%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX157^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:35 AM UTC 2026
% Result : Theorem 5.11s 1.34s
% Output : Refutation 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX157^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n019.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 16:09:07 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.21/0.29 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
% 0.51/0.46 % (978028)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.46 % (978039)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.46 % (978039)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
% 0.51/0.46 % (978036)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=1242040605: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)
% 0.51/0.46 % (978039)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=1668757115:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.46 % (978035)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2036121757:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.46 % (978034)lrs+10_16_si=on:nwc=1.5:random_seed=1819825834:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.46 % (978037)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1148539535:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.46 % (978035)Instruction limit reached!
% 0.51/0.46 % (978035)------------------------------
% 0.51/0.46 % (978035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.46 % (978035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.46 % (978035)CaDiCaL version: 2.1.3
% 0.51/0.46 % (978035)Termination reason: Instruction limit
% 0.51/0.46 % (978035)Termination phase: shuffling
% 0.51/0.46 % (978035)Time elapsed: 0.002 s
% 0.51/0.46 % (978035)Peak memory usage: 9 MB
% 0.51/0.46 % (978035)Instructions burned: 3 (million)
% 0.51/0.46 % (978033)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2330682714:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.46 % (978038)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1228626766:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.46 % (978034)Instruction limit reached!
% 0.51/0.46 % (978034)------------------------------
% 0.51/0.46 % (978034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.46 % (978034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.46 % (978034)CaDiCaL version: 2.1.3
% 0.51/0.46 % (978034)Termination reason: Instruction limit
% 0.51/0.46 % (978034)Termination phase: shuffling
% 0.51/0.46 % (978034)Time elapsed: 0.016 s
% 0.51/0.46 % (978034)Peak memory usage: 10 MB
% 0.51/0.46 % (978034)Instructions burned: 19 (million)
% 0.51/0.46 % (978037)Instruction limit reached!
% 0.51/0.46 % (978037)------------------------------
% 0.51/0.46 % (978037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.46 % (978037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.46 % (978037)CaDiCaL version: 2.1.3
% 0.51/0.46 % (978037)Termination reason: Instruction limit
% 0.51/0.46 % (978037)Termination phase: Property scanning
% 0.51/0.46 % (978037)Time elapsed: 0.019 s
% 0.51/0.46 % (978037)Peak memory usage: 10 MB
% 0.51/0.46 % (978037)Instructions burned: 24 (million)
% 0.51/0.46 % (978045)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2176216460:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.46 % (978045)Instruction limit reached!
% 0.51/0.46 % (978045)------------------------------
% 0.51/0.46 % (978045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.46 % (978045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.46 % (978045)CaDiCaL version: 2.1.3
% 0.51/0.46 % (978045)Termination reason: Instruction limit
% 0.51/0.46 % (978045)Termination phase: shuffling
% 0.51/0.46 % (978045)Time elapsed: 0.003 s
% 0.51/0.46 % (978045)Peak memory usage: 9 MB
% 0.51/0.46 % (978045)Instructions burned: 5 (million)
% 0.51/0.46 % (978048)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2109162885:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.46 % (978049)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.15/0.52 % (978048)Instruction limit reached!
% 1.15/0.52 % (978048)------------------------------
% 1.15/0.52 % (978048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978048)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978048)Termination reason: Instruction limit
% 1.15/0.52 % (978048)Termination phase: shuffling
% 1.15/0.52 % (978048)Time elapsed: 0.003 s
% 1.15/0.52 % (978048)Peak memory usage: 9 MB
% 1.15/0.52 % (978048)Instructions burned: 6 (million)
% 1.15/0.52 % (978038)Instruction limit reached!
% 1.15/0.52 % (978038)------------------------------
% 1.15/0.52 % (978038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978038)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978038)Termination reason: Instruction limit
% 1.15/0.52 % (978038)Termination phase: Preprocessing 3
% 1.15/0.52 % (978038)Time elapsed: 0.038 s
% 1.15/0.52 % (978038)Peak memory usage: 12 MB
% 1.15/0.52 % (978038)Instructions burned: 77 (million)
% 1.15/0.52 % (978033)Instruction limit reached!
% 1.15/0.52 % (978033)------------------------------
% 1.15/0.52 % (978033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978033)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978033)Termination reason: Instruction limit
% 1.15/0.52 % (978033)Termination phase: Preprocessing 3
% 1.15/0.52 % (978033)Time elapsed: 0.043 s
% 1.15/0.52 % (978033)Peak memory usage: 12 MB
% 1.15/0.52 % (978033)Instructions burned: 88 (million)
% 1.15/0.52 % (978051)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=829898895:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.15/0.52 % (978049)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2701364904:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.15/0.52 % (978051)Instruction limit reached!
% 1.15/0.52 % (978051)------------------------------
% 1.15/0.52 % (978051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978051)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978051)Termination reason: Instruction limit
% 1.15/0.52 % (978051)Termination phase: shuffling
% 1.15/0.52 % (978051)Time elapsed: 0.005 s
% 1.15/0.52 % (978051)Peak memory usage: 10 MB
% 1.15/0.52 % (978051)Instructions burned: 12 (million)
% 1.15/0.52 % (978049)Instruction limit reached!
% 1.15/0.52 % (978049)------------------------------
% 1.15/0.52 % (978049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978049)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978049)Termination reason: Instruction limit
% 1.15/0.52 % (978049)Termination phase: shuffling
% 1.15/0.52 % (978049)Time elapsed: 0.007 s
% 1.15/0.52 % (978049)Peak memory usage: 10 MB
% 1.15/0.52 % (978049)Instructions burned: 8 (million)
% 1.15/0.52 % (978039)Instruction limit reached!
% 1.15/0.52 % (978039)------------------------------
% 1.15/0.52 % (978039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.15/0.52 % (978039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.15/0.52 % (978039)CaDiCaL version: 2.1.3
% 1.15/0.52 % (978039)Termination reason: Instruction limit
% 1.15/0.52 % (978039)Termination phase: Property scanning
% 1.15/0.52 % (978039)Time elapsed: 0.074 s
% 1.15/0.52 % (978039)Peak memory usage: 13 MB
% 1.15/0.52 % (978039)Instructions burned: 158 (million)
% 1.15/0.52 % (978054)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=2200284157:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.15/0.52 % (978058)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.15/0.52 % (978056)lrs+10_1_si=on:cs=on:random_seed=154094843:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.15/0.52 % (978053)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
% 1.58/0.60 % (978053)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.58/0.60 % (978058)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=4019102495:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.58/0.60 % (978056)Instruction limit reached!
% 1.58/0.60 % (978056)------------------------------
% 1.58/0.60 % (978056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.58/0.60 % (978056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.58/0.60 % (978056)CaDiCaL version: 2.1.3
% 1.58/0.60 % (978056)Termination reason: Instruction limit
% 1.58/0.60 % (978056)Termination phase: shuffling
% 1.58/0.60 % (978056)Time elapsed: 0.004 s
% 1.58/0.60 % (978056)Peak memory usage: 9 MB
% 1.58/0.60 % (978056)Instructions burned: 8 (million)
% 1.58/0.60 % (978058)Instruction limit reached!
% 1.58/0.60 % (978058)------------------------------
% 1.58/0.60 % (978058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.58/0.60 % (978058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.58/0.60 % (978058)CaDiCaL version: 2.1.3
% 1.58/0.60 % (978058)Termination reason: Instruction limit
% 1.58/0.60 % (978058)Termination phase: shuffling
% 1.58/0.60 % (978058)Time elapsed: 0.001 s
% 1.58/0.60 % (978058)Peak memory usage: 9 MB
% 1.58/0.60 % (978058)Instructions burned: 3 (million)
% 1.58/0.60 % (978053)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3176842088:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.58/0.60 % (978059)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1921831637:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.58/0.60 % (978064)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2873965447:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.58/0.60 % (978065)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4076740598:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.58/0.60 % (978059)Refutation not found, incomplete strategy
% 1.58/0.60 % (978059)------------------------------
% 1.58/0.60 % (978059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.58/0.60 % (978059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.58/0.60 % (978059)CaDiCaL version: 2.1.3
% 1.58/0.60 % (978059)Termination reason: Refutation not found, incomplete strategy
% 1.58/0.60 % (978059)Time elapsed: 0.016 s
% 1.58/0.60 % (978059)Peak memory usage: 12 MB
% 1.58/0.60 % (978059)Instructions burned: 37 (million)
% 1.58/0.60 % (978059)------------------------------
% 1.58/0.60 % (978059)------------------------------
% 1.58/0.60 % (978054)Instruction limit reached!
% 1.58/0.60 % (978054)------------------------------
% 1.58/0.60 % (978054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.58/0.60 % (978054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.58/0.60 % (978054)CaDiCaL version: 2.1.3
% 1.58/0.60 % (978054)Termination reason: Instruction limit
% 1.58/0.60 % (978054)Termination phase: Saturation
% 1.58/0.60 % (978054)Time elapsed: 0.037 s
% 1.58/0.60 % (978054)Peak memory usage: 12 MB
% 1.58/0.60 % (978054)Instructions burned: 88 (million)
% 1.58/0.60 % (978065)Instruction limit reached!
% 1.58/0.60 % (978065)------------------------------
% 1.58/0.60 % (978065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.58/0.60 % (978065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.58/0.60 % (978065)CaDiCaL version: 2.1.3
% 1.58/0.60 % (978060)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1671858744:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.58/0.60 % (978065)Termination reason: Instruction limit
% 1.58/0.60 % (978065)Termination phase: shuffling
% 1.58/0.60 % (978065)Time elapsed: 0.006 s
% 1.58/0.60 % (978065)Peak memory usage: 10 MB
% 1.58/0.60 % (978065)Instructions burned: 15 (million)
% 1.86/0.68 % (978053)Instruction limit reached!
% 1.86/0.68 % (978053)------------------------------
% 1.86/0.68 % (978053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.68 % (978053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.68 % (978053)CaDiCaL version: 2.1.3
% 1.86/0.68 % (978053)Termination reason: Instruction limit
% 1.86/0.68 % (978053)Termination phase: shuffling
% 1.86/0.68 % (978053)Time elapsed: 0.024 s
% 1.86/0.68 % (978053)Peak memory usage: 10 MB
% 1.86/0.68 % (978053)Instructions burned: 29 (million)
% 1.86/0.68 % (978064)Instruction limit reached!
% 1.86/0.68 % (978064)------------------------------
% 1.86/0.68 % (978064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.68 % (978064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.68 % (978064)CaDiCaL version: 2.1.3
% 1.86/0.68 % (978064)Termination reason: Instruction limit
% 1.86/0.68 % (978064)Termination phase: Property scanning
% 1.86/0.68 % (978064)Time elapsed: 0.012 s
% 1.86/0.68 % (978064)Peak memory usage: 10 MB
% 1.86/0.68 % (978064)Instructions burned: 25 (million)
% 1.86/0.69 % (978073)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3554071662: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)
% 1.86/0.69 % (978073)Instruction limit reached!
% 1.86/0.69 % (978073)------------------------------
% 1.86/0.69 % (978073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.69 % (978073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.69 % (978073)CaDiCaL version: 2.1.3
% 1.86/0.69 % (978073)Termination reason: Instruction limit
% 1.86/0.69 % (978073)Termination phase: shuffling
% 1.86/0.69 % (978073)Time elapsed: 0.002 s
% 1.86/0.69 % (978073)Peak memory usage: 9 MB
% 1.86/0.69 % (978073)Instructions burned: 5 (million)
% 1.86/0.69 % (978075)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2845254220:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.86/0.69 % (978072)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2277582751:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.86/0.69 % (978072)Instruction limit reached!
% 1.86/0.69 % (978072)------------------------------
% 1.86/0.69 % (978072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.69 % (978072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.69 % (978072)CaDiCaL version: 2.1.3
% 1.86/0.69 % (978072)Termination reason: Instruction limit
% 1.86/0.69 % (978072)Termination phase: shuffling
% 1.86/0.69 % (978072)Time elapsed: 0.007 s
% 1.86/0.69 % (978072)Peak memory usage: 10 MB
% 1.86/0.69 % (978072)Instructions burned: 16 (million)
% 1.86/0.69 % (978075)Instruction limit reached!
% 1.86/0.69 % (978075)------------------------------
% 1.86/0.69 % (978075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.69 % (978075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/0.69 % (978075)CaDiCaL version: 2.1.3
% 1.86/0.69 % (978075)Termination reason: Instruction limit
% 1.86/0.69 % (978075)Termination phase: shuffling
% 1.86/0.69 % (978075)Time elapsed: 0.010 s
% 1.86/0.69 % (978075)Peak memory usage: 10 MB
% 1.86/0.69 % (978075)Instructions burned: 23 (million)
% 1.86/0.69 % (978070)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2358936300:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.86/0.69 % (978074)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2667014728:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.86/0.69 % (978081)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.86/0.69 % (978081)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=2698738242:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.86/0.69 % (978081)Instruction limit reached!
