%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX168^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:37 AM UTC 2026
% Result : Theorem 6.12s 1.29s
% Output : Refutation 6.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX168^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n001.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 16:15:21 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.44 % (1436878)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.44 % (1436886)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=380399804: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)
% 0.50/0.44 % (1436884)lrs+10_16_si=on:nwc=1.5:random_seed=2219484433:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.44 % (1436885)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3579200586:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.44 % (1436887)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2049805287:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.44 % (1436885)Instruction limit reached!
% 0.50/0.44 % (1436885)------------------------------
% 0.50/0.44 % (1436885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.44 % (1436885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.44 % (1436885)CaDiCaL version: 2.1.3
% 0.50/0.44 % (1436885)Termination reason: Instruction limit
% 0.50/0.44 % (1436885)Termination phase: shuffling
% 0.50/0.44 % (1436885)Time elapsed: 0.003 s
% 0.50/0.44 % (1436885)Peak memory usage: 10 MB
% 0.50/0.44 % (1436885)Instructions burned: 5 (million)
% 0.50/0.44 % (1436888)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2178156527:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.44 % (1436884)Instruction limit reached!
% 0.50/0.44 % (1436884)------------------------------
% 0.50/0.44 % (1436884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.44 % (1436884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.44 % (1436884)CaDiCaL version: 2.1.3
% 0.50/0.44 % (1436884)Termination reason: Instruction limit
% 0.50/0.44 % (1436884)Termination phase: shuffling
% 0.50/0.44 % (1436884)Time elapsed: 0.009 s
% 0.50/0.44 % (1436884)Peak memory usage: 10 MB
% 0.50/0.44 % (1436884)Instructions burned: 20 (million)
% 0.50/0.44 % (1436889)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.44 % (1436889)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
% 0.50/0.44 % (1436887)Instruction limit reached!
% 0.50/0.44 % (1436887)------------------------------
% 0.50/0.44 % (1436887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.44 % (1436887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.44 % (1436887)CaDiCaL version: 2.1.3
% 0.50/0.44 % (1436887)Termination reason: Instruction limit
% 0.50/0.44 % (1436887)Termination phase: Property scanning
% 0.50/0.44 % (1436887)Time elapsed: 0.011 s
% 0.50/0.44 % (1436887)Peak memory usage: 10 MB
% 0.50/0.44 % (1436887)Instructions burned: 25 (million)
% 0.50/0.44 % (1436883)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=397827912:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.44 % (1436889)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=1467984900:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.44 % (1436894)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4080157500:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.44 % (1436894)Instruction limit reached!
% 0.50/0.44 % (1436894)------------------------------
% 0.50/0.44 % (1436894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.44 % (1436894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.44 % (1436894)CaDiCaL version: 2.1.3
% 0.50/0.44 % (1436894)Termination reason: Instruction limit
% 0.50/0.44 % (1436894)Termination phase: shuffling
% 0.50/0.44 % (1436894)Time elapsed: 0.003 s
% 0.50/0.44 % (1436894)Peak memory usage: 9 MB
% 0.50/0.44 % (1436894)Instructions burned: 5 (million)
% 0.50/0.44 % (1436897)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.32/0.50 % (1436897)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2284882417:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.32/0.50 % (1436896)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2767037884:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.32/0.50 % (1436897)Instruction limit reached!
% 1.32/0.50 % (1436897)------------------------------
% 1.32/0.50 % (1436897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (1436897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (1436897)CaDiCaL version: 2.1.3
% 1.32/0.50 % (1436897)Termination reason: Instruction limit
% 1.32/0.50 % (1436897)Termination phase: shuffling
% 1.32/0.50 % (1436897)Time elapsed: 0.004 s
% 1.32/0.50 % (1436897)Peak memory usage: 10 MB
% 1.32/0.50 % (1436897)Instructions burned: 7 (million)
% 1.32/0.50 % (1436896)Instruction limit reached!
% 1.32/0.50 % (1436896)------------------------------
% 1.32/0.50 % (1436896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (1436896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (1436896)CaDiCaL version: 2.1.3
% 1.32/0.50 % (1436896)Termination reason: Instruction limit
% 1.32/0.50 % (1436896)Termination phase: shuffling
% 1.32/0.50 % (1436896)Time elapsed: 0.005 s
% 1.32/0.50 % (1436896)Peak memory usage: 10 MB
% 1.32/0.50 % (1436896)Instructions burned: 5 (million)
% 1.32/0.50 % (1436901)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2163357367:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.32/0.50 % (1436901)Instruction limit reached!
% 1.32/0.50 % (1436901)------------------------------
% 1.32/0.50 % (1436901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (1436901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (1436901)CaDiCaL version: 2.1.3
% 1.32/0.50 % (1436901)Termination reason: Instruction limit
% 1.32/0.50 % (1436901)Termination phase: shuffling
% 1.32/0.50 % (1436901)Time elapsed: 0.006 s
% 1.32/0.50 % (1436901)Peak memory usage: 10 MB
% 1.32/0.50 % (1436901)Instructions burned: 14 (million)
% 1.32/0.50 % (1436904)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
% 1.32/0.50 % (1436904)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.32/0.50 % (1436904)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2337560994:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.32/0.50 % (1436905)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=360169454:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.32/0.50 % (1436888)Instruction limit reached!
% 1.32/0.50 % (1436888)------------------------------
% 1.32/0.50 % (1436888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (1436888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (1436888)CaDiCaL version: 2.1.3
% 1.32/0.50 % (1436888)Termination reason: Instruction limit
% 1.32/0.50 % (1436888)Termination phase: Preprocessing 3
% 1.32/0.50 % (1436888)Time elapsed: 0.061 s
% 1.32/0.50 % (1436888)Peak memory usage: 12 MB
% 1.32/0.50 % (1436888)Instructions burned: 75 (million)
% 1.32/0.50 % (1436904)Instruction limit reached!
% 1.32/0.50 % (1436904)------------------------------
% 1.32/0.50 % (1436904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.50 % (1436904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.50 % (1436904)CaDiCaL version: 2.1.3
% 1.32/0.50 % (1436904)Termination reason: Instruction limit
% 1.32/0.50 % (1436904)Termination phase: shuffling
% 1.32/0.50 % (1436904)Time elapsed: 0.013 s
% 1.32/0.50 % (1436904)Peak memory usage: 10 MB
% 1.32/0.50 % (1436904)Instructions burned: 29 (million)
% 1.32/0.50 % (1436907)lrs+10_1_si=on:cs=on:random_seed=1001042705:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.32/0.50 % (1436907)Instruction limit reached!
% 1.32/0.52 % (1436907)------------------------------
% 1.32/0.52 % (1436907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436907)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436907)Termination reason: Instruction limit
% 1.32/0.52 % (1436907)Termination phase: shuffling
% 1.32/0.52 % (1436907)Time elapsed: 0.004 s
% 1.32/0.52 % (1436907)Peak memory usage: 10 MB
% 1.32/0.52 % (1436907)Instructions burned: 8 (million)
% 1.32/0.52 % (1436910)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.32/0.52 % (1436889)Instruction limit reached!
% 1.32/0.52 % (1436889)------------------------------
% 1.32/0.52 % (1436889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436889)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436889)Termination reason: Instruction limit
% 1.32/0.52 % (1436889)Termination phase: Property scanning
% 1.32/0.52 % (1436889)Time elapsed: 0.070 s
% 1.32/0.52 % (1436889)Peak memory usage: 13 MB
% 1.32/0.52 % (1436889)Instructions burned: 157 (million)
% 1.32/0.52 % (1436883)Instruction limit reached!
% 1.32/0.52 % (1436883)------------------------------
% 1.32/0.52 % (1436883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436883)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436883)Termination reason: Instruction limit
% 1.32/0.52 % (1436883)Termination phase: Preprocessing 3
% 1.32/0.52 % (1436883)Time elapsed: 0.073 s
% 1.32/0.52 % (1436883)Peak memory usage: 12 MB
% 1.32/0.52 % (1436883)Instructions burned: 87 (million)
% 1.32/0.52 % (1436910)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=4219902453:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.32/0.52 % (1436911)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1478533159:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.32/0.52 % (1436910)Instruction limit reached!
% 1.32/0.52 % (1436910)------------------------------
% 1.32/0.52 % (1436910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436910)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436910)Termination reason: Instruction limit
% 1.32/0.52 % (1436910)Termination phase: shuffling
% 1.32/0.52 % (1436910)Time elapsed: 0.002 s
% 1.32/0.52 % (1436910)Peak memory usage: 10 MB
% 1.32/0.52 % (1436910)Instructions burned: 4 (million)
% 1.32/0.52 % (1436905)Instruction limit reached!
% 1.32/0.52 % (1436905)------------------------------
% 1.32/0.52 % (1436905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436905)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436905)Termination reason: Instruction limit
% 1.32/0.52 % (1436905)Termination phase: Saturation
% 1.32/0.52 % (1436905)Time elapsed: 0.037 s
% 1.32/0.52 % (1436905)Peak memory usage: 12 MB
% 1.32/0.52 % (1436905)Instructions burned: 87 (million)
% 1.32/0.52 % (1436913)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1345255135:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.32/0.52 % (1436915)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=30938980:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.32/0.52 % (1436911)Instruction limit reached!
% 1.32/0.52 % (1436911)------------------------------
% 1.32/0.52 % (1436911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.52 % (1436911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.52 % (1436911)CaDiCaL version: 2.1.3
% 1.32/0.52 % (1436911)Termination reason: Instruction limit
% 1.32/0.52 % (1436911)Termination phase: Property scanning
% 1.32/0.52 % (1436911)Time elapsed: 0.017 s
% 1.32/0.52 % (1436911)Peak memory usage: 11 MB
% 1.32/0.52 % (1436911)Instructions burned: 38 (million)
% 1.32/0.52 % (1436918)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3935905799:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.32/0.58 % (1436915)Instruction limit reached!
% 1.32/0.58 % (1436915)------------------------------
% 1.32/0.58 % (1436915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.58 % (1436915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.58 % (1436915)CaDiCaL version: 2.1.3
% 1.32/0.58 % (1436915)Termination reason: Instruction limit
% 1.32/0.58 % (1436915)Termination phase: shuffling
% 1.32/0.58 % (1436915)Time elapsed: 0.007 s
% 1.32/0.58 % (1436915)Peak memory usage: 10 MB
% 1.32/0.58 % (1436915)Instructions burned: 15 (million)
% 1.32/0.58 % (1436914)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2004750588:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.32/0.58 % (1436922)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3712597802: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)
% 1.32/0.58 % (1436919)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1927618200:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.32/0.58 % (1436922)Instruction limit reached!
% 1.32/0.58 % (1436922)------------------------------
% 1.32/0.58 % (1436922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.58 % (1436922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.58 % (1436922)CaDiCaL version: 2.1.3
% 1.32/0.58 % (1436922)Termination reason: Instruction limit
% 1.32/0.58 % (1436922)Termination phase: shuffling
% 1.32/0.58 % (1436922)Time elapsed: 0.002 s
% 1.32/0.58 % (1436922)Peak memory usage: 10 MB
% 1.32/0.58 % (1436922)Instructions burned: 3 (million)
% 1.32/0.58 % (1436924)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=304757738:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.32/0.58 % (1436914)Instruction limit reached!
% 1.32/0.58 % (1436914)------------------------------
% 1.32/0.58 % (1436914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.58 % (1436914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.58 % (1436914)CaDiCaL version: 2.1.3
% 1.32/0.58 % (1436914)Termination reason: Instruction limit
% 1.32/0.58 % (1436914)Termination phase: Property scanning
% 1.32/0.58 % (1436914)Time elapsed: 0.020 s
% 1.32/0.58 % (1436914)Peak memory usage: 10 MB
% 1.32/0.58 % (1436914)Instructions burned: 26 (million)
% 1.32/0.58 % (1436919)Instruction limit reached!
% 1.32/0.58 % (1436919)------------------------------
% 1.32/0.58 % (1436919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.58 % (1436919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.58 % (1436919)CaDiCaL version: 2.1.3
% 1.32/0.58 % (1436919)Termination reason: Instruction limit
% 1.32/0.58 % (1436919)Termination phase: shuffling
% 1.32/0.58 % (1436919)Time elapsed: 0.014 s
% 1.32/0.58 % (1436919)Peak memory usage: 10 MB
% 1.32/0.58 % (1436919)Instructions burned: 14 (million)
% 1.32/0.58 % (1436924)Instruction limit reached!
% 1.32/0.58 % (1436924)------------------------------
% 1.32/0.58 % (1436924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.58 % (1436924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.58 % (1436924)CaDiCaL version: 2.1.3
% 1.32/0.58 % (1436924)Termination reason: Instruction limit
% 1.32/0.58 % (1436924)Termination phase: shuffling
% 1.32/0.58 % (1436924)Time elapsed: 0.012 s
% 1.32/0.58 % (1436924)Peak memory usage: 10 MB
% 1.32/0.58 % (1436924)Instructions burned: 26 (million)
% 1.32/0.58 % (1436928)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1038449463:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.32/0.58 % (1436932)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.32/0.58 % (1436932)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=3115411926:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.32/0.58 % (1436928)Instruction limit reached!
% 1.32/0.58 % (1436928)------------------------------
% 1.32/0.58 % (1436928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436928)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436928)Termination reason: Instruction limit
% 2.00/0.62 % (1436928)Termination phase: shuffling
% 2.00/0.62 % (1436928)Time elapsed: 0.011 s
% 2.00/0.62 % (1436928)Peak memory usage: 10 MB
% 2.00/0.62 % (1436928)Instructions burned: 25 (million)
% 2.00/0.62 % (1436930)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2027521197:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.00/0.62 % (1436932)Instruction limit reached!
% 2.00/0.62 % (1436932)------------------------------
% 2.00/0.62 % (1436932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436932)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436932)Termination reason: Instruction limit
% 2.00/0.62 % (1436932)Termination phase: shuffling
% 2.00/0.62 % (1436932)Time elapsed: 0.004 s
% 2.00/0.62 % (1436932)Peak memory usage: 9 MB
% 2.00/0.62 % (1436932)Instructions burned: 9 (million)
% 2.00/0.62 % (1436931)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.00/0.62 % (1436931)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.00/0.62 % (1436931)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=1343953891:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.00/0.62 % (1436935)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=3564587877:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.00/0.62 % (1436886)Instruction limit reached!
% 2.00/0.62 % (1436886)------------------------------
% 2.00/0.62 % (1436886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436886)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436886)Termination reason: Instruction limit
% 2.00/0.62 % (1436886)Termination phase: Saturation
% 2.00/0.62 % (1436886)Time elapsed: 0.193 s
% 2.00/0.62 % (1436886)Peak memory usage: 18 MB
% 2.00/0.62 % (1436886)Instructions burned: 634 (million)
% 2.00/0.62 % (1436937)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3266447380:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.00/0.62 % (1436931)Instruction limit reached!
% 2.00/0.62 % (1436931)------------------------------
% 2.00/0.62 % (1436931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436931)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436931)Termination reason: Instruction limit
% 2.00/0.62 % (1436931)Termination phase: shuffling
% 2.00/0.62 % (1436931)Time elapsed: 0.011 s
% 2.00/0.62 % (1436931)Peak memory usage: 9 MB
% 2.00/0.62 % (1436931)Instructions burned: 14 (million)
% 2.00/0.62 % (1436937)Instruction limit reached!
% 2.00/0.62 % (1436937)------------------------------
% 2.00/0.62 % (1436937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436937)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436937)Termination reason: Instruction limit
% 2.00/0.62 % (1436937)Termination phase: shuffling
% 2.00/0.62 % (1436937)Time elapsed: 0.004 s
% 2.00/0.62 % (1436937)Peak memory usage: 9 MB
% 2.00/0.62 % (1436937)Instructions burned: 9 (million)
% 2.00/0.62 % (1436930)Instruction limit reached!
% 2.00/0.62 % (1436930)------------------------------
% 2.00/0.62 % (1436930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.62 % (1436930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.62 % (1436930)CaDiCaL version: 2.1.3
% 2.00/0.62 % (1436930)Termination reason: Instruction limit
% 2.00/0.62 % (1436930)Termination phase: Preprocessing 3
% 2.00/0.62 % (1436930)Time elapsed: 0.026 s
% 2.00/0.62 % (1436930)Peak memory usage: 11 MB
% 2.28/0.69 % (1436930)Instructions burned: 60 (million)
% 2.28/0.69 % (1436940)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=415355087:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.28/0.69 % (1436935)Instruction limit reached!
% 2.28/0.69 % (1436935)------------------------------
% 2.28/0.69 % (1436935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.28/0.69 % (1436935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.69 % (1436935)CaDiCaL version: 2.1.3
% 2.28/0.69 % (1436935)Termination reason: Instruction limit
% 2.28/0.69 % (1436935)Termination phase: Property scanning
% 2.28/0.69 % (1436935)Time elapsed: 0.014 s
% 2.28/0.69 % (1436935)Peak memory usage: 10 MB
% 2.28/0.69 % (1436935)Instructions burned: 33 (million)
% 2.28/0.69 % (1436940)Instruction limit reached!
% 2.28/0.69 % (1436940)------------------------------
% 2.28/0.69 % (1436940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.28/0.69 % (1436940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.69 % (1436940)CaDiCaL version: 2.1.3
% 2.28/0.69 % (1436940)Termination reason: Instruction limit
% 2.28/0.69 % (1436940)Termination phase: shuffling
% 2.28/0.69 % (1436940)Time elapsed: 0.005 s
% 2.28/0.69 % (1436940)Peak memory usage: 10 MB
% 2.28/0.69 % (1436940)Instructions burned: 25 (million)
% 2.28/0.69 % (1436944)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3552464278:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.28/0.69 % (1436947)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2583703603:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.28/0.69 % (1436946)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1243582233:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.28/0.69 % (1436947)Instruction limit reached!
% 2.28/0.69 % (1436947)------------------------------
% 2.28/0.69 % (1436947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.28/0.69 % (1436947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.69 % (1436947)CaDiCaL version: 2.1.3
% 2.28/0.69 % (1436947)Termination reason: Instruction limit
% 2.28/0.69 % (1436947)Termination phase: Naming
% 2.28/0.69 % (1436947)Time elapsed: 0.010 s
% 2.28/0.69 % (1436947)Peak memory usage: 11 MB
% 2.28/0.69 % (1436947)Instructions burned: 43 (million)
% 2.28/0.69 % (1436943)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1873847677:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.28/0.69 % (1436942)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3710729777:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.28/0.69 % (1436942)Instruction limit reached!
% 2.28/0.69 % (1436942)------------------------------
% 2.28/0.69 % (1436942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.28/0.69 % (1436942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.69 % (1436942)CaDiCaL version: 2.1.3
% 2.28/0.69 % (1436942)Termination reason: Instruction limit
% 2.28/0.69 % (1436942)Termination phase: shuffling
% 2.28/0.69 % (1436942)Time elapsed: 0.009 s
% 2.28/0.69 % (1436942)Peak memory usage: 10 MB
% 2.28/0.69 % (1436942)Instructions burned: 22 (million)
% 2.28/0.69 % (1436913)Instruction limit reached!
% 2.28/0.69 % (1436913)------------------------------
% 2.28/0.69 % (1436913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.28/0.69 % (1436913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.69 % (1436913)CaDiCaL version: 2.1.3
% 2.28/0.69 % (1436913)Termination reason: Instruction limit
% 2.28/0.69 % (1436913)Termination phase: Saturation
% 2.28/0.69 % (1436913)Time elapsed: 0.134 s
% 2.28/0.69 % (1436913)Peak memory usage: 15 MB
% 2.28/0.69 % (1436913)Instructions burned: 251 (million)
% 2.28/0.69 % (1436951)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.28/0.69 % (1436951)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3684244365:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.28/0.69 % (1436951)Instruction limit reached!
% 2.28/0.69 % (1436951)------------------------------
% 2.55/0.77 % (1436951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436951)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436951)Termination reason: Instruction limit
% 2.55/0.77 % (1436951)Termination phase: shuffling
% 2.55/0.77 % (1436951)Time elapsed: 0.004 s
% 2.55/0.77 % (1436951)Peak memory usage: 9 MB
% 2.55/0.77 % (1436951)Instructions burned: 8 (million)
% 2.55/0.77 % (1436954)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2898882853:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.55/0.77 % (1436955)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=3917360197:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.55/0.77 % (1436918)Instruction limit reached!
% 2.55/0.77 % (1436918)------------------------------
% 2.55/0.77 % (1436918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436918)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436918)Termination reason: Instruction limit
% 2.55/0.77 % (1436918)Termination phase: Saturation
% 2.55/0.77 % (1436918)Time elapsed: 0.152 s
% 2.55/0.77 % (1436918)Peak memory usage: 16 MB
% 2.55/0.77 % (1436918)Instructions burned: 328 (million)
% 2.55/0.77 % (1436957)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.55/0.77 % (1436957)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3565645334:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.55/0.77 % (1436946)Instruction limit reached!
% 2.55/0.77 % (1436946)------------------------------
% 2.55/0.77 % (1436946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436946)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436946)Termination reason: Instruction limit
% 2.55/0.77 % (1436946)Termination phase: Saturation
% 2.55/0.77 % (1436946)Time elapsed: 0.055 s
% 2.55/0.77 % (1436946)Peak memory usage: 13 MB
% 2.55/0.77 % (1436946)Instructions burned: 195 (million)
% 2.55/0.77 % (1436957)Instruction limit reached!
% 2.55/0.77 % (1436957)------------------------------
% 2.55/0.77 % (1436957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436957)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436957)Termination reason: Instruction limit
% 2.55/0.77 % (1436957)Termination phase: shuffling
% 2.55/0.77 % (1436957)Time elapsed: 0.003 s
% 2.55/0.77 % (1436957)Peak memory usage: 10 MB
% 2.55/0.77 % (1436957)Instructions burned: 6 (million)
% 2.55/0.77 % (1436962)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3628202607:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.55/0.77 % (1436954)Refutation not found, incomplete strategy
% 2.55/0.77 % (1436954)------------------------------
% 2.55/0.77 % (1436954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436960)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1940426707:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.55/0.77 % (1436954)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436954)Termination reason: Refutation not found, incomplete strategy
% 2.55/0.77 % (1436954)Time elapsed: 0.029 s
% 2.55/0.77 % (1436954)Peak memory usage: 13 MB
% 2.55/0.77 % (1436954)Instructions burned: 62 (million)
% 2.55/0.77 % (1436954)------------------------------
% 2.55/0.77 % (1436954)------------------------------
% 2.55/0.77 % (1436962)Instruction limit reached!
% 2.55/0.77 % (1436962)------------------------------
% 2.55/0.77 % (1436962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.77 % (1436962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.77 % (1436962)CaDiCaL version: 2.1.3
% 2.55/0.77 % (1436962)Termination reason: Instruction limit
% 3.30/0.87 % (1436962)Termination phase: shuffling
% 3.30/0.87 % (1436962)Time elapsed: 0.005 s
% 3.30/0.87 % (1436962)Peak memory usage: 10 MB
% 3.30/0.87 % (1436962)Instructions burned: 23 (million)
% 3.30/0.87 % (1436963)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1049805947:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 3.30/0.87 % (1436960)Instruction limit reached!
% 3.30/0.87 % (1436960)------------------------------
% 3.30/0.87 % (1436960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.87 % (1436960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.87 % (1436960)CaDiCaL version: 2.1.3
% 3.30/0.87 % (1436960)Termination reason: Instruction limit
% 3.30/0.87 % (1436960)Termination phase: shuffling
% 3.30/0.87 % (1436960)Time elapsed: 0.010 s
% 3.30/0.87 % (1436960)Peak memory usage: 10 MB
% 3.30/0.87 % (1436960)Instructions burned: 22 (million)
% 3.30/0.87 % (1436967)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1336799169:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 3.30/0.87 % (1436966)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3283539465:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 3.30/0.87 % (1436944)Instruction limit reached!
% 3.30/0.87 % (1436944)------------------------------
% 3.30/0.87 % (1436944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.87 % (1436944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.87 % (1436944)CaDiCaL version: 2.1.3
% 3.30/0.87 % (1436944)Termination reason: Instruction limit
% 3.30/0.87 % (1436944)Termination phase: Function definition elimination
% 3.30/0.87 % (1436944)Time elapsed: 0.095 s
% 3.30/0.87 % (1436944)Peak memory usage: 12 MB
% 3.30/0.87 % (1436944)Instructions burned: 144 (million)
% 3.30/0.87 % (1436967)Instruction limit reached!
% 3.30/0.87 % (1436967)------------------------------
% 3.30/0.87 % (1436967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.87 % (1436967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.87 % (1436967)CaDiCaL version: 2.1.3
% 3.30/0.87 % (1436967)Termination reason: Instruction limit
% 3.30/0.87 % (1436967)Termination phase: SInE selection
% 3.30/0.87 % (1436967)Time elapsed: 0.016 s
% 3.30/0.87 % (1436967)Peak memory usage: 10 MB
% 3.30/0.87 % (1436967)Instructions burned: 46 (million)
% 3.30/0.87 % (1436969)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1810210242:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.30/0.87 % (1436972)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=392187256:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.30/0.87 % (1436974)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.30/0.87 % (1436974)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=4141479721:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.30/0.87 % (1436972)Instruction limit reached!
% 3.30/0.87 % (1436972)------------------------------
% 3.30/0.87 % (1436972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.87 % (1436972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.87 % (1436972)CaDiCaL version: 2.1.3
% 3.30/0.87 % (1436972)Termination reason: Instruction limit
% 3.30/0.87 % (1436972)Termination phase: shuffling
% 3.30/0.87 % (1436972)Time elapsed: 0.010 s
% 3.30/0.87 % (1436972)Peak memory usage: 10 MB
% 3.30/0.87 % (1436972)Instructions burned: 23 (million)
% 3.30/0.87 % (1436955)Instruction limit reached!
% 3.30/0.87 % (1436955)------------------------------
% 3.30/0.87 % (1436955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.87 % (1436955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.87 % (1436955)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436955)Termination reason: Instruction limit
% 5.09/1.08 % (1436955)Termination phase: Property scanning
% 5.09/1.08 % (1436955)Time elapsed: 0.098 s
% 5.09/1.08 % (1436955)Peak memory usage: 13 MB
% 5.09/1.08 % (1436955)Instructions burned: 170 (million)
% 5.09/1.08 % (1436977)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1315950873:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 5.09/1.08 % (1436977)Instruction limit reached!
% 5.09/1.08 % (1436977)------------------------------
% 5.09/1.08 % (1436977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.09/1.08 % (1436977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.09/1.08 % (1436977)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436977)Termination reason: Instruction limit
% 5.09/1.08 % (1436977)Termination phase: shuffling
% 5.09/1.08 % (1436977)Time elapsed: 0.007 s
% 5.09/1.08 % (1436977)Peak memory usage: 10 MB
% 5.09/1.08 % (1436977)Instructions burned: 15 (million)
% 5.09/1.08 % (1436979)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=2845437539:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.09/1.08 % (1436980)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1700443431:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.09/1.08 % (1436974)Instruction limit reached!
% 5.09/1.08 % (1436974)------------------------------
% 5.09/1.08 % (1436974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.09/1.08 % (1436974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.09/1.08 % (1436974)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436974)Termination reason: Instruction limit
% 5.09/1.08 % (1436974)Termination phase: Saturation
% 5.09/1.08 % (1436974)Time elapsed: 0.049 s
% 5.09/1.08 % (1436974)Peak memory usage: 14 MB
% 5.09/1.08 % (1436974)Instructions burned: 205 (million)
% 5.09/1.08 % (1436983)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1735586490:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.09/1.08 % (1436983)Instruction limit reached!
% 5.09/1.08 % (1436983)------------------------------
% 5.09/1.08 % (1436983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.09/1.08 % (1436983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.09/1.08 % (1436983)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436983)Termination reason: Instruction limit
% 5.09/1.08 % (1436983)Termination phase: shuffling
% 5.09/1.08 % (1436983)Time elapsed: 0.008 s
% 5.09/1.08 % (1436983)Peak memory usage: 10 MB
% 5.09/1.08 % (1436983)Instructions burned: 31 (million)
% 5.09/1.08 % (1436980)Instruction limit reached!
% 5.09/1.08 % (1436980)------------------------------
% 5.09/1.08 % (1436980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.09/1.08 % (1436980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.09/1.08 % (1436980)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436980)Termination reason: Instruction limit
% 5.09/1.08 % (1436980)Termination phase: Preprocessing 3
% 5.09/1.08 % (1436980)Time elapsed: 0.023 s
% 5.09/1.08 % (1436980)Peak memory usage: 11 MB
% 5.09/1.08 % (1436980)Instructions burned: 52 (million)
% 5.09/1.08 % (1436985)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=856946159:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.09/1.08 % (1436986)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3239274132:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 5.09/1.08 % (1436979)Instruction limit reached!
% 5.09/1.08 % (1436979)------------------------------
% 5.09/1.08 % (1436979)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.09/1.08 % (1436979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.09/1.08 % (1436979)CaDiCaL version: 2.1.3
% 5.09/1.08 % (1436979)Termination reason: Instruction limit
% 5.09/1.08 % (1436979)Termination phase: SInE selection
% 5.09/1.08 % (1436979)Time elapsed: 0.044 s
% 5.09/1.08 % (1436979)Peak memory usage: 11 MB
% 5.09/1.08 % (1436979)Instructions burned: 67 (million)
% 5.09/1.08 % (1436986)Instruction limit reached!
% 5.09/1.08 % (1436986)------------------------------
% 5.09/1.08 % (1436986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436986)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436986)Termination reason: Instruction limit
% 6.12/1.23 % (1436986)Termination phase: Property scanning
% 6.12/1.23 % (1436986)Time elapsed: 0.015 s
% 6.12/1.23 % (1436986)Peak memory usage: 10 MB
% 6.12/1.23 % (1436986)Instructions burned: 34 (million)
% 6.12/1.23 % (1436989)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1316654357:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 6.12/1.23 % (1436985)Instruction limit reached!
% 6.12/1.23 % (1436985)------------------------------
% 6.12/1.23 % (1436985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436985)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436985)Termination reason: Instruction limit
% 6.12/1.23 % (1436985)Termination phase: Function definition elimination
% 6.12/1.23 % (1436985)Time elapsed: 0.035 s
% 6.12/1.23 % (1436985)Peak memory usage: 13 MB
% 6.12/1.23 % (1436985)Instructions burned: 137 (million)
% 6.12/1.23 % (1436969)Refutation not found, incomplete strategy
% 6.12/1.23 % (1436969)------------------------------
% 6.12/1.23 % (1436969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436969)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436969)Termination reason: Refutation not found, incomplete strategy
% 6.12/1.23 % (1436969)Time elapsed: 0.136 s
% 6.12/1.23 % (1436969)Peak memory usage: 16 MB
% 6.12/1.23 % (1436969)Instructions burned: 274 (million)
% 6.12/1.23 % (1436990)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.12/1.23 % (1436969)------------------------------
% 6.12/1.23 % (1436969)------------------------------
% 6.12/1.23 % (1436990)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3209209670:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 6.12/1.23 % (1436992)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=773062701:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 6.12/1.23 % (1436963)Instruction limit reached!
% 6.12/1.23 % (1436963)------------------------------
% 6.12/1.23 % (1436963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436963)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436963)Termination reason: Instruction limit
% 6.12/1.23 % (1436963)Termination phase: Saturation
% 6.12/1.23 % (1436963)Time elapsed: 0.172 s
% 6.12/1.23 % (1436963)Peak memory usage: 15 MB
% 6.12/1.23 % (1436963)Instructions burned: 317 (million)
% 6.12/1.23 % (1436993)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=3853698198:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 6.12/1.23 % (1436996)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1166831671:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 6.12/1.23 % (1436989)Instruction limit reached!
% 6.12/1.23 % (1436989)------------------------------
% 6.12/1.23 % (1436989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436989)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436989)Termination reason: Instruction limit
% 6.12/1.23 % (1436989)Termination phase: Preprocessing 3
% 6.12/1.23 % (1436989)Time elapsed: 0.048 s
% 6.12/1.23 % (1436989)Peak memory usage: 12 MB
% 6.12/1.23 % (1436989)Instructions burned: 67 (million)
% 6.12/1.23 % (1436999)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1849254365:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 6.12/1.23 % (1436993)Instruction limit reached!
% 6.12/1.23 % (1436993)------------------------------
% 6.12/1.23 % (1436993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.23 % (1436993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.23 % (1436993)CaDiCaL version: 2.1.3
% 6.12/1.23 % (1436993)Termination reason: Instruction limit
% 6.12/1.23 % (1436993)Termination phase: Property scanning
% 6.12/1.23 % (1436993)Time elapsed: 0.056 s
% 6.12/1.29 % (1436993)Peak memory usage: 12 MB
% 6.12/1.29 % (1436993)Instructions burned: 96 (million)
% 6.12/1.29 % (1436990)Instruction limit reached!
% 6.12/1.29 % (1436990)------------------------------
% 6.12/1.29 % (1436990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1436990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1436990)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1436990)Termination reason: Instruction limit
% 6.12/1.29 % (1436990)Termination phase: Saturation
% 6.12/1.29 % (1436990)Time elapsed: 0.074 s
% 6.12/1.29 % (1436990)Peak memory usage: 12 MB
% 6.12/1.29 % (1436990)Instructions burned: 181 (million)
% 6.12/1.29 % (1436992)Instruction limit reached!
% 6.12/1.29 % (1436992)------------------------------
% 6.12/1.29 % (1436992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1436992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1436992)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1436992)Termination reason: Instruction limit
% 6.12/1.29 % (1436992)Termination phase: Saturation
% 6.12/1.29 % (1436992)Time elapsed: 0.075 s
% 6.12/1.29 % (1436992)Peak memory usage: 15 MB
% 6.12/1.29 % (1436992)Instructions burned: 247 (million)
% 6.12/1.29 % (1437002)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=528946178:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 6.12/1.29 % (1437001)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=4109901890:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 6.12/1.29 % (1437003)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3273386904:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 6.12/1.29 % (1437003)Instruction limit reached!
% 6.12/1.29 % (1437003)------------------------------
% 6.12/1.29 % (1437003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437003)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437003)Termination reason: Instruction limit
% 6.12/1.29 % (1437003)Termination phase: Property scanning
% 6.12/1.29 % (1437003)Time elapsed: 0.041 s
% 6.12/1.29 % (1437003)Peak memory usage: 10 MB
% 6.12/1.29 % (1437003)Instructions burned: 45 (million)
% 6.12/1.29 % (1437007)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=3028541245:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 6.12/1.29 % (1437002)Refutation not found, incomplete strategy
% 6.12/1.29 % (1437002)------------------------------
% 6.12/1.29 % (1437002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437002)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437002)Termination reason: Refutation not found, incomplete strategy
% 6.12/1.29 % (1437002)Time elapsed: 0.075 s
% 6.12/1.29 % (1437002)Peak memory usage: 13 MB
% 6.12/1.29 % (1437002)Instructions burned: 93 (million)
% 6.12/1.29 % (1437002)------------------------------
% 6.12/1.29 % (1437002)------------------------------
% 6.12/1.29 % (1437009)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=1127829245:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.12/1.29 % (1436966)Instruction limit reached!
% 6.12/1.29 % (1436966)------------------------------
% 6.12/1.29 % (1436966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1436966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1436966)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1436966)Termination reason: Instruction limit
% 6.12/1.29 % (1436966)Termination phase: Saturation
% 6.12/1.29 % (1436966)Time elapsed: 0.405 s
% 6.12/1.29 % (1436966)Peak memory usage: 19 MB
% 6.12/1.29 % (1436966)Instructions burned: 853 (million)
% 6.12/1.29 % (1437011)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=3724836096:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 6.12/1.29 % (1437007)Refutation not found, incomplete strategy
% 6.12/1.29 % (1437007)------------------------------
% 6.12/1.29 % (1437007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437007)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437007)Termination reason: Refutation not found, incomplete strategy
% 6.12/1.29 % (1437007)Time elapsed: 0.116 s
% 6.12/1.29 % (1437007)Peak memory usage: 17 MB
% 6.12/1.29 % (1437007)Instructions burned: 385 (million)
% 6.12/1.29 % (1437007)------------------------------
% 6.12/1.29 % (1437007)------------------------------
% 6.12/1.29 % (1437013)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=4244560149:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2992 on theBenchmark for (2992ds/65Mi)
% 6.12/1.29 % (1437011)Instruction limit reached!
% 6.12/1.29 % (1437011)------------------------------
% 6.12/1.29 % (1437011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437011)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437011)Termination reason: Instruction limit
% 6.12/1.29 % (1437011)Termination phase: Property scanning
% 6.12/1.29 % (1437011)Time elapsed: 0.043 s
% 6.12/1.29 % (1437011)Peak memory usage: 12 MB
% 6.12/1.29 % (1437011)Instructions burned: 97 (million)
% 6.12/1.29 % (1437013)Instruction limit reached!
% 6.12/1.29 % (1437013)------------------------------
% 6.12/1.29 % (1437013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437013)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437013)Termination reason: Instruction limit
% 6.12/1.29 % (1437013)Termination phase: Property scanning
% 6.12/1.29 % (1437013)Time elapsed: 0.016 s
% 6.12/1.29 % (1437013)Peak memory usage: 11 MB
% 6.12/1.29 % (1437013)Instructions burned: 68 (million)
% 6.12/1.29 % (1437016)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=591651239:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 6.12/1.29 % (1437015)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=1350690222:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2991 on theBenchmark for (2991ds/105Mi)
% 6.12/1.29 % (1436996)Instruction limit reached!
% 6.12/1.29 % (1436996)------------------------------
% 6.12/1.29 % (1436996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1436996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1436996)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1436996)Termination reason: Instruction limit
% 6.12/1.29 % (1436996)Termination phase: Saturation
% 6.12/1.29 % (1436996)Time elapsed: 0.314 s
% 6.12/1.29 % (1436996)Peak memory usage: 14 MB
% 6.12/1.29 % (1436996)Instructions burned: 428 (million)
% 6.12/1.29 % (1437019)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3936490014:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 6.12/1.29 % (1437015)Instruction limit reached!
% 6.12/1.29 % (1437015)------------------------------
% 6.12/1.29 % (1437015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437015)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437015)Termination reason: Instruction limit
% 6.12/1.29 % (1437015)Termination phase: Saturation
% 6.12/1.29 % (1437015)Time elapsed: 0.044 s
% 6.12/1.29 % (1437015)Peak memory usage: 12 MB
% 6.12/1.29 % (1437015)Instructions burned: 108 (million)
% 6.12/1.29 % (1437021)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3551020601:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2991 on theBenchmark for (2991ds/495Mi)
% 6.12/1.29 % (1436999) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1436878-1436999"...
% 6.12/1.29 % (1437009)Instruction limit reached!
% 6.12/1.29 % (1437009)------------------------------
% 6.12/1.29 % (1437009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437009)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437009)Termination reason: Instruction limit
% 6.12/1.29 % (1437009)Termination phase: Saturation
% 6.12/1.29 % (1437009)Time elapsed: 0.234 s
% 6.12/1.29 % (1437009)Peak memory usage: 17 MB
% 6.12/1.29 % (1437009)Instructions burned: 451 (million)
% 6.12/1.29 % (1437023)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2466354868:cond=on:i=34:hud=10:nm=10:rtra=on_2990 on theBenchmark for (2990ds/34Mi)
% 6.12/1.29 % (1437023)Instruction limit reached!
% 6.12/1.29 % (1437023)------------------------------
% 6.12/1.29 % (1437023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1437023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1437023)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1437023)Termination reason: Instruction limit
% 6.12/1.29 % (1437023)Termination phase: Property scanning
% 6.12/1.29 % (1437023)Time elapsed: 0.015 s
% 6.12/1.29 % (1437023)Peak memory usage: 10 MB
% 6.12/1.29 % (1437023)Instructions burned: 34 (million)
% 6.12/1.29 % (1436943)Instruction limit reached!
% 6.12/1.29 % (1436943)------------------------------
% 6.12/1.29 % (1436943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.12/1.29 % (1436943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.12/1.29 % (1436943)CaDiCaL version: 2.1.3
% 6.12/1.29 % (1436943)Termination reason: Instruction limit
% 6.12/1.29 % (1436943)Termination phase: Saturation
% 6.12/1.29 % (1436943)Time elapsed: 0.712 s
% 6.12/1.29 % (1436943)Peak memory usage: 14 MB
% 6.12/1.29 % (1436943)Instructions burned: 1240 (million)
% 6.12/1.29 % (1436999)...printing done.
% 6.12/1.29 % (1436999)Refutation found. Thanks to Tanya!
% 6.12/1.29 % SZS status Theorem for theBenchmark
% 6.12/1.29 % SZS output start Proof for theBenchmark
% 6.12/1.29 thf(type_def_5, type, term: $tType).
% 6.12/1.29 thf(type_def_6, type, subst: $tType).
% 6.12/1.29 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.12/1.29 thf(type_def_8, type, d_term: $tType).
% 6.12/1.29 thf(type_def_9, type, d_subst: $tType).
% 6.12/1.29 thf(func_def_0, type, one: term).
% 6.12/1.29 thf(func_def_1, type, ap: (term > term > term)).
% 6.12/1.29 thf(func_def_2, type, lam: (term > term)).
% 6.12/1.29 thf(func_def_3, type, sub: (term > subst > term)).
% 6.12/1.29 thf(func_def_4, type, id: subst).
% 6.12/1.29 thf(func_def_5, type, sh: subst).
% 6.12/1.29 thf(func_def_6, type, push: (term > subst > subst)).
% 6.12/1.29 thf(func_def_7, type, comp: (subst > subst > subst)).
% 6.12/1.29 thf(func_def_8, type, var: (term > $o)).
% 6.12/1.29 thf(func_def_9, type, pushprop_lem1v2: $o).
% 6.12/1.29 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 6.12/1.29 thf(func_def_11, type, axmap: $o).
% 6.12/1.29 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 6.12/1.29 thf(func_def_13, type, shinj: $o).
% 6.12/1.29 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 6.12/1.29 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 6.12/1.29 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 6.12/1.29 thf(func_def_17, type, induction2lem: $o).
% 6.12/1.29 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 6.12/1.29 thf(func_def_19, type, axvarshift: $o).
% 6.12/1.29 thf(func_def_20, type, hoasapinj2: $o).
% 6.12/1.29 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 6.12/1.29 thf(func_def_22, type, hoasapinj1: $o).
% 6.12/1.29 thf(func_def_23, type, ulamvar1: $o).
% 6.12/1.29 thf(func_def_24, type, induction2lem_lthm: $o).
% 6.12/1.29 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 6.12/1.29 thf(func_def_26, type, apnotvar: $o).
% 6.12/1.29 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 6.12/1.29 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 6.12/1.29 thf(func_def_29, type, hoasinduction_lthm: $o).
% 6.12/1.29 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 6.12/1.29 thf(func_def_31, type, hoaslaminj: $o).
% 6.12/1.29 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 6.12/1.29 thf(func_def_33, type, induction2lem_gthm: $o).
% 6.12/1.29 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 6.12/1.29 thf(func_def_35, type, hoasinduction_lem3: $o).
% 6.12/1.29 thf(func_def_36, type, hoasinduction_lem2: $o).
% 6.12/1.29 thf(func_def_37, type, termmset_lthm: $o).
% 6.12/1.29 thf(func_def_38, type, hoasinduction_lem1: $o).
% 6.12/1.29 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 6.12/1.29 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 6.12/1.29 thf(func_def_41, type, hoasapnotvar: $o).
% 6.12/1.29 thf(func_def_42, type, hoasinduction_lem0: $o).
% 6.12/1.29 thf(func_def_43, type, hoasinduction: $o).
% 6.12/1.29 thf(func_def_44, type, hoasinduction_gthm: $o).
% 6.12/1.29 thf(func_def_45, type, axapp: $o).
% 6.12/1.29 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 6.12/1.29 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 6.12/1.29 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 6.12/1.29 thf(func_def_49, type, ulamvarind: $o).
% 6.12/1.29 thf(func_def_50, type, induction: $o).
% 6.12/1.29 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 6.12/1.29 thf(func_def_52, type, termmset_gthm: $o).
% 6.12/1.29 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 6.12/1.29 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 6.12/1.29 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 6.12/1.29 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 6.12/1.29 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 6.12/1.29 thf(func_def_58, type, pushprop_lem2v2: $o).
% 6.12/1.29 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 6.12/1.29 thf(func_def_60, type, axclos: $o).
% 6.12/1.29 thf(func_def_61, type, axassoc: $o).
% 6.12/1.29 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 6.12/1.29 thf(func_def_63, type, pushprop_lthm: $o).
% 6.12/1.29 thf(func_def_64, type, apinj2: $o).
% 6.12/1.29 thf(func_def_65, type, apinj1: $o).
% 6.12/1.29 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 6.12/1.29 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 6.12/1.29 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 6.12/1.29 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 6.12/1.29 thf(func_def_70, type, axvarcons: $o).
% 6.12/1.29 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 6.12/1.29 thf(func_def_72, type, axscons: $o).
% 6.12/1.29 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 6.12/1.29 thf(func_def_74, type, axidr: $o).
% 6.12/1.29 thf(func_def_75, type, pushprop_lem1: $o).
% 6.12/1.29 thf(func_def_76, type, laminj: $o).
% 6.12/1.29 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 6.12/1.29 thf(func_def_78, type, pushprop_lem0: $o).
% 6.12/1.29 thf(func_def_79, type, pushprop_gthm: $o).
% 6.12/1.29 thf(func_def_80, type, axabs: $o).
% 6.12/1.29 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 6.12/1.29 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 6.12/1.29 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 6.12/1.29 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 6.12/1.29 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 6.12/1.29 thf(func_def_86, type, lamnotap: $o).
% 6.12/1.29 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 6.12/1.29 thf(func_def_88, type, hoaslamnotvar: $o).
% 6.12/1.29 thf(func_def_89, type, axidl: $o).
% 6.12/1.29 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 6.12/1.29 thf(func_def_91, type, induction2_lthm: $o).
% 6.12/1.29 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 6.12/1.29 thf(func_def_93, type, substmonoid_lthm: $o).
% 6.12/1.29 thf(func_def_94, type, pushprop: $o).
% 6.12/1.29 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 6.12/1.29 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 6.12/1.29 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 6.12/1.29 thf(func_def_98, type, substmonoid: $o).
% 6.12/1.29 thf(func_def_99, type, lamnotvar: $o).
% 6.12/1.29 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 6.12/1.29 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 6.12/1.29 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 6.12/1.29 thf(func_def_103, type, induction2_gthm: $o).
% 6.12/1.29 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 6.12/1.29 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_106, type, hoaslamnotap: $o).
% 6.12/1.29 thf(func_def_107, type, substmonoid_gthm: $o).
% 6.12/1.29 thf(func_def_108, type, ulamvarsh: $o).
% 6.12/1.29 thf(func_def_109, type, induction2: $o).
% 6.12/1.29 thf(func_def_110, type, pushprop_lem3v2: $o).
% 6.12/1.29 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 6.12/1.29 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 6.12/1.29 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 6.12/1.29 thf(func_def_114, type, axshiftcons: $o).
% 6.12/1.29 thf(func_def_115, type, termmset: $o).
% 6.12/1.29 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 6.12/1.29 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 6.12/1.29 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 6.12/1.29 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 6.12/1.29 thf(func_def_120, type, axvarid: $o).
% 6.12/1.29 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 6.12/1.29 thf(func_def_122, type, d2term: (d_term > term)).
% 6.12/1.29 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 6.12/1.29 thf(func_def_124, type, d_one: d_term).
% 6.12/1.29 thf(func_def_125, type, d_id: d_subst).
% 6.12/1.29 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.12/1.29 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 6.12/1.29 thf(func_def_129, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.12/1.29 thf(func_def_130, type, vAND: ($o > $o > $o)).
% 6.12/1.29 thf(func_def_131, type, db4: !>[X0: $tType]:(X0)).
% 6.12/1.29 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 6.12/1.29 thf(func_def_133, type, db0: !>[X0: $tType]:(X0)).
% 6.12/1.29 thf(func_def_134, type, db2: !>[X0: $tType]:(X0)).
% 6.12/1.29 thf(func_def_135, type, db3: !>[X0: $tType]:(X0)).
% 6.12/1.29 thf(func_def_136, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.12/1.29 thf(func_def_137, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.12/1.29 thf(func_def_140, type, sP0: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_141, type, sP1: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_142, type, sP2: $o).
% 6.12/1.29 thf(func_def_143, type, sP3: $o).
% 6.12/1.29 thf(func_def_144, type, sP4: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_145, type, sP5: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_146, type, sP6: $o).
% 6.12/1.29 thf(func_def_147, type, sP7: $o).
% 6.12/1.29 thf(func_def_148, type, sP8: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_149, type, sP9: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_150, type, sP10: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_151, type, sP11: $o).
% 6.12/1.29 thf(func_def_152, type, sP12: $o).
% 6.12/1.29 thf(func_def_153, type, sP13: $o).
% 6.12/1.29 thf(func_def_154, type, sP14: $o).
% 6.12/1.29 thf(func_def_155, type, sP15: $o).
% 6.12/1.29 thf(func_def_156, type, sP16: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_157, type, sP17: $o).
% 6.12/1.29 thf(func_def_158, type, sP18: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_159, type, sP19: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_160, type, sP20: $o).
% 6.12/1.29 thf(func_def_161, type, sP21: $o).
% 6.12/1.29 thf(func_def_162, type, sP22: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_163, type, sP23: $o).
% 6.12/1.29 thf(func_def_164, type, sP24: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_165, type, sP25: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_166, type, sP26: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_167, type, sP27: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_168, type, sP28: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_169, type, sP29: $o).
% 6.12/1.29 thf(func_def_170, type, sP30: $o).
% 6.12/1.29 thf(func_def_171, type, sP31: $o).
% 6.12/1.29 thf(func_def_172, type, sP32: $o).
% 6.12/1.29 thf(func_def_173, type, sP33: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_174, type, sP34: $o).
% 6.12/1.29 thf(func_def_175, type, sP35: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_176, type, sP36: $o).
% 6.12/1.29 thf(func_def_177, type, sP37: $o).
% 6.12/1.29 thf(func_def_178, type, sP38: $o).
% 6.12/1.29 thf(func_def_179, type, sP39: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_180, type, sP40: $o).
% 6.12/1.29 thf(func_def_181, type, sP41: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_182, type, sP42: $o).
% 6.12/1.29 thf(func_def_183, type, sP43: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_184, type, sP44: $o).
% 6.12/1.29 thf(func_def_185, type, sP45: $o).
% 6.12/1.29 thf(func_def_186, type, sP46: $o).
% 6.12/1.29 thf(func_def_187, type, sP47: $o).
% 6.12/1.29 thf(func_def_188, type, sP48: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_189, type, sP49: $o).
% 6.12/1.29 thf(func_def_190, type, sP50: $o).
% 6.12/1.29 thf(func_def_191, type, sP51: ((term > $o) > $o)).
% 6.12/1.29 thf(func_def_192, type, sP52: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_193, type, sP53: $o).
% 6.12/1.29 thf(func_def_194, type, sP54: $o).
% 6.12/1.29 thf(func_def_195, type, sP55: $o).
% 6.12/1.29 thf(func_def_196, type, sP56: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_197, type, sP57: ((subst > term > subst > $o) > $o)).
% 6.12/1.29 thf(func_def_198, type, sP58: $o).
% 6.12/1.29 thf(func_def_199, type, sK59: term).
% 6.12/1.29 thf(func_def_200, type, sK60: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_201, type, sK61: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_202, type, sK62: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_203, type, sK63: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_204, type, sK64: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_205, type, sK65: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_206, type, sK66: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_207, type, sK67: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_208, type, sK68: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_209, type, sK69: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_210, type, sK70: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_211, type, sK71: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_212, type, sK72: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_213, type, sK73: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_214, type, sK74: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_215, type, sK75: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_216, type, sK76: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_217, type, sK77: term).
% 6.12/1.29 thf(func_def_218, type, sK78: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_219, type, sK79: ((subst > term > subst > $o) > term > $o)).
% 6.12/1.29 thf(func_def_220, type, sK80: term).
% 6.12/1.29 thf(func_def_221, type, sK81: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_222, type, sK82: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_223, type, sK83: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_224, type, sK84: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_225, type, sK85: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_226, type, sK86: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_227, type, sK87: (term > $o)).
% 6.12/1.29 thf(func_def_228, type, sK88: term).
% 6.12/1.29 thf(func_def_229, type, sK89: (term > term)).
% 6.12/1.29 thf(func_def_230, type, sK90: ((term > $o) > term > term)).
% 6.12/1.29 thf(func_def_231, type, sK91: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_232, type, sK92: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_233, type, sK93: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_234, type, sK94: term).
% 6.12/1.29 thf(func_def_235, type, sK95: (term > $o)).
% 6.12/1.29 thf(func_def_236, type, sK96: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_237, type, sK97: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_238, type, sK98: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_239, type, sK99: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_240, type, sK100: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_241, type, sK101: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_242, type, sK102: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_243, type, sK103: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_244, type, sK104: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_245, type, sK105: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_246, type, sK106: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_247, type, sK107: term).
% 6.12/1.29 thf(func_def_248, type, sK108: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_249, type, sK109: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_250, type, sK110: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_251, type, sK111: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_252, type, sK112: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_253, type, sK113: ((subst > term > subst > $o) > term > term)).
% 6.12/1.29 thf(func_def_254, type, sK114: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_255, type, sK115: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_256, type, sK116: term).
% 6.12/1.29 thf(func_def_257, type, sK117: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_258, type, sK118: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_259, type, sK119: ((subst > term > term) > term > term)).
% 6.12/1.29 thf(func_def_260, type, sK120: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_261, type, sK121: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_262, type, sK122: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_263, type, sK123: ((subst > term > term) > term > term)).
% 6.12/1.29 thf(func_def_264, type, sK124: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_265, type, sK125: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_266, type, sK126: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_267, type, sK127: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_268, type, sK128: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_269, type, sK129: (subst > term > term)).
% 6.12/1.29 thf(func_def_270, type, sK130: (subst > term > term)).
% 6.12/1.29 thf(func_def_271, type, sK131: term).
% 6.12/1.29 thf(func_def_272, type, sK132: subst).
% 6.12/1.29 thf(func_def_273, type, sK133: term).
% 6.12/1.29 thf(func_def_274, type, sK134: term).
% 6.12/1.29 thf(func_def_275, type, sK135: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_276, type, sK136: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_277, type, sK137: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_278, type, sK138: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_279, type, sK139: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_280, type, sK140: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_281, type, sK141: subst).
