true != ((X236 @ one)))) & ! [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) = X233)))) & (((hoasinduction_lem3 = $true) | ? [X468 : (subst > term > subst > $o),X467 : term] : (! [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true = ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) | ($true != ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) & (((sP19 @ X468)) != $true) & ! [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true = ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) | ($true != ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) & (((X468 @ id @ (lam @ X467) @ id)) != $true) & ! [X478 : term] : (($true = ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) | ($true != ((X468 @ id @ X478 @ id)))))) & (! [X468 : (subst > term > subst > $o),X467 : term] : (? [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true != ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) & ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) | (((sP19 @ X468)) = $true) | ? [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true != ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) & ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ? [X478 : term] : (($true != ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) & ($true = ((X468 @ id @ X478 @ id))))) | (hoasinduction_lem3 != $true))) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((((! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | ? [X191 : subst] : (((comp @ X191 @ id)) != X191) | ? [X190 : subst] : (((comp @ id @ X190)) != X190)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X193 : subst] : (((comp @ id @ X193)) != X193) | ? [X192 : subst] : (((comp @ X192 @ id)) != X192)) & ! [X191 : subst] : (((comp @ X191 @ id)) = X191) & ! [X190 : subst] : (((comp @ id @ X190)) = X190)))) & (((induction2lem_lthm = $true) | ($true != sP18)) & (($true = sP18) | (induction2lem_lthm != $true))) & (hoasinduction_lem2_gthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | (! [X414 : term] : ? [X415 : (subst > term > term)] : ! [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) = ((sub @ X414 @ (push @ X416 @ X417)))) & ? [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true != ((X419 @ (lam @ X420)))) & ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) != ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) | ? [X425 : term] : (($true != ((X421 @ id @ (X424 @ id @ X425) @ id))) & (((X421 @ id @ X425 @ id)) = $true))) & ! [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) = $true) | ($true != ((X419 @ X423)))) & ! [X422 : term] : (((X421 @ id @ X422 @ id)) = ((X419 @ X422)))) & ! [X418 : term] : (((sub @ X418 @ id)) = X418))) & ((? [X414 : term] : ! [X415 : (subst > term > term)] : ? [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) != ((sub @ X414 @ (push @ X416 @ X417)))) | ! [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true = ((X419 @ (lam @ X420)))) | ? [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) != $true) & ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) & ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ? [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) != $true) & ($true = ((X419 @ X423)))) | ? [X422 : term] : (((X421 @ id @ X422 @ id)) != ((X419 @ X422)))) | ? [X418 : term] : (((sub @ X418 @ id)) != X418)) | (hoasinduction_lem3v2a_lthm != $true))) & (((? [X262 : (subst > term > subst > $o),X261 : term] : (! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) & (((sP13 @ X262)) = $true) & ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) & (((X262 @ id @ (lam @ X261) @ id)) != $true) & ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) | (sP15 = $true) | (sP14 = $true) | (sP16 = $true)) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (! [X262 : (subst > term > subst > $o),X261 : term] : (? [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) = $true) & ($true != ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) | (((sP13 @ X262)) != $true) | ? [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true != ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) & ($true = ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) | (((X262 @ id @ (lam @ X261) @ id)) = $true) | ? [X276 : term] : (($true = ((X262 @ id @ X276 @ id))) & ($true != ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) & (sP15 != $true) & (sP14 != $true) & (sP16 != $true)))) & ((! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true != ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) & (((X171 @ X167)) = $true)))) & ((($true = sP10) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP10))) & (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)))))))))))) & ((! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) | (axscons != $true)) & ((axscons = $true) | ? [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) != X189))) & ((($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9))) & ((! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X125 : (subst > term > subst > $o)] : ! [X126 : (term > $o)] : ? [X127 : term] : (((X126 @ X127)) != ((X125 @ id @ X127 @ id))))) & (((hoasinduction_lem2 = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem2 != $true))) & (((hoasinduction_lem3_lthm = $true) | (! [X54 : term,X53 : (subst > term > subst > $o)] : (($true = ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) | ? [X56 : (subst > term > term)] : (! [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) & ($true != ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) & ! [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) = $true) | ($true != ((X53 @ id @ X60 @ id))))) | ? [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) != $true) & ($true = ((X53 @ id @ X55 @ id))))) & ! [X52 : term] : (((sub @ X52 @ id)) = X52) & (sP7 != $true))) & ((? [X54 : term,X53 : (subst > term > subst > $o)] : (($true != ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) & ! [X56 : (subst > term > term)] : (? [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) != ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ? [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) != $true) & ($true = ((X53 @ id @ X60 @ id))))) & ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id))))) | ? [X52 : term] : (((sub @ X52 @ id)) != X52) | (sP7 = $true)) | (hoasinduction_lem3_lthm != $true))) & ((! [X175 : term,X174 : (subst > term > subst > $o)] : (($true = ((X174 @ id @ X175 @ id))) | ? [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) != $true) & ($true = ((X174 @ id @ X182 @ id))) & (((X174 @ id @ X181 @ id)) = $true)) | ? [X176 : (subst > term > term)] : (! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) & (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) != $true))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X175 : term,X174 : (subst > term > subst > $o)] : (($true != ((X174 @ id @ X175 @ id))) & ! [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) = $true) | ($true != ((X174 @ id @ X182 @ id))) | (((X174 @ id @ X181 @ id)) != $true)) & ! [X176 : (subst > term > term)] : (? [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) != ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) | ? [X177 : term] : (($true = ((X174 @ id @ X177 @ id))) & ($true != ((X174 @ id @ (X176 @ id @ X177) @ id)))) | (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true))))) & ((! [X185 : term] : ? [X186 : (subst > term > term)] : ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X185 : term] : ! [X186 : (subst > term > term)] : ? [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) != ((sub @ X185 @ (push @ X187 @ X188)))))) & (pushprop_lem2v2 = $true) & (((hoaslamnotap = $true) | ? [X463 : term,X461 : (subst > term > term),X462 : term] : (! [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) = ((sub @ (X461 @ X464 @ X465) @ X466))) & (((lam @ (X461 @ sh @ one))) = ((ap @ (sub @ X462 @ id) @ X463))))) & (! [X463 : term,X461 : (subst > term > term),X462 : term] : (? [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) != ((sub @ (X461 @ X464 @ X465) @ X466))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463)))) | (hoaslamnotap != $true))) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & (((hoasinduction_lem3aa_lthm = $true) | ? [X296 : (subst > term > subst > $o),X295 : term] : (! [X302 : term] : ((((X296 @ id @ X302 @ id)) != $true) | ($true = ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) & (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) != $true) & ! [X297 : (subst > term > term)] : (? [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) != $true) & ($true = ((X296 @ id @ X301 @ id)))) | (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ? [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X297 @ X298 @ X299) @ X300)))))) & (! [X296 : (subst > term > subst > $o),X295 : term] : (? [X302 : term] : ((((X296 @ id @ X302 @ id)) = $true) & ($true != ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ? [X297 : (subst > term > term)] : (! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) & (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true) & ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300))))) | (hoasinduction_lem3aa_lthm != $true))) & ((! [X129 : term] : ? [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) = ((X130 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X129 : term] : ! [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) != ((X130 @ sh @ one))))) & (((d2subst @ d_id)) = id) & ! [X393 : d_subst,X392 : d_subst] : ((((d2subst @ X392)) != ((d2subst @ X393))) | (X392 = X393)) & ((($true = sP5) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP5))) & ((! [X305 : term,X306 : (subst > term > subst > $o)] : (? [X307 : term] : (($true = ((X306 @ id @ X307 @ id))) & ($true != ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ? [X308 : (subst > term > term)] : (! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true)) & ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ? [X305 : term,X306 : (subst > term > subst > $o)] : (! [X307 : term] : (($true != ((X306 @ id @ X307 @ id))) | ($true = ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) & ! [X308 : (subst > term > term)] : (? [X312 : term] : (($true = ((X306 @ id @ X312 @ id))) & (((X306 @ id @ (X308 @ id @ X312) @ id)) != $true)) | ? [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) != ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) | ($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) & ($true != ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))))) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((($true = sP3) | ? [X357 : (subst > term > subst > $o)] : ! [X358 : (term > $o)] : ? [X359 : term] : (((X357 @ id @ X359 @ id)) != ((X358 @ X359))) | ($true = sP2) | ? [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) & ($true != ((X370 @ (lam @ X369)))) & ! [X371 : (subst > term > term)] : (? [X372 : term] : (($true = ((X368 @ id @ X372 @ id))) & ($true != ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ? [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) != ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) & ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true))) | ? [X367 : term] : (((sub @ X367 @ id)) != X367)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP3) & ! [X357 : (subst > term > subst > $o)] : ? [X358 : (term > $o)] : ! [X359 : term] : (((X357 @ id @ X359 @ id)) = ((X358 @ X359))) & ($true != sP2) & ! [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (? [X376 : term] : (((X370 @ X376)) != ((X368 @ id @ X376 @ id))) | ($true = ((X370 @ (lam @ X369)))) | ? [X371 : (subst > term > term)] : (! [X372 : term] : (($true != ((X368 @ id @ X372 @ id))) | ($true = ((X368 @ id @ (X371 @ id @ X372) @ id)))) & ($true != ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) & ! [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) = ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) | ? [X377 : term] : ((((X370 @ X377)) = $true) & (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) != $true))) & ! [X367 : term] : (((sub @ X367 @ id)) = X367)))) & (((axvarid = $true) | ? [X124 : term] : (((sub @ X124 @ id)) != X124)) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) | (axvarid != $true))) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & ((! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X142 : term,X141 : term] : ((X141 != X142) & (((sub @ X142 @ sh)) = ((sub @ X141 @ sh)))))) & (((induction = $true) | ? [X450 : (term > $o),X449 : term] : (! [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) = $true) | ($true != ((X450 @ X452))) | ($true != ((X450 @ X451)))) & ! [X454 : term] : (($true != ((X450 @ X454))) | (((X450 @ (lam @ X454))) = $true)) & (((X450 @ X449)) != $true) & ! [X453 : term] : ((((X450 @ X453)) = $true) | (((var @ X453)) != $true)))) & (! [X450 : (term > $o),X449 : term] : (? [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) != $true) & ($true = ((X450 @ X452))) & ($true = ((X450 @ X451)))) | ? [X454 : term] : (($true = ((X450 @ X454))) & (((X450 @ (lam @ X454))) != $true)) | (((X450 @ X449)) = $true) | ? [X453 : term] : ((((X450 @ X453)) != $true) & (((var @ X453)) = $true))) | (induction != $true))) & (pushprop_lem3v2 = $true) & ((! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) | (laminj != $true)) & ((laminj = $true) | ? [X131 : term,X132 : term] : ((X131 != X132) & (((lam @ X131)) = ((lam @ X132)))))) & (((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X123 : subst] : (((comp @ id @ X123)) != X123) | ? [X122 : subst] : (((comp @ X122 @ id)) != X122)))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X51 : d_subst] : (d_id = X51) & ! [X239 : d_term] : (d_one = X239) & (hoasinduction_lem2v2_gthm = $true) & ((! [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true != ((X389 @ X387))) | (((X390 @ one)) = $true) | ? [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) != ((X390 @ X391)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true = ((X389 @ X387))) & (((X390 @ one)) != $true) & ! [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) = ((X390 @ X391)))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & ((($true = sP1) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP1))) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) != X121))) & ((! [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (? [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) & (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) != $true)) | ($true = ((sP0 @ X338))) | ? [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true != ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) & (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true)) | ? [X354 : term] : (((X338 @ id @ X354 @ id)) != ((X337 @ X354))) | ? [X344 : term] : (($true = ((X337 @ X344))) & ($true != ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ($true = ((X337 @ (lam @ X339))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (! [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true != ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) | (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) = $true)) & ($true != ((sP0 @ X338))) & ! [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true = ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) | (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) != $true)) & ! [X354 : term] : (((X338 @ id @ X354 @ id)) = ((X337 @ X354))) & ! [X344 : term] : (($true != ((X337 @ X344))) | ($true = ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) & ($true != ((X337 @ (lam @ X339))))))) & ((! [X128 : term] : (((sub @ X128 @ id)) = X128) | (termmset != $true)) & ((termmset = $true) | ? [X128 : term] : (((sub @ X128 @ id)) != X128))) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X183 : d_term,X184 : d_term] : ((X183 = X184) | (((d2term @ X184)) != ((d2term @ X183)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(nnf_transformation,[],[f42])).
% 1.38/0.56 thf(f130,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & ((axidl = $true) | ? [X240 : subst] : (((comp @ id @ X240)) != X240)) & (! [X240 : subst] : (((comp @ id @ X240)) = X240) | (axidl != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (? [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (! [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true = ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) | (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) != $true)) & ($true != ((X198 @ (lam @ X197)))) & ! [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) != $true) | (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) = $true)) & ! [X203 : term] : (((X196 @ id @ X203 @ id)) = ((X198 @ X203))) & ! [X204 : term] : (($true != ((X198 @ X204))) | (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) = $true)) & (((sP27 @ X196)) != $true)) & ! [X195 : term] : (((sub @ X195 @ id)) = X195))) & (! [X197 : term,X196 : (subst > term > subst > $o),X198 : (term > $o)] : (? [X205 : subst,X207 : subst,X206 : term,X208 : subst] : (($true != ((X196 @ X208 @ X206 @ (comp @ X207 @ X205)))) & (((X196 @ (comp @ X208 @ X207) @ (sub @ X206 @ X207) @ X205)) = $true)) | ($true = ((X198 @ (lam @ X197)))) | ? [X201 : subst,X200 : subst,X199 : subst,X202 : term] : ((((X196 @ X201 @ X202 @ (comp @ X199 @ X200))) = $true) & (((X196 @ (comp @ X201 @ X199) @ (sub @ X202 @ X199) @ X200)) != $true)) | ? [X203 : term] : (((X196 @ id @ X203 @ id)) != ((X198 @ X203))) | ? [X204 : term] : (($true = ((X198 @ X204))) & (((X198 @ (sub @ X197 @ (push @ X204 @ id)))) != $true)) | (((sP27 @ X196)) = $true)) | ? [X195 : term] : (((sub @ X195 @ id)) != X195) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X531 : term] : (((sub @ X531 @ id)) = X531) & ? [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) = ((ap @ (sub @ X539 @ id) @ X536))) & (X537 != X539)) & ! [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) != ((ap @ X534 @ X533))) | (X534 = X535)))) & (? [X531 : term] : (((sub @ X531 @ id)) != X531) | ! [X537 : term,X536 : term,X538 : term,X539 : term] : ((((ap @ (sub @ X537 @ id) @ X538)) != ((ap @ (sub @ X539 @ id) @ X536))) | (X537 = X539)) | ? [X534 : term,X533 : term,X535 : term,X532 : term] : ((((ap @ X535 @ X532)) = ((ap @ X534 @ X533))) & (X534 != X535)) | (hoasapinj1_lthm != $true)) & ((hoaslaminj = $true) | ? [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (! [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) = ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) & (((X430 @ X432 @ X431)) != ((X429 @ X432 @ X431))) & ! [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) = ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) & (((lam @ (X429 @ sh @ one))) = ((lam @ (X430 @ sh @ one)))))) & (! [X431 : term,X432 : subst,X429 : (subst > term > term),X430 : (subst > term > term)] : (? [X438 : term,X436 : subst,X437 : subst] : (((sub @ (X430 @ X436 @ X438) @ X437)) != ((X430 @ (comp @ X436 @ X437) @ (sub @ X438 @ X437)))) | (((X430 @ X432 @ X431)) = ((X429 @ X432 @ X431))) | ? [X435 : term,X433 : subst,X434 : subst] : (((sub @ (X429 @ X433 @ X435) @ X434)) != ((X429 @ (comp @ X433 @ X434) @ (sub @ X435 @ X434)))) | (((lam @ (X429 @ sh @ one))) != ((lam @ (X430 @ sh @ one))))) | (hoaslaminj != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (! [X194 : subst] : (((comp @ X194 @ id)) = X194) | (axidr != $true)) & ((axidr = $true) | ? [X194 : subst] : (((comp @ X194 @ id)) != X194)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X355 : subst] : ? [X356 : d_subst] : (((d2subst @ X356)) = X355) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | ? [X214 : term,X215 : (subst > term > subst > $o)] : (! [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true != ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) | ($true = ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) & (((sP26 @ X215)) != $true) & (((X215 @ id @ X214 @ id)) != $true) & (((sP25 @ X215)) != $true) & ! [X216 : term] : (($true != ((var @ (sub @ X216 @ id)))) | ($true = ((X215 @ id @ X216 @ id)))) & ! [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true = ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) | (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) != $true)))) & (! [X214 : term,X215 : (subst > term > subst > $o)] : (? [X224 : subst,X225 : subst,X223 : term,X226 : subst] : (($true = ((X215 @ X224 @ X223 @ (comp @ X226 @ X225)))) & ($true != ((X215 @ (comp @ X224 @ X226) @ (sub @ X223 @ X226) @ X225)))) | (((sP26 @ X215)) = $true) | (((X215 @ id @ X214 @ id)) = $true) | (((sP25 @ X215)) = $true) | ? [X216 : term] : (($true = ((var @ (sub @ X216 @ id)))) & ($true != ((X215 @ id @ X216 @ id)))) | ? [X218 : term,X220 : subst,X217 : subst,X219 : subst] : (($true != ((X215 @ X220 @ X218 @ (comp @ X219 @ X217)))) & (((X215 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219) @ X217)) = $true))) | (hoasinduction != $true)) & (? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X0 @ id @ X2 @ id)) != ((X1 @ X2))) | ? [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true != ((X12 @ (lam @ X13)))) & ! [X14 : (subst > term > term)] : (? [X15 : term] : (($true = ((X11 @ id @ X15 @ id))) & ($true != ((X11 @ id @ (X14 @ id @ X15) @ id)))) | ? [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) != ((sub @ (X14 @ X18 @ X16) @ X17))) | ($true = ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) & ! [X19 : term] : (($true = ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) | ($true != ((X12 @ X19)))) & ! [X20 : term] : (((X12 @ X20)) = ((X11 @ id @ X20 @ id)))) | ($true = sP24) | ? [X10 : term] : (((sub @ X10 @ id)) != X10) | (sP23 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X0 @ id @ X2 @ id)) = ((X1 @ X2))) & ! [X12 : (term > $o),X13 : term,X11 : (subst > term > subst > $o)] : (($true = ((X12 @ (lam @ X13)))) | ? [X14 : (subst > term > term)] : (! [X15 : term] : (($true != ((X11 @ id @ X15 @ id))) | ($true = ((X11 @ id @ (X14 @ id @ X15) @ id)))) & ! [X17 : subst,X16 : term,X18 : subst] : (((X14 @ (comp @ X18 @ X17) @ (sub @ X16 @ X17))) = ((sub @ (X14 @ X18 @ X16) @ X17))) & ($true != ((X11 @ id @ (lam @ (X14 @ sh @ one)) @ id)))) | ? [X19 : term] : (($true != ((X12 @ (sub @ X13 @ (push @ X19 @ id))))) & ($true = ((X12 @ X19)))) | ? [X20 : term] : (((X12 @ X20)) != ((X11 @ id @ X20 @ id)))) & ($true != sP24) & ! [X10 : term] : (((sub @ X10 @ id)) = X10) & (sP23 != $true))) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & ((pushprop_lem0 = $true) | ? [X314 : subst,X313 : (term > $o),X315 : term] : ! [X316 : (term > $o)] : ? [X317 : term] : (((X316 @ X317)) != ((X313 @ (sub @ X317 @ (push @ X315 @ X314)))))) & (! [X314 : subst,X313 : (term > $o),X315 : term] : ? [X316 : (term > $o)] : ! [X317 : term] : (((X316 @ X317)) = ((X313 @ (sub @ X317 @ (push @ X315 @ X314))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X40 : (subst > term > subst > $o),X39 : term] : (($true != ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) & ! [X41 : (subst > term > term),X42 : term] : (? [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) != ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) | ? [X49 : term] : (($true != ((X40 @ id @ (X41 @ id @ X49) @ id))) & ($true = ((X40 @ id @ X49 @ id)))) | (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) = $true) | ? [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) != ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) & ! [X50 : term] : ((((X40 @ id @ X50 @ id)) != $true) | (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) = $true)))) & (! [X40 : (subst > term > subst > $o),X39 : term] : (($true = ((X40 @ id @ (lam @ (sub @ X39 @ (push @ one @ sh))) @ id))) | ? [X41 : (subst > term > term),X42 : term] : (! [X43 : term,X45 : subst,X44 : subst] : (((sub @ X42 @ (push @ (sub @ X43 @ X45) @ (comp @ X44 @ X45)))) = ((X41 @ (comp @ X44 @ X45) @ (sub @ X43 @ X45)))) & ! [X49 : term] : (($true = ((X40 @ id @ (X41 @ id @ X49) @ id))) | ($true != ((X40 @ id @ X49 @ id)))) & (((X40 @ id @ (lam @ (X41 @ sh @ one)) @ id)) != $true) & ! [X47 : term,X46 : subst,X48 : subst] : (((sub @ (X41 @ X48 @ X47) @ X46)) = ((sub @ (sub @ X42 @ (push @ X47 @ X48)) @ X46)))) | ? [X50 : term] : ((((X40 @ id @ X50 @ id)) = $true) & (((X40 @ id @ (sub @ X39 @ (push @ X50 @ id)) @ id)) != $true))) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem0_gthm = $true) & ((apinj2 = $true) | ? [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 != X161) & (((ap @ X162 @ X161)) = ((ap @ X160 @ X159))))) & (! [X159 : term,X160 : term,X162 : term,X161 : term] : ((X159 = X161) | (((ap @ X162 @ X161)) != ((ap @ X160 @ X159)))) | (apinj2 != $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 = X80) | (((ap @ (sub @ X77 @ id) @ X80)) != ((ap @ (sub @ X78 @ id) @ X79)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X77 : term,X80 : term,X78 : term,X79 : term] : ((X79 != X80) & (((ap @ (sub @ X77 @ id) @ X80)) = ((ap @ (sub @ X78 @ id) @ X79))))) & ((apinj1 = $true) | ? [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) = ((ap @ X459 @ X458))) & (X459 != X460))) & (! [X458 : term,X460 : term,X457 : term,X459 : term] : ((((ap @ X460 @ X457)) != ((ap @ X459 @ X458))) | (X459 = X460)) | (apinj1 != $true)) & (($true = sP20) | ? [X514 : term] : (((sub @ X514 @ id)) != X514) | ? [X516 : (subst > term > subst > $o),X515 : term] : (! [X518 : (subst > term > term)] : (? [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) != ((sub @ (X518 @ X519 @ X520) @ X521))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ? [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) != $true) & (((X516 @ id @ X522 @ id)) = $true))) & ! [X517 : term] : (($true = ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) | (((X516 @ id @ X517 @ id)) != $true)) & (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) != $true)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP20) & ! [X514 : term] : (((sub @ X514 @ id)) = X514) & ! [X516 : (subst > term > subst > $o),X515 : term] : (? [X518 : (subst > term > term)] : (! [X521 : subst,X520 : term,X519 : subst] : (((X518 @ (comp @ X519 @ X521) @ (sub @ X520 @ X521))) = ((sub @ (X518 @ X519 @ X520) @ X521))) & ($true != ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) & ! [X522 : term] : ((((X516 @ id @ (X518 @ id @ X522) @ id)) = $true) | (((X516 @ id @ X522 @ id)) != $true))) | ? [X517 : term] : (($true != ((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id))) & (((X516 @ id @ X517 @ id)) = $true)) | (((X516 @ id @ (lam @ (sub @ X515 @ (push @ one @ sh))) @ id)) = $true)))) & (ulamvarind = $true) & (! [X163 : term] : ? [X164 : (subst > term > term)] : ! [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) = ((sub @ X163 @ (push @ X165 @ X166)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X163 : term] : ! [X164 : (subst > term > term)] : ? [X166 : subst,X165 : term] : (((X164 @ X166 @ X165)) != ((sub @ X163 @ (push @ X165 @ X166))))) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (! [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) = X455) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X456 : subst,X455 : term] : (((sub @ one @ (push @ X455 @ X456))) != X455)) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & (! [X103 : (subst > term > subst > $o),X104 : term] : (($true = ((X103 @ id @ (lam @ X104) @ id))) | ? [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) != $true) & ! [X109 : term] : (($true != ((X103 @ id @ X109 @ id))) | ($true = ((X103 @ id @ (X105 @ id @ X109) @ id)))) & ! [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) = ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) | ? [X110 : term] : (($true = ((X103 @ id @ X110 @ id))) & ($true != ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id))))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X103 : (subst > term > subst > $o),X104 : term] : (($true != ((X103 @ id @ (lam @ X104) @ id))) & ! [X105 : (subst > term > term)] : ((((X103 @ id @ (lam @ (X105 @ sh @ one)) @ id)) = $true) | ? [X109 : term] : (($true = ((X103 @ id @ X109 @ id))) & ($true != ((X103 @ id @ (X105 @ id @ X109) @ id)))) | ? [X106 : subst,X107 : term,X108 : subst] : (((sub @ (X105 @ X108 @ X107) @ X106)) != ((X105 @ (comp @ X108 @ X106) @ (sub @ X107 @ X106))))) & ! [X110 : term] : (($true != ((X103 @ id @ X110 @ id))) | ($true = ((X103 @ id @ (sub @ X104 @ (push @ X110 @ id)) @ id)))))) & ((hoasapinj1 = $true) | ? [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) = ((ap @ (sub @ X333 @ id) @ X334))) & (X333 != X336))) & (! [X335 : term,X334 : term,X336 : term,X333 : term] : ((((ap @ (sub @ X336 @ id) @ X335)) != ((ap @ (sub @ X333 @ id) @ X334))) | (X333 = X336)) | (hoasapinj1 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) = X114) & ? [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) = $true) & (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) != $true)) & ! [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) = X111))) & (? [X114 : subst,X113 : term] : (((comp @ sh @ (push @ X113 @ X114))) != X114) | ! [X118 : term,X117 : (term > $o),X119 : (term > $o),X116 : subst,X115 : term] : ((((X119 @ X118)) != $true) | (((X117 @ (sub @ X118 @ (push @ X115 @ X116)))) = $true)) | ? [X112 : subst,X111 : term] : (((sub @ one @ (push @ X111 @ X112))) != X111) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X410 : term,X411 : (term > $o),X409 : subst] : ! [X412 : (term > $o)] : ? [X413 : term] : (((X412 @ X413)) != ((X411 @ (sub @ X413 @ (push @ X410 @ X409)))))) & (! [X410 : term,X411 : (term > $o),X409 : subst] : ? [X412 : (term > $o)] : ! [X413 : term] : (((X412 @ X413)) = ((X411 @ (sub @ X413 @ (push @ X410 @ X409))))) | (pushprop_lem0_lthm != $true)) & (apnotvar = $true) & ! [X172 : term] : ? [X173 : d_term] : (((d2term @ X173)) = X172) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) | (! [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) != ((ap @ X133 @ X136))) | (X134 = X136)) & ? [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 != X140) & (((ap @ (sub @ X138 @ id) @ X137)) = ((ap @ (sub @ X139 @ id) @ X140)))))) & (? [X133 : term,X135 : term,X136 : term,X134 : term] : ((((ap @ X135 @ X134)) = ((ap @ X133 @ X136))) & (X134 != X136)) | ! [X137 : term,X138 : term,X140 : term,X139 : term] : ((X137 = X140) | (((ap @ (sub @ X138 @ id) @ X137)) != ((ap @ (sub @ X139 @ id) @ X140)))) | (hoasapinj2_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X100 : (subst > term > subst > $o)] : ! [X101 : (term > $o)] : ? [X102 : term] : (((X100 @ id @ X102 @ id)) != ((X101 @ X102)))) & (! [X100 : (subst > term > subst > $o)] : ? [X101 : (term > $o)] : ! [X102 : term] : (((X100 @ id @ X102 @ id)) = ((X101 @ X102))) | (hoasinduction_lem0_lthm != $true)) & (axclos = $true) & (hoasapinj2_gthm = $true) & (! [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) = $true) | ? [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) != $true) & ($true = ((X439 @ X447)))) | ? [X442 : (subst > term > term)] : (! [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) = ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) & (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) != $true) & ! [X443 : term] : (($true != ((X440 @ id @ X443 @ id))) | ($true = ((X440 @ id @ (X442 @ id @ X443) @ id))))) | ? [X448 : term] : (((X439 @ X448)) != ((X440 @ id @ X448 @ id)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X441 : term,X439 : (term > $o),X440 : (subst > term > subst > $o)] : ((((X439 @ (lam @ X441))) != $true) & ! [X447 : term] : ((((X439 @ (sub @ X441 @ (push @ X447 @ id)))) = $true) | ($true != ((X439 @ X447)))) & ! [X442 : (subst > term > term)] : (? [X446 : subst,X444 : subst,X445 : term] : (((sub @ (X442 @ X446 @ X445) @ X444)) != ((X442 @ (comp @ X446 @ X444) @ (sub @ X445 @ X444)))) | (((X440 @ id @ (lam @ (X442 @ sh @ one)) @ id)) = $true) | ? [X443 : term] : (($true = ((X440 @ id @ X443 @ id))) & ($true != ((X440 @ id @ (X442 @ id @ X443) @ id))))) & ! [X448 : term] : (((X439 @ X448)) = ((X440 @ id @ X448 @ id))))) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) | (! [X147 : term,X148 : term] : ((X147 = X148) | (((lam @ X148)) != ((lam @ X147)))) & ? [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (! [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) = ((sub @ (X150 @ X157 @ X158) @ X156))) & ! [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) = ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) & (((X150 @ X152 @ X151)) != ((X149 @ X152 @ X151))) & (((lam @ (X149 @ sh @ one))) = ((lam @ (X150 @ sh @ one))))) & ! [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) = X145) & ! [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) = X144))) & (? [X147 : term,X148 : term] : ((X147 != X148) & (((lam @ X148)) = ((lam @ X147)))) | ! [X152 : subst,X149 : (subst > term > term),X151 : term,X150 : (subst > term > term)] : (? [X157 : subst,X156 : subst,X158 : term] : (((X150 @ (comp @ X157 @ X156) @ (sub @ X158 @ X156))) != ((sub @ (X150 @ X157 @ X158) @ X156))) | ? [X153 : subst,X154 : subst,X155 : term] : (((sub @ (X149 @ X154 @ X155) @ X153)) != ((X149 @ (comp @ X154 @ X153) @ (sub @ X155 @ X153)))) | (((X150 @ X152 @ X151)) = ((X149 @ X152 @ X151))) | (((lam @ (X149 @ sh @ one))) != ((lam @ (X150 @ sh @ one))))) | ? [X146 : term,X145 : subst] : (((comp @ sh @ (push @ X146 @ X145))) != X145) | ? [X144 : term,X143 : subst] : (((sub @ one @ (push @ X144 @ X143))) != X144) | (hoaslaminj_lthm != $true)) & (! [X304 : term] : (((sub @ X304 @ id)) = X304) | ? [X303 : term] : (((sub @ X303 @ id)) != X303) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X304 : term] : (((sub @ X304 @ id)) != X304) & ! [X303 : term] : (((sub @ X303 @ id)) = X303))) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X394 : term] : ? [X395 : (subst > term > term)] : (((X395 @ sh @ one)) = ((sub @ X394 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X394 : term] : ! [X395 : (subst > term > term)] : (((X395 @ sh @ one)) != ((sub @ X394 @ (push @ one @ sh))))) & (! [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) != $true) | ? [X238 : term] : (((X236 @ X238)) != ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) | ($true = ((X236 @ one)))) | ? [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) != X233) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X236 : (term > $o),X234 : (term > $o),X237 : subst,X235 : term] : ((((X234 @ X235)) = $true) & ! [X238 : term] : (((X236 @ X238)) = ((X234 @ (sub @ X238 @ (push @ X235 @ X237))))) & ($true != ((X236 @ one)))) & ! [X233 : term,X232 : subst] : (((sub @ one @ (push @ X233 @ X232))) = X233))) & ((hoasinduction_lem3 = $true) | ? [X468 : (subst > term > subst > $o),X467 : term] : (! [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true = ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) | ($true != ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) & (((sP19 @ X468)) != $true) & ! [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true = ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) | ($true != ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) & (((X468 @ id @ (lam @ X467) @ id)) != $true) & ! [X478 : term] : (($true = ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) | ($true != ((X468 @ id @ X478 @ id)))))) & (! [X468 : (subst > term > subst > $o),X467 : term] : (? [X481 : subst,X479 : subst,X482 : subst,X480 : term] : (($true != ((X468 @ (comp @ X482 @ X479) @ (sub @ X480 @ X479) @ X481))) & ($true = ((X468 @ X482 @ X480 @ (comp @ X479 @ X481))))) | (((sP19 @ X468)) = $true) | ? [X470 : subst,X471 : subst,X469 : subst,X472 : term] : (($true != ((X468 @ X470 @ X472 @ (comp @ X469 @ X471)))) & ($true = ((X468 @ (comp @ X470 @ X469) @ (sub @ X472 @ X469) @ X471)))) | (((X468 @ id @ (lam @ X467) @ id)) = $true) | ? [X478 : term] : (($true != ((X468 @ id @ (sub @ X467 @ (push @ X478 @ id)) @ id))) & ($true = ((X468 @ id @ X478 @ id))))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X193 : subst] : (((comp @ id @ X193)) = X193) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | ? [X191 : subst] : (((comp @ X191 @ id)) != X191) | ? [X190 : subst] : (((comp @ id @ X190)) != X190) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X193 : subst] : (((comp @ id @ X193)) != X193) | ? [X192 : subst] : (((comp @ X192 @ id)) != X192)) & ! [X191 : subst] : (((comp @ X191 @ id)) = X191) & ! [X190 : subst] : (((comp @ id @ X190)) = X190))) & ((induction2lem_lthm = $true) | ($true != sP18)) & (($true = sP18) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X414 : term] : ? [X415 : (subst > term > term)] : ! [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) = ((sub @ X414 @ (push @ X416 @ X417)))) & ? [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true != ((X419 @ (lam @ X420)))) & ! [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) != ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) | ? [X425 : term] : (($true != ((X421 @ id @ (X424 @ id @ X425) @ id))) & (((X421 @ id @ X425 @ id)) = $true))) & ! [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) = $true) | ($true != ((X419 @ X423)))) & ! [X422 : term] : (((X421 @ id @ X422 @ id)) = ((X419 @ X422)))) & ! [X418 : term] : (((sub @ X418 @ id)) = X418))) & (? [X414 : term] : ! [X415 : (subst > term > term)] : ? [X417 : subst,X416 : term] : (((X415 @ X417 @ X416)) != ((sub @ X414 @ (push @ X416 @ X417)))) | ! [X420 : term,X421 : (subst > term > subst > $o),X419 : (term > $o)] : (($true = ((X419 @ (lam @ X420)))) | ? [X424 : (subst > term > term)] : ((((X421 @ id @ (lam @ (X424 @ sh @ one)) @ id)) != $true) & ! [X426 : subst,X427 : subst,X428 : term] : (((sub @ (X424 @ X426 @ X428) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X428 @ X427)))) & ! [X425 : term] : (($true = ((X421 @ id @ (X424 @ id @ X425) @ id))) | (((X421 @ id @ X425 @ id)) != $true))) | ? [X423 : term] : ((((X419 @ (sub @ X420 @ (push @ X423 @ id)))) != $true) & ($true = ((X419 @ X423)))) | ? [X422 : term] : (((X421 @ id @ X422 @ id)) != ((X419 @ X422)))) | ? [X418 : term] : (((sub @ X418 @ id)) != X418) | (hoasinduction_lem3v2a_lthm != $true)) & (? [X262 : (subst > term > subst > $o),X261 : term] : (! [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) != $true) | ($true = ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) & (((sP13 @ X262)) = $true) & ! [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true = ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) | ($true != ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) & (((X262 @ id @ (lam @ X261) @ id)) != $true) & ! [X276 : term] : (($true != ((X262 @ id @ X276 @ id))) | ($true = ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) | (sP15 = $true) | (sP14 = $true) | (sP16 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (! [X262 : (subst > term > subst > $o),X261 : term] : (? [X275 : subst,X274 : subst,X273 : term,X272 : subst] : ((((X262 @ (comp @ X275 @ X272) @ (sub @ X273 @ X272) @ X274)) = $true) & ($true != ((X262 @ X275 @ X273 @ (comp @ X272 @ X274))))) | (((sP13 @ X262)) != $true) | ? [X264 : term,X265 : subst,X263 : subst,X266 : subst] : (($true != ((X262 @ (comp @ X265 @ X266) @ (sub @ X264 @ X266) @ X263))) & ($true = ((X262 @ X265 @ X264 @ (comp @ X266 @ X263))))) | (((X262 @ id @ (lam @ X261) @ id)) = $true) | ? [X276 : term] : (($true = ((X262 @ id @ X276 @ id))) & ($true != ((X262 @ id @ (sub @ X261 @ (push @ X276 @ id)) @ id))))) & (sP15 != $true) & (sP14 != $true) & (sP16 != $true))) & (! [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true = ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) | (((X171 @ X167)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X168 : (term > $o),X169 : subst,X171 : (term > $o),X167 : term,X170 : term] : (($true != ((X168 @ (sub @ X167 @ (push @ X170 @ X169))))) & (((X171 @ X167)) = $true))) & (($true = sP10) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP10)) & (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)))))))))))) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) | (axscons != $true)) & ((axscons = $true) | ? [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) != X189)) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (! [X125 : (subst > term > subst > $o)] : ? [X126 : (term > $o)] : ! [X127 : term] : (((X126 @ X127)) = ((X125 @ id @ X127 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X125 : (subst > term > subst > $o)] : ! [X126 : (term > $o)] : ? [X127 : term] : (((X126 @ X127)) != ((X125 @ id @ X127 @ id)))) & ((hoasinduction_lem2 = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X54 : term,X53 : (subst > term > subst > $o)] : (($true = ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) | ? [X56 : (subst > term > term)] : (! [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) = ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) & ($true != ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) & ! [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) = $true) | ($true != ((X53 @ id @ X60 @ id))))) | ? [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) != $true) & ($true = ((X53 @ id @ X55 @ id))))) & ! [X52 : term] : (((sub @ X52 @ id)) = X52) & (sP7 != $true))) & (? [X54 : term,X53 : (subst > term > subst > $o)] : (($true != ((X53 @ id @ (lam @ (sub @ X54 @ (push @ one @ sh))) @ id))) & ! [X56 : (subst > term > term)] : (? [X57 : term,X59 : subst,X58 : subst] : (((sub @ (X56 @ X58 @ X57) @ X59)) != ((X56 @ (comp @ X58 @ X59) @ (sub @ X57 @ X59)))) | ($true = ((X53 @ id @ (lam @ (X56 @ sh @ one)) @ id))) | ? [X60 : term] : ((((X53 @ id @ (X56 @ id @ X60) @ id)) != $true) & ($true = ((X53 @ id @ X60 @ id))))) & ! [X55 : term] : ((((X53 @ id @ (sub @ X54 @ (push @ X55 @ id)) @ id)) = $true) | ($true != ((X53 @ id @ X55 @ id))))) | ? [X52 : term] : (((sub @ X52 @ id)) != X52) | (sP7 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X175 : term,X174 : (subst > term > subst > $o)] : (($true = ((X174 @ id @ X175 @ id))) | ? [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) != $true) & ($true = ((X174 @ id @ X182 @ id))) & (((X174 @ id @ X181 @ id)) = $true)) | ? [X176 : (subst > term > term)] : (! [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) = ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) & ! [X177 : term] : (($true != ((X174 @ id @ X177 @ id))) | ($true = ((X174 @ id @ (X176 @ id @ X177) @ id)))) & (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) != $true))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X175 : term,X174 : (subst > term > subst > $o)] : (($true != ((X174 @ id @ X175 @ id))) & ! [X182 : term,X181 : term] : ((((X174 @ id @ (ap @ (sub @ X181 @ id) @ X182) @ id)) = $true) | ($true != ((X174 @ id @ X182 @ id))) | (((X174 @ id @ X181 @ id)) != $true)) & ! [X176 : (subst > term > term)] : (? [X180 : term,X179 : subst,X178 : subst] : (((sub @ (X176 @ X179 @ X180) @ X178)) != ((X176 @ (comp @ X179 @ X178) @ (sub @ X180 @ X178)))) | ? [X177 : term] : (($true = ((X174 @ id @ X177 @ id))) & ($true != ((X174 @ id @ (X176 @ id @ X177) @ id)))) | (((X174 @ id @ (lam @ (X176 @ sh @ one)) @ id)) = $true)))) & (! [X185 : term] : ? [X186 : (subst > term > term)] : ! [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) = ((sub @ X185 @ (push @ X187 @ X188)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X185 : term] : ! [X186 : (subst > term > term)] : ? [X188 : subst,X187 : term] : (((X186 @ X188 @ X187)) != ((sub @ X185 @ (push @ X187 @ X188))))) & (pushprop_lem2v2 = $true) & ((hoaslamnotap = $true) | ? [X463 : term,X461 : (subst > term > term),X462 : term] : (! [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) = ((sub @ (X461 @ X464 @ X465) @ X466))) & (((lam @ (X461 @ sh @ one))) = ((ap @ (sub @ X462 @ id) @ X463))))) & (! [X463 : term,X461 : (subst > term > term),X462 : term] : (? [X466 : subst,X464 : subst,X465 : term] : (((X461 @ (comp @ X464 @ X466) @ (sub @ X465 @ X466))) != ((sub @ (X461 @ X464 @ X465) @ X466))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X462 @ id) @ X463)))) | (hoaslamnotap != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3aa_lthm = $true) | ? [X296 : (subst > term > subst > $o),X295 : term] : (! [X302 : term] : ((((X296 @ id @ X302 @ id)) != $true) | ($true = ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) & (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) != $true) & ! [X297 : (subst > term > term)] : (? [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) != $true) & ($true = ((X296 @ id @ X301 @ id)))) | (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ? [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) != ((sub @ (X297 @ X298 @ X299) @ X300)))))) & (! [X296 : (subst > term > subst > $o),X295 : term] : (? [X302 : term] : ((((X296 @ id @ X302 @ id)) = $true) & ($true != ((X296 @ id @ (sub @ X295 @ (push @ X302 @ id)) @ id)))) | (((X296 @ id @ (lam @ (sub @ X295 @ (push @ one @ sh))) @ id)) = $true) | ? [X297 : (subst > term > term)] : (! [X301 : term] : ((((X296 @ id @ (X297 @ id @ X301) @ id)) = $true) | ($true != ((X296 @ id @ X301 @ id)))) & (((X296 @ id @ (lam @ (X297 @ sh @ one)) @ id)) != $true) & ! [X300 : subst,X298 : subst,X299 : term] : (((X297 @ (comp @ X298 @ X300) @ (sub @ X299 @ X300))) = ((sub @ (X297 @ X298 @ X299) @ X300))))) | (hoasinduction_lem3aa_lthm != $true)) & (! [X129 : term] : ? [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) = ((X130 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X129 : term] : ! [X130 : (subst > term > term)] : (((sub @ X129 @ (push @ one @ sh))) != ((X130 @ sh @ one)))) & (((d2subst @ d_id)) = id) & ! [X393 : d_subst,X392 : d_subst] : ((((d2subst @ X392)) != ((d2subst @ X393))) | (X392 = X393)) & (($true = sP5) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP5)) & (! [X305 : term,X306 : (subst > term > subst > $o)] : (? [X307 : term] : (($true = ((X306 @ id @ X307 @ id))) & ($true != ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) | ? [X308 : (subst > term > term)] : (! [X312 : term] : (($true != ((X306 @ id @ X312 @ id))) | (((X306 @ id @ (X308 @ id @ X312) @ id)) = $true)) & ! [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) = ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) & ($true != ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) | ($true = ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id)))) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ? [X305 : term,X306 : (subst > term > subst > $o)] : (! [X307 : term] : (($true != ((X306 @ id @ X307 @ id))) | ($true = ((X306 @ id @ (sub @ X305 @ (push @ X307 @ id)) @ id)))) & ! [X308 : (subst > term > term)] : (? [X312 : term] : (($true = ((X306 @ id @ X312 @ id))) & (((X306 @ id @ (X308 @ id @ X312) @ id)) != $true)) | ? [X309 : term,X310 : subst,X311 : subst] : (((sub @ (X308 @ X311 @ X309) @ X310)) != ((X308 @ (comp @ X311 @ X310) @ (sub @ X309 @ X310)))) | ($true = ((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)))) & ($true != ((X306 @ id @ (lam @ (sub @ X305 @ (push @ one @ sh))) @ id))))) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP3) | ? [X357 : (subst > term > subst > $o)] : ! [X358 : (term > $o)] : ? [X359 : term] : (((X357 @ id @ X359 @ id)) != ((X358 @ X359))) | ($true = sP2) | ? [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (! [X376 : term] : (((X370 @ X376)) = ((X368 @ id @ X376 @ id))) & ($true != ((X370 @ (lam @ X369)))) & ! [X371 : (subst > term > term)] : (? [X372 : term] : (($true = ((X368 @ id @ X372 @ id))) & ($true != ((X368 @ id @ (X371 @ id @ X372) @ id)))) | ($true = ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) | ? [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) != ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) & ! [X377 : term] : ((((X370 @ X377)) != $true) | (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) = $true))) | ? [X367 : term] : (((sub @ X367 @ id)) != X367) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP3) & ! [X357 : (subst > term > subst > $o)] : ? [X358 : (term > $o)] : ! [X359 : term] : (((X357 @ id @ X359 @ id)) = ((X358 @ X359))) & ($true != sP2) & ! [X368 : (subst > term > subst > $o),X370 : (term > $o),X369 : term] : (? [X376 : term] : (((X370 @ X376)) != ((X368 @ id @ X376 @ id))) | ($true = ((X370 @ (lam @ X369)))) | ? [X371 : (subst > term > term)] : (! [X372 : term] : (($true != ((X368 @ id @ X372 @ id))) | ($true = ((X368 @ id @ (X371 @ id @ X372) @ id)))) & ($true != ((X368 @ id @ (lam @ (X371 @ sh @ one)) @ id))) & ! [X375 : subst,X373 : term,X374 : subst] : (((sub @ (X371 @ X374 @ X373) @ X375)) = ((X371 @ (comp @ X374 @ X375) @ (sub @ X373 @ X375))))) | ? [X377 : term] : ((((X370 @ X377)) = $true) & (((X370 @ (sub @ X369 @ (push @ X377 @ id)))) != $true))) & ! [X367 : term] : (((sub @ X367 @ id)) = X367))) & ((axvarid = $true) | ? [X124 : term] : (((sub @ X124 @ id)) != X124)) & (! [X124 : term] : (((sub @ X124 @ id)) = X124) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X142 : term,X141 : term] : ((X141 = X142) | (((sub @ X142 @ sh)) != ((sub @ X141 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X142 : term,X141 : term] : ((X141 != X142) & (((sub @ X142 @ sh)) = ((sub @ X141 @ sh))))) & ((induction = $true) | ? [X450 : (term > $o),X449 : term] : (! [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) = $true) | ($true != ((X450 @ X452))) | ($true != ((X450 @ X451)))) & ! [X454 : term] : (($true != ((X450 @ X454))) | (((X450 @ (lam @ X454))) = $true)) & (((X450 @ X449)) != $true) & ! [X453 : term] : ((((X450 @ X453)) = $true) | (((var @ X453)) != $true)))) & (! [X450 : (term > $o),X449 : term] : (? [X451 : term,X452 : term] : ((((X450 @ (ap @ X451 @ X452))) != $true) & ($true = ((X450 @ X452))) & ($true = ((X450 @ X451)))) | ? [X454 : term] : (($true = ((X450 @ X454))) & (((X450 @ (lam @ X454))) != $true)) | (((X450 @ X449)) = $true) | ? [X453 : term] : ((((X450 @ X453)) != $true) & (((var @ X453)) = $true))) | (induction != $true)) & (pushprop_lem3v2 = $true) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X131)) != ((lam @ X132)))) | (laminj != $true)) & ((laminj = $true) | ? [X131 : term,X132 : term] : ((X131 != X132) & (((lam @ X131)) = ((lam @ X132))))) & ((! [X123 : subst] : (((comp @ id @ X123)) = X123) & ! [X122 : subst] : (((comp @ X122 @ id)) = X122)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X123 : subst] : (((comp @ id @ X123)) != X123) | ? [X122 : subst] : (((comp @ X122 @ id)) != X122)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X51 : d_subst] : (d_id = X51) & ! [X239 : d_term] : (d_one = X239) & (hoasinduction_lem2v2_gthm = $true) & (! [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true != ((X389 @ X387))) | (((X390 @ one)) = $true) | ? [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) != ((X390 @ X391)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X390 : (term > $o),X388 : subst,X389 : (term > $o),X387 : term] : (($true = ((X389 @ X387))) & (((X390 @ one)) != $true) & ! [X391 : term] : (((X389 @ (sub @ X391 @ (push @ X387 @ X388)))) = ((X390 @ X391))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & (($true = sP1) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP1)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) = X121) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X121 : subst,X120 : term] : (((comp @ sh @ (push @ X120 @ X121))) != X121)) & (! [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (? [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true = ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) & (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) != $true)) | ($true = ((sP0 @ X338))) | ? [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true != ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) & (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) = $true)) | ? [X354 : term] : (((X338 @ id @ X354 @ id)) != ((X337 @ X354))) | ? [X344 : term] : (($true = ((X337 @ X344))) & ($true != ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) | ($true = ((X337 @ (lam @ X339))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X337 : (term > $o),X339 : term,X338 : (subst > term > subst > $o)] : (! [X342 : term,X343 : subst,X340 : subst,X341 : subst] : (($true != ((X338 @ X341 @ X342 @ (comp @ X343 @ X340)))) | (((X338 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343) @ X340)) = $true)) & ($true != ((sP0 @ X338))) & ! [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true = ((X338 @ X350 @ X352 @ (comp @ X351 @ X353)))) | (((X338 @ (comp @ X350 @ X351) @ (sub @ X352 @ X351) @ X353)) != $true)) & ! [X354 : term] : (((X338 @ id @ X354 @ id)) = ((X337 @ X354))) & ! [X344 : term] : (($true != ((X337 @ X344))) | ($true = ((X337 @ (sub @ X339 @ (push @ X344 @ id)))))) & ($true != ((X337 @ (lam @ X339)))))) & (! [X128 : term] : (((sub @ X128 @ id)) = X128) | (termmset != $true)) & ((termmset = $true) | ? [X128 : term] : (((sub @ X128 @ id)) != X128)) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X183 : d_term,X184 : d_term] : ((X183 = X184) | (((d2term @ X184)) != ((d2term @ X183)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(flattening,[],[f129])).
% 1.38/0.56 thf(f131,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & ((axidl = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0)) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (? [X2 : term,X3 : (subst > term > subst > $o),X4 : (term > $o)] : (! [X5 : subst,X6 : subst,X7 : term,X8 : subst] : ((((X3 @ X8 @ X7 @ (comp @ X6 @ X5))) = $true) | ($true != ((X3 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6) @ X5)))) & ($true != ((X4 @ (lam @ X2)))) & ! [X9 : subst,X10 : subst,X11 : subst,X12 : term] : (($true != ((X3 @ X9 @ X12 @ (comp @ X11 @ X10)))) | ($true = ((X3 @ (comp @ X9 @ X11) @ (sub @ X12 @ X11) @ X10)))) & ! [X13 : term] : (((X4 @ X13)) = ((X3 @ id @ X13 @ id))) & ! [X14 : term] : ((((X4 @ X14)) != $true) | ($true = ((X4 @ (sub @ X2 @ (push @ X14 @ id)))))) & (((sP27 @ X3)) != $true)) & ! [X15 : term] : (((sub @ X15 @ id)) = X15))) & (! [X16 : term,X17 : (subst > term > subst > $o),X18 : (term > $o)] : (? [X19 : subst,X20 : subst,X21 : term,X22 : subst] : (($true != ((X17 @ X22 @ X21 @ (comp @ X20 @ X19)))) & ($true = ((X17 @ (comp @ X22 @ X20) @ (sub @ X21 @ X20) @ X19)))) | ($true = ((X18 @ (lam @ X16)))) | ? [X23 : subst,X24 : subst,X25 : subst,X26 : term] : ((((X17 @ X23 @ X26 @ (comp @ X25 @ X24))) = $true) & ($true != ((X17 @ (comp @ X23 @ X25) @ (sub @ X26 @ X25) @ X24)))) | ? [X27 : term] : (((X17 @ id @ X27 @ id)) != ((X18 @ X27))) | ? [X28 : term] : (($true = ((X18 @ X28))) & ($true != ((X18 @ (sub @ X16 @ (push @ X28 @ id)))))) | ($true = ((sP27 @ X17)))) | ? [X29 : term] : (((sub @ X29 @ id)) != X29) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X30 : term] : (((sub @ X30 @ id)) = X30) & ? [X31 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X32)) = ((ap @ (sub @ X31 @ id) @ X33))) & (X31 != X34)) & ! [X35 : term,X36 : term,X37 : term,X38 : term] : ((((ap @ X37 @ X38)) != ((ap @ X35 @ X36))) | (X35 = X37)))) & (? [X39 : term] : (((sub @ X39 @ id)) != X39) | ! [X40 : term,X41 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X43 @ id) @ X41)) != ((ap @ (sub @ X40 @ id) @ X42))) | (X40 = X43)) | ? [X44 : term,X45 : term,X46 : term,X47 : term] : ((((ap @ X44 @ X45)) = ((ap @ X46 @ X47))) & (X44 != X46)) | (hoasapinj1_lthm != $true)) & ((hoaslaminj = $true) | ? [X48 : term,X49 : subst,X50 : (subst > term > term),X51 : (subst > term > term)] : (! [X52 : term,X53 : subst,X54 : subst] : (((X51 @ (comp @ X53 @ X54) @ (sub @ X52 @ X54))) = ((sub @ (X51 @ X53 @ X52) @ X54))) & (((X51 @ X49 @ X48)) != ((X50 @ X49 @ X48))) & ! [X55 : term,X56 : subst,X57 : subst] : (((X50 @ (comp @ X56 @ X57) @ (sub @ X55 @ X57))) = ((sub @ (X50 @ X56 @ X55) @ X57))) & (((lam @ (X50 @ sh @ one))) = ((lam @ (X51 @ sh @ one)))))) & (! [X58 : term,X59 : subst,X60 : (subst > term > term),X61 : (subst > term > term)] : (? [X62 : term,X63 : subst,X64 : subst] : (((sub @ (X61 @ X63 @ X62) @ X64)) != ((X61 @ (comp @ X63 @ X64) @ (sub @ X62 @ X64)))) | (((X60 @ X59 @ X58)) = ((X61 @ X59 @ X58))) | ? [X65 : term,X66 : subst,X67 : subst] : (((sub @ (X60 @ X66 @ X65) @ X67)) != ((X60 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) | (((lam @ (X61 @ sh @ one))) != ((lam @ (X60 @ sh @ one))))) | (hoaslaminj != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (! [X68 : subst] : (((comp @ X68 @ id)) = X68) | (axidr != $true)) & ((axidr = $true) | ? [X69 : subst] : (((comp @ X69 @ id)) != X69)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X70 : subst] : ? [X71 : d_subst] : (((d2subst @ X71)) = X70) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | ? [X72 : term,X73 : (subst > term > subst > $o)] : (! [X74 : subst,X75 : subst,X76 : term,X77 : subst] : ((((X73 @ X74 @ X76 @ (comp @ X77 @ X75))) != $true) | ($true = ((X73 @ (comp @ X74 @ X77) @ (sub @ X76 @ X77) @ X75)))) & (((sP26 @ X73)) != $true) & ($true != ((X73 @ id @ X72 @ id))) & ($true != ((sP25 @ X73))) & ! [X78 : term] : ((((var @ (sub @ X78 @ id))) != $true) | (((X73 @ id @ X78 @ id)) = $true)) & ! [X79 : term,X80 : subst,X81 : subst,X82 : subst] : (($true = ((X73 @ X80 @ X79 @ (comp @ X82 @ X81)))) | ($true != ((X73 @ (comp @ X80 @ X82) @ (sub @ X79 @ X82) @ X81)))))) & (! [X83 : term,X84 : (subst > term > subst > $o)] : (? [X85 : subst,X86 : subst,X87 : term,X88 : subst] : ((((X84 @ X85 @ X87 @ (comp @ X88 @ X86))) = $true) & ($true != ((X84 @ (comp @ X85 @ X88) @ (sub @ X87 @ X88) @ X86)))) | ($true = ((sP26 @ X84))) | ($true = ((X84 @ id @ X83 @ id))) | (((sP25 @ X84)) = $true) | ? [X89 : term] : (($true = ((var @ (sub @ X89 @ id)))) & ($true != ((X84 @ id @ X89 @ id)))) | ? [X90 : term,X91 : subst,X92 : subst,X93 : subst] : (($true != ((X84 @ X91 @ X90 @ (comp @ X93 @ X92)))) & (((X84 @ (comp @ X91 @ X93) @ (sub @ X90 @ X93) @ X92)) = $true))) | (hoasinduction != $true)) & (? [X94 : (subst > term > subst > $o)] : ! [X95 : (term > $o)] : ? [X96 : term] : (((X95 @ X96)) != ((X94 @ id @ X96 @ id))) | ? [X97 : (term > $o),X98 : term,X99 : (subst > term > subst > $o)] : ((((X97 @ (lam @ X98))) != $true) & ! [X100 : (subst > term > term)] : (? [X101 : term] : (($true = ((X99 @ id @ X101 @ id))) & ($true != ((X99 @ id @ (X100 @ id @ X101) @ id)))) | ? [X102 : subst,X103 : term,X104 : subst] : (((sub @ (X100 @ X104 @ X103) @ X102)) != ((X100 @ (comp @ X104 @ X102) @ (sub @ X103 @ X102)))) | ($true = ((X99 @ id @ (lam @ (X100 @ sh @ one)) @ id)))) & ! [X105 : term] : ((((X97 @ (sub @ X98 @ (push @ X105 @ id)))) = $true) | ($true != ((X97 @ X105)))) & ! [X106 : term] : (((X99 @ id @ X106 @ id)) = ((X97 @ X106)))) | ($true = sP24) | ? [X107 : term] : (((sub @ X107 @ id)) != X107) | (sP23 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X108 : (subst > term > subst > $o)] : ? [X109 : (term > $o)] : ! [X110 : term] : (((X108 @ id @ X110 @ id)) = ((X109 @ X110))) & ! [X111 : (term > $o),X112 : term,X113 : (subst > term > subst > $o)] : (($true = ((X111 @ (lam @ X112)))) | ? [X114 : (subst > term > term)] : (! [X115 : term] : ((((X113 @ id @ X115 @ id)) != $true) | ($true = ((X113 @ id @ (X114 @ id @ X115) @ id)))) & ! [X116 : subst,X117 : term,X118 : subst] : (((X114 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116))) = ((sub @ (X114 @ X118 @ X117) @ X116))) & (((X113 @ id @ (lam @ (X114 @ sh @ one)) @ id)) != $true)) | ? [X119 : term] : ((((X111 @ (sub @ X112 @ (push @ X119 @ id)))) != $true) & (((X111 @ X119)) = $true)) | ? [X120 : term] : (((X113 @ id @ X120 @ id)) != ((X111 @ X120)))) & ($true != sP24) & ! [X121 : term] : (((sub @ X121 @ id)) = X121) & (sP23 != $true))) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & ((pushprop_lem0 = $true) | ? [X122 : subst,X123 : (term > $o),X124 : term] : ! [X125 : (term > $o)] : ? [X126 : term] : (((X123 @ (sub @ X126 @ (push @ X124 @ X122)))) != ((X125 @ X126)))) & (! [X127 : subst,X128 : (term > $o),X129 : term] : ? [X130 : (term > $o)] : ! [X131 : term] : (((X130 @ X131)) = ((X128 @ (sub @ X131 @ (push @ X129 @ X127))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X132 : (subst > term > subst > $o),X133 : term] : (($true != ((X132 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id))) & ! [X134 : (subst > term > term),X135 : term] : (? [X136 : term,X137 : subst,X138 : subst] : (((sub @ X135 @ (push @ (sub @ X136 @ X137) @ (comp @ X138 @ X137)))) != ((X134 @ (comp @ X138 @ X137) @ (sub @ X136 @ X137)))) | ? [X139 : term] : ((((X132 @ id @ (X134 @ id @ X139) @ id)) != $true) & (((X132 @ id @ X139 @ id)) = $true)) | ($true = ((X132 @ id @ (lam @ (X134 @ sh @ one)) @ id))) | ? [X140 : term,X141 : subst,X142 : subst] : (((sub @ (sub @ X135 @ (push @ X140 @ X142)) @ X141)) != ((sub @ (X134 @ X142 @ X140) @ X141)))) & ! [X143 : term] : (($true != ((X132 @ id @ X143 @ id))) | ($true = ((X132 @ id @ (sub @ X133 @ (push @ X143 @ id)) @ id)))))) & (! [X144 : (subst > term > subst > $o),X145 : term] : ((((X144 @ id @ (lam @ (sub @ X145 @ (push @ one @ sh))) @ id)) = $true) | ? [X146 : (subst > term > term),X147 : term] : (! [X148 : term,X149 : subst,X150 : subst] : (((sub @ X147 @ (push @ (sub @ X148 @ X149) @ (comp @ X150 @ X149)))) = ((X146 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149)))) & ! [X151 : term] : (($true = ((X144 @ id @ (X146 @ id @ X151) @ id))) | ($true != ((X144 @ id @ X151 @ id)))) & ($true != ((X144 @ id @ (lam @ (X146 @ sh @ one)) @ id))) & ! [X152 : term,X153 : subst,X154 : subst] : (((sub @ (sub @ X147 @ (push @ X152 @ X154)) @ X153)) = ((sub @ (X146 @ X154 @ X152) @ X153)))) | ? [X155 : term] : ((((X144 @ id @ X155 @ id)) = $true) & (((X144 @ id @ (sub @ X145 @ (push @ X155 @ id)) @ id)) != $true))) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem0_gthm = $true) & ((apinj2 = $true) | ? [X156 : term,X157 : term,X158 : term,X159 : term] : ((X156 != X159) & (((ap @ X157 @ X156)) = ((ap @ X158 @ X159))))) & (! [X160 : term,X161 : term,X162 : term,X163 : term] : ((X160 = X163) | (((ap @ X162 @ X163)) != ((ap @ X161 @ X160)))) | (apinj2 != $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X165 = X167) | (((ap @ (sub @ X164 @ id) @ X165)) != ((ap @ (sub @ X166 @ id) @ X167)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X168 : term,X169 : term,X170 : term,X171 : term] : ((X169 != X171) & (((ap @ (sub @ X170 @ id) @ X171)) = ((ap @ (sub @ X168 @ id) @ X169))))) & ((apinj1 = $true) | ? [X172 : term,X173 : term,X174 : term,X175 : term] : ((((ap @ X173 @ X174)) = ((ap @ X175 @ X172))) & (X173 != X175))) & (! [X176 : term,X177 : term,X178 : term,X179 : term] : ((((ap @ X177 @ X178)) != ((ap @ X179 @ X176))) | (X177 = X179)) | (apinj1 != $true)) & (($true = sP20) | ? [X180 : term] : (((sub @ X180 @ id)) != X180) | ? [X181 : (subst > term > subst > $o),X182 : term] : (! [X183 : (subst > term > term)] : (? [X184 : subst,X185 : term,X186 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) != ((sub @ (X183 @ X186 @ X185) @ X184))) | ($true = ((X181 @ id @ (lam @ (X183 @ sh @ one)) @ id))) | ? [X187 : term] : (($true != ((X181 @ id @ (X183 @ id @ X187) @ id))) & ($true = ((X181 @ id @ X187 @ id))))) & ! [X188 : term] : (($true = ((X181 @ id @ (sub @ X182 @ (push @ X188 @ id)) @ id))) | ($true != ((X181 @ id @ X188 @ id)))) & (((X181 @ id @ (lam @ (sub @ X182 @ (push @ one @ sh))) @ id)) != $true)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP20) & ! [X189 : term] : (((sub @ X189 @ id)) = X189) & ! [X190 : (subst > term > subst > $o),X191 : term] : (? [X192 : (subst > term > term)] : (! [X193 : subst,X194 : term,X195 : subst] : (((X192 @ (comp @ X195 @ X193) @ (sub @ X194 @ X193))) = ((sub @ (X192 @ X195 @ X194) @ X193))) & (((X190 @ id @ (lam @ (X192 @ sh @ one)) @ id)) != $true) & ! [X196 : term] : (($true = ((X190 @ id @ (X192 @ id @ X196) @ id))) | ($true != ((X190 @ id @ X196 @ id))))) | ? [X197 : term] : ((((X190 @ id @ (sub @ X191 @ (push @ X197 @ id)) @ id)) != $true) & (((X190 @ id @ X197 @ id)) = $true)) | ($true = ((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)))))) & (ulamvarind = $true) & (! [X198 : term] : ? [X199 : (subst > term > term)] : ! [X200 : subst,X201 : term] : (((X199 @ X200 @ X201)) = ((sub @ X198 @ (push @ X201 @ X200)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X202 : term] : ! [X203 : (subst > term > term)] : ? [X204 : subst,X205 : term] : (((X203 @ X204 @ X205)) != ((sub @ X202 @ (push @ X205 @ X204))))) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (! [X206 : subst,X207 : term] : (((sub @ one @ (push @ X207 @ X206))) = X207) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X208 : subst,X209 : term] : (((sub @ one @ (push @ X209 @ X208))) != X209)) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & (! [X210 : (subst > term > subst > $o),X211 : term] : ((((X210 @ id @ (lam @ X211) @ id)) = $true) | ? [X212 : (subst > term > term)] : ((((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id)) != $true) & ! [X213 : term] : (($true != ((X210 @ id @ X213 @ id))) | ($true = ((X210 @ id @ (X212 @ id @ X213) @ id)))) & ! [X214 : subst,X215 : term,X216 : subst] : (((sub @ (X212 @ X216 @ X215) @ X214)) = ((X212 @ (comp @ X216 @ X214) @ (sub @ X215 @ X214))))) | ? [X217 : term] : ((((X210 @ id @ X217 @ id)) = $true) & (((X210 @ id @ (sub @ X211 @ (push @ X217 @ id)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X218 : (subst > term > subst > $o),X219 : term] : (($true != ((X218 @ id @ (lam @ X219) @ id))) & ! [X220 : (subst > term > term)] : (($true = ((X218 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ? [X221 : term] : (($true = ((X218 @ id @ X221 @ id))) & (((X218 @ id @ (X220 @ id @ X221) @ id)) != $true)) | ? [X222 : subst,X223 : term,X224 : subst] : (((X220 @ (comp @ X224 @ X222) @ (sub @ X223 @ X222))) != ((sub @ (X220 @ X224 @ X223) @ X222)))) & ! [X225 : term] : (($true != ((X218 @ id @ X225 @ id))) | ($true = ((X218 @ id @ (sub @ X219 @ (push @ X225 @ id)) @ id)))))) & ((hoasapinj1 = $true) | ? [X226 : term,X227 : term,X228 : term,X229 : term] : ((((ap @ (sub @ X229 @ id) @ X227)) = ((ap @ (sub @ X228 @ id) @ X226))) & (X228 != X229))) & (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ (sub @ X232 @ id) @ X230)) != ((ap @ (sub @ X233 @ id) @ X231))) | (X232 = X233)) | (hoasapinj1 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X234 : subst,X235 : term] : (((comp @ sh @ (push @ X235 @ X234))) = X234) & ? [X236 : term,X237 : (term > $o),X238 : (term > $o),X239 : subst,X240 : term] : (($true = ((X238 @ X236))) & ($true != ((X237 @ (sub @ X236 @ (push @ X240 @ X239)))))) & ! [X241 : subst,X242 : term] : (((sub @ one @ (push @ X242 @ X241))) = X242))) & (? [X243 : subst,X244 : term] : (((comp @ sh @ (push @ X244 @ X243))) != X243) | ! [X245 : term,X246 : (term > $o),X247 : (term > $o),X248 : subst,X249 : term] : ((((X247 @ X245)) != $true) | (((X246 @ (sub @ X245 @ (push @ X249 @ X248)))) = $true)) | ? [X250 : subst,X251 : term] : (((sub @ one @ (push @ X251 @ X250))) != X251) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X252 : term,X253 : (term > $o),X254 : subst] : ! [X255 : (term > $o)] : ? [X256 : term] : (((X255 @ X256)) != ((X253 @ (sub @ X256 @ (push @ X252 @ X254)))))) & (! [X257 : term,X258 : (term > $o),X259 : subst] : ? [X260 : (term > $o)] : ! [X261 : term] : (((X258 @ (sub @ X261 @ (push @ X257 @ X259)))) = ((X260 @ X261))) | (pushprop_lem0_lthm != $true)) & (apnotvar = $true) & ! [X262 : term] : ? [X263 : d_term] : (((d2term @ X263)) = X262) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) | (! [X264 : term,X265 : term,X266 : term,X267 : term] : ((((ap @ X265 @ X267)) != ((ap @ X264 @ X266))) | (X266 = X267)) & ? [X268 : term,X269 : term,X270 : term,X271 : term] : ((X268 != X270) & (((ap @ (sub @ X271 @ id) @ X270)) = ((ap @ (sub @ X269 @ id) @ X268)))))) & (? [X272 : term,X273 : term,X274 : term,X275 : term] : ((((ap @ X273 @ X275)) = ((ap @ X272 @ X274))) & (X274 != X275)) | ! [X276 : term,X277 : term,X278 : term,X279 : term] : ((X276 = X278) | (((ap @ (sub @ X277 @ id) @ X276)) != ((ap @ (sub @ X279 @ id) @ X278)))) | (hoasapinj2_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X280 : (subst > term > subst > $o)] : ! [X281 : (term > $o)] : ? [X282 : term] : (((X281 @ X282)) != ((X280 @ id @ X282 @ id)))) & (! [X283 : (subst > term > subst > $o)] : ? [X284 : (term > $o)] : ! [X285 : term] : (((X284 @ X285)) = ((X283 @ id @ X285 @ id))) | (hoasinduction_lem0_lthm != $true)) & (axclos = $true) & (hoasapinj2_gthm = $true) & (! [X286 : term,X287 : (term > $o),X288 : (subst > term > subst > $o)] : (($true = ((X287 @ (lam @ X286)))) | ? [X289 : term] : (($true != ((X287 @ (sub @ X286 @ (push @ X289 @ id))))) & ($true = ((X287 @ X289)))) | ? [X290 : (subst > term > term)] : (! [X291 : subst,X292 : subst,X293 : term] : (((X290 @ (comp @ X291 @ X292) @ (sub @ X293 @ X292))) = ((sub @ (X290 @ X291 @ X293) @ X292))) & (((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id)) != $true) & ! [X294 : term] : ((((X288 @ id @ X294 @ id)) != $true) | ($true = ((X288 @ id @ (X290 @ id @ X294) @ id))))) | ? [X295 : term] : (((X288 @ id @ X295 @ id)) != ((X287 @ X295)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ? [X296 : term,X297 : (term > $o),X298 : (subst > term > subst > $o)] : ((((X297 @ (lam @ X296))) != $true) & ! [X299 : term] : (($true = ((X297 @ (sub @ X296 @ (push @ X299 @ id))))) | ($true != ((X297 @ X299)))) & ! [X300 : (subst > term > term)] : (? [X301 : subst,X302 : subst,X303 : term] : (((X300 @ (comp @ X301 @ X302) @ (sub @ X303 @ X302))) != ((sub @ (X300 @ X301 @ X303) @ X302))) | ($true = ((X298 @ id @ (lam @ (X300 @ sh @ one)) @ id))) | ? [X304 : term] : ((((X298 @ id @ X304 @ id)) = $true) & ($true != ((X298 @ id @ (X300 @ id @ X304) @ id))))) & ! [X305 : term] : (((X298 @ id @ X305 @ id)) = ((X297 @ X305))))) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) | (! [X306 : term,X307 : term] : ((X306 = X307) | (((lam @ X306)) != ((lam @ X307)))) & ? [X308 : subst,X309 : (subst > term > term),X310 : term,X311 : (subst > term > term)] : (! [X312 : subst,X313 : subst,X314 : term] : (((sub @ (X311 @ X312 @ X314) @ X313)) = ((X311 @ (comp @ X312 @ X313) @ (sub @ X314 @ X313)))) & ! [X315 : subst,X316 : subst,X317 : term] : (((sub @ (X309 @ X316 @ X317) @ X315)) = ((X309 @ (comp @ X316 @ X315) @ (sub @ X317 @ X315)))) & (((X311 @ X308 @ X310)) != ((X309 @ X308 @ X310))) & (((lam @ (X311 @ sh @ one))) = ((lam @ (X309 @ sh @ one))))) & ! [X318 : term,X319 : subst] : (((comp @ sh @ (push @ X318 @ X319))) = X319) & ! [X320 : term,X321 : subst] : (((sub @ one @ (push @ X320 @ X321))) = X320))) & (? [X322 : term,X323 : term] : ((X322 != X323) & (((lam @ X323)) = ((lam @ X322)))) | ! [X324 : subst,X325 : (subst > term > term),X326 : term,X327 : (subst > term > term)] : (? [X328 : subst,X329 : subst,X330 : term] : (((X327 @ (comp @ X328 @ X329) @ (sub @ X330 @ X329))) != ((sub @ (X327 @ X328 @ X330) @ X329))) | ? [X331 : subst,X332 : subst,X333 : term] : (((X325 @ (comp @ X332 @ X331) @ (sub @ X333 @ X331))) != ((sub @ (X325 @ X332 @ X333) @ X331))) | (((X327 @ X324 @ X326)) = ((X325 @ X324 @ X326))) | (((lam @ (X325 @ sh @ one))) != ((lam @ (X327 @ sh @ one))))) | ? [X334 : term,X335 : subst] : (((comp @ sh @ (push @ X334 @ X335))) != X335) | ? [X336 : term,X337 : subst] : (((sub @ one @ (push @ X336 @ X337))) != X336) | (hoaslaminj_lthm != $true)) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) | ? [X339 : term] : (((sub @ X339 @ id)) != X339) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X340 : term] : (((sub @ X340 @ id)) != X340) & ! [X341 : term] : (((sub @ X341 @ id)) = X341))) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X342 : term] : ? [X343 : (subst > term > term)] : (((X343 @ sh @ one)) = ((sub @ X342 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X344 : term] : ! [X345 : (subst > term > term)] : (((X345 @ sh @ one)) != ((sub @ X344 @ (push @ one @ sh))))) & (! [X346 : (term > $o),X347 : (term > $o),X348 : subst,X349 : term] : (($true != ((X347 @ X349))) | ? [X350 : term] : (((X347 @ (sub @ X350 @ (push @ X349 @ X348)))) != ((X346 @ X350))) | (((X346 @ one)) = $true)) | ? [X351 : term,X352 : subst] : (((sub @ one @ (push @ X351 @ X352))) != X351) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X353 : (term > $o),X354 : (term > $o),X355 : subst,X356 : term] : (($true = ((X354 @ X356))) & ! [X357 : term] : (((X354 @ (sub @ X357 @ (push @ X356 @ X355)))) = ((X353 @ X357))) & (((X353 @ one)) != $true)) & ! [X358 : term,X359 : subst] : (((sub @ one @ (push @ X358 @ X359))) = X358))) & ((hoasinduction_lem3 = $true) | ? [X360 : (subst > term > subst > $o),X361 : term] : (! [X362 : subst,X363 : subst,X364 : subst,X365 : term] : (($true = ((X360 @ (comp @ X364 @ X363) @ (sub @ X365 @ X363) @ X362))) | ($true != ((X360 @ X364 @ X365 @ (comp @ X363 @ X362))))) & ($true != ((sP19 @ X360))) & ! [X366 : subst,X367 : subst,X368 : subst,X369 : term] : ((((X360 @ X366 @ X369 @ (comp @ X368 @ X367))) = $true) | ($true != ((X360 @ (comp @ X366 @ X368) @ (sub @ X369 @ X368) @ X367)))) & (((X360 @ id @ (lam @ X361) @ id)) != $true) & ! [X370 : term] : ((((X360 @ id @ (sub @ X361 @ (push @ X370 @ id)) @ id)) = $true) | ($true != ((X360 @ id @ X370 @ id)))))) & (! [X371 : (subst > term > subst > $o),X372 : term] : (? [X373 : subst,X374 : subst,X375 : subst,X376 : term] : (($true != ((X371 @ (comp @ X375 @ X374) @ (sub @ X376 @ X374) @ X373))) & ($true = ((X371 @ X375 @ X376 @ (comp @ X374 @ X373))))) | ($true = ((sP19 @ X371))) | ? [X377 : subst,X378 : subst,X379 : subst,X380 : term] : (($true != ((X371 @ X377 @ X380 @ (comp @ X379 @ X378)))) & ($true = ((X371 @ (comp @ X377 @ X379) @ (sub @ X380 @ X379) @ X378)))) | ($true = ((X371 @ id @ (lam @ X372) @ id))) | ? [X381 : term] : ((((X371 @ id @ (sub @ X372 @ (push @ X381 @ id)) @ id)) != $true) & ($true = ((X371 @ id @ X381 @ id))))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X382 : subst] : (((comp @ id @ X382)) = X382) & ! [X383 : subst] : (((comp @ X383 @ id)) = X383)) | ? [X384 : subst] : (((comp @ X384 @ id)) != X384) | ? [X385 : subst] : (((comp @ id @ X385)) != X385) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X386 : subst] : (((comp @ id @ X386)) != X386) | ? [X387 : subst] : (((comp @ X387 @ id)) != X387)) & ! [X388 : subst] : (((comp @ X388 @ id)) = X388) & ! [X389 : subst] : (((comp @ id @ X389)) = X389))) & ((induction2lem_lthm = $true) | ($true != sP18)) & (($true = sP18) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X390 : term] : ? [X391 : (subst > term > term)] : ! [X392 : subst,X393 : term] : (((sub @ X390 @ (push @ X393 @ X392))) = ((X391 @ X392 @ X393))) & ? [X394 : term,X395 : (subst > term > subst > $o),X396 : (term > $o)] : ((((X396 @ (lam @ X394))) != $true) & ! [X397 : (subst > term > term)] : ((((X395 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true) | ? [X398 : subst,X399 : subst,X400 : term] : (((sub @ (X397 @ X398 @ X400) @ X399)) != ((X397 @ (comp @ X398 @ X399) @ (sub @ X400 @ X399)))) | ? [X401 : term] : ((((X395 @ id @ (X397 @ id @ X401) @ id)) != $true) & ($true = ((X395 @ id @ X401 @ id))))) & ! [X402 : term] : (($true = ((X396 @ (sub @ X394 @ (push @ X402 @ id))))) | ($true != ((X396 @ X402)))) & ! [X403 : term] : (((X396 @ X403)) = ((X395 @ id @ X403 @ id)))) & ! [X404 : term] : (((sub @ X404 @ id)) = X404))) & (? [X405 : term] : ! [X406 : (subst > term > term)] : ? [X407 : subst,X408 : term] : (((X406 @ X407 @ X408)) != ((sub @ X405 @ (push @ X408 @ X407)))) | ! [X409 : term,X410 : (subst > term > subst > $o),X411 : (term > $o)] : (($true = ((X411 @ (lam @ X409)))) | ? [X412 : (subst > term > term)] : ((((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id)) != $true) & ! [X413 : subst,X414 : subst,X415 : term] : (((X412 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))) = ((sub @ (X412 @ X413 @ X415) @ X414))) & ! [X416 : term] : (($true = ((X410 @ id @ (X412 @ id @ X416) @ id))) | (((X410 @ id @ X416 @ id)) != $true))) | ? [X417 : term] : (($true != ((X411 @ (sub @ X409 @ (push @ X417 @ id))))) & ($true = ((X411 @ X417)))) | ? [X418 : term] : (((X411 @ X418)) != ((X410 @ id @ X418 @ id)))) | ? [X419 : term] : (((sub @ X419 @ id)) != X419) | (hoasinduction_lem3v2a_lthm != $true)) & (? [X420 : (subst > term > subst > $o),X421 : term] : (! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : ((((X420 @ (comp @ X422 @ X425) @ (sub @ X424 @ X425) @ X423)) != $true) | ($true = ((X420 @ X422 @ X424 @ (comp @ X425 @ X423))))) & (((sP13 @ X420)) = $true) & ! [X426 : term,X427 : subst,X428 : subst,X429 : subst] : ((((X420 @ (comp @ X427 @ X429) @ (sub @ X426 @ X429) @ X428)) = $true) | ($true != ((X420 @ X427 @ X426 @ (comp @ X429 @ X428))))) & (((X420 @ id @ (lam @ X421) @ id)) != $true) & ! [X430 : term] : ((((X420 @ id @ X430 @ id)) != $true) | (((X420 @ id @ (sub @ X421 @ (push @ X430 @ id)) @ id)) = $true))) | (sP15 = $true) | (sP14 = $true) | (sP16 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (! [X431 : (subst > term > subst > $o),X432 : term] : (? [X433 : subst,X434 : subst,X435 : term,X436 : subst] : (($true = ((X431 @ (comp @ X433 @ X436) @ (sub @ X435 @ X436) @ X434))) & (((X431 @ X433 @ X435 @ (comp @ X436 @ X434))) != $true)) | ($true != ((sP13 @ X431))) | ? [X437 : term,X438 : subst,X439 : subst,X440 : subst] : (($true != ((X431 @ (comp @ X438 @ X440) @ (sub @ X437 @ X440) @ X439))) & ($true = ((X431 @ X438 @ X437 @ (comp @ X440 @ X439))))) | ($true = ((X431 @ id @ (lam @ X432) @ id))) | ? [X441 : term] : ((((X431 @ id @ X441 @ id)) = $true) & (((X431 @ id @ (sub @ X432 @ (push @ X441 @ id)) @ id)) != $true))) & (sP15 != $true) & (sP14 != $true) & (sP16 != $true))) & (! [X442 : (term > $o),X443 : subst,X444 : (term > $o),X445 : term,X446 : term] : (($true = ((X442 @ (sub @ X445 @ (push @ X446 @ X443))))) | (((X444 @ X445)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X447 : (term > $o),X448 : subst,X449 : (term > $o),X450 : term,X451 : term] : (($true != ((X447 @ (sub @ X450 @ (push @ X451 @ X448))))) & (((X449 @ X450)) = $true))) & (($true = sP10) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP10)) & (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)))))))))))) & (! [X452 : subst] : (((push @ (sub @ one @ X452) @ (comp @ sh @ X452))) = X452) | (axscons != $true)) & ((axscons = $true) | ? [X453 : subst] : (((push @ (sub @ one @ X453) @ (comp @ sh @ X453))) != X453)) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (! [X454 : (subst > term > subst > $o)] : ? [X455 : (term > $o)] : ! [X456 : term] : (((X455 @ X456)) = ((X454 @ id @ X456 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X457 : (subst > term > subst > $o)] : ! [X458 : (term > $o)] : ? [X459 : term] : (((X457 @ id @ X459 @ id)) != ((X458 @ X459)))) & ((hoasinduction_lem2 = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X460 : term,X461 : (subst > term > subst > $o)] : (($true = ((X461 @ id @ (lam @ (sub @ X460 @ (push @ one @ sh))) @ id))) | ? [X462 : (subst > term > term)] : (! [X463 : term,X464 : subst,X465 : subst] : (((X462 @ (comp @ X465 @ X464) @ (sub @ X463 @ X464))) = ((sub @ (X462 @ X465 @ X463) @ X464))) & ($true != ((X461 @ id @ (lam @ (X462 @ sh @ one)) @ id))) & ! [X466 : term] : (($true = ((X461 @ id @ (X462 @ id @ X466) @ id))) | ($true != ((X461 @ id @ X466 @ id))))) | ? [X467 : term] : (($true != ((X461 @ id @ (sub @ X460 @ (push @ X467 @ id)) @ id))) & (((X461 @ id @ X467 @ id)) = $true))) & ! [X468 : term] : (((sub @ X468 @ id)) = X468) & (sP7 != $true))) & (? [X469 : term,X470 : (subst > term > subst > $o)] : (($true != ((X470 @ id @ (lam @ (sub @ X469 @ (push @ one @ sh))) @ id))) & ! [X471 : (subst > term > term)] : (? [X472 : term,X473 : subst,X474 : subst] : (((sub @ (X471 @ X474 @ X472) @ X473)) != ((X471 @ (comp @ X474 @ X473) @ (sub @ X472 @ X473)))) | (((X470 @ id @ (lam @ (X471 @ sh @ one)) @ id)) = $true) | ? [X475 : term] : ((((X470 @ id @ (X471 @ id @ X475) @ id)) != $true) & ($true = ((X470 @ id @ X475 @ id))))) & ! [X476 : term] : (($true = ((X470 @ id @ (sub @ X469 @ (push @ X476 @ id)) @ id))) | ($true != ((X470 @ id @ X476 @ id))))) | ? [X477 : term] : (((sub @ X477 @ id)) != X477) | (sP7 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X478 : term,X479 : (subst > term > subst > $o)] : (($true = ((X479 @ id @ X478 @ id))) | ? [X480 : term,X481 : term] : (($true != ((X479 @ id @ (ap @ (sub @ X481 @ id) @ X480) @ id))) & (((X479 @ id @ X480 @ id)) = $true) & (((X479 @ id @ X481 @ id)) = $true)) | ? [X482 : (subst > term > term)] : (! [X483 : term,X484 : subst,X485 : subst] : (((X482 @ (comp @ X484 @ X485) @ (sub @ X483 @ X485))) = ((sub @ (X482 @ X484 @ X483) @ X485))) & ! [X486 : term] : (($true != ((X479 @ id @ X486 @ id))) | (((X479 @ id @ (X482 @ id @ X486) @ id)) = $true)) & ($true != ((X479 @ id @ (lam @ (X482 @ sh @ one)) @ id))))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X487 : term,X488 : (subst > term > subst > $o)] : ((((X488 @ id @ X487 @ id)) != $true) & ! [X489 : term,X490 : term] : (($true = ((X488 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id))) | (((X488 @ id @ X489 @ id)) != $true) | ($true != ((X488 @ id @ X490 @ id)))) & ! [X491 : (subst > term > term)] : (? [X492 : term,X493 : subst,X494 : subst] : (((sub @ (X491 @ X493 @ X492) @ X494)) != ((X491 @ (comp @ X493 @ X494) @ (sub @ X492 @ X494)))) | ? [X495 : term] : (($true = ((X488 @ id @ X495 @ id))) & ($true != ((X488 @ id @ (X491 @ id @ X495) @ id)))) | (((X488 @ id @ (lam @ (X491 @ sh @ one)) @ id)) = $true)))) & (! [X496 : term] : ? [X497 : (subst > term > term)] : ! [X498 : subst,X499 : term] : (((X497 @ X498 @ X499)) = ((sub @ X496 @ (push @ X499 @ X498)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X500 : term] : ! [X501 : (subst > term > term)] : ? [X502 : subst,X503 : term] : (((sub @ X500 @ (push @ X503 @ X502))) != ((X501 @ X502 @ X503)))) & (pushprop_lem2v2 = $true) & ((hoaslamnotap = $true) | ? [X504 : term,X505 : (subst > term > term),X506 : term] : (! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X505 @ X508 @ X509) @ X507)) = ((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) & (((ap @ (sub @ X506 @ id) @ X504)) = ((lam @ (X505 @ sh @ one)))))) & (! [X510 : term,X511 : (subst > term > term),X512 : term] : (? [X513 : subst,X514 : subst,X515 : term] : (((sub @ (X511 @ X514 @ X515) @ X513)) != ((X511 @ (comp @ X514 @ X513) @ (sub @ X515 @ X513)))) | (((lam @ (X511 @ sh @ one))) != ((ap @ (sub @ X512 @ id) @ X510)))) | (hoaslamnotap != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3aa_lthm = $true) | ? [X516 : (subst > term > subst > $o),X517 : term] : (! [X518 : term] : (($true != ((X516 @ id @ X518 @ id))) | ($true = ((X516 @ id @ (sub @ X517 @ (push @ X518 @ id)) @ id)))) & ($true != ((X516 @ id @ (lam @ (sub @ X517 @ (push @ one @ sh))) @ id))) & ! [X519 : (subst > term > term)] : (? [X520 : term] : ((((X516 @ id @ (X519 @ id @ X520) @ id)) != $true) & (((X516 @ id @ X520 @ id)) = $true)) | ($true = ((X516 @ id @ (lam @ (X519 @ sh @ one)) @ id))) | ? [X521 : subst,X522 : subst,X523 : term] : (((sub @ (X519 @ X522 @ X523) @ X521)) != ((X519 @ (comp @ X522 @ X521) @ (sub @ X523 @ X521))))))) & (! [X524 : (subst > term > subst > $o),X525 : term] : (? [X526 : term] : (($true = ((X524 @ id @ X526 @ id))) & ($true != ((X524 @ id @ (sub @ X525 @ (push @ X526 @ id)) @ id)))) | ($true = ((X524 @ id @ (lam @ (sub @ X525 @ (push @ one @ sh))) @ id))) | ? [X527 : (subst > term > term)] : (! [X528 : term] : ((((X524 @ id @ (X527 @ id @ X528) @ id)) = $true) | (((X524 @ id @ X528 @ id)) != $true)) & (((X524 @ id @ (lam @ (X527 @ sh @ one)) @ id)) != $true) & ! [X529 : subst,X530 : subst,X531 : term] : (((sub @ (X527 @ X530 @ X531) @ X529)) = ((X527 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529)))))) | (hoasinduction_lem3aa_lthm != $true)) & (! [X532 : term] : ? [X533 : (subst > term > term)] : (((sub @ X532 @ (push @ one @ sh))) = ((X533 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X534 : term] : ! [X535 : (subst > term > term)] : (((sub @ X534 @ (push @ one @ sh))) != ((X535 @ sh @ one)))) & (((d2subst @ d_id)) = id) & ! [X536 : d_subst,X537 : d_subst] : ((((d2subst @ X536)) != ((d2subst @ X537))) | (X536 = X537)) & (($true = sP5) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP5)) & (! [X538 : term,X539 : (subst > term > subst > $o)] : (? [X540 : term] : ((((X539 @ id @ X540 @ id)) = $true) & (((X539 @ id @ (sub @ X538 @ (push @ X540 @ id)) @ id)) != $true)) | ? [X541 : (subst > term > term)] : (! [X542 : term] : ((((X539 @ id @ X542 @ id)) != $true) | (((X539 @ id @ (X541 @ id @ X542) @ id)) = $true)) & ! [X543 : term,X544 : subst,X545 : subst] : (((X541 @ (comp @ X545 @ X544) @ (sub @ X543 @ X544))) = ((sub @ (X541 @ X545 @ X543) @ X544))) & ($true != ((X539 @ id @ (lam @ (X541 @ sh @ one)) @ id)))) | (((X539 @ id @ (lam @ (sub @ X538 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ? [X546 : term,X547 : (subst > term > subst > $o)] : (! [X548 : term] : (($true != ((X547 @ id @ X548 @ id))) | ($true = ((X547 @ id @ (sub @ X546 @ (push @ X548 @ id)) @ id)))) & ! [X549 : (subst > term > term)] : (? [X550 : term] : ((((X547 @ id @ X550 @ id)) = $true) & ($true != ((X547 @ id @ (X549 @ id @ X550) @ id)))) | ? [X551 : term,X552 : subst,X553 : subst] : (((sub @ (X549 @ X553 @ X551) @ X552)) != ((X549 @ (comp @ X553 @ X552) @ (sub @ X551 @ X552)))) | (((X547 @ id @ (lam @ (X549 @ sh @ one)) @ id)) = $true)) & ($true != ((X547 @ id @ (lam @ (sub @ X546 @ (push @ one @ sh))) @ id))))) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP3) | ? [X554 : (subst > term > subst > $o)] : ! [X555 : (term > $o)] : ? [X556 : term] : (((X554 @ id @ X556 @ id)) != ((X555 @ X556))) | ($true = sP2) | ? [X557 : (subst > term > subst > $o),X558 : (term > $o),X559 : term] : (! [X560 : term] : (((X557 @ id @ X560 @ id)) = ((X558 @ X560))) & ($true != ((X558 @ (lam @ X559)))) & ! [X561 : (subst > term > term)] : (? [X562 : term] : (($true = ((X557 @ id @ X562 @ id))) & (((X557 @ id @ (X561 @ id @ X562) @ id)) != $true)) | (((X557 @ id @ (lam @ (X561 @ sh @ one)) @ id)) = $true) | ? [X563 : subst,X564 : term,X565 : subst] : (((X561 @ (comp @ X565 @ X563) @ (sub @ X564 @ X563))) != ((sub @ (X561 @ X565 @ X564) @ X563)))) & ! [X566 : term] : ((((X558 @ X566)) != $true) | ($true = ((X558 @ (sub @ X559 @ (push @ X566 @ id))))))) | ? [X567 : term] : (((sub @ X567 @ id)) != X567) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP3) & ! [X568 : (subst > term > subst > $o)] : ? [X569 : (term > $o)] : ! [X570 : term] : (((X569 @ X570)) = ((X568 @ id @ X570 @ id))) & ($true != sP2) & ! [X571 : (subst > term > subst > $o),X572 : (term > $o),X573 : term] : (? [X574 : term] : (((X572 @ X574)) != ((X571 @ id @ X574 @ id))) | ($true = ((X572 @ (lam @ X573)))) | ? [X575 : (subst > term > term)] : (! [X576 : term] : (($true != ((X571 @ id @ X576 @ id))) | ($true = ((X571 @ id @ (X575 @ id @ X576) @ id)))) & ($true != ((X571 @ id @ (lam @ (X575 @ sh @ one)) @ id))) & ! [X577 : subst,X578 : term,X579 : subst] : (((sub @ (X575 @ X579 @ X578) @ X577)) = ((X575 @ (comp @ X579 @ X577) @ (sub @ X578 @ X577))))) | ? [X580 : term] : (($true = ((X572 @ X580))) & ($true != ((X572 @ (sub @ X573 @ (push @ X580 @ id))))))) & ! [X581 : term] : (((sub @ X581 @ id)) = X581))) & ((axvarid = $true) | ? [X582 : term] : (((sub @ X582 @ id)) != X582)) & (! [X583 : term] : (((sub @ X583 @ id)) = X583) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X584 : term,X585 : term] : ((X584 = X585) | (((sub @ X584 @ sh)) != ((sub @ X585 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ? [X586 : term,X587 : term] : ((X586 != X587) & (((sub @ X586 @ sh)) = ((sub @ X587 @ sh))))) & ((induction = $true) | ? [X588 : (term > $o),X589 : term] : (! [X590 : term,X591 : term] : (($true = ((X588 @ (ap @ X590 @ X591)))) | (((X588 @ X591)) != $true) | ($true != ((X588 @ X590)))) & ! [X592 : term] : (($true != ((X588 @ X592))) | ($true = ((X588 @ (lam @ X592))))) & ($true != ((X588 @ X589))) & ! [X593 : term] : (($true = ((X588 @ X593))) | ($true != ((var @ X593)))))) & (! [X594 : (term > $o),X595 : term] : (? [X596 : term,X597 : term] : (($true != ((X594 @ (ap @ X596 @ X597)))) & ($true = ((X594 @ X597))) & (((X594 @ X596)) = $true)) | ? [X598 : term] : (($true = ((X594 @ X598))) & ($true != ((X594 @ (lam @ X598))))) | (((X594 @ X595)) = $true) | ? [X599 : term] : (($true != ((X594 @ X599))) & (((var @ X599)) = $true))) | (induction != $true)) & (pushprop_lem3v2 = $true) & (! [X600 : term,X601 : term] : ((X600 = X601) | (((lam @ X601)) != ((lam @ X600)))) | (laminj != $true)) & ((laminj = $true) | ? [X602 : term,X603 : term] : ((X602 != X603) & (((lam @ X602)) = ((lam @ X603))))) & ((! [X604 : subst] : (((comp @ id @ X604)) = X604) & ! [X605 : subst] : (((comp @ X605 @ id)) = X605)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X606 : subst] : (((comp @ id @ X606)) != X606) | ? [X607 : subst] : (((comp @ X607 @ id)) != X607)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X608 : d_subst] : (d_id = X608) & ! [X609 : d_term] : (d_one = X609) & (hoasinduction_lem2v2_gthm = $true) & (! [X610 : (term > $o),X611 : subst,X612 : (term > $o),X613 : term] : (($true != ((X612 @ X613))) | ($true = ((X610 @ one))) | ? [X614 : term] : (((X610 @ X614)) != ((X612 @ (sub @ X614 @ (push @ X613 @ X611)))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X615 : (term > $o),X616 : subst,X617 : (term > $o),X618 : term] : (($true = ((X617 @ X618))) & ($true != ((X615 @ one))) & ! [X619 : term] : (((X617 @ (sub @ X619 @ (push @ X618 @ X616)))) = ((X615 @ X619))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & (($true = sP1) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP1)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X620 : subst,X621 : term] : (((comp @ sh @ (push @ X621 @ X620))) = X620) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X622 : subst,X623 : term] : (((comp @ sh @ (push @ X623 @ X622))) != X622)) & (! [X624 : (term > $o),X625 : term,X626 : (subst > term > subst > $o)] : (? [X627 : term,X628 : subst,X629 : subst,X630 : subst] : (($true = ((X626 @ X630 @ X627 @ (comp @ X628 @ X629)))) & (((X626 @ (comp @ X630 @ X628) @ (sub @ X627 @ X628) @ X629)) != $true)) | ($true = ((sP0 @ X626))) | ? [X631 : subst,X632 : subst,X633 : subst,X634 : term] : ((((X626 @ X632 @ X634 @ (comp @ X631 @ X633))) != $true) & (((X626 @ (comp @ X632 @ X631) @ (sub @ X634 @ X631) @ X633)) = $true)) | ? [X635 : term] : (((X626 @ id @ X635 @ id)) != ((X624 @ X635))) | ? [X636 : term] : (($true = ((X624 @ X636))) & ($true != ((X624 @ (sub @ X625 @ (push @ X636 @ id)))))) | (((X624 @ (lam @ X625))) = $true)) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X637 : (term > $o),X638 : term,X639 : (subst > term > subst > $o)] : (! [X640 : term,X641 : subst,X642 : subst,X643 : subst] : (($true != ((X639 @ X643 @ X640 @ (comp @ X641 @ X642)))) | ($true = ((X639 @ (comp @ X643 @ X641) @ (sub @ X640 @ X641) @ X642)))) & ($true != ((sP0 @ X639))) & ! [X644 : subst,X645 : subst,X646 : subst,X647 : term] : ((((X639 @ X645 @ X647 @ (comp @ X644 @ X646))) = $true) | (((X639 @ (comp @ X645 @ X644) @ (sub @ X647 @ X644) @ X646)) != $true)) & ! [X648 : term] : (((X637 @ X648)) = ((X639 @ id @ X648 @ id))) & ! [X649 : term] : (($true != ((X637 @ X649))) | ($true = ((X637 @ (sub @ X638 @ (push @ X649 @ id)))))) & ($true != ((X637 @ (lam @ X638)))))) & (! [X650 : term] : (((sub @ X650 @ id)) = X650) | (termmset != $true)) & ((termmset = $true) | ? [X651 : term] : (((sub @ X651 @ id)) != X651)) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X652 : d_term,X653 : d_term] : ((X652 = X653) | (((d2term @ X652)) != ((d2term @ X653)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(rectify,[],[f130])).
% 1.38/0.56 thf(f132,plain,(
% 1.38/0.56 (pushprop_lem2v2_gthm = $true) & ((axidl = $true) | (((comp @ id @ sK236)) != sK236)) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & ((hoasinduction_lem3v2_lthm = $true) | ((! [X5 : subst,X6 : subst,X7 : term,X8 : subst] : (($true = ((sK238 @ X8 @ X7 @ (comp @ X6 @ X5)))) | ($true != ((sK238 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6) @ X5)))) & (((sK239 @ (lam @ sK237))) != $true) & ! [X9 : subst,X10 : subst,X11 : subst,X12 : term] : (($true != ((sK238 @ X9 @ X12 @ (comp @ X11 @ X10)))) | ($true = ((sK238 @ (comp @ X9 @ X11) @ (sub @ X12 @ X11) @ X10)))) & ! [X13 : term] : (((sK239 @ X13)) = ((sK238 @ id @ X13 @ id))) & ! [X14 : term] : (($true != ((sK239 @ X14))) | (((sK239 @ (sub @ sK237 @ (push @ X14 @ id)))) = $true)) & (((sP27 @ sK238)) != $true)) & ! [X15 : term] : (((sub @ X15 @ id)) = X15))) & (! [X16 : term,X17 : (subst > term > subst > $o),X18 : (term > $o)] : ((($true != ((X17 @ (sK243 @ X17) @ (sK242 @ X17) @ (comp @ (sK241 @ X17) @ (sK240 @ X17))))) & ($true = ((X17 @ (comp @ (sK243 @ X17) @ (sK241 @ X17)) @ (sub @ (sK242 @ X17) @ (sK241 @ X17)) @ (sK240 @ X17))))) | ($true = ((X18 @ (lam @ X16)))) | ((((X17 @ (sK244 @ X17) @ (sK247 @ X17) @ (comp @ (sK246 @ X17) @ (sK245 @ X17)))) = $true) & ($true != ((X17 @ (comp @ (sK244 @ X17) @ (sK246 @ X17)) @ (sub @ (sK247 @ X17) @ (sK246 @ X17)) @ (sK245 @ X17))))) | (((X17 @ id @ (sK248 @ X18 @ X17) @ id)) != ((X18 @ (sK248 @ X18 @ X17)))) | (($true = ((X18 @ (sK249 @ X18 @ X16)))) & (((X18 @ (sub @ X16 @ (push @ (sK249 @ X18 @ X16) @ id)))) != $true)) | ($true = ((sP27 @ X17)))) | (sK250 != ((sub @ sK250 @ id))) | (hoasinduction_lem3v2_lthm != $true)) & (hoaslamnotvar_lthm = $true) & ((hoasapinj1_lthm = $true) | (! [X30 : term] : (((sub @ X30 @ id)) = X30) & ((((ap @ (sub @ sK251 @ id) @ sK253)) = ((ap @ (sub @ sK254 @ id) @ sK252))) & (sK254 != sK251)) & ! [X35 : term,X36 : term,X37 : term,X38 : term] : ((((ap @ X37 @ X38)) != ((ap @ X35 @ X36))) | (X35 = X37)))) & ((((sub @ sK255 @ id)) != sK255) | ! [X40 : term,X41 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X43 @ id) @ X41)) != ((ap @ (sub @ X40 @ id) @ X42))) | (X40 = X43)) | ((((ap @ sK256 @ sK257)) = ((ap @ sK258 @ sK259))) & (sK256 != sK258)) | (hoasapinj1_lthm != $true)) & ((hoaslaminj = $true) | (! [X52 : term,X53 : subst,X54 : subst] : (((sK263 @ (comp @ X53 @ X54) @ (sub @ X52 @ X54))) = ((sub @ (sK263 @ X53 @ X52) @ X54))) & (((sK263 @ sK261 @ sK260)) != ((sK262 @ sK261 @ sK260))) & ! [X55 : term,X56 : subst,X57 : subst] : (((sub @ (sK262 @ X56 @ X55) @ X57)) = ((sK262 @ (comp @ X56 @ X57) @ (sub @ X55 @ X57)))) & (((lam @ (sK262 @ sh @ one))) = ((lam @ (sK263 @ sh @ one)))))) & (! [X58 : term,X59 : subst,X60 : (subst > term > term),X61 : (subst > term > term)] : ((((X61 @ (comp @ (sK265 @ X61) @ (sK266 @ X61)) @ (sub @ (sK264 @ X61) @ (sK266 @ X61)))) != ((sub @ (X61 @ (sK265 @ X61) @ (sK264 @ X61)) @ (sK266 @ X61)))) | (((X60 @ X59 @ X58)) = ((X61 @ X59 @ X58))) | (((X60 @ (comp @ (sK268 @ X60) @ (sK269 @ X60)) @ (sub @ (sK267 @ X60) @ (sK269 @ X60)))) != ((sub @ (X60 @ (sK268 @ X60) @ (sK267 @ X60)) @ (sK269 @ X60)))) | (((lam @ (X61 @ sh @ one))) != ((lam @ (X60 @ sh @ one))))) | (hoaslaminj != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (! [X68 : subst] : (((comp @ X68 @ id)) = X68) | (axidr != $true)) & ((axidr = $true) | (sK270 != ((comp @ sK270 @ id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X70 : subst] : (((d2subst @ (sK271 @ X70))) = X70) & (hoaslamnotap_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction = $true) | (! [X74 : subst,X75 : subst,X76 : term,X77 : subst] : (($true != ((sK273 @ X74 @ X76 @ (comp @ X77 @ X75)))) | (((sK273 @ (comp @ X74 @ X77) @ (sub @ X76 @ X77) @ X75)) = $true)) & ($true != ((sP26 @ sK273))) & ($true != ((sK273 @ id @ sK272 @ id))) & ($true != ((sP25 @ sK273))) & ! [X78 : term] : ((((var @ (sub @ X78 @ id))) != $true) | ($true = ((sK273 @ id @ X78 @ id)))) & ! [X79 : term,X80 : subst,X81 : subst,X82 : subst] : ((((sK273 @ X80 @ X79 @ (comp @ X82 @ X81))) = $true) | ($true != ((sK273 @ (comp @ X80 @ X82) @ (sub @ X79 @ X82) @ X81)))))) & (! [X83 : term,X84 : (subst > term > subst > $o)] : (((((X84 @ (sK274 @ X84) @ (sK276 @ X84) @ (comp @ (sK277 @ X84) @ (sK275 @ X84)))) = $true) & ($true != ((X84 @ (comp @ (sK274 @ X84) @ (sK277 @ X84)) @ (sub @ (sK276 @ X84) @ (sK277 @ X84)) @ (sK275 @ X84))))) | ($true = ((sP26 @ X84))) | ($true = ((X84 @ id @ X83 @ id))) | (((sP25 @ X84)) = $true) | (($true = ((var @ (sub @ (sK278 @ X84) @ id)))) & ($true != ((X84 @ id @ (sK278 @ X84) @ id)))) | (($true != ((X84 @ (sK280 @ X84) @ (sK279 @ X84) @ (comp @ (sK282 @ X84) @ (sK281 @ X84))))) & ($true = ((X84 @ (comp @ (sK280 @ X84) @ (sK282 @ X84)) @ (sub @ (sK279 @ X84) @ (sK282 @ X84)) @ (sK281 @ X84)))))) | (hoasinduction != $true)) & (! [X95 : (term > $o)] : (((sK283 @ id @ (sK284 @ X95) @ id)) != ((X95 @ (sK284 @ X95)))) | (($true != ((sK285 @ (lam @ sK286)))) & ! [X100 : (subst > term > term)] : ((($true = ((sK287 @ id @ (sK288 @ X100) @ id))) & ($true != ((sK287 @ id @ (X100 @ id @ (sK288 @ X100)) @ id)))) | (((sub @ (X100 @ (sK291 @ X100) @ (sK290 @ X100)) @ (sK289 @ X100))) != ((X100 @ (comp @ (sK291 @ X100) @ (sK289 @ X100)) @ (sub @ (sK290 @ X100) @ (sK289 @ X100))))) | (((sK287 @ id @ (lam @ (X100 @ sh @ one)) @ id)) = $true)) & ! [X105 : term] : (($true = ((sK285 @ (sub @ sK286 @ (push @ X105 @ id))))) | ($true != ((sK285 @ X105)))) & ! [X106 : term] : (((sK285 @ X106)) = ((sK287 @ id @ X106 @ id)))) | ($true = sP24) | (sK292 != ((sub @ sK292 @ id))) | (sP23 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X108 : (subst > term > subst > $o)] : ! [X110 : term] : (((X108 @ id @ X110 @ id)) = ((sK293 @ X108 @ X110))) & ! [X111 : (term > $o),X112 : term,X113 : (subst > term > subst > $o)] : (($true = ((X111 @ (lam @ X112)))) | (! [X115 : term] : ((((X113 @ id @ X115 @ id)) != $true) | (((X113 @ id @ (sK294 @ X113 @ id @ X115) @ id)) = $true)) & ! [X116 : subst,X117 : term,X118 : subst] : (((sK294 @ X113 @ (comp @ X118 @ X116) @ (sub @ X117 @ X116))) = ((sub @ (sK294 @ X113 @ X118 @ X117) @ X116))) & (((X113 @ id @ (lam @ (sK294 @ X113 @ sh @ one)) @ id)) != $true)) | (($true != ((X111 @ (sub @ X112 @ (push @ (sK295 @ X112 @ X111) @ id))))) & ($true = ((X111 @ (sK295 @ X112 @ X111))))) | (((X113 @ id @ (sK296 @ X113 @ X111) @ id)) != ((X111 @ (sK296 @ X113 @ X111))))) & ($true != sP24) & ! [X121 : term] : (((sub @ X121 @ id)) = X121) & (sP23 != $true))) & (hoaslamnotap_lthm = $true) & (axmap = $true) & (hoasapnotvar_gthm = $true) & ((pushprop_lem0 = $true) | ! [X125 : (term > $o)] : (((sK298 @ (sub @ (sK300 @ X125) @ (push @ sK299 @ sK297)))) != ((X125 @ (sK300 @ X125))))) & (! [X127 : subst,X128 : (term > $o),X129 : term] : ! [X131 : term] : (((sK301 @ X129 @ X128 @ X127 @ X131)) = ((X128 @ (sub @ X131 @ (push @ X129 @ X127))))) | (pushprop_lem0 != $true)) & ((hoasinduction_lem3aaa = $true) | (($true != ((sK302 @ id @ (lam @ (sub @ sK303 @ (push @ one @ sh))) @ id))) & ! [X134 : (subst > term > term),X135 : term] : ((((sub @ X135 @ (push @ (sub @ (sK304 @ X135 @ X134) @ (sK305 @ X135 @ X134)) @ (comp @ (sK306 @ X135 @ X134) @ (sK305 @ X135 @ X134))))) != ((X134 @ (comp @ (sK306 @ X135 @ X134) @ (sK305 @ X135 @ X134)) @ (sub @ (sK304 @ X135 @ X134) @ (sK305 @ X135 @ X134))))) | (($true != ((sK302 @ id @ (X134 @ id @ (sK307 @ X134)) @ id))) & ($true = ((sK302 @ id @ (sK307 @ X134) @ id)))) | ($true = ((sK302 @ id @ (lam @ (X134 @ sh @ one)) @ id))) | (((sub @ (sub @ X135 @ (push @ (sK308 @ X135 @ X134) @ (sK310 @ X135 @ X134))) @ (sK309 @ X135 @ X134))) != ((sub @ (X134 @ (sK310 @ X135 @ X134) @ (sK308 @ X135 @ X134)) @ (sK309 @ X135 @ X134))))) & ! [X143 : term] : ((((sK302 @ id @ X143 @ id)) != $true) | (((sK302 @ id @ (sub @ sK303 @ (push @ X143 @ id)) @ id)) = $true)))) & (! [X144 : (subst > term > subst > $o),X145 : term] : ((((X144 @ id @ (lam @ (sub @ X145 @ (push @ one @ sh))) @ id)) = $true) | (! [X148 : term,X149 : subst,X150 : subst] : (((sK311 @ X144 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) = ((sub @ (sK312 @ X144) @ (push @ (sub @ X148 @ X149) @ (comp @ X150 @ X149))))) & ! [X151 : term] : (($true = ((X144 @ id @ (sK311 @ X144 @ id @ X151) @ id))) | ($true != ((X144 @ id @ X151 @ id)))) & ($true != ((X144 @ id @ (lam @ (sK311 @ X144 @ sh @ one)) @ id))) & ! [X152 : term,X153 : subst,X154 : subst] : (((sub @ (sK311 @ X144 @ X154 @ X152) @ X153)) = ((sub @ (sub @ (sK312 @ X144) @ (push @ X152 @ X154)) @ X153)))) | (($true = ((X144 @ id @ (sK313 @ X145 @ X144) @ id))) & ($true != ((X144 @ id @ (sub @ X145 @ (push @ (sK313 @ X145 @ X144) @ id)) @ id))))) | (hoasinduction_lem3aaa != $true)) & (pushprop_lem0_gthm = $true) & ((apinj2 = $true) | ((sK317 != sK314) & (((ap @ sK315 @ sK314)) = ((ap @ sK316 @ sK317))))) & (! [X160 : term,X161 : term,X162 : term,X163 : term] : ((X160 = X163) | (((ap @ X162 @ X163)) != ((ap @ X161 @ X160)))) | (apinj2 != $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X164 : term,X165 : term,X166 : term,X167 : term] : ((X165 = X167) | (((ap @ (sub @ X164 @ id) @ X165)) != ((ap @ (sub @ X166 @ id) @ X167)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((sK319 != sK321) & (((ap @ (sub @ sK318 @ id) @ sK319)) = ((ap @ (sub @ sK320 @ id) @ sK321))))) & ((apinj1 = $true) | ((((ap @ sK323 @ sK324)) = ((ap @ sK325 @ sK322))) & (sK325 != sK323))) & (! [X176 : term,X177 : term,X178 : term,X179 : term] : ((((ap @ X177 @ X178)) != ((ap @ X179 @ X176))) | (X177 = X179)) | (apinj1 != $true)) & (($true = sP20) | (((sub @ sK326 @ id)) != sK326) | (! [X183 : (subst > term > term)] : ((((sub @ (X183 @ (sK331 @ X183) @ (sK330 @ X183)) @ (sK329 @ X183))) != ((X183 @ (comp @ (sK331 @ X183) @ (sK329 @ X183)) @ (sub @ (sK330 @ X183) @ (sK329 @ X183))))) | ($true = ((sK327 @ id @ (lam @ (X183 @ sh @ one)) @ id))) | ((((sK327 @ id @ (X183 @ id @ (sK332 @ X183)) @ id)) != $true) & ($true = ((sK327 @ id @ (sK332 @ X183) @ id))))) & ! [X188 : term] : (($true = ((sK327 @ id @ (sub @ sK328 @ (push @ X188 @ id)) @ id))) | (((sK327 @ id @ X188 @ id)) != $true)) & (((sK327 @ id @ (lam @ (sub @ sK328 @ (push @ one @ sh))) @ id)) != $true)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP20) & ! [X189 : term] : (((sub @ X189 @ id)) = X189) & ! [X190 : (subst > term > subst > $o),X191 : term] : ((! [X193 : subst,X194 : term,X195 : subst] : (((sK333 @ X190 @ (comp @ X195 @ X193) @ (sub @ X194 @ X193))) = ((sub @ (sK333 @ X190 @ X195 @ X194) @ X193))) & ($true != ((X190 @ id @ (lam @ (sK333 @ X190 @ sh @ one)) @ id))) & ! [X196 : term] : (($true = ((X190 @ id @ (sK333 @ X190 @ id @ X196) @ id))) | ($true != ((X190 @ id @ X196 @ id))))) | (($true != ((X190 @ id @ (sub @ X191 @ (push @ (sK334 @ X191 @ X190) @ id)) @ id))) & ($true = ((X190 @ id @ (sK334 @ X191 @ X190) @ id)))) | ($true = ((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)))))) & (ulamvarind = $true) & (! [X198 : term] : ! [X200 : subst,X201 : term] : (((sK335 @ X198 @ X200 @ X201)) = ((sub @ X198 @ (push @ X201 @ X200)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X203 : (subst > term > term)] : (((sub @ sK336 @ (push @ (sK338 @ X203) @ (sK337 @ X203)))) != ((X203 @ (sK337 @ X203) @ (sK338 @ X203))))) & (pushprop_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1 = $true) & (! [X206 : subst,X207 : term] : (((sub @ one @ (push @ X207 @ X206))) = X207) | (axvarcons != $true)) & ((axvarcons = $true) | (sK340 != ((sub @ one @ (push @ sK340 @ sK339))))) & (axassoc = $true) & (hoasinduction_lem1_lthm = $true) & (hoasapnotvar = $true) & (lamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (hoaslaminj_gthm = $true) & (axapp = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (pushprop_lem3v2_lthm = $true) & (! [X210 : (subst > term > subst > $o),X211 : term] : ((((X210 @ id @ (lam @ X211) @ id)) = $true) | ((((X210 @ id @ (lam @ (sK341 @ X210 @ sh @ one)) @ id)) != $true) & ! [X213 : term] : (($true != ((X210 @ id @ X213 @ id))) | ($true = ((X210 @ id @ (sK341 @ X210 @ id @ X213) @ id)))) & ! [X214 : subst,X215 : term,X216 : subst] : (((sK341 @ X210 @ (comp @ X216 @ X214) @ (sub @ X215 @ X214))) = ((sub @ (sK341 @ X210 @ X216 @ X215) @ X214)))) | (($true = ((X210 @ id @ (sK342 @ X211 @ X210) @ id))) & (((X210 @ id @ (sub @ X211 @ (push @ (sK342 @ X211 @ X210) @ id)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ((((sK343 @ id @ (lam @ sK344) @ id)) != $true) & ! [X220 : (subst > term > term)] : ((((sK343 @ id @ (lam @ (X220 @ sh @ one)) @ id)) = $true) | ((((sK343 @ id @ (sK345 @ X220) @ id)) = $true) & (((sK343 @ id @ (X220 @ id @ (sK345 @ X220)) @ id)) != $true)) | (((X220 @ (comp @ (sK348 @ X220) @ (sK346 @ X220)) @ (sub @ (sK347 @ X220) @ (sK346 @ X220)))) != ((sub @ (X220 @ (sK348 @ X220) @ (sK347 @ X220)) @ (sK346 @ X220))))) & ! [X225 : term] : ((((sK343 @ id @ X225 @ id)) != $true) | (((sK343 @ id @ (sub @ sK344 @ (push @ X225 @ id)) @ id)) = $true)))) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK352 @ id) @ sK350)) = ((ap @ (sub @ sK351 @ id) @ sK349))) & (sK351 != sK352))) & (! [X230 : term,X231 : term,X232 : term,X233 : term] : ((((ap @ (sub @ X232 @ id) @ X230)) != ((ap @ (sub @ X233 @ id) @ X231))) | (X232 = X233)) | (hoasapinj1 != $true)) & ((pushprop_lem1_lthm = $true) | (! [X234 : subst,X235 : term] : (((comp @ sh @ (push @ X235 @ X234))) = X234) & (($true = ((sK355 @ sK353))) & ($true != ((sK354 @ (sub @ sK353 @ (push @ sK357 @ sK356)))))) & ! [X241 : subst,X242 : term] : (((sub @ one @ (push @ X242 @ X241))) = X242))) & ((sK358 != ((comp @ sh @ (push @ sK359 @ sK358)))) | ! [X245 : term,X246 : (term > $o),X247 : (term > $o),X248 : subst,X249 : term] : ((((X247 @ X245)) != $true) | (((X246 @ (sub @ X245 @ (push @ X249 @ X248)))) = $true)) | (((sub @ one @ (push @ sK361 @ sK360))) != sK361) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X255 : (term > $o)] : (((X255 @ (sK365 @ X255))) != ((sK363 @ (sub @ (sK365 @ X255) @ (push @ sK362 @ sK364)))))) & (! [X257 : term,X258 : (term > $o),X259 : subst] : ! [X261 : term] : (((X258 @ (sub @ X261 @ (push @ X257 @ X259)))) = ((sK366 @ X259 @ X258 @ X257 @ X261))) | (pushprop_lem0_lthm != $true)) & (apnotvar = $true) & ! [X262 : term] : (((d2term @ (sK367 @ X262))) = X262) & (one = ((d2term @ d_one))) & ((hoasapinj2_lthm = $true) | (! [X264 : term,X265 : term,X266 : term,X267 : term] : ((((ap @ X265 @ X267)) != ((ap @ X264 @ X266))) | (X266 = X267)) & ((sK368 != sK370) & (((ap @ (sub @ sK369 @ id) @ sK368)) = ((ap @ (sub @ sK371 @ id) @ sK370)))))) & (((((ap @ sK372 @ sK374)) = ((ap @ sK373 @ sK375))) & (sK375 != sK374)) | ! [X276 : term,X277 : term,X278 : term,X279 : term] : ((X276 = X278) | (((ap @ (sub @ X277 @ id) @ X276)) != ((ap @ (sub @ X279 @ id) @ X278)))) | (hoasapinj2_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X281 : (term > $o)] : (((sK376 @ id @ (sK377 @ X281) @ id)) != ((X281 @ (sK377 @ X281))))) & (! [X283 : (subst > term > subst > $o)] : ! [X285 : term] : (((sK378 @ X283 @ X285)) = ((X283 @ id @ X285 @ id))) | (hoasinduction_lem0_lthm != $true)) & (axclos = $true) & (hoasapinj2_gthm = $true) & (! [X286 : term,X287 : (term > $o),X288 : (subst > term > subst > $o)] : (($true = ((X287 @ (lam @ X286)))) | ((((X287 @ (sub @ X286 @ (push @ (sK379 @ X287 @ X286) @ id)))) != $true) & ($true = ((X287 @ (sK379 @ X287 @ X286))))) | (! [X291 : subst,X292 : subst,X293 : term] : (((sub @ (sK380 @ X288 @ X291 @ X293) @ X292)) = ((sK380 @ X288 @ (comp @ X291 @ X292) @ (sub @ X293 @ X292)))) & ($true != ((X288 @ id @ (lam @ (sK380 @ X288 @ sh @ one)) @ id))) & ! [X294 : term] : ((((X288 @ id @ X294 @ id)) != $true) | ($true = ((X288 @ id @ (sK380 @ X288 @ id @ X294) @ id))))) | (((X287 @ (sK381 @ X288 @ X287))) != ((X288 @ id @ (sK381 @ X288 @ X287) @ id)))) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ((((sK383 @ (lam @ sK382))) != $true) & ! [X299 : term] : (($true = ((sK383 @ (sub @ sK382 @ (push @ X299 @ id))))) | (((sK383 @ X299)) != $true)) & ! [X300 : (subst > term > term)] : ((((X300 @ (comp @ (sK385 @ X300) @ (sK386 @ X300)) @ (sub @ (sK387 @ X300) @ (sK386 @ X300)))) != ((sub @ (X300 @ (sK385 @ X300) @ (sK387 @ X300)) @ (sK386 @ X300)))) | ($true = ((sK384 @ id @ (lam @ (X300 @ sh @ one)) @ id))) | ((((sK384 @ id @ (sK388 @ X300) @ id)) = $true) & (((sK384 @ id @ (X300 @ id @ (sK388 @ X300)) @ id)) != $true))) & ! [X305 : term] : (((sK383 @ X305)) = ((sK384 @ id @ X305 @ id))))) & (axvarshift = $true) & ((hoaslaminj_lthm = $true) | (! [X306 : term,X307 : term] : ((X306 = X307) | (((lam @ X306)) != ((lam @ X307)))) & (! [X312 : subst,X313 : subst,X314 : term] : (((sub @ (sK392 @ X312 @ X314) @ X313)) = ((sK392 @ (comp @ X312 @ X313) @ (sub @ X314 @ X313)))) & ! [X315 : subst,X316 : subst,X317 : term] : (((sK390 @ (comp @ X316 @ X315) @ (sub @ X317 @ X315))) = ((sub @ (sK390 @ X316 @ X317) @ X315))) & (((sK392 @ sK389 @ sK391)) != ((sK390 @ sK389 @ sK391))) & (((lam @ (sK392 @ sh @ one))) = ((lam @ (sK390 @ sh @ one))))) & ! [X318 : term,X319 : subst] : (((comp @ sh @ (push @ X318 @ X319))) = X319) & ! [X320 : term,X321 : subst] : (((sub @ one @ (push @ X320 @ X321))) = X320))) & (((sK394 != sK393) & (((lam @ sK394)) = ((lam @ sK393)))) | ! [X324 : subst,X325 : (subst > term > term),X326 : term,X327 : (subst > term > term)] : ((((X327 @ (comp @ (sK395 @ X327) @ (sK396 @ X327)) @ (sub @ (sK397 @ X327) @ (sK396 @ X327)))) != ((sub @ (X327 @ (sK395 @ X327) @ (sK397 @ X327)) @ (sK396 @ X327)))) | (((sub @ (X325 @ (sK399 @ X325) @ (sK400 @ X325)) @ (sK398 @ X325))) != ((X325 @ (comp @ (sK399 @ X325) @ (sK398 @ X325)) @ (sub @ (sK400 @ X325) @ (sK398 @ X325))))) | (((X327 @ X324 @ X326)) = ((X325 @ X324 @ X326))) | (((lam @ (X325 @ sh @ one))) != ((lam @ (X327 @ sh @ one))))) | (((comp @ sh @ (push @ sK401 @ sK402))) != sK402) | (((sub @ one @ (push @ sK403 @ sK404))) != sK403) | (hoaslaminj_lthm != $true)) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) | (sK405 != ((sub @ sK405 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK406 @ id)) != sK406) & ! [X341 : term] : (((sub @ X341 @ id)) = X341))) & (induction2lem_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X342 : term] : (((sK407 @ X342 @ sh @ one)) = ((sub @ X342 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X345 : (subst > term > term)] : (((sub @ sK408 @ (push @ one @ sh))) != ((X345 @ sh @ one)))) & (! [X346 : (term > $o),X347 : (term > $o),X348 : subst,X349 : term] : (($true != ((X347 @ X349))) | (((X347 @ (sub @ (sK409 @ X349 @ X348 @ X347 @ X346) @ (push @ X349 @ X348)))) != ((X346 @ (sK409 @ X349 @ X348 @ X347 @ X346)))) | (((X346 @ one)) = $true)) | (sK410 != ((sub @ one @ (push @ sK410 @ sK411)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (((((sK413 @ sK415)) = $true) & ! [X357 : term] : (((sK413 @ (sub @ X357 @ (push @ sK415 @ sK414)))) = ((sK412 @ X357))) & (((sK412 @ one)) != $true)) & ! [X358 : term,X359 : subst] : (((sub @ one @ (push @ X358 @ X359))) = X358))) & ((hoasinduction_lem3 = $true) | (! [X362 : subst,X363 : subst,X364 : subst,X365 : term] : (($true = ((sK416 @ (comp @ X364 @ X363) @ (sub @ X365 @ X363) @ X362))) | (((sK416 @ X364 @ X365 @ (comp @ X363 @ X362))) != $true)) & (((sP19 @ sK416)) != $true) & ! [X366 : subst,X367 : subst,X368 : subst,X369 : term] : (($true = ((sK416 @ X366 @ X369 @ (comp @ X368 @ X367)))) | ($true != ((sK416 @ (comp @ X366 @ X368) @ (sub @ X369 @ X368) @ X367)))) & (((sK416 @ id @ (lam @ sK417) @ id)) != $true) & ! [X370 : term] : (($true = ((sK416 @ id @ (sub @ sK417 @ (push @ X370 @ id)) @ id))) | ($true != ((sK416 @ id @ X370 @ id)))))) & (! [X371 : (subst > term > subst > $o),X372 : term] : ((($true != ((X371 @ (comp @ (sK420 @ X371) @ (sK419 @ X371)) @ (sub @ (sK421 @ X371) @ (sK419 @ X371)) @ (sK418 @ X371)))) & ($true = ((X371 @ (sK420 @ X371) @ (sK421 @ X371) @ (comp @ (sK419 @ X371) @ (sK418 @ X371)))))) | ($true = ((sP19 @ X371))) | (($true != ((X371 @ (sK422 @ X371) @ (sK425 @ X371) @ (comp @ (sK424 @ X371) @ (sK423 @ X371))))) & ($true = ((X371 @ (comp @ (sK422 @ X371) @ (sK424 @ X371)) @ (sub @ (sK425 @ X371) @ (sK424 @ X371)) @ (sK423 @ X371))))) | ($true = ((X371 @ id @ (lam @ X372) @ id))) | (($true != ((X371 @ id @ (sub @ X372 @ (push @ (sK426 @ X372 @ X371) @ id)) @ id))) & (((X371 @ id @ (sK426 @ X372 @ X371) @ id)) = $true))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem1v2 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X382 : subst] : (((comp @ id @ X382)) = X382) & ! [X383 : subst] : (((comp @ X383 @ id)) = X383)) | (((comp @ sK427 @ id)) != sK427) | (((comp @ id @ sK428)) != sK428) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (((((comp @ id @ sK429)) != sK429) | (((comp @ sK430 @ id)) != sK430)) & ! [X388 : subst] : (((comp @ X388 @ id)) = X388) & ! [X389 : subst] : (((comp @ id @ X389)) = X389))) & ((induction2lem_lthm = $true) | ($true != sP18)) & (($true = sP18) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X390 : term] : ! [X392 : subst,X393 : term] : (((sub @ X390 @ (push @ X393 @ X392))) = ((sK431 @ X390 @ X392 @ X393))) & (($true != ((sK434 @ (lam @ sK432)))) & ! [X397 : (subst > term > term)] : (($true = ((sK433 @ id @ (lam @ (X397 @ sh @ one)) @ id))) | (((X397 @ (comp @ (sK435 @ X397) @ (sK436 @ X397)) @ (sub @ (sK437 @ X397) @ (sK436 @ X397)))) != ((sub @ (X397 @ (sK435 @ X397) @ (sK437 @ X397)) @ (sK436 @ X397)))) | (($true != ((sK433 @ id @ (X397 @ id @ (sK438 @ X397)) @ id))) & (((sK433 @ id @ (sK438 @ X397) @ id)) = $true))) & ! [X402 : term] : (($true = ((sK434 @ (sub @ sK432 @ (push @ X402 @ id))))) | ($true != ((sK434 @ X402)))) & ! [X403 : term] : (((sK434 @ X403)) = ((sK433 @ id @ X403 @ id)))) & ! [X404 : term] : (((sub @ X404 @ id)) = X404))) & (! [X406 : (subst > term > term)] : (((X406 @ (sK440 @ X406) @ (sK441 @ X406))) != ((sub @ sK439 @ (push @ (sK441 @ X406) @ (sK440 @ X406))))) | ! [X409 : term,X410 : (subst > term > subst > $o),X411 : (term > $o)] : (($true = ((X411 @ (lam @ X409)))) | (($true != ((X410 @ id @ (lam @ (sK442 @ X410 @ sh @ one)) @ id))) & ! [X413 : subst,X414 : subst,X415 : term] : (((sK442 @ X410 @ (comp @ X413 @ X414) @ (sub @ X415 @ X414))) = ((sub @ (sK442 @ X410 @ X413 @ X415) @ X414))) & ! [X416 : term] : ((((X410 @ id @ (sK442 @ X410 @ id @ X416) @ id)) = $true) | (((X410 @ id @ X416 @ id)) != $true))) | (($true != ((X411 @ (sub @ X409 @ (push @ (sK443 @ X411 @ X409) @ id))))) & ($true = ((X411 @ (sK443 @ X411 @ X409))))) | (((X411 @ (sK444 @ X411 @ X410))) != ((X410 @ id @ (sK444 @ X411 @ X410) @ id)))) | (sK445 != ((sub @ sK445 @ id))) | (hoasinduction_lem3v2a_lthm != $true)) & ((! [X422 : subst,X423 : subst,X424 : term,X425 : subst] : (($true != ((sK446 @ (comp @ X422 @ X425) @ (sub @ X424 @ X425) @ X423))) | ($true = ((sK446 @ X422 @ X424 @ (comp @ X425 @ X423))))) & ($true = ((sP13 @ sK446))) & ! [X426 : term,X427 : subst,X428 : subst,X429 : subst] : ((((sK446 @ (comp @ X427 @ X429) @ (sub @ X426 @ X429) @ X428)) = $true) | (((sK446 @ X427 @ X426 @ (comp @ X429 @ X428))) != $true)) & (((sK446 @ id @ (lam @ sK447) @ id)) != $true) & ! [X430 : term] : ((((sK446 @ id @ X430 @ id)) != $true) | (((sK446 @ id @ (sub @ sK447 @ (push @ X430 @ id)) @ id)) = $true))) | (sP15 = $true) | (sP14 = $true) | (sP16 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (! [X431 : (subst > term > subst > $o),X432 : term] : ((($true = ((X431 @ (comp @ (sK448 @ X431) @ (sK451 @ X431)) @ (sub @ (sK450 @ X431) @ (sK451 @ X431)) @ (sK449 @ X431)))) & ($true != ((X431 @ (sK448 @ X431) @ (sK450 @ X431) @ (comp @ (sK451 @ X431) @ (sK449 @ X431)))))) | ($true != ((sP13 @ X431))) | (($true != ((X431 @ (comp @ (sK453 @ X431) @ (sK455 @ X431)) @ (sub @ (sK452 @ X431) @ (sK455 @ X431)) @ (sK454 @ X431)))) & (((X431 @ (sK453 @ X431) @ (sK452 @ X431) @ (comp @ (sK455 @ X431) @ (sK454 @ X431)))) = $true)) | ($true = ((X431 @ id @ (lam @ X432) @ id))) | ((((X431 @ id @ (sK456 @ X432 @ X431) @ id)) = $true) & (((X431 @ id @ (sub @ X432 @ (push @ (sK456 @ X432 @ X431) @ id)) @ id)) != $true))) & (sP15 != $true) & (sP14 != $true) & (sP16 != $true))) & (! [X442 : (term > $o),X443 : subst,X444 : (term > $o),X445 : term,X446 : term] : (($true = ((X442 @ (sub @ X445 @ (push @ X446 @ X443))))) | (((X444 @ X445)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK457 @ (sub @ sK460 @ (push @ sK461 @ sK458)))) != $true) & ($true = ((sK459 @ sK460))))) & (($true = sP10) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP10)) & (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)))))))))))) & (! [X452 : subst] : (((push @ (sub @ one @ X452) @ (comp @ sh @ X452))) = X452) | (axscons != $true)) & ((axscons = $true) | (sK462 != ((push @ (sub @ one @ sK462) @ (comp @ sh @ sK462))))) & (($true = sP9) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP9)) & (! [X454 : (subst > term > subst > $o)] : ! [X456 : term] : (((sK463 @ X454 @ X456)) = ((X454 @ id @ X456 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X458 : (term > $o)] : (((sK464 @ id @ (sK465 @ X458) @ id)) != ((X458 @ (sK465 @ X458))))) & ((hoasinduction_lem2 = $true) | ($true != sP8)) & (($true = sP8) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X460 : term,X461 : (subst > term > subst > $o)] : (($true = ((X461 @ id @ (lam @ (sub @ X460 @ (push @ one @ sh))) @ id))) | (! [X463 : term,X464 : subst,X465 : subst] : (((sub @ (sK466 @ X461 @ X465 @ X463) @ X464)) = ((sK466 @ X461 @ (comp @ X465 @ X464) @ (sub @ X463 @ X464)))) & ($true != ((X461 @ id @ (lam @ (sK466 @ X461 @ sh @ one)) @ id))) & ! [X466 : term] : (($true = ((X461 @ id @ (sK466 @ X461 @ id @ X466) @ id))) | ($true != ((X461 @ id @ X466 @ id))))) | (($true != ((X461 @ id @ (sub @ X460 @ (push @ (sK467 @ X461 @ X460) @ id)) @ id))) & ($true = ((X461 @ id @ (sK467 @ X461 @ X460) @ id))))) & ! [X468 : term] : (((sub @ X468 @ id)) = X468) & (sP7 != $true))) & ((($true != ((sK469 @ id @ (lam @ (sub @ sK468 @ (push @ one @ sh))) @ id))) & ! [X471 : (subst > term > term)] : ((((sub @ (X471 @ (sK472 @ X471) @ (sK470 @ X471)) @ (sK471 @ X471))) != ((X471 @ (comp @ (sK472 @ X471) @ (sK471 @ X471)) @ (sub @ (sK470 @ X471) @ (sK471 @ X471))))) | ($true = ((sK469 @ id @ (lam @ (X471 @ sh @ one)) @ id))) | (($true != ((sK469 @ id @ (X471 @ id @ (sK473 @ X471)) @ id))) & ($true = ((sK469 @ id @ (sK473 @ X471) @ id))))) & ! [X476 : term] : (($true = ((sK469 @ id @ (sub @ sK468 @ (push @ X476 @ id)) @ id))) | ($true != ((sK469 @ id @ X476 @ id))))) | (sK474 != ((sub @ sK474 @ id))) | (sP7 = $true) | (hoasinduction_lem3_lthm != $true)) & (! [X478 : term,X479 : (subst > term > subst > $o)] : (($true = ((X479 @ id @ X478 @ id))) | ((((X479 @ id @ (ap @ (sub @ (sK476 @ X479) @ id) @ (sK475 @ X479)) @ id)) != $true) & ($true = ((X479 @ id @ (sK475 @ X479) @ id))) & ($true = ((X479 @ id @ (sK476 @ X479) @ id)))) | (! [X483 : term,X484 : subst,X485 : subst] : (((sK477 @ X479 @ (comp @ X484 @ X485) @ (sub @ X483 @ X485))) = ((sub @ (sK477 @ X479 @ X484 @ X483) @ X485))) & ! [X486 : term] : (($true != ((X479 @ id @ X486 @ id))) | (((X479 @ id @ (sK477 @ X479 @ id @ X486) @ id)) = $true)) & ($true != ((X479 @ id @ (lam @ (sK477 @ X479 @ sh @ one)) @ id))))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK479 @ id @ sK478 @ id)) != $true) & ! [X489 : term,X490 : term] : (($true = ((sK479 @ id @ (ap @ (sub @ X490 @ id) @ X489) @ id))) | ($true != ((sK479 @ id @ X489 @ id))) | (((sK479 @ id @ X490 @ id)) != $true)) & ! [X491 : (subst > term > term)] : ((((X491 @ (comp @ (sK481 @ X491) @ (sK482 @ X491)) @ (sub @ (sK480 @ X491) @ (sK482 @ X491)))) != ((sub @ (X491 @ (sK481 @ X491) @ (sK480 @ X491)) @ (sK482 @ X491)))) | (($true = ((sK479 @ id @ (sK483 @ X491) @ id))) & ($true != ((sK479 @ id @ (X491 @ id @ (sK483 @ X491)) @ id)))) | ($true = ((sK479 @ id @ (lam @ (X491 @ sh @ one)) @ id)))))) & (! [X496 : term] : ! [X498 : subst,X499 : term] : (((sK484 @ X496 @ X498 @ X499)) = ((sub @ X496 @ (push @ X499 @ X498)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X501 : (subst > term > term)] : (((X501 @ (sK486 @ X501) @ (sK487 @ X501))) != ((sub @ sK485 @ (push @ (sK487 @ X501) @ (sK486 @ X501)))))) & (pushprop_lem2v2 = $true) & ((hoaslamnotap = $true) | (! [X507 : subst,X508 : subst,X509 : term] : (((sK489 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (sK489 @ X508 @ X509) @ X507))) & (((ap @ (sub @ sK490 @ id) @ sK488)) = ((lam @ (sK489 @ sh @ one)))))) & (! [X510 : term,X511 : (subst > term > term),X512 : term] : ((((X511 @ (comp @ (sK492 @ X511) @ (sK491 @ X511)) @ (sub @ (sK493 @ X511) @ (sK491 @ X511)))) != ((sub @ (X511 @ (sK492 @ X511) @ (sK493 @ X511)) @ (sK491 @ X511)))) | (((lam @ (X511 @ sh @ one))) != ((ap @ (sub @ X512 @ id) @ X510)))) | (hoaslamnotap != $true)) & (hoaslamnotvar = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3aa_lthm = $true) | (! [X518 : term] : (($true != ((sK494 @ id @ X518 @ id))) | (((sK494 @ id @ (sub @ sK495 @ (push @ X518 @ id)) @ id)) = $true)) & (((sK494 @ id @ (lam @ (sub @ sK495 @ (push @ one @ sh))) @ id)) != $true) & ! [X519 : (subst > term > term)] : ((($true != ((sK494 @ id @ (X519 @ id @ (sK496 @ X519)) @ id))) & (((sK494 @ id @ (sK496 @ X519) @ id)) = $true)) | (((sK494 @ id @ (lam @ (X519 @ sh @ one)) @ id)) = $true) | (((X519 @ (comp @ (sK498 @ X519) @ (sK497 @ X519)) @ (sub @ (sK499 @ X519) @ (sK497 @ X519)))) != ((sub @ (X519 @ (sK498 @ X519) @ (sK499 @ X519)) @ (sK497 @ X519))))))) & (! [X524 : (subst > term > subst > $o),X525 : term] : (((((X524 @ id @ (sK500 @ X525 @ X524) @ id)) = $true) & (((X524 @ id @ (sub @ X525 @ (push @ (sK500 @ X525 @ X524) @ id)) @ id)) != $true)) | ($true = ((X524 @ id @ (lam @ (sub @ X525 @ (push @ one @ sh))) @ id))) | (! [X528 : term] : ((((X524 @ id @ (sK501 @ X524 @ id @ X528) @ id)) = $true) | (((X524 @ id @ X528 @ id)) != $true)) & ($true != ((X524 @ id @ (lam @ (sK501 @ X524 @ sh @ one)) @ id))) & ! [X529 : subst,X530 : subst,X531 : term] : (((sub @ (sK501 @ X524 @ X530 @ X531) @ X529)) = ((sK501 @ X524 @ (comp @ X530 @ X529) @ (sub @ X531 @ X529)))))) | (hoasinduction_lem3aa_lthm != $true)) & (! [X532 : term] : (((sub @ X532 @ (push @ one @ sh))) = ((sK502 @ X532 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X535 : (subst > term > term)] : (((sub @ sK503 @ (push @ one @ sh))) != ((X535 @ sh @ one)))) & (((d2subst @ d_id)) = id) & ! [X536 : d_subst,X537 : d_subst] : ((((d2subst @ X536)) != ((d2subst @ X537))) | (X536 = X537)) & (($true = sP5) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP5)) & (! [X538 : term,X539 : (subst > term > subst > $o)] : (((((X539 @ id @ (sK504 @ X539 @ X538) @ id)) = $true) & ($true != ((X539 @ id @ (sub @ X538 @ (push @ (sK504 @ X539 @ X538) @ id)) @ id)))) | (! [X542 : term] : ((((X539 @ id @ X542 @ id)) != $true) | (((X539 @ id @ (sK505 @ X539 @ id @ X542) @ id)) = $true)) & ! [X543 : term,X544 : subst,X545 : subst] : (((sK505 @ X539 @ (comp @ X545 @ X544) @ (sub @ X543 @ X544))) = ((sub @ (sK505 @ X539 @ X545 @ X543) @ X544))) & ($true != ((X539 @ id @ (lam @ (sK505 @ X539 @ sh @ one)) @ id)))) | (((X539 @ id @ (lam @ (sub @ X538 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (! [X548 : term] : ((((sK507 @ id @ X548 @ id)) != $true) | (((sK507 @ id @ (sub @ sK506 @ (push @ X548 @ id)) @ id)) = $true)) & ! [X549 : (subst > term > term)] : ((($true = ((sK507 @ id @ (sK508 @ X549) @ id))) & ($true != ((sK507 @ id @ (X549 @ id @ (sK508 @ X549)) @ id)))) | (((sub @ (X549 @ (sK511 @ X549) @ (sK509 @ X549)) @ (sK510 @ X549))) != ((X549 @ (comp @ (sK511 @ X549) @ (sK510 @ X549)) @ (sub @ (sK509 @ X549) @ (sK510 @ X549))))) | (((sK507 @ id @ (lam @ (X549 @ sh @ one)) @ id)) = $true)) & ($true != ((sK507 @ id @ (lam @ (sub @ sK506 @ (push @ one @ sh))) @ id))))) & (induction2_gthm = $true) & (axabs = $true) & (ulamvarsh = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (($true = sP3) | ! [X555 : (term > $o)] : (((sK512 @ id @ (sK513 @ X555) @ id)) != ((X555 @ (sK513 @ X555)))) | ($true = sP2) | (! [X560 : term] : (((sK515 @ X560)) = ((sK514 @ id @ X560 @ id))) & (((sK515 @ (lam @ sK516))) != $true) & ! [X561 : (subst > term > term)] : ((($true = ((sK514 @ id @ (sK517 @ X561) @ id))) & (((sK514 @ id @ (X561 @ id @ (sK517 @ X561)) @ id)) != $true)) | ($true = ((sK514 @ id @ (lam @ (X561 @ sh @ one)) @ id))) | (((X561 @ (comp @ (sK520 @ X561) @ (sK518 @ X561)) @ (sub @ (sK519 @ X561) @ (sK518 @ X561)))) != ((sub @ (X561 @ (sK520 @ X561) @ (sK519 @ X561)) @ (sK518 @ X561))))) & ! [X566 : term] : ((((sK515 @ X566)) != $true) | ($true = ((sK515 @ (sub @ sK516 @ (push @ X566 @ id))))))) | (((sub @ sK521 @ id)) != sK521) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (($true != sP3) & ! [X568 : (subst > term > subst > $o)] : ! [X570 : term] : (((sK522 @ X568 @ X570)) = ((X568 @ id @ X570 @ id))) & ($true != sP2) & ! [X571 : (subst > term > subst > $o),X572 : (term > $o),X573 : term] : ((((X571 @ id @ (sK523 @ X572 @ X571) @ id)) != ((X572 @ (sK523 @ X572 @ X571)))) | ($true = ((X572 @ (lam @ X573)))) | (! [X576 : term] : (($true != ((X571 @ id @ X576 @ id))) | ($true = ((X571 @ id @ (sK524 @ X571 @ id @ X576) @ id)))) & (((X571 @ id @ (lam @ (sK524 @ X571 @ sh @ one)) @ id)) != $true) & ! [X577 : subst,X578 : term,X579 : subst] : (((sub @ (sK524 @ X571 @ X579 @ X578) @ X577)) = ((sK524 @ X571 @ (comp @ X579 @ X577) @ (sub @ X578 @ X577))))) | ((((X572 @ (sK525 @ X573 @ X572))) = $true) & ($true != ((X572 @ (sub @ X573 @ (push @ (sK525 @ X573 @ X572) @ id))))))) & ! [X581 : term] : (((sub @ X581 @ id)) = X581))) & ((axvarid = $true) | (((sub @ sK526 @ id)) != sK526)) & (! [X583 : term] : (((sub @ X583 @ id)) = X583) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X584 : term,X585 : term] : ((X584 = X585) | (((sub @ X584 @ sh)) != ((sub @ X585 @ sh)))) | (shinj != $true)) & ((shinj = $true) | ((sK527 != sK528) & (((sub @ sK528 @ sh)) = ((sub @ sK527 @ sh))))) & ((induction = $true) | (! [X590 : term,X591 : term] : (($true = ((sK529 @ (ap @ X590 @ X591)))) | (((sK529 @ X591)) != $true) | (((sK529 @ X590)) != $true)) & ! [X592 : term] : (($true != ((sK529 @ X592))) | (((sK529 @ (lam @ X592))) = $true)) & (((sK529 @ sK530)) != $true) & ! [X593 : term] : (($true = ((sK529 @ X593))) | ($true != ((var @ X593)))))) & (! [X594 : (term > $o),X595 : term] : (((((X594 @ (ap @ (sK531 @ X594) @ (sK532 @ X594)))) != $true) & ($true = ((X594 @ (sK532 @ X594)))) & (((X594 @ (sK531 @ X594))) = $true)) | ((((X594 @ (sK533 @ X594))) = $true) & (((X594 @ (lam @ (sK533 @ X594)))) != $true)) | (((X594 @ X595)) = $true) | (($true != ((X594 @ (sK534 @ X594)))) & ($true = ((var @ (sK534 @ X594)))))) | (induction != $true)) & (pushprop_lem3v2 = $true) & (! [X600 : term,X601 : term] : ((X600 = X601) | (((lam @ X601)) != ((lam @ X600)))) | (laminj != $true)) & ((laminj = $true) | ((sK535 != sK536) & (((lam @ sK536)) = ((lam @ sK535))))) & ((! [X604 : subst] : (((comp @ id @ X604)) = X604) & ! [X605 : subst] : (((comp @ X605 @ id)) = X605)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ id @ sK537)) != sK537) | (sK538 != ((comp @ sK538 @ id)))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X608 : d_subst] : (d_id = X608) & ! [X609 : d_term] : (d_one = X609) & (hoasinduction_lem2v2_gthm = $true) & (! [X610 : (term > $o),X611 : subst,X612 : (term > $o),X613 : term] : (($true != ((X612 @ X613))) | ($true = ((X610 @ one))) | (((X612 @ (sub @ (sK539 @ X613 @ X612 @ X611 @ X610) @ (push @ X613 @ X611)))) != ((X610 @ (sK539 @ X613 @ X612 @ X611 @ X610))))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ((((sK542 @ sK543)) = $true) & ($true != ((sK540 @ one))) & ! [X619 : term] : (((sK542 @ (sub @ X619 @ (push @ sK543 @ sK541)))) = ((sK540 @ X619))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_gthm = $true) & (lamnotap != $true) & (($true = sP1) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP1)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (! [X620 : subst,X621 : term] : (((comp @ sh @ (push @ X621 @ X620))) = X620) | (axshiftcons != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK545 @ sK544))) != sK544)) & (! [X624 : (term > $o),X625 : term,X626 : (subst > term > subst > $o)] : ((($true = ((X626 @ (sK549 @ X626) @ (sK546 @ X626) @ (comp @ (sK547 @ X626) @ (sK548 @ X626))))) & ($true != ((X626 @ (comp @ (sK549 @ X626) @ (sK547 @ X626)) @ (sub @ (sK546 @ X626) @ (sK547 @ X626)) @ (sK548 @ X626))))) | ($true = ((sP0 @ X626))) | ((((X626 @ (sK551 @ X626) @ (sK553 @ X626) @ (comp @ (sK550 @ X626) @ (sK552 @ X626)))) != $true) & ($true = ((X626 @ (comp @ (sK551 @ X626) @ (sK550 @ X626)) @ (sub @ (sK553 @ X626) @ (sK550 @ X626)) @ (sK552 @ X626))))) | (((X626 @ id @ (sK554 @ X626 @ X624) @ id)) != ((X624 @ (sK554 @ X626 @ X624)))) | (($true = ((X624 @ (sK555 @ X625 @ X624)))) & ($true != ((X624 @ (sub @ X625 @ (push @ (sK555 @ X625 @ X624) @ id)))))) | (((X624 @ (lam @ X625))) = $true)) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (! [X640 : term,X641 : subst,X642 : subst,X643 : subst] : (($true != ((sK558 @ X643 @ X640 @ (comp @ X641 @ X642)))) | (((sK558 @ (comp @ X643 @ X641) @ (sub @ X640 @ X641) @ X642)) = $true)) & ($true != ((sP0 @ sK558))) & ! [X644 : subst,X645 : subst,X646 : subst,X647 : term] : (($true = ((sK558 @ X645 @ X647 @ (comp @ X644 @ X646)))) | ($true != ((sK558 @ (comp @ X645 @ X644) @ (sub @ X647 @ X644) @ X646)))) & ! [X648 : term] : (((sK556 @ X648)) = ((sK558 @ id @ X648 @ id))) & ! [X649 : term] : ((((sK556 @ X649)) != $true) | ($true = ((sK556 @ (sub @ sK557 @ (push @ X649 @ id)))))) & ($true != ((sK556 @ (lam @ sK557)))))) & (! [X650 : term] : (((sub @ X650 @ id)) = X650) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK559 @ id)) != sK559)) & (termmset_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop = $true) & (substmonoid_gthm = $true) & ! [X652 : d_term,X653 : d_term] : ((X652 = X653) | (((d2term @ X652)) != ((d2term @ X653)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))))),
% 1.38/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK236,sK237,sK238,sK239,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK250,sK251,sK252,sK253,sK254,sK255,sK256,sK257,sK258,sK259,sK260,sK261,sK262,sK263,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK270,vAPP,sK272,sK273,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK283,vAPP,sK285,sK286,sK287,vAPP,vAPP,vAPP,vAPP,sK292,vAPP,vAPP,vAPP,vAPP,sK297,sK298,sK299,vAPP,vAPP,sK302,sK303,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK314,sK315,sK316,sK317,sK318,sK319,sK320,sK321,sK322,sK323,sK324,sK325,sK326,sK327,sK328,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK336,vAPP,vAPP,sK339,sK340,vAPP,vAPP,sK343,sK344,vAPP,vAPP,vAPP,vAPP,sK349,sK350,sK351,sK352,sK353,sK354,sK355,sK356,sK357,sK358,sK359,sK360,sK361,sK362,sK363,sK364,vAPP,vAPP,vAPP,sK368,sK369,sK370,sK371,sK372,sK373,sK374,sK375,sK376,vAPP,vAPP,vAPP,vAPP,vAPP,sK382,sK383,sK384,vAPP,vAPP,vAPP,vAPP,sK389,sK390,sK391,sK392,sK393,sK394,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK401,sK402,sK403,sK404,sK405,sK406,vAPP,sK408,vAPP,sK410,sK411,sK412,sK413,sK414,sK415,sK416,sK417,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK427,sK428,sK429,sK430,vAPP,sK432,sK433,sK434,vAPP,vAPP,vAPP,vAPP,sK439,vAPP,vAPP,vAPP,vAPP,vAPP,sK445,sK446,sK447,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK457,sK458,sK459,sK460,sK461,sK462,vAPP,sK464,vAPP,vAPP,vAPP,sK468,sK469,vAPP,vAPP,vAPP,vAPP,sK474,vAPP,vAPP,vAPP,sK478,sK479,vAPP,vAPP,vAPP,vAPP,vAPP,sK485,vAPP,vAPP,sK488,sK489,sK490,vAPP,vAPP,vAPP,sK494,sK495,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK503,vAPP,vAPP,sK506,sK507,vAPP,vAPP,vAPP,vAPP,sK512,vAPP,sK514,sK515,sK516,vAPP,vAPP,vAPP,vAPP,sK521,vAPP,vAPP,vAPP,vAPP,sK526,sK527,sK528,sK529,sK530,vAPP,vAPP,vAPP,vAPP,sK535,sK536,sK537,sK538,vAPP,sK540,sK541,sK542,sK543,sK544,sK545,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK556,sK557,sK558,sK559]),skolemize(X0,sK236),skolemize(X2,sK237),skolemize(X3,sK238),skolemize(X4,sK239),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X29,sK250),skolemize(X31,sK251),skolemize(X32,sK252),skolemize(X33,sK253),skolemize(X34,sK254),skolemize(X39,sK255),skolemize(X44,sK256),skolemize(X45,sK257),skolemize(X46,sK258),skolemize(X47,sK259),skolemize(X48,sK260),skolemize(X49,sK261),skolemize(X50,sK262),skolemize(X51,sK263),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X69,sK270),skolemize(X6,sK32 @ X0),skolemize(X72,sK272),skolemize(X73,sK273),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X94,sK283),skolemize(X6,sK32 @ X0),skolemize(X97,sK285),skolemize(X98,sK286),skolemize(X99,sK287),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X107,sK292),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X122,sK297),skolemize(X123,sK298),skolemize(X124,sK299),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X132,sK302),skolemize(X133,sK303),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X156,sK314),skolemize(X157,sK315),skolemize(X158,sK316),skolemize(X159,sK317),skolemize(X168,sK318),skolemize(X169,sK319),skolemize(X170,sK320),skolemize(X171,sK321),skolemize(X172,sK322),skolemize(X173,sK323),skolemize(X174,sK324),skolemize(X175,sK325),skolemize(X180,sK326),skolemize(X181,sK327),skolemize(X182,sK328),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X202,sK336),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X208,sK339),skolemize(X209,sK340),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X218,sK343),skolemize(X219,sK344),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X226,sK349),skolemize(X227,sK350),skolemize(X228,sK351),skolemize(X229,sK352),skolemize(X236,sK353),skolemize(X237,sK354),skolemize(X238,sK355),skolemize(X239,sK356),skolemize(X240,sK357),skolemize(X243,sK358),skolemize(X244,sK359),skolemize(X250,sK360),skolemize(X251,sK361),skolemize(X252,sK362),skolemize(X253,sK363),skolemize(X254,sK364),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X268,sK368),skolemize(X269,sK369),skolemize(X270,sK370),skolemize(X271,sK371),skolemize(X272,sK372),skolemize(X273,sK373),skolemize(X274,sK374),skolemize(X275,sK375),skolemize(X280,sK376),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X296,sK382),skolemize(X297,sK383),skolemize(X298,sK384),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X308,sK389),skolemize(X309,sK390),skolemize(X310,sK391),skolemize(X311,sK392),skolemize(X322,sK393),skolemize(X323,sK394),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X334,sK401),skolemize(X335,sK402),skolemize(X336,sK403),skolemize(X337,sK404),skolemize(X339,sK405),skolemize(X340,sK406),skolemize(X6,sK32 @ X0),skolemize(X344,sK408),skolemize(X6,sK32 @ X0),skolemize(X351,sK410),skolemize(X352,sK411),skolemize(X353,sK412),skolemize(X354,sK413),skolemize(X355,sK414),skolemize(X356,sK415),skolemize(X360,sK416),skolemize(X361,sK417),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X384,sK427),skolemize(X385,sK428),skolemize(X386,sK429),skolemize(X387,sK430),skolemize(X6,sK32 @ X0),skolemize(X394,sK432),skolemize(X395,sK433),skolemize(X396,sK434),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X405,sK439),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X419,sK445),skolemize(X420,sK446),skolemize(X421,sK447),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X447,sK457),skolemize(X448,sK458),skolemize(X449,sK459),skolemize(X450,sK460),skolemize(X451,sK461),skolemize(X453,sK462),skolemize(X6,sK32 @ X0),skolemize(X457,sK464),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X469,sK468),skolemize(X470,sK469),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X477,sK474),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X487,sK478),skolemize(X488,sK479),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X500,sK485),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X504,sK488),skolemize(X505,sK489),skolemize(X506,sK490),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X516,sK494),skolemize(X517,sK495),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X534,sK503),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X546,sK506),skolemize(X547,sK507),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X554,sK512),skolemize(X6,sK32 @ X0),skolemize(X557,sK514),skolemize(X558,sK515),skolemize(X559,sK516),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X567,sK521),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X582,sK526),skolemize(X586,sK527),skolemize(X587,sK528),skolemize(X588,sK529),skolemize(X589,sK530),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X602,sK535),skolemize(X603,sK536),skolemize(X606,sK537),skolemize(X607,sK538),skolemize(X6,sK32 @ X0),skolemize(X615,sK540),skolemize(X616,sK541),skolemize(X617,sK542),skolemize(X618,sK543),skolemize(X622,sK544),skolemize(X623,sK545),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X6,sK32 @ X0),skolemize(X637,sK556),skolemize(X638,sK557),skolemize(X639,sK558),skolemize(X651,sK559)],[f131])).