% 1.86/0.69 % (978081)------------------------------
% 1.86/0.69 % (978081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.86/0.69 % (978081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978081)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978081)Termination reason: Instruction limit
% 2.16/0.74 % (978081)Termination phase: shuffling
% 2.16/0.74 % (978081)Time elapsed: 0.004 s
% 2.16/0.74 % (978081)Peak memory usage: 10 MB
% 2.16/0.74 % (978081)Instructions burned: 8 (million)
% 2.16/0.74 % (978085)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=676279612:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.16/0.74 % (978080)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
% 2.16/0.74 % (978080)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.16/0.74 % (978074)Instruction limit reached!
% 2.16/0.74 % (978074)------------------------------
% 2.16/0.74 % (978074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.74 % (978074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978074)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978074)Termination reason: Instruction limit
% 2.16/0.74 % (978074)Termination phase: shuffling
% 2.16/0.74 % (978074)Time elapsed: 0.045 s
% 2.16/0.74 % (978074)Peak memory usage: 10 MB
% 2.16/0.74 % (978074)Instructions burned: 27 (million)
% 2.16/0.74 % (978079)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1705042027:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.16/0.74 % (978080)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=1350121408:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.16/0.74 % (978080)Instruction limit reached!
% 2.16/0.74 % (978080)------------------------------
% 2.16/0.74 % (978080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.74 % (978080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978080)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978080)Termination reason: Instruction limit
% 2.16/0.74 % (978080)Termination phase: shuffling
% 2.16/0.74 % (978080)Time elapsed: 0.006 s
% 2.16/0.74 % (978080)Peak memory usage: 10 MB
% 2.16/0.74 % (978080)Instructions burned: 15 (million)
% 2.16/0.74 % (978085)Instruction limit reached!
% 2.16/0.74 % (978085)------------------------------
% 2.16/0.74 % (978085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.74 % (978085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978085)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978085)Termination reason: Instruction limit
% 2.16/0.74 % (978085)Termination phase: Property scanning
% 2.16/0.74 % (978085)Time elapsed: 0.028 s
% 2.16/0.74 % (978085)Peak memory usage: 10 MB
% 2.16/0.74 % (978085)Instructions burned: 31 (million)
% 2.16/0.74 % (978087)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1656121973:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.16/0.74 % (978090)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2540095532:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.16/0.74 % (978087)Instruction limit reached!
% 2.16/0.74 % (978087)------------------------------
% 2.16/0.74 % (978087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.74 % (978087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978087)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978087)Termination reason: Instruction limit
% 2.16/0.74 % (978087)Termination phase: shuffling
% 2.16/0.74 % (978087)Time elapsed: 0.008 s
% 2.16/0.74 % (978087)Peak memory usage: 10 MB
% 2.16/0.74 % (978087)Instructions burned: 8 (million)
% 2.16/0.74 % (978090)Instruction limit reached!
% 2.16/0.74 % (978090)------------------------------
% 2.16/0.74 % (978090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.16/0.74 % (978090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/0.74 % (978090)CaDiCaL version: 2.1.3
% 2.16/0.74 % (978090)Termination reason: Instruction limit
% 2.16/0.74 % (978090)Termination phase: shuffling
% 2.16/0.74 % (978090)Time elapsed: 0.011 s
% 2.16/0.74 % (978090)Peak memory usage: 10 MB
% 2.16/0.74 % (978090)Instructions burned: 24 (million)
% 2.55/0.83 % (978091)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=623801325:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.55/0.83 % (978091)Instruction limit reached!
% 2.55/0.83 % (978091)------------------------------
% 2.55/0.83 % (978091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978091)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978091)Termination reason: Instruction limit
% 2.55/0.83 % (978091)Termination phase: shuffling
% 2.55/0.83 % (978091)Time elapsed: 0.009 s
% 2.55/0.83 % (978091)Peak memory usage: 10 MB
% 2.55/0.83 % (978091)Instructions burned: 21 (million)
% 2.55/0.83 % (978094)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3951444355:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.55/0.83 % (978079)Instruction limit reached!
% 2.55/0.83 % (978079)------------------------------
% 2.55/0.83 % (978079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978079)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978079)Termination reason: Instruction limit
% 2.55/0.83 % (978079)Termination phase: Preprocessing 3
% 2.55/0.83 % (978079)Time elapsed: 0.055 s
% 2.55/0.83 % (978079)Peak memory usage: 11 MB
% 2.55/0.83 % (978079)Instructions burned: 61 (million)
% 2.55/0.83 % (978095)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3949732857:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 2.55/0.83 % (978097)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=880298107:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 2.55/0.83 % (978099)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=551458728:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 2.55/0.83 % (978099)Instruction limit reached!
% 2.55/0.83 % (978099)------------------------------
% 2.55/0.83 % (978099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978099)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978099)Termination reason: Instruction limit
% 2.55/0.83 % (978099)Termination phase: Naming
% 2.55/0.83 % (978099)Time elapsed: 0.019 s
% 2.55/0.83 % (978099)Peak memory usage: 11 MB
% 2.55/0.83 % (978099)Instructions burned: 44 (million)
% 2.55/0.83 % (978060)Instruction limit reached!
% 2.55/0.83 % (978060)------------------------------
% 2.55/0.83 % (978060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978060)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978060)Termination reason: Instruction limit
% 2.55/0.83 % (978060)Termination phase: Saturation
% 2.55/0.83 % (978060)Time elapsed: 0.207 s
% 2.55/0.83 % (978060)Peak memory usage: 15 MB
% 2.55/0.83 % (978060)Instructions burned: 249 (million)
% 2.55/0.83 % (978103)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.55/0.83 % (978095)Instruction limit reached!
% 2.55/0.83 % (978095)------------------------------
% 2.55/0.83 % (978095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978095)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978095)Termination reason: Instruction limit
% 2.55/0.83 % (978095)Termination phase: Function definition elimination
% 2.55/0.83 % (978095)Time elapsed: 0.061 s
% 2.55/0.83 % (978095)Peak memory usage: 13 MB
% 2.55/0.83 % (978095)Instructions burned: 144 (million)
% 2.55/0.83 % (978103)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=243946742:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 2.55/0.83 % (978103)Instruction limit reached!
% 2.55/0.83 % (978103)------------------------------
% 2.55/0.83 % (978103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.55/0.83 % (978103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/0.83 % (978103)CaDiCaL version: 2.1.3
% 2.55/0.83 % (978103)Termination reason: Instruction limit
% 2.80/0.94 % (978103)Termination phase: shuffling
% 2.80/0.94 % (978103)Time elapsed: 0.004 s
% 2.80/0.94 % (978103)Peak memory usage: 9 MB
% 2.80/0.94 % (978103)Instructions burned: 9 (million)
% 2.80/0.94 % (978036)Instruction limit reached!
% 2.80/0.94 % (978036)------------------------------
% 2.80/0.94 % (978036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/0.94 % (978036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/0.94 % (978036)CaDiCaL version: 2.1.3
% 2.80/0.94 % (978036)Termination reason: Instruction limit
% 2.80/0.94 % (978036)Termination phase: Saturation
% 2.80/0.94 % (978036)Time elapsed: 0.345 s
% 2.80/0.94 % (978036)Peak memory usage: 18 MB
% 2.80/0.94 % (978036)Instructions burned: 635 (million)
% 2.80/0.94 % (978105)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=639473031:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 2.80/0.94 % (978108)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1224063583:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.80/0.94 % (978104)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=3054851339:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 2.80/0.94 % (978097)Instruction limit reached!
% 2.80/0.94 % (978097)------------------------------
% 2.80/0.94 % (978097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/0.94 % (978097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/0.94 % (978097)CaDiCaL version: 2.1.3
% 2.80/0.94 % (978097)Termination reason: Instruction limit
% 2.80/0.94 % (978097)Termination phase: Property scanning
% 2.80/0.94 % (978097)Time elapsed: 0.082 s
% 2.80/0.94 % (978097)Peak memory usage: 13 MB
% 2.80/0.94 % (978097)Instructions burned: 195 (million)
% 2.80/0.94 % (978107)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.80/0.94 % (978070)Instruction limit reached!
% 2.80/0.94 % (978070)------------------------------
% 2.80/0.94 % (978070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/0.94 % (978070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/0.94 % (978070)CaDiCaL version: 2.1.3
% 2.80/0.94 % (978070)Termination reason: Instruction limit
% 2.80/0.94 % (978070)Termination phase: Saturation
% 2.80/0.94 % (978070)Time elapsed: 0.217 s
% 2.80/0.94 % (978070)Peak memory usage: 16 MB
% 2.80/0.94 % (978070)Instructions burned: 328 (million)
% 2.80/0.94 % (978108)Instruction limit reached!
% 2.80/0.94 % (978108)------------------------------
% 2.80/0.94 % (978108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/0.94 % (978108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/0.94 % (978108)CaDiCaL version: 2.1.3
% 2.80/0.94 % (978108)Termination reason: Instruction limit
% 2.80/0.94 % (978108)Termination phase: shuffling
% 2.80/0.94 % (978108)Time elapsed: 0.010 s
% 2.80/0.94 % (978108)Peak memory usage: 10 MB
% 2.80/0.94 % (978108)Instructions burned: 23 (million)
% 2.80/0.94 % (978107)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=819499031:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.80/0.94 % (978107)Instruction limit reached!
% 2.80/0.94 % (978107)------------------------------
% 2.80/0.94 % (978107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/0.94 % (978107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/0.94 % (978107)CaDiCaL version: 2.1.3
% 2.80/0.94 % (978107)Termination reason: Instruction limit
% 2.80/0.94 % (978107)Termination phase: shuffling
% 2.80/0.94 % (978107)Time elapsed: 0.008 s
% 2.80/0.94 % (978107)Peak memory usage: 10 MB
% 2.80/0.94 % (978107)Instructions burned: 8 (million)
% 2.80/0.94 % (978114)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=331168674:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 2.80/0.94 % (978104)Refutation not found, incomplete strategy
% 2.80/0.94 % (978104)------------------------------
% 2.80/0.94 % (978104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/1.06 % (978104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.06 % (978104)CaDiCaL version: 2.1.3
% 2.80/1.06 % (978104)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.06 % (978104)Time elapsed: 0.032 s
% 2.80/1.06 % (978104)Peak memory usage: 13 MB
% 2.80/1.06 % (978104)Instructions burned: 40 (million)
% 2.80/1.06 % (978104)------------------------------
% 2.80/1.06 % (978104)------------------------------
% 2.80/1.06 % (978112)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1990507404:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 2.80/1.06 % (978113)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=2472223556:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 2.80/1.06 % (978116)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=2806305823:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 2.80/1.06 % (978112)Instruction limit reached!
% 2.80/1.06 % (978112)------------------------------
% 2.80/1.06 % (978112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/1.06 % (978112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.06 % (978112)CaDiCaL version: 2.1.3
% 2.80/1.06 % (978112)Termination reason: Instruction limit
% 2.80/1.06 % (978112)Termination phase: shuffling
% 2.80/1.06 % (978112)Time elapsed: 0.017 s
% 2.80/1.06 % (978112)Peak memory usage: 10 MB
% 2.80/1.06 % (978112)Instructions burned: 20 (million)
% 2.80/1.06 % (978105)Instruction limit reached!
% 2.80/1.06 % (978105)------------------------------
% 2.80/1.06 % (978105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/1.06 % (978105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.06 % (978105)CaDiCaL version: 2.1.3
% 2.80/1.06 % (978105)Termination reason: Instruction limit
% 2.80/1.06 % (978105)Termination phase: Property scanning
% 2.80/1.06 % (978105)Time elapsed: 0.073 s
% 2.80/1.06 % (978105)Peak memory usage: 13 MB
% 2.80/1.06 % (978105)Instructions burned: 171 (million)
% 2.80/1.06 % (978118)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=1554691275:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 2.80/1.06 % (978116)Instruction limit reached!
% 2.80/1.06 % (978116)------------------------------
% 2.80/1.06 % (978116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/1.06 % (978116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.06 % (978116)CaDiCaL version: 2.1.3
% 2.80/1.06 % (978116)Termination reason: Instruction limit
% 2.80/1.06 % (978116)Termination phase: SInE selection
% 2.80/1.06 % (978116)Time elapsed: 0.027 s
% 2.80/1.06 % (978116)Peak memory usage: 10 MB
% 2.80/1.06 % (978116)Instructions burned: 46 (million)
% 2.80/1.06 % (978123)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.80/1.06 % (978123)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2317632953:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 2.80/1.06 % (978122)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=315293697:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 2.80/1.06 % (978122)Instruction limit reached!