% 6.12/1.29 thf(func_def_282, type, sK142: term).
% 6.12/1.29 thf(func_def_283, type, sK143: subst).
% 6.12/1.29 thf(func_def_284, type, sK144: term).
% 6.12/1.29 thf(func_def_285, type, sK145: term).
% 6.12/1.29 thf(func_def_286, type, sK146: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_287, type, sK147: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_288, type, sK148: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_289, type, sK149: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_290, type, sK150: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_291, type, sK151: ((subst > term > subst > $o) > term > term)).
% 6.12/1.29 thf(func_def_292, type, sK152: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_293, type, sK153: term).
% 6.12/1.29 thf(func_def_294, type, sK154: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_295, type, sK155: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_296, type, sK156: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_297, type, sK157: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_298, type, sK158: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_299, type, sK159: ((subst > term > subst > $o) > term > term)).
% 6.12/1.29 thf(func_def_300, type, sK160: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_301, type, sK161: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_302, type, sK162: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_303, type, sK163: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_304, type, sK164: term).
% 6.12/1.29 thf(func_def_305, type, sK165: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_306, type, sK166: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_307, type, sK167: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_308, type, sK168: term).
% 6.12/1.29 thf(func_def_309, type, sK169: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_310, type, sK170: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_311, type, sK171: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_312, type, sK172: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_313, type, sK173: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_314, type, sK174: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_315, type, sK175: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_316, type, sK176: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_317, type, sK177: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_318, type, sK178: (term > $o)).
% 6.12/1.29 thf(func_def_319, type, sK179: subst).
% 6.12/1.29 thf(func_def_320, type, sK180: term).
% 6.12/1.29 thf(func_def_321, type, sK181: (term > term)).
% 6.12/1.29 thf(func_def_322, type, sK182: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_323, type, sK183: (subst > (term > $o) > term)).
% 6.12/1.29 thf(func_def_324, type, sK184: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_325, type, sK185: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_326, type, sK186: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_327, type, sK187: term).
% 6.12/1.29 thf(func_def_328, type, sK188: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_329, type, sK189: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_330, type, sK190: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_331, type, sK191: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_332, type, sK192: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_333, type, sK193: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_334, type, sK194: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_335, type, sK195: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_336, type, sK196: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_337, type, sK197: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_338, type, sK198: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_339, type, sK199: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_340, type, sK200: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_341, type, sK201: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_342, type, sK202: (term > subst > term > term)).
% 6.12/1.29 thf(func_def_343, type, sK203: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_344, type, sK204: term).
% 6.12/1.29 thf(func_def_345, type, sK205: (term > $o)).
% 6.12/1.29 thf(func_def_346, type, sK206: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_347, type, sK207: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_348, type, sK208: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_349, type, sK209: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_350, type, sK210: term).
% 6.12/1.29 thf(func_def_351, type, sK211: term).
% 6.12/1.29 thf(func_def_352, type, sK212: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_353, type, sK213: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_354, type, sK214: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_355, type, sK215: ((term > $o) > term > term)).
% 6.12/1.29 thf(func_def_356, type, sK216: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_357, type, sK217: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_358, type, sK218: term).
% 6.12/1.29 thf(func_def_359, type, sK219: (term > $o)).
% 6.12/1.29 thf(func_def_360, type, sK220: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_361, type, sK221: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_362, type, sK222: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_363, type, sK223: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_364, type, sK224: ((term > $o) > term > term)).
% 6.12/1.29 thf(func_def_365, type, sK225: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_366, type, sK226: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_367, type, sK227: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_368, type, sK228: (term > $o)).
% 6.12/1.29 thf(func_def_369, type, sK229: term).
% 6.12/1.29 thf(func_def_370, type, sK230: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_371, type, sK231: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_372, type, sK232: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_373, type, sK233: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_374, type, sK234: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_375, type, sK235: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_376, type, sK236: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_377, type, sK237: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_378, type, sK238: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_379, type, sK239: (term > (term > $o) > term)).
% 6.12/1.29 thf(func_def_380, type, sK240: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_381, type, sK241: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_382, type, sK242: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_383, type, sK243: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_384, type, sK244: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_385, type, sK245: term).
% 6.12/1.29 thf(func_def_386, type, sK246: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_387, type, sK247: term).
% 6.12/1.29 thf(func_def_388, type, sK248: (term > $o)).
% 6.12/1.29 thf(func_def_389, type, sK249: ((term > $o) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_390, type, sK250: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_391, type, sK251: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_392, type, sK252: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_393, type, sK253: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_394, type, sK254: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_395, type, sK255: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_396, type, sK256: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_397, type, sK257: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_398, type, sK258: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_399, type, sK259: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_400, type, sK260: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_401, type, sK261: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_402, type, sK262: term).
% 6.12/1.29 thf(func_def_403, type, sK263: (term > $o)).
% 6.12/1.29 thf(func_def_404, type, sK264: (term > term)).
% 6.12/1.29 thf(func_def_405, type, sK265: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_406, type, sK266: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_407, type, sK267: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_408, type, sK268: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_409, type, sK269: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_410, type, sK270: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_411, type, sK271: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_412, type, sK272: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_413, type, sK273: term).
% 6.12/1.29 thf(func_def_414, type, sK274: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_415, type, sK275: term).
% 6.12/1.29 thf(func_def_416, type, sK276: term).
% 6.12/1.29 thf(func_def_417, type, sK277: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_418, type, sK278: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_419, type, sK279: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_420, type, sK280: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_421, type, sK281: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_422, type, sK282: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_423, type, sK283: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_424, type, sK284: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_425, type, sK285: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_426, type, sK286: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_427, type, sK287: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_428, type, sK288: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_429, type, sK289: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_430, type, sK290: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_431, type, sK291: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_432, type, sK292: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_433, type, sK293: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_434, type, sK294: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_435, type, sK295: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_436, type, sK296: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_437, type, sK297: term).
% 6.12/1.29 thf(func_def_438, type, sK298: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_439, type, sK299: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_440, type, sK300: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_441, type, sK301: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_442, type, sK302: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_443, type, sK303: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_444, type, sK304: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_445, type, sK305: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_446, type, sK306: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_447, type, sK307: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_448, type, sK308: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_449, type, sK309: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_450, type, sK310: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_451, type, sK311: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_452, type, sK312: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_453, type, sK313: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_454, type, sK314: term).
% 6.12/1.29 thf(func_def_455, type, sK315: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_456, type, sK316: term).
% 6.12/1.29 thf(func_def_457, type, sK317: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_458, type, sK318: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_459, type, sK319: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_460, type, sK320: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_461, type, sK321: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_462, type, sK322: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_463, type, sK323: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_464, type, sK324: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_465, type, sK325: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_466, type, sK326: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_467, type, sK327: ((term > $o) > subst > term)).
% 6.12/1.29 thf(func_def_468, type, sK328: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_469, type, sK329: term).
% 6.12/1.29 thf(func_def_470, type, sK330: subst).
% 6.12/1.29 thf(func_def_471, type, sK331: term).
% 6.12/1.29 thf(func_def_472, type, sK332: (term > $o)).
% 6.12/1.29 thf(func_def_473, type, sK333: (term > term)).
% 6.12/1.29 thf(func_def_474, type, sK334: term).
% 6.12/1.29 thf(func_def_475, type, sK335: (term > $o)).
% 6.12/1.29 thf(func_def_476, type, sK336: (term > term)).
% 6.12/1.29 thf(func_def_477, type, sK337: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_478, type, sK338: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_479, type, sK339: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_480, type, sK340: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_481, type, sK341: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_482, type, sK342: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_483, type, sK343: term).
% 6.12/1.29 thf(func_def_484, type, sK344: (term > $o)).
% 6.12/1.29 thf(func_def_485, type, sK345: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_486, type, sK346: term).
% 6.12/1.29 thf(func_def_487, type, sK347: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.12/1.29 thf(func_def_488, type, sK348: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_489, type, sK349: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_490, type, sK350: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_491, type, sK351: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_492, type, sK352: ((term > $o) > term > term)).
% 6.12/1.29 thf(func_def_493, type, sK353: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_494, type, sK354: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_495, type, sK355: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_496, type, sK356: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_497, type, sK357: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_498, type, sK358: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_499, type, sK359: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_500, type, sK360: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_501, type, sK361: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_502, type, sK362: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_503, type, sK363: term).
% 6.12/1.29 thf(func_def_504, type, sK364: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_505, type, sK365: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_506, type, sK366: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_507, type, sK367: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_508, type, sK368: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_509, type, sK369: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_510, type, sK370: term).
% 6.12/1.29 thf(func_def_511, type, sK371: ((subst > term > subst > $o) > term > term)).
% 6.12/1.29 thf(func_def_512, type, sK372: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_513, type, sK373: term).
% 6.12/1.29 thf(func_def_514, type, sK374: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_515, type, sK375: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_516, type, sK376: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_517, type, sK377: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_518, type, sK378: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_519, type, sK379: ((subst > term > subst > $o) > term > $o)).
% 6.12/1.29 thf(func_def_520, type, sK380: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_521, type, sK381: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_522, type, sK382: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_523, type, sK383: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_524, type, sK384: term).
% 6.12/1.29 thf(func_def_525, type, sK385: term).
% 6.12/1.29 thf(func_def_526, type, sK386: (term > $o)).
% 6.12/1.29 thf(func_def_527, type, sK387: (term > term)).
% 6.12/1.29 thf(func_def_528, type, sK388: (term > (term > $o) > term)).
% 6.12/1.29 thf(func_def_529, type, sK389: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_530, type, sK390: ((subst > term > subst > $o) > (term > $o) > term)).
% 6.12/1.29 thf(func_def_531, type, sK391: (term > $o)).
% 6.12/1.29 thf(func_def_532, type, sK392: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_533, type, sK393: term).
% 6.12/1.29 thf(func_def_534, type, sK394: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_535, type, sK395: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_536, type, sK396: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_537, type, sK397: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_538, type, sK398: term).
% 6.12/1.29 thf(func_def_539, type, sK399: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_540, type, sK400: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_541, type, sK401: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_542, type, sK402: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_543, type, sK403: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_544, type, sK404: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_545, type, sK405: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_546, type, sK406: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_547, type, sK407: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_548, type, sK408: ((subst > term > subst > $o) > subst)).
% 6.12/1.29 thf(func_def_549, type, sK409: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_550, type, sK410: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_551, type, sK411: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_552, type, sK412: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_553, type, sK413: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_554, type, sK414: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_555, type, sK415: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_556, type, sK416: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_557, type, sK417: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_558, type, sK418: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_559, type, sK419: term).
% 6.12/1.29 thf(func_def_560, type, sK420: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_561, type, sK421: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_562, type, sK422: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_563, type, sK423: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_564, type, sK424: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_565, type, sK425: (term > (subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_566, type, sK426: term).
% 6.12/1.29 thf(func_def_567, type, sK427: (term > $o)).
% 6.12/1.29 thf(func_def_568, type, sK428: (term > term)).
% 6.12/1.29 thf(func_def_569, type, sK429: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_570, type, sK430: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_571, type, sK431: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_572, type, sK432: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_573, type, sK433: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_574, type, sK434: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(func_def_575, type, sK435: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_576, type, sK436: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_577, type, sK437: subst).
% 6.12/1.29 thf(func_def_578, type, sK438: subst).
% 6.12/1.29 thf(func_def_579, type, sK439: term).
% 6.12/1.29 thf(func_def_580, type, sK440: term).
% 6.12/1.29 thf(func_def_581, type, sK441: subst).
% 6.12/1.29 thf(func_def_582, type, sK442: term).
% 6.12/1.29 thf(func_def_583, type, sK443: (term > $o)).
% 6.12/1.29 thf(func_def_584, type, sK444: subst).
% 6.12/1.29 thf(func_def_585, type, sK445: (term > $o)).
% 6.12/1.29 thf(func_def_586, type, sK446: term).
% 6.12/1.29 thf(func_def_587, type, sK447: (term > term)).
% 6.12/1.29 thf(func_def_588, type, sK448: ((term > $o) > subst > term)).
% 6.12/1.29 thf(func_def_589, type, sK449: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_590, type, sK450: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_591, type, sK451: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_592, type, sK452: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_593, type, sK453: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_594, type, sK454: (term > subst > term > term)).
% 6.12/1.29 thf(func_def_595, type, sK455: term).
% 6.12/1.29 thf(func_def_596, type, sK456: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_597, type, sK457: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_598, type, sK458: ((subst > term > subst > $o) > term > $o)).
% 6.12/1.29 thf(func_def_599, type, sK459: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_600, type, sK460: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_601, type, sK461: term).
% 6.12/1.29 thf(func_def_602, type, sK462: term).
% 6.12/1.29 thf(func_def_603, type, sK463: term).
% 6.12/1.29 thf(func_def_604, type, sK464: term).
% 6.12/1.29 thf(func_def_605, type, sK465: term).
% 6.12/1.29 thf(func_def_606, type, sK466: term).
% 6.12/1.29 thf(func_def_607, type, sK467: term).
% 6.12/1.29 thf(func_def_608, type, sK468: term).
% 6.12/1.29 thf(func_def_609, type, sK469: term).
% 6.12/1.29 thf(func_def_610, type, sK470: term).
% 6.12/1.29 thf(func_def_611, type, sK471: term).
% 6.12/1.29 thf(func_def_612, type, sK472: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_613, type, sK473: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_614, type, sK474: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_615, type, sK475: (subst > term > term)).
% 6.12/1.29 thf(func_def_616, type, sK476: term).
% 6.12/1.29 thf(func_def_617, type, sK477: term).
% 6.12/1.29 thf(func_def_618, type, sK478: subst).
% 6.12/1.29 thf(func_def_619, type, sK479: (term > $o)).
% 6.12/1.29 thf(func_def_620, type, sK480: term).
% 6.12/1.29 thf(func_def_621, type, sK481: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_622, type, sK482: (term > (term > $o) > subst > term > $o)).
% 6.12/1.29 thf(func_def_623, type, sK483: term).
% 6.12/1.29 thf(func_def_624, type, sK484: subst).
% 6.12/1.29 thf(func_def_625, type, sK485: (term > d_term)).
% 6.12/1.29 thf(func_def_626, type, sK486: (term > subst > term > term)).
% 6.12/1.29 thf(func_def_627, type, sK487: term).
% 6.12/1.29 thf(func_def_628, type, sK488: term).
% 6.12/1.29 thf(func_def_629, type, sK489: term).
% 6.12/1.29 thf(func_def_630, type, sK490: term).
% 6.12/1.29 thf(func_def_631, type, sK491: term).
% 6.12/1.29 thf(func_def_632, type, sK492: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_633, type, sK493: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_634, type, sK494: term).
% 6.12/1.29 thf(func_def_635, type, sK495: (term > $o)).
% 6.12/1.29 thf(func_def_636, type, sK496: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_637, type, sK497: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_638, type, sK498: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_639, type, sK499: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_640, type, sK500: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_641, type, sK501: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_642, type, sK502: subst).
% 6.12/1.29 thf(func_def_643, type, sK503: (subst > term > term)).
% 6.12/1.29 thf(func_def_644, type, sK504: (subst > term > term)).
% 6.12/1.29 thf(func_def_645, type, sK505: term).
% 6.12/1.29 thf(func_def_646, type, sK506: term).
% 6.12/1.29 thf(func_def_647, type, sK507: term).
% 6.12/1.29 thf(func_def_648, type, sK508: term).
% 6.12/1.29 thf(func_def_649, type, sK509: term).
% 6.12/1.29 thf(func_def_650, type, sK510: term).
% 6.12/1.29 thf(func_def_651, type, sK511: term).
% 6.12/1.29 thf(func_def_652, type, sK512: term).
% 6.12/1.29 thf(func_def_653, type, sK513: term).
% 6.12/1.29 thf(func_def_654, type, sK514: term).
% 6.12/1.29 thf(func_def_655, type, sK515: subst).
% 6.12/1.29 thf(func_def_656, type, sK516: subst).
% 6.12/1.29 thf(func_def_657, type, sK517: term).
% 6.12/1.29 thf(func_def_658, type, sK518: term).
% 6.12/1.29 thf(func_def_659, type, sK519: subst).
% 6.12/1.29 thf(func_def_660, type, sK520: (term > $o)).
% 6.12/1.29 thf(func_def_661, type, sK521: term).
% 6.12/1.29 thf(func_def_662, type, sK522: (term > $o)).
% 6.12/1.29 thf(func_def_663, type, sK523: ((term > $o) > term > subst > term > $o)).
% 6.12/1.29 thf(func_def_664, type, sK524: subst).
% 6.12/1.29 thf(func_def_665, type, sK525: term).
% 6.12/1.29 thf(func_def_666, type, sK526: (term > $o)).
% 6.12/1.29 thf(func_def_667, type, sK527: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_668, type, sK528: (subst > d_subst)).
% 6.12/1.29 thf(func_def_669, type, sK529: subst).
% 6.12/1.29 thf(func_def_670, type, sK530: term).
% 6.12/1.29 thf(func_def_671, type, sK531: term).
% 6.12/1.29 thf(func_def_672, type, sK532: term).
% 6.12/1.29 thf(func_def_673, type, sK533: subst).
% 6.12/1.29 thf(func_def_674, type, sK534: term).
% 6.12/1.29 thf(func_def_675, type, sK535: (subst > (term > $o) > term > (term > $o) > term)).
% 6.12/1.29 thf(func_def_676, type, sK536: (term > $o)).
% 6.12/1.29 thf(func_def_677, type, sK537: term).
% 6.12/1.29 thf(func_def_678, type, sK538: (term > $o)).
% 6.12/1.29 thf(func_def_679, type, sK539: subst).
% 6.12/1.29 thf(func_def_680, type, sK540: subst).
% 6.12/1.29 thf(func_def_681, type, sK541: subst).
% 6.12/1.29 thf(func_def_682, type, sK542: subst).
% 6.12/1.29 thf(func_def_683, type, sK543: subst).
% 6.12/1.29 thf(func_def_684, type, sK544: (term > $o)).
% 6.12/1.29 thf(func_def_685, type, sK545: subst).
% 6.12/1.29 thf(func_def_686, type, sK546: term).
% 6.12/1.29 thf(func_def_687, type, sK547: term).
% 6.12/1.29 thf(func_def_688, type, sK548: (term > $o)).
% 6.12/1.29 thf(func_def_689, type, sK549: subst).
% 6.12/1.29 thf(func_def_690, type, sK550: term).
% 6.12/1.29 thf(func_def_691, type, sK551: term).
% 6.12/1.29 thf(func_def_692, type, sK552: term).
% 6.12/1.29 thf(func_def_693, type, sK553: term).
% 6.12/1.29 thf(func_def_694, type, sK554: term).
% 6.12/1.29 thf(func_def_695, type, sK555: term).
% 6.12/1.29 thf(func_def_696, type, sK556: term).
% 6.12/1.29 thf(func_def_697, type, sK557: term).
% 6.12/1.29 thf(func_def_698, type, sK558: term).
% 6.12/1.29 thf(func_def_699, type, sK559: term).
% 6.12/1.29 thf(func_def_700, type, sK560: term).
% 6.12/1.29 thf(func_def_701, type, sK561: term).
% 6.12/1.29 thf(func_def_702, type, sK562: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_703, type, sK563: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_704, type, sK564: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_705, type, sK565: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_706, type, sK566: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_707, type, sK567: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_708, type, sK568: (term > subst > term > term)).
% 6.12/1.29 thf(func_def_709, type, sK569: term).
% 6.12/1.29 thf(func_def_710, type, sK570: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_711, type, sK571: ((subst > term > term) > subst)).
% 6.12/1.29 thf(func_def_712, type, sK572: term).
% 6.12/1.29 thf(func_def_713, type, sK573: term).
% 6.12/1.29 thf(func_def_714, type, sK574: term).
% 6.12/1.29 thf(func_def_715, type, sK575: term).
% 6.12/1.29 thf(func_def_716, type, sK576: term).
% 6.12/1.29 thf(func_def_717, type, sK577: (term > subst > term > term)).
% 6.12/1.29 thf(func_def_718, type, sK578: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_719, type, sK579: ((term > $o) > term)).
% 6.12/1.29 thf(func_def_720, type, sK580: ((subst > term > subst > $o) > term > $o)).
% 6.12/1.29 thf(func_def_721, type, sK581: subst).
% 6.12/1.29 thf(func_def_722, type, sK582: subst).
% 6.12/1.29 thf(func_def_723, type, sK583: subst).
% 6.12/1.29 thf(func_def_724, type, sK584: ((term > $o) > (term > $o) > term > subst > term)).
% 6.12/1.29 thf(func_def_725, type, sK585: subst).
% 6.12/1.29 thf(func_def_726, type, sK586: term).
% 6.12/1.29 thf(func_def_727, type, sK587: (term > $o)).
% 6.12/1.29 thf(func_def_728, type, sK588: (term > $o)).
% 6.12/1.29 thf(func_def_729, type, sK589: subst).
% 6.12/1.29 thf(func_def_730, type, sK590: term).
% 6.12/1.29 thf(func_def_731, type, vNOT: ($o > $o)).
% 6.12/1.29 thf(func_def_732, type, sK591: (subst > term > subst > $o)).
% 6.12/1.29 thf(func_def_733, type, sK592: ((subst > term > term) > term)).
% 6.12/1.29 thf(func_def_734, type, sK593: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_735, type, sK594: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_736, type, sK595: ((subst > term > term) > term > term)).
% 6.12/1.29 thf(func_def_737, type, sK596: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_738, type, sK597: ((subst > term > term) > term > subst)).
% 6.12/1.29 thf(func_def_739, type, sK598: ((subst > term > term) > term > term)).
% 6.12/1.29 thf(func_def_740, type, sK599: term).
% 6.12/1.29 thf(func_def_741, type, sK600: ((subst > term > subst > $o) > subst > term > term)).
% 6.12/1.29 thf(func_def_742, type, sK601: ((subst > term > subst > $o) > term > term)).
% 6.12/1.29 thf(func_def_743, type, sK602: ((subst > term > subst > $o) > term)).
% 6.12/1.29 thf(f1,axiom,(
% 6.12/1.29 pushprop_lem2v2_lthm & hoaslamnotvar & hoasapnotvar & ((! [X19 : term,X15 : term,X13 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X20 : term,X15 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj2_lthm) & hoasinduction_lem3b_gthm & (hoasinduction_lem3v2 <=> ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : 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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) & (apinj1 <=> ! [X19 : term,X15 : term,X20 : term,X13 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & hoaslamnotap_gthm & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & pushprop_lem3v2_lthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~(X10 @ id @ X23 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & ! [X5 : d_subst] : (X5 = d_id) & pushprop_lem1_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & (laminj <=> ! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & apnotvar & hoasapinj2_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (induction2lem <=> ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & axapp & induction2lem_gthm & ~(var @ (d2term @ d_one)) & (hoasapinj2 <=> ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (pushprop_lem1 <=> ! [X10 : (term > $o),X13 : term,X15 : term,X26 : (term > $o),X14 : subst] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))) & (axshiftcons <=> ! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [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) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))))) <=> hoasinduction_no_psi_cond_lthm) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & lamnotvar & induction2_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & ! [X1 : d_term] : (X1 = d_one) & (hoasinduction_lem3a <=> ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id))) & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & hoaslamnotvar_lthm & hoaslaminj_gthm & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (hoasinduction_lem3aa_lthm <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ 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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X13 : term,X15 : term,X26 : (term > $o),X14 : subst] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & hoasapnotvar_lthm & (induction2lem_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => ! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)))))))) & pushprop_lem2v2_gthm & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoasinduction_lem3v2_gthm & hoasinduction_lem1v2 & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : 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 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X10 : (subst > term > subst > $o),X24 : term,X23 : term] : (~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)))))) <=> hoasinduction_lthm) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (id = ((d2subst @ d_id))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & pushprop_lthm & pushprop & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & hoasinduction_lem3a_gthm & (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) <=> induction2) & hoasinduction_lem1v2_gthm & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X11 : (term > $o),X14 : subst,X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) <=> pushprop_lem1v2_lthm) & (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) <=> induction) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X31 : (subst > term > term),X33 : term,X32 : subst,X18 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & hoasinduction_lem2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (sh = ((d2subst @ d_id))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => ! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))))) <=> induction2_lthm) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : (~ ! [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 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [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))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) <=> hoasinduction_lem3v2_lthm) & hoasapinj1_gthm & termmset_gthm & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id))) & (one = ((d2term @ d_one))) & (hoasapinj1 <=> ! [X19 : term,X13 : term,X20 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))) & (! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X40 : term,X41 : subst,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ 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) & (! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoasinduction_lem1 & hoasinduction_lem1_lthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & hoasinduction_lem2_lthm & hoasinduction_gthm & ~lamnotap & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_gthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) <=> substmonoid) & ulamvarind & pushprop_gthm & (hoaslaminj <=> ! [X18 : (subst > term > term),X32 : subst,X33 : term,X31 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & hoasinduction_lem1_gthm & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X44 : term,X11 : (term > $o),X45 : term] : ((X11 @ (ap @ X44 @ X45)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X11 @ X45) | ~(X11 @ X44) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (hoaslamnotap <=> ! [X18 : (subst > term > term),X47 : term,X46 : 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_lem3_gthm & pushprop_lem1v2_gthm & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))))) <=> hoasinduction_lem3v2a_lthm) & (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))))) & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem3v2a) & pushprop_lem3v2 & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X19 : term,X15 : term,X20 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X19 : term,X13 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & (! [X13 : term,X15 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & substmonoid_gthm & ulamvarsh & axmap & (apinj2 <=> ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & pushprop_lem0_gthm & (! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ 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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_no_psi_cond) & (! [X14 : subst,X11 : (term > $o),X13 : term,X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2) & axclos & axassoc & hoaslamnotap_lthm & axabs & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~ulamvar1 & pushprop_lthm_orig & axvarshift & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & hoasapnotvar_gthm & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))))),
% 6.12/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 6.12/1.29 thf(f2,conjecture,(
% 6.12/1.29 (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X2 : term] : ! [X4 : term,X3 : subst,X5 : subst] : ((((sub @ X2 @ (push @ (sub @ X4 @ X5) @ (comp @ X3 @ X5)))) = ((X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) & (((sub @ (X1 @ X3 @ X4) @ X5)) = ((sub @ (sub @ X2 @ (push @ X4 @ X3)) @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X1 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X1 @ X3 @ X4)))) @ id))) => ! [X4 : term] : (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (sub @ X4 @ (push @ X6 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 6.12/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aaa)).
% 6.12/1.29 thf(f3,negated_conjecture,(
% 6.12/1.29 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X2 : term] : ! [X4 : term,X3 : subst,X5 : subst] : ((((sub @ X2 @ (push @ (sub @ X4 @ X5) @ (comp @ X3 @ X5)))) = ((X1 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5)))) & (((sub @ (X1 @ X3 @ X4) @ X5)) = ((sub @ (sub @ X2 @ (push @ X4 @ X3)) @ X5)))) => (! [X4 : term] : ((X0 @ id @ X4 @ id) => (X0 @ id @ (X1 @ id @ X4) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X3 : subst, X4 : term] : ((X1 @ X3 @ X4)))) @ id))) => ! [X4 : term] : (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (sub @ X4 @ (push @ X6 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X4 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 6.12/1.29 inference(negated_conjecture,[status(cth)],[f2])).
% 6.12/1.29 thf(f4,plain,(
% 6.12/1.29 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : (subst > term > term)] : (? [X2 : term] : ! [X3 : term,X4 : subst,X5 : subst] : ((((X1 @ (comp @ X4 @ X5) @ (sub @ X3 @ X5))) = ((sub @ X2 @ (push @ (sub @ X3 @ X5) @ (comp @ X4 @ X5))))) & (((sub @ (X1 @ X4 @ X3) @ X5)) = ((sub @ (sub @ X2 @ (push @ X3 @ X4)) @ X5)))) => (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (X1 @ id @ X6) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : ((X1 @ X7 @ X8)))) @ id))) => ! [X9 : term] : (! [X10 : term] : ((X0 @ id @ X10 @ id) => (X0 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 6.12/1.29 inference(rectify,[],[f3])).
% 6.12/1.29 thf(f5,plain,(
% 6.12/1.29 ~ (hoasinduction_lem3aaa = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.12/1.29 inference(fool_elimination,[],[f4])).
% 6.12/1.29 thf(f6,plain,(
% 6.12/1.29 pushprop_lem2v2_lthm & hoaslamnotvar & hoasapnotvar & ((! [X0 : term,X1 : term,X2 : term,X3 : term] : ((((ap @ X2 @ X0)) != ((ap @ X1 @ X3))) | (X0 = X3)) => ! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4))))) <=> hoasapinj2_lthm) & hoasinduction_lem3b_gthm & (hoasinduction_lem3v2 <=> ! [X8 : (term > $o),X9 : (subst > term > subst > $o),X10 : term] : (~ ! [X11 : (subst > term > term)] : ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id) | ~ ! [X12 : subst,X13 : subst,X14 : term] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))) | ~ ! [X15 : term] : (~(X9 @ id @ X15 @ id) | (X9 @ id @ (X11 @ id @ X15) @ id))) | ~ ! [X16 : subst,X17 : subst,X18 : subst,X19 : term] : (~(X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16) | (X9 @ X17 @ X19 @ (comp @ X18 @ X16))) | ~ ! [X20 : subst,X21 : subst,X22 : subst,X23 : term] : (~(X9 @ X21 @ X23 @ (comp @ X22 @ X20)) | (X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20)) | ~ ! [X24 : term] : (~(X8 @ X24) | (X8 @ (sub @ X10 @ (push @ X24 @ id)))) | (X8 @ (lam @ X10)) | ~ ! [X25 : term] : (((X8 @ X25)) = ((X9 @ id @ X25 @ id))))) & (apinj1 <=> ! [X26 : term,X27 : term,X28 : term,X29 : term] : ((X27 = X29) | (((ap @ X27 @ X28)) != ((ap @ X29 @ X26))))) & hoaslamnotap_gthm & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> termmset) & (axidl <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & pushprop_lem3v2_lthm & (! [X32 : term] : ~ ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & (hoasinduction_lem2 <=> ! [X34 : (subst > term > subst > $o),X35 : term,X36 : term] : (~(X34 @ id @ X35 @ id) | ~ ! [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (~(X34 @ X39 @ X40 @ (comp @ X38 @ X37)) | (X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37)) | ~ ! [X41 : subst,X42 : term,X43 : subst,X44 : subst] : (~(X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43) | (X34 @ X44 @ X42 @ (comp @ X41 @ X43))) | (X34 @ id @ (ap @ X35 @ X36) @ id) | ~(X34 @ id @ X36 @ id) | ~ ! [X45 : term,X46 : term] : (~(X34 @ id @ X45 @ id) | (X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id) | ~(X34 @ id @ X46 @ id)))) & (hoasinduction_lem3b <=> ! [X47 : term] : ~ ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one)))) & ! [X49 : d_subst] : (d_id = X49) & pushprop_lem1_gthm & ((! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : term] : (~ ! [X53 : (subst > term > term)] : (~ ! [X54 : term] : (~(X51 @ id @ X54 @ id) | (X51 @ id @ (X53 @ id @ X54) @ id)) | ~ ! [X55 : subst,X56 : term,X57 : subst] : (((sub @ (X53 @ X57 @ X56) @ X55)) = ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) | (X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id) | ~ ! [X58 : term] : (~(X51 @ id @ X58 @ id) | (X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id))) => ! [X59 : (subst > term > subst > $o),X60 : term] : (~ ! [X61 : term] : (~(X59 @ id @ X61 @ id) | (X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~(X59 @ id @ X63 @ id) | (X59 @ id @ (X62 @ id @ X63) @ id)) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) | (X59 @ id @ (lam @ X60) @ id)))) <=> hoasinduction_lem3a_lthm) & (laminj <=> ! [X67 : term,X68 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & apnotvar & hoasapinj2_gthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (induction2lem <=> ! [X69 : (term > $o),X70 : subst,X71 : term] : (~ ! [X72 : term,X73 : term] : (~(X69 @ X73) | ~(X69 @ X72) | (X69 @ (ap @ X73 @ X72))) | ~ ! [X74 : term] : ((X69 @ (lam @ X74)) | ~ ! [X75 : term] : ((X69 @ (sub @ X74 @ (push @ X75 @ id))) | ~(X69 @ X75))) | ~ ! [X76 : term] : (~(var @ X76) | (X69 @ (sub @ X76 @ X70))) | (X69 @ (sub @ X71 @ X70)))) & ! [X77 : d_subst,X78 : d_subst] : ((((d2subst @ X78)) = ((d2subst @ X77))) => (X77 = X78)) & axapp & induction2lem_gthm & ~(var @ (d2term @ d_one)) & (hoasapinj2 <=> ! [X79 : term,X80 : term,X81 : term,X82 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & (pushprop_lem1 <=> ! [X83 : (term > $o),X84 : term,X85 : term,X86 : (term > $o),X87 : subst] : ((X86 @ (sub @ X84 @ (push @ X85 @ X87))) | ~(X83 @ X84))) & (axshiftcons <=> ! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88)) & (hoasinduction <=> ! [X90 : term,X91 : (subst > term > subst > $o)] : (~ ! [X92 : term] : ((X91 @ id @ X92 @ id) | ~(var @ (sub @ X92 @ id))) | ~ ! [X93 : term,X94 : term] : ((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id) | ~(X91 @ id @ X94 @ id) | ~(X91 @ id @ X93 @ id)) | ~ ! [X95 : (subst > term > term)] : (~ ! [X96 : term] : ((X91 @ id @ (X95 @ id @ X96) @ id) | ~(X91 @ id @ X96 @ id)) | ~ ! [X97 : term,X98 : subst,X99 : subst] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) | (X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)) | (X91 @ id @ X90 @ id) | ~ ! [X100 : subst,X101 : subst,X102 : subst,X103 : term] : (~(X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100) | (X91 @ X101 @ X103 @ (comp @ X102 @ X100))) | ~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~(X91 @ X105 @ X104 @ (comp @ X107 @ X106)) | (X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)))) & ((! [X108 : (subst > term > subst > $o)] : ~ ! [X109 : (term > $o)] : ~ ! [X110 : term] : (((X109 @ X110)) = ((X108 @ id @ X110 @ id))) => (! [X111 : term,X112 : (term > $o)] : (~ ! [X113 : term] : ((X112 @ (lam @ X113)) | ~ ! [X114 : term] : (~(X112 @ X114) | (X112 @ (sub @ X113 @ (push @ X114 @ id))))) | ~ ! [X115 : term] : (~(var @ X115) | (X112 @ X115)) | (X112 @ X111) | ~ ! [X116 : term,X117 : term] : (~(X112 @ X117) | (X112 @ (ap @ X116 @ X117)) | ~(X112 @ X116))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X119 : (term > $o),X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term] : (~(X119 @ X122) | (X119 @ (sub @ X120 @ (push @ X122 @ id)))) | ~ ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) | ~ ! [X124 : (subst > term > term)] : (~ ! [X125 : term] : ((X121 @ id @ (X124 @ id @ X125) @ id) | ~(X121 @ id @ X125 @ id)) | ~ ! [X126 : subst,X127 : term,X128 : subst] : (((sub @ (X124 @ X126 @ X127) @ X128)) = ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | (X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)) | (X119 @ (lam @ X120))) => ! [X129 : (subst > term > subst > $o),X130 : term] : ((X129 @ id @ X130 @ id) | ~ ! [X131 : term,X132 : term] : ((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id) | ~(X129 @ id @ X132 @ id) | ~(X129 @ id @ X131 @ id)) | ~ ! [X133 : (subst > term > term)] : ((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id) | ~ ! [X134 : term] : ((X129 @ id @ (X133 @ id @ X134) @ id) | ~(X129 @ id @ X134 @ id)) | ~ ! [X135 : term,X136 : subst,X137 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))))))))) <=> hoasinduction_no_psi_cond_lthm) & (axscons <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & (! [X139 : subst,X140 : term,X141 : (term > $o)] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139))))) <=> pushprop_lem0_lthm) & lamnotvar & induction2_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & ! [X144 : d_term] : (d_one = X144) & (hoasinduction_lem3a <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : (~ ! [X147 : (subst > term > term)] : ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id) | ~ ! [X148 : subst,X149 : subst,X150 : term] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) | ~ ! [X151 : term] : ((X146 @ id @ (X147 @ id @ X151) @ id) | ~(X146 @ id @ X151 @ id))) | ~ ! [X152 : term] : ((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id) | ~(X146 @ id @ X152 @ id)) | (X146 @ id @ (lam @ X145) @ id))) & (hoasinduction_lem3aa <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (~ ! [X155 : term] : (~(X153 @ id @ X155 @ id) | (X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)) | ~ ! [X156 : (subst > term > term)] : (~ ! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) | ~ ! [X160 : term] : ((X153 @ id @ (X156 @ id @ X160) @ id) | ~(X153 @ id @ X160 @ id)) | (X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) | (X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))) & hoaslamnotvar_lthm & hoaslaminj_gthm & (hoasinduction_p_and_p_prime = (^[X161 : (subst > term > subst > $o), X162 : (term > $o)] : (! [X163 : term] : (((X161 @ id @ X163 @ id)) = ((X162 @ X163)))))) & (hoasinduction_lem3aa_lthm <=> ! [X164 : term,X165 : (subst > term > subst > $o)] : ((X165 @ id @ (lam @ (sub @ X164 @ (push @ one @ sh))) @ id) | ~ ! [X166 : (subst > term > term)] : (~ ! [X167 : subst,X168 : subst,X169 : term] : (((sub @ (X166 @ X167 @ X169) @ X168)) = ((X166 @ (comp @ X167 @ X168) @ (sub @ X169 @ X168)))) | (X165 @ id @ (lam @ (X166 @ sh @ one)) @ id) | ~ ! [X170 : term] : (~(X165 @ id @ X170 @ id) | (X165 @ id @ (X166 @ id @ X170) @ id))) | ~ ! [X171 : term] : (~(X165 @ id @ X171 @ id) | (X165 @ id @ (sub @ X164 @ (push @ X171 @ id)) @ id)))) & (! [X172 : term] : ~ ! [X173 : (subst > term > term)] : ~ ! [X174 : subst,X175 : term] : (((sub @ X172 @ (push @ X175 @ X174))) = ((X173 @ X174 @ X175))) <=> hoasinduction_lem3v2_f) & ((! [X176 : term,X177 : subst] : (((sub @ one @ (push @ X176 @ X177))) = X176) => (! [X178 : subst,X179 : term] : (((comp @ sh @ (push @ X179 @ X178))) = X178) => ! [X180 : (term > $o),X181 : term,X182 : term,X183 : (term > $o),X184 : subst] : (~(X180 @ X181) | (X183 @ (sub @ X181 @ (push @ X182 @ X184)))))) <=> pushprop_lem1_lthm) & hoasapnotvar_lthm & (induction2lem_lthm <=> (! [X185 : subst,X186 : term] : (((sub @ one @ (push @ X186 @ X185))) = X186) => (! [X187 : subst,X188 : term] : (((comp @ sh @ (push @ X188 @ X187))) = X187) => (! [X189 : subst] : (((comp @ X189 @ id)) = X189) => (! [X190 : term,X191 : (term > $o)] : (~ ! [X192 : term,X193 : term] : (~(X191 @ X192) | (X191 @ (ap @ X193 @ X192)) | ~(X191 @ X193)) | ~ ! [X194 : term] : (~(X191 @ X194) | (X191 @ (lam @ X194))) | (X191 @ X190) | ~ ! [X195 : term] : ((X191 @ X195) | ~(var @ X195))) => ! [X196 : term,X197 : (term > $o),X198 : subst] : (~ ! [X199 : term] : (~ ! [X200 : term] : ((X197 @ (sub @ X199 @ (push @ X200 @ id))) | ~(X197 @ X200)) | (X197 @ (lam @ X199))) | ~ ! [X201 : term,X202 : term] : (~(X197 @ X202) | ~(X197 @ X201) | (X197 @ (ap @ X201 @ X202))) | ~ ! [X203 : term] : ((X197 @ (sub @ X203 @ X198)) | ~(var @ X203)) | (X197 @ (sub @ X196 @ X198)))))))) & pushprop_lem2v2_gthm & (! [X204 : term] : (((sub @ X204 @ id)) = X204) <=> axvarid) & ((^[X205 : subst, X206 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (axidr <=> ! [X207 : subst] : (((comp @ X207 @ id)) = X207)) & hoasinduction_lem3v2_gthm & hoasinduction_lem1v2 & (hoasinduction_lem3_lthm <=> (! [X208 : term] : (((sub @ X208 @ id)) = X208) => (! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X211 : term] : ((X210 @ id @ (sub @ X209 @ (push @ X211 @ id)) @ id) | ~(X210 @ id @ X211 @ id)) | ~ ! [X212 : (subst > term > term)] : (~ ! [X213 : term] : (~(X210 @ id @ X213 @ id) | (X210 @ id @ (X212 @ id @ X213) @ id)) | (X210 @ id @ (lam @ (X212 @ sh @ one)) @ id) | ~ ! [X214 : subst,X215 : term,X216 : subst] : (((sub @ (X212 @ X216 @ X215) @ X214)) = ((X212 @ (comp @ X216 @ X214) @ (sub @ X215 @ X214))))) | (X210 @ id @ (lam @ (sub @ X209 @ (push @ one @ sh))) @ id)) => ! [X217 : (subst > term > subst > $o),X218 : term] : (~ ! [X219 : (subst > term > term)] : (~ ! [X220 : subst,X221 : subst,X222 : term] : (((X219 @ (comp @ X221 @ X220) @ (sub @ X222 @ X220))) = ((sub @ (X219 @ X221 @ X222) @ X220))) | (X217 @ id @ (lam @ (X219 @ sh @ one)) @ id) | ~ ! [X223 : term] : (~(X217 @ id @ X223 @ id) | (X217 @ id @ (X219 @ id @ X223) @ id))) | ~ ! [X224 : term] : ((X217 @ id @ (sub @ X218 @ (push @ X224 @ id)) @ id) | ~(X217 @ id @ X224 @ id)) | (X217 @ id @ (lam @ X218) @ id) | ~ ! [X225 : subst,X226 : term,X227 : subst,X228 : subst] : (~(X217 @ X228 @ X226 @ (comp @ X227 @ X225)) | (X217 @ (comp @ X228 @ X227) @ (sub @ X226 @ X227) @ X225)) | ~ ! [X229 : subst,X230 : subst,X231 : term,X232 : subst] : ((X217 @ X230 @ X231 @ (comp @ X232 @ X229)) | ~(X217 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232) @ X229)))))) & ((! [X233 : (term > $o),X234 : term] : (~ ! [X235 : term] : ((X233 @ (lam @ X235)) | ~ ! [X236 : term] : ((X233 @ (sub @ X235 @ (push @ X236 @ id))) | ~(X233 @ X236))) | (X233 @ X234) | ~ ! [X237 : term,X238 : term] : ((X233 @ (ap @ X238 @ X237)) | ~(X233 @ X237) | ~(X233 @ X238)) | ~ ! [X239 : term] : (~(var @ X239) | (X233 @ X239))) => (! [X240 : (subst > term > subst > $o),X241 : term,X242 : term] : (~(X240 @ id @ X242 @ id) | (X240 @ id @ (ap @ X242 @ X241) @ id) | ~ ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : ((X240 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246) | ~(X240 @ X244 @ X245 @ (comp @ X243 @ X246))) | ~ ! [X247 : subst,X248 : subst,X249 : term,X250 : subst] : ((X240 @ X248 @ X249 @ (comp @ X250 @ X247)) | ~(X240 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250) @ X247)) | ~(X240 @ id @ X241 @ id) | ~ ! [X251 : term,X252 : term] : (~(X240 @ id @ X252 @ id) | (X240 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id) | ~(X240 @ id @ X251 @ id))) => (! [X253 : (subst > term > subst > $o),X254 : term] : (~ ! [X255 : term,X256 : subst,X257 : subst,X258 : subst] : ((X253 @ (comp @ X258 @ X256) @ (sub @ X255 @ X256) @ X257) | ~(X253 @ X258 @ X255 @ (comp @ X256 @ X257))) | ~ ! [X259 : (subst > term > term)] : (~ ! [X260 : term] : (~(X253 @ id @ X260 @ id) | (X253 @ id @ (X259 @ id @ X260) @ id)) | ~ ! [X261 : subst,X262 : subst,X263 : term] : (((sub @ (X259 @ X261 @ X263) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262)))) | (X253 @ id @ (lam @ (X259 @ sh @ one)) @ id)) | ~ ! [X264 : term] : ((X253 @ id @ (sub @ X254 @ (push @ X264 @ id)) @ id) | ~(X253 @ id @ X264 @ id)) | (X253 @ id @ (lam @ X254) @ id) | ~ ! [X265 : subst,X266 : subst,X267 : term,X268 : subst] : (~(X253 @ (comp @ X268 @ X265) @ (sub @ X267 @ X265) @ X266) | (X253 @ X268 @ X267 @ (comp @ X265 @ X266)))) => ! [X269 : term,X270 : (subst > term > subst > $o)] : (~ ! [X271 : subst,X272 : term,X273 : subst,X274 : subst] : ((X270 @ X271 @ X272 @ (comp @ X273 @ X274)) | ~(X270 @ (comp @ X271 @ X273) @ (sub @ X272 @ X273) @ X274)) | ~ ! [X275 : subst,X276 : term,X277 : subst,X278 : subst] : ((X270 @ (comp @ X278 @ X275) @ (sub @ X276 @ X275) @ X277) | ~(X270 @ X278 @ X276 @ (comp @ X275 @ X277))) | ~ ! [X279 : term] : (~(var @ (sub @ X279 @ id)) | (X270 @ id @ X279 @ id)) | (X270 @ id @ X269 @ id) | ~ ! [X280 : (subst > term > term)] : ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id) | ~ ! [X281 : subst,X282 : term,X283 : subst] : (((X280 @ (comp @ X281 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X280 @ X281 @ X282) @ X283))) | ~ ! [X284 : term] : ((X270 @ id @ (X280 @ id @ X284) @ id) | ~(X270 @ id @ X284 @ id))) | ~ ! [X285 : term,X286 : term] : (~(X270 @ id @ X285 @ id) | (X270 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id) | ~(X270 @ id @ X286 @ id)))))) <=> hoasinduction_lthm) & (hoasinduction_lem0 <=> ! [X287 : (subst > term > subst > $o)] : ~ ! [X288 : (term > $o)] : ~ ! [X289 : term] : (((X287 @ id @ X289 @ id)) = ((X288 @ X289)))) & (id = ((d2subst @ d_id))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & pushprop_lthm & pushprop & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & hoasinduction_lem3a_gthm & (! [X292 : term,X293 : (term > $o)] : (~ ! [X294 : term] : ((X293 @ X294) | ~(var @ X294)) | (X293 @ X292) | ~ ! [X295 : term,X296 : term] : ((X293 @ (ap @ X295 @ X296)) | ~(X293 @ X295) | ~(X293 @ X296)) | ~ ! [X297 : term] : ((X293 @ (lam @ X297)) | ~ ! [X298 : term] : ((X293 @ (sub @ X297 @ (push @ X298 @ id))) | ~(X293 @ X298)))) <=> induction2) & hoasinduction_lem1v2_gthm & ((! [X299 : term,X300 : subst] : (((sub @ one @ (push @ X299 @ X300))) = X299) => ! [X301 : term,X302 : (term > $o),X303 : subst,X304 : (term > $o)] : ((X302 @ one) | ~(X304 @ X301) | ~ ! [X305 : term] : (((X304 @ (sub @ X305 @ (push @ X301 @ X303)))) = ((X302 @ X305))))) <=> pushprop_lem1v2_lthm) & (! [X306 : term,X307 : (term > $o)] : ((X307 @ X306) | ~ ! [X308 : term] : (~(var @ X308) | (X307 @ X308)) | ~ ! [X309 : term,X310 : term] : (~(X307 @ X309) | ~(X307 @ X310) | (X307 @ (ap @ X309 @ X310))) | ~ ! [X311 : term] : ((X307 @ (lam @ X311)) | ~(X307 @ X311))) <=> induction) & ((! [X312 : term,X313 : subst] : (((sub @ one @ (push @ X312 @ X313))) = X312) => (! [X314 : term,X315 : subst] : (((comp @ sh @ (push @ X314 @ X315))) = X315) => (! [X316 : term,X317 : term] : ((((lam @ X316)) != ((lam @ X317))) | (X316 = X317)) => ! [X318 : (subst > term > term),X319 : term,X320 : subst,X321 : (subst > term > term)] : ((((X321 @ X320 @ X319)) = ((X318 @ X320 @ X319))) | (((lam @ (X318 @ sh @ one))) != ((lam @ (X321 @ sh @ one)))) | ~ ! [X322 : subst,X323 : subst,X324 : term] : (((sub @ (X321 @ X323 @ X324) @ X322)) = ((X321 @ (comp @ X323 @ X322) @ (sub @ X324 @ X322)))) | ~ ! [X325 : subst,X326 : subst,X327 : term] : (((sub @ (X318 @ X325 @ X327) @ X326)) = ((X318 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)))))))) <=> hoaslaminj_lthm) & ! [X328 : d_term,X329 : d_term] : ((((d2term @ X328)) = ((d2term @ X329))) => (X328 = X329)) & hoasinduction_lem2_gthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (pushprop_p_and_p_prime = (^[X330 : term, X331 : subst, X332 : (term > $o), X333 : (term > $o)] : (! [X334 : term] : (((X333 @ X334)) = ((X332 @ (sub @ X334 @ (push @ X330 @ X331)))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (sh = ((d2subst @ d_id))) & (! [X335 : subst,X336 : term] : (((sub @ one @ (push @ X336 @ X335))) = X336) <=> axvarcons) & ((! [X337 : term] : (((sub @ X337 @ id)) = X337) => (! [X338 : (term > $o),X339 : term,X340 : subst] : (~ ! [X341 : term] : ((X338 @ (sub @ X341 @ X340)) | ~(var @ X341)) | ~ ! [X342 : term,X343 : term] : (~(X338 @ X343) | ~(X338 @ X342) | (X338 @ (ap @ X342 @ X343))) | (X338 @ (sub @ X339 @ X340)) | ~ ! [X344 : term] : (~ ! [X345 : term] : ((X338 @ (sub @ X344 @ (push @ X345 @ id))) | ~(X338 @ X345)) | (X338 @ (lam @ X344)))) => ! [X346 : (term > $o),X347 : term] : ((X346 @ X347) | ~ ! [X348 : term] : (~ ! [X349 : term] : (~(X346 @ X349) | (X346 @ (sub @ X348 @ (push @ X349 @ id)))) | (X346 @ (lam @ X348))) | ~ ! [X350 : term,X351 : term] : ((X346 @ (ap @ X351 @ X350)) | ~(X346 @ X350) | ~(X346 @ X351)) | ~ ! [X352 : term] : (~(var @ X352) | (X346 @ X352))))) <=> induction2_lthm) & ((! [X353 : term] : (((sub @ X353 @ id)) = X353) => ! [X354 : (subst > term > subst > $o),X355 : (term > $o),X356 : term] : (~ ! [X357 : term] : (((X354 @ id @ X357 @ id)) = ((X355 @ X357))) | (X355 @ (lam @ X356)) | ~ ! [X358 : term] : (~(X355 @ X358) | (X355 @ (sub @ X356 @ (push @ X358 @ id)))) | ~ ! [X359 : subst,X360 : term,X361 : subst,X362 : subst] : ((X354 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359) | ~(X354 @ X362 @ X360 @ (comp @ X361 @ X359))) | ~ ! [X363 : (subst > term > term)] : ((X354 @ id @ (lam @ (X363 @ sh @ one)) @ id) | ~ ! [X364 : subst,X365 : subst,X366 : term] : (((X363 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365))) = ((sub @ (X363 @ X364 @ X366) @ X365))) | ~ ! [X367 : term] : (~(X354 @ id @ X367 @ id) | (X354 @ id @ (X363 @ id @ X367) @ id))) | ~ ! [X368 : subst,X369 : subst,X370 : term,X371 : subst] : (~(X354 @ (comp @ X368 @ X371) @ (sub @ X370 @ X371) @ X369) | (X354 @ X368 @ X370 @ (comp @ X371 @ X369))))) <=> hoasinduction_lem3v2_lthm) & hoasapinj1_gthm & termmset_gthm & (hoasinduction_lem3 <=> ! [X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : (subst > term > term)] : (~ ! [X375 : term] : ((X373 @ id @ (X374 @ id @ X375) @ id) | ~(X373 @ id @ X375 @ id)) | (X373 @ id @ (lam @ (X374 @ sh @ one)) @ id) | ~ ! [X376 : subst,X377 : subst,X378 : term] : (((X374 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377))) = ((sub @ (X374 @ X376 @ X378) @ X377)))) | ~ ! [X379 : subst,X380 : term,X381 : subst,X382 : subst] : (~(X373 @ (comp @ X381 @ X379) @ (sub @ X380 @ X379) @ X382) | (X373 @ X381 @ X380 @ (comp @ X379 @ X382))) | ~ ! [X383 : term] : (~(X373 @ id @ X383 @ id) | (X373 @ id @ (sub @ X372 @ (push @ X383 @ id)) @ id)) | ~ ! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (~(X373 @ X384 @ X387 @ (comp @ X386 @ X385)) | (X373 @ (comp @ X384 @ X386) @ (sub @ X387 @ X386) @ X385)) | (X373 @ id @ (lam @ X372) @ id))) & (one = ((d2term @ d_one))) & (hoasapinj1 <=> ! [X388 : term,X389 : term,X390 : term,X391 : term] : ((((ap @ (sub @ X389 @ id) @ X388)) != ((ap @ (sub @ X391 @ id) @ X390))) | (X389 = X391))) & (! [X392 : (subst > term > subst > $o),X393 : term] : (~ ! [X394 : (subst > term > term),X395 : term] : (~ ! [X396 : term,X397 : subst,X398 : subst] : (((sub @ X395 @ (push @ (sub @ X396 @ X397) @ (comp @ X398 @ X397)))) = ((X394 @ (comp @ X398 @ X397) @ (sub @ X396 @ X397)))) | (X392 @ id @ (lam @ (X394 @ sh @ one)) @ id) | ~ ! [X399 : term,X400 : subst,X401 : subst] : (((sub @ (sub @ X395 @ (push @ X399 @ X401)) @ X400)) = ((sub @ (X394 @ X401 @ X399) @ X400))) | ~ ! [X402 : term] : (~(X392 @ id @ X402 @ id) | (X392 @ id @ (X394 @ id @ X402) @ id))) | ~ ! [X403 : term] : (~(X392 @ id @ X403 @ id) | (X392 @ id @ (sub @ X393 @ (push @ X403 @ id)) @ id)) | (X392 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & (! [X404 : term,X405 : subst,X406 : (term > $o)] : ~ ! [X407 : (term > $o)] : ~ ! [X408 : term] : (((X407 @ X408)) = ((X406 @ (sub @ X408 @ (push @ X404 @ X405))))) <=> pushprop_lem0) & ! [X409 : subst] : ? [X410 : d_subst] : (((d2subst @ X410)) = X409) & hoasinduction_lem1 & hoasinduction_lem1_lthm & (! [X411 : (subst > term > subst > $o)] : ~ ! [X412 : (term > $o)] : ~ ! [X413 : term] : (((X411 @ id @ X413 @ id)) = ((X412 @ X413))) <=> hoasinduction_lem0_lthm) & hoasinduction_lem2_lthm & hoasinduction_gthm & ~lamnotap & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_gthm & ((! [X414 : subst] : (((comp @ id @ X414)) = X414) & ! [X415 : subst] : (((comp @ X415 @ id)) = X415)) <=> substmonoid) & ulamvarind & pushprop_gthm & (hoaslaminj <=> ! [X416 : (subst > term > term),X417 : subst,X418 : term,X419 : (subst > term > term)] : ((((lam @ (X416 @ sh @ one))) != ((lam @ (X419 @ sh @ one)))) | (((X419 @ X417 @ X418)) = ((X416 @ X417 @ X418))) | ~ ! [X420 : subst,X421 : term,X422 : subst] : (((X416 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X416 @ X422 @ X421) @ X420))) | ~ ! [X423 : subst,X424 : term,X425 : subst] : (((X419 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425))) = ((sub @ (X419 @ X423 @ X424) @ X425))))) & hoasinduction_lem1_gthm & (hoasinduction_lem2v2 <=> ! [X426 : (subst > term > subst > $o),X427 : term,X428 : (term > $o),X429 : term] : ((X428 @ (ap @ X427 @ X429)) | ~ ! [X430 : term] : (((X426 @ id @ X430 @ id)) = ((X428 @ X430))) | ~ ! [X431 : term,X432 : term] : (~(X426 @ id @ X431 @ id) | ~(X426 @ id @ X432 @ id) | (X426 @ id @ (ap @ (sub @ X431 @ id) @ X432) @ id)) | ~(X428 @ X429) | ~(X428 @ X427) | ~ ! [X433 : subst,X434 : subst,X435 : subst,X436 : term] : ((X426 @ X434 @ X436 @ (comp @ X433 @ X435)) | ~(X426 @ (comp @ X434 @ X433) @ (sub @ X436 @ X433) @ X435)) | ~ ! [X437 : subst,X438 : term,X439 : subst,X440 : subst] : (~(X426 @ X439 @ X438 @ (comp @ X437 @ X440)) | (X426 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437) @ X440)))) & (hoaslamnotap <=> ! [X441 : (subst > term > term),X442 : term,X443 : term] : ((((ap @ (sub @ X443 @ id) @ X442)) != ((lam @ (X441 @ sh @ one)))) | ~ ! [X444 : subst,X445 : term,X446 : subst] : (((sub @ (X441 @ X444 @ X445) @ X446)) = ((X441 @ (comp @ X444 @ X446) @ (sub @ X445 @ X446)))))) & hoasinduction_lem3_gthm & pushprop_lem1v2_gthm & ((! [X447 : term] : ~ ! [X448 : (subst > term > term)] : ~ ! [X449 : subst,X450 : term] : (((sub @ X447 @ (push @ X450 @ X449))) = ((X448 @ X449 @ X450))) => (! [X451 : term] : (((sub @ X451 @ id)) = X451) => ! [X452 : (subst > term > subst > $o),X453 : term,X454 : (term > $o)] : (~ ! [X455 : term] : (((X454 @ X455)) = ((X452 @ id @ X455 @ id))) | (X454 @ (lam @ X453)) | ~ ! [X456 : (subst > term > term)] : (~ ! [X457 : term,X458 : subst,X459 : subst] : (((X456 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458))) = ((sub @ (X456 @ X459 @ X457) @ X458))) | ~ ! [X460 : term] : (~(X452 @ id @ X460 @ id) | (X452 @ id @ (X456 @ id @ X460) @ id)) | (X452 @ id @ (lam @ (X456 @ sh @ one)) @ id)) | ~ ! [X461 : term] : ((X454 @ (sub @ X453 @ (push @ X461 @ id))) | ~(X454 @ X461))))) <=> hoasinduction_lem3v2a_lthm) & (hoasinduction_lthm_3 <=> (! [X462 : (subst > term > subst > $o)] : ~ ! [X463 : (term > $o)] : ~ ! [X464 : term] : (((X462 @ id @ X464 @ id)) = ((X463 @ X464))) => (! [X465 : (term > $o),X466 : term] : (~ ! [X467 : term] : (~ ! [X468 : term] : ((X465 @ (sub @ X467 @ (push @ X468 @ id))) | ~(X465 @ X468)) | (X465 @ (lam @ X467))) | ~ ! [X469 : term,X470 : term] : (~(X465 @ X469) | ~(X465 @ X470) | (X465 @ (ap @ X469 @ X470))) | (X465 @ X466) | ~ ! [X471 : term] : (~(var @ X471) | (X465 @ X471))) => (! [X472 : term] : (((sub @ X472 @ id)) = X472) => (! [X473 : (term > $o),X474 : (subst > term > subst > $o),X475 : term] : (~ ! [X476 : term] : ((X473 @ (sub @ X475 @ (push @ X476 @ id))) | ~(X473 @ X476)) | (X473 @ (lam @ X475)) | ~ ! [X477 : (subst > term > term)] : (~ ! [X478 : term] : (~(X474 @ id @ X478 @ id) | (X474 @ id @ (X477 @ id @ X478) @ id)) | (X474 @ id @ (lam @ (X477 @ sh @ one)) @ id) | ~ ! [X479 : term,X480 : subst,X481 : subst] : (((sub @ (X477 @ X481 @ X479) @ X480)) = ((X477 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))))) | ~ ! [X482 : term] : (((X474 @ id @ X482 @ id)) = ((X473 @ X482)))) => ! [X483 : term,X484 : (subst > term > subst > $o)] : ((X484 @ id @ X483 @ id) | ~ ! [X485 : term,X486 : term] : (~(X484 @ id @ X486 @ id) | ~(X484 @ id @ X485 @ id) | (X484 @ id @ (ap @ (sub @ X486 @ id) @ X485) @ id)) | ~ ! [X487 : term,X488 : subst,X489 : subst,X490 : subst] : ((X484 @ X489 @ X487 @ (comp @ X490 @ X488)) | ~(X484 @ (comp @ X489 @ X490) @ (sub @ X487 @ X490) @ X488)) | ~ ! [X491 : (subst > term > term)] : ((X484 @ id @ (lam @ (X491 @ sh @ one)) @ id) | ~ ! [X492 : term] : ((X484 @ id @ (X491 @ id @ X492) @ id) | ~(X484 @ id @ X492 @ id)) | ~ ! [X493 : subst,X494 : term,X495 : subst] : (((sub @ (X491 @ X495 @ X494) @ X493)) = ((X491 @ (comp @ X495 @ X493) @ (sub @ X494 @ X493))))) | ~ ! [X496 : term] : ((X484 @ id @ X496 @ id) | ~(var @ (sub @ X496 @ id))) | ~ ! [X497 : subst,X498 : subst,X499 : term,X500 : subst] : (~(X484 @ X500 @ X499 @ (comp @ X498 @ X497)) | (X484 @ (comp @ X500 @ X498) @ (sub @ X499 @ X498) @ X497)))))))) & (! [X501 : (term > $o),X502 : (subst > term > subst > $o),X503 : term] : ((X501 @ (lam @ X503)) | ~ ! [X504 : term] : ((X501 @ (sub @ X503 @ (push @ X504 @ id))) | ~(X501 @ X504)) | ~ ! [X505 : (subst > term > term)] : ((X502 @ id @ (lam @ (X505 @ sh @ one)) @ id) | ~ ! [X506 : term,X507 : subst,X508 : subst] : (((sub @ (X505 @ X507 @ X506) @ X508)) = ((X505 @ (comp @ X507 @ X508) @ (sub @ X506 @ X508)))) | ~ ! [X509 : term] : (~(X502 @ id @ X509 @ id) | (X502 @ id @ (X505 @ id @ X509) @ id))) | ~ ! [X510 : term] : (((X501 @ X510)) = ((X502 @ id @ X510 @ id)))) <=> hoasinduction_lem3v2a) & pushprop_lem3v2 & (hoasapinj1_lthm <=> (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : term,X513 : term,X514 : term,X515 : term] : ((((ap @ X515 @ X512)) != ((ap @ X513 @ X514))) | (X513 = X515)) => ! [X516 : term,X517 : term,X518 : term,X519 : term] : ((X517 = X519) | (((ap @ (sub @ X517 @ id) @ X516)) != ((ap @ (sub @ X519 @ id) @ X518))))))) & (! [X520 : term,X521 : term] : ((((sub @ X521 @ sh)) != ((sub @ X520 @ sh))) | (X520 = X521)) <=> shinj) & ((! [X522 : subst] : (((comp @ id @ X522)) = X522) => (! [X523 : subst] : (((comp @ X523 @ id)) = X523) => (! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)))) <=> substmonoid_lthm) & substmonoid_gthm & ulamvarsh & axmap & (apinj2 <=> ! [X526 : term,X527 : term,X528 : term,X529 : term] : ((((ap @ X527 @ X526)) != ((ap @ X528 @ X529))) | (X526 = X529))) & pushprop_lem0_gthm & (! [X530 : term,X531 : (subst > term > subst > $o)] : ((X531 @ id @ X530 @ id) | ~ ! [X532 : (subst > term > term)] : (~ ! [X533 : term,X534 : subst,X535 : subst] : (((sub @ (X532 @ X534 @ X533) @ X535)) = ((X532 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | (X531 @ id @ (lam @ (X532 @ sh @ one)) @ id) | ~ ! [X536 : term] : (~(X531 @ id @ X536 @ id) | (X531 @ id @ (X532 @ id @ X536) @ id))) | ~ ! [X537 : term,X538 : term] : (~(X531 @ id @ X537 @ id) | (X531 @ id @ (ap @ (sub @ X537 @ id) @ X538) @ id) | ~(X531 @ id @ X538 @ id))) <=> hoasinduction_no_psi_cond) & (! [X539 : subst,X540 : (term > $o),X541 : term,X542 : (term > $o)] : ((X540 @ one) | ~(X542 @ X541) | ~ ! [X543 : term] : (((X540 @ X543)) = ((X542 @ (sub @ X543 @ (push @ X541 @ X539)))))) <=> pushprop_lem1v2) & axclos & axassoc & hoaslamnotap_lthm & axabs & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~ulamvar1 & pushprop_lthm_orig & axvarshift & (! [X544 : term] : ~ ! [X545 : (subst > term > term)] : ~ ! [X546 : term,X547 : subst] : (((X545 @ X547 @ X546)) = ((sub @ X544 @ (push @ X546 @ X547)))) <=> hoasinduction_lem3v2_f_lthm) & hoasapnotvar_gthm & (termmset_lthm <=> (! [X548 : term] : (((sub @ X548 @ id)) = X548) => ! [X549 : term] : (((sub @ X549 @ id)) = X549)))),
% 6.12/1.29 inference(rectify,[],[f1])).