% 1.38/0.56 thf(f133,plain,(
% 1.38/0.56 ((pushprop_lem2v2 != $true) | ? [X3 : term,X0 : (term > $o),X1 : (term > $o),X2 : subst] : (? [X5 : term] : ((((X0 @ (sub @ X5 @ sh))) != $true) & (((var @ X5)) = $true) & (((X0 @ X5)) = $true)) & ! [X4 : term] : (($true = ((X1 @ (sub @ X4 @ X2)))) | (((var @ X4)) != $true)) & (((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0)) = $true))) & ((pushprop_lem2v2 = $true) | ! [X3 : term,X0 : (term > $o),X1 : (term > $o),X2 : subst] : (! [X5 : term] : ((((X0 @ (sub @ X5 @ sh))) = $true) | (((var @ X5)) != $true) | (((X0 @ X5)) != $true)) | ? [X4 : term] : (($true != ((X1 @ (sub @ X4 @ X2)))) & (((var @ X4)) = $true)) | (((pushprop_p_and_p_prime @ X3 @ X2 @ X1 @ X0)) != $true)))),
% 1.38/0.56 inference(nnf_transformation,[],[f13])).
% 1.38/0.56 thf(f134,plain,(
% 1.38/0.56 ((pushprop_lem2v2 != $true) | ? [X0 : term,X1 : (term > $o),X2 : (term > $o),X3 : subst] : (? [X4 : term] : (($true != ((X1 @ (sub @ X4 @ sh)))) & (((var @ X4)) = $true) & (((X1 @ X4)) = $true)) & ! [X5 : term] : (($true = ((X2 @ (sub @ X5 @ X3)))) | (((var @ X5)) != $true)) & ($true = ((pushprop_p_and_p_prime @ X0 @ X3 @ X2 @ X1))))) & ((pushprop_lem2v2 = $true) | ! [X6 : term,X7 : (term > $o),X8 : (term > $o),X9 : subst] : (! [X10 : term] : ((((X7 @ (sub @ X10 @ sh))) = $true) | (((var @ X10)) != $true) | ($true != ((X7 @ X10)))) | ? [X11 : term] : ((((X8 @ (sub @ X11 @ X9))) != $true) & (((var @ X11)) = $true)) | ($true != ((pushprop_p_and_p_prime @ X6 @ X9 @ X8 @ X7)))))),
% 1.38/0.56 inference(rectify,[],[f133])).
% 1.38/0.56 thf(f135,plain,(
% 1.38/0.56 ((pushprop_lem2v2 != $true) | ((($true != ((sK561 @ (sub @ sK564 @ sh)))) & ($true = ((var @ sK564))) & (((sK561 @ sK564)) = $true)) & ! [X5 : term] : ((((sK562 @ (sub @ X5 @ sK563))) = $true) | (((var @ X5)) != $true)) & (((pushprop_p_and_p_prime @ sK560 @ sK563 @ sK562 @ sK561)) = $true))) & ((pushprop_lem2v2 = $true) | ! [X6 : term,X7 : (term > $o),X8 : (term > $o),X9 : subst] : (! [X10 : term] : ((((X7 @ (sub @ X10 @ sh))) = $true) | (((var @ X10)) != $true) | ($true != ((X7 @ X10)))) | (($true != ((X8 @ (sub @ (sK565 @ X9 @ X8) @ X9)))) & ($true = ((var @ (sK565 @ X9 @ X8))))) | ($true != ((pushprop_p_and_p_prime @ X6 @ X9 @ X8 @ X7)))))),
% 1.38/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK560,sK561,sK562,sK563,sK564,vAPP]),skolemize(X0,sK560),skolemize(X1,sK561),skolemize(X2,sK562),skolemize(X3,sK563),skolemize(X4,sK564),skolemize(X6,sK32 @ X0)],[f134])).
% 1.38/0.56 thf(f502,plain,(
% 1.38/0.56 ( ! [X609 : d_term] : ((d_one = X609)) )),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f571,plain,(
% 1.38/0.56 (((d2subst @ d_id)) = id)),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f589,plain,(
% 1.38/0.56 (pushprop_lem2v2 = $true)),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f725,plain,(
% 1.38/0.56 (one = ((d2term @ d_one)))),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f726,plain,(
% 1.38/0.56 ( ! [X262 : term] : ((((d2term @ (sK367 @ X262))) = X262)) )),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f749,plain,(
% 1.38/0.56 (((d2subst @ d_id)) = sh)),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f836,plain,(
% 1.38/0.56 (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id))))),
% 1.38/0.56 inference(cnf_transformation,[],[f132])).
% 1.38/0.56 thf(f878,plain,(
% 1.38/0.56 (pushprop_lem2v2 != $true) | (((sK561 @ sK564)) = $true)),
% 1.38/0.56 inference(cnf_transformation,[],[f135])).
% 1.38/0.56 thf(f880,plain,(
% 1.38/0.56 ($true != ((sK561 @ (sub @ sK564 @ sh)))) | (pushprop_lem2v2 != $true)),
% 1.38/0.56 inference(cnf_transformation,[],[f135])).
% 1.38/0.56 thf(f1135,definition,(
% 1.38/0.56 spl566_21 <=> ! [X30 : term] : (((sub @ X30 @ id)) = X30)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_21])],[avatar_definition])).
% 1.38/0.56 thf(f1136,plain,(
% 1.38/0.56 ( ! [X30 : term] : ((((sub @ X30 @ id)) = X30)) ) | ~spl566_21),
% 1.38/0.56 inference(avatar_component_clause,[],[f1135])).
% 1.38/0.56 thf(f1296,definition,(
% 1.38/0.56 spl566_59 <=> (pushprop_lem2v2 = $true)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_59])],[avatar_definition])).
% 1.38/0.56 thf(f1300,definition,(
% 1.38/0.56 spl566_60 <=> ($true = ((sK561 @ (sub @ sK564 @ sh))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_60])],[avatar_definition])).
% 1.38/0.56 thf(f1302,plain,(
% 1.38/0.56 ($true != ((sK561 @ (sub @ sK564 @ sh)))) | spl566_60),
% 1.38/0.56 inference(avatar_component_clause,[],[f1300])).
% 1.38/0.56 thf(f1303,plain,(
% 1.38/0.56 ~spl566_59 | ~spl566_60),
% 1.38/0.56 inference(avatar_split_clause,[],[f880,f1300,f1296])).
% 1.38/0.56 thf(f2442,definition,(
% 1.38/0.56 spl566_331 <=> (one = ((d2term @ d_one)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_331])],[avatar_definition])).
% 1.38/0.56 thf(f2444,plain,(
% 1.38/0.56 (one = ((d2term @ d_one))) | ~spl566_331),
% 1.38/0.56 inference(avatar_component_clause,[],[f2442])).
% 1.38/0.56 thf(f2445,plain,(
% 1.38/0.56 spl566_331),
% 1.38/0.56 inference(avatar_split_clause,[],[f725,f2442])).
% 1.38/0.56 thf(f3295,plain,(
% 1.38/0.56 spl566_59),
% 1.38/0.56 inference(avatar_split_clause,[],[f589,f1296])).
% 1.38/0.56 thf(f3382,definition,(
% 1.38/0.56 spl566_549 <=> (((sK561 @ sK564)) = $true)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_549])],[avatar_definition])).
% 1.38/0.56 thf(f3384,plain,(
% 1.38/0.56 (((sK561 @ sK564)) = $true) | ~spl566_549),
% 1.38/0.56 inference(avatar_component_clause,[],[f3382])).
% 1.38/0.56 thf(f3385,plain,(
% 1.38/0.56 ~spl566_59 | spl566_549),
% 1.38/0.56 inference(avatar_split_clause,[],[f878,f3382,f1296])).
% 1.38/0.56 thf(f4176,definition,(
% 1.38/0.56 spl566_732 <=> (((d2subst @ d_id)) = id)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_732])],[avatar_definition])).
% 1.38/0.56 thf(f4178,plain,(
% 1.38/0.56 (((d2subst @ d_id)) = id) | ~spl566_732),
% 1.38/0.56 inference(avatar_component_clause,[],[f4176])).
% 1.38/0.56 thf(f4179,plain,(
% 1.38/0.56 spl566_732),
% 1.38/0.56 inference(avatar_split_clause,[],[f571,f4176])).
% 1.38/0.56 thf(f4469,definition,(
% 1.38/0.56 spl566_800 <=> (((d2subst @ d_id)) = sh)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_800])],[avatar_definition])).
% 1.38/0.56 thf(f4471,plain,(
% 1.38/0.56 (((d2subst @ d_id)) = sh) | ~spl566_800),
% 1.38/0.56 inference(avatar_component_clause,[],[f4469])).
% 1.38/0.56 thf(f4472,plain,(
% 1.38/0.56 spl566_800),
% 1.38/0.56 inference(avatar_split_clause,[],[f749,f4469])).
% 1.38/0.56 thf(f4504,definition,(
% 1.38/0.56 spl566_808 <=> (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id))))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_808])],[avatar_definition])).
% 1.38/0.56 thf(f4506,plain,(
% 1.38/0.56 (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) | ~spl566_808),
% 1.38/0.56 inference(avatar_component_clause,[],[f4504])).
% 1.38/0.56 thf(f4507,plain,(
% 1.38/0.56 spl566_808),
% 1.38/0.56 inference(avatar_split_clause,[],[f836,f4504])).
% 1.38/0.56 thf(f4751,plain,(
% 1.38/0.56 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) ) | ~spl566_331),
% 1.38/0.56 inference(superposition,[],[f2444,f502])).
% 1.38/0.56 thf(f4761,plain,(
% 1.38/0.56 (id = sh) | (~spl566_732 | ~spl566_800)),
% 1.38/0.56 inference(forward_demodulation,[],[f4471,f4178])).
% 1.38/0.56 thf(f4763,definition,(
% 1.38/0.56 spl566_831 <=> (id = sh)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_831])],[avatar_definition])).
% 1.38/0.56 thf(f4765,plain,(
% 1.38/0.56 (id = sh) | ~spl566_831),
% 1.38/0.56 inference(avatar_component_clause,[],[f4763])).
% 1.38/0.56 thf(f4766,plain,(
% 1.38/0.56 spl566_831 | ~spl566_732 | ~spl566_800),
% 1.38/0.56 inference(avatar_split_clause,[],[f4761,f4469,f4176,f4763])).
% 1.38/0.56 thf(f4767,plain,(
% 1.38/0.56 (((sK561 @ (sub @ sK564 @ id))) != $true) | (spl566_60 | ~spl566_831)),
% 1.38/0.56 inference(superposition,[],[f1302,f4765])).
% 1.38/0.56 thf(f4769,definition,(
% 1.38/0.56 spl566_832 <=> (((sK561 @ (sub @ sK564 @ id))) = $true)),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_832])],[avatar_definition])).
% 1.38/0.56 thf(f4771,plain,(
% 1.38/0.56 (((sK561 @ (sub @ sK564 @ id))) != $true) | spl566_832),
% 1.38/0.56 inference(avatar_component_clause,[],[f4769])).
% 1.38/0.56 thf(f4772,plain,(
% 1.38/0.56 ~spl566_832 | spl566_60 | ~spl566_831),
% 1.38/0.56 inference(avatar_split_clause,[],[f4767,f4763,f1300,f4769])).
% 1.38/0.56 thf(f4781,plain,(
% 1.38/0.56 (((sK561 @ sK564)) != $true) | (~spl566_21 | spl566_832)),
% 1.38/0.56 inference(superposition,[],[f4771,f1136])).
% 1.38/0.56 thf(f4782,plain,(
% 1.38/0.56 $false | (~spl566_21 | ~spl566_549 | spl566_832)),
% 1.38/0.56 inference(forward_subsumption_resolution,[],[f4781,f3384])).
% 1.38/0.56 thf(f4783,plain,(
% 1.38/0.56 ~spl566_21 | ~spl566_549 | spl566_832),
% 1.38/0.56 inference(avatar_contradiction_clause,[],[f4782])).
% 1.38/0.56 thf(f4881,plain,(
% 1.38/0.56 (one = ((sub @ one @ (d2subst @ d_id)))) | (~spl566_331 | ~spl566_808)),
% 1.38/0.56 inference(forward_demodulation,[],[f4506,f2444])).
% 1.38/0.56 thf(f5096,plain,(
% 1.38/0.56 (one = ((sub @ one @ id))) | (~spl566_331 | ~spl566_732 | ~spl566_808)),
% 1.38/0.56 inference(forward_demodulation,[],[f4881,f4178])).
% 1.38/0.56 thf(f5099,definition,(
% 1.38/0.56 spl566_861 <=> (one = ((sub @ one @ id)))),
% 1.38/0.56 introduced(definition,[new_symbols(definition,[spl566_861])],[avatar_definition])).
% 1.38/0.56 thf(f5101,plain,(
% 1.38/0.56 (one = ((sub @ one @ id))) | ~spl566_861),
% 1.38/0.56 inference(avatar_component_clause,[],[f5099])).
% 1.38/0.56 thf(f5102,plain,(
% 1.38/0.56 spl566_861 | ~spl566_331 | ~spl566_732 | ~spl566_808),
% 1.38/0.56 inference(avatar_split_clause,[],[f5096,f4504,f4176,f2442,f5099])).
% 1.38/0.56 thf(f5160,plain,(
% 1.38/0.56 ( ! [X0 : term] : ((one = X0)) ) | ~spl566_331),
% 1.38/0.56 inference(superposition,[],[f4751,f726])).
% 1.38/0.56 thf(f5171,plain,(
% 1.38/0.56 ( ! [X0 : term] : ((((sub @ X0 @ id)) = X0)) ) | (~spl566_331 | ~spl566_861)),
% 1.38/0.56 inference(superposition,[],[f5101,f5160])).
% 1.38/0.56 thf(f5172,plain,(
% 1.38/0.56 spl566_21 | ~spl566_331 | ~spl566_861),
% 1.38/0.56 inference(avatar_split_clause,[],[f5171,f5099,f2442,f1135])).
% 1.38/0.56 cnf(s33, plain, ~spl566_59 | ~spl566_60, inference(sat_conversion,[],[f1303])).
% 1.38/0.56 cnf(s268, plain, spl566_331, inference(sat_conversion,[],[f2445])).
% 1.38/0.56 cnf(s468, plain, spl566_59, inference(sat_conversion,[],[f3295])).
% 1.38/0.56 cnf(s491, plain, ~spl566_59 | spl566_549, inference(sat_conversion,[],[f3385])).
% 1.38/0.56 cnf(s691, plain, spl566_732, inference(sat_conversion,[],[f4179])).
% 1.38/0.56 cnf(s764, plain, spl566_800, inference(sat_conversion,[],[f4472])).
% 1.38/0.56 cnf(s772, plain, spl566_808, inference(sat_conversion,[],[f4507])).
% 1.38/0.56 cnf(s795, plain, ~spl566_732 | ~spl566_800 | spl566_831, inference(sat_conversion,[],[f4766])).
% 1.38/0.56 cnf(s796, plain, spl566_60 | ~spl566_831 | ~spl566_832, inference(sat_conversion,[],[f4772])).
% 1.38/0.56 cnf(s798, plain, ~spl566_21 | ~spl566_549 | spl566_832, inference(sat_conversion,[],[f4783])).
% 1.38/0.56 cnf(s825, plain, ~spl566_331 | ~spl566_732 | ~spl566_808 | spl566_861, inference(sat_conversion,[],[f5102])).
% 1.38/0.56 cnf(s827, plain, spl566_21 | ~spl566_331 | ~spl566_861, inference(sat_conversion,[],[f5172])).
% 1.38/0.56 cnf(s828, plain, spl566_831, inference(rat,[],[s795,s764,s691])).
% 1.38/0.56 cnf(s831, plain, spl566_549, inference(rat,[],[s491,s468])).
% 1.38/0.56 cnf(s834, plain, spl566_861, inference(rat,[],[s825,s691,s772,s268])).
% 1.38/0.56 cnf(s836, plain, spl566_21, inference(rat,[],[s827,s268,s834])).
% 1.38/0.56 cnf(s837, plain, spl566_832, inference(rat,[],[s798,s831,s836])).
% 1.38/0.56 cnf(s838, plain, spl566_60, inference(rat,[],[s796,s828,s837])).
% 1.38/0.56 cnf(s843, plain, $false, inference(rat,[],[s33,s838,s468])).
% 1.38/0.56 thf(f5173,plain,(
% 1.38/0.56 $false),
% 1.38/0.56 inference(avatar_sat_refutation,[],[s843])).
% 1.38/0.56 % SZS output end Proof for theBenchmark
% 1.38/0.56 % (518339)------------------------------
% 1.38/0.56 % (518339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.56 % (518339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.56 % (518339)CaDiCaL version: 2.1.3
% 1.38/0.56 % (518339)Termination reason: Refutation
% 1.38/0.56 % (518339)Time elapsed: 0.243 s
% 1.38/0.56 % (518339)Peak memory usage: 18 MB
% 1.38/0.56 % (518339)Instructions burned: 511 (million)
% 1.38/0.56 % (518331)Success in time 0.295 s
% 1.38/0.56 % Vampire exiting
%------------------------------------------------------------------------------