% 2.80/1.06 % (978122)------------------------------
% 2.80/1.06 % (978122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.80/1.06 % (978122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.06 % (978122)CaDiCaL version: 2.1.3
% 2.80/1.06 % (978122)Termination reason: Instruction limit
% 2.80/1.06 % (978122)Termination phase: shuffling
% 2.80/1.06 % (978122)Time elapsed: 0.020 s
% 2.80/1.06 % (978122)Peak memory usage: 10 MB
% 2.80/1.06 % (978122)Instructions burned: 22 (million)
% 2.80/1.06 % (978126)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4196664689:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 2.80/1.06 % (978126)Instruction limit reached!
% 4.89/1.19 % (978126)------------------------------
% 4.89/1.19 % (978126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978126)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978126)Termination reason: Instruction limit
% 4.89/1.19 % (978126)Termination phase: shuffling
% 4.89/1.19 % (978126)Time elapsed: 0.006 s
% 4.89/1.19 % (978126)Peak memory usage: 10 MB
% 4.89/1.19 % (978126)Instructions burned: 13 (million)
% 4.89/1.19 % (978128)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=1642870897:i=66:s2at=3:nm=2:rtra=on:rawr=on_2994 on theBenchmark for (2994ds/66Mi)
% 4.89/1.19 % (978130)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2766981958:i=51:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/51Mi)
% 4.89/1.19 % (978128)Instruction limit reached!
% 4.89/1.19 % (978128)------------------------------
% 4.89/1.19 % (978128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978128)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978128)Termination reason: Instruction limit
% 4.89/1.19 % (978128)Termination phase: Preprocessing 1
% 4.89/1.19 % (978128)Time elapsed: 0.027 s
% 4.89/1.19 % (978128)Peak memory usage: 11 MB
% 4.89/1.19 % (978128)Instructions burned: 66 (million)
% 4.89/1.19 % (978123)Instruction limit reached!
% 4.89/1.19 % (978123)------------------------------
% 4.89/1.19 % (978123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978123)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978123)Termination reason: Instruction limit
% 4.89/1.19 % (978123)Termination phase: Saturation
% 4.89/1.19 % (978123)Time elapsed: 0.085 s
% 4.89/1.19 % (978123)Peak memory usage: 14 MB
% 4.89/1.19 % (978123)Instructions burned: 200 (million)
% 4.89/1.19 % (978130)Instruction limit reached!
% 4.89/1.19 % (978130)------------------------------
% 4.89/1.19 % (978130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978130)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978130)Termination reason: Instruction limit
% 4.89/1.19 % (978130)Termination phase: Preprocessing 3
% 4.89/1.19 % (978130)Time elapsed: 0.023 s
% 4.89/1.19 % (978130)Peak memory usage: 11 MB
% 4.89/1.19 % (978130)Instructions burned: 53 (million)
% 4.89/1.19 % (978135)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2691803921:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 4.89/1.19 % (978136)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=2262627112:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 4.89/1.19 % (978133)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=605603885:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 4.89/1.19 % (978136)Instruction limit reached!
% 4.89/1.19 % (978136)------------------------------
% 4.89/1.19 % (978136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978136)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978136)Termination reason: Instruction limit
% 4.89/1.19 % (978136)Termination phase: Property scanning
% 4.89/1.19 % (978136)Time elapsed: 0.015 s
% 4.89/1.19 % (978136)Peak memory usage: 10 MB
% 4.89/1.19 % (978136)Instructions burned: 34 (million)
% 4.89/1.19 % (978133)Instruction limit reached!
% 4.89/1.19 % (978133)------------------------------
% 4.89/1.19 % (978133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.89/1.19 % (978133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.89/1.19 % (978133)CaDiCaL version: 2.1.3
% 4.89/1.19 % (978133)Termination reason: Instruction limit
% 4.89/1.19 % (978133)Termination phase: Property scanning
% 4.89/1.19 % (978133)Time elapsed: 0.025 s
% 4.89/1.19 % (978133)Peak memory usage: 10 MB
% 4.89/1.19 % (978133)Instructions burned: 31 (million)
% 4.89/1.19 % (978140)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=873437918:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2993 on theBenchmark for (2993ds/67Mi)
% 5.11/1.34 % (978141)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.11/1.34 % (978135)Instruction limit reached!
% 5.11/1.34 % (978135)------------------------------
% 5.11/1.34 % (978135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978135)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978135)Termination reason: Instruction limit
% 5.11/1.34 % (978135)Termination phase: Property scanning
% 5.11/1.34 % (978135)Time elapsed: 0.060 s
% 5.11/1.34 % (978135)Peak memory usage: 13 MB
% 5.11/1.34 % (978135)Instructions burned: 138 (million)
% 5.11/1.34 % (978113)Instruction limit reached!
% 5.11/1.34 % (978113)------------------------------
% 5.11/1.34 % (978113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978113)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978113)Termination reason: Instruction limit
% 5.11/1.34 % (978113)Termination phase: Saturation
% 5.11/1.34 % (978113)Time elapsed: 0.204 s
% 5.11/1.34 % (978113)Peak memory usage: 15 MB
% 5.11/1.34 % (978113)Instructions burned: 316 (million)
% 5.11/1.34 % (978141)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=855448713:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2993 on theBenchmark for (2993ds/180Mi)
% 5.11/1.34 % (978143)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=983797984:st=2:i=246:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/246Mi)
% 5.11/1.34 % (978144)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2095128815:cond=on:i=96:bd=all:rtra=on_2993 on theBenchmark for (2993ds/96Mi)
% 5.11/1.34 % (978118)Refutation not found, incomplete strategy
% 5.11/1.34 % (978118)------------------------------
% 5.11/1.34 % (978118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978118)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978118)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.34 % (978118)Time elapsed: 0.223 s
% 5.11/1.34 % (978118)Peak memory usage: 16 MB
% 5.11/1.34 % (978118)Instructions burned: 263 (million)
% 5.11/1.34 % (978118)------------------------------
% 5.11/1.34 % (978118)------------------------------
% 5.11/1.34 % (978140)Instruction limit reached!
% 5.11/1.34 % (978140)------------------------------
% 5.11/1.34 % (978140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978140)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978140)Termination reason: Instruction limit
% 5.11/1.34 % (978140)Termination phase: Preprocessing 3
% 5.11/1.34 % (978140)Time elapsed: 0.062 s
% 5.11/1.34 % (978140)Peak memory usage: 12 MB
% 5.11/1.34 % (978140)Instructions burned: 68 (million)
% 5.11/1.34 % (978144)Instruction limit reached!
% 5.11/1.34 % (978144)------------------------------
% 5.11/1.34 % (978144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978144)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978144)Termination reason: Instruction limit
% 5.11/1.34 % (978144)Termination phase: Property scanning
% 5.11/1.34 % (978144)Time elapsed: 0.061 s
% 5.11/1.34 % (978144)Peak memory usage: 12 MB
% 5.11/1.34 % (978144)Instructions burned: 96 (million)
% 5.11/1.34 % (978149)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1627457534:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/874Mi)
% 5.11/1.34 % (978148)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3815903797:i=427:sd=1:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/427Mi)
% 5.11/1.34 % (978148)Refutation not found, incomplete strategy
% 5.11/1.34 % (978148)------------------------------
% 5.11/1.34 % (978148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978148)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978148)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.34 % (978148)Time elapsed: 0.018 s
% 5.11/1.34 % (978148)Peak memory usage: 12 MB
% 5.11/1.34 % (978148)Instructions burned: 39 (million)
% 5.11/1.34 % (978148)------------------------------
% 5.11/1.34 % (978148)------------------------------
% 5.11/1.34 % (978141)Instruction limit reached!
% 5.11/1.34 % (978141)------------------------------
% 5.11/1.34 % (978141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978141)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978141)Termination reason: Instruction limit
% 5.11/1.34 % (978141)Termination phase: Saturation
% 5.11/1.34 % (978141)Time elapsed: 0.109 s
% 5.11/1.34 % (978141)Peak memory usage: 12 MB
% 5.11/1.34 % (978141)Instructions burned: 180 (million)
% 5.11/1.34 % (978151)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3783409706:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/515Mi)
% 5.11/1.34 % (978153)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=2835700293:st=1.5:i=130:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/130Mi)
% 5.11/1.34 % (978154)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1804516140:i=44:ep=R:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/44Mi)
% 5.11/1.34 % (978154)Instruction limit reached!
% 5.11/1.34 % (978154)------------------------------
% 5.11/1.34 % (978154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978154)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978154)Termination reason: Instruction limit
% 5.11/1.34 % (978154)Termination phase: Property scanning
% 5.11/1.34 % (978154)Time elapsed: 0.034 s
% 5.11/1.34 % (978154)Peak memory usage: 10 MB
% 5.11/1.34 % (978154)Instructions burned: 46 (million)
% 5.11/1.34 % (978153)Refutation not found, incomplete strategy
% 5.11/1.34 % (978153)------------------------------
% 5.11/1.34 % (978153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978153)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978153)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.34 % (978153)Time elapsed: 0.062 s
% 5.11/1.34 % (978153)Peak memory usage: 13 MB
% 5.11/1.34 % (978153)Instructions burned: 67 (million)
% 5.11/1.34 % (978153)------------------------------
% 5.11/1.34 % (978153)------------------------------
% 5.11/1.34 % (978143)Instruction limit reached!
% 5.11/1.34 % (978143)------------------------------
% 5.11/1.34 % (978143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978143)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978143)Termination reason: Instruction limit
% 5.11/1.34 % (978143)Termination phase: Saturation
% 5.11/1.34 % (978143)Time elapsed: 0.187 s
% 5.11/1.34 % (978143)Peak memory usage: 15 MB
% 5.11/1.34 % (978143)Instructions burned: 246 (million)
% 5.11/1.34 % (978114)Instruction limit reached!
% 5.11/1.34 % (978114)------------------------------
% 5.11/1.34 % (978114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978114)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978114)Termination reason: Instruction limit
% 5.11/1.34 % (978114)Termination phase: Saturation
% 5.11/1.34 % (978114)Time elapsed: 0.429 s
% 5.11/1.34 % (978114)Peak memory usage: 18 MB
% 5.11/1.34 % (978114)Instructions burned: 853 (million)
% 5.11/1.34 % (978159)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3999635756:i=450:rtra=on:ixr=off:ntd=on_2991 on theBenchmark for (2991ds/450Mi)
% 5.11/1.34 % (978094)Instruction limit reached!
% 5.11/1.34 % (978094)------------------------------
% 5.11/1.34 % (978094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978094)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978094)Termination reason: Instruction limit
% 5.11/1.34 % (978094)Termination phase: Saturation
% 5.11/1.34 % (978094)Time elapsed: 0.566 s
% 5.11/1.34 % (978094)Peak memory usage: 13 MB
% 5.11/1.34 % (978094)Instructions burned: 1240 (million)
% 5.11/1.34 % (978161)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=628718347:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2991 on theBenchmark for (2991ds/65Mi)
% 5.11/1.34 % (978158)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=960915502:s2a=on:i=571:nm=16:rtra=on_2991 on theBenchmark for (2991ds/571Mi)
% 5.11/1.34 % (978163)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=1349830091: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)
% 5.11/1.34 % (978160)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1933494192:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2991 on theBenchmark for (2991ds/95Mi)
% 5.11/1.34 % (978161)Instruction limit reached!
% 5.11/1.34 % (978161)------------------------------
% 5.11/1.34 % (978161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978161)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978161)Termination reason: Instruction limit
% 5.11/1.34 % (978161)Termination phase: Property scanning
% 5.11/1.34 % (978161)Time elapsed: 0.028 s
% 5.11/1.34 % (978161)Peak memory usage: 11 MB
% 5.11/1.34 % (978161)Instructions burned: 65 (million)
% 5.11/1.34 % (978168)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=398126360:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2990 on theBenchmark for (2990ds/5755Mi)
% 5.11/1.34 % (978163)Instruction limit reached!
% 5.11/1.34 % (978163)------------------------------
% 5.11/1.34 % (978163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978163)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978163)Termination reason: Instruction limit
% 5.11/1.34 % (978163)Termination phase: Saturation
% 5.11/1.34 % (978163)Time elapsed: 0.044 s
% 5.11/1.34 % (978163)Peak memory usage: 12 MB
% 5.11/1.34 % (978163)Instructions burned: 107 (million)
% 5.11/1.34 % (978170)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=251462166:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2990 on theBenchmark for (2990ds/375Mi)
% 5.11/1.34 % (978149) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-978028-978149"...
% 5.11/1.34 % (978160)Instruction limit reached!
% 5.11/1.34 % (978160)------------------------------
% 5.11/1.34 % (978160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.34 % (978160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.34 % (978160)CaDiCaL version: 2.1.3
% 5.11/1.34 % (978160)Termination reason: Instruction limit
% 5.11/1.34 % (978160)Termination phase: Property scanning
% 5.11/1.34 % (978160)Time elapsed: 0.087 s
% 5.11/1.34 % (978160)Peak memory usage: 13 MB
% 5.11/1.34 % (978160)Instructions burned: 97 (million)
% 5.11/1.34 % (978172)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4155643716:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2990 on theBenchmark for (2990ds/495Mi)
% 5.11/1.34 % (978149)...printing done.