% 6.12/1.29 thf(f7,plain,(
% 6.12/1.29 (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar = $true) & (hoasapnotvar = $true) & ((! [X0 : term,X2 : term,X1 : term,X3 : term] : ((((ap @ X2 @ X0)) != ((ap @ X1 @ X3))) | (X0 = X3)) => ! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4))))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X8 : (term > $o),X9 : (subst > term > subst > $o),X10 : term] : (~ ! [X11 : (subst > term > term)] : (($true = ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) | ~ ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))) | ~ ! [X15 : term] : (~ (((X9 @ id @ X15 @ id)) = $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true))) | ~ ! [X16 : subst,X17 : subst,X18 : subst,X19 : term] : (~ (((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) = $true) | (((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) = $true)) | ~ ! [X20 : subst,X21 : subst,X22 : subst,X23 : term] : (~ ($true = ((X9 @ X21 @ X23 @ (comp @ X22 @ X20)))) | ($true = ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20)))) | ~ ! [X24 : term] : (~ (((X8 @ X24)) = $true) | ($true = ((X8 @ (sub @ X10 @ (push @ X24 @ id)))))) | ($true = ((X8 @ (lam @ X10)))) | ~ ! [X25 : term] : (((X8 @ X25)) = ((X9 @ id @ X25 @ id))))) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ~ ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one)))) & ((hoasinduction_lem2 = $true) <=> ! [X34 : (subst > term > subst > $o),X35 : term,X36 : term] : (~ (((X34 @ id @ X35 @ id)) = $true) | ~ ! [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (~ (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) = $true) | ($true = ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37)))) | ~ ! [X41 : subst,X42 : term,X43 : subst,X44 : subst] : (~ (((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) = $true) | (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) = $true)) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | ~ (((X34 @ id @ X36 @ id)) = $true) | ~ ! [X45 : term,X46 : term] : (~ ($true = ((X34 @ id @ X45 @ id))) | ($true = ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) | ~ (((X34 @ id @ X46 @ id)) = $true)))) & (! [X47 : term] : ~ ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem1_gthm = $true) & ((! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : term] : (~ ! [X53 : (subst > term > term)] : (~ ! [X54 : term] : (~ (((X51 @ id @ X54 @ id)) = $true) | (((X51 @ id @ (X53 @ id @ X54) @ id)) = $true)) | ~ ! [X55 : subst,X57 : subst,X56 : term] : (((sub @ (X53 @ X57 @ X56) @ X55)) = ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true)) | ($true = ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id))) | ~ ! [X58 : term] : (~ (((X51 @ id @ X58 @ id)) = $true) | (((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true))) => ! [X59 : (subst > term > subst > $o),X60 : term] : (~ ! [X61 : term] : (~ (((X59 @ id @ X61 @ id)) = $true) | (((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) = $true)) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~ (((X59 @ id @ X63 @ id)) = $true) | (((X59 @ id @ (X62 @ id @ X63) @ id)) = $true)) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true)) | (((X59 @ id @ (lam @ X60) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((induction2lem = $true) <=> ! [X69 : (term > $o),X70 : subst,X71 : term] : (~ ! [X72 : term,X73 : term] : (~ (((X69 @ X73)) = $true) | ~ (((X69 @ X72)) = $true) | (((X69 @ (ap @ X73 @ X72))) = $true)) | ~ ! [X74 : term] : ((((X69 @ (lam @ X74))) = $true) | ~ ! [X75 : term] : ((((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true) | ~ ($true = ((X69 @ X75))))) | ~ ! [X76 : term] : (~ (((var @ X76)) = $true) | ($true = ((X69 @ (sub @ X76 @ X70))))) | (((X69 @ (sub @ X71 @ X70))) = $true))) & ! [X77 : d_subst,X78 : d_subst] : ((((d2subst @ X78)) = ((d2subst @ X77))) => (X77 = X78)) & (axapp = $true) & (induction2lem_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & ((pushprop_lem1 = $true) <=> ! [X83 : (term > $o),X84 : term,X85 : term,X86 : (term > $o),X87 : subst] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ~ ($true = ((X83 @ X84))))) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true)) & ((hoasinduction = $true) <=> ! [X90 : term,X91 : (subst > term > subst > $o)] : (~ ! [X92 : term] : (($true = ((X91 @ id @ X92 @ id))) | ~ (((var @ (sub @ X92 @ id))) = $true)) | ~ ! [X93 : term,X94 : term] : ((((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) = $true) | ~ (((X91 @ id @ X94 @ id)) = $true) | ~ (((X91 @ id @ X93 @ id)) = $true)) | ~ ! [X95 : (subst > term > term)] : (~ ! [X96 : term] : ((((X91 @ id @ (X95 @ id @ X96) @ id)) = $true) | ~ (((X91 @ id @ X96 @ id)) = $true)) | ~ ! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) | ($true = ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))) | (((X91 @ id @ X90 @ id)) = $true) | ~ ! [X100 : subst,X101 : subst,X102 : subst,X103 : term] : (~ (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) = $true) | (((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) = $true)) | ~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~ (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) = $true) | (((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) = $true)))) & ((! [X108 : (subst > term > subst > $o)] : ~ ! [X109 : (term > $o)] : ~ ! [X110 : term] : (((X109 @ X110)) = ((X108 @ id @ X110 @ id))) => (! [X111 : term,X112 : (term > $o)] : (~ ! [X113 : term] : ((((X112 @ (lam @ X113))) = $true) | ~ ! [X114 : term] : (~ (((X112 @ X114)) = $true) | (((X112 @ (sub @ X113 @ (push @ X114 @ id)))) = $true))) | ~ ! [X115 : term] : (~ (((var @ X115)) = $true) | (((X112 @ X115)) = $true)) | (((X112 @ X111)) = $true) | ~ ! [X116 : term,X117 : term] : (~ (((X112 @ X117)) = $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | ~ (((X112 @ X116)) = $true))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X119 : (term > $o),X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term] : (~ (((X119 @ X122)) = $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true)) | ~ ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) | ~ ! [X124 : (subst > term > term)] : (~ ! [X125 : term] : ((((X121 @ id @ (X124 @ id @ X125) @ id)) = $true) | ~ ($true = ((X121 @ id @ X125 @ id)))) | ~ ! [X128 : subst,X126 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) = ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)))) | (((X119 @ (lam @ X120))) = $true)) => ! [X129 : (subst > term > subst > $o),X130 : term] : (($true = ((X129 @ id @ X130 @ id))) | ~ ! [X131 : term,X132 : term] : ((((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) = $true) | ~ (((X129 @ id @ X132 @ id)) = $true) | ~ (((X129 @ id @ X131 @ id)) = $true)) | ~ ! [X133 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) = $true) | ~ ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | ~ (((X129 @ id @ X134 @ id)) = $true)) | ~ ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (lamnotvar = $true) & (induction2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & ! [X144 : d_term] : (d_one = X144) & ((hoasinduction_lem3a = $true) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : (~ ! [X147 : (subst > term > term)] : (($true = ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) | ~ ! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) | ~ ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | ~ (((X146 @ id @ X151 @ id)) = $true))) | ~ ! [X152 : term] : ((((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) = $true) | ~ (((X146 @ id @ X152 @ id)) = $true)) | (((X146 @ id @ (lam @ X145) @ id)) = $true))) & ((hoasinduction_lem3aa = $true) <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (~ ! [X155 : term] : (~ (((X153 @ id @ X155 @ id)) = $true) | ($true = ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))) | ~ ! [X156 : (subst > term > term)] : (~ ! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) | ~ ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ~ ($true = ((X153 @ id @ X160 @ id)))) | (((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) = $true)) | ($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))))) & (hoaslamnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X164 : term,X165 : (subst > term > subst > $o)] : ((((X165 @ id @ (lam @ (sub @ X164 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X166 : (subst > term > term)] : (~ ! [X167 : subst,X168 : subst,X169 : term] : (((sub @ (X166 @ X167 @ X169) @ X168)) = ((X166 @ (comp @ X167 @ X168) @ (sub @ X169 @ X168)))) | (((X165 @ id @ (lam @ (X166 @ sh @ one)) @ id)) = $true) | ~ ! [X170 : term] : (~ (((X165 @ id @ X170 @ id)) = $true) | (((X165 @ id @ (X166 @ id @ X170) @ id)) = $true))) | ~ ! [X171 : term] : (~ (((X165 @ id @ X171 @ id)) = $true) | (((X165 @ id @ (sub @ X164 @ (push @ X171 @ id)) @ id)) = $true)))) & (! [X172 : term] : ~ ! [X173 : (subst > term > term)] : ~ ! [X174 : subst,X175 : term] : (((sub @ X172 @ (push @ X175 @ X174))) = ((X173 @ X174 @ X175))) <=> (hoasinduction_lem3v2_f = $true)) & ((! [X176 : term,X177 : subst] : (((sub @ one @ (push @ X176 @ X177))) = X176) => (! [X178 : subst,X179 : term] : (((comp @ sh @ (push @ X179 @ X178))) = X178) => ! [X180 : (term > $o),X181 : term,X182 : term,X183 : (term > $o),X184 : subst] : (~ (((X180 @ X181)) = $true) | ($true = ((X183 @ (sub @ X181 @ (push @ X182 @ X184)))))))) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X185 : subst,X186 : term] : (((sub @ one @ (push @ X186 @ X185))) = X186) => (! [X187 : subst,X188 : term] : (((comp @ sh @ (push @ X188 @ X187))) = X187) => (! [X189 : subst] : (((comp @ X189 @ id)) = X189) => (! [X190 : term,X191 : (term > $o)] : (~ ! [X192 : term,X193 : term] : (~ (((X191 @ X192)) = $true) | (((X191 @ (ap @ X193 @ X192))) = $true) | ~ ($true = ((X191 @ X193)))) | ~ ! [X194 : term] : (~ (((X191 @ X194)) = $true) | (((X191 @ (lam @ X194))) = $true)) | (((X191 @ X190)) = $true) | ~ ! [X195 : term] : ((((X191 @ X195)) = $true) | ~ (((var @ X195)) = $true))) => ! [X196 : term,X197 : (term > $o),X198 : subst] : (~ ! [X199 : term] : (~ ! [X200 : term] : ((((X197 @ (sub @ X199 @ (push @ X200 @ id)))) = $true) | ~ (((X197 @ X200)) = $true)) | (((X197 @ (lam @ X199))) = $true)) | ~ ! [X201 : term,X202 : term] : (~ (((X197 @ X202)) = $true) | ~ (((X197 @ X201)) = $true) | ($true = ((X197 @ (ap @ X201 @ X202))))) | ~ ! [X203 : term] : (($true = ((X197 @ (sub @ X203 @ X198)))) | ~ (((var @ X203)) = $true)) | (((X197 @ (sub @ X196 @ X198))) = $true))))))) & (pushprop_lem2v2_gthm = $true) & (! [X204 : term] : (((sub @ X204 @ id)) = X204) <=> (axvarid = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((axidr = $true) <=> ! [X207 : subst] : (((comp @ X207 @ id)) = X207)) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X208 : term] : (((sub @ X208 @ id)) = X208) => (! [X209 : term,X210 : (subst > term > subst > $o)] : (~ ! [X211 : term] : (($true = ((X210 @ id @ (sub @ X209 @ (push @ X211 @ id)) @ id))) | ~ ($true = ((X210 @ id @ X211 @ id)))) | ~ ! [X212 : (subst > term > term)] : (~ ! [X213 : term] : (~ (((X210 @ id @ X213 @ id)) = $true) | (((X210 @ id @ (X212 @ id @ X213) @ id)) = $true)) | ($true = ((X210 @ id @ (lam @ (X212 @ sh @ one)) @ id))) | ~ ! [X214 : subst,X215 : term,X216 : subst] : (((sub @ (X212 @ X216 @ X215) @ X214)) = ((X212 @ (comp @ X216 @ X214) @ (sub @ X215 @ X214))))) | (((X210 @ id @ (lam @ (sub @ X209 @ (push @ one @ sh))) @ id)) = $true)) => ! [X217 : (subst > term > subst > $o),X218 : term] : (~ ! [X219 : (subst > term > term)] : (~ ! [X220 : subst,X221 : subst,X222 : term] : (((X219 @ (comp @ X221 @ X220) @ (sub @ X222 @ X220))) = ((sub @ (X219 @ X221 @ X222) @ X220))) | (((X217 @ id @ (lam @ (X219 @ sh @ one)) @ id)) = $true) | ~ ! [X223 : term] : (~ (((X217 @ id @ X223 @ id)) = $true) | (((X217 @ id @ (X219 @ id @ X223) @ id)) = $true))) | ~ ! [X224 : term] : ((((X217 @ id @ (sub @ X218 @ (push @ X224 @ id)) @ id)) = $true) | ~ (((X217 @ id @ X224 @ id)) = $true)) | (((X217 @ id @ (lam @ X218) @ id)) = $true) | ~ ! [X225 : subst,X226 : term,X227 : subst,X228 : subst] : (~ (((X217 @ X228 @ X226 @ (comp @ X227 @ X225))) = $true) | (((X217 @ (comp @ X228 @ X227) @ (sub @ X226 @ X227) @ X225)) = $true)) | ~ ! [X229 : subst,X230 : subst,X231 : term,X232 : subst] : (($true = ((X217 @ X230 @ X231 @ (comp @ X232 @ X229)))) | ~ (((X217 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232) @ X229)) = $true)))))) & ((! [X233 : (term > $o),X234 : term] : (~ ! [X235 : term] : ((((X233 @ (lam @ X235))) = $true) | ~ ! [X236 : term] : (($true = ((X233 @ (sub @ X235 @ (push @ X236 @ id))))) | ~ (((X233 @ X236)) = $true))) | (((X233 @ X234)) = $true) | ~ ! [X237 : term,X238 : term] : ((((X233 @ (ap @ X238 @ X237))) = $true) | ~ ($true = ((X233 @ X237))) | ~ (((X233 @ X238)) = $true)) | ~ ! [X239 : term] : (~ (((var @ X239)) = $true) | (((X233 @ X239)) = $true))) => (! [X240 : (subst > term > subst > $o),X241 : term,X242 : term] : (~ ($true = ((X240 @ id @ X242 @ id))) | ($true = ((X240 @ id @ (ap @ X242 @ X241) @ id))) | ~ ! [X243 : subst,X244 : subst,X245 : term,X246 : subst] : (($true = ((X240 @ (comp @ X244 @ X243) @ (sub @ X245 @ X243) @ X246))) | ~ (((X240 @ X244 @ X245 @ (comp @ X243 @ X246))) = $true)) | ~ ! [X247 : subst,X248 : subst,X249 : term,X250 : subst] : (($true = ((X240 @ X248 @ X249 @ (comp @ X250 @ X247)))) | ~ (((X240 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250) @ X247)) = $true)) | ~ (((X240 @ id @ X241 @ id)) = $true) | ~ ! [X251 : term,X252 : term] : (~ (((X240 @ id @ X252 @ id)) = $true) | (((X240 @ id @ (ap @ (sub @ X252 @ id) @ X251) @ id)) = $true) | ~ (((X240 @ id @ X251 @ id)) = $true))) => (! [X253 : (subst > term > subst > $o),X254 : term] : (~ ! [X255 : term,X256 : subst,X257 : subst,X258 : subst] : ((((X253 @ (comp @ X258 @ X256) @ (sub @ X255 @ X256) @ X257)) = $true) | ~ (((X253 @ X258 @ X255 @ (comp @ X256 @ X257))) = $true)) | ~ ! [X259 : (subst > term > term)] : (~ ! [X260 : term] : (~ (((X253 @ id @ X260 @ id)) = $true) | ($true = ((X253 @ id @ (X259 @ id @ X260) @ id)))) | ~ ! [X261 : subst,X262 : subst,X263 : term] : (((sub @ (X259 @ X261 @ X263) @ X262)) = ((X259 @ (comp @ X261 @ X262) @ (sub @ X263 @ X262)))) | ($true = ((X253 @ id @ (lam @ (X259 @ sh @ one)) @ id)))) | ~ ! [X264 : term] : ((((X253 @ id @ (sub @ X254 @ (push @ X264 @ id)) @ id)) = $true) | ~ (((X253 @ id @ X264 @ id)) = $true)) | (((X253 @ id @ (lam @ X254) @ id)) = $true) | ~ ! [X265 : subst,X266 : subst,X267 : term,X268 : subst] : (~ (((X253 @ (comp @ X268 @ X265) @ (sub @ X267 @ X265) @ X266)) = $true) | (((X253 @ X268 @ X267 @ (comp @ X265 @ X266))) = $true))) => ! [X269 : term,X270 : (subst > term > subst > $o)] : (~ ! [X271 : subst,X272 : term,X273 : subst,X274 : subst] : ((((X270 @ X271 @ X272 @ (comp @ X273 @ X274))) = $true) | ~ (((X270 @ (comp @ X271 @ X273) @ (sub @ X272 @ X273) @ X274)) = $true)) | ~ ! [X275 : subst,X276 : term,X277 : subst,X278 : subst] : ((((X270 @ (comp @ X278 @ X275) @ (sub @ X276 @ X275) @ X277)) = $true) | ~ ($true = ((X270 @ X278 @ X276 @ (comp @ X275 @ X277))))) | ~ ! [X279 : term] : (~ (((var @ (sub @ X279 @ id))) = $true) | (((X270 @ id @ X279 @ id)) = $true)) | (((X270 @ id @ X269 @ id)) = $true) | ~ ! [X280 : (subst > term > term)] : ((((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id)) = $true) | ~ ! [X281 : subst,X282 : term,X283 : subst] : (((X280 @ (comp @ X281 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X280 @ X281 @ X282) @ X283))) | ~ ! [X284 : term] : ((((X270 @ id @ (X280 @ id @ X284) @ id)) = $true) | ~ (((X270 @ id @ X284 @ id)) = $true))) | ~ ! [X285 : term,X286 : term] : (~ (((X270 @ id @ X285 @ id)) = $true) | (((X270 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id)) = $true) | ~ (((X270 @ id @ X286 @ id)) = $true)))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X287 : (subst > term > subst > $o)] : ~ ! [X288 : (term > $o)] : ~ ! [X289 : term] : (((X287 @ id @ X289 @ id)) = ((X288 @ X289)))) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lthm = $true) & (pushprop = $true) & ! [X290 : term] : ? [X291 : d_term] : (((d2term @ X291)) = X290) & (hoasinduction_lem3a_gthm = $true) & (! [X292 : term,X293 : (term > $o)] : (~ ! [X294 : term] : ((((X293 @ X294)) = $true) | ~ (((var @ X294)) = $true)) | (((X293 @ X292)) = $true) | ~ ! [X295 : term,X296 : term] : ((((X293 @ (ap @ X295 @ X296))) = $true) | ~ (((X293 @ X295)) = $true) | ~ (((X293 @ X296)) = $true)) | ~ ! [X297 : term] : ((((X293 @ (lam @ X297))) = $true) | ~ ! [X298 : term] : ((((X293 @ (sub @ X297 @ (push @ X298 @ id)))) = $true) | ~ (((X293 @ X298)) = $true)))) <=> (induction2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((! [X299 : term,X300 : subst] : (((sub @ one @ (push @ X299 @ X300))) = X299) => ! [X301 : term,X302 : (term > $o),X303 : subst,X304 : (term > $o)] : ((((X302 @ one)) = $true) | ~ (((X304 @ X301)) = $true) | ~ ! [X305 : term] : (((X304 @ (sub @ X305 @ (push @ X301 @ X303)))) = ((X302 @ X305))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X306 : term,X307 : (term > $o)] : ((((X307 @ X306)) = $true) | ~ ! [X308 : term] : (~ ($true = ((var @ X308))) | (((X307 @ X308)) = $true)) | ~ ! [X309 : term,X310 : term] : (~ (((X307 @ X309)) = $true) | ~ (((X307 @ X310)) = $true) | (((X307 @ (ap @ X309 @ X310))) = $true)) | ~ ! [X311 : term] : ((((X307 @ (lam @ X311))) = $true) | ~ (((X307 @ X311)) = $true))) <=> (induction = $true)) & ((! [X312 : term,X313 : subst] : (((sub @ one @ (push @ X312 @ X313))) = X312) => (! [X314 : term,X315 : subst] : (((comp @ sh @ (push @ X314 @ X315))) = X315) => (! [X316 : term,X317 : term] : ((((lam @ X316)) != ((lam @ X317))) | (X316 = X317)) => ! [X318 : (subst > term > term),X319 : term,X320 : subst,X321 : (subst > term > term)] : ((((X321 @ X320 @ X319)) = ((X318 @ X320 @ X319))) | (((lam @ (X318 @ sh @ one))) != ((lam @ (X321 @ sh @ one)))) | ~ ! [X322 : subst,X323 : subst,X324 : term] : (((sub @ (X321 @ X323 @ X324) @ X322)) = ((X321 @ (comp @ X323 @ X322) @ (sub @ X324 @ X322)))) | ~ ! [X325 : subst,X326 : subst,X327 : term] : (((sub @ (X318 @ X325 @ X327) @ X326)) = ((X318 @ (comp @ X325 @ X326) @ (sub @ X327 @ X326)))))))) <=> (hoaslaminj_lthm = $true)) & ! [X328 : d_term,X329 : d_term] : ((((d2term @ X328)) = ((d2term @ X329))) => (X328 = X329)) & (hoasinduction_lem2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & (! [X335 : subst,X336 : term] : (((sub @ one @ (push @ X336 @ X335))) = X336) <=> (axvarcons = $true)) & ((! [X337 : term] : (((sub @ X337 @ id)) = X337) => (! [X338 : (term > $o),X339 : term,X340 : subst] : (~ ! [X341 : term] : ((((X338 @ (sub @ X341 @ X340))) = $true) | ~ (((var @ X341)) = $true)) | ~ ! [X342 : term,X343 : term] : (~ (((X338 @ X343)) = $true) | ~ (((X338 @ X342)) = $true) | (((X338 @ (ap @ X342 @ X343))) = $true)) | (((X338 @ (sub @ X339 @ X340))) = $true) | ~ ! [X344 : term] : (~ ! [X345 : term] : ((((X338 @ (sub @ X344 @ (push @ X345 @ id)))) = $true) | ~ ($true = ((X338 @ X345)))) | ($true = ((X338 @ (lam @ X344)))))) => ! [X346 : (term > $o),X347 : term] : ((((X346 @ X347)) = $true) | ~ ! [X348 : term] : (~ ! [X349 : term] : (~ (((X346 @ X349)) = $true) | (((X346 @ (sub @ X348 @ (push @ X349 @ id)))) = $true)) | (((X346 @ (lam @ X348))) = $true)) | ~ ! [X350 : term,X351 : term] : ((((X346 @ (ap @ X351 @ X350))) = $true) | ~ (((X346 @ X350)) = $true) | ~ (((X346 @ X351)) = $true)) | ~ ! [X352 : term] : (~ ($true = ((var @ X352))) | (((X346 @ X352)) = $true))))) <=> (induction2_lthm = $true)) & ((! [X353 : term] : (((sub @ X353 @ id)) = X353) => ! [X354 : (subst > term > subst > $o),X355 : (term > $o),X356 : term] : (~ ! [X357 : term] : (((X354 @ id @ X357 @ id)) = ((X355 @ X357))) | (((X355 @ (lam @ X356))) = $true) | ~ ! [X358 : term] : (~ (((X355 @ X358)) = $true) | (((X355 @ (sub @ X356 @ (push @ X358 @ id)))) = $true)) | ~ ! [X359 : subst,X360 : term,X361 : subst,X362 : subst] : ((((X354 @ (comp @ X362 @ X361) @ (sub @ X360 @ X361) @ X359)) = $true) | ~ (((X354 @ X362 @ X360 @ (comp @ X361 @ X359))) = $true)) | ~ ! [X363 : (subst > term > term)] : ((((X354 @ id @ (lam @ (X363 @ sh @ one)) @ id)) = $true) | ~ ! [X364 : subst,X365 : subst,X366 : term] : (((X363 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365))) = ((sub @ (X363 @ X364 @ X366) @ X365))) | ~ ! [X367 : term] : (~ (((X354 @ id @ X367 @ id)) = $true) | ($true = ((X354 @ id @ (X363 @ id @ X367) @ id))))) | ~ ! [X368 : subst,X369 : subst,X370 : term,X371 : subst] : (~ (((X354 @ (comp @ X368 @ X371) @ (sub @ X370 @ X371) @ X369)) = $true) | (((X354 @ X368 @ X370 @ (comp @ X371 @ X369))) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : (subst > term > term)] : (~ ! [X375 : term] : ((((X373 @ id @ (X374 @ id @ X375) @ id)) = $true) | ~ (((X373 @ id @ X375 @ id)) = $true)) | (((X373 @ id @ (lam @ (X374 @ sh @ one)) @ id)) = $true) | ~ ! [X376 : subst,X377 : subst,X378 : term] : (((X374 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377))) = ((sub @ (X374 @ X376 @ X378) @ X377)))) | ~ ! [X379 : subst,X380 : term,X381 : subst,X382 : subst] : (~ (((X373 @ (comp @ X381 @ X379) @ (sub @ X380 @ X379) @ X382)) = $true) | ($true = ((X373 @ X381 @ X380 @ (comp @ X379 @ X382))))) | ~ ! [X383 : term] : (~ (((X373 @ id @ X383 @ id)) = $true) | (((X373 @ id @ (sub @ X372 @ (push @ X383 @ id)) @ id)) = $true)) | ~ ! [X384 : subst,X385 : subst,X386 : subst,X387 : term] : (~ (((X373 @ X384 @ X387 @ (comp @ X386 @ X385))) = $true) | (((X373 @ (comp @ X384 @ X386) @ (sub @ X387 @ X386) @ X385)) = $true)) | (((X373 @ id @ (lam @ X372) @ id)) = $true))) & (one = ((d2term @ d_one))) & ((hoasapinj1 = $true) <=> ! [X388 : term,X389 : term,X390 : term,X391 : term] : ((((ap @ (sub @ X389 @ id) @ X388)) != ((ap @ (sub @ X391 @ id) @ X390))) | (X389 = X391))) & (! [X392 : (subst > term > subst > $o),X393 : term] : (~ ! [X394 : (subst > term > term),X395 : term] : (~ ! [X396 : term,X397 : subst,X398 : subst] : (((sub @ X395 @ (push @ (sub @ X396 @ X397) @ (comp @ X398 @ X397)))) = ((X394 @ (comp @ X398 @ X397) @ (sub @ X396 @ X397)))) | (((X392 @ id @ (lam @ (X394 @ sh @ one)) @ id)) = $true) | ~ ! [X399 : term,X400 : subst,X401 : subst] : (((sub @ (sub @ X395 @ (push @ X399 @ X401)) @ X400)) = ((sub @ (X394 @ X401 @ X399) @ X400))) | ~ ! [X402 : term] : (~ (((X392 @ id @ X402 @ id)) = $true) | (((X392 @ id @ (X394 @ id @ X402) @ id)) = $true))) | ~ ! [X403 : term] : (~ ($true = ((X392 @ id @ X403 @ id))) | (((X392 @ id @ (sub @ X393 @ (push @ X403 @ id)) @ id)) = $true)) | (((X392 @ id @ (lam @ (sub @ X393 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (! [X404 : term,X405 : subst,X406 : (term > $o)] : ~ ! [X407 : (term > $o)] : ~ ! [X408 : term] : (((X407 @ X408)) = ((X406 @ (sub @ X408 @ (push @ X404 @ X405))))) <=> (pushprop_lem0 = $true)) & ! [X409 : subst] : ? [X410 : d_subst] : (((d2subst @ X410)) = X409) & (hoasinduction_lem1 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X411 : (subst > term > subst > $o)] : ~ ! [X412 : (term > $o)] : ~ ! [X413 : term] : (((X411 @ id @ X413 @ id)) = ((X412 @ X413))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & ((! [X414 : subst] : (((comp @ id @ X414)) = X414) & ! [X415 : subst] : (((comp @ X415 @ id)) = X415)) <=> (substmonoid = $true)) & (ulamvarind = $true) & (pushprop_gthm = $true) & ((hoaslaminj = $true) <=> ! [X416 : (subst > term > term),X417 : subst,X418 : term,X419 : (subst > term > term)] : ((((lam @ (X416 @ sh @ one))) != ((lam @ (X419 @ sh @ one)))) | (((X419 @ X417 @ X418)) = ((X416 @ X417 @ X418))) | ~ ! [X420 : subst,X421 : term,X422 : subst] : (((X416 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X416 @ X422 @ X421) @ X420))) | ~ ! [X423 : subst,X424 : term,X425 : subst] : (((X419 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425))) = ((sub @ (X419 @ X423 @ X424) @ X425))))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X426 : (subst > term > subst > $o),X427 : term,X428 : (term > $o),X429 : term] : ((((X428 @ (ap @ X427 @ X429))) = $true) | ~ ! [X430 : term] : (((X426 @ id @ X430 @ id)) = ((X428 @ X430))) | ~ ! [X431 : term,X432 : term] : (~ (((X426 @ id @ X431 @ id)) = $true) | ~ ($true = ((X426 @ id @ X432 @ id))) | (((X426 @ id @ (ap @ (sub @ X431 @ id) @ X432) @ id)) = $true)) | ~ ($true = ((X428 @ X429))) | ~ (((X428 @ X427)) = $true) | ~ ! [X433 : subst,X434 : subst,X435 : subst,X436 : term] : ((((X426 @ X434 @ X436 @ (comp @ X433 @ X435))) = $true) | ~ (((X426 @ (comp @ X434 @ X433) @ (sub @ X436 @ X433) @ X435)) = $true)) | ~ ! [X437 : subst,X438 : term,X439 : subst,X440 : subst] : (~ (((X426 @ X439 @ X438 @ (comp @ X437 @ X440))) = $true) | (((X426 @ (comp @ X439 @ X437) @ (sub @ X438 @ X437) @ X440)) = $true)))) & ((hoaslamnotap = $true) <=> ! [X441 : (subst > term > term),X442 : term,X443 : term] : ((((ap @ (sub @ X443 @ id) @ X442)) != ((lam @ (X441 @ sh @ one)))) | ~ ! [X444 : subst,X445 : term,X446 : subst] : (((sub @ (X441 @ X444 @ X445) @ X446)) = ((X441 @ (comp @ X444 @ X446) @ (sub @ X445 @ X446)))))) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((! [X447 : term] : ~ ! [X448 : (subst > term > term)] : ~ ! [X449 : subst,X450 : term] : (((sub @ X447 @ (push @ X450 @ X449))) = ((X448 @ X449 @ X450))) => (! [X451 : term] : (((sub @ X451 @ id)) = X451) => ! [X452 : (subst > term > subst > $o),X453 : term,X454 : (term > $o)] : (~ ! [X455 : term] : (((X454 @ X455)) = ((X452 @ id @ X455 @ id))) | (((X454 @ (lam @ X453))) = $true) | ~ ! [X456 : (subst > term > term)] : (~ ! [X457 : term,X458 : subst,X459 : subst] : (((X456 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458))) = ((sub @ (X456 @ X459 @ X457) @ X458))) | ~ ! [X460 : term] : (~ (((X452 @ id @ X460 @ id)) = $true) | (((X452 @ id @ (X456 @ id @ X460) @ id)) = $true)) | (((X452 @ id @ (lam @ (X456 @ sh @ one)) @ id)) = $true)) | ~ ! [X461 : term] : (($true = ((X454 @ (sub @ X453 @ (push @ X461 @ id))))) | ~ (((X454 @ X461)) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X462 : (subst > term > subst > $o)] : ~ ! [X463 : (term > $o)] : ~ ! [X464 : term] : (((X462 @ id @ X464 @ id)) = ((X463 @ X464))) => (! [X465 : (term > $o),X466 : term] : (~ ! [X467 : term] : (~ ! [X468 : term] : ((((X465 @ (sub @ X467 @ (push @ X468 @ id)))) = $true) | ~ (((X465 @ X468)) = $true)) | (((X465 @ (lam @ X467))) = $true)) | ~ ! [X469 : term,X470 : term] : (~ (((X465 @ X469)) = $true) | ~ (((X465 @ X470)) = $true) | ($true = ((X465 @ (ap @ X469 @ X470))))) | (((X465 @ X466)) = $true) | ~ ! [X471 : term] : (~ (((var @ X471)) = $true) | (((X465 @ X471)) = $true))) => (! [X472 : term] : (((sub @ X472 @ id)) = X472) => (! [X473 : (term > $o),X474 : (subst > term > subst > $o),X475 : term] : (~ ! [X476 : term] : ((((X473 @ (sub @ X475 @ (push @ X476 @ id)))) = $true) | ~ (((X473 @ X476)) = $true)) | (((X473 @ (lam @ X475))) = $true) | ~ ! [X477 : (subst > term > term)] : (~ ! [X478 : term] : (~ (((X474 @ id @ X478 @ id)) = $true) | (((X474 @ id @ (X477 @ id @ X478) @ id)) = $true)) | ($true = ((X474 @ id @ (lam @ (X477 @ sh @ one)) @ id))) | ~ ! [X479 : term,X480 : subst,X481 : subst] : (((sub @ (X477 @ X481 @ X479) @ X480)) = ((X477 @ (comp @ X481 @ X480) @ (sub @ X479 @ X480))))) | ~ ! [X482 : term] : (((X474 @ id @ X482 @ id)) = ((X473 @ X482)))) => ! [X483 : term,X484 : (subst > term > subst > $o)] : ((((X484 @ id @ X483 @ id)) = $true) | ~ ! [X485 : term,X486 : term] : (~ (((X484 @ id @ X486 @ id)) = $true) | ~ (((X484 @ id @ X485 @ id)) = $true) | ($true = ((X484 @ id @ (ap @ (sub @ X486 @ id) @ X485) @ id)))) | ~ ! [X487 : term,X488 : subst,X489 : subst,X490 : subst] : (($true = ((X484 @ X489 @ X487 @ (comp @ X490 @ X488)))) | ~ (((X484 @ (comp @ X489 @ X490) @ (sub @ X487 @ X490) @ X488)) = $true)) | ~ ! [X491 : (subst > term > term)] : ((((X484 @ id @ (lam @ (X491 @ sh @ one)) @ id)) = $true) | ~ ! [X492 : term] : (($true = ((X484 @ id @ (X491 @ id @ X492) @ id))) | ~ (((X484 @ id @ X492 @ id)) = $true)) | ~ ! [X493 : subst,X494 : term,X495 : subst] : (((sub @ (X491 @ X495 @ X494) @ X493)) = ((X491 @ (comp @ X495 @ X493) @ (sub @ X494 @ X493))))) | ~ ! [X496 : term] : ((((X484 @ id @ X496 @ id)) = $true) | ~ (((var @ (sub @ X496 @ id))) = $true)) | ~ ! [X497 : subst,X498 : subst,X499 : term,X500 : subst] : (~ (((X484 @ X500 @ X499 @ (comp @ X498 @ X497))) = $true) | ($true = ((X484 @ (comp @ X500 @ X498) @ (sub @ X499 @ X498) @ X497)))))))))) & (! [X501 : (term > $o),X502 : (subst > term > subst > $o),X503 : term] : ((((X501 @ (lam @ X503))) = $true) | ~ ! [X504 : term] : (($true = ((X501 @ (sub @ X503 @ (push @ X504 @ id))))) | ~ (((X501 @ X504)) = $true)) | ~ ! [X505 : (subst > term > term)] : ((((X502 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true) | ~ ! [X506 : term,X507 : subst,X508 : subst] : (((sub @ (X505 @ X507 @ X506) @ X508)) = ((X505 @ (comp @ X507 @ X508) @ (sub @ X506 @ X508)))) | ~ ! [X509 : term] : (~ (((X502 @ id @ X509 @ id)) = $true) | (((X502 @ id @ (X505 @ id @ X509) @ id)) = $true))) | ~ ! [X510 : term] : (((X501 @ X510)) = ((X502 @ id @ X510 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem3v2 = $true) & ((hoasapinj1_lthm = $true) <=> (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : term,X513 : term,X514 : term,X515 : term] : ((((ap @ X515 @ X512)) != ((ap @ X513 @ X514))) | (X513 = X515)) => ! [X516 : term,X517 : term,X518 : term,X519 : term] : ((X517 = X519) | (((ap @ (sub @ X517 @ id) @ X516)) != ((ap @ (sub @ X519 @ id) @ X518))))))) & (! [X520 : term,X521 : term] : ((((sub @ X521 @ sh)) != ((sub @ X520 @ sh))) | (X520 = X521)) <=> (shinj = $true)) & ((! [X522 : subst] : (((comp @ id @ X522)) = X522) => (! [X523 : subst] : (((comp @ X523 @ id)) = X523) => (! [X524 : subst] : (((comp @ X524 @ id)) = X524) & ! [X525 : subst] : (((comp @ id @ X525)) = X525)))) <=> (substmonoid_lthm = $true)) & (substmonoid_gthm = $true) & (ulamvarsh = $true) & (axmap = $true) & ((apinj2 = $true) <=> ! [X526 : term,X527 : term,X528 : term,X529 : term] : ((((ap @ X527 @ X526)) != ((ap @ X528 @ X529))) | (X526 = X529))) & (pushprop_lem0_gthm = $true) & (! [X530 : term,X531 : (subst > term > subst > $o)] : ((((X531 @ id @ X530 @ id)) = $true) | ~ ! [X532 : (subst > term > term)] : (~ ! [X533 : term,X534 : subst,X535 : subst] : (((sub @ (X532 @ X534 @ X533) @ X535)) = ((X532 @ (comp @ X534 @ X535) @ (sub @ X533 @ X535)))) | (((X531 @ id @ (lam @ (X532 @ sh @ one)) @ id)) = $true) | ~ ! [X536 : term] : (~ (((X531 @ id @ X536 @ id)) = $true) | ($true = ((X531 @ id @ (X532 @ id @ X536) @ id))))) | ~ ! [X537 : term,X538 : term] : (~ (((X531 @ id @ X537 @ id)) = $true) | (((X531 @ id @ (ap @ (sub @ X537 @ id) @ X538) @ id)) = $true) | ~ ($true = ((X531 @ id @ X538 @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X539 : subst,X540 : (term > $o),X541 : term,X542 : (term > $o)] : ((((X540 @ one)) = $true) | ~ (((X542 @ X541)) = $true) | ~ ! [X543 : term] : (((X540 @ X543)) = ((X542 @ (sub @ X543 @ (push @ X541 @ X539)))))) <=> (pushprop_lem1v2 = $true)) & (axclos = $true) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (ulamvar1 = $true) & (pushprop_lthm_orig = $true) & (axvarshift = $true) & (! [X544 : term] : ~ ! [X545 : (subst > term > term)] : ~ ! [X546 : term,X547 : subst] : (((X545 @ X547 @ X546)) = ((sub @ X544 @ (push @ X546 @ X547)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasapnotvar_gthm = $true) & ((termmset_lthm = $true) <=> (! [X548 : term] : (((sub @ X548 @ id)) = X548) => ! [X549 : term] : (((sub @ X549 @ id)) = X549)))),
% 6.12/1.29 inference(fool_elimination,[],[f6])).
% 6.12/1.29 thf(f8,plain,(
% 6.12/1.29 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.12/1.29 inference(flattening,[],[f5])).
% 6.12/1.29 thf(f9,plain,(
% 6.12/1.29 (pushprop_lem2v2_lthm = $true) & (hoaslamnotvar = $true) & (hoasapnotvar = $true) & ((! [X0 : term,X2 : term,X1 : term,X3 : term] : ((((ap @ X2 @ X0)) != ((ap @ X1 @ X3))) | (X0 = X3)) => ! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4))))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X8 : (term > $o),X9 : (subst > term > subst > $o),X10 : term] : (~ ! [X11 : (subst > term > term)] : (($true = ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) | ~ ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))) | ~ ! [X15 : term] : (~ (((X9 @ id @ X15 @ id)) = $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true))) | ~ ! [X16 : subst,X17 : subst,X18 : subst,X19 : term] : (~ (((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) = $true) | (((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) = $true)) | ~ ! [X20 : subst,X21 : subst,X22 : subst,X23 : term] : (~ ($true = ((X9 @ X21 @ X23 @ (comp @ X22 @ X20)))) | ($true = ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20)))) | ~ ! [X24 : term] : (~ (((X8 @ X24)) = $true) | ($true = ((X8 @ (sub @ X10 @ (push @ X24 @ id)))))) | ($true = ((X8 @ (lam @ X10)))) | ~ ! [X25 : term] : (((X8 @ X25)) = ((X9 @ id @ X25 @ id))))) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (hoaslamnotap_gthm = $true) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ~ ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one)))) & ((hoasinduction_lem2 = $true) <=> ! [X34 : (subst > term > subst > $o),X35 : term,X36 : term] : (~ (((X34 @ id @ X35 @ id)) = $true) | ~ ! [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (~ (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) = $true) | ($true = ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37)))) | ~ ! [X41 : subst,X42 : term,X43 : subst,X44 : subst] : (~ (((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) = $true) | (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) = $true)) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | ~ (((X34 @ id @ X36 @ id)) = $true) | ~ ! [X45 : term,X46 : term] : (~ ($true = ((X34 @ id @ X45 @ id))) | ($true = ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) | ~ (((X34 @ id @ X46 @ id)) = $true)))) & (! [X47 : term] : ~ ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem1_gthm = $true) & ((! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X51 : (subst > term > subst > $o),X52 : term] : (~ ! [X53 : (subst > term > term)] : (~ ! [X54 : term] : (~ (((X51 @ id @ X54 @ id)) = $true) | (((X51 @ id @ (X53 @ id @ X54) @ id)) = $true)) | ~ ! [X55 : subst,X57 : subst,X56 : term] : (((sub @ (X53 @ X57 @ X56) @ X55)) = ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true)) | ($true = ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id))) | ~ ! [X58 : term] : (~ (((X51 @ id @ X58 @ id)) = $true) | (((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true))) => ! [X59 : (subst > term > subst > $o),X60 : term] : (~ ! [X61 : term] : (~ (((X59 @ id @ X61 @ id)) = $true) | (((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) = $true)) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~ (((X59 @ id @ X63 @ id)) = $true) | (((X59 @ id @ (X62 @ id @ X63) @ id)) = $true)) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true)) | (((X59 @ id @ (lam @ X60) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((induction2lem = $true) <=> ! [X69 : (term > $o),X70 : subst,X71 : term] : (~ ! [X72 : term,X73 : term] : (~ (((X69 @ X73)) = $true) | ~ (((X69 @ X72)) = $true) | (((X69 @ (ap @ X73 @ X72))) = $true)) | ~ ! [X74 : term] : ((((X69 @ (lam @ X74))) = $true) | ~ ! [X75 : term] : ((((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true) | ~ ($true = ((X69 @ X75))))) | ~ ! [X76 : term] : (~ (((var @ X76)) = $true) | ($true = ((X69 @ (sub @ X76 @ X70))))) | (((X69 @ (sub @ X71 @ X70))) = $true))) & ! [X77 : d_subst,X78 : d_subst] : ((((d2subst @ X78)) = ((d2subst @ X77))) => (X77 = X78)) & (axapp = $true) & (induction2lem_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & ((pushprop_lem1 = $true) <=> ! [X83 : (term > $o),X84 : term,X85 : term,X86 : (term > $o),X87 : subst] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ~ ($true = ((X83 @ X84))))) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true)) & ((hoasinduction = $true) <=> ! [X90 : term,X91 : (subst > term > subst > $o)] : (~ ! [X92 : term] : (($true = ((X91 @ id @ X92 @ id))) | ~ (((var @ (sub @ X92 @ id))) = $true)) | ~ ! [X93 : term,X94 : term] : ((((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) = $true) | ~ (((X91 @ id @ X94 @ id)) = $true) | ~ (((X91 @ id @ X93 @ id)) = $true)) | ~ ! [X95 : (subst > term > term)] : (~ ! [X96 : term] : ((((X91 @ id @ (X95 @ id @ X96) @ id)) = $true) | ~ (((X91 @ id @ X96 @ id)) = $true)) | ~ ! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) | ($true = ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))) | (((X91 @ id @ X90 @ id)) = $true) | ~ ! [X100 : subst,X101 : subst,X102 : subst,X103 : term] : (~ (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) = $true) | (((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) = $true)) | ~ ! [X104 : term,X105 : subst,X106 : subst,X107 : subst] : (~ (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) = $true) | (((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) = $true)))) & ((! [X108 : (subst > term > subst > $o)] : ~ ! [X109 : (term > $o)] : ~ ! [X110 : term] : (((X109 @ X110)) = ((X108 @ id @ X110 @ id))) => (! [X111 : term,X112 : (term > $o)] : (~ ! [X113 : term] : ((((X112 @ (lam @ X113))) = $true) | ~ ! [X114 : term] : (~ (((X112 @ X114)) = $true) | (((X112 @ (sub @ X113 @ (push @ X114 @ id)))) = $true))) | ~ ! [X115 : term] : (~ (((var @ X115)) = $true) | (((X112 @ X115)) = $true)) | (((X112 @ X111)) = $true) | ~ ! [X116 : term,X117 : term] : (~ (((X112 @ X117)) = $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | ~ (((X112 @ X116)) = $true))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X119 : (term > $o),X120 : term,X121 : (subst > term > subst > $o)] : (~ ! [X122 : term] : (~ (((X119 @ X122)) = $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true)) | ~ ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) | ~ ! [X124 : (subst > term > term)] : (~ ! [X125 : term] : ((((X121 @ id @ (X124 @ id @ X125) @ id)) = $true) | ~ ($true = ((X121 @ id @ X125 @ id)))) | ~ ! [X128 : subst,X126 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) = ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)))) | (((X119 @ (lam @ X120))) = $true)) => ! [X129 : (subst > term > subst > $o),X130 : term] : (($true = ((X129 @ id @ X130 @ id))) | ~ ! [X131 : term,X132 : term] : ((((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) = $true) | ~ (((X129 @ id @ X132 @ id)) = $true) | ~ (((X129 @ id @ X131 @ id)) = $true)) | ~ ! [X133 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) = $true) | ~ ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | ~ (((X129 @ id @ X134 @ id)) = $true)) | ~ ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (lamnotvar = $true) & (induction2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & ! [X144 : d_term] : (d_one = X144) & ((hoasinduction_lem3a = $true) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : (~ ! [X147 : (subst > term > term)] : (($true = ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) | ~ ! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) | ~ ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | ~ (((X146 @ id @ X151 @ id)) = $true))) | ~ ! [X152 : term] : ((((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) = $true) | ~ (((X146 @ id @ X152 @ id)) = $true)) | (((X146 @ id @ (lam @ X145) @ id)) = $true))) & ((hoasinduction_lem3aa = $true) <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (~ ! [X155 : term] : (~ (((X153 @ id @ X155 @ id)) = $true) | ($true = ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))) | ~ ! [X156 : (subst > term > term)] : (~ ! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) | ~ ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ~ ($true = ((X153 @ id @ X160 @ id)))) | (((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) = $true)) | ($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))))) & (hoaslamnotvar_lthm = $true) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X161 : term,X162 : (subst > term > subst > $o)] : ((((X162 @ id @ (lam @ (sub @ X161 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X163 : (subst > term > term)] : (~ ! [X165 : subst,X164 : subst,X166 : term] : (((X163 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) = ((sub @ (X163 @ X164 @ X166) @ X165))) | ($true = ((X162 @ id @ (lam @ (X163 @ sh @ one)) @ id))) | ~ ! [X167 : term] : (~ ($true = ((X162 @ id @ X167 @ id))) | (((X162 @ id @ (X163 @ id @ X167) @ id)) = $true))) | ~ ! [X168 : term] : (~ ($true = ((X162 @ id @ X168 @ id))) | ($true = ((X162 @ id @ (sub @ X161 @ (push @ X168 @ id)) @ id)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X169 : term] : ~ ! [X170 : (subst > term > term)] : ~ ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171))))) & ((! [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) = X173) => (! [X176 : term,X175 : subst] : (((comp @ sh @ (push @ X176 @ X175))) = X175) => ! [X177 : (term > $o),X178 : term,X179 : term,X180 : (term > $o),X181 : subst] : (~ (((X177 @ X178)) = $true) | ($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181)))))))) <=> (pushprop_lem1_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X183 : term,X182 : subst] : (((sub @ one @ (push @ X183 @ X182))) = X183) => (! [X185 : term,X184 : subst] : (((comp @ sh @ (push @ X185 @ X184))) = X184) => (! [X186 : subst] : (((comp @ X186 @ id)) = X186) => (! [X187 : term,X188 : (term > $o)] : (~ ! [X189 : term,X190 : term] : (~ (((X188 @ X189)) = $true) | (((X188 @ (ap @ X190 @ X189))) = $true) | ~ (((X188 @ X190)) = $true)) | ~ ! [X191 : term] : (~ (((X188 @ X191)) = $true) | (((X188 @ (lam @ X191))) = $true)) | ($true = ((X188 @ X187))) | ~ ! [X192 : term] : ((((X188 @ X192)) = $true) | ~ (((var @ X192)) = $true))) => ! [X193 : term,X194 : (term > $o),X195 : subst] : (~ ! [X196 : term] : (~ ! [X197 : term] : ((((X194 @ (sub @ X196 @ (push @ X197 @ id)))) = $true) | ~ (((X194 @ X197)) = $true)) | (((X194 @ (lam @ X196))) = $true)) | ~ ! [X198 : term,X199 : term] : (~ (((X194 @ X199)) = $true) | ~ ($true = ((X194 @ X198))) | (((X194 @ (ap @ X198 @ X199))) = $true)) | ~ ! [X200 : term] : ((((X194 @ (sub @ X200 @ X195))) = $true) | ~ (((var @ X200)) = $true)) | (((X194 @ (sub @ X193 @ X195))) = $true))))))) & (pushprop_lem2v2_gthm = $true) & ((axvarid = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) <=> (axidr = $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X203 : term] : (((sub @ X203 @ id)) = X203) => (! [X204 : term,X205 : (subst > term > subst > $o)] : (~ ! [X206 : term] : (($true = ((X205 @ id @ (sub @ X204 @ (push @ X206 @ id)) @ id))) | ~ (((X205 @ id @ X206 @ id)) = $true)) | ~ ! [X207 : (subst > term > term)] : (~ ! [X208 : term] : (~ (((X205 @ id @ X208 @ id)) = $true) | (((X205 @ id @ (X207 @ id @ X208) @ id)) = $true)) | ($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ~ ! [X210 : term,X209 : subst,X211 : subst] : (((X207 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209))) = ((sub @ (X207 @ X211 @ X210) @ X209)))) | (((X205 @ id @ (lam @ (sub @ X204 @ (push @ one @ sh))) @ id)) = $true)) => ! [X212 : (subst > term > subst > $o),X213 : term] : (~ ! [X214 : (subst > term > term)] : (~ ! [X216 : subst,X217 : term,X215 : subst] : (((X214 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))) = ((sub @ (X214 @ X216 @ X217) @ X215))) | (((X212 @ id @ (lam @ (X214 @ sh @ one)) @ id)) = $true) | ~ ! [X218 : term] : (~ (((X212 @ id @ X218 @ id)) = $true) | (((X212 @ id @ (X214 @ id @ X218) @ id)) = $true))) | ~ ! [X219 : term] : ((((X212 @ id @ (sub @ X213 @ (push @ X219 @ id)) @ id)) = $true) | ~ (((X212 @ id @ X219 @ id)) = $true)) | (((X212 @ id @ (lam @ X213) @ id)) = $true) | ~ ! [X220 : subst,X221 : term,X222 : subst,X223 : subst] : (~ (((X212 @ X223 @ X221 @ (comp @ X222 @ X220))) = $true) | (((X212 @ (comp @ X223 @ X222) @ (sub @ X221 @ X222) @ X220)) = $true)) | ~ ! [X224 : subst,X225 : subst,X226 : term,X227 : subst] : ((((X212 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true) | ~ (((X212 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true)))))) & ((! [X228 : (term > $o),X229 : term] : (~ ! [X230 : term] : ((((X228 @ (lam @ X230))) = $true) | ~ ! [X231 : term] : ((((X228 @ (sub @ X230 @ (push @ X231 @ id)))) = $true) | ~ (((X228 @ X231)) = $true))) | (((X228 @ X229)) = $true) | ~ ! [X232 : term,X233 : term] : ((((X228 @ (ap @ X233 @ X232))) = $true) | ~ (((X228 @ X232)) = $true) | ~ ($true = ((X228 @ X233)))) | ~ ! [X234 : term] : (~ (((var @ X234)) = $true) | (((X228 @ X234)) = $true))) => (! [X235 : (subst > term > subst > $o),X236 : term,X237 : term] : (~ ($true = ((X235 @ id @ X237 @ id))) | (((X235 @ id @ (ap @ X237 @ X236) @ id)) = $true) | ~ ! [X238 : subst,X239 : subst,X240 : term,X241 : subst] : ((((X235 @ (comp @ X239 @ X238) @ (sub @ X240 @ X238) @ X241)) = $true) | ~ (((X235 @ X239 @ X240 @ (comp @ X238 @ X241))) = $true)) | ~ ! [X242 : subst,X243 : subst,X244 : term,X245 : subst] : ((((X235 @ X243 @ X244 @ (comp @ X245 @ X242))) = $true) | ~ (((X235 @ (comp @ X243 @ X245) @ (sub @ X244 @ X245) @ X242)) = $true)) | ~ (((X235 @ id @ X236 @ id)) = $true) | ~ ! [X246 : term,X247 : term] : (~ (((X235 @ id @ X247 @ id)) = $true) | (((X235 @ id @ (ap @ (sub @ X247 @ id) @ X246) @ id)) = $true) | ~ (((X235 @ id @ X246 @ id)) = $true))) => (! [X248 : (subst > term > subst > $o),X249 : term] : (~ ! [X250 : term,X251 : subst,X252 : subst,X253 : subst] : ((((X248 @ (comp @ X253 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true) | ~ (((X248 @ X253 @ X250 @ (comp @ X251 @ X252))) = $true)) | ~ ! [X254 : (subst > term > term)] : (~ ! [X255 : term] : (~ ($true = ((X248 @ id @ X255 @ id))) | (((X248 @ id @ (X254 @ id @ X255) @ id)) = $true)) | ~ ! [X258 : term,X257 : subst,X256 : subst] : (((X254 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257))) = ((sub @ (X254 @ X256 @ X258) @ X257))) | (((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true)) | ~ ! [X259 : term] : ((((X248 @ id @ (sub @ X249 @ (push @ X259 @ id)) @ id)) = $true) | ~ (((X248 @ id @ X259 @ id)) = $true)) | ($true = ((X248 @ id @ (lam @ X249) @ id))) | ~ ! [X260 : subst,X261 : subst,X262 : term,X263 : subst] : (~ ($true = ((X248 @ (comp @ X263 @ X260) @ (sub @ X262 @ X260) @ X261))) | (((X248 @ X263 @ X262 @ (comp @ X260 @ X261))) = $true))) => ! [X264 : term,X265 : (subst > term > subst > $o)] : (~ ! [X266 : subst,X267 : term,X268 : subst,X269 : subst] : ((((X265 @ X266 @ X267 @ (comp @ X268 @ X269))) = $true) | ~ (((X265 @ (comp @ X266 @ X268) @ (sub @ X267 @ X268) @ X269)) = $true)) | ~ ! [X270 : subst,X271 : term,X272 : subst,X273 : subst] : ((((X265 @ (comp @ X273 @ X270) @ (sub @ X271 @ X270) @ X272)) = $true) | ~ (((X265 @ X273 @ X271 @ (comp @ X270 @ X272))) = $true)) | ~ ! [X274 : term] : (~ (((var @ (sub @ X274 @ id))) = $true) | (((X265 @ id @ X274 @ id)) = $true)) | (((X265 @ id @ X264 @ id)) = $true) | ~ ! [X275 : (subst > term > term)] : ((((X265 @ id @ (lam @ (X275 @ sh @ one)) @ id)) = $true) | ~ ! [X276 : subst,X278 : subst,X277 : term] : (((sub @ (X275 @ X276 @ X277) @ X278)) = ((X275 @ (comp @ X276 @ X278) @ (sub @ X277 @ X278)))) | ~ ! [X279 : term] : ((((X265 @ id @ (X275 @ id @ X279) @ id)) = $true) | ~ (((X265 @ id @ X279 @ id)) = $true))) | ~ ! [X280 : term,X281 : term] : (~ ($true = ((X265 @ id @ X280 @ id))) | (((X265 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id)) = $true) | ~ (((X265 @ id @ X281 @ id)) = $true)))))) <=> (hoasinduction_lthm = $true)) & (! [X282 : (subst > term > subst > $o)] : ~ ! [X283 : (term > $o)] : ~ ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) <=> (hoasinduction_lem0 = $true)) & (((d2subst @ d_id)) = id) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lthm = $true) & (pushprop = $true) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & (hoasinduction_lem3a_gthm = $true) & (! [X287 : term,X288 : (term > $o)] : (~ ! [X289 : term] : (($true = ((X288 @ X289))) | ~ (((var @ X289)) = $true)) | (((X288 @ X287)) = $true) | ~ ! [X290 : term,X291 : term] : (($true = ((X288 @ (ap @ X290 @ X291)))) | ~ ($true = ((X288 @ X290))) | ~ (((X288 @ X291)) = $true)) | ~ ! [X292 : term] : ((((X288 @ (lam @ X292))) = $true) | ~ ! [X293 : term] : ((((X288 @ (sub @ X292 @ (push @ X293 @ id)))) = $true) | ~ (((X288 @ X293)) = $true)))) <=> (induction2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((! [X294 : term,X295 : subst] : (((sub @ one @ (push @ X294 @ X295))) = X294) => ! [X296 : term,X297 : (term > $o),X298 : subst,X299 : (term > $o)] : ((((X297 @ one)) = $true) | ~ (((X299 @ X296)) = $true) | ~ ! [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) = ((X297 @ X300))))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X301 : term,X302 : (term > $o)] : (($true = ((X302 @ X301))) | ~ ! [X303 : term] : (~ (((var @ X303)) = $true) | (((X302 @ X303)) = $true)) | ~ ! [X304 : term,X305 : term] : (~ (((X302 @ X304)) = $true) | ~ ($true = ((X302 @ X305))) | (((X302 @ (ap @ X304 @ X305))) = $true)) | ~ ! [X306 : term] : (($true = ((X302 @ (lam @ X306)))) | ~ (((X302 @ X306)) = $true))) <=> (induction = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X307 : term,X308 : subst] : (((sub @ one @ (push @ X307 @ X308))) = X307) => (! [X309 : term,X310 : subst] : (((comp @ sh @ (push @ X309 @ X310))) = X310) => (! [X311 : term,X312 : term] : ((X311 = X312) | (((lam @ X311)) != ((lam @ X312)))) => ! [X316 : (subst > term > term),X313 : (subst > term > term),X315 : subst,X314 : term] : ((((X316 @ X315 @ X314)) = ((X313 @ X315 @ X314))) | ~ ! [X321 : subst,X322 : term,X320 : subst] : (((sub @ (X313 @ X320 @ X322) @ X321)) = ((X313 @ (comp @ X320 @ X321) @ (sub @ X322 @ X321)))) | (((lam @ (X316 @ sh @ one))) != ((lam @ (X313 @ sh @ one)))) | ~ ! [X318 : subst,X319 : term,X317 : subst] : (((X316 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) = ((sub @ (X316 @ X318 @ X319) @ X317)))))))) & ! [X324 : d_term,X323 : d_term] : ((((d2term @ X323)) = ((d2term @ X324))) => (X323 = X324)) & (hoasinduction_lem2_gthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2subst @ d_id)) = sh) & ((axvarcons = $true) <=> ! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326)) & ((! [X327 : term] : (((sub @ X327 @ id)) = X327) => (! [X328 : (term > $o),X329 : term,X330 : subst] : (~ ! [X331 : term] : ((((X328 @ (sub @ X331 @ X330))) = $true) | ~ (((var @ X331)) = $true)) | ~ ! [X332 : term,X333 : term] : (~ (((X328 @ X333)) = $true) | ~ (((X328 @ X332)) = $true) | (((X328 @ (ap @ X332 @ X333))) = $true)) | (((X328 @ (sub @ X329 @ X330))) = $true) | ~ ! [X334 : term] : (~ ! [X335 : term] : ((((X328 @ (sub @ X334 @ (push @ X335 @ id)))) = $true) | ~ (((X328 @ X335)) = $true)) | (((X328 @ (lam @ X334))) = $true))) => ! [X336 : (term > $o),X337 : term] : ((((X336 @ X337)) = $true) | ~ ! [X338 : term] : (~ ! [X339 : term] : (~ ($true = ((X336 @ X339))) | ($true = ((X336 @ (sub @ X338 @ (push @ X339 @ id)))))) | (((X336 @ (lam @ X338))) = $true)) | ~ ! [X340 : term,X341 : term] : ((((X336 @ (ap @ X341 @ X340))) = $true) | ~ (((X336 @ X340)) = $true) | ~ ($true = ((X336 @ X341)))) | ~ ! [X342 : term] : (~ (((var @ X342)) = $true) | ($true = ((X336 @ X342))))))) <=> (induction2_lthm = $true)) & ((! [X343 : term] : (((sub @ X343 @ id)) = X343) => ! [X344 : (subst > term > subst > $o),X345 : (term > $o),X346 : term] : (~ ! [X347 : term] : (((X345 @ X347)) = ((X344 @ id @ X347 @ id))) | (((X345 @ (lam @ X346))) = $true) | ~ ! [X348 : term] : (~ ($true = ((X345 @ X348))) | (((X345 @ (sub @ X346 @ (push @ X348 @ id)))) = $true)) | ~ ! [X349 : subst,X350 : term,X351 : subst,X352 : subst] : ((((X344 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X349)) = $true) | ~ ($true = ((X344 @ X352 @ X350 @ (comp @ X351 @ X349))))) | ~ ! [X353 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true) | ~ ! [X356 : term,X354 : subst,X355 : subst] : (((sub @ (X353 @ X354 @ X356) @ X355)) = ((X353 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355)))) | ~ ! [X357 : term] : (~ ($true = ((X344 @ id @ X357 @ id))) | (((X344 @ id @ (X353 @ id @ X357) @ id)) = $true))) | ~ ! [X358 : subst,X359 : subst,X360 : term,X361 : subst] : (~ ($true = ((X344 @ (comp @ X358 @ X361) @ (sub @ X360 @ X361) @ X359))) | (((X344 @ X358 @ X360 @ (comp @ X361 @ X359))) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X362 : term,X363 : (subst > term > subst > $o)] : (~ ! [X364 : (subst > term > term)] : (~ ! [X365 : term] : ((((X363 @ id @ (X364 @ id @ X365) @ id)) = $true) | ~ (((X363 @ id @ X365 @ id)) = $true)) | (((X363 @ id @ (lam @ (X364 @ sh @ one)) @ id)) = $true) | ~ ! [X368 : term,X366 : subst,X367 : subst] : (((sub @ (X364 @ X366 @ X368) @ X367)) = ((X364 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367))))) | ~ ! [X369 : subst,X370 : term,X371 : subst,X372 : subst] : (~ ($true = ((X363 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369) @ X372))) | (((X363 @ X371 @ X370 @ (comp @ X369 @ X372))) = $true)) | ~ ! [X373 : term] : (~ ($true = ((X363 @ id @ X373 @ id))) | ($true = ((X363 @ id @ (sub @ X362 @ (push @ X373 @ id)) @ id)))) | ~ ! [X374 : subst,X375 : subst,X376 : subst,X377 : term] : (~ (((X363 @ X374 @ X377 @ (comp @ X376 @ X375))) = $true) | (((X363 @ (comp @ X374 @ X376) @ (sub @ X377 @ X376) @ X375)) = $true)) | (((X363 @ id @ (lam @ X362) @ id)) = $true))) & (one = ((d2term @ d_one))) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) <=> (hoasapinj1 = $true)) & (! [X382 : (subst > term > subst > $o),X383 : term] : (~ ! [X384 : (subst > term > term),X385 : term] : (~ ! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) | (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) = $true) | ~ ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) | ~ ! [X392 : term] : (~ (((X382 @ id @ X392 @ id)) = $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true))) | ~ ! [X393 : term] : (~ (((X382 @ id @ X393 @ id)) = $true) | ($true = ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id)))) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) <=> (pushprop_lem0 = $true)) & ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & (hoasinduction_lem1 = $true) & (hoasinduction_lem1_lthm = $true) & (! [X401 : (subst > term > subst > $o)] : ~ ! [X402 : (term > $o)] : ~ ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & ((substmonoid = $true) <=> (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & (ulamvarind = $true) & (pushprop_gthm = $true) & (! [X407 : subst,X406 : (subst > term > term),X409 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408))) | ~ ! [X412 : subst,X411 : term,X410 : subst] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) = ((sub @ (X406 @ X412 @ X411) @ X410))) | ~ ! [X413 : subst,X414 : term,X415 : subst] : (((sub @ (X409 @ X413 @ X414) @ X415)) = ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415))))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X416 : (subst > term > subst > $o),X417 : term,X418 : (term > $o),X419 : term] : ((((X418 @ (ap @ X417 @ X419))) = $true) | ~ ! [X420 : term] : (((X418 @ X420)) = ((X416 @ id @ X420 @ id))) | ~ ! [X421 : term,X422 : term] : (~ (((X416 @ id @ X421 @ id)) = $true) | ~ (((X416 @ id @ X422 @ id)) = $true) | ($true = ((X416 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id)))) | ~ (((X418 @ X419)) = $true) | ~ (((X418 @ X417)) = $true) | ~ ! [X423 : subst,X424 : subst,X425 : subst,X426 : term] : ((((X416 @ X424 @ X426 @ (comp @ X423 @ X425))) = $true) | ~ ($true = ((X416 @ (comp @ X424 @ X423) @ (sub @ X426 @ X423) @ X425)))) | ~ ! [X427 : subst,X428 : term,X429 : subst,X430 : subst] : (~ (((X416 @ X429 @ X428 @ (comp @ X427 @ X430))) = $true) | (((X416 @ (comp @ X429 @ X427) @ (sub @ X428 @ X427) @ X430)) = $true)))) & (! [X432 : term,X431 : (subst > term > term),X433 : term] : (~ ! [X435 : term,X436 : subst,X434 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((! [X437 : term] : ~ ! [X438 : (subst > term > term)] : ~ ! [X440 : term,X439 : subst] : (((sub @ X437 @ (push @ X440 @ X439))) = ((X438 @ X439 @ X440))) => (! [X441 : term] : (((sub @ X441 @ id)) = X441) => ! [X442 : (subst > term > subst > $o),X443 : term,X444 : (term > $o)] : (~ ! [X445 : term] : (((X444 @ X445)) = ((X442 @ id @ X445 @ id))) | (((X444 @ (lam @ X443))) = $true) | ~ ! [X446 : (subst > term > term)] : (~ ! [X447 : term,X448 : subst,X449 : subst] : (((X446 @ (comp @ X449 @ X448) @ (sub @ X447 @ X448))) = ((sub @ (X446 @ X449 @ X447) @ X448))) | ~ ! [X450 : term] : (~ ($true = ((X442 @ id @ X450 @ id))) | (((X442 @ id @ (X446 @ id @ X450) @ id)) = $true)) | (((X442 @ id @ (lam @ (X446 @ sh @ one)) @ id)) = $true)) | ~ ! [X451 : term] : (($true = ((X444 @ (sub @ X443 @ (push @ X451 @ id))))) | ~ ($true = ((X444 @ X451))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lthm_3 = $true) <=> (! [X452 : (subst > term > subst > $o)] : ~ ! [X453 : (term > $o)] : ~ ! [X454 : term] : (((X452 @ id @ X454 @ id)) = ((X453 @ X454))) => (! [X455 : (term > $o),X456 : term] : (~ ! [X457 : term] : (~ ! [X458 : term] : ((((X455 @ (sub @ X457 @ (push @ X458 @ id)))) = $true) | ~ (((X455 @ X458)) = $true)) | (((X455 @ (lam @ X457))) = $true)) | ~ ! [X459 : term,X460 : term] : (~ (((X455 @ X459)) = $true) | ~ (((X455 @ X460)) = $true) | (((X455 @ (ap @ X459 @ X460))) = $true)) | ($true = ((X455 @ X456))) | ~ ! [X461 : term] : (~ (((var @ X461)) = $true) | (((X455 @ X461)) = $true))) => (! [X462 : term] : (((sub @ X462 @ id)) = X462) => (! [X463 : (term > $o),X464 : (subst > term > subst > $o),X465 : term] : (~ ! [X466 : term] : ((((X463 @ (sub @ X465 @ (push @ X466 @ id)))) = $true) | ~ (((X463 @ X466)) = $true)) | (((X463 @ (lam @ X465))) = $true) | ~ ! [X467 : (subst > term > term)] : (~ ! [X468 : term] : (~ ($true = ((X464 @ id @ X468 @ id))) | (((X464 @ id @ (X467 @ id @ X468) @ id)) = $true)) | (((X464 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true) | ~ ! [X469 : term,X471 : subst,X470 : subst] : (((X467 @ (comp @ X471 @ X470) @ (sub @ X469 @ X470))) = ((sub @ (X467 @ X471 @ X469) @ X470)))) | ~ ! [X472 : term] : (((X464 @ id @ X472 @ id)) = ((X463 @ X472)))) => ! [X473 : term,X474 : (subst > term > subst > $o)] : (($true = ((X474 @ id @ X473 @ id))) | ~ ! [X475 : term,X476 : term] : (~ (((X474 @ id @ X476 @ id)) = $true) | ~ (((X474 @ id @ X475 @ id)) = $true) | (((X474 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) = $true)) | ~ ! [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((((X474 @ X479 @ X477 @ (comp @ X480 @ X478))) = $true) | ~ (((X474 @ (comp @ X479 @ X480) @ (sub @ X477 @ X480) @ X478)) = $true)) | ~ ! [X481 : (subst > term > term)] : (($true = ((X474 @ id @ (lam @ (X481 @ sh @ one)) @ id))) | ~ ! [X482 : term] : ((((X474 @ id @ (X481 @ id @ X482) @ id)) = $true) | ~ (((X474 @ id @ X482 @ id)) = $true)) | ~ ! [X485 : subst,X484 : term,X483 : subst] : (((X481 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) = ((sub @ (X481 @ X485 @ X484) @ X483)))) | ~ ! [X486 : term] : ((((X474 @ id @ X486 @ id)) = $true) | ~ ($true = ((var @ (sub @ X486 @ id))))) | ~ ! [X487 : subst,X488 : subst,X489 : term,X490 : subst] : (~ (((X474 @ X490 @ X489 @ (comp @ X488 @ X487))) = $true) | (((X474 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X487)) = $true)))))))) & (! [X491 : (term > $o),X492 : (subst > term > subst > $o),X493 : term] : ((((X491 @ (lam @ X493))) = $true) | ~ ! [X494 : term] : ((((X491 @ (sub @ X493 @ (push @ X494 @ id)))) = $true) | ~ (((X491 @ X494)) = $true)) | ~ ! [X495 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X495 @ sh @ one)) @ id)) = $true) | ~ ! [X498 : subst,X496 : term,X497 : subst] : (((X495 @ (comp @ X497 @ X498) @ (sub @ X496 @ X498))) = ((sub @ (X495 @ X497 @ X496) @ X498))) | ~ ! [X499 : term] : (~ (((X492 @ id @ X499 @ id)) = $true) | (((X492 @ id @ (X495 @ id @ X499) @ id)) = $true))) | ~ ! [X500 : term] : (((X491 @ X500)) = ((X492 @ id @ X500 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem3v2 = $true) & ((hoasapinj1_lthm = $true) <=> (! [X501 : term] : (((sub @ X501 @ id)) = X501) => (! [X502 : term,X505 : term,X503 : term,X504 : term] : ((((ap @ X503 @ X504)) != ((ap @ X505 @ X502))) | (X503 = X505)) => ! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508))))))) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) <=> (shinj = $true)) & ((substmonoid_lthm = $true) <=> (! [X512 : subst] : (((comp @ id @ X512)) = X512) => (! [X513 : subst] : (((comp @ X513 @ id)) = X513) => (! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515))))) & (substmonoid_gthm = $true) & (ulamvarsh = $true) & (axmap = $true) & ((apinj2 = $true) <=> ! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519))) & (pushprop_lem0_gthm = $true) & (! [X520 : term,X521 : (subst > term > subst > $o)] : ((((X521 @ id @ X520 @ id)) = $true) | ~ ! [X522 : (subst > term > term)] : (~ ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) | (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true) | ~ ! [X526 : term] : (~ (((X521 @ id @ X526 @ id)) = $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true))) | ~ ! [X527 : term,X528 : term] : (~ (((X521 @ id @ X527 @ id)) = $true) | (((X521 @ id @ (ap @ (sub @ X527 @ id) @ X528) @ id)) = $true) | ~ (((X521 @ id @ X528 @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X529 : subst,X530 : (term > $o),X531 : term,X532 : (term > $o)] : ((((X530 @ one)) = $true) | ~ (((X532 @ X531)) = $true) | ~ ! [X533 : term] : (((X530 @ X533)) = ((X532 @ (sub @ X533 @ (push @ X531 @ X529)))))) <=> (pushprop_lem1v2 = $true)) & (axclos = $true) & (axassoc = $true) & (hoaslamnotap_lthm = $true) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (ulamvar1 = $true) & (pushprop_lthm_orig = $true) & (axvarshift = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X534 : term] : ~ ! [X535 : (subst > term > term)] : ~ ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537))))) & (hoasapnotvar_gthm = $true) & ((termmset_lthm = $true) <=> (! [X538 : term] : (((sub @ X538 @ id)) = X538) => ! [X539 : term] : (((sub @ X539 @ id)) = X539)))),
% 6.12/1.29 inference(rectify,[],[f7])).
% 6.12/1.29 thf(f10,plain,(
% 6.12/1.29 ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & (axassoc = $true) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & ((hoaslaminj_lthm = $true) <=> (! [X307 : term,X308 : subst] : (((sub @ one @ (push @ X307 @ X308))) = X307) => (! [X309 : term,X310 : subst] : (((comp @ sh @ (push @ X309 @ X310))) = X310) => (! [X311 : term,X312 : term] : ((X311 = X312) | (((lam @ X311)) != ((lam @ X312)))) => ! [X316 : (subst > term > term),X313 : (subst > term > term),X315 : subst,X314 : term] : ((((X316 @ X315 @ X314)) = ((X313 @ X315 @ X314))) | ~ ! [X321 : subst,X322 : term,X320 : subst] : (((sub @ (X313 @ X320 @ X322) @ X321)) = ((X313 @ (comp @ X320 @ X321) @ (sub @ X322 @ X321)))) | (((lam @ (X316 @ sh @ one))) != ((lam @ (X313 @ sh @ one)))) | ~ ! [X318 : subst,X319 : term,X317 : subst] : (((X316 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) = ((sub @ (X316 @ X318 @ X319) @ X317)))))))) & ((axvarid = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & ((! [X327 : term] : (((sub @ X327 @ id)) = X327) => (! [X330 : subst,X329 : term,X328 : (term > $o)] : (~ ! [X333 : term,X332 : term] : ((((X328 @ X332)) != $true) | (((X328 @ (ap @ X332 @ X333))) = $true) | (((X328 @ X333)) != $true)) | (((X328 @ (sub @ X329 @ X330))) = $true) | ~ ! [X334 : term] : (~ ! [X335 : term] : ((((X328 @ X335)) != $true) | (((X328 @ (sub @ X334 @ (push @ X335 @ id)))) = $true)) | (((X328 @ (lam @ X334))) = $true)) | ~ ! [X331 : term] : ((((var @ X331)) != $true) | (((X328 @ (sub @ X331 @ X330))) = $true))) => ! [X336 : (term > $o),X337 : term] : (~ ! [X340 : term,X341 : term] : ((((X336 @ X340)) != $true) | (((X336 @ (ap @ X341 @ X340))) = $true) | ($true != ((X336 @ X341)))) | (((X336 @ X337)) = $true) | ~ ! [X342 : term] : ((((var @ X342)) != $true) | ($true = ((X336 @ X342)))) | ~ ! [X338 : term] : (~ ! [X339 : term] : (($true = ((X336 @ (sub @ X338 @ (push @ X339 @ id))))) | ($true != ((X336 @ X339)))) | (((X336 @ (lam @ X338))) = $true))))) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X534 : term] : ~ ! [X535 : (subst > term > term)] : ~ ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537))))) & ((! [X108 : (subst > term > subst > $o)] : ~ ! [X109 : (term > $o)] : ~ ! [X110 : term] : (((X109 @ X110)) = ((X108 @ id @ X110 @ id))) => (! [X111 : term,X112 : (term > $o)] : (~ ! [X117 : term,X116 : term] : ((((X112 @ X117)) != $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | (((X112 @ X116)) != $true)) | (((X112 @ X111)) = $true) | ~ ! [X115 : term] : ((((var @ X115)) != $true) | (((X112 @ X115)) = $true)) | ~ ! [X113 : term] : ((((X112 @ (lam @ X113))) = $true) | ~ ! [X114 : term] : ((((X112 @ (sub @ X113 @ (push @ X114 @ id)))) = $true) | (((X112 @ X114)) != $true)))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => (! [X121 : (subst > term > subst > $o),X120 : term,X119 : (term > $o)] : (~ ! [X124 : (subst > term > term)] : (($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id))) | ~ ! [X128 : subst,X126 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) = ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ~ ! [X125 : term] : (($true != ((X121 @ id @ X125 @ id))) | (((X121 @ id @ (X124 @ id @ X125) @ id)) = $true))) | ~ ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) | (((X119 @ (lam @ X120))) = $true) | ~ ! [X122 : term] : ((((X119 @ X122)) != $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true))) => ! [X129 : (subst > term > subst > $o),X130 : term] : (~ ! [X132 : term,X131 : term] : ((((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) = $true) | (((X129 @ id @ X131 @ id)) != $true) | (((X129 @ id @ X132 @ id)) != $true)) | ~ ! [X133 : (subst > term > term)] : (~ ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))) | (((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) = $true) | ~ ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | (((X129 @ id @ X134 @ id)) != $true))) | ($true = ((X129 @ id @ X130 @ id)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & (! [X90 : term,X91 : (subst > term > subst > $o)] : (~ ! [X95 : (subst > term > term)] : (~ ! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) | ~ ! [X96 : term] : ((((X91 @ id @ X96 @ id)) != $true) | (((X91 @ id @ (X95 @ id @ X96) @ id)) = $true)) | ($true = ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))) | ~ ! [X92 : term] : (($true = ((X91 @ id @ X92 @ id))) | (((var @ (sub @ X92 @ id))) != $true)) | (((X91 @ id @ X90 @ id)) = $true) | ~ ! [X94 : term,X93 : term] : ((((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) = $true) | (((X91 @ id @ X93 @ id)) != $true) | (((X91 @ id @ X94 @ id)) != $true)) | ~ ! [X103 : term,X101 : subst,X100 : subst,X102 : subst] : ((((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) = $true) | (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) != $true)) | ~ ! [X105 : subst,X107 : subst,X104 : term,X106 : subst] : ((((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) = $true) | (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) != $true))) <=> (hoasinduction = $true)) & (pushprop_lthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_gthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (lamnotap != $true) & (! [X530 : (term > $o),X531 : term,X529 : subst,X532 : (term > $o)] : ((((X530 @ one)) = $true) | (((X532 @ X531)) != $true) | ~ ! [X533 : term] : (((X530 @ X533)) = ((X532 @ (sub @ X533 @ (push @ X531 @ X529)))))) <=> (pushprop_lem1v2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X169 : term] : ~ ! [X170 : (subst > term > term)] : ~ ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171))))) & ((substmonoid = $true) <=> (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & ((axvarcons = $true) <=> ! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326)) & (induction2_gthm = $true) & (ulamvarsh = $true) & ((apinj2 = $true) <=> ! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519))) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (hoasinduction_lem2v2_gthm = $true) & (! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) <=> (pushprop_lem1 = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X294 : term,X295 : subst] : (((sub @ one @ (push @ X294 @ X295))) = X294) => ! [X296 : term,X298 : subst,X297 : (term > $o),X299 : (term > $o)] : ((((X299 @ X296)) != $true) | ~ ! [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) = ((X297 @ X300))) | (((X297 @ one)) = $true)))) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (termmset_gthm = $true) & (! [X71 : term,X69 : (term > $o),X70 : subst] : (~ ! [X72 : term,X73 : term] : ((((X69 @ (ap @ X73 @ X72))) = $true) | (((X69 @ X72)) != $true) | (((X69 @ X73)) != $true)) | (((X69 @ (sub @ X71 @ X70))) = $true) | ~ ! [X74 : term] : (~ ! [X75 : term] : (($true != ((X69 @ X75))) | (((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true)) | (((X69 @ (lam @ X74))) = $true)) | ~ ! [X76 : term] : ((((var @ X76)) != $true) | ($true = ((X69 @ (sub @ X76 @ X70)))))) <=> (induction2lem = $true)) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem3_lthm = $true) <=> (! [X203 : term] : (((sub @ X203 @ id)) = X203) => (! [X205 : (subst > term > subst > $o),X204 : term] : (~ ! [X207 : (subst > term > term)] : (($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ~ ! [X208 : term] : ((((X205 @ id @ X208 @ id)) != $true) | (((X205 @ id @ (X207 @ id @ X208) @ id)) = $true)) | ~ ! [X210 : term,X209 : subst,X211 : subst] : (((X207 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209))) = ((sub @ (X207 @ X211 @ X210) @ X209)))) | (((X205 @ id @ (lam @ (sub @ X204 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X206 : term] : (($true = ((X205 @ id @ (sub @ X204 @ (push @ X206 @ id)) @ id))) | (((X205 @ id @ X206 @ id)) != $true))) => ! [X213 : term,X212 : (subst > term > subst > $o)] : (~ ! [X225 : subst,X227 : subst,X226 : term,X224 : subst] : ((((X212 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true) | (((X212 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) != $true)) | ~ ! [X222 : subst,X221 : term,X223 : subst,X220 : subst] : ((((X212 @ X223 @ X221 @ (comp @ X222 @ X220))) != $true) | (((X212 @ (comp @ X223 @ X222) @ (sub @ X221 @ X222) @ X220)) = $true)) | (((X212 @ id @ (lam @ X213) @ id)) = $true) | ~ ! [X219 : term] : ((((X212 @ id @ X219 @ id)) != $true) | (((X212 @ id @ (sub @ X213 @ (push @ X219 @ id)) @ id)) = $true)) | ~ ! [X214 : (subst > term > term)] : (~ ! [X216 : subst,X217 : term,X215 : subst] : (((X214 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))) = ((sub @ (X214 @ X216 @ X217) @ X215))) | (((X212 @ id @ (lam @ (X214 @ sh @ one)) @ id)) = $true) | ~ ! [X218 : term] : ((((X212 @ id @ X218 @ id)) != $true) | (((X212 @ id @ (X214 @ id @ X218) @ id)) = $true))))))) & (hoaslamnotvar = $true) & ((! [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) = X173) => (! [X176 : term,X175 : subst] : (((comp @ sh @ (push @ X176 @ X175))) = X175) => ! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)))) <=> (pushprop_lem1_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X10 : term,X9 : (subst > term > subst > $o),X8 : (term > $o)] : (~ ! [X20 : subst,X23 : term,X22 : subst,X21 : subst] : (($true = ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20))) | ($true != ((X9 @ X21 @ X23 @ (comp @ X22 @ X20))))) | ~ ! [X11 : (subst > term > term)] : (($true = ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) | ~ ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))) | ~ ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true))) | ~ ! [X18 : subst,X19 : term,X16 : subst,X17 : subst] : ((((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) = $true) | (((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) != $true)) | ($true = ((X8 @ (lam @ X10)))) | ~ ! [X24 : term] : (($true = ((X8 @ (sub @ X10 @ (push @ X24 @ id))))) | (((X8 @ X24)) != $true)) | ~ ! [X25 : term] : (((X8 @ X25)) = ((X9 @ id @ X25 @ id))))) & (hoasinduction_lem3_gthm = $true) & (axclos = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoaslamnotvar_gthm = $true) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ~ ! [X397 : (term > $o)] : ~ ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X324 : d_term,X323 : d_term] : ((((d2term @ X323)) = ((d2term @ X324))) => (X323 = X324)) & (hoasinduction_lem1v2_gthm = $true) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) <=> (shinj = $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X144 : d_term] : (d_one = X144) & (! [X363 : (subst > term > subst > $o),X362 : term] : ((((X363 @ id @ (lam @ X362) @ id)) = $true) | ~ ! [X373 : term] : (($true != ((X363 @ id @ X373 @ id))) | ($true = ((X363 @ id @ (sub @ X362 @ (push @ X373 @ id)) @ id)))) | ~ ! [X364 : (subst > term > term)] : (~ ! [X368 : term,X366 : subst,X367 : subst] : (((sub @ (X364 @ X366 @ X368) @ X367)) = ((X364 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))) | ~ ! [X365 : term] : ((((X363 @ id @ (X364 @ id @ X365) @ id)) = $true) | (((X363 @ id @ X365 @ id)) != $true)) | (((X363 @ id @ (lam @ (X364 @ sh @ one)) @ id)) = $true)) | ~ ! [X369 : subst,X370 : term,X372 : subst,X371 : subst] : ((((X363 @ X371 @ X370 @ (comp @ X369 @ X372))) = $true) | ($true != ((X363 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369) @ X372)))) | ~ ! [X377 : term,X376 : subst,X374 : subst,X375 : subst] : ((((X363 @ X374 @ X377 @ (comp @ X376 @ X375))) != $true) | (((X363 @ (comp @ X374 @ X376) @ (sub @ X377 @ X376) @ X375)) = $true))) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem1 = $true) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ~ ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one)))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X50 : term] : (((sub @ X50 @ id)) = X50) => (! [X52 : term,X51 : (subst > term > subst > $o)] : (~ ! [X53 : (subst > term > term)] : (~ ! [X54 : term] : ((((X51 @ id @ (X53 @ id @ X54) @ id)) = $true) | (((X51 @ id @ X54 @ id)) != $true)) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true) | ~ ! [X55 : subst,X57 : subst,X56 : term] : (((sub @ (X53 @ X57 @ X56) @ X55)) = ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55))))) | ($true = ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id))) | ~ ! [X58 : term] : ((((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true) | (((X51 @ id @ X58 @ id)) != $true))) => ! [X59 : (subst > term > subst > $o),X60 : term] : (~ ! [X62 : (subst > term > term)] : (~ ! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) | (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true) | ~ ! [X63 : term] : ((((X59 @ id @ (X62 @ id @ X63) @ id)) = $true) | (((X59 @ id @ X63 @ id)) != $true))) | ~ ! [X61 : term] : ((((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) = $true) | (((X59 @ id @ X61 @ id)) != $true)) | (((X59 @ id @ (lam @ X60) @ id)) = $true))))) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) <=> (axidr = $true)) & (lamnotvar = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X452 : (subst > term > subst > $o)] : ~ ! [X453 : (term > $o)] : ~ ! [X454 : term] : (((X452 @ id @ X454 @ id)) = ((X453 @ X454))) => (! [X456 : term,X455 : (term > $o)] : (~ ! [X459 : term,X460 : term] : ((((X455 @ X459)) != $true) | (((X455 @ (ap @ X459 @ X460))) = $true) | (((X455 @ X460)) != $true)) | ~ ! [X457 : term] : (~ ! [X458 : term] : ((((X455 @ X458)) != $true) | (((X455 @ (sub @ X457 @ (push @ X458 @ id)))) = $true)) | (((X455 @ (lam @ X457))) = $true)) | ~ ! [X461 : term] : ((((var @ X461)) != $true) | (((X455 @ X461)) = $true)) | ($true = ((X455 @ X456)))) => (! [X462 : term] : (((sub @ X462 @ id)) = X462) => (! [X464 : (subst > term > subst > $o),X465 : term,X463 : (term > $o)] : (~ ! [X467 : (subst > term > term)] : (~ ! [X469 : term,X471 : subst,X470 : subst] : (((X467 @ (comp @ X471 @ X470) @ (sub @ X469 @ X470))) = ((sub @ (X467 @ X471 @ X469) @ X470))) | (((X464 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true) | ~ ! [X468 : term] : ((((X464 @ id @ (X467 @ id @ X468) @ id)) = $true) | ($true != ((X464 @ id @ X468 @ id))))) | (((X463 @ (lam @ X465))) = $true) | ~ ! [X466 : term] : ((((X463 @ X466)) != $true) | (((X463 @ (sub @ X465 @ (push @ X466 @ id)))) = $true)) | ~ ! [X472 : term] : (((X464 @ id @ X472 @ id)) = ((X463 @ X472)))) => ! [X474 : (subst > term > subst > $o),X473 : term] : (~ ! [X475 : term,X476 : term] : ((((X474 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) = $true) | (((X474 @ id @ X476 @ id)) != $true) | (((X474 @ id @ X475 @ id)) != $true)) | ~ ! [X488 : subst,X489 : term,X487 : subst,X490 : subst] : ((((X474 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X487)) = $true) | (((X474 @ X490 @ X489 @ (comp @ X488 @ X487))) != $true)) | ~ ! [X486 : term] : (($true != ((var @ (sub @ X486 @ id)))) | (((X474 @ id @ X486 @ id)) = $true)) | ~ ! [X481 : (subst > term > term)] : (~ ! [X482 : term] : ((((X474 @ id @ X482 @ id)) != $true) | (((X474 @ id @ (X481 @ id @ X482) @ id)) = $true)) | ~ ! [X485 : subst,X484 : term,X483 : subst] : (((X481 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) = ((sub @ (X481 @ X485 @ X484) @ X483))) | ($true = ((X474 @ id @ (lam @ (X481 @ sh @ one)) @ id)))) | ($true = ((X474 @ id @ X473 @ id))) | ~ ! [X479 : subst,X477 : term,X478 : subst,X480 : subst] : ((((X474 @ X479 @ X477 @ (comp @ X480 @ X478))) = $true) | (((X474 @ (comp @ X479 @ X480) @ (sub @ X477 @ X480) @ X478)) != $true)))))))) & (! [X47 : term] : ~ ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (! [X162 : (subst > term > subst > $o),X161 : term] : (~ ! [X168 : term] : (($true != ((X162 @ id @ X168 @ id))) | ($true = ((X162 @ id @ (sub @ X161 @ (push @ X168 @ id)) @ id)))) | (((X162 @ id @ (lam @ (sub @ X161 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X163 : (subst > term > term)] : (~ ! [X165 : subst,X164 : subst,X166 : term] : (((X163 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) = ((sub @ (X163 @ X164 @ X166) @ X165))) | ~ ! [X167 : term] : ((((X162 @ id @ (X163 @ id @ X167) @ id)) = $true) | ($true != ((X162 @ id @ X167 @ id)))) | ($true = ((X162 @ id @ (lam @ (X163 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & (axabs = $true) & (! [X154 : term,X153 : (subst > term > subst > $o)] : (($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))) | ~ ! [X156 : (subst > term > term)] : ((((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) = $true) | ~ ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ($true != ((X153 @ id @ X160 @ id)))) | ~ ! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157)))) | ~ ! [X155 : term] : ((((X153 @ id @ X155 @ id)) != $true) | ($true = ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & (! [X35 : term,X36 : term,X34 : (subst > term > subst > $o)] : (~ ! [X43 : subst,X41 : subst,X42 : term,X44 : subst] : ((((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) != $true) | (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) = $true)) | (((X34 @ id @ X35 @ id)) != $true) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | ~ ! [X37 : subst,X40 : term,X38 : subst,X39 : subst] : (($true = ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37))) | (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) != $true)) | ~ ! [X45 : term,X46 : term] : (($true = ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) | ($true != ((X34 @ id @ X45 @ id))) | (((X34 @ id @ X46 @ id)) != $true)) | (((X34 @ id @ X36 @ id)) != $true)) <=> (hoasinduction_lem2 = $true)) & (((d2subst @ d_id)) = id) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X407 : subst,X406 : (subst > term > term),X409 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408))) | ~ ! [X412 : subst,X411 : term,X410 : subst] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) = ((sub @ (X406 @ X412 @ X411) @ X410))) | ~ ! [X413 : subst,X414 : term,X415 : subst] : (((sub @ (X409 @ X413 @ X414) @ X415)) = ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415))))) <=> (hoaslaminj = $true)) & (induction2lem_gthm = $true) & ((! [X0 : term,X2 : term,X1 : term,X3 : term] : ((((ap @ X2 @ X0)) != ((ap @ X1 @ X3))) | (X0 = X3)) => ! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4))))) <=> (hoasapinj2_lthm = $true)) & (! [X288 : (term > $o),X287 : term] : ((((X288 @ X287)) = $true) | ~ ! [X290 : term,X291 : term] : (($true = ((X288 @ (ap @ X290 @ X291)))) | (((X288 @ X291)) != $true) | ($true != ((X288 @ X290)))) | ~ ! [X289 : term] : ((((var @ X289)) != $true) | ($true = ((X288 @ X289)))) | ~ ! [X292 : term] : ((((X288 @ (lam @ X292))) = $true) | ~ ! [X293 : term] : ((((X288 @ X293)) != $true) | (((X288 @ (sub @ X292 @ (push @ X293 @ id)))) = $true)))) <=> (induction2 = $true)) & (! [X432 : term,X431 : (subst > term > term),X433 : term] : (~ ! [X435 : term,X436 : subst,X434 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) <=> (hoaslamnotap = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((termmset_lthm = $true) <=> (! [X538 : term] : (((sub @ X538 @ id)) = X538) => ! [X539 : term] : (((sub @ X539 @ id)) = X539))) & ((hoasapinj1_lthm = $true) <=> (! [X501 : term] : (((sub @ X501 @ id)) = X501) => (! [X502 : term,X505 : term,X503 : term,X504 : term] : ((((ap @ X503 @ X504)) != ((ap @ X505 @ X502))) | (X503 = X505)) => ! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508))))))) & (pushprop = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X301 : term,X302 : (term > $o)] : (($true = ((X302 @ X301))) | ~ ! [X305 : term,X304 : term] : ((((X302 @ X304)) != $true) | (((X302 @ (ap @ X304 @ X305))) = $true) | ($true != ((X302 @ X305)))) | ~ ! [X306 : term] : (($true = ((X302 @ (lam @ X306)))) | (((X302 @ X306)) != $true)) | ~ ! [X303 : term] : ((((X302 @ X303)) = $true) | (((var @ X303)) != $true))) <=> (induction = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X520 : term,X521 : (subst > term > subst > $o)] : ((((X521 @ id @ X520 @ id)) = $true) | ~ ! [X528 : term,X527 : term] : ((((X521 @ id @ (ap @ (sub @ X527 @ id) @ X528) @ id)) = $true) | (((X521 @ id @ X527 @ id)) != $true) | (((X521 @ id @ X528 @ id)) != $true)) | ~ ! [X522 : (subst > term > term)] : (~ ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) | ~ ! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) | (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (pushprop_gthm = $true) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X416 : (subst > term > subst > $o),X419 : term,X418 : (term > $o),X417 : term] : (~ ! [X426 : term,X424 : subst,X423 : subst,X425 : subst] : ((((X416 @ X424 @ X426 @ (comp @ X423 @ X425))) = $true) | ($true != ((X416 @ (comp @ X424 @ X423) @ (sub @ X426 @ X423) @ X425)))) | ~ ! [X430 : subst,X428 : term,X427 : subst,X429 : subst] : ((((X416 @ X429 @ X428 @ (comp @ X427 @ X430))) != $true) | (((X416 @ (comp @ X429 @ X427) @ (sub @ X428 @ X427) @ X430)) = $true)) | ~ ! [X420 : term] : (((X418 @ X420)) = ((X416 @ id @ X420 @ id))) | (((X418 @ X417)) != $true) | (((X418 @ X419)) != $true) | ~ ! [X421 : term,X422 : term] : ((((X416 @ id @ X422 @ id)) != $true) | (((X416 @ id @ X421 @ id)) != $true) | ($true = ((X416 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id)))) | (((X418 @ (ap @ X417 @ X419))) = $true))) & ((induction2lem_lthm = $true) <=> (! [X183 : term,X182 : subst] : (((sub @ one @ (push @ X183 @ X182))) = X183) => (! [X185 : term,X184 : subst] : (((comp @ sh @ (push @ X185 @ X184))) = X184) => (! [X186 : subst] : (((comp @ X186 @ id)) = X186) => (! [X187 : term,X188 : (term > $o)] : (($true = ((X188 @ X187))) | ~ ! [X191 : term] : ((((X188 @ (lam @ X191))) = $true) | (((X188 @ X191)) != $true)) | ~ ! [X192 : term] : ((((var @ X192)) != $true) | (((X188 @ X192)) = $true)) | ~ ! [X189 : term,X190 : term] : ((((X188 @ X189)) != $true) | (((X188 @ (ap @ X190 @ X189))) = $true) | (((X188 @ X190)) != $true))) => ! [X195 : subst,X194 : (term > $o),X193 : term] : (~ ! [X198 : term,X199 : term] : (($true != ((X194 @ X198))) | (((X194 @ (ap @ X198 @ X199))) = $true) | (((X194 @ X199)) != $true)) | (((X194 @ (sub @ X193 @ X195))) = $true) | ~ ! [X200 : term] : ((((X194 @ (sub @ X200 @ X195))) = $true) | (((var @ X200)) != $true)) | ~ ! [X196 : term] : ((((X194 @ (lam @ X196))) = $true) | ~ ! [X197 : term] : ((((X194 @ X197)) != $true) | (((X194 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))))))))) & (! [X282 : (subst > term > subst > $o)] : ~ ! [X283 : (term > $o)] : ~ ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) <=> (hoasinduction_lem0 = $true)) & (axmap = $true) & ((hoasinduction_lem3a = $true) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : ((((X146 @ id @ (lam @ X145) @ id)) = $true) | ~ ! [X152 : term] : ((((X146 @ id @ X152 @ id)) != $true) | (((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) = $true)) | ~ ! [X147 : (subst > term > term)] : (($true = ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) | ~ ! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) | ~ ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | (((X146 @ id @ X151 @ id)) != $true))))) & (! [X401 : (subst > term > subst > $o)] : ~ ! [X402 : (term > $o)] : ~ ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ((! [X228 : (term > $o),X229 : term] : (~ ! [X234 : term] : ((((X228 @ X234)) = $true) | (((var @ X234)) != $true)) | ~ ! [X232 : term,X233 : term] : ((((X228 @ X232)) != $true) | ($true != ((X228 @ X233))) | (((X228 @ (ap @ X233 @ X232))) = $true)) | (((X228 @ X229)) = $true) | ~ ! [X230 : term] : (~ ! [X231 : term] : ((((X228 @ X231)) != $true) | (((X228 @ (sub @ X230 @ (push @ X231 @ id)))) = $true)) | (((X228 @ (lam @ X230))) = $true))) => (! [X236 : term,X237 : term,X235 : (subst > term > subst > $o)] : (($true != ((X235 @ id @ X237 @ id))) | ~ ! [X238 : subst,X241 : subst,X239 : subst,X240 : term] : ((((X235 @ X239 @ X240 @ (comp @ X238 @ X241))) != $true) | (((X235 @ (comp @ X239 @ X238) @ (sub @ X240 @ X238) @ X241)) = $true)) | ~ ! [X247 : term,X246 : term] : ((((X235 @ id @ X246 @ id)) != $true) | (((X235 @ id @ X247 @ id)) != $true) | (((X235 @ id @ (ap @ (sub @ X247 @ id) @ X246) @ id)) = $true)) | (((X235 @ id @ (ap @ X237 @ X236) @ id)) = $true) | (((X235 @ id @ X236 @ id)) != $true) | ~ ! [X244 : term,X245 : subst,X242 : subst,X243 : subst] : ((((X235 @ (comp @ X243 @ X245) @ (sub @ X244 @ X245) @ X242)) != $true) | (((X235 @ X243 @ X244 @ (comp @ X245 @ X242))) = $true))) => (! [X249 : term,X248 : (subst > term > subst > $o)] : (~ ! [X253 : subst,X251 : subst,X252 : subst,X250 : term] : ((((X248 @ X253 @ X250 @ (comp @ X251 @ X252))) != $true) | (((X248 @ (comp @ X253 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true)) | ($true = ((X248 @ id @ (lam @ X249) @ id))) | ~ ! [X259 : term] : ((((X248 @ id @ X259 @ id)) != $true) | (((X248 @ id @ (sub @ X249 @ (push @ X259 @ id)) @ id)) = $true)) | ~ ! [X263 : subst,X260 : subst,X261 : subst,X262 : term] : ((((X248 @ X263 @ X262 @ (comp @ X260 @ X261))) = $true) | ($true != ((X248 @ (comp @ X263 @ X260) @ (sub @ X262 @ X260) @ X261)))) | ~ ! [X254 : (subst > term > term)] : (~ ! [X258 : term,X257 : subst,X256 : subst] : (((X254 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257))) = ((sub @ (X254 @ X256 @ X258) @ X257))) | ~ ! [X255 : term] : ((((X248 @ id @ (X254 @ id @ X255) @ id)) = $true) | ($true != ((X248 @ id @ X255 @ id)))) | (((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true))) => ! [X264 : term,X265 : (subst > term > subst > $o)] : (~ ! [X266 : subst,X268 : subst,X267 : term,X269 : subst] : ((((X265 @ (comp @ X266 @ X268) @ (sub @ X267 @ X268) @ X269)) != $true) | (((X265 @ X266 @ X267 @ (comp @ X268 @ X269))) = $true)) | ~ ! [X270 : subst,X272 : subst,X271 : term,X273 : subst] : ((((X265 @ (comp @ X273 @ X270) @ (sub @ X271 @ X270) @ X272)) = $true) | (((X265 @ X273 @ X271 @ (comp @ X270 @ X272))) != $true)) | ~ ! [X274 : term] : ((((X265 @ id @ X274 @ id)) = $true) | (((var @ (sub @ X274 @ id))) != $true)) | ~ ! [X275 : (subst > term > term)] : (~ ! [X276 : subst,X278 : subst,X277 : term] : (((sub @ (X275 @ X276 @ X277) @ X278)) = ((X275 @ (comp @ X276 @ X278) @ (sub @ X277 @ X278)))) | (((X265 @ id @ (lam @ (X275 @ sh @ one)) @ id)) = $true) | ~ ! [X279 : term] : ((((X265 @ id @ (X275 @ id @ X279) @ id)) = $true) | (((X265 @ id @ X279 @ id)) != $true))) | ~ ! [X281 : term,X280 : term] : ((((X265 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id)) = $true) | ($true != ((X265 @ id @ X280 @ id))) | (((X265 @ id @ X281 @ id)) != $true)) | (((X265 @ id @ X264 @ id)) = $true))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X382 : (subst > term > subst > $o),X383 : term] : (~ ! [X384 : (subst > term > term),X385 : term] : (~ ! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) | ~ ! [X392 : term] : ((((X382 @ id @ X392 @ id)) != $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true)) | ~ ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) | (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) = $true)) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id))) | ~ ! [X393 : term] : (($true = ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) | (((X382 @ id @ X393 @ id)) != $true)))) & (apnotvar = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X437 : term] : ~ ! [X438 : (subst > term > term)] : ~ ! [X440 : term,X439 : subst] : (((sub @ X437 @ (push @ X440 @ X439))) = ((X438 @ X439 @ X440))) => (! [X441 : term] : (((sub @ X441 @ id)) = X441) => ! [X444 : (term > $o),X443 : term,X442 : (subst > term > subst > $o)] : (~ ! [X446 : (subst > term > term)] : ((((X442 @ id @ (lam @ (X446 @ sh @ one)) @ id)) = $true) | ~ ! [X450 : term] : (($true != ((X442 @ id @ X450 @ id))) | (((X442 @ id @ (X446 @ id @ X450) @ id)) = $true)) | ~ ! [X447 : term,X448 : subst,X449 : subst] : (((X446 @ (comp @ X449 @ X448) @ (sub @ X447 @ X448))) = ((sub @ (X446 @ X449 @ X447) @ X448)))) | (((X444 @ (lam @ X443))) = $true) | ~ ! [X451 : term] : (($true != ((X444 @ X451))) | ($true = ((X444 @ (sub @ X443 @ (push @ X451 @ id)))))) | ~ ! [X445 : term] : (((X444 @ X445)) = ((X442 @ id @ X445 @ id))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X49 : d_subst] : (d_id = X49) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X343 : term] : (((sub @ X343 @ id)) = X343) => ! [X346 : term,X344 : (subst > term > subst > $o),X345 : (term > $o)] : (~ ! [X347 : term] : (((X345 @ X347)) = ((X344 @ id @ X347 @ id))) | ~ ! [X361 : subst,X359 : subst,X358 : subst,X360 : term] : ((((X344 @ X358 @ X360 @ (comp @ X361 @ X359))) = $true) | ($true != ((X344 @ (comp @ X358 @ X361) @ (sub @ X360 @ X361) @ X359)))) | ~ ! [X351 : subst,X349 : subst,X350 : term,X352 : subst] : (($true != ((X344 @ X352 @ X350 @ (comp @ X351 @ X349)))) | (((X344 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X349)) = $true)) | ~ ! [X348 : term] : (($true != ((X345 @ X348))) | (((X345 @ (sub @ X346 @ (push @ X348 @ id)))) = $true)) | (((X345 @ (lam @ X346))) = $true) | ~ ! [X353 : (subst > term > term)] : (~ ! [X356 : term,X354 : subst,X355 : subst] : (((sub @ (X353 @ X354 @ X356) @ X355)) = ((X353 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355)))) | ~ ! [X357 : term] : (($true != ((X344 @ id @ X357 @ id))) | (((X344 @ id @ (X353 @ id @ X357) @ id)) = $true)) | (((X344 @ id @ (lam @ (X353 @ sh @ one)) @ id)) = $true))))) & (axapp = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ! [X77 : d_subst,X78 : d_subst] : ((((d2subst @ X78)) = ((d2subst @ X77))) => (X77 = X78)) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X492 : (subst > term > subst > $o),X491 : (term > $o),X493 : term] : (~ ! [X495 : (subst > term > term)] : (~ ! [X498 : subst,X496 : term,X497 : subst] : (((X495 @ (comp @ X497 @ X498) @ (sub @ X496 @ X498))) = ((sub @ (X495 @ X497 @ X496) @ X498))) | (((X492 @ id @ (lam @ (X495 @ sh @ one)) @ id)) = $true) | ~ ! [X499 : term] : ((((X492 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X492 @ id @ X499 @ id)) != $true))) | (((X491 @ (lam @ X493))) = $true) | ~ ! [X500 : term] : (((X491 @ X500)) = ((X492 @ id @ X500 @ id))) | ~ ! [X494 : term] : ((((X491 @ (sub @ X493 @ (push @ X494 @ id)))) = $true) | (((X491 @ X494)) != $true)))) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true)) & ((substmonoid_lthm = $true) <=> (! [X512 : subst] : (((comp @ id @ X512)) = X512) => (! [X513 : subst] : (((comp @ X513 @ id)) = X513) => (! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515))))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true)),
% 6.12/1.30 inference(flattening,[],[f9])).