% 5.11/1.34 % (978149)Refutation found. Thanks to Tanya!
% 5.11/1.34 % SZS status Theorem for theBenchmark
% 5.11/1.34 % SZS output start Proof for theBenchmark
% 5.11/1.34 thf(type_def_5, type, term: $tType).
% 5.11/1.34 thf(type_def_6, type, subst: $tType).
% 5.11/1.34 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 5.11/1.34 thf(type_def_8, type, d_term: $tType).
% 5.11/1.34 thf(type_def_9, type, d_subst: $tType).
% 5.11/1.34 thf(func_def_0, type, one: term).
% 5.11/1.34 thf(func_def_1, type, ap: (term > term > term)).
% 5.11/1.34 thf(func_def_2, type, lam: (term > term)).
% 5.11/1.34 thf(func_def_3, type, sub: (term > subst > term)).
% 5.11/1.34 thf(func_def_4, type, id: subst).
% 5.11/1.34 thf(func_def_5, type, sh: subst).
% 5.11/1.34 thf(func_def_6, type, push: (term > subst > subst)).
% 5.11/1.34 thf(func_def_7, type, comp: (subst > subst > subst)).
% 5.11/1.34 thf(func_def_8, type, var: (term > $o)).
% 5.11/1.34 thf(func_def_9, type, pushprop_lem1v2: $o).
% 5.11/1.34 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 5.11/1.34 thf(func_def_11, type, axmap: $o).
% 5.11/1.34 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 5.11/1.34 thf(func_def_13, type, shinj: $o).
% 5.11/1.34 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 5.11/1.34 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 5.11/1.34 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 5.11/1.34 thf(func_def_17, type, induction2lem: $o).
% 5.11/1.34 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 5.11/1.34 thf(func_def_19, type, axvarshift: $o).
% 5.11/1.34 thf(func_def_20, type, hoasapinj2: $o).
% 5.11/1.34 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 5.11/1.34 thf(func_def_22, type, hoasapinj1: $o).
% 5.11/1.34 thf(func_def_23, type, ulamvar1: $o).
% 5.11/1.34 thf(func_def_24, type, induction2lem_lthm: $o).
% 5.11/1.34 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 5.11/1.34 thf(func_def_26, type, apnotvar: $o).
% 5.11/1.34 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 5.11/1.34 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 5.11/1.34 thf(func_def_29, type, hoasinduction_lthm: $o).
% 5.11/1.34 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 5.11/1.34 thf(func_def_31, type, hoaslaminj: $o).
% 5.11/1.34 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 5.11/1.34 thf(func_def_33, type, induction2lem_gthm: $o).
% 5.11/1.34 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 5.11/1.34 thf(func_def_35, type, hoasinduction_lem3: $o).
% 5.11/1.34 thf(func_def_36, type, hoasinduction_lem2: $o).
% 5.11/1.34 thf(func_def_37, type, termmset_lthm: $o).
% 5.11/1.34 thf(func_def_38, type, hoasinduction_lem1: $o).
% 5.11/1.34 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 5.11/1.34 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 5.11/1.34 thf(func_def_41, type, hoasapnotvar: $o).
% 5.11/1.34 thf(func_def_42, type, hoasinduction_lem0: $o).
% 5.11/1.34 thf(func_def_43, type, hoasinduction: $o).
% 5.11/1.34 thf(func_def_44, type, hoasinduction_gthm: $o).
% 5.11/1.34 thf(func_def_45, type, axapp: $o).
% 5.11/1.34 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 5.11/1.34 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 5.11/1.34 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 5.11/1.34 thf(func_def_49, type, ulamvarind: $o).
% 5.11/1.34 thf(func_def_50, type, induction: $o).
% 5.11/1.34 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 5.11/1.34 thf(func_def_52, type, termmset_gthm: $o).
% 5.11/1.34 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 5.11/1.34 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 5.11/1.34 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 5.11/1.34 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 5.11/1.34 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 5.11/1.34 thf(func_def_58, type, pushprop_lem2v2: $o).
% 5.11/1.34 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 5.11/1.34 thf(func_def_60, type, axclos: $o).
% 5.11/1.34 thf(func_def_61, type, axassoc: $o).
% 5.11/1.34 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 5.11/1.34 thf(func_def_63, type, pushprop_lthm: $o).
% 5.11/1.34 thf(func_def_64, type, apinj2: $o).
% 5.11/1.34 thf(func_def_65, type, apinj1: $o).
% 5.11/1.34 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 5.11/1.34 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 5.11/1.34 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 5.11/1.34 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 5.11/1.34 thf(func_def_70, type, axvarcons: $o).
% 5.11/1.34 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 5.11/1.34 thf(func_def_72, type, axscons: $o).
% 5.11/1.34 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 5.11/1.34 thf(func_def_74, type, axidr: $o).
% 5.11/1.34 thf(func_def_75, type, pushprop_lem1: $o).
% 5.11/1.34 thf(func_def_76, type, laminj: $o).
% 5.11/1.34 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 5.11/1.34 thf(func_def_78, type, pushprop_lem0: $o).
% 5.11/1.34 thf(func_def_79, type, pushprop_gthm: $o).
% 5.11/1.34 thf(func_def_80, type, axabs: $o).
% 5.11/1.34 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 5.11/1.34 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 5.11/1.34 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 5.11/1.34 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 5.11/1.34 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 5.11/1.34 thf(func_def_86, type, lamnotap: $o).
% 5.11/1.34 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 5.11/1.34 thf(func_def_88, type, hoaslamnotvar: $o).
% 5.11/1.34 thf(func_def_89, type, axidl: $o).
% 5.11/1.34 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 5.11/1.34 thf(func_def_91, type, induction2_lthm: $o).
% 5.11/1.34 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 5.11/1.34 thf(func_def_93, type, substmonoid_lthm: $o).
% 5.11/1.34 thf(func_def_94, type, pushprop: $o).
% 5.11/1.34 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 5.11/1.34 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 5.11/1.34 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 5.11/1.34 thf(func_def_98, type, substmonoid: $o).
% 5.11/1.34 thf(func_def_99, type, lamnotvar: $o).
% 5.11/1.34 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 5.11/1.34 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 5.11/1.34 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 5.11/1.34 thf(func_def_103, type, induction2_gthm: $o).
% 5.11/1.34 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 5.11/1.34 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_106, type, hoaslamnotap: $o).
% 5.11/1.34 thf(func_def_107, type, substmonoid_gthm: $o).
% 5.11/1.34 thf(func_def_108, type, ulamvarsh: $o).
% 5.11/1.34 thf(func_def_109, type, induction2: $o).
% 5.11/1.34 thf(func_def_110, type, pushprop_lem3v2: $o).
% 5.11/1.34 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 5.11/1.34 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 5.11/1.34 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 5.11/1.34 thf(func_def_114, type, axshiftcons: $o).
% 5.11/1.34 thf(func_def_115, type, termmset: $o).
% 5.11/1.34 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 5.11/1.34 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 5.11/1.34 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 5.11/1.34 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 5.11/1.34 thf(func_def_120, type, axvarid: $o).
% 5.11/1.34 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 5.11/1.34 thf(func_def_122, type, d2term: (d_term > term)).
% 5.11/1.34 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 5.11/1.34 thf(func_def_124, type, d_one: d_term).
% 5.11/1.34 thf(func_def_125, type, d_id: d_subst).
% 5.11/1.34 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.11/1.34 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 5.11/1.34 thf(func_def_129, type, db2: !>[X0: $tType]:(X0)).
% 5.11/1.34 thf(func_def_130, type, db0: !>[X0: $tType]:(X0)).
% 5.11/1.34 thf(func_def_131, type, db3: !>[X0: $tType]:(X0)).
% 5.11/1.34 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 5.11/1.34 thf(func_def_133, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.11/1.34 thf(func_def_136, type, db4: !>[X0: $tType]:(X0)).
% 5.11/1.34 thf(func_def_137, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.11/1.34 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_139, type, sP1: $o).
% 5.11/1.34 thf(func_def_140, type, sP2: $o).
% 5.11/1.34 thf(func_def_141, type, sP3: $o).
% 5.11/1.34 thf(func_def_142, type, sP4: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_144, type, sP6: $o).
% 5.11/1.34 thf(func_def_145, type, sP7: $o).
% 5.11/1.34 thf(func_def_146, type, sP8: $o).
% 5.11/1.34 thf(func_def_147, type, sP9: $o).
% 5.11/1.34 thf(func_def_148, type, sP10: $o).
% 5.11/1.34 thf(func_def_149, type, sP11: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_150, type, sP12: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_151, type, sP13: $o).
% 5.11/1.34 thf(func_def_152, type, sP14: $o).
% 5.11/1.34 thf(func_def_153, type, sP15: $o).
% 5.11/1.34 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_155, type, sP17: $o).
% 5.11/1.34 thf(func_def_156, type, sP18: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_157, type, sP19: $o).
% 5.11/1.34 thf(func_def_158, type, sP20: $o).
% 5.11/1.34 thf(func_def_159, type, sP21: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_160, type, sP22: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_161, type, sP23: $o).
% 5.11/1.34 thf(func_def_162, type, sP24: $o).
% 5.11/1.34 thf(func_def_163, type, sP25: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_164, type, sP26: $o).
% 5.11/1.34 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_166, type, sP28: $o).
% 5.11/1.34 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_168, type, sP30: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_169, type, sP31: $o).
% 5.11/1.34 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_171, type, sP33: $o).
% 5.11/1.34 thf(func_def_172, type, sP34: $o).
% 5.11/1.34 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_174, type, sP36: $o).
% 5.11/1.34 thf(func_def_175, type, sP37: $o).
% 5.11/1.34 thf(func_def_176, type, sP38: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_177, type, sP39: $o).
% 5.11/1.34 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_180, type, sP42: $o).
% 5.11/1.34 thf(func_def_181, type, sP43: $o).
% 5.11/1.34 thf(func_def_182, type, sP44: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_184, type, sP46: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_185, type, sP47: $o).
% 5.11/1.34 thf(func_def_186, type, sP48: $o).
% 5.11/1.34 thf(func_def_187, type, sP49: $o).
% 5.11/1.34 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_189, type, sP51: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_190, type, sP52: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 5.11/1.34 thf(func_def_192, type, sP54: ((term > $o) > $o)).
% 5.11/1.34 thf(func_def_193, type, sP55: $o).
% 5.11/1.34 thf(func_def_194, type, sP56: $o).
% 5.11/1.34 thf(func_def_195, type, sP57: $o).
% 5.11/1.34 thf(func_def_196, type, sP58: $o).
% 5.11/1.34 thf(func_def_197, type, sK59: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_198, type, sK60: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_199, type, sK61: (term > $o)).
% 5.11/1.34 thf(func_def_200, type, sK62: term).
% 5.11/1.34 thf(func_def_201, type, sK63: (term > term)).
% 5.11/1.34 thf(func_def_202, type, sK64: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_203, type, sK65: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_206, type, sK68: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_208, type, sK70: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_209, type, sK71: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_210, type, sK72: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_211, type, sK73: term).
% 5.11/1.34 thf(func_def_212, type, sK74: term).
% 5.11/1.34 thf(func_def_213, type, sK75: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_214, type, sK76: term).
% 5.11/1.34 thf(func_def_215, type, sK77: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_216, type, sK78: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_217, type, sK79: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_218, type, sK80: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_219, type, sK81: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_220, type, sK82: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_222, type, sK84: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_223, type, sK85: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_225, type, sK87: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_226, type, sK88: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_227, type, sK89: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_228, type, sK90: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_229, type, sK91: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_230, type, sK92: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_231, type, sK93: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_232, type, sK94: ((subst > term > subst > $o) > term > term)).
% 5.11/1.34 thf(func_def_233, type, sK95: term).
% 5.11/1.34 thf(func_def_234, type, sK96: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_235, type, sK97: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_236, type, sK98: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_237, type, sK99: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_238, type, sK100: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_239, type, sK101: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_240, type, sK102: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_241, type, sK103: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_242, type, sK104: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_243, type, sK105: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_244, type, sK106: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_245, type, sK107: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_246, type, sK108: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_247, type, sK109: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_248, type, sK110: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_249, type, sK111: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_250, type, sK112: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_251, type, sK113: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_252, type, sK114: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_253, type, sK115: ((subst > term > subst > $o) > term > $o)).
% 5.11/1.34 thf(func_def_254, type, sK116: term).
% 5.11/1.34 thf(func_def_255, type, sK117: (term > $o)).
% 5.11/1.34 thf(func_def_256, type, sK118: (term > term)).
% 5.11/1.34 thf(func_def_257, type, sK119: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_258, type, sK120: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_259, type, sK121: term).
% 5.11/1.34 thf(func_def_260, type, sK122: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_261, type, sK123: term).
% 5.11/1.34 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_270, type, sK132: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_272, type, sK134: (term > (term > $o) > term)).