% 6.12/1.30 thf(f11,plain,(
% 6.12/1.30 ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & (axassoc = $true) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & ((hoaslaminj_lthm = $true) <=> (((! [X316 : (subst > term > term),X313 : (subst > term > term),X314 : term,X315 : subst] : ((((lam @ (X316 @ sh @ one))) != ((lam @ (X313 @ sh @ one)))) | ? [X318 : subst,X317 : subst,X319 : term] : (((X316 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) != ((sub @ (X316 @ X318 @ X319) @ X317))) | ? [X322 : term,X321 : subst,X320 : subst] : (((sub @ (X313 @ X320 @ X322) @ X321)) != ((X313 @ (comp @ X320 @ X321) @ (sub @ X322 @ X321)))) | (((X316 @ X315 @ X314)) = ((X313 @ X315 @ X314)))) | ? [X312 : term,X311 : term] : ((((lam @ X311)) = ((lam @ X312))) & (X311 != X312))) | ? [X310 : subst,X309 : term] : (((comp @ sh @ (push @ X309 @ X310))) != X310)) | ? [X308 : subst,X307 : term] : (((sub @ one @ (push @ X307 @ X308))) != X307))) & ((axvarid = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (((! [X337 : term,X336 : (term > $o)] : (? [X341 : term,X340 : term] : ((((X336 @ (ap @ X341 @ X340))) != $true) & (((X336 @ X340)) = $true) & ($true = ((X336 @ X341)))) | ? [X342 : term] : (($true != ((X336 @ X342))) & (((var @ X342)) = $true)) | ? [X338 : term] : ((((X336 @ (lam @ X338))) != $true) & ! [X339 : term] : (($true = ((X336 @ (sub @ X338 @ (push @ X339 @ id))))) | ($true != ((X336 @ X339))))) | (((X336 @ X337)) = $true)) | ? [X330 : subst,X329 : term,X328 : (term > $o)] : (! [X331 : term] : ((((var @ X331)) != $true) | (((X328 @ (sub @ X331 @ X330))) = $true)) & ! [X334 : term] : (? [X335 : term] : ((((X328 @ X335)) = $true) & (((X328 @ (sub @ X334 @ (push @ X335 @ id)))) != $true)) | (((X328 @ (lam @ X334))) = $true)) & ! [X333 : term,X332 : term] : ((((X328 @ X332)) != $true) | (((X328 @ (ap @ X332 @ X333))) = $true) | (((X328 @ X333)) != $true)) & (((X328 @ (sub @ X329 @ X330))) != $true))) | ? [X327 : term] : (((sub @ X327 @ id)) != X327)) <=> (induction2_lthm = $true)) & (! [X534 : term] : ? [X535 : (subst > term > term)] : ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (((((! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X131 : term,X132 : term] : ((((X129 @ id @ X132 @ id)) = $true) & (((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) != $true) & (((X129 @ id @ X131 @ id)) = $true)) | ($true = ((X129 @ id @ X130 @ id))) | ? [X133 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) != $true) & ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))) & ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | (((X129 @ id @ X134 @ id)) != $true)))) | ? [X121 : (subst > term > subst > $o),X120 : term,X119 : (term > $o)] : (! [X122 : term] : ((((X119 @ X122)) != $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true)) & ! [X124 : (subst > term > term)] : (? [X126 : subst,X128 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) != ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ? [X125 : term] : ((((X121 @ id @ (X124 @ id @ X125) @ id)) != $true) & ($true = ((X121 @ id @ X125 @ id)))) | ($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)))) & ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) & (((X119 @ (lam @ X120))) != $true))) | ? [X118 : term] : (((sub @ X118 @ id)) != X118)) | ? [X112 : (term > $o),X111 : term] : (! [X117 : term,X116 : term] : ((((X112 @ X117)) != $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | (((X112 @ X116)) != $true)) & ! [X113 : term] : (? [X114 : term] : ((((X112 @ (sub @ X113 @ (push @ X114 @ id)))) != $true) & (((X112 @ X114)) = $true)) | (((X112 @ (lam @ X113))) = $true)) & (((X112 @ X111)) != $true) & ! [X115 : term] : ((((var @ X115)) != $true) | (((X112 @ X115)) = $true)))) | ? [X108 : (subst > term > subst > $o)] : ! [X109 : (term > $o)] : ? [X110 : term] : (((X109 @ X110)) != ((X108 @ id @ X110 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (ulamvar1 != $true) & (pushprop_lem3v2 = $true) & (! [X90 : term,X91 : (subst > term > subst > $o)] : (? [X95 : (subst > term > term)] : (! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) & ! [X96 : term] : ((((X91 @ id @ X96 @ id)) != $true) | (((X91 @ id @ (X95 @ id @ X96) @ id)) = $true)) & ($true != ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))) | ? [X93 : term,X94 : term] : ((((X91 @ id @ X93 @ id)) = $true) & (((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) != $true) & (((X91 @ id @ X94 @ id)) = $true)) | ? [X92 : term] : ((((var @ (sub @ X92 @ id))) = $true) & ($true != ((X91 @ id @ X92 @ id)))) | (((X91 @ id @ X90 @ id)) = $true) | ? [X104 : term,X105 : subst,X106 : subst,X107 : subst] : ((((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) != $true) & (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) = $true)) | ? [X103 : term,X100 : subst,X101 : subst,X102 : subst] : ((((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) != $true) & (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) = $true))) <=> (hoasinduction = $true)) & (pushprop_lthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_gthm = $true) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (lamnotap != $true) & (! [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) = $true) | ? [X533 : term] : (((X530 @ X533)) != ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) | (((X532 @ X531)) != $true)) <=> (pushprop_lem1v2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem1v2_gthm = $true) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & (! [X169 : term] : ? [X170 : (subst > term > term)] : ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171)))) <=> (hoasinduction_lem3v2_f = $true)) & ((substmonoid = $true) <=> (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & ((axvarcons = $true) <=> ! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326)) & (induction2_gthm = $true) & (ulamvarsh = $true) & ((apinj2 = $true) <=> ! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519))) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (hoasinduction_lem2v2_gthm = $true) & (! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) <=> (pushprop_lem1 = $true)) & ((? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ! [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) = $true) | (((X299 @ X296)) != $true) | ? [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) != ((X297 @ X300))))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (termmset_gthm = $true) & (! [X69 : (term > $o),X70 : subst,X71 : term] : (? [X73 : term,X72 : term] : ((((X69 @ X73)) = $true) & (((X69 @ X72)) = $true) & (((X69 @ (ap @ X73 @ X72))) != $true)) | (((X69 @ (sub @ X71 @ X70))) = $true) | ? [X74 : term] : ((((X69 @ (lam @ X74))) != $true) & ! [X75 : term] : (($true != ((X69 @ X75))) | (((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true))) | ? [X76 : term] : ((((var @ X76)) = $true) & ($true != ((X69 @ (sub @ X76 @ X70)))))) <=> (induction2lem = $true)) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X213 : term,X212 : (subst > term > subst > $o)] : (? [X220 : subst,X221 : term,X222 : subst,X223 : subst] : ((((X212 @ X223 @ X221 @ (comp @ X222 @ X220))) = $true) & (((X212 @ (comp @ X223 @ X222) @ (sub @ X221 @ X222) @ X220)) != $true)) | (((X212 @ id @ (lam @ X213) @ id)) = $true) | ? [X214 : (subst > term > term)] : (! [X218 : term] : ((((X212 @ id @ X218 @ id)) != $true) | (((X212 @ id @ (X214 @ id @ X218) @ id)) = $true)) & (((X212 @ id @ (lam @ (X214 @ sh @ one)) @ id)) != $true) & ! [X216 : subst,X217 : term,X215 : subst] : (((X214 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))) = ((sub @ (X214 @ X216 @ X217) @ X215)))) | ? [X219 : term] : ((((X212 @ id @ (sub @ X213 @ (push @ X219 @ id)) @ id)) != $true) & (((X212 @ id @ X219 @ id)) = $true)) | ? [X227 : subst,X225 : subst,X226 : term,X224 : subst] : ((((X212 @ X225 @ X226 @ (comp @ X227 @ X224))) != $true) & (((X212 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true))) | ? [X205 : (subst > term > subst > $o),X204 : term] : (! [X207 : (subst > term > term)] : (? [X209 : subst,X210 : term,X211 : subst] : (((X207 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209))) != ((sub @ (X207 @ X211 @ X210) @ X209))) | ($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ? [X208 : term] : ((((X205 @ id @ X208 @ id)) = $true) & (((X205 @ id @ (X207 @ id @ X208) @ id)) != $true))) & (((X205 @ id @ (lam @ (sub @ X204 @ (push @ one @ sh))) @ id)) != $true) & ! [X206 : term] : (($true = ((X205 @ id @ (sub @ X204 @ (push @ X206 @ id)) @ id))) | (((X205 @ id @ X206 @ id)) != $true)))) | ? [X203 : term] : (((sub @ X203 @ id)) != X203))) & (hoaslamnotvar = $true) & (((! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)) | ? [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) != X175)) | ? [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) != X173)) <=> (pushprop_lem1_lthm = $true)) & (! [X9 : (subst > term > subst > $o),X8 : (term > $o),X10 : term] : (? [X23 : term,X21 : subst,X20 : subst,X22 : subst] : (($true != ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20))) & ($true = ((X9 @ X21 @ X23 @ (comp @ X22 @ X20))))) | ? [X25 : term] : (((X8 @ X25)) != ((X9 @ id @ X25 @ id))) | ($true = ((X8 @ (lam @ X10)))) | ? [X19 : term,X16 : subst,X17 : subst,X18 : subst] : ((((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) = $true) & (((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) != $true)) | ? [X24 : term] : (($true != ((X8 @ (sub @ X10 @ (push @ X24 @ id))))) & (((X8 @ X24)) = $true)) | ? [X11 : (subst > term > term)] : (($true != ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) & ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true)) & ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem3_gthm = $true) & (axclos = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoaslamnotvar_gthm = $true) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ! [X323 : d_term,X324 : d_term] : ((((d2term @ X323)) != ((d2term @ X324))) | (X323 = X324)) & (hoasinduction_lem1v2_gthm = $true) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (hoasinduction_lem2_gthm = $true) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) <=> (shinj = $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X144 : d_term] : (d_one = X144) & (! [X363 : (subst > term > subst > $o),X362 : term] : (? [X376 : subst,X375 : subst,X377 : term,X374 : subst] : ((((X363 @ X374 @ X377 @ (comp @ X376 @ X375))) = $true) & (((X363 @ (comp @ X374 @ X376) @ (sub @ X377 @ X376) @ X375)) != $true)) | ? [X373 : term] : (($true != ((X363 @ id @ (sub @ X362 @ (push @ X373 @ id)) @ id))) & ($true = ((X363 @ id @ X373 @ id)))) | ? [X364 : (subst > term > term)] : ((((X363 @ id @ (lam @ (X364 @ sh @ one)) @ id)) != $true) & ! [X368 : term,X366 : subst,X367 : subst] : (((sub @ (X364 @ X366 @ X368) @ X367)) = ((X364 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))) & ! [X365 : term] : ((((X363 @ id @ (X364 @ id @ X365) @ id)) = $true) | (((X363 @ id @ X365 @ id)) != $true))) | ? [X371 : subst,X370 : term,X372 : subst,X369 : subst] : (($true = ((X363 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369) @ X372))) & (((X363 @ X371 @ X370 @ (comp @ X369 @ X372))) != $true)) | (((X363 @ id @ (lam @ X362) @ id)) = $true)) <=> (hoasinduction_lem3 = $true)) & (hoasinduction_lem1 = $true) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one)))) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X59 : (subst > term > subst > $o),X60 : term] : ((((X59 @ id @ (lam @ X60) @ id)) = $true) | ? [X61 : term] : ((((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) != $true) & (((X59 @ id @ X61 @ id)) = $true)) | ? [X62 : (subst > term > term)] : (! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & ! [X63 : term] : ((((X59 @ id @ (X62 @ id @ X63) @ id)) = $true) | (((X59 @ id @ X63 @ id)) != $true)) & (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true))) | ? [X52 : term,X51 : (subst > term > subst > $o)] : (! [X58 : term] : ((((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true) | (((X51 @ id @ X58 @ id)) != $true)) & ! [X53 : (subst > term > term)] : (? [X57 : subst,X56 : term,X55 : subst] : (((sub @ (X53 @ X57 @ X56) @ X55)) != ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true) | ? [X54 : term] : ((((X51 @ id @ X54 @ id)) = $true) & (((X51 @ id @ (X53 @ id @ X54) @ id)) != $true))) & ($true != ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id))))) | ? [X50 : term] : (((sub @ X50 @ id)) != X50))) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) <=> (axidr = $true)) & (lamnotvar = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X473 : term,X474 : (subst > term > subst > $o)] : (? [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((((X474 @ X479 @ X477 @ (comp @ X480 @ X478))) != $true) & (((X474 @ (comp @ X479 @ X480) @ (sub @ X477 @ X480) @ X478)) = $true)) | ? [X486 : term] : (($true = ((var @ (sub @ X486 @ id)))) & (((X474 @ id @ X486 @ id)) != $true)) | ($true = ((X474 @ id @ X473 @ id))) | ? [X476 : term,X475 : term] : ((((X474 @ id @ X476 @ id)) = $true) & (((X474 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) != $true) & (((X474 @ id @ X475 @ id)) = $true)) | ? [X481 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X481 @ sh @ one)) @ id))) & ! [X482 : term] : ((((X474 @ id @ X482 @ id)) != $true) | (((X474 @ id @ (X481 @ id @ X482) @ id)) = $true)) & ! [X485 : subst,X484 : term,X483 : subst] : (((X481 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) = ((sub @ (X481 @ X485 @ X484) @ X483)))) | ? [X487 : subst,X489 : term,X490 : subst,X488 : subst] : ((((X474 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X487)) != $true) & (((X474 @ X490 @ X489 @ (comp @ X488 @ X487))) = $true))) | ? [X463 : (term > $o),X464 : (subst > term > subst > $o),X465 : term] : (! [X466 : term] : ((((X463 @ X466)) != $true) | (((X463 @ (sub @ X465 @ (push @ X466 @ id)))) = $true)) & ! [X467 : (subst > term > term)] : (? [X468 : term] : (($true = ((X464 @ id @ X468 @ id))) & (((X464 @ id @ (X467 @ id @ X468) @ id)) != $true)) | ? [X470 : subst,X471 : subst,X469 : term] : (((X467 @ (comp @ X471 @ X470) @ (sub @ X469 @ X470))) != ((sub @ (X467 @ X471 @ X469) @ X470))) | (((X464 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true)) & (((X463 @ (lam @ X465))) != $true) & ! [X472 : term] : (((X464 @ id @ X472 @ id)) = ((X463 @ X472))))) | ? [X462 : term] : (((sub @ X462 @ id)) != X462)) | ? [X456 : term,X455 : (term > $o)] : (($true != ((X455 @ X456))) & ! [X457 : term] : ((((X455 @ (lam @ X457))) = $true) | ? [X458 : term] : ((((X455 @ (sub @ X457 @ (push @ X458 @ id)))) != $true) & (((X455 @ X458)) = $true))) & ! [X461 : term] : ((((var @ X461)) != $true) | (((X455 @ X461)) = $true)) & ! [X459 : term,X460 : term] : ((((X455 @ X459)) != $true) | (((X455 @ (ap @ X459 @ X460))) = $true) | (((X455 @ X460)) != $true)))) | ? [X452 : (subst > term > subst > $o)] : ! [X453 : (term > $o)] : ? [X454 : term] : (((X452 @ id @ X454 @ id)) != ((X453 @ X454))))) & (! [X47 : term] : ? [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) = ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X161 : term,X162 : (subst > term > subst > $o)] : (? [X168 : term] : (($true != ((X162 @ id @ (sub @ X161 @ (push @ X168 @ id)) @ id))) & ($true = ((X162 @ id @ X168 @ id)))) | (((X162 @ id @ (lam @ (sub @ X161 @ (push @ one @ sh))) @ id)) = $true) | ? [X163 : (subst > term > term)] : (($true != ((X162 @ id @ (lam @ (X163 @ sh @ one)) @ id))) & ! [X165 : subst,X164 : subst,X166 : term] : (((X163 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) = ((sub @ (X163 @ X164 @ X166) @ X165))) & ! [X167 : term] : ((((X162 @ id @ (X163 @ id @ X167) @ id)) = $true) | ($true != ((X162 @ id @ X167 @ id))))))) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & (axabs = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (? [X156 : (subst > term > term)] : (! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) & ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ($true != ((X153 @ id @ X160 @ id)))) & (((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) != $true)) | ($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))) | ? [X155 : term] : ((((X153 @ id @ X155 @ id)) = $true) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))))) & (! [X36 : term,X34 : (subst > term > subst > $o),X35 : term] : (? [X44 : subst,X41 : subst,X42 : term,X43 : subst] : ((((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) = $true) & (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) != $true)) | ? [X46 : term,X45 : term] : (($true != ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) & (((X34 @ id @ X46 @ id)) = $true) & ($true = ((X34 @ id @ X45 @ id)))) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | (((X34 @ id @ X35 @ id)) != $true) | (((X34 @ id @ X36 @ id)) != $true) | ? [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (($true != ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37))) & (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) = $true))) <=> (hoasinduction_lem2 = $true)) & (((d2subst @ d_id)) = id) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | ? [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) != ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) | ? [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) != ((sub @ (X406 @ X412 @ X411) @ X410))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408)))) <=> (hoaslaminj = $true)) & (induction2lem_gthm = $true) & ((! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4)))) | ? [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 != X3) & (((ap @ X2 @ X0)) = ((ap @ X1 @ X3))))) <=> (hoasapinj2_lthm = $true)) & (! [X287 : term,X288 : (term > $o)] : ((((X288 @ X287)) = $true) | ? [X291 : term,X290 : term] : (($true != ((X288 @ (ap @ X290 @ X291)))) & ($true = ((X288 @ X290))) & (((X288 @ X291)) = $true)) | ? [X289 : term] : ((((var @ X289)) = $true) & ($true != ((X288 @ X289)))) | ? [X292 : term] : (! [X293 : term] : ((((X288 @ X293)) != $true) | (((X288 @ (sub @ X292 @ (push @ X293 @ id)))) = $true)) & (((X288 @ (lam @ X292))) != $true))) <=> (induction2 = $true)) & (! [X431 : (subst > term > term),X433 : term,X432 : term] : (? [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) != ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) <=> (hoaslamnotap = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((? [X538 : term] : (((sub @ X538 @ id)) != X538) | ! [X539 : term] : (((sub @ X539 @ id)) = X539)) <=> (termmset_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508)))) | ? [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) = ((ap @ X505 @ X502))) & (X503 != X505))) | ? [X501 : term] : (((sub @ X501 @ id)) != X501))) & (pushprop = $true) & (((var @ (d2term @ d_one))) != $true) & (hoasapnotvar = $true) & (hoasapinj1_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X301 : term,X302 : (term > $o)] : (? [X306 : term] : (($true != ((X302 @ (lam @ X306)))) & (((X302 @ X306)) = $true)) | ? [X303 : term] : ((((var @ X303)) = $true) & (((X302 @ X303)) != $true)) | ($true = ((X302 @ X301))) | ? [X304 : term,X305 : term] : ((((X302 @ (ap @ X304 @ X305))) != $true) & ($true = ((X302 @ X305))) & (((X302 @ X304)) = $true))) <=> (induction = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X520 : term,X521 : (subst > term > subst > $o)] : (? [X522 : (subst > term > term)] : (! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) & ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) & (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true)) | (((X521 @ id @ X520 @ id)) = $true) | ? [X527 : term,X528 : term] : ((((X521 @ id @ X527 @ id)) = $true) & (((X521 @ id @ X528 @ id)) = $true) & (((X521 @ id @ (ap @ (sub @ X527 @ id) @ X528) @ id)) != $true)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & (pushprop_gthm = $true) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X417 : term,X416 : (subst > term > subst > $o),X419 : term,X418 : (term > $o)] : (? [X420 : term] : (((X418 @ X420)) != ((X416 @ id @ X420 @ id))) | (((X418 @ X417)) != $true) | (((X418 @ (ap @ X417 @ X419))) = $true) | (((X418 @ X419)) != $true) | ? [X421 : term,X422 : term] : (($true != ((X416 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & (((X416 @ id @ X422 @ id)) = $true) & (((X416 @ id @ X421 @ id)) = $true)) | ? [X428 : term,X427 : subst,X429 : subst,X430 : subst] : ((((X416 @ X429 @ X428 @ (comp @ X427 @ X430))) = $true) & (((X416 @ (comp @ X429 @ X427) @ (sub @ X428 @ X427) @ X430)) != $true)) | ? [X425 : subst,X426 : term,X424 : subst,X423 : subst] : ((((X416 @ X424 @ X426 @ (comp @ X423 @ X425))) != $true) & ($true = ((X416 @ (comp @ X424 @ X423) @ (sub @ X426 @ X423) @ X425)))))) & ((induction2lem_lthm = $true) <=> ((((! [X195 : subst,X194 : (term > $o),X193 : term] : ((((X194 @ (sub @ X193 @ X195))) = $true) | ? [X200 : term] : ((((X194 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | ? [X196 : term] : ((((X194 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X194 @ X197)) != $true) | (((X194 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | ? [X199 : term,X198 : term] : (($true = ((X194 @ X198))) & (((X194 @ X199)) = $true) & (((X194 @ (ap @ X198 @ X199))) != $true))) | ? [X187 : term,X188 : (term > $o)] : (($true != ((X188 @ X187))) & ! [X191 : term] : ((((X188 @ (lam @ X191))) = $true) | (((X188 @ X191)) != $true)) & ! [X189 : term,X190 : term] : ((((X188 @ X189)) != $true) | (((X188 @ (ap @ X190 @ X189))) = $true) | (((X188 @ X190)) != $true)) & ! [X192 : term] : ((((var @ X192)) != $true) | (((X188 @ X192)) = $true)))) | ? [X186 : subst] : (((comp @ X186 @ id)) != X186)) | ? [X184 : subst,X185 : term] : (((comp @ sh @ (push @ X185 @ X184))) != X184)) | ? [X183 : term,X182 : subst] : (((sub @ one @ (push @ X183 @ X182))) != X183))) & (! [X282 : (subst > term > subst > $o)] : ? [X283 : (term > $o)] : ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) <=> (hoasinduction_lem0 = $true)) & (axmap = $true) & ((hoasinduction_lem3a = $true) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : ((((X146 @ id @ (lam @ X145) @ id)) = $true) | ? [X152 : term] : ((((X146 @ id @ X152 @ id)) = $true) & (((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) != $true)) | ? [X147 : (subst > term > term)] : (! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) & ($true != ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) & ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | (((X146 @ id @ X151 @ id)) != $true))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X401 : (subst > term > subst > $o)] : ? [X402 : (term > $o)] : ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id)))) & ((((! [X264 : term,X265 : (subst > term > subst > $o)] : (? [X269 : subst,X266 : subst,X267 : term,X268 : subst] : ((((X265 @ (comp @ X266 @ X268) @ (sub @ X267 @ X268) @ X269)) = $true) & (((X265 @ X266 @ X267 @ (comp @ X268 @ X269))) != $true)) | (((X265 @ id @ X264 @ id)) = $true) | ? [X274 : term] : ((((var @ (sub @ X274 @ id))) = $true) & (((X265 @ id @ X274 @ id)) != $true)) | ? [X280 : term,X281 : term] : ((((X265 @ id @ X281 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id)) != $true) & ($true = ((X265 @ id @ X280 @ id)))) | ? [X272 : subst,X271 : term,X270 : subst,X273 : subst] : ((((X265 @ X273 @ X271 @ (comp @ X270 @ X272))) = $true) & (((X265 @ (comp @ X273 @ X270) @ (sub @ X271 @ X270) @ X272)) != $true)) | ? [X275 : (subst > term > term)] : (! [X276 : subst,X278 : subst,X277 : term] : (((sub @ (X275 @ X276 @ X277) @ X278)) = ((X275 @ (comp @ X276 @ X278) @ (sub @ X277 @ X278)))) & ! [X279 : term] : ((((X265 @ id @ (X275 @ id @ X279) @ id)) = $true) | (((X265 @ id @ X279 @ id)) != $true)) & (((X265 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true))) | ? [X248 : (subst > term > subst > $o),X249 : term] : (($true != ((X248 @ id @ (lam @ X249) @ id))) & ! [X259 : term] : ((((X248 @ id @ X259 @ id)) != $true) | (((X248 @ id @ (sub @ X249 @ (push @ X259 @ id)) @ id)) = $true)) & ! [X254 : (subst > term > term)] : ((((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true) | ? [X256 : subst,X258 : term,X257 : subst] : (((X254 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257))) != ((sub @ (X254 @ X256 @ X258) @ X257))) | ? [X255 : term] : ((((X248 @ id @ (X254 @ id @ X255) @ id)) != $true) & ($true = ((X248 @ id @ X255 @ id))))) & ! [X263 : subst,X260 : subst,X261 : subst,X262 : term] : ((((X248 @ X263 @ X262 @ (comp @ X260 @ X261))) = $true) | ($true != ((X248 @ (comp @ X263 @ X260) @ (sub @ X262 @ X260) @ X261)))) & ! [X253 : subst,X251 : subst,X252 : subst,X250 : term] : ((((X248 @ X253 @ X250 @ (comp @ X251 @ X252))) != $true) | (((X248 @ (comp @ X253 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true)))) | ? [X236 : term,X235 : (subst > term > subst > $o),X237 : term] : (! [X244 : term,X245 : subst,X242 : subst,X243 : subst] : ((((X235 @ (comp @ X243 @ X245) @ (sub @ X244 @ X245) @ X242)) != $true) | (((X235 @ X243 @ X244 @ (comp @ X245 @ X242))) = $true)) & ! [X247 : term,X246 : term] : ((((X235 @ id @ X246 @ id)) != $true) | (((X235 @ id @ X247 @ id)) != $true) | (((X235 @ id @ (ap @ (sub @ X247 @ id) @ X246) @ id)) = $true)) & ! [X238 : subst,X241 : subst,X239 : subst,X240 : term] : ((((X235 @ X239 @ X240 @ (comp @ X238 @ X241))) != $true) | (((X235 @ (comp @ X239 @ X238) @ (sub @ X240 @ X238) @ X241)) = $true)) & ($true = ((X235 @ id @ X237 @ id))) & (((X235 @ id @ (ap @ X237 @ X236) @ id)) != $true) & (((X235 @ id @ X236 @ id)) = $true))) | ? [X229 : term,X228 : (term > $o)] : (! [X230 : term] : (? [X231 : term] : ((((X228 @ X231)) = $true) & (((X228 @ (sub @ X230 @ (push @ X231 @ id)))) != $true)) | (((X228 @ (lam @ X230))) = $true)) & (((X228 @ X229)) != $true) & ! [X234 : term] : ((((X228 @ X234)) = $true) | (((var @ X234)) != $true)) & ! [X232 : term,X233 : term] : ((((X228 @ X232)) != $true) | ($true != ((X228 @ X233))) | (((X228 @ (ap @ X233 @ X232))) = $true)))) <=> (hoasinduction_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (! [X382 : (subst > term > subst > $o),X383 : term] : (? [X393 : term] : (($true != ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) & (((X382 @ id @ X393 @ id)) = $true)) | ? [X385 : term,X384 : (subst > term > term)] : (! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) & ! [X392 : term] : ((((X382 @ id @ X392 @ id)) != $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true)) & ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) & (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) != $true)) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (apnotvar = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X442 : (subst > term > subst > $o),X443 : term,X444 : (term > $o)] : ((((X444 @ (lam @ X443))) = $true) | ? [X445 : term] : (((X444 @ X445)) != ((X442 @ id @ X445 @ id))) | ? [X451 : term] : (($true != ((X444 @ (sub @ X443 @ (push @ X451 @ id))))) & ($true = ((X444 @ X451)))) | ? [X446 : (subst > term > term)] : (! [X447 : term,X448 : subst,X449 : subst] : (((X446 @ (comp @ X449 @ X448) @ (sub @ X447 @ X448))) = ((sub @ (X446 @ X449 @ X447) @ X448))) & (((X442 @ id @ (lam @ (X446 @ sh @ one)) @ id)) != $true) & ! [X450 : term] : (($true != ((X442 @ id @ X450 @ id))) | (((X442 @ id @ (X446 @ id @ X450) @ id)) = $true)))) | ? [X441 : term] : (((sub @ X441 @ id)) != X441)) | ? [X437 : term] : ! [X438 : (subst > term > term)] : ? [X440 : term,X439 : subst] : (((sub @ X437 @ (push @ X440 @ X439))) != ((X438 @ X439 @ X440))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X49 : d_subst] : (d_id = X49) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & ((? [X343 : term] : (((sub @ X343 @ id)) != X343) | ! [X346 : term,X345 : (term > $o),X344 : (subst > term > subst > $o)] : (? [X347 : term] : (((X345 @ X347)) != ((X344 @ id @ X347 @ id))) | ? [X359 : subst,X358 : subst,X361 : subst,X360 : term] : ((((X344 @ X358 @ X360 @ (comp @ X361 @ X359))) != $true) & ($true = ((X344 @ (comp @ X358 @ X361) @ (sub @ X360 @ X361) @ X359)))) | (((X345 @ (lam @ X346))) = $true) | ? [X348 : term] : (($true = ((X345 @ X348))) & (((X345 @ (sub @ X346 @ (push @ X348 @ id)))) != $true)) | ? [X353 : (subst > term > term)] : (! [X356 : term,X354 : subst,X355 : subst] : (((sub @ (X353 @ X354 @ X356) @ X355)) = ((X353 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355)))) & ! [X357 : term] : (($true != ((X344 @ id @ X357 @ id))) | (((X344 @ id @ (X353 @ id @ X357) @ id)) = $true)) & (((X344 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true)) | ? [X351 : subst,X350 : term,X352 : subst,X349 : subst] : ((((X344 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X349)) != $true) & ($true = ((X344 @ X352 @ X350 @ (comp @ X351 @ X349))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (axapp = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (one = ((d2term @ d_one))) & (ulamvarind = $true) & ! [X78 : d_subst,X77 : d_subst] : ((((d2subst @ X78)) != ((d2subst @ X77))) | (X77 = X78)) & (pushprop_lem3v2_lthm = $true) & (! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | (((X491 @ (lam @ X493))) = $true) | ? [X495 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X498 : subst,X496 : term,X497 : subst] : (((X495 @ (comp @ X497 @ X498) @ (sub @ X496 @ X498))) = ((sub @ (X495 @ X497 @ X496) @ X498))) & ! [X499 : term] : ((((X492 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X492 @ id @ X499 @ id)) != $true))) | ? [X500 : term] : (((X491 @ X500)) != ((X492 @ id @ X500 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true)) & ((substmonoid_lthm = $true) <=> (((! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515)) | ? [X513 : subst] : (((comp @ X513 @ id)) != X513)) | ? [X512 : subst] : (((comp @ id @ X512)) != X512))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem1v2 = $true)),
% 6.12/1.30 inference(ennf_transformation,[],[f10])).