% 5.11/1.34 thf(func_def_273, type, sK135: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_274, type, sK136: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_275, type, sK137: (term > $o)).
% 5.11/1.34 thf(func_def_276, type, sK138: term).
% 5.11/1.34 thf(func_def_277, type, sK139: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_278, type, sK140: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_279, type, sK141: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_280, type, sK142: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_281, type, sK143: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_282, type, sK144: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_283, type, sK145: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_284, type, sK146: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_285, type, sK147: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_286, type, sK148: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_288, type, sK150: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_289, type, sK151: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_290, type, sK152: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_291, type, sK153: (term > $o)).
% 5.11/1.34 thf(func_def_292, type, sK154: term).
% 5.11/1.34 thf(func_def_293, type, sK155: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_294, type, sK156: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_295, type, sK157: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_296, type, sK158: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_297, type, sK159: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_298, type, sK160: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_299, type, sK161: (term > (term > $o) > term)).
% 5.11/1.34 thf(func_def_300, type, sK162: term).
% 5.11/1.34 thf(func_def_301, type, sK163: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_302, type, sK164: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_303, type, sK165: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_305, type, sK167: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_306, type, sK168: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_307, type, sK169: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_309, type, sK171: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_313, type, sK175: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_314, type, sK176: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_315, type, sK177: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_316, type, sK178: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_318, type, sK180: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_319, type, sK181: term).
% 5.11/1.34 thf(func_def_320, type, sK182: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_322, type, sK184: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_323, type, sK185: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_324, type, sK186: (term > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_325, type, sK187: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_327, type, sK189: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_329, type, sK191: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_330, type, sK192: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_331, type, sK193: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_332, type, sK194: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_333, type, sK195: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_334, type, sK196: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_335, type, sK197: term).
% 5.11/1.34 thf(func_def_336, type, sK198: term).
% 5.11/1.34 thf(func_def_337, type, sK199: (term > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_342, type, sK204: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_343, type, sK205: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > term > term)).
% 5.11/1.34 thf(func_def_348, type, sK210: term).
% 5.11/1.34 thf(func_def_349, type, sK211: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_350, type, sK212: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_351, type, sK213: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_352, type, sK214: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_353, type, sK215: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_354, type, sK216: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_355, type, sK217: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_356, type, sK218: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_357, type, sK219: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_358, type, sK220: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_359, type, sK221: term).
% 5.11/1.34 thf(func_def_360, type, sK222: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_361, type, sK223: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_362, type, sK224: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_363, type, sK225: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_364, type, sK226: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_365, type, sK227: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > term > term)).
% 5.11/1.34 thf(func_def_367, type, sK229: term).
% 5.11/1.34 thf(func_def_368, type, sK230: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_369, type, sK231: (term > $o)).
% 5.11/1.34 thf(func_def_370, type, sK232: term).
% 5.11/1.34 thf(func_def_371, type, sK233: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_375, type, sK237: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_376, type, sK238: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_380, type, sK242: ((term > $o) > term > term)).
% 5.11/1.34 thf(func_def_381, type, sK243: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_382, type, sK244: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_383, type, sK245: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_384, type, sK246: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_386, type, sK248: subst).
% 5.11/1.34 thf(func_def_387, type, sK249: (subst > term > term)).
% 5.11/1.34 thf(func_def_388, type, sK250: term).
% 5.11/1.34 thf(func_def_389, type, sK251: (subst > term > term)).
% 5.11/1.34 thf(func_def_390, type, sK252: term).
% 5.11/1.34 thf(func_def_391, type, sK253: subst).
% 5.11/1.34 thf(func_def_392, type, sK254: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_393, type, sK255: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_394, type, sK256: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_395, type, sK257: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_396, type, sK258: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_397, type, sK259: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_398, type, sK260: term).
% 5.11/1.34 thf(func_def_399, type, sK261: term).
% 5.11/1.34 thf(func_def_400, type, sK262: subst).
% 5.11/1.34 thf(func_def_401, type, sK263: term).
% 5.11/1.34 thf(func_def_402, type, sK264: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_403, type, sK265: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_404, type, sK266: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_405, type, sK267: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_406, type, sK268: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_407, type, sK269: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_409, type, sK271: term).
% 5.11/1.34 thf(func_def_410, type, sK272: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_411, type, sK273: term).
% 5.11/1.34 thf(func_def_412, type, sK274: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_413, type, sK275: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_414, type, sK276: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_415, type, sK277: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_417, type, sK279: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_418, type, sK280: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_419, type, sK281: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_422, type, sK284: subst).
% 5.11/1.34 thf(func_def_423, type, sK285: term).
% 5.11/1.34 thf(func_def_424, type, sK286: (term > $o)).
% 5.11/1.34 thf(func_def_425, type, sK287: (term > term)).
% 5.11/1.34 thf(func_def_426, type, sK288: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_427, type, sK289: ((term > $o) > subst > term)).
% 5.11/1.34 thf(func_def_428, type, sK290: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_429, type, sK291: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_430, type, sK292: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_431, type, sK293: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_432, type, sK294: subst).
% 5.11/1.34 thf(func_def_433, type, sK295: subst).
% 5.11/1.34 thf(func_def_434, type, sK296: term).
% 5.11/1.34 thf(func_def_435, type, sK297: subst).
% 5.11/1.34 thf(func_def_436, type, sK298: term).
% 5.11/1.34 thf(func_def_437, type, sK299: (term > $o)).
% 5.11/1.34 thf(func_def_438, type, sK300: term).
% 5.11/1.34 thf(func_def_439, type, sK301: (term > $o)).
% 5.11/1.34 thf(func_def_440, type, sK302: subst).
% 5.11/1.34 thf(func_def_441, type, sK303: term).
% 5.11/1.34 thf(func_def_442, type, sK304: (term > term)).
% 5.11/1.34 thf(func_def_443, type, sK305: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_444, type, sK306: (subst > (term > $o) > term)).
% 5.11/1.34 thf(func_def_445, type, sK307: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_446, type, sK308: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_447, type, sK309: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_448, type, sK310: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_449, type, sK311: (term > subst > term > term)).
% 5.11/1.34 thf(func_def_450, type, sK312: (term > $o)).
% 5.11/1.34 thf(func_def_451, type, sK313: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_452, type, sK314: term).
% 5.11/1.34 thf(func_def_453, type, sK315: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_454, type, sK316: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_455, type, sK317: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_456, type, sK318: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_457, type, sK319: term).
% 5.11/1.34 thf(func_def_458, type, sK320: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_459, type, sK321: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.11/1.34 thf(func_def_461, type, sK323: (term > (term > $o) > term)).
% 5.11/1.34 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_463, type, sK325: term).
% 5.11/1.34 thf(func_def_464, type, sK326: (term > $o)).
% 5.11/1.34 thf(func_def_465, type, sK327: term).
% 5.11/1.34 thf(func_def_466, type, sK328: (term > term)).
% 5.11/1.34 thf(func_def_467, type, sK329: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_468, type, sK330: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_469, type, sK331: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_470, type, sK332: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_471, type, sK333: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_472, type, sK334: term).
% 5.11/1.34 thf(func_def_473, type, sK335: (term > $o)).
% 5.11/1.34 thf(func_def_474, type, sK336: ((term > $o) > term > term)).
% 5.11/1.34 thf(func_def_475, type, sK337: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_477, type, sK339: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_478, type, sK340: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_479, type, sK341: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_480, type, sK342: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_481, type, sK343: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_482, type, sK344: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_483, type, sK345: ((subst > term > subst > $o) > subst)).
% 5.11/1.34 thf(func_def_484, type, sK346: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_485, type, sK347: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_486, type, sK348: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_487, type, sK349: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_489, type, sK351: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_490, type, sK352: term).
% 5.11/1.34 thf(func_def_491, type, sK353: ((subst > term > subst > $o) > term > $o)).
% 5.11/1.34 thf(func_def_492, type, sK354: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_493, type, sK355: ((subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_494, type, sK356: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_495, type, sK357: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_496, type, sK358: term).
% 5.11/1.34 thf(func_def_497, type, sK359: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_498, type, sK360: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_499, type, sK361: term).
% 5.11/1.34 thf(func_def_500, type, sK362: (term > $o)).
% 5.11/1.34 thf(func_def_501, type, sK363: (term > term)).
% 5.11/1.34 thf(func_def_502, type, sK364: ((term > $o) > term > term)).
% 5.11/1.34 thf(func_def_503, type, sK365: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_505, type, sK367: term).
% 5.11/1.34 thf(func_def_506, type, sK368: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_507, type, sK369: (term > $o)).
% 5.11/1.34 thf(func_def_508, type, sK370: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_509, type, sK371: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_510, type, sK372: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_511, type, sK373: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_512, type, sK374: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_513, type, sK375: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_514, type, sK376: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_515, type, sK377: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_517, type, sK379: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_518, type, sK380: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_519, type, sK381: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_520, type, sK382: term).
% 5.11/1.34 thf(func_def_521, type, sK383: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_522, type, sK384: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_523, type, sK385: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_524, type, sK386: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_526, type, sK388: (term > (subst > term > subst > $o) > term)).
% 5.11/1.34 thf(func_def_527, type, sK389: term).
% 5.11/1.34 thf(func_def_528, type, sK390: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_529, type, sK391: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_530, type, sK392: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_531, type, sK393: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_532, type, sK394: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > term > term)).
% 5.11/1.34 thf(func_def_534, type, sK396: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_535, type, sK397: term).
% 5.11/1.34 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > term > term)).
% 5.11/1.34 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.34 thf(func_def_538, type, sK400: term).
% 5.11/1.34 thf(func_def_539, type, sK401: (subst > term > subst > $o)).
% 5.11/1.34 thf(func_def_540, type, sK402: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_541, type, sK403: ((subst > term > term) > term)).
% 5.11/1.34 thf(func_def_542, type, sK404: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_543, type, sK405: ((subst > term > term) > subst)).
% 5.11/1.34 thf(func_def_544, type, sK406: ((term > $o) > term)).
% 5.11/1.34 thf(func_def_545, type, sK407: ((term > $o) > subst > term)).
% 5.11/1.34 thf(func_def_546, type, sK408: subst).
% 5.11/1.34 thf(func_def_547, type, sK409: (term > $o)).
% 5.11/1.34 thf(func_def_548, type, sK410: term).
% 5.11/1.34 thf(func_def_549, type, sK411: (term > term)).
% 5.11/1.34 thf(func_def_550, type, sK412: term).
% 5.11/1.34 thf(func_def_551, type, sK413: (term > $o)).
% 5.11/1.34 thf(func_def_552, type, sK414: term).
% 5.11/1.34 thf(func_def_553, type, sK415: (term > term)).
% 5.11/1.35 thf(func_def_554, type, sK416: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_555, type, sK417: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_556, type, sK418: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_557, type, sK419: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_558, type, sK420: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_559, type, sK421: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_560, type, sK422: term).
% 5.11/1.35 thf(func_def_561, type, sK423: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_562, type, sK424: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_563, type, sK425: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_565, type, sK427: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > term > term)).
% 5.11/1.35 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.35 thf(func_def_568, type, sK430: term).
% 5.11/1.35 thf(func_def_569, type, sK431: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_570, type, sK432: (term > (subst > term > term) > term)).
% 5.11/1.35 thf(func_def_571, type, sK433: (term > (subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_572, type, sK434: (term > (subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_573, type, sK435: (term > (subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_574, type, sK436: (term > (subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_575, type, sK437: (term > (subst > term > term) > term)).
% 5.11/1.35 thf(func_def_576, type, sK438: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_577, type, sK439: ((subst > term > subst > $o) > subst > term > term)).
% 5.11/1.35 thf(func_def_578, type, sK440: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > term > term)).
% 5.11/1.35 thf(func_def_580, type, sK442: (term > $o)).
% 5.11/1.35 thf(func_def_581, type, sK443: term).
% 5.11/1.35 thf(func_def_582, type, sK444: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_583, type, sK445: term).
% 5.11/1.35 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.11/1.35 thf(func_def_585, type, sK447: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_588, type, sK450: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_589, type, sK451: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_590, type, sK452: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_591, type, sK453: ((subst > term > subst > $o) > subst)).
% 5.11/1.35 thf(func_def_592, type, sK454: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_593, type, sK455: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_595, type, sK457: subst).
% 5.11/1.35 thf(func_def_596, type, sK458: subst).
% 5.11/1.35 thf(func_def_597, type, sK459: ((term > $o) > subst > term > term > $o)).
% 5.11/1.35 thf(func_def_598, type, sK460: term).
% 5.11/1.35 thf(func_def_599, type, sK461: subst).
% 5.11/1.35 thf(func_def_600, type, sK462: (term > $o)).
% 5.11/1.35 thf(func_def_601, type, sK463: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_602, type, sK464: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_603, type, sK465: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_604, type, sK466: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_605, type, sK467: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_606, type, sK468: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_607, type, sK469: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_608, type, sK470: (subst > term > term)).