% 6.12/1.30 thf(f12,plain,(
% 6.12/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & (! [X90 : term,X91 : (subst > term > subst > $o)] : (? [X95 : (subst > term > term)] : (! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) & ! [X96 : term] : ((((X91 @ id @ X96 @ id)) != $true) | (((X91 @ id @ (X95 @ id @ X96) @ id)) = $true)) & ($true != ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))) | ? [X93 : term,X94 : term] : ((((X91 @ id @ X93 @ id)) = $true) & (((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) != $true) & (((X91 @ id @ X94 @ id)) = $true)) | ? [X92 : term] : ((((var @ (sub @ X92 @ id))) = $true) & ($true != ((X91 @ id @ X92 @ id)))) | (((X91 @ id @ X90 @ id)) = $true) | ? [X104 : term,X105 : subst,X106 : subst,X107 : subst] : ((((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) != $true) & (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) = $true)) | ? [X103 : term,X100 : subst,X101 : subst,X102 : subst] : ((((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) != $true) & (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) = $true))) <=> (hoasinduction = $true)) & (ulamvar1 != $true) & (! [X534 : term] : ? [X535 : (subst > term > term)] : ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & ! [X323 : d_term,X324 : d_term] : ((((d2term @ X323)) != ((d2term @ X324))) | (X323 = X324)) & (! [X282 : (subst > term > subst > $o)] : ? [X283 : (term > $o)] : ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) <=> (hoasinduction_lem0 = $true)) & ((? [X118 : term] : (((sub @ X118 @ id)) != X118) | ? [X121 : (subst > term > subst > $o),X120 : term,X119 : (term > $o)] : (! [X122 : term] : ((((X119 @ X122)) != $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true)) & ! [X124 : (subst > term > term)] : (? [X126 : subst,X128 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) != ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ? [X125 : term] : ((((X121 @ id @ (X124 @ id @ X125) @ id)) != $true) & ($true = ((X121 @ id @ X125 @ id)))) | ($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)))) & ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) & (((X119 @ (lam @ X120))) != $true)) | ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X131 : term,X132 : term] : ((((X129 @ id @ X132 @ id)) = $true) & (((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) != $true) & (((X129 @ id @ X131 @ id)) = $true)) | ($true = ((X129 @ id @ X130 @ id))) | ? [X133 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) != $true) & ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))) & ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | (((X129 @ id @ X134 @ id)) != $true)))) | ? [X108 : (subst > term > subst > $o)] : ! [X109 : (term > $o)] : ? [X110 : term] : (((X109 @ X110)) != ((X108 @ id @ X110 @ id))) | ? [X112 : (term > $o),X111 : term] : (! [X117 : term,X116 : term] : ((((X112 @ X117)) != $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | (((X112 @ X116)) != $true)) & ! [X113 : term] : (? [X114 : term] : ((((X112 @ (sub @ X113 @ (push @ X114 @ id)))) != $true) & (((X112 @ X114)) = $true)) | (((X112 @ (lam @ X113))) = $true)) & (((X112 @ X111)) != $true) & ! [X115 : term] : ((((var @ X115)) != $true) | (((X112 @ X115)) = $true)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((? [X538 : term] : (((sub @ X538 @ id)) != X538) | ! [X539 : term] : (((sub @ X539 @ id)) = X539)) <=> (termmset_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508)))) | ? [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) = ((ap @ X505 @ X502))) & (X503 != X505)) | ? [X501 : term] : (((sub @ X501 @ id)) != X501))) & (! [X431 : (subst > term > term),X433 : term,X432 : term] : (? [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) != ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X161 : term,X162 : (subst > term > subst > $o)] : (? [X168 : term] : (($true != ((X162 @ id @ (sub @ X161 @ (push @ X168 @ id)) @ id))) & ($true = ((X162 @ id @ X168 @ id)))) | (((X162 @ id @ (lam @ (sub @ X161 @ (push @ one @ sh))) @ id)) = $true) | ? [X163 : (subst > term > term)] : (($true != ((X162 @ id @ (lam @ (X163 @ sh @ one)) @ id))) & ! [X165 : subst,X164 : subst,X166 : term] : (((X163 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) = ((sub @ (X163 @ X164 @ X166) @ X165))) & ! [X167 : term] : ((((X162 @ id @ (X163 @ id @ X167) @ id)) = $true) | ($true != ((X162 @ id @ X167 @ id))))))) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((axvarcons = $true) <=> ! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326)) & (! [X382 : (subst > term > subst > $o),X383 : term] : (? [X393 : term] : (($true != ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) & (((X382 @ id @ X393 @ id)) = $true)) | ? [X385 : term,X384 : (subst > term > term)] : (! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) & ! [X392 : term] : ((((X382 @ id @ X392 @ id)) != $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true)) & ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) & (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) != $true)) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem2v2_gthm = $true) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (! [X47 : term] : ? [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) = ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (pushprop_lem1_gthm = $true) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (! [X301 : term,X302 : (term > $o)] : (? [X306 : term] : (($true != ((X302 @ (lam @ X306)))) & (((X302 @ X306)) = $true)) | ? [X303 : term] : ((((var @ X303)) = $true) & (((X302 @ X303)) != $true)) | ($true = ((X302 @ X301))) | ? [X304 : term,X305 : term] : ((((X302 @ (ap @ X304 @ X305))) != $true) & ($true = ((X302 @ X305))) & (((X302 @ X304)) = $true))) <=> (induction = $true)) & (one = ((d2term @ d_one))) & (! [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | ? [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) != ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) | ? [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) != ((sub @ (X406 @ X412 @ X411) @ X410))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & ((? [X312 : term,X311 : term] : ((((lam @ X311)) = ((lam @ X312))) & (X311 != X312)) | ! [X316 : (subst > term > term),X313 : (subst > term > term),X314 : term,X315 : subst] : ((((lam @ (X316 @ sh @ one))) != ((lam @ (X313 @ sh @ one)))) | ? [X318 : subst,X317 : subst,X319 : term] : (((X316 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) != ((sub @ (X316 @ X318 @ X319) @ X317))) | ? [X322 : term,X321 : subst,X320 : subst] : (((sub @ (X313 @ X320 @ X322) @ X321)) != ((X313 @ (comp @ X320 @ X321) @ (sub @ X322 @ X321)))) | (((X316 @ X315 @ X314)) = ((X313 @ X315 @ X314)))) | ? [X310 : subst,X309 : term] : (((comp @ sh @ (push @ X309 @ X310))) != X310) | ? [X308 : subst,X307 : term] : (((sub @ one @ (push @ X307 @ X308))) != X307)) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : ((((X146 @ id @ (lam @ X145) @ id)) = $true) | ? [X152 : term] : ((((X146 @ id @ X152 @ id)) = $true) & (((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) != $true)) | ? [X147 : (subst > term > term)] : (! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) & ($true != ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) & ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | (((X146 @ id @ X151 @ id)) != $true))))) & ((? [X205 : (subst > term > subst > $o),X204 : term] : (! [X207 : (subst > term > term)] : (? [X209 : subst,X210 : term,X211 : subst] : (((X207 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209))) != ((sub @ (X207 @ X211 @ X210) @ X209))) | ($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ? [X208 : term] : ((((X205 @ id @ X208 @ id)) = $true) & (((X205 @ id @ (X207 @ id @ X208) @ id)) != $true))) & (((X205 @ id @ (lam @ (sub @ X204 @ (push @ one @ sh))) @ id)) != $true) & ! [X206 : term] : (($true = ((X205 @ id @ (sub @ X204 @ (push @ X206 @ id)) @ id))) | (((X205 @ id @ X206 @ id)) != $true))) | ! [X213 : term,X212 : (subst > term > subst > $o)] : (? [X220 : subst,X221 : term,X222 : subst,X223 : subst] : ((((X212 @ X223 @ X221 @ (comp @ X222 @ X220))) = $true) & (((X212 @ (comp @ X223 @ X222) @ (sub @ X221 @ X222) @ X220)) != $true)) | (((X212 @ id @ (lam @ X213) @ id)) = $true) | ? [X214 : (subst > term > term)] : (! [X218 : term] : ((((X212 @ id @ X218 @ id)) != $true) | (((X212 @ id @ (X214 @ id @ X218) @ id)) = $true)) & (((X212 @ id @ (lam @ (X214 @ sh @ one)) @ id)) != $true) & ! [X216 : subst,X217 : term,X215 : subst] : (((X214 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))) = ((sub @ (X214 @ X216 @ X217) @ X215)))) | ? [X219 : term] : ((((X212 @ id @ (sub @ X213 @ (push @ X219 @ id)) @ id)) != $true) & (((X212 @ id @ X219 @ id)) = $true)) | ? [X227 : subst,X225 : subst,X226 : term,X224 : subst] : ((((X212 @ X225 @ X226 @ (comp @ X227 @ X224))) != $true) & (((X212 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true))) | ? [X203 : term] : (((sub @ X203 @ id)) != X203)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X69 : (term > $o),X70 : subst,X71 : term] : (? [X73 : term,X72 : term] : ((((X69 @ X73)) = $true) & (((X69 @ X72)) = $true) & (((X69 @ (ap @ X73 @ X72))) != $true)) | (((X69 @ (sub @ X71 @ X70))) = $true) | ? [X74 : term] : ((((X69 @ (lam @ X74))) != $true) & ! [X75 : term] : (($true != ((X69 @ X75))) | (((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true))) | ? [X76 : term] : ((((var @ X76)) = $true) & ($true != ((X69 @ (sub @ X76 @ X70)))))) <=> (induction2lem = $true)) & ((! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4)))) | ? [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 != X3) & (((ap @ X2 @ X0)) = ((ap @ X1 @ X3))))) <=> (hoasapinj2_lthm = $true)) & ((? [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) != X173) | ! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)) | ? [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) != X175)) <=> (pushprop_lem1_lthm = $true)) & (! [X363 : (subst > term > subst > $o),X362 : term] : (? [X376 : subst,X375 : subst,X377 : term,X374 : subst] : ((((X363 @ X374 @ X377 @ (comp @ X376 @ X375))) = $true) & (((X363 @ (comp @ X374 @ X376) @ (sub @ X377 @ X376) @ X375)) != $true)) | ? [X373 : term] : (($true != ((X363 @ id @ (sub @ X362 @ (push @ X373 @ id)) @ id))) & ($true = ((X363 @ id @ X373 @ id)))) | ? [X364 : (subst > term > term)] : ((((X363 @ id @ (lam @ (X364 @ sh @ one)) @ id)) != $true) & ! [X368 : term,X366 : subst,X367 : subst] : (((sub @ (X364 @ X366 @ X368) @ X367)) = ((X364 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))) & ! [X365 : term] : ((((X363 @ id @ (X364 @ id @ X365) @ id)) = $true) | (((X363 @ id @ X365 @ id)) != $true))) | ? [X371 : subst,X370 : term,X372 : subst,X369 : subst] : (($true = ((X363 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369) @ X372))) & (((X363 @ X371 @ X370 @ (comp @ X369 @ X372))) != $true)) | (((X363 @ id @ (lam @ X362) @ id)) = $true)) <=> (hoasinduction_lem3 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) <=> (pushprop_lem0 = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & ((? [X441 : term] : (((sub @ X441 @ id)) != X441) | ? [X437 : term] : ! [X438 : (subst > term > term)] : ? [X440 : term,X439 : subst] : (((sub @ X437 @ (push @ X440 @ X439))) != ((X438 @ X439 @ X440))) | ! [X442 : (subst > term > subst > $o),X443 : term,X444 : (term > $o)] : ((((X444 @ (lam @ X443))) = $true) | ? [X445 : term] : (((X444 @ X445)) != ((X442 @ id @ X445 @ id))) | ? [X451 : term] : (($true != ((X444 @ (sub @ X443 @ (push @ X451 @ id))))) & ($true = ((X444 @ X451)))) | ? [X446 : (subst > term > term)] : (! [X447 : term,X448 : subst,X449 : subst] : (((X446 @ (comp @ X449 @ X448) @ (sub @ X447 @ X448))) = ((sub @ (X446 @ X449 @ X447) @ X448))) & (((X442 @ id @ (lam @ (X446 @ sh @ one)) @ id)) != $true) & ! [X450 : term] : (($true != ((X442 @ id @ X450 @ id))) | (((X442 @ id @ (X446 @ id @ X450) @ id)) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2subst @ d_id)) = sh) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) <=> (axidr = $true)) & (termmset_gthm = $true) & (pushprop = $true) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & (! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | (((X491 @ (lam @ X493))) = $true) | ? [X495 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X498 : subst,X496 : term,X497 : subst] : (((X495 @ (comp @ X497 @ X498) @ (sub @ X496 @ X498))) = ((sub @ (X495 @ X497 @ X496) @ X498))) & ! [X499 : term] : ((((X492 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X492 @ id @ X499 @ id)) != $true))) | ? [X500 : term] : (((X491 @ X500)) != ((X492 @ id @ X500 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & ((axvarid = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (hoasapinj1_gthm = $true) & (! [X9 : (subst > term > subst > $o),X8 : (term > $o),X10 : term] : (? [X23 : term,X21 : subst,X20 : subst,X22 : subst] : (($true != ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20))) & ($true = ((X9 @ X21 @ X23 @ (comp @ X22 @ X20))))) | ? [X25 : term] : (((X8 @ X25)) != ((X9 @ id @ X25 @ id))) | ($true = ((X8 @ (lam @ X10)))) | ? [X19 : term,X16 : subst,X17 : subst,X18 : subst] : ((((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) = $true) & (((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) != $true)) | ? [X24 : term] : (($true != ((X8 @ (sub @ X10 @ (push @ X24 @ id))))) & (((X8 @ X24)) = $true)) | ? [X11 : (subst > term > term)] : (($true != ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) & ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true)) & ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13))))) <=> (hoasinduction_lem3v2 = $true)) & (axclos = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X417 : term,X416 : (subst > term > subst > $o),X419 : term,X418 : (term > $o)] : (? [X420 : term] : (((X418 @ X420)) != ((X416 @ id @ X420 @ id))) | (((X418 @ X417)) != $true) | (((X418 @ (ap @ X417 @ X419))) = $true) | (((X418 @ X419)) != $true) | ? [X421 : term,X422 : term] : (($true != ((X416 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & (((X416 @ id @ X422 @ id)) = $true) & (((X416 @ id @ X421 @ id)) = $true)) | ? [X428 : term,X427 : subst,X429 : subst,X430 : subst] : ((((X416 @ X429 @ X428 @ (comp @ X427 @ X430))) = $true) & (((X416 @ (comp @ X429 @ X427) @ (sub @ X428 @ X427) @ X430)) != $true)) | ? [X425 : subst,X426 : term,X424 : subst,X423 : subst] : ((((X416 @ X424 @ X426 @ (comp @ X423 @ X425))) != $true) & ($true = ((X416 @ (comp @ X424 @ X423) @ (sub @ X426 @ X423) @ X425)))))) & ((? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ! [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) = $true) | (((X299 @ X296)) != $true) | ? [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) != ((X297 @ X300))))) <=> (pushprop_lem1v2_lthm = $true)) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & ((? [X229 : term,X228 : (term > $o)] : (! [X230 : term] : (? [X231 : term] : ((((X228 @ X231)) = $true) & (((X228 @ (sub @ X230 @ (push @ X231 @ id)))) != $true)) | (((X228 @ (lam @ X230))) = $true)) & (((X228 @ X229)) != $true) & ! [X234 : term] : ((((X228 @ X234)) = $true) | (((var @ X234)) != $true)) & ! [X232 : term,X233 : term] : ((((X228 @ X232)) != $true) | ($true != ((X228 @ X233))) | (((X228 @ (ap @ X233 @ X232))) = $true))) | ? [X236 : term,X235 : (subst > term > subst > $o),X237 : term] : (! [X244 : term,X245 : subst,X242 : subst,X243 : subst] : ((((X235 @ (comp @ X243 @ X245) @ (sub @ X244 @ X245) @ X242)) != $true) | (((X235 @ X243 @ X244 @ (comp @ X245 @ X242))) = $true)) & ! [X247 : term,X246 : term] : ((((X235 @ id @ X246 @ id)) != $true) | (((X235 @ id @ X247 @ id)) != $true) | (((X235 @ id @ (ap @ (sub @ X247 @ id) @ X246) @ id)) = $true)) & ! [X238 : subst,X241 : subst,X239 : subst,X240 : term] : ((((X235 @ X239 @ X240 @ (comp @ X238 @ X241))) != $true) | (((X235 @ (comp @ X239 @ X238) @ (sub @ X240 @ X238) @ X241)) = $true)) & ($true = ((X235 @ id @ X237 @ id))) & (((X235 @ id @ (ap @ X237 @ X236) @ id)) != $true) & (((X235 @ id @ X236 @ id)) = $true)) | ? [X248 : (subst > term > subst > $o),X249 : term] : (($true != ((X248 @ id @ (lam @ X249) @ id))) & ! [X259 : term] : ((((X248 @ id @ X259 @ id)) != $true) | (((X248 @ id @ (sub @ X249 @ (push @ X259 @ id)) @ id)) = $true)) & ! [X254 : (subst > term > term)] : ((((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true) | ? [X256 : subst,X258 : term,X257 : subst] : (((X254 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257))) != ((sub @ (X254 @ X256 @ X258) @ X257))) | ? [X255 : term] : ((((X248 @ id @ (X254 @ id @ X255) @ id)) != $true) & ($true = ((X248 @ id @ X255 @ id))))) & ! [X263 : subst,X260 : subst,X261 : subst,X262 : term] : ((((X248 @ X263 @ X262 @ (comp @ X260 @ X261))) = $true) | ($true != ((X248 @ (comp @ X263 @ X260) @ (sub @ X262 @ X260) @ X261)))) & ! [X253 : subst,X251 : subst,X252 : subst,X250 : term] : ((((X248 @ X253 @ X250 @ (comp @ X251 @ X252))) != $true) | (((X248 @ (comp @ X253 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true))) | ! [X264 : term,X265 : (subst > term > subst > $o)] : (? [X269 : subst,X266 : subst,X267 : term,X268 : subst] : ((((X265 @ (comp @ X266 @ X268) @ (sub @ X267 @ X268) @ X269)) = $true) & (((X265 @ X266 @ X267 @ (comp @ X268 @ X269))) != $true)) | (((X265 @ id @ X264 @ id)) = $true) | ? [X274 : term] : ((((var @ (sub @ X274 @ id))) = $true) & (((X265 @ id @ X274 @ id)) != $true)) | ? [X280 : term,X281 : term] : ((((X265 @ id @ X281 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id)) != $true) & ($true = ((X265 @ id @ X280 @ id)))) | ? [X272 : subst,X271 : term,X270 : subst,X273 : subst] : ((((X265 @ X273 @ X271 @ (comp @ X270 @ X272))) = $true) & (((X265 @ (comp @ X273 @ X270) @ (sub @ X271 @ X270) @ X272)) != $true)) | ? [X275 : (subst > term > term)] : (! [X276 : subst,X278 : subst,X277 : term] : (((sub @ (X275 @ X276 @ X277) @ X278)) = ((X275 @ (comp @ X276 @ X278) @ (sub @ X277 @ X278)))) & ! [X279 : term] : ((((X265 @ id @ (X275 @ id @ X279) @ id)) = $true) | (((X265 @ id @ X279 @ id)) != $true)) & (((X265 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true)))) <=> (hoasinduction_lthm = $true)) & ! [X144 : d_term] : (d_one = X144) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515)) | ? [X512 : subst] : (((comp @ id @ X512)) != X512) | ? [X513 : subst] : (((comp @ X513 @ id)) != X513)) <=> (substmonoid_lthm = $true)) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X36 : term,X34 : (subst > term > subst > $o),X35 : term] : (? [X44 : subst,X41 : subst,X42 : term,X43 : subst] : ((((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) = $true) & (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) != $true)) | ? [X46 : term,X45 : term] : (($true != ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) & (((X34 @ id @ X46 @ id)) = $true) & ($true = ((X34 @ id @ X45 @ id)))) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | (((X34 @ id @ X35 @ id)) != $true) | (((X34 @ id @ X36 @ id)) != $true) | ? [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (($true != ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37))) & (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) = $true))) <=> (hoasinduction_lem2 = $true)) & (! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) <=> (pushprop_lem1 = $true)) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) <=> (shinj = $true)) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((induction2_lthm = $true) <=> (! [X337 : term,X336 : (term > $o)] : (? [X341 : term,X340 : term] : ((((X336 @ (ap @ X341 @ X340))) != $true) & (((X336 @ X340)) = $true) & ($true = ((X336 @ X341)))) | ? [X342 : term] : (($true != ((X336 @ X342))) & (((var @ X342)) = $true)) | ? [X338 : term] : ((((X336 @ (lam @ X338))) != $true) & ! [X339 : term] : (($true = ((X336 @ (sub @ X338 @ (push @ X339 @ id))))) | ($true != ((X336 @ X339))))) | (((X336 @ X337)) = $true)) | ? [X327 : term] : (((sub @ X327 @ id)) != X327) | ? [X330 : subst,X329 : term,X328 : (term > $o)] : (! [X331 : term] : ((((var @ X331)) != $true) | (((X328 @ (sub @ X331 @ X330))) = $true)) & ! [X334 : term] : (? [X335 : term] : ((((X328 @ X335)) = $true) & (((X328 @ (sub @ X334 @ (push @ X335 @ id)))) != $true)) | (((X328 @ (lam @ X334))) = $true)) & ! [X333 : term,X332 : term] : ((((X328 @ X332)) != $true) | (((X328 @ (ap @ X332 @ X333))) = $true) | (((X328 @ X333)) != $true)) & (((X328 @ (sub @ X329 @ X330))) != $true)))) & ((? [X343 : term] : (((sub @ X343 @ id)) != X343) | ! [X346 : term,X345 : (term > $o),X344 : (subst > term > subst > $o)] : (? [X347 : term] : (((X345 @ X347)) != ((X344 @ id @ X347 @ id))) | ? [X359 : subst,X358 : subst,X361 : subst,X360 : term] : ((((X344 @ X358 @ X360 @ (comp @ X361 @ X359))) != $true) & ($true = ((X344 @ (comp @ X358 @ X361) @ (sub @ X360 @ X361) @ X359)))) | (((X345 @ (lam @ X346))) = $true) | ? [X348 : term] : (($true = ((X345 @ X348))) & (((X345 @ (sub @ X346 @ (push @ X348 @ id)))) != $true)) | ? [X353 : (subst > term > term)] : (! [X356 : term,X354 : subst,X355 : subst] : (((sub @ (X353 @ X354 @ X356) @ X355)) = ((X353 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355)))) & ! [X357 : term] : (($true != ((X344 @ id @ X357 @ id))) | (((X344 @ id @ (X353 @ id @ X357) @ id)) = $true)) & (((X344 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true)) | ? [X351 : subst,X350 : term,X352 : subst,X349 : subst] : ((((X344 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X349)) != $true) & ($true = ((X344 @ X352 @ X350 @ (comp @ X351 @ X349))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (induction2_gthm = $true) & ((? [X52 : term,X51 : (subst > term > subst > $o)] : (! [X58 : term] : ((((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true) | (((X51 @ id @ X58 @ id)) != $true)) & ! [X53 : (subst > term > term)] : (? [X57 : subst,X56 : term,X55 : subst] : (((sub @ (X53 @ X57 @ X56) @ X55)) != ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true) | ? [X54 : term] : ((((X51 @ id @ X54 @ id)) = $true) & (((X51 @ id @ (X53 @ id @ X54) @ id)) != $true))) & ($true != ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id)))) | ! [X59 : (subst > term > subst > $o),X60 : term] : ((((X59 @ id @ (lam @ X60) @ id)) = $true) | ? [X61 : term] : ((((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) != $true) & (((X59 @ id @ X61 @ id)) = $true)) | ? [X62 : (subst > term > term)] : (! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & ! [X63 : term] : ((((X59 @ id @ (X62 @ id @ X63) @ id)) = $true) | (((X59 @ id @ X63 @ id)) != $true)) & (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true))) | ? [X50 : term] : (((sub @ X50 @ id)) != X50)) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X78 : d_subst,X77 : d_subst] : ((((d2subst @ X78)) != ((d2subst @ X77))) | (X77 = X78)) & ((hoasinduction_lthm_3 = $true) <=> (? [X452 : (subst > term > subst > $o)] : ! [X453 : (term > $o)] : ? [X454 : term] : (((X452 @ id @ X454 @ id)) != ((X453 @ X454))) | ? [X462 : term] : (((sub @ X462 @ id)) != X462) | ? [X463 : (term > $o),X464 : (subst > term > subst > $o),X465 : term] : (! [X466 : term] : ((((X463 @ X466)) != $true) | (((X463 @ (sub @ X465 @ (push @ X466 @ id)))) = $true)) & ! [X467 : (subst > term > term)] : (? [X468 : term] : (($true = ((X464 @ id @ X468 @ id))) & (((X464 @ id @ (X467 @ id @ X468) @ id)) != $true)) | ? [X470 : subst,X471 : subst,X469 : term] : (((X467 @ (comp @ X471 @ X470) @ (sub @ X469 @ X470))) != ((sub @ (X467 @ X471 @ X469) @ X470))) | (((X464 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true)) & (((X463 @ (lam @ X465))) != $true) & ! [X472 : term] : (((X464 @ id @ X472 @ id)) = ((X463 @ X472)))) | ! [X473 : term,X474 : (subst > term > subst > $o)] : (? [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((((X474 @ X479 @ X477 @ (comp @ X480 @ X478))) != $true) & (((X474 @ (comp @ X479 @ X480) @ (sub @ X477 @ X480) @ X478)) = $true)) | ? [X486 : term] : (($true = ((var @ (sub @ X486 @ id)))) & (((X474 @ id @ X486 @ id)) != $true)) | ($true = ((X474 @ id @ X473 @ id))) | ? [X476 : term,X475 : term] : ((((X474 @ id @ X476 @ id)) = $true) & (((X474 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) != $true) & (((X474 @ id @ X475 @ id)) = $true)) | ? [X481 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X481 @ sh @ one)) @ id))) & ! [X482 : term] : ((((X474 @ id @ X482 @ id)) != $true) | (((X474 @ id @ (X481 @ id @ X482) @ id)) = $true)) & ! [X485 : subst,X484 : term,X483 : subst] : (((X481 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) = ((sub @ (X481 @ X485 @ X484) @ X483)))) | ? [X487 : subst,X489 : term,X490 : subst,X488 : subst] : ((((X474 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X487)) != $true) & (((X474 @ X490 @ X489 @ (comp @ X488 @ X487))) = $true))) | ? [X456 : term,X455 : (term > $o)] : (($true != ((X455 @ X456))) & ! [X457 : term] : ((((X455 @ (lam @ X457))) = $true) | ? [X458 : term] : ((((X455 @ (sub @ X457 @ (push @ X458 @ id)))) != $true) & (((X455 @ X458)) = $true))) & ! [X461 : term] : ((((var @ X461)) != $true) | (((X455 @ X461)) = $true)) & ! [X459 : term,X460 : term] : ((((X455 @ X459)) != $true) | (((X455 @ (ap @ X459 @ X460))) = $true) | (((X455 @ X460)) != $true))))) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & (axmap = $true) & ((apinj2 = $true) <=> ! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519))) & ((hoasinduction_lem3aa = $true) <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (? [X156 : (subst > term > term)] : (! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) & ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ($true != ((X153 @ id @ X160 @ id)))) & (((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) != $true)) | ($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))) | ? [X155 : term] : ((((X153 @ id @ X155 @ id)) = $true) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))))) & (! [X287 : term,X288 : (term > $o)] : ((((X288 @ X287)) = $true) | ? [X291 : term,X290 : term] : (($true != ((X288 @ (ap @ X290 @ X291)))) & ($true = ((X288 @ X290))) & (((X288 @ X291)) = $true)) | ? [X289 : term] : ((((var @ X289)) = $true) & ($true != ((X288 @ X289)))) | ? [X292 : term] : (! [X293 : term] : ((((X288 @ X293)) != $true) | (((X288 @ (sub @ X292 @ (push @ X293 @ id)))) = $true)) & (((X288 @ (lam @ X292))) != $true))) <=> (induction2 = $true)) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) <=> (hoasapinj1 = $true)) & (lamnotap != $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X520 : term,X521 : (subst > term > subst > $o)] : (? [X522 : (subst > term > term)] : (! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) & ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) & (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true)) | (((X521 @ id @ X520 @ id)) = $true) | ? [X527 : term,X528 : term] : ((((X521 @ id @ X527 @ id)) = $true) & (((X521 @ id @ X528 @ id)) = $true) & (((X521 @ id @ (ap @ (sub @ X527 @ id) @ X528) @ id)) != $true)))) & (hoasapinj2_gthm = $true) & (! [X169 : term] : ? [X170 : (subst > term > term)] : ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171)))) <=> (hoasinduction_lem3v2_f = $true)) & ((? [X186 : subst] : (((comp @ X186 @ id)) != X186) | ? [X184 : subst,X185 : term] : (((comp @ sh @ (push @ X185 @ X184))) != X184) | ! [X195 : subst,X194 : (term > $o),X193 : term] : ((((X194 @ (sub @ X193 @ X195))) = $true) | ? [X200 : term] : ((((X194 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | ? [X196 : term] : ((((X194 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X194 @ X197)) != $true) | (((X194 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | ? [X199 : term,X198 : term] : (($true = ((X194 @ X198))) & (((X194 @ X199)) = $true) & (((X194 @ (ap @ X198 @ X199))) != $true))) | ? [X183 : term,X182 : subst] : (((sub @ one @ (push @ X183 @ X182))) != X183) | ? [X187 : term,X188 : (term > $o)] : (($true != ((X188 @ X187))) & ! [X191 : term] : ((((X188 @ (lam @ X191))) = $true) | (((X188 @ X191)) != $true)) & ! [X189 : term,X190 : term] : ((((X188 @ X189)) != $true) | (((X188 @ (ap @ X190 @ X189))) = $true) | (((X188 @ X190)) != $true)) & ! [X192 : term] : ((((var @ X192)) != $true) | (((X188 @ X192)) = $true)))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X401 : (subst > term > subst > $o)] : ? [X402 : (term > $o)] : ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id)))) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & ((substmonoid = $true) <=> (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & (hoaslamnotvar = $true) & (! [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) = $true) | ? [X533 : term] : (((X530 @ X533)) != ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) | (((X532 @ X531)) != $true)) <=> (pushprop_lem1v2 = $true)) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true))),
% 6.12/1.30 inference(flattening,[],[f11])).
% 6.12/1.30 thf(f13,definition,(
% 6.12/1.30 ! [X188 : (term > $o)] : ((((sP0 @ X188)) = $true) <=> ! [X189 : term,X190 : term] : ((((X188 @ X189)) != $true) | (((X188 @ (ap @ X190 @ X189))) = $true) | (((X188 @ X190)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f14,definition,(
% 6.12/1.30 ! [X194 : (term > $o)] : ((((sP1 @ X194)) = $true) <=> ? [X199 : term,X198 : term] : (($true = ((X194 @ X198))) & (((X194 @ X199)) = $true) & (((X194 @ (ap @ X198 @ X199))) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f15,definition,(
% 6.12/1.30 (sP2 = $true) <=> ! [X195 : subst,X194 : (term > $o),X193 : term] : ((((X194 @ (sub @ X193 @ X195))) = $true) | ? [X200 : term] : ((((X194 @ (sub @ X200 @ X195))) != $true) & (((var @ X200)) = $true)) | ? [X196 : term] : ((((X194 @ (lam @ X196))) != $true) & ! [X197 : term] : ((((X194 @ X197)) != $true) | (((X194 @ (sub @ X196 @ (push @ X197 @ id)))) = $true))) | (((sP1 @ X194)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f16,definition,(
% 6.12/1.30 (sP3 = $true) <=> (? [X186 : subst] : (((comp @ X186 @ id)) != X186) | ? [X184 : subst,X185 : term] : (((comp @ sh @ (push @ X185 @ X184))) != X184) | (sP2 = $true) | ? [X183 : term,X182 : subst] : (((sub @ one @ (push @ X183 @ X182))) != X183) | ? [X187 : term,X188 : (term > $o)] : (($true != ((X188 @ X187))) & ! [X191 : term] : ((((X188 @ (lam @ X191))) = $true) | (((X188 @ X191)) != $true)) & (((sP0 @ X188)) = $true) & ! [X192 : term] : ((((var @ X192)) != $true) | (((X188 @ X192)) = $true))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f17,definition,(
% 6.12/1.30 ! [X521 : (subst > term > subst > $o)] : ((((sP4 @ X521)) = $true) <=> ? [X527 : term,X528 : term] : ((((X521 @ id @ X527 @ id)) = $true) & (((X521 @ id @ X528 @ id)) = $true) & (((X521 @ id @ (ap @ (sub @ X527 @ id) @ X528) @ id)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f18,definition,(
% 6.12/1.30 ! [X288 : (term > $o)] : ((((sP5 @ X288)) = $true) <=> ? [X291 : term,X290 : term] : (($true != ((X288 @ (ap @ X290 @ X291)))) & ($true = ((X288 @ X290))) & (((X288 @ X291)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f19,definition,(
% 6.12/1.30 (sP6 = $true) <=> ! [X287 : term,X288 : (term > $o)] : ((((X288 @ X287)) = $true) | (((sP5 @ X288)) = $true) | ? [X289 : term] : ((((var @ X289)) = $true) & ($true != ((X288 @ X289)))) | ? [X292 : term] : (! [X293 : term] : ((((X288 @ X293)) != $true) | (((X288 @ (sub @ X292 @ (push @ X293 @ id)))) = $true)) & (((X288 @ (lam @ X292))) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f20,definition,(
% 6.12/1.30 (sP7 = $true) <=> ! [X153 : (subst > term > subst > $o),X154 : term] : (? [X156 : (subst > term > term)] : (! [X157 : subst,X158 : subst,X159 : term] : (((X156 @ (comp @ X158 @ X157) @ (sub @ X159 @ X157))) = ((sub @ (X156 @ X158 @ X159) @ X157))) & ! [X160 : term] : ((((X153 @ id @ (X156 @ id @ X160) @ id)) = $true) | ($true != ((X153 @ id @ X160 @ id)))) & (((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id)) != $true)) | ($true = ((X153 @ id @ (lam @ (sub @ X154 @ (push @ one @ sh))) @ id))) | ? [X155 : term] : ((((X153 @ id @ X155 @ id)) = $true) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f21,definition,(
% 6.12/1.30 ! [X455 : (term > $o)] : ((((sP8 @ X455)) = $true) <=> ! [X459 : term,X460 : term] : ((((X455 @ X459)) != $true) | (((X455 @ (ap @ X459 @ X460))) = $true) | (((X455 @ X460)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f22,definition,(
% 6.12/1.30 ! [X474 : (subst > term > subst > $o)] : ((((sP9 @ X474)) = $true) <=> ? [X481 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X481 @ sh @ one)) @ id))) & ! [X482 : term] : ((((X474 @ id @ X482 @ id)) != $true) | (((X474 @ id @ (X481 @ id @ X482) @ id)) = $true)) & ! [X485 : subst,X484 : term,X483 : subst] : (((X481 @ (comp @ X485 @ X483) @ (sub @ X484 @ X483))) = ((sub @ (X481 @ X485 @ X484) @ X483)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f23,definition,(
% 6.12/1.30 ! [X474 : (subst > term > subst > $o)] : ((((sP10 @ X474)) = $true) <=> ? [X476 : term,X475 : term] : ((((X474 @ id @ X476 @ id)) = $true) & (((X474 @ id @ (ap @ (sub @ X476 @ id) @ X475) @ id)) != $true) & (((X474 @ id @ X475 @ id)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f24,definition,(
% 6.12/1.30 (sP11 = $true) <=> ! [X473 : term,X474 : (subst > term > subst > $o)] : (? [X477 : term,X478 : subst,X479 : subst,X480 : subst] : ((((X474 @ X479 @ X477 @ (comp @ X480 @ X478))) != $true) & (((X474 @ (comp @ X479 @ X480) @ (sub @ X477 @ X480) @ X478)) = $true)) | ? [X486 : term] : (($true = ((var @ (sub @ X486 @ id)))) & (((X474 @ id @ X486 @ id)) != $true)) | ($true = ((X474 @ id @ X473 @ id))) | (((sP10 @ X474)) = $true) | (((sP9 @ X474)) = $true) | ? [X487 : subst,X489 : term,X490 : subst,X488 : subst] : ((((X474 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X487)) != $true) & (((X474 @ X490 @ X489 @ (comp @ X488 @ X487))) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f25,definition,(
% 6.12/1.30 (sP12 = $true) <=> ? [X463 : (term > $o),X464 : (subst > term > subst > $o),X465 : term] : (! [X466 : term] : ((((X463 @ X466)) != $true) | (((X463 @ (sub @ X465 @ (push @ X466 @ id)))) = $true)) & ! [X467 : (subst > term > term)] : (? [X468 : term] : (($true = ((X464 @ id @ X468 @ id))) & (((X464 @ id @ (X467 @ id @ X468) @ id)) != $true)) | ? [X470 : subst,X471 : subst,X469 : term] : (((X467 @ (comp @ X471 @ X470) @ (sub @ X469 @ X470))) != ((sub @ (X467 @ X471 @ X469) @ X470))) | (((X464 @ id @ (lam @ (X467 @ sh @ one)) @ id)) = $true)) & (((X463 @ (lam @ X465))) != $true) & ! [X472 : term] : (((X464 @ id @ X472 @ id)) = ((X463 @ X472))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f26,definition,(
% 6.12/1.30 (sP13 = $true) <=> (? [X452 : (subst > term > subst > $o)] : ! [X453 : (term > $o)] : ? [X454 : term] : (((X452 @ id @ X454 @ id)) != ((X453 @ X454))) | ? [X462 : term] : (((sub @ X462 @ id)) != X462) | (sP12 = $true) | (sP11 = $true) | ? [X456 : term,X455 : (term > $o)] : (($true != ((X455 @ X456))) & ! [X457 : term] : ((((X455 @ (lam @ X457))) = $true) | ? [X458 : term] : ((((X455 @ (sub @ X457 @ (push @ X458 @ id)))) != $true) & (((X455 @ X458)) = $true))) & ! [X461 : term] : ((((var @ X461)) != $true) | (((X455 @ X461)) = $true)) & (((sP8 @ X455)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f27,definition,(
% 6.12/1.30 (sP14 = $true) <=> ? [X52 : term,X51 : (subst > term > subst > $o)] : (! [X58 : term] : ((((X51 @ id @ (sub @ X52 @ (push @ X58 @ id)) @ id)) = $true) | (((X51 @ id @ X58 @ id)) != $true)) & ! [X53 : (subst > term > term)] : (? [X57 : subst,X56 : term,X55 : subst] : (((sub @ (X53 @ X57 @ X56) @ X55)) != ((X53 @ (comp @ X57 @ X55) @ (sub @ X56 @ X55)))) | (((X51 @ id @ (lam @ (X53 @ sh @ one)) @ id)) = $true) | ? [X54 : term] : ((((X51 @ id @ X54 @ id)) = $true) & (((X51 @ id @ (X53 @ id @ X54) @ id)) != $true))) & ($true != ((X51 @ id @ (lam @ (sub @ X52 @ (push @ one @ sh))) @ id))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f28,definition,(
% 6.12/1.30 ($true = sP15) <=> ((sP14 = $true) | ! [X59 : (subst > term > subst > $o),X60 : term] : ((((X59 @ id @ (lam @ X60) @ id)) = $true) | ? [X61 : term] : ((((X59 @ id @ (sub @ X60 @ (push @ X61 @ id)) @ id)) != $true) & (((X59 @ id @ X61 @ id)) = $true)) | ? [X62 : (subst > term > term)] : (! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & ! [X63 : term] : ((((X59 @ id @ (X62 @ id @ X63) @ id)) = $true) | (((X59 @ id @ X63 @ id)) != $true)) & (((X59 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true))) | ? [X50 : term] : (((sub @ X50 @ id)) != X50))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f29,definition,(
% 6.12/1.30 ! [X344 : (subst > term > subst > $o)] : (($true = ((sP16 @ X344))) <=> ? [X353 : (subst > term > term)] : (! [X356 : term,X354 : subst,X355 : subst] : (((sub @ (X353 @ X354 @ X356) @ X355)) = ((X353 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355)))) & ! [X357 : term] : (($true != ((X344 @ id @ X357 @ id))) | (((X344 @ id @ (X353 @ id @ X357) @ id)) = $true)) & (((X344 @ id @ (lam @ (X353 @ sh @ one)) @ id)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f30,definition,(
% 6.12/1.30 (sP17 = $true) <=> (? [X343 : term] : (((sub @ X343 @ id)) != X343) | ! [X346 : term,X345 : (term > $o),X344 : (subst > term > subst > $o)] : (? [X347 : term] : (((X345 @ X347)) != ((X344 @ id @ X347 @ id))) | ? [X359 : subst,X358 : subst,X361 : subst,X360 : term] : ((((X344 @ X358 @ X360 @ (comp @ X361 @ X359))) != $true) & ($true = ((X344 @ (comp @ X358 @ X361) @ (sub @ X360 @ X361) @ X359)))) | (((X345 @ (lam @ X346))) = $true) | ? [X348 : term] : (($true = ((X345 @ X348))) & (((X345 @ (sub @ X346 @ (push @ X348 @ id)))) != $true)) | ($true = ((sP16 @ X344))) | ? [X351 : subst,X350 : term,X352 : subst,X349 : subst] : ((((X344 @ (comp @ X352 @ X351) @ (sub @ X350 @ X351) @ X349)) != $true) & ($true = ((X344 @ X352 @ X350 @ (comp @ X351 @ X349)))))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f31,definition,(
% 6.12/1.30 ! [X328 : (term > $o)] : (($true = ((sP18 @ X328))) <=> ! [X333 : term,X332 : term] : ((((X328 @ X332)) != $true) | (((X328 @ (ap @ X332 @ X333))) = $true) | (((X328 @ X333)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f32,definition,(
% 6.12/1.30 ! [X336 : (term > $o)] : ((((sP19 @ X336)) = $true) <=> ? [X341 : term,X340 : term] : ((((X336 @ (ap @ X341 @ X340))) != $true) & (((X336 @ X340)) = $true) & ($true = ((X336 @ X341)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f33,definition,(
% 6.12/1.30 (sP20 = $true) <=> ! [X337 : term,X336 : (term > $o)] : ((((sP19 @ X336)) = $true) | ? [X342 : term] : (($true != ((X336 @ X342))) & (((var @ X342)) = $true)) | ? [X338 : term] : ((((X336 @ (lam @ X338))) != $true) & ! [X339 : term] : (($true = ((X336 @ (sub @ X338 @ (push @ X339 @ id))))) | ($true != ((X336 @ X339))))) | (((X336 @ X337)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f34,definition,(
% 6.12/1.30 (sP21 = $true) <=> ((sP20 = $true) | ? [X327 : term] : (((sub @ X327 @ id)) != X327) | ? [X330 : subst,X329 : term,X328 : (term > $o)] : (! [X331 : term] : ((((var @ X331)) != $true) | (((X328 @ (sub @ X331 @ X330))) = $true)) & ! [X334 : term] : (? [X335 : term] : ((((X328 @ X335)) = $true) & (((X328 @ (sub @ X334 @ (push @ X335 @ id)))) != $true)) | (((X328 @ (lam @ X334))) = $true)) & ($true = ((sP18 @ X328))) & (((X328 @ (sub @ X329 @ X330))) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f35,definition,(
% 6.12/1.30 ! [X34 : (subst > term > subst > $o)] : (($true = ((sP22 @ X34))) <=> ? [X46 : term,X45 : term] : (($true != ((X34 @ id @ (ap @ (sub @ X46 @ id) @ X45) @ id))) & (((X34 @ id @ X46 @ id)) = $true) & ($true = ((X34 @ id @ X45 @ id)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f36,definition,(
% 6.12/1.30 (sP23 = $true) <=> ! [X36 : term,X34 : (subst > term > subst > $o),X35 : term] : (? [X44 : subst,X41 : subst,X42 : term,X43 : subst] : ((((X34 @ (comp @ X44 @ X41) @ (sub @ X42 @ X41) @ X43)) = $true) & (((X34 @ X44 @ X42 @ (comp @ X41 @ X43))) != $true)) | ($true = ((sP22 @ X34))) | (((X34 @ id @ (ap @ X35 @ X36) @ id)) = $true) | (((X34 @ id @ X35 @ id)) != $true) | (((X34 @ id @ X36 @ id)) != $true) | ? [X37 : subst,X38 : subst,X39 : subst,X40 : term] : (($true != ((X34 @ (comp @ X39 @ X38) @ (sub @ X40 @ X38) @ X37))) & (((X34 @ X39 @ X40 @ (comp @ X38 @ X37))) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f37,definition,(
% 6.12/1.30 ! [X265 : (subst > term > subst > $o)] : ((((sP24 @ X265)) = $true) <=> ? [X275 : (subst > term > term)] : (! [X276 : subst,X278 : subst,X277 : term] : (((sub @ (X275 @ X276 @ X277) @ X278)) = ((X275 @ (comp @ X276 @ X278) @ (sub @ X277 @ X278)))) & ! [X279 : term] : ((((X265 @ id @ (X275 @ id @ X279) @ id)) = $true) | (((X265 @ id @ X279 @ id)) != $true)) & (((X265 @ id @ (lam @ (X275 @ sh @ one)) @ id)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f38,definition,(
% 6.12/1.30 ! [X265 : (subst > term > subst > $o)] : ((((sP25 @ X265)) = $true) <=> ? [X280 : term,X281 : term] : ((((X265 @ id @ X281 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X281 @ id) @ X280) @ id)) != $true) & ($true = ((X265 @ id @ X280 @ id)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f39,definition,(
% 6.12/1.30 ! [X248 : (subst > term > subst > $o)] : ((((sP26 @ X248)) = $true) <=> ! [X254 : (subst > term > term)] : ((((X248 @ id @ (lam @ (X254 @ sh @ one)) @ id)) = $true) | ? [X256 : subst,X258 : term,X257 : subst] : (((X254 @ (comp @ X256 @ X257) @ (sub @ X258 @ X257))) != ((sub @ (X254 @ X256 @ X258) @ X257))) | ? [X255 : term] : ((((X248 @ id @ (X254 @ id @ X255) @ id)) != $true) & ($true = ((X248 @ id @ X255 @ id))))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f40,definition,(
% 6.12/1.30 ! [X235 : (subst > term > subst > $o)] : ((((sP27 @ X235)) = $true) <=> ! [X247 : term,X246 : term] : ((((X235 @ id @ X246 @ id)) != $true) | (((X235 @ id @ X247 @ id)) != $true) | (((X235 @ id @ (ap @ (sub @ X247 @ id) @ X246) @ id)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f41,definition,(
% 6.12/1.30 ! [X228 : (term > $o)] : ((((sP28 @ X228)) = $true) <=> ! [X232 : term,X233 : term] : ((((X228 @ X232)) != $true) | ($true != ((X228 @ X233))) | (((X228 @ (ap @ X233 @ X232))) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f42,definition,(
% 6.12/1.30 (sP29 = $true) <=> ? [X248 : (subst > term > subst > $o),X249 : term] : (($true != ((X248 @ id @ (lam @ X249) @ id))) & ! [X259 : term] : ((((X248 @ id @ X259 @ id)) != $true) | (((X248 @ id @ (sub @ X249 @ (push @ X259 @ id)) @ id)) = $true)) & (((sP26 @ X248)) = $true) & ! [X263 : subst,X260 : subst,X261 : subst,X262 : term] : ((((X248 @ X263 @ X262 @ (comp @ X260 @ X261))) = $true) | ($true != ((X248 @ (comp @ X263 @ X260) @ (sub @ X262 @ X260) @ X261)))) & ! [X253 : subst,X251 : subst,X252 : subst,X250 : term] : ((((X248 @ X253 @ X250 @ (comp @ X251 @ X252))) != $true) | (((X248 @ (comp @ X253 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f43,definition,(
% 6.12/1.30 ($true = sP30) <=> ! [X264 : term,X265 : (subst > term > subst > $o)] : (? [X269 : subst,X266 : subst,X267 : term,X268 : subst] : ((((X265 @ (comp @ X266 @ X268) @ (sub @ X267 @ X268) @ X269)) = $true) & (((X265 @ X266 @ X267 @ (comp @ X268 @ X269))) != $true)) | (((X265 @ id @ X264 @ id)) = $true) | ? [X274 : term] : ((((var @ (sub @ X274 @ id))) = $true) & (((X265 @ id @ X274 @ id)) != $true)) | (((sP25 @ X265)) = $true) | ? [X272 : subst,X271 : term,X270 : subst,X273 : subst] : ((((X265 @ X273 @ X271 @ (comp @ X270 @ X272))) = $true) & (((X265 @ (comp @ X273 @ X270) @ (sub @ X271 @ X270) @ X272)) != $true)) | (((sP24 @ X265)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f44,definition,(
% 6.12/1.30 (sP31 = $true) <=> ? [X236 : term,X235 : (subst > term > subst > $o),X237 : term] : (! [X244 : term,X245 : subst,X242 : subst,X243 : subst] : ((((X235 @ (comp @ X243 @ X245) @ (sub @ X244 @ X245) @ X242)) != $true) | (((X235 @ X243 @ X244 @ (comp @ X245 @ X242))) = $true)) & (((sP27 @ X235)) = $true) & ! [X238 : subst,X241 : subst,X239 : subst,X240 : term] : ((((X235 @ X239 @ X240 @ (comp @ X238 @ X241))) != $true) | (((X235 @ (comp @ X239 @ X238) @ (sub @ X240 @ X238) @ X241)) = $true)) & ($true = ((X235 @ id @ X237 @ id))) & (((X235 @ id @ (ap @ X237 @ X236) @ id)) != $true) & (((X235 @ id @ X236 @ id)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f45,definition,(
% 6.12/1.30 (sP32 = $true) <=> (? [X229 : term,X228 : (term > $o)] : (! [X230 : term] : (? [X231 : term] : ((((X228 @ X231)) = $true) & (((X228 @ (sub @ X230 @ (push @ X231 @ id)))) != $true)) | (((X228 @ (lam @ X230))) = $true)) & (((X228 @ X229)) != $true) & ! [X234 : term] : ((((X228 @ X234)) = $true) | (((var @ X234)) != $true)) & (((sP28 @ X228)) = $true)) | (sP31 = $true) | (sP29 = $true) | ($true = sP30))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f46,definition,(
% 6.12/1.30 ! [X416 : (subst > term > subst > $o)] : ((((sP33 @ X416)) = $true) <=> ? [X421 : term,X422 : term] : (($true != ((X416 @ id @ (ap @ (sub @ X421 @ id) @ X422) @ id))) & (((X416 @ id @ X422 @ id)) = $true) & (((X416 @ id @ X421 @ id)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f47,definition,(
% 6.12/1.30 ($true = sP34) <=> ! [X417 : term,X416 : (subst > term > subst > $o),X419 : term,X418 : (term > $o)] : (? [X420 : term] : (((X418 @ X420)) != ((X416 @ id @ X420 @ id))) | (((X418 @ X417)) != $true) | (((X418 @ (ap @ X417 @ X419))) = $true) | (((X418 @ X419)) != $true) | (((sP33 @ X416)) = $true) | ? [X428 : term,X427 : subst,X429 : subst,X430 : subst] : ((((X416 @ X429 @ X428 @ (comp @ X427 @ X430))) = $true) & (((X416 @ (comp @ X429 @ X427) @ (sub @ X428 @ X427) @ X430)) != $true)) | ? [X425 : subst,X426 : term,X424 : subst,X423 : subst] : ((((X416 @ X424 @ X426 @ (comp @ X423 @ X425))) != $true) & ($true = ((X416 @ (comp @ X424 @ X423) @ (sub @ X426 @ X423) @ X425)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f48,definition,(
% 6.12/1.30 ! [X9 : (subst > term > subst > $o)] : ((((sP35 @ X9)) = $true) <=> ? [X11 : (subst > term > term)] : (($true != ((X9 @ id @ (lam @ (X11 @ sh @ one)) @ id))) & ! [X15 : term] : ((((X9 @ id @ X15 @ id)) != $true) | (((X9 @ id @ (X11 @ id @ X15) @ id)) = $true)) & ! [X14 : term,X13 : subst,X12 : subst] : (((X11 @ (comp @ X12 @ X13) @ (sub @ X14 @ X13))) = ((sub @ (X11 @ X12 @ X14) @ X13)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f49,definition,(
% 6.12/1.30 (sP36 = $true) <=> ! [X9 : (subst > term > subst > $o),X8 : (term > $o),X10 : term] : (? [X23 : term,X21 : subst,X20 : subst,X22 : subst] : (($true != ((X9 @ (comp @ X21 @ X22) @ (sub @ X23 @ X22) @ X20))) & ($true = ((X9 @ X21 @ X23 @ (comp @ X22 @ X20))))) | ? [X25 : term] : (((X8 @ X25)) != ((X9 @ id @ X25 @ id))) | ($true = ((X8 @ (lam @ X10)))) | ? [X19 : term,X16 : subst,X17 : subst,X18 : subst] : ((((X9 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18) @ X16)) = $true) & (((X9 @ X17 @ X19 @ (comp @ X18 @ X16))) != $true)) | ? [X24 : term] : (($true != ((X8 @ (sub @ X10 @ (push @ X24 @ id))))) & (((X8 @ X24)) = $true)) | (((sP35 @ X9)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f50,definition,(
% 6.12/1.30 ($true = sP37) <=> ! [X492 : (subst > term > subst > $o),X493 : term,X491 : (term > $o)] : (? [X494 : term] : ((((X491 @ X494)) = $true) & (((X491 @ (sub @ X493 @ (push @ X494 @ id)))) != $true)) | (((X491 @ (lam @ X493))) = $true) | ? [X495 : (subst > term > term)] : ((((X492 @ id @ (lam @ (X495 @ sh @ one)) @ id)) != $true) & ! [X498 : subst,X496 : term,X497 : subst] : (((X495 @ (comp @ X497 @ X498) @ (sub @ X496 @ X498))) = ((sub @ (X495 @ X497 @ X496) @ X498))) & ! [X499 : term] : ((((X492 @ id @ (X495 @ id @ X499) @ id)) = $true) | (((X492 @ id @ X499 @ id)) != $true))) | ? [X500 : term] : (((X491 @ X500)) != ((X492 @ id @ X500 @ id))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f51,definition,(
% 6.12/1.30 (sP38 = $true) <=> (? [X441 : term] : (((sub @ X441 @ id)) != X441) | ? [X437 : term] : ! [X438 : (subst > term > term)] : ? [X440 : term,X439 : subst] : (((sub @ X437 @ (push @ X440 @ X439))) != ((X438 @ X439 @ X440))) | ! [X442 : (subst > term > subst > $o),X443 : term,X444 : (term > $o)] : ((((X444 @ (lam @ X443))) = $true) | ? [X445 : term] : (((X444 @ X445)) != ((X442 @ id @ X445 @ id))) | ? [X451 : term] : (($true != ((X444 @ (sub @ X443 @ (push @ X451 @ id))))) & ($true = ((X444 @ X451)))) | ? [X446 : (subst > term > term)] : (! [X447 : term,X448 : subst,X449 : subst] : (((X446 @ (comp @ X449 @ X448) @ (sub @ X447 @ X448))) = ((sub @ (X446 @ X449 @ X447) @ X448))) & (((X442 @ id @ (lam @ (X446 @ sh @ one)) @ id)) != $true) & ! [X450 : term] : (($true != ((X442 @ id @ X450 @ id))) | (((X442 @ id @ (X446 @ id @ X450) @ id)) = $true)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f52,definition,(
% 6.12/1.30 ! [X363 : (subst > term > subst > $o)] : ((((sP39 @ X363)) = $true) <=> ? [X364 : (subst > term > term)] : ((((X363 @ id @ (lam @ (X364 @ sh @ one)) @ id)) != $true) & ! [X368 : term,X366 : subst,X367 : subst] : (((sub @ (X364 @ X366 @ X368) @ X367)) = ((X364 @ (comp @ X366 @ X367) @ (sub @ X368 @ X367)))) & ! [X365 : term] : ((((X363 @ id @ (X364 @ id @ X365) @ id)) = $true) | (((X363 @ id @ X365 @ id)) != $true))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f53,definition,(
% 6.12/1.30 (sP40 = $true) <=> ! [X363 : (subst > term > subst > $o),X362 : term] : (? [X376 : subst,X375 : subst,X377 : term,X374 : subst] : ((((X363 @ X374 @ X377 @ (comp @ X376 @ X375))) = $true) & (((X363 @ (comp @ X374 @ X376) @ (sub @ X377 @ X376) @ X375)) != $true)) | ? [X373 : term] : (($true != ((X363 @ id @ (sub @ X362 @ (push @ X373 @ id)) @ id))) & ($true = ((X363 @ id @ X373 @ id)))) | (((sP39 @ X363)) = $true) | ? [X371 : subst,X370 : term,X372 : subst,X369 : subst] : (($true = ((X363 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369) @ X372))) & (((X363 @ X371 @ X370 @ (comp @ X369 @ X372))) != $true)) | (((X363 @ id @ (lam @ X362) @ id)) = $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f54,definition,(
% 6.12/1.30 ! [X69 : (term > $o)] : ((((sP41 @ X69)) = $true) <=> ? [X73 : term,X72 : term] : ((((X69 @ X73)) = $true) & (((X69 @ X72)) = $true) & (((X69 @ (ap @ X73 @ X72))) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f55,definition,(
% 6.12/1.30 (sP42 = $true) <=> ! [X69 : (term > $o),X70 : subst,X71 : term] : ((((sP41 @ X69)) = $true) | (((X69 @ (sub @ X71 @ X70))) = $true) | ? [X74 : term] : ((((X69 @ (lam @ X74))) != $true) & ! [X75 : term] : (($true != ((X69 @ X75))) | (((X69 @ (sub @ X74 @ (push @ X75 @ id)))) = $true))) | ? [X76 : term] : ((((var @ X76)) = $true) & ($true != ((X69 @ (sub @ X76 @ X70))))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f56,definition,(
% 6.12/1.30 ! [X212 : (subst > term > subst > $o)] : ((((sP43 @ X212)) = $true) <=> ? [X214 : (subst > term > term)] : (! [X218 : term] : ((((X212 @ id @ X218 @ id)) != $true) | (((X212 @ id @ (X214 @ id @ X218) @ id)) = $true)) & (((X212 @ id @ (lam @ (X214 @ sh @ one)) @ id)) != $true) & ! [X216 : subst,X217 : term,X215 : subst] : (((X214 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215))) = ((sub @ (X214 @ X216 @ X217) @ X215)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f57,definition,(
% 6.12/1.30 (sP44 = $true) <=> ? [X205 : (subst > term > subst > $o),X204 : term] : (! [X207 : (subst > term > term)] : (? [X209 : subst,X210 : term,X211 : subst] : (((X207 @ (comp @ X211 @ X209) @ (sub @ X210 @ X209))) != ((sub @ (X207 @ X211 @ X210) @ X209))) | ($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ? [X208 : term] : ((((X205 @ id @ X208 @ id)) = $true) & (((X205 @ id @ (X207 @ id @ X208) @ id)) != $true))) & (((X205 @ id @ (lam @ (sub @ X204 @ (push @ one @ sh))) @ id)) != $true) & ! [X206 : term] : (($true = ((X205 @ id @ (sub @ X204 @ (push @ X206 @ id)) @ id))) | (((X205 @ id @ X206 @ id)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f58,definition,(
% 6.12/1.30 (sP45 = $true) <=> ((sP44 = $true) | ! [X213 : term,X212 : (subst > term > subst > $o)] : (? [X220 : subst,X221 : term,X222 : subst,X223 : subst] : ((((X212 @ X223 @ X221 @ (comp @ X222 @ X220))) = $true) & (((X212 @ (comp @ X223 @ X222) @ (sub @ X221 @ X222) @ X220)) != $true)) | (((X212 @ id @ (lam @ X213) @ id)) = $true) | (((sP43 @ X212)) = $true) | ? [X219 : term] : ((((X212 @ id @ (sub @ X213 @ (push @ X219 @ id)) @ id)) != $true) & (((X212 @ id @ X219 @ id)) = $true)) | ? [X227 : subst,X225 : subst,X226 : term,X224 : subst] : ((((X212 @ X225 @ X226 @ (comp @ X227 @ X224))) != $true) & (((X212 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true))) | ? [X203 : term] : (((sub @ X203 @ id)) != X203))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f59,definition,(
% 6.12/1.30 ($true = sP46) <=> ! [X145 : term,X146 : (subst > term > subst > $o)] : ((((X146 @ id @ (lam @ X145) @ id)) = $true) | ? [X152 : term] : ((((X146 @ id @ X152 @ id)) = $true) & (((X146 @ id @ (sub @ X145 @ (push @ X152 @ id)) @ id)) != $true)) | ? [X147 : (subst > term > term)] : (! [X150 : term,X148 : subst,X149 : subst] : (((X147 @ (comp @ X149 @ X148) @ (sub @ X150 @ X148))) = ((sub @ (X147 @ X149 @ X150) @ X148))) & ($true != ((X146 @ id @ (lam @ (X147 @ sh @ one)) @ id))) & ! [X151 : term] : (($true = ((X146 @ id @ (X147 @ id @ X151) @ id))) | (((X146 @ id @ X151 @ id)) != $true))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f60,definition,(
% 6.12/1.30 ($true = sP47) <=> (? [X312 : term,X311 : term] : ((((lam @ X311)) = ((lam @ X312))) & (X311 != X312)) | ! [X316 : (subst > term > term),X313 : (subst > term > term),X314 : term,X315 : subst] : ((((lam @ (X316 @ sh @ one))) != ((lam @ (X313 @ sh @ one)))) | ? [X318 : subst,X317 : subst,X319 : term] : (((X316 @ (comp @ X318 @ X317) @ (sub @ X319 @ X317))) != ((sub @ (X316 @ X318 @ X319) @ X317))) | ? [X322 : term,X321 : subst,X320 : subst] : (((sub @ (X313 @ X320 @ X322) @ X321)) != ((X313 @ (comp @ X320 @ X321) @ (sub @ X322 @ X321)))) | (((X316 @ X315 @ X314)) = ((X313 @ X315 @ X314)))) | ? [X310 : subst,X309 : term] : (((comp @ sh @ (push @ X309 @ X310))) != X310) | ? [X308 : subst,X307 : term] : (((sub @ one @ (push @ X307 @ X308))) != X307))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f61,definition,(
% 6.12/1.30 ! [X302 : (term > $o)] : (($true = ((sP48 @ X302))) <=> ? [X304 : term,X305 : term] : ((((X302 @ (ap @ X304 @ X305))) != $true) & ($true = ((X302 @ X305))) & (((X302 @ X304)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f62,definition,(
% 6.12/1.30 (sP49 = $true) <=> ! [X382 : (subst > term > subst > $o),X383 : term] : (? [X393 : term] : (($true != ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) & (((X382 @ id @ X393 @ id)) = $true)) | ? [X385 : term,X384 : (subst > term > term)] : (! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) & ! [X392 : term] : ((((X382 @ id @ X392 @ id)) != $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true)) & ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) & (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) != $true)) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f63,definition,(
% 6.12/1.30 (sP50 = $true) <=> ! [X161 : term,X162 : (subst > term > subst > $o)] : (? [X168 : term] : (($true != ((X162 @ id @ (sub @ X161 @ (push @ X168 @ id)) @ id))) & ($true = ((X162 @ id @ X168 @ id)))) | (((X162 @ id @ (lam @ (sub @ X161 @ (push @ one @ sh))) @ id)) = $true) | ? [X163 : (subst > term > term)] : (($true != ((X162 @ id @ (lam @ (X163 @ sh @ one)) @ id))) & ! [X165 : subst,X164 : subst,X166 : term] : (((X163 @ (comp @ X164 @ X165) @ (sub @ X166 @ X165))) = ((sub @ (X163 @ X164 @ X166) @ X165))) & ! [X167 : term] : ((((X162 @ id @ (X163 @ id @ X167) @ id)) = $true) | ($true != ((X162 @ id @ X167 @ id))))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f64,definition,(
% 6.12/1.30 ! [X112 : (term > $o)] : (($true = ((sP51 @ X112))) <=> ! [X117 : term,X116 : term] : ((((X112 @ X117)) != $true) | (((X112 @ (ap @ X116 @ X117))) = $true) | (((X112 @ X116)) != $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f65,definition,(
% 6.12/1.30 ! [X129 : (subst > term > subst > $o)] : ((((sP52 @ X129)) = $true) <=> ? [X133 : (subst > term > term)] : ((((X129 @ id @ (lam @ (X133 @ sh @ one)) @ id)) != $true) & ! [X137 : subst,X135 : term,X136 : subst] : (((X133 @ (comp @ X137 @ X136) @ (sub @ X135 @ X136))) = ((sub @ (X133 @ X137 @ X135) @ X136))) & ! [X134 : term] : ((((X129 @ id @ (X133 @ id @ X134) @ id)) = $true) | (((X129 @ id @ X134 @ id)) != $true))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f66,definition,(
% 6.12/1.30 (sP53 = $true) <=> ? [X121 : (subst > term > subst > $o),X120 : term,X119 : (term > $o)] : (! [X122 : term] : ((((X119 @ X122)) != $true) | (((X119 @ (sub @ X120 @ (push @ X122 @ id)))) = $true)) & ! [X124 : (subst > term > term)] : (? [X126 : subst,X128 : subst,X127 : term] : (((sub @ (X124 @ X126 @ X127) @ X128)) != ((X124 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128)))) | ? [X125 : term] : ((((X121 @ id @ (X124 @ id @ X125) @ id)) != $true) & ($true = ((X121 @ id @ X125 @ id)))) | ($true = ((X121 @ id @ (lam @ (X124 @ sh @ one)) @ id)))) & ! [X123 : term] : (((X121 @ id @ X123 @ id)) = ((X119 @ X123))) & (((X119 @ (lam @ X120))) != $true))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f67,definition,(
% 6.12/1.30 ($true = sP54) <=> ? [X112 : (term > $o),X111 : term] : (($true = ((sP51 @ X112))) & ! [X113 : term] : (? [X114 : term] : ((((X112 @ (sub @ X113 @ (push @ X114 @ id)))) != $true) & (((X112 @ X114)) = $true)) | (((X112 @ (lam @ X113))) = $true)) & (((X112 @ X111)) != $true) & ! [X115 : term] : ((((var @ X115)) != $true) | (((X112 @ X115)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f68,definition,(
% 6.12/1.30 (sP55 = $true) <=> (? [X118 : term] : (((sub @ X118 @ id)) != X118) | (sP53 = $true) | ! [X130 : term,X129 : (subst > term > subst > $o)] : (? [X131 : term,X132 : term] : ((((X129 @ id @ X132 @ id)) = $true) & (((X129 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id)) != $true) & (((X129 @ id @ X131 @ id)) = $true)) | ($true = ((X129 @ id @ X130 @ id))) | (((sP52 @ X129)) = $true)) | ? [X108 : (subst > term > subst > $o)] : ! [X109 : (term > $o)] : ? [X110 : term] : (((X109 @ X110)) != ((X108 @ id @ X110 @ id))) | ($true = sP54))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f69,definition,(
% 6.12/1.30 ! [X91 : (subst > term > subst > $o)] : ((((sP56 @ X91)) = $true) <=> ? [X93 : term,X94 : term] : ((((X91 @ id @ X93 @ id)) = $true) & (((X91 @ id @ (ap @ (sub @ X93 @ id) @ X94) @ id)) != $true) & (((X91 @ id @ X94 @ id)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f70,definition,(
% 6.12/1.30 ! [X91 : (subst > term > subst > $o)] : ((((sP57 @ X91)) = $true) <=> ? [X95 : (subst > term > term)] : (! [X98 : subst,X99 : subst,X97 : term] : (((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98))) = ((sub @ (X95 @ X99 @ X97) @ X98))) & ! [X96 : term] : ((((X91 @ id @ X96 @ id)) != $true) | (((X91 @ id @ (X95 @ id @ X96) @ id)) = $true)) & ($true != ((X91 @ id @ (lam @ (X95 @ sh @ one)) @ id)))))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f71,definition,(
% 6.12/1.30 ($true = sP58) <=> ! [X90 : term,X91 : (subst > term > subst > $o)] : ((((sP57 @ X91)) = $true) | (((sP56 @ X91)) = $true) | ? [X92 : term] : ((((var @ (sub @ X92 @ id))) = $true) & ($true != ((X91 @ id @ X92 @ id)))) | (((X91 @ id @ X90 @ id)) = $true) | ? [X104 : term,X105 : subst,X106 : subst,X107 : subst] : ((((X91 @ (comp @ X105 @ X107) @ (sub @ X104 @ X107) @ X106)) != $true) & (((X91 @ X105 @ X104 @ (comp @ X107 @ X106))) = $true)) | ? [X103 : term,X100 : subst,X101 : subst,X102 : subst] : ((((X91 @ X101 @ X103 @ (comp @ X102 @ X100))) != $true) & (((X91 @ (comp @ X101 @ X102) @ (sub @ X103 @ X102) @ X100)) = $true)))),
% 6.12/1.30 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 6.12/1.30 thf(f72,plain,(
% 6.12/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & (($true = sP58) <=> (hoasinduction = $true)) & (ulamvar1 != $true) & (! [X534 : term] : ? [X535 : (subst > term > term)] : ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem1v2_gthm = $true) & ! [X323 : d_term,X324 : d_term] : ((((d2term @ X323)) != ((d2term @ X324))) | (X323 = X324)) & (! [X282 : (subst > term > subst > $o)] : ? [X283 : (term > $o)] : ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) <=> (hoasinduction_lem0 = $true)) & ((sP55 = $true) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((? [X538 : term] : (((sub @ X538 @ id)) != X538) | ! [X539 : term] : (((sub @ X539 @ id)) = X539)) <=> (termmset_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508)))) | ? [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) = ((ap @ X505 @ X502))) & (X503 != X505)) | ? [X501 : term] : (((sub @ X501 @ id)) != X501))) & (! [X431 : (subst > term > term),X433 : term,X432 : term] : (? [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) != ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0_lthm = $true) <=> ! [X139 : subst,X141 : (term > $o),X140 : term] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> (sP50 = $true)) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((axvarcons = $true) <=> ! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326)) & ((sP49 = $true) <=> (hoasinduction_lem3aaa = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem2v2_gthm = $true) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (! [X47 : term] : ? [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) = ((X48 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (pushprop_lem1_gthm = $true) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) <=> (apinj1 = $true)) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (! [X301 : term,X302 : (term > $o)] : (? [X306 : term] : (($true != ((X302 @ (lam @ X306)))) & (((X302 @ X306)) = $true)) | ? [X303 : term] : ((((var @ X303)) = $true) & (((X302 @ X303)) != $true)) | ($true = ((X302 @ X301))) | ($true = ((sP48 @ X302)))) <=> (induction = $true)) & (one = ((d2term @ d_one))) & (! [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | ? [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) != ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) | ? [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) != ((sub @ (X406 @ X412 @ X411) @ X410))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (($true = sP47) <=> (hoaslaminj_lthm = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP46)) & ((sP45 = $true) <=> (hoasinduction_lem3_lthm = $true)) & ((sP42 = $true) <=> (induction2lem = $true)) & ((! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4)))) | ? [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 != X3) & (((ap @ X2 @ X0)) = ((ap @ X1 @ X3))))) <=> (hoasapinj2_lthm = $true)) & ((? [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) != X173) | ! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)) | ? [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) != X175)) <=> (pushprop_lem1_lthm = $true)) & ((sP40 = $true) <=> (hoasinduction_lem3 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) <=> (pushprop_lem0 = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & ((sP38 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2subst @ d_id)) = sh) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) <=> (axidr = $true)) & (termmset_gthm = $true) & (pushprop = $true) & ((laminj = $true) <=> ! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68))) & (($true = sP37) <=> (hoasinduction_lem3v2a = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & ((axvarid = $true) <=> ! [X201 : term] : (((sub @ X201 @ id)) = X201)) & (hoasapinj1_gthm = $true) & ((sP36 = $true) <=> (hoasinduction_lem3v2 = $true)) & (axclos = $true) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP34)) & ((? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ! [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) = $true) | (((X299 @ X296)) != $true) | ? [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) != ((X297 @ X300))))) <=> (pushprop_lem1v2_lthm = $true)) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & ((sP32 = $true) <=> (hoasinduction_lthm = $true)) & ! [X144 : d_term] : (d_one = X144) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515)) | ? [X512 : subst] : (((comp @ id @ X512)) != X512) | ? [X513 : subst] : (((comp @ X513 @ id)) != X513)) <=> (substmonoid_lthm = $true)) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP23 = $true) <=> (hoasinduction_lem2 = $true)) & (! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) <=> (pushprop_lem1 = $true)) & ((axidl = $true) <=> ! [X31 : subst] : (((comp @ id @ X31)) = X31)) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) <=> (shinj = $true)) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((induction2_lthm = $true) <=> (sP21 = $true)) & ((sP17 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & (induction2_gthm = $true) & (($true = sP15) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X78 : d_subst,X77 : d_subst] : ((((d2subst @ X78)) != ((d2subst @ X77))) | (X77 = X78)) & ((hoasinduction_lthm_3 = $true) <=> (sP13 = $true)) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) <=> (termmset = $true)) & (axmap = $true) & ((apinj2 = $true) <=> ! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519))) & ((hoasinduction_lem3aa = $true) <=> (sP7 = $true)) & ((sP6 = $true) <=> (induction2 = $true)) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) <=> (hoasapinj1 = $true)) & (lamnotap != $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X520 : term,X521 : (subst > term > subst > $o)] : (? [X522 : (subst > term > term)] : (! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) & ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) & (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true)) | (((X521 @ id @ X520 @ id)) = $true) | (((sP4 @ X521)) = $true))) & (hoasapinj2_gthm = $true) & (! [X169 : term] : ? [X170 : (subst > term > term)] : ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171)))) <=> (hoasinduction_lem3v2_f = $true)) & ((sP3 = $true) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X401 : (subst > term > subst > $o)] : ? [X402 : (term > $o)] : ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id)))) & ((axscons = $true) <=> ! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138)) & ((substmonoid = $true) <=> (! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & (hoaslamnotvar = $true) & (! [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) = $true) | ? [X533 : term] : (((X530 @ X533)) != ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) | (((X532 @ X531)) != $true)) <=> (pushprop_lem1v2 = $true)) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) <=> (axshiftcons = $true))),
% 6.12/1.30 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 6.12/1.30 thf(f101,plain,(
% 6.12/1.30 ((sP49 = $true) | ? [X382 : (subst > term > subst > $o),X383 : term] : (! [X393 : term] : (($true = ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) | (((X382 @ id @ X393 @ id)) != $true)) & ! [X385 : term,X384 : (subst > term > term)] : (? [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) != ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) | ? [X392 : term] : ((((X382 @ id @ X392 @ id)) = $true) & (((X382 @ id @ (X384 @ id @ X392) @ id)) != $true)) | ? [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) != ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) | (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) = $true)) & ($true != ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id))))) & (! [X382 : (subst > term > subst > $o),X383 : term] : (? [X393 : term] : (($true != ((X382 @ id @ (sub @ X383 @ (push @ X393 @ id)) @ id))) & (((X382 @ id @ X393 @ id)) = $true)) | ? [X385 : term,X384 : (subst > term > term)] : (! [X388 : subst,X387 : subst,X386 : term] : (((sub @ X385 @ (push @ (sub @ X386 @ X387) @ (comp @ X388 @ X387)))) = ((X384 @ (comp @ X388 @ X387) @ (sub @ X386 @ X387)))) & ! [X392 : term] : ((((X382 @ id @ X392 @ id)) != $true) | (((X382 @ id @ (X384 @ id @ X392) @ id)) = $true)) & ! [X390 : subst,X391 : subst,X389 : term] : (((sub @ (X384 @ X391 @ X389) @ X390)) = ((sub @ (sub @ X385 @ (push @ X389 @ X391)) @ X390))) & (((X382 @ id @ (lam @ (X384 @ sh @ one)) @ id)) != $true)) | ($true = ((X382 @ id @ (lam @ (sub @ X383 @ (push @ one @ sh))) @ id)))) | (sP49 != $true))),
% 6.12/1.30 inference(nnf_transformation,[],[f62])).
% 6.12/1.30 thf(f102,plain,(
% 6.12/1.30 ((sP49 = $true) | ? [X0 : (subst > term > subst > $o),X1 : term] : (! [X2 : term] : ((((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id)) = $true) | ($true != ((X0 @ id @ X2 @ id)))) & ! [X3 : term,X4 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((X4 @ (comp @ X5 @ X6) @ (sub @ X7 @ X6))) != ((sub @ X3 @ (push @ (sub @ X7 @ X6) @ (comp @ X5 @ X6))))) | ? [X8 : term] : (($true = ((X0 @ id @ X8 @ id))) & (((X0 @ id @ (X4 @ id @ X8) @ id)) != $true)) | ? [X9 : subst,X10 : subst,X11 : term] : (((sub @ (X4 @ X10 @ X11) @ X9)) != ((sub @ (sub @ X3 @ (push @ X11 @ X10)) @ X9))) | (((X0 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true)) & ($true != ((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id))))) & (! [X12 : (subst > term > subst > $o),X13 : term] : (? [X14 : term] : ((((X12 @ id @ (sub @ X13 @ (push @ X14 @ id)) @ id)) != $true) & (((X12 @ id @ X14 @ id)) = $true)) | ? [X15 : term,X16 : (subst > term > term)] : (! [X17 : subst,X18 : subst,X19 : term] : (((X16 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18))) = ((sub @ X15 @ (push @ (sub @ X19 @ X18) @ (comp @ X17 @ X18))))) & ! [X20 : term] : (($true != ((X12 @ id @ X20 @ id))) | ($true = ((X12 @ id @ (X16 @ id @ X20) @ id)))) & ! [X21 : subst,X22 : subst,X23 : term] : (((sub @ (sub @ X15 @ (push @ X23 @ X22)) @ X21)) = ((sub @ (X16 @ X22 @ X23) @ X21))) & ($true != ((X12 @ id @ (lam @ (X16 @ sh @ one)) @ id)))) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true)) | (sP49 != $true))),
% 6.12/1.30 inference(rectify,[],[f101])).
% 6.12/1.30 thf(f103,plain,(
% 6.12/1.30 ((sP49 = $true) | (! [X2 : term] : (($true = ((sK115 @ id @ (sub @ sK116 @ (push @ X2 @ id)) @ id))) | ($true != ((sK115 @ id @ X2 @ id)))) & ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) != ((X4 @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | ((((sK115 @ id @ (sK120 @ X4) @ id)) = $true) & (((sK115 @ id @ (X4 @ id @ (sK120 @ X4)) @ id)) != $true)) | (((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (sK122 @ X4 @ X3))) @ (sK121 @ X4 @ X3))) != ((sub @ (X4 @ (sK122 @ X4 @ X3) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3)))) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true)) & (((sK115 @ id @ (lam @ (sub @ sK116 @ (push @ one @ sh))) @ id)) != $true))) & (! [X12 : (subst > term > subst > $o),X13 : term] : (((((X12 @ id @ (sub @ X13 @ (push @ (sK124 @ X13 @ X12) @ id)) @ id)) != $true) & (((X12 @ id @ (sK124 @ X13 @ X12) @ id)) = $true)) | (! [X17 : subst,X18 : subst,X19 : term] : (((sK126 @ X12 @ (comp @ X17 @ X18) @ (sub @ X19 @ X18))) = ((sub @ (sK125 @ X12) @ (push @ (sub @ X19 @ X18) @ (comp @ X17 @ X18))))) & ! [X20 : term] : (($true != ((X12 @ id @ X20 @ id))) | (((X12 @ id @ (sK126 @ X12 @ id @ X20) @ id)) = $true)) & ! [X21 : subst,X22 : subst,X23 : term] : (((sub @ (sub @ (sK125 @ X12) @ (push @ X23 @ X22)) @ X21)) = ((sub @ (sK126 @ X12 @ X22 @ X23) @ X21))) & (((X12 @ id @ (lam @ (sK126 @ X12 @ sh @ one)) @ id)) != $true)) | (((X12 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id)) = $true)) | (sP49 != $true))),
% 6.12/1.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK115,sK116,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK115),skolemize(X1,sK116),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12)],[f102])).
% 6.12/1.30 thf(f260,plain,(
% 6.12/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & ((($true = sP58) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP58))) & (ulamvar1 != $true) & ((! [X534 : term] : ? [X535 : (subst > term > term)] : ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X534 : term] : ! [X535 : (subst > term > term)] : ? [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) != ((sub @ X534 @ (push @ X536 @ X537)))))) & (pushprop_lem1v2_gthm = $true) & ! [X323 : d_term,X324 : d_term] : ((((d2term @ X323)) != ((d2term @ X324))) | (X323 = X324)) & ((! [X282 : (subst > term > subst > $o)] : ? [X283 : (term > $o)] : ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X282 : (subst > term > subst > $o)] : ! [X283 : (term > $o)] : ? [X284 : term] : (((X283 @ X284)) != ((X282 @ id @ X284 @ id))))) & (((sP55 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP55 != $true))) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (((? [X538 : term] : (((sub @ X538 @ id)) != X538) | ! [X539 : term] : (((sub @ X539 @ id)) = X539)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X538 : term] : (((sub @ X538 @ id)) = X538) & ? [X539 : term] : (((sub @ X539 @ id)) != X539)))) & (((hoasapinj1_lthm = $true) | (? [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 != X509) & (((ap @ (sub @ X507 @ id) @ X506)) = ((ap @ (sub @ X509 @ id) @ X508)))) & ! [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) != ((ap @ X505 @ X502))) | (X503 = X505)) & ! [X501 : term] : (((sub @ X501 @ id)) = X501))) & ((! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508)))) | ? [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) = ((ap @ X505 @ X502))) & (X503 != X505)) | ? [X501 : term] : (((sub @ X501 @ id)) != X501)) | (hoasapinj1_lthm != $true))) & ((! [X431 : (subst > term > term),X433 : term,X432 : term] : (? [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) != ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X431 : (subst > term > term),X433 : term,X432 : term] : (! [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X431 @ X434 @ X435) @ X436))) & (((lam @ (X431 @ sh @ one))) = ((ap @ (sub @ X433 @ id) @ X432)))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & (((pushprop_lem0_lthm = $true) | ? [X139 : subst,X141 : (term > $o),X140 : term] : ! [X142 : (term > $o)] : ? [X143 : term] : (((X142 @ X143)) != ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (! [X139 : subst,X141 : (term > $o),X140 : term] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139))))) | (pushprop_lem0_lthm != $true))) & (hoaslamnotap_lthm = $true) & (((hoasinduction_lem3aa_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem3aa_lthm != $true))) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (((axvarcons = $true) | ? [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) != X326)) & (! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326) | (axvarcons != $true))) & (((sP49 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP49 != $true))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem2v2_gthm = $true) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & ((! [X47 : term] : ? [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) = ((X48 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X47 : term] : ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one))))) & (pushprop_lem1_gthm = $true) & ((! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) = ((ap @ X29 @ X26))) & (X27 != X29)))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & ((! [X301 : term,X302 : (term > $o)] : (? [X306 : term] : (($true != ((X302 @ (lam @ X306)))) & (((X302 @ X306)) = $true)) | ? [X303 : term] : ((((var @ X303)) = $true) & (((X302 @ X303)) != $true)) | ($true = ((X302 @ X301))) | ($true = ((sP48 @ X302)))) | (induction != $true)) & ((induction = $true) | ? [X301 : term,X302 : (term > $o)] : (! [X306 : term] : (($true = ((X302 @ (lam @ X306)))) | (((X302 @ X306)) != $true)) & ! [X303 : term] : ((((var @ X303)) != $true) | (((X302 @ X303)) = $true)) & ($true != ((X302 @ X301))) & ($true != ((sP48 @ X302)))))) & (one = ((d2term @ d_one))) & ((! [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | ? [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) != ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) | ? [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) != ((sub @ (X406 @ X412 @ X411) @ X410))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) = ((lam @ (X409 @ sh @ one)))) & ! [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) = ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) & ! [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) = ((sub @ (X406 @ X412 @ X411) @ X410))) & (((X406 @ X407 @ X408)) != ((X409 @ X407 @ X408)))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & ((($true = sP47) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP47))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & (((hoasinduction_lem3a = $true) | ($true != sP46)) & (($true = sP46) | (hoasinduction_lem3a != $true))) & (((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true))) & (((sP42 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP42 != $true))) & (((! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4)))) | ? [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 != X3) & (((ap @ X2 @ X0)) = ((ap @ X1 @ X3))))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 != X6) & (((ap @ (sub @ X7 @ id) @ X6)) = ((ap @ (sub @ X5 @ id) @ X4)))) & ! [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 = X3) | (((ap @ X2 @ X0)) != ((ap @ X1 @ X3))))))) & (((? [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) != X173) | ! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)) | ? [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) != X175)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) = X173) & ? [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true != ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) & (((X177 @ X178)) = $true)) & ! [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) = X175)))) & (((sP40 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP40 != $true))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & ((! [X395 : subst,X394 : term,X396 : (term > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X395 : subst,X394 : term,X396 : (term > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) != ((X397 @ X398))))) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & (((sP38 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP38 != $true))) & (((d2subst @ d_id)) = sh) & ((! [X202 : subst] : (((comp @ X202 @ id)) = X202) | (axidr != $true)) & ((axidr = $true) | ? [X202 : subst] : (((comp @ X202 @ id)) != X202))) & (termmset_gthm = $true) & (pushprop = $true) & (((laminj = $true) | ? [X68 : term,X67 : term] : ((((lam @ X67)) = ((lam @ X68))) & (X67 != X68))) & (! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68)) | (laminj != $true))) & ((($true = sP37) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP37))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & (((axvarid = $true) | ? [X201 : term] : (((sub @ X201 @ id)) != X201)) & (! [X201 : term] : (((sub @ X201 @ id)) = X201) | (axvarid != $true))) & (hoasapinj1_gthm = $true) & (((sP36 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP36 != $true))) & (axclos = $true) & (((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true))) & (((? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ! [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) = $true) | (((X299 @ X296)) != $true) | ? [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) != ((X297 @ X300))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) = X294) & ? [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) != $true) & (((X299 @ X296)) = $true) & ! [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) = ((X297 @ X300))))))) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & (((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true))) & ! [X144 : d_term] : (d_one = X144) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((((! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515)) | ? [X512 : subst] : (((comp @ id @ X512)) != X512) | ? [X513 : subst] : (((comp @ X513 @ id)) != X513)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X514 : subst] : (((comp @ X514 @ id)) != X514) | ? [X515 : subst] : (((comp @ id @ X515)) != X515)) & ! [X512 : subst] : (((comp @ id @ X512)) = X512) & ! [X513 : subst] : (((comp @ X513 @ id)) = X513)))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & (((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP23 != $true))) & ((! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) != $true) & ($true = ((X83 @ X84)))))) & (((axidl = $true) | ? [X31 : subst] : (((comp @ id @ X31)) != X31)) & (! [X31 : subst] : (((comp @ id @ X31)) = X31) | (axidl != $true))) & ((! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) | (shinj != $true)) & ((shinj = $true) | ? [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) = ((sub @ X511 @ sh))) & (X510 != X511)))) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((induction2_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2_lthm != $true))) & (((sP17 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP17 != $true))) & (induction2_gthm = $true) & ((($true = sP15) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP15))) & ! [X78 : d_subst,X77 : d_subst] : ((((d2subst @ X78)) != ((d2subst @ X77))) | (X77 = X78)) & (((hoasinduction_lthm_3 = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm_3 != $true))) & ((! [X30 : term] : (((sub @ X30 @ id)) = X30) | (termmset != $true)) & ((termmset = $true) | ? [X30 : term] : (((sub @ X30 @ id)) != X30))) & (axmap = $true) & (((apinj2 = $true) | ? [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) = ((ap @ X517 @ X516))) & (X516 != X519))) & (! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519)) | (apinj2 != $true))) & (((hoasinduction_lem3aa = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa != $true))) & (((sP6 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP6 != $true))) & ((! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) = ((ap @ (sub @ X381 @ id) @ X380))) & (X379 != X381)))) & (lamnotap != $true) & (((hoasinduction_no_psi_cond = $true) | ? [X520 : term,X521 : (subst > term > subst > $o)] : (! [X522 : (subst > term > term)] : (? [X526 : term] : ((((X521 @ id @ X526 @ id)) = $true) & (((X521 @ id @ (X522 @ id @ X526) @ id)) != $true)) | ? [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) != ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) | (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true)) & (((X521 @ id @ X520 @ id)) != $true) & (((sP4 @ X521)) != $true))) & (! [X520 : term,X521 : (subst > term > subst > $o)] : (? [X522 : (subst > term > term)] : (! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) & ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) & (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true)) | (((X521 @ id @ X520 @ id)) = $true) | (((sP4 @ X521)) = $true)) | (hoasinduction_no_psi_cond != $true))) & (hoasapinj2_gthm = $true) & ((! [X169 : term] : ? [X170 : (subst > term > term)] : ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X169 : term] : ! [X170 : (subst > term > term)] : ? [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) != ((sub @ X169 @ (push @ X172 @ X171)))))) & (((sP3 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP3 != $true))) & (hoasinduction_lem1_gthm = $true) & (((hoasapinj2 = $true) | ? [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 != X81) & (((ap @ (sub @ X79 @ id) @ X80)) = ((ap @ (sub @ X82 @ id) @ X81))))) & (! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81)))) | (hoasapinj2 != $true))) & (((hoasinduction_lem3b_lthm = $true) | ? [X32 : term] : ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one)))) & (! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((hoasinduction_lem0_lthm = $true) | ? [X401 : (subst > term > subst > $o)] : ! [X402 : (term > $o)] : ? [X403 : term] : (((X402 @ X403)) != ((X401 @ id @ X403 @ id)))) & (! [X401 : (subst > term > subst > $o)] : ? [X402 : (term > $o)] : ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((axscons = $true) | ? [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) != X138)) & (! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138) | (axscons != $true))) & (((substmonoid = $true) | (? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404))) & ((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404)) | (substmonoid != $true))) & (hoaslamnotvar = $true) & ((! [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) = $true) | ? [X533 : term] : (((X530 @ X533)) != ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) | (((X532 @ X531)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) != $true) & ! [X533 : term] : (((X530 @ X533)) = ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) & (((X532 @ X531)) = $true)))) & ((! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) != X88)))),
% 6.12/1.30 inference(nnf_transformation,[],[f72])).
% 6.12/1.30 thf(f261,plain,(
% 6.12/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & (($true = sP58) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP58)) & (ulamvar1 != $true) & (! [X534 : term] : ? [X535 : (subst > term > term)] : ! [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) = ((sub @ X534 @ (push @ X536 @ X537)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X534 : term] : ! [X535 : (subst > term > term)] : ? [X537 : subst,X536 : term] : (((X535 @ X537 @ X536)) != ((sub @ X534 @ (push @ X536 @ X537))))) & (pushprop_lem1v2_gthm = $true) & ! [X323 : d_term,X324 : d_term] : ((((d2term @ X323)) != ((d2term @ X324))) | (X323 = X324)) & (! [X282 : (subst > term > subst > $o)] : ? [X283 : (term > $o)] : ! [X284 : term] : (((X283 @ X284)) = ((X282 @ id @ X284 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X282 : (subst > term > subst > $o)] : ! [X283 : (term > $o)] : ? [X284 : term] : (((X283 @ X284)) != ((X282 @ id @ X284 @ id)))) & ((sP55 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP55 != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (? [X538 : term] : (((sub @ X538 @ id)) != X538) | ! [X539 : term] : (((sub @ X539 @ id)) = X539) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X538 : term] : (((sub @ X538 @ id)) = X538) & ? [X539 : term] : (((sub @ X539 @ id)) != X539))) & ((hoasapinj1_lthm = $true) | (? [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 != X509) & (((ap @ (sub @ X507 @ id) @ X506)) = ((ap @ (sub @ X509 @ id) @ X508)))) & ! [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) != ((ap @ X505 @ X502))) | (X503 = X505)) & ! [X501 : term] : (((sub @ X501 @ id)) = X501))) & (! [X508 : term,X506 : term,X507 : term,X509 : term] : ((X507 = X509) | (((ap @ (sub @ X507 @ id) @ X506)) != ((ap @ (sub @ X509 @ id) @ X508)))) | ? [X502 : term,X505 : term,X504 : term,X503 : term] : ((((ap @ X503 @ X504)) = ((ap @ X505 @ X502))) & (X503 != X505)) | ? [X501 : term] : (((sub @ X501 @ id)) != X501) | (hoasapinj1_lthm != $true)) & (! [X431 : (subst > term > term),X433 : term,X432 : term] : (? [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) != ((sub @ (X431 @ X434 @ X435) @ X436))) | (((lam @ (X431 @ sh @ one))) != ((ap @ (sub @ X433 @ id) @ X432)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X431 : (subst > term > term),X433 : term,X432 : term] : (! [X434 : subst,X435 : term,X436 : subst] : (((X431 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436))) = ((sub @ (X431 @ X434 @ X435) @ X436))) & (((lam @ (X431 @ sh @ one))) = ((ap @ (sub @ X433 @ id) @ X432))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0_lthm = $true) | ? [X139 : subst,X141 : (term > $o),X140 : term] : ! [X142 : (term > $o)] : ? [X143 : term] : (((X142 @ X143)) != ((X141 @ (sub @ X143 @ (push @ X140 @ X139)))))) & (! [X139 : subst,X141 : (term > $o),X140 : term] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X141 @ (sub @ X143 @ (push @ X140 @ X139))))) | (pushprop_lem0_lthm != $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((axvarcons = $true) | ? [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) != X326)) & (! [X326 : term,X325 : subst] : (((sub @ one @ (push @ X326 @ X325))) = X326) | (axvarcons != $true)) & ((sP49 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP49 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X49 : d_subst] : (d_id = X49) & (pushprop_lem2v2_gthm = $true) & ! [X285 : term] : ? [X286 : d_term] : (((d2term @ X286)) = X285) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (! [X47 : term] : ? [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) = ((X48 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X47 : term] : ! [X48 : (subst > term > term)] : (((sub @ X47 @ (push @ one @ sh))) != ((X48 @ sh @ one)))) & (pushprop_lem1_gthm = $true) & (! [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) != ((ap @ X29 @ X26))) | (X27 = X29)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X28 : term,X29 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X28)) = ((ap @ X29 @ X26))) & (X27 != X29))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (! [X301 : term,X302 : (term > $o)] : (? [X306 : term] : (($true != ((X302 @ (lam @ X306)))) & (((X302 @ X306)) = $true)) | ? [X303 : term] : ((((var @ X303)) = $true) & (((X302 @ X303)) != $true)) | ($true = ((X302 @ X301))) | ($true = ((sP48 @ X302)))) | (induction != $true)) & ((induction = $true) | ? [X301 : term,X302 : (term > $o)] : (! [X306 : term] : (($true = ((X302 @ (lam @ X306)))) | (((X302 @ X306)) != $true)) & ! [X303 : term] : ((((var @ X303)) != $true) | (((X302 @ X303)) = $true)) & ($true != ((X302 @ X301))) & ($true != ((sP48 @ X302))))) & (one = ((d2term @ d_one))) & (! [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) != ((lam @ (X409 @ sh @ one)))) | ? [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) != ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) | ? [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) != ((sub @ (X406 @ X412 @ X411) @ X410))) | (((X406 @ X407 @ X408)) = ((X409 @ X407 @ X408)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X407 : subst,X409 : (subst > term > term),X406 : (subst > term > term),X408 : term] : ((((lam @ (X406 @ sh @ one))) = ((lam @ (X409 @ sh @ one)))) & ! [X415 : subst,X413 : subst,X414 : term] : (((sub @ (X409 @ X413 @ X414) @ X415)) = ((X409 @ (comp @ X413 @ X415) @ (sub @ X414 @ X415)))) & ! [X412 : subst,X410 : subst,X411 : term] : (((X406 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410))) = ((sub @ (X406 @ X412 @ X411) @ X410))) & (((X406 @ X407 @ X408)) != ((X409 @ X407 @ X408))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (($true = sP47) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP47)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP46)) & (($true = sP46) | (hoasinduction_lem3a != $true)) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & ((sP42 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP42 != $true)) & (! [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 = X6) | (((ap @ (sub @ X7 @ id) @ X6)) != ((ap @ (sub @ X5 @ id) @ X4)))) | ? [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 != X3) & (((ap @ X2 @ X0)) = ((ap @ X1 @ X3)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X7 : term,X5 : term,X4 : term,X6 : term] : ((X4 != X6) & (((ap @ (sub @ X7 @ id) @ X6)) = ((ap @ (sub @ X5 @ id) @ X4)))) & ! [X0 : term,X1 : term,X3 : term,X2 : term] : ((X0 = X3) | (((ap @ X2 @ X0)) != ((ap @ X1 @ X3)))))) & (? [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) != X173) | ! [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true = ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) | (((X177 @ X178)) != $true)) | ? [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) != X175) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X173 : term,X174 : subst] : (((sub @ one @ (push @ X173 @ X174))) = X173) & ? [X179 : term,X181 : subst,X177 : (term > $o),X178 : term,X180 : (term > $o)] : (($true != ((X180 @ (sub @ X178 @ (push @ X179 @ X181))))) & (((X177 @ X178)) = $true)) & ! [X175 : subst,X176 : term] : (((comp @ sh @ (push @ X176 @ X175))) = X175))) & ((sP40 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP40 != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (! [X395 : subst,X394 : term,X396 : (term > $o)] : ? [X397 : (term > $o)] : ! [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) = ((X397 @ X398))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X395 : subst,X394 : term,X396 : (term > $o)] : ! [X397 : (term > $o)] : ? [X398 : term] : (((X396 @ (sub @ X398 @ (push @ X394 @ X395)))) != ((X397 @ X398)))) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X399 : subst] : ? [X400 : d_subst] : (((d2subst @ X400)) = X399) & ((sP38 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP38 != $true)) & (((d2subst @ d_id)) = sh) & (! [X202 : subst] : (((comp @ X202 @ id)) = X202) | (axidr != $true)) & ((axidr = $true) | ? [X202 : subst] : (((comp @ X202 @ id)) != X202)) & (termmset_gthm = $true) & (pushprop = $true) & ((laminj = $true) | ? [X68 : term,X67 : term] : ((((lam @ X67)) = ((lam @ X68))) & (X67 != X68))) & (! [X68 : term,X67 : term] : ((((lam @ X67)) != ((lam @ X68))) | (X67 = X68)) | (laminj != $true)) & (($true = sP37) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP37)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & ((axvarid = $true) | ? [X201 : term] : (((sub @ X201 @ id)) != X201)) & (! [X201 : term] : (((sub @ X201 @ id)) = X201) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & ((sP36 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP36 != $true)) & (axclos = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & (? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ! [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) = $true) | (((X299 @ X296)) != $true) | ? [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) != ((X297 @ X300)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) = X294) & ? [X297 : (term > $o),X296 : term,X299 : (term > $o),X298 : subst] : ((((X297 @ one)) != $true) & (((X299 @ X296)) = $true) & ! [X300 : term] : (((X299 @ (sub @ X300 @ (push @ X296 @ X298)))) = ((X297 @ X300)))))) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & ! [X144 : d_term] : (d_one = X144) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515)) | ? [X512 : subst] : (((comp @ id @ X512)) != X512) | ? [X513 : subst] : (((comp @ X513 @ id)) != X513) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X514 : subst] : (((comp @ X514 @ id)) != X514) | ? [X515 : subst] : (((comp @ id @ X515)) != X515)) & ! [X512 : subst] : (((comp @ id @ X512)) = X512) & ! [X513 : subst] : (((comp @ X513 @ id)) = X513))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & (! [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) = $true) | ($true != ((X83 @ X84)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X83 : (term > $o),X87 : subst,X85 : term,X84 : term,X86 : (term > $o)] : ((((X86 @ (sub @ X84 @ (push @ X85 @ X87)))) != $true) & ($true = ((X83 @ X84))))) & ((axidl = $true) | ? [X31 : subst] : (((comp @ id @ X31)) != X31)) & (! [X31 : subst] : (((comp @ id @ X31)) = X31) | (axidl != $true)) & (! [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) != ((sub @ X511 @ sh))) | (X510 = X511)) | (shinj != $true)) & ((shinj = $true) | ? [X510 : term,X511 : term] : ((((sub @ X510 @ sh)) = ((sub @ X511 @ sh))) & (X510 != X511))) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((induction2_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP17 != $true)) & (induction2_gthm = $true) & (($true = sP15) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP15)) & ! [X78 : d_subst,X77 : d_subst] : ((((d2subst @ X78)) != ((d2subst @ X77))) | (X77 = X78)) & ((hoasinduction_lthm_3 = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm_3 != $true)) & (! [X30 : term] : (((sub @ X30 @ id)) = X30) | (termmset != $true)) & ((termmset = $true) | ? [X30 : term] : (((sub @ X30 @ id)) != X30)) & (axmap = $true) & ((apinj2 = $true) | ? [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) = ((ap @ X517 @ X516))) & (X516 != X519))) & (! [X519 : term,X517 : term,X518 : term,X516 : term] : ((((ap @ X518 @ X519)) != ((ap @ X517 @ X516))) | (X516 = X519)) | (apinj2 != $true)) & ((hoasinduction_lem3aa = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa != $true)) & ((sP6 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP6 != $true)) & (! [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) != ((ap @ (sub @ X381 @ id) @ X380))) | (X379 = X381)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X378 : term,X380 : term,X381 : term,X379 : term] : ((((ap @ (sub @ X379 @ id) @ X378)) = ((ap @ (sub @ X381 @ id) @ X380))) & (X379 != X381))) & (lamnotap != $true) & ((hoasinduction_no_psi_cond = $true) | ? [X520 : term,X521 : (subst > term > subst > $o)] : (! [X522 : (subst > term > term)] : (? [X526 : term] : ((((X521 @ id @ X526 @ id)) = $true) & (((X521 @ id @ (X522 @ id @ X526) @ id)) != $true)) | ? [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) != ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) | (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) = $true)) & (((X521 @ id @ X520 @ id)) != $true) & (((sP4 @ X521)) != $true))) & (! [X520 : term,X521 : (subst > term > subst > $o)] : (? [X522 : (subst > term > term)] : (! [X526 : term] : ((((X521 @ id @ X526 @ id)) != $true) | (((X521 @ id @ (X522 @ id @ X526) @ id)) = $true)) & ! [X523 : term,X525 : subst,X524 : subst] : (((sub @ (X522 @ X524 @ X523) @ X525)) = ((X522 @ (comp @ X524 @ X525) @ (sub @ X523 @ X525)))) & (((X521 @ id @ (lam @ (X522 @ sh @ one)) @ id)) != $true)) | (((X521 @ id @ X520 @ id)) = $true) | (((sP4 @ X521)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (hoasapinj2_gthm = $true) & (! [X169 : term] : ? [X170 : (subst > term > term)] : ! [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) = ((sub @ X169 @ (push @ X172 @ X171)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X169 : term] : ! [X170 : (subst > term > term)] : ? [X172 : term,X171 : subst] : (((X170 @ X171 @ X172)) != ((sub @ X169 @ (push @ X172 @ X171))))) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP3 != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2 = $true) | ? [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 != X81) & (((ap @ (sub @ X79 @ id) @ X80)) = ((ap @ (sub @ X82 @ id) @ X81))))) & (! [X80 : term,X82 : term,X81 : term,X79 : term] : ((X80 = X81) | (((ap @ (sub @ X79 @ id) @ X80)) != ((ap @ (sub @ X82 @ id) @ X81)))) | (hoasapinj2 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X32 : term] : ! [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) != ((X33 @ sh @ one)))) & (! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X401 : (subst > term > subst > $o)] : ! [X402 : (term > $o)] : ? [X403 : term] : (((X402 @ X403)) != ((X401 @ id @ X403 @ id)))) & (! [X401 : (subst > term > subst > $o)] : ? [X402 : (term > $o)] : ! [X403 : term] : (((X402 @ X403)) = ((X401 @ id @ X403 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((axscons = $true) | ? [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) != X138)) & (! [X138 : subst] : (((push @ (sub @ one @ X138) @ (comp @ sh @ X138))) = X138) | (axscons != $true)) & ((substmonoid = $true) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404)) & ((! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404)) | (substmonoid != $true)) & (hoaslamnotvar = $true) & (! [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) = $true) | ? [X533 : term] : (((X530 @ X533)) != ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) | (((X532 @ X531)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X529 : subst,X531 : term,X532 : (term > $o),X530 : (term > $o)] : ((((X530 @ one)) != $true) & ! [X533 : term] : (((X530 @ X533)) = ((X532 @ (sub @ X533 @ (push @ X531 @ X529))))) & (((X532 @ X531)) = $true))) & (! [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) = X88) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X88 : subst,X89 : term] : (((comp @ sh @ (push @ X89 @ X88))) != X88))),
% 6.99/1.30 inference(flattening,[],[f260])).
% 6.99/1.30 thf(f262,plain,(
% 6.99/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & (($true = sP58) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP58)) & (ulamvar1 != $true) & (! [X0 : term] : ? [X1 : (subst > term > term)] : ! [X2 : subst,X3 : term] : (((sub @ X0 @ (push @ X3 @ X2))) = ((X1 @ X2 @ X3))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X4 : term] : ! [X5 : (subst > term > term)] : ? [X6 : subst,X7 : term] : (((X5 @ X6 @ X7)) != ((sub @ X4 @ (push @ X7 @ X6))))) & (pushprop_lem1v2_gthm = $true) & ! [X8 : d_term,X9 : d_term] : ((((d2term @ X9)) != ((d2term @ X8))) | (X8 = X9)) & (! [X10 : (subst > term > subst > $o)] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X13 : (subst > term > subst > $o)] : ! [X14 : (term > $o)] : ? [X15 : term] : (((X14 @ X15)) != ((X13 @ id @ X15 @ id)))) & ((sP55 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP55 != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & (? [X16 : term] : (((sub @ X16 @ id)) != X16) | ! [X17 : term] : (((sub @ X17 @ id)) = X17) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X18 : term] : (((sub @ X18 @ id)) = X18) & ? [X19 : term] : (((sub @ X19 @ id)) != X19))) & ((hoasapinj1_lthm = $true) | (? [X20 : term,X21 : term,X22 : term,X23 : term] : ((X22 != X23) & (((ap @ (sub @ X23 @ id) @ X20)) = ((ap @ (sub @ X22 @ id) @ X21)))) & ! [X24 : term,X25 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X26)) != ((ap @ X25 @ X24))) | (X25 = X27)) & ! [X28 : term] : (((sub @ X28 @ id)) = X28))) & (! [X29 : term,X30 : term,X31 : term,X32 : term] : ((X31 = X32) | (((ap @ (sub @ X31 @ id) @ X30)) != ((ap @ (sub @ X32 @ id) @ X29)))) | ? [X33 : term,X34 : term,X35 : term,X36 : term] : ((((ap @ X36 @ X35)) = ((ap @ X34 @ X33))) & (X34 != X36)) | ? [X37 : term] : (((sub @ X37 @ id)) != X37) | (hoasapinj1_lthm != $true)) & (! [X38 : (subst > term > term),X39 : term,X40 : term] : (? [X41 : subst,X42 : term,X43 : subst] : (((X38 @ (comp @ X41 @ X43) @ (sub @ X42 @ X43))) != ((sub @ (X38 @ X41 @ X42) @ X43))) | (((ap @ (sub @ X39 @ id) @ X40)) != ((lam @ (X38 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X44 : (subst > term > term),X45 : term,X46 : term] : (! [X47 : subst,X48 : term,X49 : subst] : (((sub @ (X44 @ X47 @ X48) @ X49)) = ((X44 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49)))) & (((ap @ (sub @ X45 @ id) @ X46)) = ((lam @ (X44 @ sh @ one)))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0_lthm = $true) | ? [X50 : subst,X51 : (term > $o),X52 : term] : ! [X53 : (term > $o)] : ? [X54 : term] : (((X51 @ (sub @ X54 @ (push @ X52 @ X50)))) != ((X53 @ X54)))) & (! [X55 : subst,X56 : (term > $o),X57 : term] : ? [X58 : (term > $o)] : ! [X59 : term] : (((X56 @ (sub @ X59 @ (push @ X57 @ X55)))) = ((X58 @ X59))) | (pushprop_lem0_lthm != $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((axvarcons = $true) | ? [X60 : term,X61 : subst] : (((sub @ one @ (push @ X60 @ X61))) != X60)) & (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) | (axvarcons != $true)) & ((sP49 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP49 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X64 : d_subst] : (d_id = X64) & (pushprop_lem2v2_gthm = $true) & ! [X65 : term] : ? [X66 : d_term] : (((d2term @ X66)) = X65) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (! [X67 : term] : ? [X68 : (subst > term > term)] : (((sub @ X67 @ (push @ one @ sh))) = ((X68 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X69 : term] : ! [X70 : (subst > term > term)] : (((sub @ X69 @ (push @ one @ sh))) != ((X70 @ sh @ one)))) & (pushprop_lem1_gthm = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((((ap @ X72 @ X73)) != ((ap @ X74 @ X71))) | (X72 = X74)) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X75 : term,X76 : term,X77 : term,X78 : term] : ((((ap @ X76 @ X77)) = ((ap @ X78 @ X75))) & (X76 != X78))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (! [X79 : term,X80 : (term > $o)] : (? [X81 : term] : (($true != ((X80 @ (lam @ X81)))) & (((X80 @ X81)) = $true)) | ? [X82 : term] : (($true = ((var @ X82))) & (((X80 @ X82)) != $true)) | (((X80 @ X79)) = $true) | (((sP48 @ X80)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X83 : term,X84 : (term > $o)] : (! [X85 : term] : ((((X84 @ (lam @ X85))) = $true) | (((X84 @ X85)) != $true)) & ! [X86 : term] : ((((var @ X86)) != $true) | ($true = ((X84 @ X86)))) & (((X84 @ X83)) != $true) & (((sP48 @ X84)) != $true))) & (one = ((d2term @ d_one))) & (! [X87 : subst,X88 : (subst > term > term),X89 : (subst > term > term),X90 : term] : ((((lam @ (X89 @ sh @ one))) != ((lam @ (X88 @ sh @ one)))) | ? [X91 : subst,X92 : subst,X93 : term] : (((X88 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X88 @ X92 @ X93) @ X91))) | ? [X94 : subst,X95 : subst,X96 : term] : (((X89 @ (comp @ X94 @ X95) @ (sub @ X96 @ X95))) != ((sub @ (X89 @ X94 @ X96) @ X95))) | (((X88 @ X87 @ X90)) = ((X89 @ X87 @ X90)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X97 : subst,X98 : (subst > term > term),X99 : (subst > term > term),X100 : term] : ((((lam @ (X98 @ sh @ one))) = ((lam @ (X99 @ sh @ one)))) & ! [X101 : subst,X102 : subst,X103 : term] : (((X98 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101))) = ((sub @ (X98 @ X102 @ X103) @ X101))) & ! [X104 : subst,X105 : subst,X106 : term] : (((X99 @ (comp @ X104 @ X105) @ (sub @ X106 @ X105))) = ((sub @ (X99 @ X104 @ X106) @ X105))) & (((X99 @ X97 @ X100)) != ((X98 @ X97 @ X100))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (($true = sP47) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP47)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP46)) & (($true = sP46) | (hoasinduction_lem3a != $true)) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & ((sP42 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP42 != $true)) & (! [X107 : term,X108 : term,X109 : term,X110 : term] : ((X109 = X110) | (((ap @ (sub @ X108 @ id) @ X109)) != ((ap @ (sub @ X107 @ id) @ X110)))) | ? [X111 : term,X112 : term,X113 : term,X114 : term] : ((X111 != X113) & (((ap @ X112 @ X113)) = ((ap @ X114 @ X111)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X115 : term,X116 : term,X117 : term,X118 : term] : ((X117 != X118) & (((ap @ (sub @ X116 @ id) @ X117)) = ((ap @ (sub @ X115 @ id) @ X118)))) & ! [X119 : term,X120 : term,X121 : term,X122 : term] : ((X119 = X121) | (((ap @ X122 @ X119)) != ((ap @ X120 @ X121)))))) & (? [X123 : term,X124 : subst] : (((sub @ one @ (push @ X123 @ X124))) != X123) | ! [X125 : term,X126 : subst,X127 : (term > $o),X128 : term,X129 : (term > $o)] : ((((X129 @ (sub @ X128 @ (push @ X125 @ X126)))) = $true) | (((X127 @ X128)) != $true)) | ? [X130 : subst,X131 : term] : (((comp @ sh @ (push @ X131 @ X130))) != X130) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X132 : term,X133 : subst] : (((sub @ one @ (push @ X132 @ X133))) = X132) & ? [X134 : term,X135 : subst,X136 : (term > $o),X137 : term,X138 : (term > $o)] : ((((X138 @ (sub @ X137 @ (push @ X134 @ X135)))) != $true) & (((X136 @ X137)) = $true)) & ! [X139 : subst,X140 : term] : (((comp @ sh @ (push @ X140 @ X139))) = X139))) & ((sP40 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP40 != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (! [X141 : subst,X142 : term,X143 : (term > $o)] : ? [X144 : (term > $o)] : ! [X145 : term] : (((X144 @ X145)) = ((X143 @ (sub @ X145 @ (push @ X142 @ X141))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X146 : subst,X147 : term,X148 : (term > $o)] : ! [X149 : (term > $o)] : ? [X150 : term] : (((X148 @ (sub @ X150 @ (push @ X147 @ X146)))) != ((X149 @ X150)))) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X151 : subst] : ? [X152 : d_subst] : (((d2subst @ X152)) = X151) & ((sP38 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP38 != $true)) & (((d2subst @ d_id)) = sh) & (! [X153 : subst] : (((comp @ X153 @ id)) = X153) | (axidr != $true)) & ((axidr = $true) | ? [X154 : subst] : (((comp @ X154 @ id)) != X154)) & (termmset_gthm = $true) & (pushprop = $true) & ((laminj = $true) | ? [X155 : term,X156 : term] : ((((lam @ X155)) = ((lam @ X156))) & (X155 != X156))) & (! [X157 : term,X158 : term] : ((((lam @ X158)) != ((lam @ X157))) | (X157 = X158)) | (laminj != $true)) & (($true = sP37) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP37)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & ((axvarid = $true) | ? [X159 : term] : (((sub @ X159 @ id)) != X159)) & (! [X160 : term] : (((sub @ X160 @ id)) = X160) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & ((sP36 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP36 != $true)) & (axclos = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & (? [X161 : subst,X162 : term] : (((sub @ one @ (push @ X162 @ X161))) != X162) | ! [X163 : (term > $o),X164 : term,X165 : (term > $o),X166 : subst] : ((((X163 @ one)) = $true) | (((X165 @ X164)) != $true) | ? [X167 : term] : (((X163 @ X167)) != ((X165 @ (sub @ X167 @ (push @ X164 @ X166)))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X168 : subst,X169 : term] : (((sub @ one @ (push @ X169 @ X168))) = X169) & ? [X170 : (term > $o),X171 : term,X172 : (term > $o),X173 : subst] : (($true != ((X170 @ one))) & (((X172 @ X171)) = $true) & ! [X174 : term] : (((X170 @ X174)) = ((X172 @ (sub @ X174 @ (push @ X171 @ X173)))))))) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & ! [X175 : d_term] : (d_one = X175) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X176 : subst] : (((comp @ X176 @ id)) = X176) & ! [X177 : subst] : (((comp @ id @ X177)) = X177)) | ? [X178 : subst] : (((comp @ id @ X178)) != X178) | ? [X179 : subst] : (((comp @ X179 @ id)) != X179) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | ((? [X180 : subst] : (((comp @ X180 @ id)) != X180) | ? [X181 : subst] : (((comp @ id @ X181)) != X181)) & ! [X182 : subst] : (((comp @ id @ X182)) = X182) & ! [X183 : subst] : (((comp @ X183 @ id)) = X183))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & (! [X184 : (term > $o),X185 : subst,X186 : term,X187 : term,X188 : (term > $o)] : (($true = ((X188 @ (sub @ X187 @ (push @ X186 @ X185))))) | (((X184 @ X187)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X189 : (term > $o),X190 : subst,X191 : term,X192 : term,X193 : (term > $o)] : ((((X193 @ (sub @ X192 @ (push @ X191 @ X190)))) != $true) & (((X189 @ X192)) = $true))) & ((axidl = $true) | ? [X194 : subst] : (((comp @ id @ X194)) != X194)) & (! [X195 : subst] : (((comp @ id @ X195)) = X195) | (axidl != $true)) & (! [X196 : term,X197 : term] : ((((sub @ X197 @ sh)) != ((sub @ X196 @ sh))) | (X196 = X197)) | (shinj != $true)) & ((shinj = $true) | ? [X198 : term,X199 : term] : ((((sub @ X198 @ sh)) = ((sub @ X199 @ sh))) & (X198 != X199))) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((induction2_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP17 != $true)) & (induction2_gthm = $true) & (($true = sP15) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP15)) & ! [X200 : d_subst,X201 : d_subst] : ((((d2subst @ X201)) != ((d2subst @ X200))) | (X200 = X201)) & ((hoasinduction_lthm_3 = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm_3 != $true)) & (! [X202 : term] : (((sub @ X202 @ id)) = X202) | (termmset != $true)) & ((termmset = $true) | ? [X203 : term] : (((sub @ X203 @ id)) != X203)) & (axmap = $true) & ((apinj2 = $true) | ? [X204 : term,X205 : term,X206 : term,X207 : term] : ((((ap @ X205 @ X207)) = ((ap @ X206 @ X204))) & (X204 != X207))) & (! [X208 : term,X209 : term,X210 : term,X211 : term] : ((((ap @ X210 @ X208)) != ((ap @ X209 @ X211))) | (X208 = X211)) | (apinj2 != $true)) & ((hoasinduction_lem3aa = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa != $true)) & ((sP6 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP6 != $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((((ap @ (sub @ X215 @ id) @ X212)) != ((ap @ (sub @ X214 @ id) @ X213))) | (X214 = X215)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((((ap @ (sub @ X219 @ id) @ X216)) = ((ap @ (sub @ X218 @ id) @ X217))) & (X218 != X219))) & (lamnotap != $true) & ((hoasinduction_no_psi_cond = $true) | ? [X220 : term,X221 : (subst > term > subst > $o)] : (! [X222 : (subst > term > term)] : (? [X223 : term] : ((((X221 @ id @ X223 @ id)) = $true) & (((X221 @ id @ (X222 @ id @ X223) @ id)) != $true)) | ? [X224 : term,X225 : subst,X226 : subst] : (((sub @ (X222 @ X226 @ X224) @ X225)) != ((X222 @ (comp @ X226 @ X225) @ (sub @ X224 @ X225)))) | (((X221 @ id @ (lam @ (X222 @ sh @ one)) @ id)) = $true)) & (((X221 @ id @ X220 @ id)) != $true) & (((sP4 @ X221)) != $true))) & (! [X227 : term,X228 : (subst > term > subst > $o)] : (? [X229 : (subst > term > term)] : (! [X230 : term] : ((((X228 @ id @ X230 @ id)) != $true) | (((X228 @ id @ (X229 @ id @ X230) @ id)) = $true)) & ! [X231 : term,X232 : subst,X233 : subst] : (((sub @ (X229 @ X233 @ X231) @ X232)) = ((X229 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) & ($true != ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id)))) | (((X228 @ id @ X227 @ id)) = $true) | ($true = ((sP4 @ X228)))) | (hoasinduction_no_psi_cond != $true)) & (hoasapinj2_gthm = $true) & (! [X234 : term] : ? [X235 : (subst > term > term)] : ! [X236 : term,X237 : subst] : (((sub @ X234 @ (push @ X236 @ X237))) = ((X235 @ X237 @ X236))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X238 : term] : ! [X239 : (subst > term > term)] : ? [X240 : term,X241 : subst] : (((X239 @ X241 @ X240)) != ((sub @ X238 @ (push @ X240 @ X241))))) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP3 != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2 = $true) | ? [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 != X244) & (((ap @ (sub @ X243 @ id) @ X244)) = ((ap @ (sub @ X245 @ id) @ X242))))) & (! [X246 : term,X247 : term,X248 : term,X249 : term] : ((X246 = X248) | (((ap @ (sub @ X247 @ id) @ X248)) != ((ap @ (sub @ X249 @ id) @ X246)))) | (hoasapinj2 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X250 : term] : ! [X251 : (subst > term > term)] : (((X251 @ sh @ one)) != ((sub @ X250 @ (push @ one @ sh))))) & (! [X252 : term] : ? [X253 : (subst > term > term)] : (((X253 @ sh @ one)) = ((sub @ X252 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X254 : (subst > term > subst > $o)] : ! [X255 : (term > $o)] : ? [X256 : term] : (((X255 @ X256)) != ((X254 @ id @ X256 @ id)))) & (! [X257 : (subst > term > subst > $o)] : ? [X258 : (term > $o)] : ! [X259 : term] : (((X258 @ X259)) = ((X257 @ id @ X259 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((axscons = $true) | ? [X260 : subst] : (((push @ (sub @ one @ X260) @ (comp @ sh @ X260))) != X260)) & (! [X261 : subst] : (((push @ (sub @ one @ X261) @ (comp @ sh @ X261))) = X261) | (axscons != $true)) & ((substmonoid = $true) | ? [X262 : subst] : (((comp @ X262 @ id)) != X262) | ? [X263 : subst] : (((comp @ id @ X263)) != X263)) & ((! [X264 : subst] : (((comp @ X264 @ id)) = X264) & ! [X265 : subst] : (((comp @ id @ X265)) = X265)) | (substmonoid != $true)) & (hoaslamnotvar = $true) & (! [X266 : subst,X267 : term,X268 : (term > $o),X269 : (term > $o)] : ((((X269 @ one)) = $true) | ? [X270 : term] : (((X269 @ X270)) != ((X268 @ (sub @ X270 @ (push @ X267 @ X266))))) | (((X268 @ X267)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X271 : subst,X272 : term,X273 : (term > $o),X274 : (term > $o)] : ((((X274 @ one)) != $true) & ! [X275 : term] : (((X273 @ (sub @ X275 @ (push @ X272 @ X271)))) = ((X274 @ X275))) & (((X273 @ X272)) = $true))) & (! [X276 : subst,X277 : term] : (((comp @ sh @ (push @ X277 @ X276))) = X276) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X278 : subst,X279 : term] : (((comp @ sh @ (push @ X279 @ X278))) != X278))),
% 6.99/1.30 inference(rectify,[],[f261])).