% 5.11/1.35 thf(func_def_609, type, sK471: term).
% 5.11/1.35 thf(func_def_610, type, sK472: subst).
% 5.11/1.35 thf(func_def_611, type, sK473: (subst > term > term)).
% 5.11/1.35 thf(func_def_612, type, sK474: (term > d_term)).
% 5.11/1.35 thf(func_def_613, type, sK475: term).
% 5.11/1.35 thf(func_def_614, type, sK476: term).
% 5.11/1.35 thf(func_def_615, type, sK477: term).
% 5.11/1.35 thf(func_def_616, type, sK478: term).
% 5.11/1.35 thf(func_def_617, type, sK479: term).
% 5.11/1.35 thf(func_def_618, type, sK480: (subst > (term > $o) > term > (term > $o) > term)).
% 5.11/1.35 thf(func_def_619, type, sK481: (term > $o)).
% 5.11/1.35 thf(func_def_620, type, sK482: term).
% 5.11/1.35 thf(func_def_621, type, sK483: (term > $o)).
% 5.11/1.35 thf(func_def_622, type, sK484: subst).
% 5.11/1.35 thf(func_def_623, type, sK485: subst).
% 5.11/1.35 thf(func_def_624, type, sK486: term).
% 5.11/1.35 thf(func_def_625, type, sK487: term).
% 5.11/1.35 thf(func_def_626, type, sK488: subst).
% 5.11/1.35 thf(func_def_627, type, sK489: term).
% 5.11/1.35 thf(func_def_628, type, sK490: (term > $o)).
% 5.11/1.35 thf(func_def_629, type, sK491: term).
% 5.11/1.35 thf(func_def_630, type, sK492: subst).
% 5.11/1.35 thf(func_def_631, type, sK493: (term > $o)).
% 5.11/1.35 thf(func_def_632, type, sK494: term).
% 5.11/1.35 thf(func_def_633, type, sK495: term).
% 5.11/1.35 thf(func_def_634, type, sK496: term).
% 5.11/1.35 thf(func_def_635, type, sK497: term).
% 5.11/1.35 thf(func_def_636, type, sK498: ((subst > term > subst > $o) > term > $o)).
% 5.11/1.35 thf(func_def_637, type, sK499: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_638, type, sK500: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_639, type, sK501: term).
% 5.11/1.35 thf(func_def_640, type, sK502: subst).
% 5.11/1.35 thf(func_def_641, type, sK503: term).
% 5.11/1.35 thf(func_def_642, type, sK504: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_643, type, sK505: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_644, type, sK506: (term > subst > term > term)).
% 5.11/1.35 thf(func_def_645, type, sK507: term).
% 5.11/1.35 thf(func_def_646, type, sK508: subst).
% 5.11/1.35 thf(func_def_647, type, sK509: (term > $o)).
% 5.11/1.35 thf(func_def_648, type, sK510: (term > $o)).
% 5.11/1.35 thf(func_def_649, type, sK511: term).
% 5.11/1.35 thf(func_def_650, type, sK512: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_651, type, sK513: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_652, type, sK514: (term > $o)).
% 5.11/1.35 thf(func_def_653, type, sK515: term).
% 5.11/1.35 thf(func_def_654, type, sK516: term).
% 5.11/1.35 thf(func_def_655, type, sK517: term).
% 5.11/1.35 thf(func_def_656, type, sK518: term).
% 5.11/1.35 thf(func_def_657, type, sK519: term).
% 5.11/1.35 thf(func_def_658, type, sK520: term).
% 5.11/1.35 thf(func_def_659, type, sK521: term).
% 5.11/1.35 thf(func_def_660, type, sK522: term).
% 5.11/1.35 thf(func_def_661, type, sK523: term).
% 5.11/1.35 thf(func_def_662, type, sK524: term).
% 5.11/1.35 thf(func_def_663, type, sK525: term).
% 5.11/1.35 thf(func_def_664, type, sK526: subst).
% 5.11/1.35 thf(func_def_665, type, sK527: subst).
% 5.11/1.35 thf(func_def_666, type, sK528: subst).
% 5.11/1.35 thf(func_def_667, type, sK529: subst).
% 5.11/1.35 thf(func_def_668, type, sK530: subst).
% 5.11/1.35 thf(func_def_669, type, sK531: (subst > d_subst)).
% 5.11/1.35 thf(func_def_670, type, sK532: term).
% 5.11/1.35 thf(func_def_671, type, sK533: term).
% 5.11/1.35 thf(func_def_672, type, sK534: (term > subst > term > term)).
% 5.11/1.35 thf(func_def_673, type, sK535: term).
% 5.11/1.35 thf(func_def_674, type, sK536: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_675, type, sK537: ((subst > term > subst > $o) > term)).
% 5.11/1.35 thf(func_def_676, type, sK538: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_677, type, sK539: term).
% 5.11/1.35 thf(func_def_678, type, sK540: term).
% 5.11/1.35 thf(func_def_679, type, sK541: subst).
% 5.11/1.35 thf(func_def_680, type, sK542: term).
% 5.11/1.35 thf(func_def_681, type, sK543: term).
% 5.11/1.35 thf(func_def_682, type, sK544: term).
% 5.11/1.35 thf(func_def_683, type, sK545: subst).
% 5.11/1.35 thf(func_def_684, type, sK546: ((term > $o) > (term > $o) > term > subst > term)).
% 5.11/1.35 thf(func_def_685, type, sK547: subst).
% 5.11/1.35 thf(func_def_686, type, sK548: term).
% 5.11/1.35 thf(func_def_687, type, sK549: (term > $o)).
% 5.11/1.35 thf(func_def_688, type, sK550: (term > $o)).
% 5.11/1.35 thf(func_def_689, type, sK551: ((subst > term > subst > $o) > term > $o)).
% 5.11/1.35 thf(func_def_690, type, sK552: (subst > term > subst > $o)).
% 5.11/1.35 thf(func_def_691, type, sK553: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_692, type, sK554: (term > subst > term > term)).
% 5.11/1.35 thf(func_def_693, type, sK555: term).
% 5.11/1.35 thf(func_def_694, type, sK556: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_695, type, sK557: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_696, type, sK558: term).
% 5.11/1.35 thf(func_def_697, type, sK559: term).
% 5.11/1.35 thf(func_def_698, type, sK560: term).
% 5.11/1.35 thf(func_def_699, type, sK561: term).
% 5.11/1.35 thf(func_def_700, type, sK562: term).
% 5.11/1.35 thf(func_def_701, type, sK563: term).
% 5.11/1.35 thf(func_def_702, type, sK564: term).
% 5.11/1.35 thf(func_def_703, type, sK565: term).
% 5.11/1.35 thf(func_def_704, type, sK566: term).
% 5.11/1.35 thf(func_def_705, type, sK567: term).
% 5.11/1.35 thf(func_def_706, type, sK568: term).
% 5.11/1.35 thf(func_def_707, type, sK569: term).
% 5.11/1.35 thf(func_def_708, type, sK570: subst).
% 5.11/1.35 thf(func_def_709, type, sK571: term).
% 5.11/1.35 thf(func_def_710, type, sK572: (term > subst > term > term)).
% 5.11/1.35 thf(func_def_711, type, sK573: term).
% 5.11/1.35 thf(func_def_712, type, sK574: term).
% 5.11/1.35 thf(func_def_713, type, sK575: term).
% 5.11/1.35 thf(func_def_714, type, sK576: term).
% 5.11/1.35 thf(func_def_715, type, sK577: term).
% 5.11/1.35 thf(func_def_716, type, sK578: term).
% 5.11/1.35 thf(func_def_717, type, sK579: (subst > term > term)).
% 5.11/1.35 thf(func_def_718, type, sK580: ((subst > term > term) > term)).
% 5.11/1.35 thf(func_def_719, type, sK581: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_720, type, sK582: ((subst > term > term) > subst)).
% 5.11/1.35 thf(func_def_721, type, sK583: (term > (term > $o) > subst > term > $o)).
% 5.11/1.35 thf(func_def_722, type, sK584: subst).
% 5.11/1.35 thf(func_def_723, type, sK585: (term > $o)).
% 5.11/1.35 thf(func_def_724, type, sK586: term).
% 5.11/1.35 thf(func_def_725, type, sK587: ((term > $o) > term)).
% 5.11/1.35 thf(func_def_726, type, sK588: subst).
% 5.11/1.35 thf(func_def_727, type, sK589: term).
% 5.11/1.35 thf(func_def_728, type, sK590: term).
% 5.11/1.35 thf(func_def_729, type, vNOT: ($o > $o)).
% 5.11/1.35 thf(func_def_730, type, sK591: subst).
% 5.11/1.35 thf(func_def_731, type, sK592: (term > $o)).
% 5.11/1.35 thf(func_def_732, type, sK593: (term > $o)).
% 5.11/1.35 thf(func_def_733, type, sK594: term).
% 5.11/1.35 thf(func_def_734, type, sK595: ((term > $o) > subst > term > (term > $o) > term)).
% 5.11/1.35 thf(f1,axiom,(
% 5.11/1.35 axclos & lamnotvar & pushprop_lem2v2_gthm & (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) <=> induction) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X11 : (term > $o),X14 : subst,X10 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13))) <=> pushprop_lem1v2_lthm) & (hoasapinj1 <=> ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & hoaslamnotap_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem0 <=> ! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & induction2lem_gthm & hoasapnotvar & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & hoaslaminj_gthm & (! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))) <=> induction2lem) & hoasinduction_lem3_gthm & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & ((! [X13 : term,X20 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj2_lthm) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) & pushprop_lem1_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & substmonoid_gthm & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & axabs & pushprop_gthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => ! [X22 : term,X10 : (term > $o)] : ((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) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & ulamvarsh & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & hoasinduction_lem1 & hoasinduction_lem2_lthm & pushprop_lem2v2 & ((! [X14 : subst,X13 : term] : (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)) => ! [X32 : subst,X31 : (subst > term > term),X18 : (subst > term > term),X33 : term] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & hoaslamnotap_gthm & (! [X13 : term,X10 : (term > $o),X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & (axvarcons <=> ! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & hoasapnotvar_gthm & (sh = ((d2subst @ d_id))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (hoasinduction_lem3v2 <=> ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [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,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X48)))) & pushprop_lem3v2_lthm & (! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ 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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & hoasinduction_lem3v2_gthm & pushprop_lem3v2 & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (! [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 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) <=> induction2) & (! [X11 : (term > $o),X44 : term,X45 : term,X10 : (subst > term > subst > $o)] : (~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~(X11 @ X44) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem2v2) & axassoc & (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 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21)) => ! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))))))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & hoasinduction_lem3a_gthm & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & pushprop_lthm & (apinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (laminj <=> ! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasapinj2_gthm & (! [X14 : subst,X26 : (term > $o),X10 : (term > $o),X15 : term,X13 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & hoasinduction_lem3b_gthm & hoaslamnotvar_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X15 : term,X13 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)))) <=> hoasapinj1_lthm) & pushprop_lem2v2_lthm & induction2_gthm & hoasinduction_lem2_gthm & pushprop_lthm_orig & hoaslamnotvar & (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa) & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)))) <=> hoasinduction_lem3v2_lthm) & termmset_gthm & (hoasinduction_lthm <=> (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) => (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))))))) & (hoaslaminj <=> ! [X32 : subst,X31 : (subst > term > term),X18 : (subst > term > term),X33 : term] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & (! [X13 : term,X15 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X10 : (subst > term > subst > $o),X34 : term] : (~ ! [X18 : (subst > term > term),X35 : term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X38 : subst,X36 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))))) & ~ulamvar1 & apnotvar & axapp & ulamvarind & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & (! [X46 : term,X18 : (subst > term > term),X47 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslamnotap) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & ~(var @ (d2term @ d_one)) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & ! [X1 : d_term] : (X1 = d_one) & (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id)) <=> hoasinduction_lem2) & hoasinduction_lem1_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aa_lthm) & pushprop & axmap & hoasinduction_lem1v2 & hoasapinj1_gthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & hoasinduction_lem1_lthm & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X13 : term,X10 : (term > $o),X14 : subst,X15 : term,X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3 <=> ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id))) & ((! [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 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasapinj2 <=> ! [X20 : term,X13 : term,X15 : term,X19 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem3v2a) & hoasapnotvar_lthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ~lamnotap & ((^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) = pushprop_p_and_p_prime) & (apinj2 <=> ! [X13 : term,X15 : term,X20 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & axvarshift & (pushprop_lem1v2 <=> ! [X11 : (term > $o),X14 : subst,X10 : (term > $o),X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & (! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((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)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id))) <=> hoasinduction) & (id = ((d2subst @ d_id))) & ! [X5 : d_subst] : (X5 = d_id) & hoasinduction_lem1v2_gthm & (hoasinduction_lthm_3 <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & hoasinduction_gthm & pushprop_lem0_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & (one = ((d2term @ d_one))) & hoasinduction_lem2v2_gthm & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))),
% 5.11/1.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 5.11/1.35 thf(f2,conjecture,(
% 5.11/1.35 (! [X2 : term,X1 : (term > $o),X0 : (term > $o),X3 : subst] : ((X0 @ X2) => ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (X1 @ one))) = pushprop_lem1v2)),
% 5.11/1.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2)).