% 6.99/1.30 thf(f263,plain,(
% 6.99/1.30 (pushprop_lem2v2_lthm = $true) & (axapp = $true) & (($true = sP58) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP58)) & (ulamvar1 != $true) & (! [X0 : term] : ! [X2 : subst,X3 : term] : (((sub @ X0 @ (push @ X3 @ X2))) = ((sK454 @ X0 @ X2 @ X3))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X5 : (subst > term > term)] : (((sub @ sK455 @ (push @ (sK457 @ X5) @ (sK456 @ X5)))) != ((X5 @ (sK456 @ X5) @ (sK457 @ X5))))) & (pushprop_lem1v2_gthm = $true) & ! [X8 : d_term,X9 : d_term] : ((((d2term @ X9)) != ((d2term @ X8))) | (X8 = X9)) & (! [X10 : (subst > term > subst > $o)] : ! [X12 : term] : (((X10 @ id @ X12 @ id)) = ((sK458 @ X10 @ X12))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X14 : (term > $o)] : (((sK459 @ id @ (sK460 @ X14) @ id)) != ((X14 @ (sK460 @ X14))))) & ((sP55 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (sP55 != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (pushprop_lem2v2 = $true) & ((sK461 != ((sub @ sK461 @ id))) | ! [X17 : term] : (((sub @ X17 @ id)) = X17) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X18 : term] : (((sub @ X18 @ id)) = X18) & (sK462 != ((sub @ sK462 @ id))))) & ((hoasapinj1_lthm = $true) | (((sK465 != sK466) & (((ap @ (sub @ sK465 @ id) @ sK464)) = ((ap @ (sub @ sK466 @ id) @ sK463)))) & ! [X24 : term,X25 : term,X26 : term,X27 : term] : ((((ap @ X27 @ X26)) != ((ap @ X25 @ X24))) | (X25 = X27)) & ! [X28 : term] : (((sub @ X28 @ id)) = X28))) & (! [X29 : term,X30 : term,X31 : term,X32 : term] : ((X31 = X32) | (((ap @ (sub @ X31 @ id) @ X30)) != ((ap @ (sub @ X32 @ id) @ X29)))) | ((((ap @ sK470 @ sK469)) = ((ap @ sK468 @ sK467))) & (sK470 != sK468)) | (((sub @ sK471 @ id)) != sK471) | (hoasapinj1_lthm != $true)) & (! [X38 : (subst > term > term),X39 : term,X40 : term] : ((((sub @ (X38 @ (sK472 @ X38) @ (sK473 @ X38)) @ (sK474 @ X38))) != ((X38 @ (comp @ (sK472 @ X38) @ (sK474 @ X38)) @ (sub @ (sK473 @ X38) @ (sK474 @ X38))))) | (((ap @ (sub @ X39 @ id) @ X40)) != ((lam @ (X38 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X47 : subst,X48 : term,X49 : subst] : (((sub @ (sK475 @ X47 @ X48) @ X49)) = ((sK475 @ (comp @ X47 @ X49) @ (sub @ X48 @ X49)))) & (((ap @ (sub @ sK476 @ id) @ sK477)) = ((lam @ (sK475 @ sh @ one)))))) & (hoasinduction_lem3a_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem0_lthm = $true) | ! [X53 : (term > $o)] : (((sK479 @ (sub @ (sK481 @ X53) @ (push @ sK480 @ sK478)))) != ((X53 @ (sK481 @ X53))))) & (! [X55 : subst,X56 : (term > $o),X57 : term] : ! [X59 : term] : (((X56 @ (sub @ X59 @ (push @ X57 @ X55)))) = ((sK482 @ X57 @ X56 @ X55 @ X59))) | (pushprop_lem0_lthm != $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3aa_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lem3aa_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((axvarcons = $true) | (((sub @ one @ (push @ sK483 @ sK484))) != sK483)) & (! [X62 : term,X63 : subst] : (((sub @ one @ (push @ X62 @ X63))) = X62) | (axvarcons != $true)) & ((sP49 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP49 != $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ! [X64 : d_subst] : (d_id = X64) & (pushprop_lem2v2_gthm = $true) & ! [X65 : term] : (((d2term @ (sK485 @ X65))) = X65) & (hoasinduction_lem3b_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotap_gthm = $true) & (! [X67 : term] : (((sub @ X67 @ (push @ one @ sh))) = ((sK486 @ X67 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X70 : (subst > term > term)] : (((X70 @ sh @ one)) != ((sub @ sK487 @ (push @ one @ sh))))) & (pushprop_lem1_gthm = $true) & (! [X71 : term,X72 : term,X73 : term,X74 : term] : ((((ap @ X72 @ X73)) != ((ap @ X74 @ X71))) | (X72 = X74)) | (apinj1 != $true)) & ((apinj1 = $true) | ((((ap @ sK491 @ sK488)) = ((ap @ sK489 @ sK490))) & (sK491 != sK489))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem3v2_lthm = $true) & (substmonoid_gthm = $true) & (! [X79 : term,X80 : (term > $o)] : (((((X80 @ (lam @ (sK492 @ X80)))) != $true) & (((X80 @ (sK492 @ X80))) = $true)) | ((((var @ (sK493 @ X80))) = $true) & (((X80 @ (sK493 @ X80))) != $true)) | (((X80 @ X79)) = $true) | (((sP48 @ X80)) = $true)) | (induction != $true)) & ((induction = $true) | (! [X85 : term] : ((((sK495 @ (lam @ X85))) = $true) | ($true != ((sK495 @ X85)))) & ! [X86 : term] : ((((var @ X86)) != $true) | (((sK495 @ X86)) = $true)) & (((sK495 @ sK494)) != $true) & (((sP48 @ sK495)) != $true))) & (one = ((d2term @ d_one))) & (! [X87 : subst,X88 : (subst > term > term),X89 : (subst > term > term),X90 : term] : ((((lam @ (X89 @ sh @ one))) != ((lam @ (X88 @ sh @ one)))) | (((sub @ (X88 @ (sK497 @ X88) @ (sK498 @ X88)) @ (sK496 @ X88))) != ((X88 @ (comp @ (sK497 @ X88) @ (sK496 @ X88)) @ (sub @ (sK498 @ X88) @ (sK496 @ X88))))) | (((X89 @ (comp @ (sK499 @ X89) @ (sK500 @ X89)) @ (sub @ (sK501 @ X89) @ (sK500 @ X89)))) != ((sub @ (X89 @ (sK499 @ X89) @ (sK501 @ X89)) @ (sK500 @ X89)))) | (((X88 @ X87 @ X90)) = ((X89 @ X87 @ X90)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((lam @ (sK503 @ sh @ one))) = ((lam @ (sK504 @ sh @ one)))) & ! [X101 : subst,X102 : subst,X103 : term] : (((sK503 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101))) = ((sub @ (sK503 @ X102 @ X103) @ X101))) & ! [X104 : subst,X105 : subst,X106 : term] : (((sub @ (sK504 @ X104 @ X106) @ X105)) = ((sK504 @ (comp @ X104 @ X105) @ (sub @ X106 @ X105)))) & (((sK503 @ sK502 @ sK505)) != ((sK504 @ sK502 @ sK505))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (($true = sP47) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP47)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) | ($true != sP46)) & (($true = sP46) | (hoasinduction_lem3a != $true)) & ((sP45 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP45 != $true)) & ((sP42 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP42 != $true)) & (! [X107 : term,X108 : term,X109 : term,X110 : term] : ((X109 = X110) | (((ap @ (sub @ X108 @ id) @ X109)) != ((ap @ (sub @ X107 @ id) @ X110)))) | ((sK506 != sK508) & (((ap @ sK507 @ sK508)) = ((ap @ sK509 @ sK506)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((sK512 != sK513) & (((ap @ (sub @ sK511 @ id) @ sK512)) = ((ap @ (sub @ sK510 @ id) @ sK513)))) & ! [X119 : term,X120 : term,X121 : term,X122 : term] : ((X119 = X121) | (((ap @ X122 @ X119)) != ((ap @ X120 @ X121)))))) & ((sK514 != ((sub @ one @ (push @ sK514 @ sK515)))) | ! [X125 : term,X126 : subst,X127 : (term > $o),X128 : term,X129 : (term > $o)] : ((((X129 @ (sub @ X128 @ (push @ X125 @ X126)))) = $true) | (((X127 @ X128)) != $true)) | (((comp @ sh @ (push @ sK517 @ sK516))) != sK516) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X132 : term,X133 : subst] : (((sub @ one @ (push @ X132 @ X133))) = X132) & ((((sK522 @ (sub @ sK521 @ (push @ sK518 @ sK519)))) != $true) & ($true = ((sK520 @ sK521)))) & ! [X139 : subst,X140 : term] : (((comp @ sh @ (push @ X140 @ X139))) = X139))) & ((sP40 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP40 != $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (! [X141 : subst,X142 : term,X143 : (term > $o)] : ! [X145 : term] : (((X143 @ (sub @ X145 @ (push @ X142 @ X141)))) = ((sK523 @ X143 @ X142 @ X141 @ X145))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X149 : (term > $o)] : (((sK526 @ (sub @ (sK527 @ X149) @ (push @ sK525 @ sK524)))) != ((X149 @ (sK527 @ X149))))) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & ! [X151 : subst] : (((d2subst @ (sK528 @ X151))) = X151) & ((sP38 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP38 != $true)) & (((d2subst @ d_id)) = sh) & (! [X153 : subst] : (((comp @ X153 @ id)) = X153) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK529 @ id)) != sK529)) & (termmset_gthm = $true) & (pushprop = $true) & ((laminj = $true) | ((((lam @ sK531)) = ((lam @ sK530))) & (sK530 != sK531))) & (! [X157 : term,X158 : term] : ((((lam @ X158)) != ((lam @ X157))) | (X157 = X158)) | (laminj != $true)) & (($true = sP37) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP37)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (apnotvar = $true) & (hoasinduction_gthm = $true) & (axassoc = $true) & ((axvarid = $true) | (sK532 != ((sub @ sK532 @ id)))) & (! [X160 : term] : (((sub @ X160 @ id)) = X160) | (axvarid != $true)) & (hoasapinj1_gthm = $true) & ((sP36 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP36 != $true)) & (axclos = $true) & ((hoasinduction_lem2v2 = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem2v2 != $true)) & ((((sub @ one @ (push @ sK534 @ sK533))) != sK534) | ! [X163 : (term > $o),X164 : term,X165 : (term > $o),X166 : subst] : ((((X163 @ one)) = $true) | (((X165 @ X164)) != $true) | (((X163 @ (sK535 @ X166 @ X165 @ X164 @ X163))) != ((X165 @ (sub @ (sK535 @ X166 @ X165 @ X164 @ X163) @ (push @ X164 @ X166)))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X168 : subst,X169 : term] : (((sub @ one @ (push @ X169 @ X168))) = X169) & ((((sK536 @ one)) != $true) & (((sK538 @ sK537)) = $true) & ! [X174 : term] : (((sK536 @ X174)) = ((sK538 @ (sub @ X174 @ (push @ sK537 @ sK539)))))))) & (ulamvarsh = $true) & (pushprop_gthm = $true) & (pushprop_lem3v2 = $true) & ((sP32 = $true) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP32 != $true)) & ! [X175 : d_term] : (d_one = X175) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X176 : subst] : (((comp @ X176 @ id)) = X176) & ! [X177 : subst] : (((comp @ id @ X177)) = X177)) | (((comp @ id @ sK540)) != sK540) | (sK541 != ((comp @ sK541 @ id))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (((((comp @ sK542 @ id)) != sK542) | (((comp @ id @ sK543)) != sK543)) & ! [X182 : subst] : (((comp @ id @ X182)) = X182) & ! [X183 : subst] : (((comp @ X183 @ id)) = X183))) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasinduction_lem3v2_gthm = $true) & ((sP23 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP23 != $true)) & (! [X184 : (term > $o),X185 : subst,X186 : term,X187 : term,X188 : (term > $o)] : (($true = ((X188 @ (sub @ X187 @ (push @ X186 @ X185))))) | (((X184 @ X187)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK548 @ (sub @ sK547 @ (push @ sK546 @ sK545))))) & (((sK544 @ sK547)) = $true))) & ((axidl = $true) | (((comp @ id @ sK549)) != sK549)) & (! [X195 : subst] : (((comp @ id @ X195)) = X195) | (axidl != $true)) & (! [X196 : term,X197 : term] : ((((sub @ X197 @ sh)) != ((sub @ X196 @ sh))) | (X196 = X197)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK551 @ sh)) = ((sub @ sK550 @ sh))) & (sK550 != sK551))) & (hoasapnotvar_lthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((induction2_lthm = $true) | (sP21 != $true)) & ((sP21 = $true) | (induction2_lthm != $true)) & ((sP17 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP17 != $true)) & (induction2_gthm = $true) & (($true = sP15) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | ($true != sP15)) & ! [X200 : d_subst,X201 : d_subst] : ((((d2subst @ X201)) != ((d2subst @ X200))) | (X200 = X201)) & ((hoasinduction_lthm_3 = $true) | (sP13 != $true)) & ((sP13 = $true) | (hoasinduction_lthm_3 != $true)) & (! [X202 : term] : (((sub @ X202 @ id)) = X202) | (termmset != $true)) & ((termmset = $true) | (sK552 != ((sub @ sK552 @ id)))) & (axmap = $true) & ((apinj2 = $true) | ((((ap @ sK555 @ sK553)) = ((ap @ sK554 @ sK556))) & (sK553 != sK556))) & (! [X208 : term,X209 : term,X210 : term,X211 : term] : ((((ap @ X210 @ X208)) != ((ap @ X209 @ X211))) | (X208 = X211)) | (apinj2 != $true)) & ((hoasinduction_lem3aa = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3aa != $true)) & ((sP6 = $true) | (induction2 != $true)) & ((induction2 = $true) | (sP6 != $true)) & (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((((ap @ (sub @ X215 @ id) @ X212)) != ((ap @ (sub @ X214 @ id) @ X213))) | (X214 = X215)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK560 @ id) @ sK557)) = ((ap @ (sub @ sK559 @ id) @ sK558))) & (sK560 != sK559))) & (lamnotap != $true) & ((hoasinduction_no_psi_cond = $true) | (! [X222 : (subst > term > term)] : (((((sK562 @ id @ (sK563 @ X222) @ id)) = $true) & (((sK562 @ id @ (X222 @ id @ (sK563 @ X222)) @ id)) != $true)) | (((X222 @ (comp @ (sK566 @ X222) @ (sK565 @ X222)) @ (sub @ (sK564 @ X222) @ (sK565 @ X222)))) != ((sub @ (X222 @ (sK566 @ X222) @ (sK564 @ X222)) @ (sK565 @ X222)))) | (((sK562 @ id @ (lam @ (X222 @ sh @ one)) @ id)) = $true)) & (((sK562 @ id @ sK561 @ id)) != $true) & (((sP4 @ sK562)) != $true))) & (! [X227 : term,X228 : (subst > term > subst > $o)] : ((! [X230 : term] : ((((X228 @ id @ X230 @ id)) != $true) | ($true = ((X228 @ id @ (sK567 @ X228 @ id @ X230) @ id)))) & ! [X231 : term,X232 : subst,X233 : subst] : (((sub @ (sK567 @ X228 @ X233 @ X231) @ X232)) = ((sK567 @ X228 @ (comp @ X233 @ X232) @ (sub @ X231 @ X232)))) & ($true != ((X228 @ id @ (lam @ (sK567 @ X228 @ sh @ one)) @ id)))) | (((X228 @ id @ X227 @ id)) = $true) | ($true = ((sP4 @ X228)))) | (hoasinduction_no_psi_cond != $true)) & (hoasapinj2_gthm = $true) & (! [X234 : term] : ! [X236 : term,X237 : subst] : (((sK568 @ X234 @ X237 @ X236)) = ((sub @ X234 @ (push @ X236 @ X237)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X239 : (subst > term > term)] : (((X239 @ (sK571 @ X239) @ (sK570 @ X239))) != ((sub @ sK569 @ (push @ (sK570 @ X239) @ (sK571 @ X239)))))) & ((sP3 = $true) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | (sP3 != $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasapinj2 = $true) | ((sK572 != sK574) & (((ap @ (sub @ sK575 @ id) @ sK572)) = ((ap @ (sub @ sK573 @ id) @ sK574))))) & (! [X246 : term,X247 : term,X248 : term,X249 : term] : ((X246 = X248) | (((ap @ (sub @ X247 @ id) @ X248)) != ((ap @ (sub @ X249 @ id) @ X246)))) | (hoasapinj2 != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X251 : (subst > term > term)] : (((X251 @ sh @ one)) != ((sub @ sK576 @ (push @ one @ sh))))) & (! [X252 : term] : (((sK577 @ X252 @ sh @ one)) = ((sub @ X252 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X255 : (term > $o)] : (((sK578 @ id @ (sK579 @ X255) @ id)) != ((X255 @ (sK579 @ X255))))) & (! [X257 : (subst > term > subst > $o)] : ! [X259 : term] : (((sK580 @ X257 @ X259)) = ((X257 @ id @ X259 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK581) @ (comp @ sh @ sK581))) != sK581)) & (! [X261 : subst] : (((push @ (sub @ one @ X261) @ (comp @ sh @ X261))) = X261) | (axscons != $true)) & ((substmonoid = $true) | (((comp @ sK582 @ id)) != sK582) | (((comp @ id @ sK583)) != sK583)) & ((! [X264 : subst] : (((comp @ X264 @ id)) = X264) & ! [X265 : subst] : (((comp @ id @ X265)) = X265)) | (substmonoid != $true)) & (hoaslamnotvar = $true) & (! [X266 : subst,X267 : term,X268 : (term > $o),X269 : (term > $o)] : ((((X269 @ one)) = $true) | (((X268 @ (sub @ (sK584 @ X269 @ X268 @ X267 @ X266) @ (push @ X267 @ X266)))) != ((X269 @ (sK584 @ X269 @ X268 @ X267 @ X266)))) | (((X268 @ X267)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true != ((sK588 @ one))) & ! [X275 : term] : (((sK587 @ (sub @ X275 @ (push @ sK586 @ sK585)))) = ((sK588 @ X275))) & (((sK587 @ sK586)) = $true))) & (! [X276 : subst,X277 : term] : (((comp @ sh @ (push @ X277 @ X276))) = X276) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK589 != ((comp @ sh @ (push @ sK590 @ sK589)))))),
% 6.99/1.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK455,vAPP,vAPP,vAPP,sK459,vAPP,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,sK470,sK471,vAPP,vAPP,vAPP,sK475,sK476,sK477,sK478,sK479,sK480,vAPP,vAPP,sK483,sK484,vAPP,vAPP,sK487,sK488,sK489,sK490,sK491,vAPP,vAPP,sK494,sK495,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,vAPP,sK524,sK525,sK526,vAPP,vAPP,sK529,sK530,sK531,sK532,sK533,sK534,vAPP,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,sK560,sK561,sK562,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK569,vAPP,vAPP,sK572,sK573,sK574,sK575,sK576,vAPP,sK578,vAPP,vAPP,sK581,sK582,sK583,vAPP,sK585,sK586,sK587,sK588,sK589,sK590]),skolemize(X21,sK69 @ X12),skolemize(X4,sK455),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X13,sK459),skolemize(X21,sK69 @ X12),skolemize(X16,sK461),skolemize(X19,sK462),skolemize(X20,sK463),skolemize(X21,sK464),skolemize(X22,sK465),skolemize(X23,sK466),skolemize(X33,sK467),skolemize(X34,sK468),skolemize(X35,sK469),skolemize(X36,sK470),skolemize(X37,sK471),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X44,sK475),skolemize(X45,sK476),skolemize(X46,sK477),skolemize(X50,sK478),skolemize(X51,sK479),skolemize(X52,sK480),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X60,sK483),skolemize(X61,sK484),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X69,sK487),skolemize(X75,sK488),skolemize(X76,sK489),skolemize(X77,sK490),skolemize(X78,sK491),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X83,sK494),skolemize(X84,sK495),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X97,sK502),skolemize(X98,sK503),skolemize(X99,sK504),skolemize(X100,sK505),skolemize(X111,sK506),skolemize(X112,sK507),skolemize(X113,sK508),skolemize(X114,sK509),skolemize(X115,sK510),skolemize(X116,sK511),skolemize(X117,sK512),skolemize(X118,sK513),skolemize(X123,sK514),skolemize(X124,sK515),skolemize(X130,sK516),skolemize(X131,sK517),skolemize(X134,sK518),skolemize(X135,sK519),skolemize(X136,sK520),skolemize(X137,sK521),skolemize(X138,sK522),skolemize(X21,sK69 @ X12),skolemize(X146,sK524),skolemize(X147,sK525),skolemize(X148,sK526),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X154,sK529),skolemize(X155,sK530),skolemize(X156,sK531),skolemize(X159,sK532),skolemize(X161,sK533),skolemize(X162,sK534),skolemize(X21,sK69 @ X12),skolemize(X170,sK536),skolemize(X171,sK537),skolemize(X172,sK538),skolemize(X173,sK539),skolemize(X178,sK540),skolemize(X179,sK541),skolemize(X180,sK542),skolemize(X181,sK543),skolemize(X189,sK544),skolemize(X190,sK545),skolemize(X191,sK546),skolemize(X192,sK547),skolemize(X193,sK548),skolemize(X194,sK549),skolemize(X198,sK550),skolemize(X199,sK551),skolemize(X203,sK552),skolemize(X204,sK553),skolemize(X205,sK554),skolemize(X206,sK555),skolemize(X207,sK556),skolemize(X216,sK557),skolemize(X217,sK558),skolemize(X218,sK559),skolemize(X219,sK560),skolemize(X220,sK561),skolemize(X221,sK562),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X238,sK569),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X242,sK572),skolemize(X243,sK573),skolemize(X244,sK574),skolemize(X245,sK575),skolemize(X250,sK576),skolemize(X21,sK69 @ X12),skolemize(X254,sK578),skolemize(X21,sK69 @ X12),skolemize(X21,sK69 @ X12),skolemize(X260,sK581),skolemize(X262,sK582),skolemize(X263,sK583),skolemize(X21,sK69 @ X12),skolemize(X271,sK585),skolemize(X272,sK586),skolemize(X273,sK587),skolemize(X274,sK588),skolemize(X278,sK589),skolemize(X279,sK590)],[f262])).
% 6.99/1.30 thf(f264,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.99/1.30 inference(cnf_transformation,[],[f8])).
% 6.99/1.30 thf(f345,plain,(
% 6.99/1.30 (sP49 = $true) | (((sK115 @ id @ (lam @ (sub @ sK116 @ (push @ one @ sh))) @ id)) != $true)),
% 6.99/1.30 inference(cnf_transformation,[],[f103])).
% 6.99/1.30 thf(f347,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (sK122 @ X4 @ X3))) @ (sK121 @ X4 @ X3))) != ((sub @ (X4 @ (sK122 @ X4 @ X3) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3)))) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (sP49 = $true) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) != ((X4 @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)))))) )),
% 6.99/1.30 inference(cnf_transformation,[],[f103])).
% 6.99/1.30 thf(f348,plain,(
% 6.99/1.30 ( ! [X2 : term] : (($true != ((sK115 @ id @ X2 @ id))) | ($true = ((sK115 @ id @ (sub @ sK116 @ (push @ X2 @ id)) @ id))) | (sP49 = $true)) )),
% 6.99/1.30 inference(cnf_transformation,[],[f103])).
% 6.99/1.30 thf(f830,plain,(
% 6.99/1.30 ( ! [X175 : d_term] : ((d_one = X175)) )),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f862,plain,(
% 6.99/1.30 (((d2subst @ d_id)) = sh)),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f865,plain,(
% 6.99/1.30 ( ! [X151 : subst] : ((((d2subst @ (sK528 @ X151))) = X151)) )),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f909,plain,(
% 6.99/1.30 (one = ((d2term @ d_one)))),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f931,plain,(
% 6.99/1.30 ( ! [X65 : term] : ((((d2term @ (sK485 @ X65))) = X65)) )),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f933,plain,(
% 6.99/1.30 ( ! [X64 : d_subst] : ((d_id = X64)) )),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f935,plain,(
% 6.99/1.30 (sP49 != $true) | (hoasinduction_lem3aaa = $true)),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f947,plain,(
% 6.99/1.30 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 6.99/1.30 inference(cnf_transformation,[],[f263])).
% 6.99/1.30 thf(f981,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))))),
% 6.99/1.30 inference(definition_unfolding,[],[f264,f947])).
% 6.99/1.30 thf(f1111,plain,(
% 6.99/1.30 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))))) = $false) | (hoasinduction_lem3aaa = $false)),
% 6.99/1.30 inference(xor_proxy_clausification,[],[f981])).
% 6.99/1.30 thf(f1112,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((?? @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: (!! @ term @ (^[Y5 : term]: (((sub @ (Y1 @ Y4 @ Y5) @ Y3) = (sub @ (sub @ Y2 @ (push @ Y5 @ Y4)) @ Y3)) & ((Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y5 @ Y3)) = (sub @ Y2 @ (push @ (sub @ Y5 @ Y3) @ (comp @ Y4 @ Y3))))))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))) @ sK591)))),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1111])).
% 6.99/1.30 thf(f1113,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $false) | ($false = (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ (Y0 @ Y3 @ Y4) @ Y2) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y3)) @ Y2)) & ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2)) = (sub @ Y1 @ (push @ (sub @ Y4 @ Y2) @ (comp @ Y3 @ Y2))))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))))),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1112])).
% 6.99/1.30 thf(f1114,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $false) | ($false = ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))))))),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1113])).
% 6.99/1.30 thf(f1115,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $false) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ (Y0 @ Y3 @ Y4) @ Y2) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y3)) @ Y2)) & ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2)) = (sub @ Y1 @ (push @ (sub @ Y4 @ Y2) @ (comp @ Y3 @ Y2))))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))))) = $true)),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1113])).
% 6.99/1.30 thf(f1116,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (((((^[Y0 : subst > term > term]: ((?? @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: (((sub @ (Y0 @ Y3 @ Y4) @ Y2) = (sub @ (sub @ Y1 @ (push @ Y4 @ Y3)) @ Y2)) & ((Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y4 @ Y2)) = (sub @ Y1 @ (push @ (sub @ Y4 @ Y2) @ (comp @ Y3 @ Y2))))))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) @ X1)) = $true) | (hoasinduction_lem3aaa = $false)) )),
% 6.99/1.30 inference(pi_proxy_clausification,[],[f1115])).
% 6.99/1.30 thf(f1117,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (($true = (((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ (X1 @ Y2 @ Y3) @ Y1) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y2)) @ Y1)) & ((X1 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1)) = (sub @ Y0 @ (push @ (sub @ Y3 @ Y1) @ (comp @ Y2 @ Y1))))))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id))))) | (hoasinduction_lem3aaa = $false)) )),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1116])).
% 6.99/1.30 thf(f1118,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (($true = (((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))) => (sK591 @ id @ (d2term @ d_one) @ id)))) | (hoasinduction_lem3aaa = $false) | ($false = ((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ (X1 @ Y2 @ Y3) @ Y1) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y2)) @ Y1)) & ((X1 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1)) = (sub @ Y0 @ (push @ (sub @ Y3 @ Y1) @ (comp @ Y2 @ Y1)))))))))))))))) )),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1117])).
% 6.99/1.30 thf(f1119,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (($false = ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id)))))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = ((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ (X1 @ Y2 @ Y3) @ Y1) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y2)) @ Y1)) & ((X1 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1)) = (sub @ Y0 @ (push @ (sub @ Y3 @ Y1) @ (comp @ Y2 @ Y1))))))))))))))) | (hoasinduction_lem3aaa = $false)) )),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1118])).
% 6.99/1.30 thf(f1120,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (($false = ((?? @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ (X1 @ Y2 @ Y3) @ Y1) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y2)) @ Y1)) & ((X1 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1)) = (sub @ Y0 @ (push @ (sub @ Y3 @ Y1) @ (comp @ Y2 @ Y1))))))))))))))) | (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK592 @ X1)))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1119])).
% 6.99/1.30 thf(f1121,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($false = (((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (X1 @ id @ Y0) @ id))) @ (sK592 @ X1)))) | (hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (((sub @ (X1 @ Y2 @ Y3) @ Y1) = (sub @ (sub @ Y0 @ (push @ Y3 @ Y2)) @ Y1)) & ((X1 @ (comp @ Y2 @ Y1) @ (sub @ Y3 @ Y1)) = (sub @ Y0 @ (push @ (sub @ Y3 @ Y1) @ (comp @ Y2 @ Y1)))))))))))) @ X2)))) )),
% 6.99/1.30 inference(pi_proxy_clausification,[],[f1120])).
% 6.99/1.30 thf(f1122,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (((((sK591 @ id @ (sK592 @ X1) @ id) => (sK591 @ id @ (X1 @ id @ (sK592 @ X1)) @ id))) = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3aaa = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ (X1 @ Y1 @ Y2) @ Y0) = (sub @ (sub @ X2 @ (push @ Y2 @ Y1)) @ Y0)) & ((X1 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0)) = (sub @ X2 @ (push @ (sub @ Y2 @ Y0) @ (comp @ Y1 @ Y0)))))))))))) = $false)) )),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1121])).
% 6.99/1.30 thf(f1124,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3aaa = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ (X1 @ Y1 @ Y2) @ Y0) = (sub @ (sub @ X2 @ (push @ Y2 @ Y1)) @ Y0)) & ((X1 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0)) = (sub @ X2 @ (push @ (sub @ Y2 @ Y0) @ (comp @ Y1 @ Y0)))))))))))) = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) )),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1122])).
% 6.99/1.30 thf(f1125,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | ((((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (((sub @ (X1 @ Y1 @ Y2) @ Y0) = (sub @ (sub @ X2 @ (push @ Y2 @ Y1)) @ Y0)) & ((X1 @ (comp @ Y1 @ Y0) @ (sub @ Y2 @ Y0)) = (sub @ X2 @ (push @ (sub @ Y2 @ Y0) @ (comp @ Y1 @ Y0)))))))))) @ (sK593 @ X1 @ X2))) = $false) | (hoasinduction_lem3aaa = $false)) )),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1124])).
% 6.99/1.30 thf(f1126,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (((sub @ (X1 @ Y0 @ Y1) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y1 @ Y0)) @ (sK593 @ X1 @ X2))) & ((X1 @ (comp @ Y0 @ (sK593 @ X1 @ X2)) @ (sub @ Y1 @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ Y1 @ (sK593 @ X1 @ X2)) @ (comp @ Y0 @ (sK593 @ X1 @ X2)))))))))))) | (hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) )),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1125])).
% 6.99/1.30 thf(f1127,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3aaa = $false) | ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (((sub @ (X1 @ Y0 @ Y1) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y1 @ Y0)) @ (sK593 @ X1 @ X2))) & ((X1 @ (comp @ Y0 @ (sK593 @ X1 @ X2)) @ (sub @ Y1 @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ Y1 @ (sK593 @ X1 @ X2)) @ (comp @ Y0 @ (sK593 @ X1 @ X2))))))))) @ (sK594 @ X1 @ X2))))) )),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1126])).
% 6.99/1.30 thf(f1128,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((!! @ term @ (^[Y0 : term]: (((sub @ (X1 @ (sK594 @ X1 @ X2) @ Y0) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y0 @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2))) & ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ Y0 @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ Y0 @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2))))))))) = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1127])).
% 6.99/1.30 thf(f1129,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((^[Y0 : term]: (((sub @ (X1 @ (sK594 @ X1 @ X2) @ Y0) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ Y0 @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2))) & ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ Y0 @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ Y0 @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2))))))) @ (sK595 @ X1 @ X2))) = $false)) )),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1128])).
% 6.99/1.30 thf(f1130,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($false = ((((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2))) & ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) )),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1129])).
% 6.99/1.30 thf(f1131,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ((((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2)) = (sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2)))) = $false) | (hoasinduction_lem3aaa = $false) | ((((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))) = $false)) )),
% 6.99/1.30 inference(and_proxy_clausification,[],[f1130])).
% 6.99/1.30 thf(f1132,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2)))) | ((((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))) = (sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))) = $false) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))) )),
% 6.99/1.30 inference(equality_proxy_clausification,[],[f1131])).
% 6.99/1.30 thf(f1133,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((hoasinduction_lem3aaa = $false) | (((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) != ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))) )),
% 6.99/1.30 inference(equality_proxy_clausification,[],[f1132])).
% 6.99/1.30 thf(f1143,plain,(
% 6.99/1.30 ($false = (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) => (sK591 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))) @ sK599))) | (hoasinduction_lem3aaa = $false)),
% 6.99/1.30 inference(sigma_proxy_clausification,[],[f1114])).
% 6.99/1.30 thf(f1144,plain,(
% 6.99/1.30 ((((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) => (sK591 @ id @ (sub @ sK599 @ (push @ Y0 @ id)) @ id)))) => (sK591 @ id @ (lam @ (sub @ sK599 @ (push @ one @ sh))) @ id))) = $false) | (hoasinduction_lem3aaa = $false)),
% 6.99/1.30 inference(beta-eta_normalization,[],[f1143])).
% 6.99/1.30 thf(f1145,plain,(
% 6.99/1.30 ($false = ((sK591 @ id @ (lam @ (sub @ sK599 @ (push @ one @ sh))) @ id))) | (hoasinduction_lem3aaa = $false)),
% 6.99/1.30 inference(imp_proxy_clausification,[],[f1144])).
% 6.99/1.30 thf(f1555,definition,(
% 6.99/1.30 spl603_83 <=> (sP49 = $true)),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_83])],[avatar_definition])).
% 6.99/1.30 thf(f2044,definition,(
% 6.99/1.30 spl603_199 <=> (hoasinduction_lem3aaa = $true)),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_199])],[avatar_definition])).
% 6.99/1.30 thf(f2046,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $true) | ~spl603_199),
% 6.99/1.30 inference(avatar_component_clause,[],[f2044])).
% 6.99/1.30 thf(f2047,plain,(
% 6.99/1.30 ~spl603_83 | spl603_199),
% 6.99/1.30 inference(avatar_split_clause,[],[f935,f2044,f1555])).
% 6.99/1.30 thf(f2087,definition,(
% 6.99/1.30 spl603_209 <=> ! [X4 : (subst > term > term),X3 : term] : ((((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (sK122 @ X4 @ X3))) @ (sK121 @ X4 @ X3))) != ((sub @ (X4 @ (sK122 @ X4 @ X3) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3)))) | (((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) != ((X4 @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_209])],[avatar_definition])).
% 6.99/1.30 thf(f2088,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (sK122 @ X4 @ X3))) @ (sK121 @ X4 @ X3))) != ((sub @ (X4 @ (sK122 @ X4 @ X3) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3)))) | (((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) != ((X4 @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true)) ) | ~spl603_209),
% 6.99/1.30 inference(avatar_component_clause,[],[f2087])).
% 6.99/1.30 thf(f2089,plain,(
% 6.99/1.30 spl603_209 | spl603_83),
% 6.99/1.30 inference(avatar_split_clause,[],[f347,f1555,f2087])).
% 6.99/1.30 thf(f3087,definition,(
% 6.99/1.30 spl603_441 <=> (((sK115 @ id @ (lam @ (sub @ sK116 @ (push @ one @ sh))) @ id)) = $true)),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_441])],[avatar_definition])).
% 6.99/1.30 thf(f3089,plain,(
% 6.99/1.30 (((sK115 @ id @ (lam @ (sub @ sK116 @ (push @ one @ sh))) @ id)) != $true) | spl603_441),
% 6.99/1.30 inference(avatar_component_clause,[],[f3087])).
% 6.99/1.30 thf(f3090,plain,(
% 6.99/1.30 spl603_83 | ~spl603_441),
% 6.99/1.30 inference(avatar_split_clause,[],[f345,f3087,f1555])).
% 6.99/1.30 thf(f3644,definition,(
% 6.99/1.30 spl603_568 <=> ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2)))) | (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) != ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_568])],[avatar_definition])).
% 6.99/1.30 thf(f3645,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) != ((X1 @ (comp @ (sK594 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2))))) ) | ~spl603_568),
% 6.99/1.30 inference(avatar_component_clause,[],[f3644])).
% 6.99/1.30 thf(f3647,definition,(
% 6.99/1.30 spl603_569 <=> (hoasinduction_lem3aaa = $false)),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_569])],[avatar_definition])).
% 6.99/1.30 thf(f3649,plain,(
% 6.99/1.30 (hoasinduction_lem3aaa = $false) | ~spl603_569),
% 6.99/1.30 inference(avatar_component_clause,[],[f3647])).
% 6.99/1.30 thf(f3651,definition,(
% 6.99/1.30 spl603_570 <=> ($true = ((sK591 @ id @ (d2term @ d_one) @ id)))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_570])],[avatar_definition])).
% 6.99/1.30 thf(f3653,plain,(
% 6.99/1.30 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl603_570),
% 6.99/1.30 inference(avatar_component_clause,[],[f3651])).
% 6.99/1.30 thf(f3654,plain,(
% 6.99/1.30 spl603_568 | spl603_569 | spl603_570),
% 6.99/1.30 inference(avatar_split_clause,[],[f1133,f3651,f3647,f3644])).
% 6.99/1.30 thf(f3664,definition,(
% 6.99/1.30 spl603_573 <=> ($false = ((sK591 @ id @ (lam @ (sub @ sK599 @ (push @ one @ sh))) @ id)))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_573])],[avatar_definition])).
% 6.99/1.30 thf(f3666,plain,(
% 6.99/1.30 ($false = ((sK591 @ id @ (lam @ (sub @ sK599 @ (push @ one @ sh))) @ id))) | ~spl603_573),
% 6.99/1.30 inference(avatar_component_clause,[],[f3664])).
% 6.99/1.30 thf(f3667,plain,(
% 6.99/1.30 spl603_569 | spl603_573),
% 6.99/1.30 inference(avatar_split_clause,[],[f1145,f3664,f3647])).
% 6.99/1.30 thf(f3948,definition,(
% 6.99/1.30 spl603_636 <=> ! [X2 : term] : (($true != ((sK115 @ id @ X2 @ id))) | ($true = ((sK115 @ id @ (sub @ sK116 @ (push @ X2 @ id)) @ id))))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_636])],[avatar_definition])).
% 6.99/1.30 thf(f3949,plain,(
% 6.99/1.30 ( ! [X2 : term] : (($true = ((sK115 @ id @ (sub @ sK116 @ (push @ X2 @ id)) @ id))) | ($true != ((sK115 @ id @ X2 @ id)))) ) | ~spl603_636),
% 6.99/1.30 inference(avatar_component_clause,[],[f3948])).
% 6.99/1.30 thf(f3950,plain,(
% 6.99/1.30 spl603_83 | spl603_636),
% 6.99/1.30 inference(avatar_split_clause,[],[f348,f3948,f1555])).
% 6.99/1.30 thf(f3971,plain,(
% 6.99/1.30 ($false = $true) | (~spl603_199 | ~spl603_569)),
% 6.99/1.30 inference(forward_demodulation,[],[f2046,f3649])).
% 6.99/1.30 thf(f3972,plain,(
% 6.99/1.30 $false | (~spl603_199 | ~spl603_569)),
% 6.99/1.30 inference(trivial_inequality_removal,[],[f3971])).
% 6.99/1.30 thf(f3973,plain,(
% 6.99/1.30 ~spl603_199 | ~spl603_569),
% 6.99/1.30 inference(avatar_contradiction_clause,[],[f3972])).
% 6.99/1.30 thf(f4089,plain,(
% 6.99/1.30 ( ! [X151 : subst] : ((((d2subst @ d_id)) = X151)) )),
% 6.99/1.30 inference(forward_demodulation,[],[f865,f933])).
% 6.99/1.30 thf(f4116,plain,(
% 6.99/1.30 (((sK115 @ id @ (lam @ (sub @ sK116 @ (d2subst @ d_id))) @ id)) != $true) | spl603_441),
% 6.99/1.30 inference(forward_demodulation,[],[f3089,f4089])).
% 6.99/1.30 thf(f4120,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) != ((X4 @ (comp @ (sK117 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | (((sub @ (X4 @ (d2subst @ d_id) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3))) != ((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (d2subst @ d_id))) @ (sK121 @ X4 @ X3))))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f2088,f4089])).
% 6.99/1.30 thf(f4128,plain,(
% 6.99/1.30 (((sK115 @ id @ (lam @ (sub @ sK116 @ sh)) @ id)) != $true) | spl603_441),
% 6.99/1.30 inference(forward_demodulation,[],[f4116,f862])).
% 6.99/1.30 thf(f4132,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ (d2subst @ d_id)))) != ((X4 @ (d2subst @ d_id) @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ (X4 @ (d2subst @ d_id) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3))) != ((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (d2subst @ d_id))) @ (sK121 @ X4 @ X3))))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4120,f4089])).
% 6.99/1.30 thf(f4142,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3)) @ sh))) != ((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (sK118 @ X4 @ X3))))) | (((sub @ (X4 @ (d2subst @ d_id) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3))) != ((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (d2subst @ d_id))) @ (sK121 @ X4 @ X3)))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true)) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4132,f862])).
% 6.99/1.30 thf(f4151,definition,(
% 6.99/1.30 spl603_644 <=> ! [X2 : term] : ($true != ((sK115 @ id @ X2 @ id)))),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_644])],[avatar_definition])).
% 6.99/1.30 thf(f4152,plain,(
% 6.99/1.30 ( ! [X2 : term] : (($true != ((sK115 @ id @ X2 @ id)))) ) | ~spl603_644),
% 6.99/1.30 inference(avatar_component_clause,[],[f4151])).
% 6.99/1.30 thf(f4158,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ (X4 @ (d2subst @ d_id) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3))) != ((sub @ (sub @ X3 @ (push @ (sK123 @ X4 @ X3) @ (d2subst @ d_id))) @ (sK121 @ X4 @ X3)))) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)) @ sh)))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true)) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4142,f4089])).
% 6.99/1.30 thf(f4164,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ (sub @ X3 @ (d2subst @ d_id)) @ (sK121 @ X4 @ X3))) != ((sub @ (X4 @ (d2subst @ d_id) @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3)))) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)) @ sh))))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4158,f4089])).
% 6.99/1.30 thf(f4170,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ (sK121 @ X4 @ X3))) != ((sub @ (sub @ X3 @ sh) @ (sK121 @ X4 @ X3)))) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)) @ sh)))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true)) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4164,f862])).
% 6.99/1.30 thf(f4174,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ (d2subst @ d_id))) != ((sub @ (sub @ X3 @ sh) @ (d2subst @ d_id)))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)) @ sh))))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4170,f4089])).
% 6.99/1.30 thf(f4177,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (push @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)) @ sh)))) | (((sub @ (sub @ X3 @ sh) @ sh)) != ((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ sh)))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4174,f862])).
% 6.99/1.30 thf(f4179,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ (d2subst @ d_id)))) != ((sub @ X3 @ (d2subst @ d_id)))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ (sub @ X3 @ sh) @ sh)) != ((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ sh))) | (((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true)) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4177,f4089])).
% 6.99/1.30 thf(f4181,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sK115 @ id @ (lam @ (X4 @ sh @ one)) @ id)) = $true) | (((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ sh))) != ((sub @ X3 @ sh))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ (sub @ X3 @ sh) @ sh)) != ((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ sh)))) ) | ~spl603_209),
% 6.99/1.30 inference(forward_demodulation,[],[f4179,f862])).
% 6.99/1.30 thf(f4235,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (push @ (sK595 @ X1 @ X2) @ (sK594 @ X1 @ X2))) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (d2subst @ d_id)))) != ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f3645,f4089])).
% 6.99/1.30 thf(f4237,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (sub @ X2 @ (d2subst @ d_id)) @ (sK593 @ X1 @ X2))) != ((sub @ (X1 @ (sK594 @ X1 @ X2) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (d2subst @ d_id)))) != ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)))))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f4235,f4089])).
% 6.99/1.30 thf(f4238,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ (d2subst @ d_id)))) != ((X1 @ (d2subst @ d_id) @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) | (((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (d2subst @ d_id)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f4237,f4089])).
% 6.99/1.30 thf(f4239,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ sh))) != ((X1 @ sh @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2))))) | (((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (d2subst @ d_id)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f4238,f862])).
% 6.99/1.30 thf(f4826,plain,(
% 6.99/1.30 ( ! [X65 : term] : ((((d2term @ d_one)) = X65)) )),
% 6.99/1.30 inference(forward_demodulation,[],[f931,f830])).
% 6.99/1.30 thf(f4833,plain,(
% 6.99/1.30 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 6.99/1.30 inference(superposition,[],[f4826,f4826])).
% 6.99/1.30 thf(f4836,plain,(
% 6.99/1.30 ($false = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl603_573),
% 6.99/1.30 inference(superposition,[],[f3666,f4826])).
% 6.99/1.30 thf(f4952,plain,(
% 6.99/1.30 (((sK591 @ id @ one @ id)) = $true) | ~spl603_570),
% 6.99/1.30 inference(forward_demodulation,[],[f3653,f909])).
% 6.99/1.30 thf(f4953,plain,(
% 6.99/1.30 (((sK591 @ id @ one @ id)) = $false) | ~spl603_573),
% 6.99/1.30 inference(forward_demodulation,[],[f4836,f909])).
% 6.99/1.30 thf(f4987,plain,(
% 6.99/1.30 ($false = $true) | (~spl603_570 | ~spl603_573)),
% 6.99/1.30 inference(superposition,[],[f4952,f4953])).
% 6.99/1.30 thf(f4990,plain,(
% 6.99/1.30 $false | (~spl603_570 | ~spl603_573)),
% 6.99/1.30 inference(trivial_inequality_removal,[],[f4987])).
% 6.99/1.30 thf(f4991,plain,(
% 6.99/1.30 ~spl603_570 | ~spl603_573),
% 6.99/1.30 inference(avatar_contradiction_clause,[],[f4990])).
% 6.99/1.30 thf(f4997,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (d2subst @ d_id)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((d2term @ d_one)) != ((sub @ X2 @ (push @ (sub @ (sK595 @ X1 @ X2) @ (sK593 @ X1 @ X2)) @ sh))))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f4239,f4826])).
% 6.99/1.30 thf(f5001,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2))) != ((sub @ (sub @ X2 @ (d2subst @ d_id)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f4997,f4826])).
% 6.99/1.30 thf(f5004,plain,(
% 6.99/1.30 ( ! [X2 : term,X1 : (subst > term > term)] : ((((d2term @ d_one)) != ((sub @ (X1 @ (d2subst @ d_id) @ (sK595 @ X1 @ X2)) @ (sK593 @ X1 @ X2)))) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f5001,f4826])).
% 6.99/1.30 thf(f5007,plain,(
% 6.99/1.30 ( ! [X1 : (subst > term > term)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl603_568),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f5004,f4826])).
% 6.99/1.30 thf(f5010,plain,(
% 6.99/1.30 ($true = ((sK591 @ id @ (d2term @ d_one) @ id))) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f5007,f4826])).
% 6.99/1.30 thf(f5013,plain,(
% 6.99/1.30 (((sK591 @ id @ one @ id)) = $true) | ~spl603_568),
% 6.99/1.30 inference(forward_demodulation,[],[f5010,f909])).
% 6.99/1.30 thf(f5017,plain,(
% 6.99/1.30 ($false = $true) | (~spl603_568 | ~spl603_573)),
% 6.99/1.30 inference(forward_demodulation,[],[f5013,f4953])).
% 6.99/1.30 thf(f5018,plain,(
% 6.99/1.30 $false | (~spl603_568 | ~spl603_573)),
% 6.99/1.30 inference(trivial_inequality_removal,[],[f5017])).
% 6.99/1.30 thf(f5019,plain,(
% 6.99/1.30 ~spl603_568 | ~spl603_573),
% 6.99/1.30 inference(avatar_contradiction_clause,[],[f5018])).
% 6.99/1.30 thf(f5024,plain,(
% 6.99/1.30 ( ! [X2 : term] : (($true = ((sK115 @ id @ (d2term @ d_one) @ id))) | ($true != ((sK115 @ id @ X2 @ id)))) ) | ~spl603_636),
% 6.99/1.30 inference(forward_demodulation,[],[f3949,f4826])).
% 6.99/1.30 thf(f5029,plain,(
% 6.99/1.30 ( ! [X2 : term] : ((((sK115 @ id @ one @ id)) = $true) | ($true != ((sK115 @ id @ X2 @ id)))) ) | ~spl603_636),
% 6.99/1.30 inference(forward_demodulation,[],[f5024,f909])).
% 6.99/1.30 thf(f5032,definition,(
% 6.99/1.30 spl603_645 <=> (((sK115 @ id @ one @ id)) = $true)),
% 6.99/1.30 introduced(definition,[new_symbols(definition,[spl603_645])],[avatar_definition])).
% 6.99/1.30 thf(f5036,plain,(
% 6.99/1.30 spl603_645 | spl603_644 | ~spl603_636),
% 6.99/1.30 inference(avatar_split_clause,[],[f5029,f3948,f4151,f5032])).
% 6.99/1.30 thf(f7106,plain,(
% 6.99/1.30 ($true != ((sK115 @ id @ (d2term @ d_one) @ id))) | spl603_441),
% 6.99/1.30 inference(forward_demodulation,[],[f4128,f4826])).
% 6.99/1.30 thf(f7108,plain,(
% 6.99/1.30 (((sK115 @ id @ one @ id)) != $true) | spl603_441),
% 6.99/1.30 inference(forward_demodulation,[],[f7106,f909])).
% 6.99/1.30 thf(f7110,plain,(
% 6.99/1.30 ~spl603_645 | spl603_441),
% 6.99/1.30 inference(avatar_split_clause,[],[f7108,f3087,f5032])).
% 6.99/1.30 thf(f11484,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((X4 @ sh @ (sub @ (sK119 @ X4 @ X3) @ sh))) != ((sub @ X3 @ sh))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true) | (((sub @ (sub @ X3 @ sh) @ sh)) != ((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ sh)))) ) | (~spl603_209 | ~spl603_644)),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f4181,f4152])).
% 6.99/1.30 thf(f11485,plain,(
% 6.99/1.30 ( ! [X3 : term,X4 : (subst > term > term)] : ((((sub @ (sub @ X3 @ sh) @ sh)) != ((sub @ (X4 @ sh @ (sK123 @ X4 @ X3)) @ sh))) | (((sK115 @ id @ (sK120 @ X4) @ id)) = $true)) ) | (~spl603_209 | ~spl603_644)),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f11484,f4833])).
% 6.99/1.30 thf(f11486,plain,(
% 6.99/1.30 ( ! [X4 : (subst > term > term)] : ((((sK115 @ id @ (sK120 @ X4) @ id)) = $true)) ) | (~spl603_209 | ~spl603_644)),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f11485,f4833])).
% 6.99/1.30 thf(f11487,plain,(
% 6.99/1.30 $false | (~spl603_209 | ~spl603_644)),
% 6.99/1.30 inference(forward_subsumption_resolution,[],[f11486,f4152])).
% 6.99/1.30 thf(f11488,plain,(
% 6.99/1.30 ~spl603_209 | ~spl603_644),
% 6.99/1.30 inference(avatar_contradiction_clause,[],[f11487])).
% 6.99/1.30 cnf(s140, plain, ~spl603_83 | spl603_199, inference(sat_conversion,[],[f2047])).
% 6.99/1.30 cnf(s149, plain, spl603_83 | spl603_209, inference(sat_conversion,[],[f2089])).
% 6.99/1.30 cnf(s384, plain, spl603_83 | ~spl603_441, inference(sat_conversion,[],[f3090])).
% 6.99/1.30 cnf(s528, plain, spl603_568 | spl603_569 | spl603_570, inference(sat_conversion,[],[f3654])).
% 6.99/1.30 cnf(s531, plain, spl603_569 | spl603_573, inference(sat_conversion,[],[f3667])).
% 6.99/1.30 cnf(s609, plain, spl603_83 | spl603_636, inference(sat_conversion,[],[f3950])).
% 6.99/1.30 cnf(s615, plain, ~spl603_199 | ~spl603_569, inference(sat_conversion,[],[f3973])).
% 6.99/1.30 cnf(s636, plain, ~spl603_570 | ~spl603_573, inference(sat_conversion,[],[f4991])).
% 6.99/1.30 cnf(s638, plain, ~spl603_568 | ~spl603_573, inference(sat_conversion,[],[f5019])).
% 6.99/1.30 cnf(s640, plain, ~spl603_636 | spl603_644 | spl603_645, inference(sat_conversion,[],[f5036])).
% 6.99/1.30 cnf(s716, plain, spl603_441 | ~spl603_645, inference(sat_conversion,[],[f7110])).
% 6.99/1.30 cnf(s824, plain, ~spl603_209 | ~spl603_644, inference(sat_conversion,[],[f11488])).
% 6.99/1.30 cnf(s911, plain, spl603_569, inference(rat,[],[s528,s636,s638,s531])).
% 6.99/1.30 cnf(s912, plain, ~spl603_199, inference(rat,[],[s615,s911])).
% 6.99/1.30 cnf(s921, plain, ~spl603_83, inference(rat,[],[s140,s912])).
% 6.99/1.30 cnf(s922, plain, spl603_636, inference(rat,[],[s609,s921])).
% 6.99/1.30 cnf(s923, plain, ~spl603_441, inference(rat,[],[s384,s921])).
% 6.99/1.30 cnf(s924, plain, spl603_209, inference(rat,[],[s149,s921])).
% 6.99/1.30 cnf(s926, plain, ~spl603_645, inference(rat,[],[s716,s923])).
% 6.99/1.30 cnf(s927, plain, ~spl603_644, inference(rat,[],[s824,s924])).
% 6.99/1.30 cnf(s929, plain, $false, inference(rat,[],[s640,s922,s926,s927])).
% 6.99/1.30 thf(f11489,plain,(
% 6.99/1.30 $false),
% 6.99/1.30 inference(avatar_sat_refutation,[],[s929])).
% 6.99/1.30 % SZS output end Proof for theBenchmark
% 6.99/1.30 % (1436999)------------------------------
% 6.99/1.30 % (1436999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.99/1.30 % (1436999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.99/1.30 % (1436999)CaDiCaL version: 2.1.3
% 6.99/1.30 % (1436999)Termination reason: Refutation
% 6.99/1.30 % (1436999)Time elapsed: 0.434 s
% 6.99/1.30 % (1436999)Peak memory usage: 19 MB
% 6.99/1.30 % (1436999)Instructions burned: 899 (million)
% 6.99/1.30 % (1436878)Success in time 1.006 s
% 6.99/1.30 % Vampire exiting
%------------------------------------------------------------------------------