% 5.11/1.35 thf(f3,negated_conjecture,(
% 5.11/1.35 ~ (! [X2 : term,X1 : (term > $o),X0 : (term > $o),X3 : subst] : ((X0 @ X2) => ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (X1 @ one))) = pushprop_lem1v2)),
% 5.11/1.35 inference(negated_conjecture,[status(cth)],[f2])).
% 5.11/1.35 thf(f4,plain,(
% 5.11/1.35 ~ (! [X0 : term,X1 : (term > $o),X2 : (term > $o),X3 : subst] : ((X2 @ X0) => ((pushprop_p_and_p_prime @ X0 @ X3 @ X2 @ X1) => (X1 @ one))) = pushprop_lem1v2)),
% 5.11/1.35 inference(rectify,[],[f3])).
% 5.11/1.35 thf(f5,plain,(
% 5.11/1.35 ~ (pushprop_lem1v2 = ((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => ((pushprop_p_and_p_prime @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))))))),
% 5.11/1.35 inference(fool_elimination,[],[f4])).
% 5.11/1.35 thf(f6,plain,(
% 5.11/1.35 axclos & lamnotvar & pushprop_lem2v2_gthm & (! [X0 : term,X1 : (term > $o)] : ((X1 @ X0) | ~ ! [X2 : term,X3 : term] : ((X1 @ (ap @ X3 @ X2)) | ~(X1 @ X3) | ~(X1 @ X2)) | ~ ! [X4 : term] : ((X1 @ X4) | ~(var @ X4)) | ~ ! [X5 : term] : ((X1 @ (lam @ X5)) | ~(X1 @ X5))) <=> induction) & ((! [X6 : subst,X7 : term] : (((sub @ one @ (push @ X7 @ X6))) = X7) => ! [X8 : term,X9 : (term > $o),X10 : subst,X11 : (term > $o)] : ((X9 @ one) | ~ ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))) | ~(X11 @ X8))) <=> pushprop_lem1v2_lthm) & (hoasapinj1 <=> ! [X13 : term,X14 : term,X15 : term,X16 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & hoaslamnotap_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem0 <=> ! [X17 : term,X18 : subst,X19 : (term > $o)] : ~ ! [X20 : (term > $o)] : ~ ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21)))) & induction2lem_gthm & hoasapnotvar & (hoasinduction_lem3v2_f_lthm <=> ! [X22 : term] : ~ ! [X23 : (subst > term > term)] : ~ ! [X24 : subst,X25 : term] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25)))) & hoaslaminj_gthm & (! [X26 : subst,X27 : (term > $o),X28 : term] : (~ ! [X29 : term,X30 : term] : (~(X27 @ X29) | (X27 @ (ap @ X30 @ X29)) | ~(X27 @ X30)) | ~ ! [X31 : term] : ((X27 @ (lam @ X31)) | ~ ! [X32 : term] : ((X27 @ (sub @ X31 @ (push @ X32 @ id))) | ~(X27 @ X32))) | ~ ! [X33 : term] : ((X27 @ (sub @ X33 @ X26)) | ~(var @ X33)) | (X27 @ (sub @ X28 @ X26))) <=> induction2lem) & hoasinduction_lem3_gthm & (hoasinduction_lem3b_lthm <=> ! [X34 : term] : ~ ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one)))) & (substmonoid <=> (! [X36 : subst] : (((comp @ X36 @ id)) = X36) & ! [X37 : subst] : (((comp @ id @ X37)) = X37))) & ((! [X38 : term,X39 : term,X40 : term,X41 : term] : ((((ap @ X38 @ X41)) != ((ap @ X40 @ X39))) | (X39 = X41)) => ! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X43 = X44) | (((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))))) <=> hoasapinj2_lthm) & (hoasinduction_lem3_lthm <=> (! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X47 : (subst > term > subst > $o),X48 : term] : (~ ! [X49 : (subst > term > term)] : (~ ! [X50 : term,X51 : subst,X52 : subst] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) = ((sub @ (X49 @ X52 @ X50) @ X51))) | (X47 @ id @ (lam @ (X49 @ sh @ one)) @ id) | ~ ! [X53 : term] : ((X47 @ id @ (X49 @ id @ X53) @ id) | ~(X47 @ id @ X53 @ id))) | (X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id) | ~ ! [X54 : term] : (~(X47 @ id @ X54 @ id) | (X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))) => ! [X55 : (subst > term > subst > $o),X56 : term] : (~ ! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (~(X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60) | (X55 @ X59 @ X58 @ (comp @ X57 @ X60))) | (X55 @ id @ (lam @ X56) @ id) | ~ ! [X61 : term] : (~(X55 @ id @ X61 @ id) | (X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~(X55 @ id @ X63 @ id) | (X55 @ id @ (X62 @ id @ X63) @ id)) | (X55 @ id @ (lam @ (X62 @ sh @ one)) @ id) | ~ ! [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66))))) | ~ ! [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (~(X55 @ X67 @ X68 @ (comp @ X69 @ X70)) | (X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))))) & pushprop_lem1_gthm & (! [X71 : (subst > term > subst > $o)] : ~ ! [X72 : (term > $o)] : ~ ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> hoasinduction_lem0) & substmonoid_gthm & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> axvarid) & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & axabs & pushprop_gthm & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ((! [X77 : term] : (((sub @ X77 @ id)) = X77) => (! [X78 : (term > $o),X79 : subst,X80 : term] : (~ ! [X81 : term] : (~ ! [X82 : term] : (~(X78 @ X82) | (X78 @ (sub @ X81 @ (push @ X82 @ id)))) | (X78 @ (lam @ X81))) | (X78 @ (sub @ X80 @ X79)) | ~ ! [X83 : term] : ((X78 @ (sub @ X83 @ X79)) | ~(var @ X83)) | ~ ! [X84 : term,X85 : term] : (~(X78 @ X84) | ~(X78 @ X85) | (X78 @ (ap @ X84 @ X85)))) => ! [X86 : term,X87 : (term > $o)] : ((X87 @ X86) | ~ ! [X88 : term] : (~ ! [X89 : term] : (~(X87 @ X89) | (X87 @ (sub @ X88 @ (push @ X89 @ id)))) | (X87 @ (lam @ X88))) | ~ ! [X90 : term,X91 : term] : ((X87 @ (ap @ X91 @ X90)) | ~(X87 @ X90) | ~(X87 @ X91)) | ~ ! [X92 : term] : (~(var @ X92) | (X87 @ X92))))) <=> induction2_lthm) & (termmset_lthm <=> (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term] : (((sub @ X94 @ id)) = X94))) & ulamvarsh & ((^[X95 : (subst > term > subst > $o), X96 : (term > $o)] : (! [X97 : term] : (((X95 @ id @ X97 @ id)) = ((X96 @ X97))))) = hoasinduction_p_and_p_prime) & hoasinduction_lem1 & hoasinduction_lem2_lthm & pushprop_lem2v2 & ((! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => (! [X100 : term,X101 : subst] : (((comp @ sh @ (push @ X100 @ X101))) = X101) => (! [X102 : term,X103 : term] : ((((lam @ X102)) != ((lam @ X103))) | (X102 = X103)) => ! [X104 : subst,X105 : (subst > term > term),X106 : (subst > term > term),X107 : term] : ((((lam @ (X105 @ sh @ one))) != ((lam @ (X106 @ sh @ one)))) | (((X105 @ X104 @ X107)) = ((X106 @ X104 @ X107))) | ~ ! [X108 : subst,X109 : subst,X110 : term] : (((X106 @ (comp @ X108 @ X109) @ (sub @ X110 @ X109))) = ((sub @ (X106 @ X108 @ X110) @ X109))) | ~ ! [X111 : term,X112 : subst,X113 : subst] : (((X105 @ (comp @ X112 @ X113) @ (sub @ X111 @ X113))) = ((sub @ (X105 @ X112 @ X111) @ X113))))))) <=> hoaslaminj_lthm) & hoaslamnotap_gthm & (! [X114 : term,X115 : (term > $o),X116 : subst] : ~ ! [X117 : (term > $o)] : ~ ! [X118 : term] : (((X115 @ (sub @ X118 @ (push @ X114 @ X116)))) = ((X117 @ X118))) <=> pushprop_lem0_lthm) & (axvarcons <=> ! [X119 : subst,X120 : term] : (((sub @ one @ (push @ X120 @ X119))) = X120)) & hoasapnotvar_gthm & (sh = ((d2subst @ d_id))) & (hoaslam = (^[X121 : subst, X122 : (subst > term > term)] : ((d2term @ d_one)))) & (hoasinduction_lem3v2 <=> ! [X123 : term,X124 : (term > $o),X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id) | ~ ! [X127 : subst,X128 : subst,X129 : term] : (((sub @ (X126 @ X127 @ X129) @ X128)) = ((X126 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128)))) | ~ ! [X130 : term] : (~(X125 @ id @ X130 @ id) | (X125 @ id @ (X126 @ id @ X130) @ id))) | ~ ! [X131 : subst,X132 : term,X133 : subst,X134 : subst] : (~(X125 @ (comp @ X131 @ X133) @ (sub @ X132 @ X133) @ X134) | (X125 @ X131 @ X132 @ (comp @ X133 @ X134))) | ~ ! [X135 : term] : (((X124 @ X135)) = ((X125 @ id @ X135 @ id))) | ~ ! [X136 : subst,X137 : subst,X138 : subst,X139 : term] : (~(X125 @ X137 @ X139 @ (comp @ X136 @ X138)) | (X125 @ (comp @ X137 @ X136) @ (sub @ X139 @ X136) @ X138)) | ~ ! [X140 : term] : ((X124 @ (sub @ X123 @ (push @ X140 @ id))) | ~(X124 @ X140)) | (X124 @ (lam @ X123)))) & pushprop_lem3v2_lthm & (! [X141 : term,X142 : (subst > term > subst > $o)] : (~ ! [X143 : term,X144 : term] : (~(X142 @ id @ X143 @ id) | (X142 @ id @ (ap @ (sub @ X143 @ id) @ X144) @ id) | ~(X142 @ id @ X144 @ id)) | ~ ! [X145 : (subst > term > term)] : (~ ! [X146 : subst,X147 : subst,X148 : term] : (((sub @ (X145 @ X147 @ X148) @ X146)) = ((X145 @ (comp @ X147 @ X146) @ (sub @ X148 @ X146)))) | ~ ! [X149 : term] : (~(X142 @ id @ X149 @ id) | (X142 @ id @ (X145 @ id @ X149) @ id)) | (X142 @ id @ (lam @ (X145 @ sh @ one)) @ id)) | (X142 @ id @ X141 @ id)) <=> hoasinduction_no_psi_cond) & hoasinduction_lem3v2_gthm & pushprop_lem3v2 & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (! [X150 : (term > $o),X151 : term] : (~ ! [X152 : term] : ((X150 @ (lam @ X152)) | ~ ! [X153 : term] : ((X150 @ (sub @ X152 @ (push @ X153 @ id))) | ~(X150 @ X153))) | (X150 @ X151) | ~ ! [X154 : term,X155 : term] : (~(X150 @ X155) | (X150 @ (ap @ X155 @ X154)) | ~(X150 @ X154)) | ~ ! [X156 : term] : ((X150 @ X156) | ~(var @ X156))) <=> induction2) & (! [X157 : (term > $o),X158 : term,X159 : term,X160 : (subst > term > subst > $o)] : (~(X157 @ X159) | (X157 @ (ap @ X158 @ X159)) | ~ ! [X161 : term,X162 : subst,X163 : subst,X164 : subst] : (~(X160 @ (comp @ X164 @ X162) @ (sub @ X161 @ X162) @ X163) | (X160 @ X164 @ X161 @ (comp @ X162 @ X163))) | ~ ! [X165 : term,X166 : term] : (~(X160 @ id @ X166 @ id) | ~(X160 @ id @ X165 @ id) | (X160 @ id @ (ap @ (sub @ X166 @ id) @ X165) @ id)) | ~(X157 @ X158) | ~ ! [X167 : subst,X168 : subst,X169 : subst,X170 : term] : (~(X160 @ X168 @ X170 @ (comp @ X167 @ X169)) | (X160 @ (comp @ X168 @ X167) @ (sub @ X170 @ X167) @ X169)) | ~ ! [X171 : term] : (((X160 @ id @ X171 @ id)) = ((X157 @ X171)))) <=> hoasinduction_lem2v2) & axassoc & (induction2lem_lthm <=> (! [X172 : subst,X173 : term] : (((sub @ one @ (push @ X173 @ X172))) = X173) => (! [X174 : subst,X175 : term] : (((comp @ sh @ (push @ X175 @ X174))) = X174) => (! [X176 : subst] : (((comp @ X176 @ id)) = X176) => (! [X177 : term,X178 : (term > $o)] : (~ ! [X179 : term,X180 : term] : (~(X178 @ X180) | (X178 @ (ap @ X180 @ X179)) | ~(X178 @ X179)) | ~ ! [X181 : term] : ((X178 @ X181) | ~(var @ X181)) | ~ ! [X182 : term] : ((X178 @ (lam @ X182)) | ~(X178 @ X182)) | (X178 @ X177)) => ! [X183 : term,X184 : subst,X185 : (term > $o)] : (~ ! [X186 : term,X187 : term] : ((X185 @ (ap @ X187 @ X186)) | ~(X185 @ X187) | ~(X185 @ X186)) | ~ ! [X188 : term] : (~(var @ X188) | (X185 @ (sub @ X188 @ X184))) | (X185 @ (sub @ X183 @ X184)) | ~ ! [X189 : term] : ((X185 @ (lam @ X189)) | ~ ! [X190 : term] : (~(X185 @ X190) | (X185 @ (sub @ X189 @ (push @ X190 @ id))))))))))) & (! [X191 : term] : ~ ! [X192 : (subst > term > term)] : (((X192 @ sh @ one)) != ((sub @ X191 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (axscons <=> ! [X193 : subst] : (((push @ (sub @ one @ X193) @ (comp @ sh @ X193))) = X193)) & hoasinduction_lem3a_gthm & ((! [X194 : term] : ~ ! [X195 : (subst > term > term)] : ~ ! [X196 : term,X197 : subst] : (((sub @ X194 @ (push @ X196 @ X197))) = ((X195 @ X197 @ X196))) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => ! [X199 : term,X200 : (term > $o),X201 : (subst > term > subst > $o)] : (~ ! [X202 : term] : ((X200 @ (sub @ X199 @ (push @ X202 @ id))) | ~(X200 @ X202)) | ~ ! [X203 : (subst > term > term)] : ((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id) | ~ ! [X204 : subst,X205 : subst,X206 : term] : (((sub @ (X203 @ X204 @ X206) @ X205)) = ((X203 @ (comp @ X204 @ X205) @ (sub @ X206 @ X205)))) | ~ ! [X207 : term] : (~(X201 @ id @ X207 @ id) | (X201 @ id @ (X203 @ id @ X207) @ id))) | (X200 @ (lam @ X199)) | ~ ! [X208 : term] : (((X200 @ X208)) = ((X201 @ id @ X208 @ id)))))) <=> hoasinduction_lem3v2a_lthm) & pushprop_lthm & (apinj1 <=> ! [X209 : term,X210 : term,X211 : term,X212 : term] : ((X209 = X211) | (((ap @ X211 @ X210)) != ((ap @ X209 @ X212))))) & (laminj <=> ! [X213 : term,X214 : term] : ((((lam @ X214)) != ((lam @ X213))) | (X213 = X214))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasapinj2_gthm & (! [X215 : subst,X216 : (term > $o),X217 : (term > $o),X218 : term,X219 : term] : (~(X217 @ X219) | (X216 @ (sub @ X219 @ (push @ X218 @ X215)))) <=> pushprop_lem1) & hoasinduction_lem3b_gthm & hoaslamnotvar_lthm & ((! [X220 : term] : (((sub @ X220 @ id)) = X220) => (! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X221 = X222) | (((ap @ X222 @ X223)) != ((ap @ X221 @ X224)))) => ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((((ap @ (sub @ X227 @ id) @ X226)) != ((ap @ (sub @ X228 @ id) @ X225))) | (X227 = X228)))) <=> hoasapinj1_lthm) & pushprop_lem2v2_lthm & induction2_gthm & hoasinduction_lem2_gthm & pushprop_lthm_orig & hoaslamnotvar & (! [X229 : (subst > term > subst > $o),X230 : term] : (~ ! [X231 : (subst > term > term)] : ((X229 @ id @ (lam @ (X231 @ sh @ one)) @ id) | ~ ! [X232 : subst,X233 : subst,X234 : term] : (((sub @ (X231 @ X232 @ X234) @ X233)) = ((X231 @ (comp @ X232 @ X233) @ (sub @ X234 @ X233)))) | ~ ! [X235 : term] : ((X229 @ id @ (X231 @ id @ X235) @ id) | ~(X229 @ id @ X235 @ id))) | (X229 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id) | ~ ! [X236 : term] : (~(X229 @ id @ X236 @ id) | (X229 @ id @ (sub @ X230 @ (push @ X236 @ id)) @ id))) <=> hoasinduction_lem3aa) & (hoasinduction_lem3a <=> ! [X237 : (subst > term > subst > $o),X238 : term] : ((X237 @ id @ (lam @ X238) @ id) | ~ ! [X239 : (subst > term > term)] : (~ ! [X240 : term] : ((X237 @ id @ (X239 @ id @ X240) @ id) | ~(X237 @ id @ X240 @ id)) | (X237 @ id @ (lam @ (X239 @ sh @ one)) @ id) | ~ ! [X241 : term,X242 : subst,X243 : subst] : (((X239 @ (comp @ X242 @ X243) @ (sub @ X241 @ X243))) = ((sub @ (X239 @ X242 @ X241) @ X243)))) | ~ ! [X244 : term] : (~(X237 @ id @ X244 @ id) | (X237 @ id @ (sub @ X238 @ (push @ X244 @ id)) @ id)))) & ((! [X245 : term] : (((sub @ X245 @ id)) = X245) => ! [X246 : (subst > term > subst > $o),X247 : (term > $o),X248 : term] : (~ ! [X249 : (subst > term > term)] : (~ ! [X250 : subst,X251 : term,X252 : subst] : (((sub @ (X249 @ X252 @ X251) @ X250)) = ((X249 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250)))) | ~ ! [X253 : term] : ((X246 @ id @ (X249 @ id @ X253) @ id) | ~(X246 @ id @ X253 @ id)) | (X246 @ id @ (lam @ (X249 @ sh @ one)) @ id)) | ~ ! [X254 : subst,X255 : term,X256 : subst,X257 : subst] : ((X246 @ (comp @ X257 @ X254) @ (sub @ X255 @ X254) @ X256) | ~(X246 @ X257 @ X255 @ (comp @ X254 @ X256))) | (X247 @ (lam @ X248)) | ~ ! [X258 : term] : (((X246 @ id @ X258 @ id)) = ((X247 @ X258))) | ~ ! [X259 : subst,X260 : subst,X261 : subst,X262 : term] : ((X246 @ X260 @ X262 @ (comp @ X261 @ X259)) | ~(X246 @ (comp @ X260 @ X261) @ (sub @ X262 @ X261) @ X259)) | ~ ! [X263 : term] : ((X247 @ (sub @ X248 @ (push @ X263 @ id))) | ~(X247 @ X263)))) <=> hoasinduction_lem3v2_lthm) & termmset_gthm & (hoasinduction_lthm <=> (! [X264 : (term > $o),X265 : term] : ((X264 @ X265) | ~ ! [X266 : term,X267 : term] : (~(X264 @ X267) | (X264 @ (ap @ X267 @ X266)) | ~(X264 @ X266)) | ~ ! [X268 : term] : ((X264 @ (lam @ X268)) | ~ ! [X269 : term] : (~(X264 @ X269) | (X264 @ (sub @ X268 @ (push @ X269 @ id))))) | ~ ! [X270 : term] : ((X264 @ X270) | ~(var @ X270))) => (! [X271 : term,X272 : term,X273 : (subst > term > subst > $o)] : (~(X273 @ id @ X271 @ id) | ~ ! [X274 : term,X275 : term] : (~(X273 @ id @ X275 @ id) | ~(X273 @ id @ X274 @ id) | (X273 @ id @ (ap @ (sub @ X274 @ id) @ X275) @ id)) | (X273 @ id @ (ap @ X271 @ X272) @ id) | ~ ! [X276 : subst,X277 : subst,X278 : term,X279 : subst] : ((X273 @ (comp @ X277 @ X279) @ (sub @ X278 @ X279) @ X276) | ~(X273 @ X277 @ X278 @ (comp @ X279 @ X276))) | ~(X273 @ id @ X272 @ id) | ~ ! [X280 : term,X281 : subst,X282 : subst,X283 : subst] : (~(X273 @ (comp @ X282 @ X283) @ (sub @ X280 @ X283) @ X281) | (X273 @ X282 @ X280 @ (comp @ X283 @ X281)))) => (! [X284 : (subst > term > subst > $o),X285 : term] : (~ ! [X286 : term] : ((X284 @ id @ (sub @ X285 @ (push @ X286 @ id)) @ id) | ~(X284 @ id @ X286 @ id)) | ~ ! [X287 : (subst > term > term)] : ((X284 @ id @ (lam @ (X287 @ sh @ one)) @ id) | ~ ! [X288 : term] : (~(X284 @ id @ X288 @ id) | (X284 @ id @ (X287 @ id @ X288) @ id)) | ~ ! [X289 : subst,X290 : term,X291 : subst] : (((sub @ (X287 @ X291 @ X290) @ X289)) = ((X287 @ (comp @ X291 @ X289) @ (sub @ X290 @ X289))))) | ~ ! [X292 : subst,X293 : term,X294 : subst,X295 : subst] : (~(X284 @ (comp @ X294 @ X295) @ (sub @ X293 @ X295) @ X292) | (X284 @ X294 @ X293 @ (comp @ X295 @ X292))) | (X284 @ id @ (lam @ X285) @ id) | ~ ! [X296 : subst,X297 : subst,X298 : subst,X299 : term] : (~(X284 @ X298 @ X299 @ (comp @ X297 @ X296)) | (X284 @ (comp @ X298 @ X297) @ (sub @ X299 @ X297) @ X296))) => ! [X300 : term,X301 : (subst > term > subst > $o)] : (~ ! [X302 : term] : ((X301 @ id @ X302 @ id) | ~(var @ (sub @ X302 @ id))) | ~ ! [X303 : subst,X304 : subst,X305 : term,X306 : subst] : ((X301 @ (comp @ X303 @ X306) @ (sub @ X305 @ X306) @ X304) | ~(X301 @ X303 @ X305 @ (comp @ X306 @ X304))) | ~ ! [X307 : subst,X308 : term,X309 : subst,X310 : subst] : (~(X301 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307) @ X310) | (X301 @ X309 @ X308 @ (comp @ X307 @ X310))) | ~ ! [X311 : (subst > term > term)] : (~ ! [X312 : term] : (~(X301 @ id @ X312 @ id) | (X301 @ id @ (X311 @ id @ X312) @ id)) | ~ ! [X313 : subst,X314 : term,X315 : subst] : (((sub @ (X311 @ X313 @ X314) @ X315)) = ((X311 @ (comp @ X313 @ X315) @ (sub @ X314 @ X315)))) | (X301 @ id @ (lam @ (X311 @ sh @ one)) @ id)) | (X301 @ id @ X300 @ id) | ~ ! [X316 : term,X317 : term] : (~(X301 @ id @ X317 @ id) | (X301 @ id @ (ap @ (sub @ X317 @ id) @ X316) @ id) | ~(X301 @ id @ X316 @ id))))))) & (hoaslaminj <=> ! [X318 : subst,X319 : (subst > term > term),X320 : (subst > term > term),X321 : term] : ((((lam @ (X319 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | ~ ! [X322 : subst,X323 : term,X324 : subst] : (((sub @ (X319 @ X322 @ X323) @ X324)) = ((X319 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324)))) | ~ ! [X325 : term,X326 : subst,X327 : subst] : (((sub @ (X320 @ X327 @ X325) @ X326)) = ((X320 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)))) | (((X319 @ X318 @ X321)) = ((X320 @ X318 @ X321))))) & (! [X328 : term,X329 : term] : ((X328 = X329) | (((sub @ X329 @ sh)) != ((sub @ X328 @ sh)))) <=> shinj) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (! [X330 : (subst > term > subst > $o),X331 : term] : (~ ! [X332 : (subst > term > term),X333 : term] : ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id) | ~ ! [X334 : term,X335 : subst,X336 : subst] : (((X332 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ X333 @ (push @ (sub @ X334 @ X336) @ (comp @ X335 @ X336))))) | ~ ! [X337 : term] : ((X330 @ id @ (X332 @ id @ X337) @ id) | ~(X330 @ id @ X337 @ id)) | ~ ! [X338 : subst,X339 : subst,X340 : term] : (((sub @ (X332 @ X339 @ X340) @ X338)) = ((sub @ (sub @ X333 @ (push @ X340 @ X339)) @ X338)))) | ~ ! [X341 : term] : ((X330 @ id @ (sub @ X331 @ (push @ X341 @ id)) @ id) | ~(X330 @ id @ X341 @ id)) | (X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3a_lthm <=> (! [X342 : term] : (((sub @ X342 @ id)) = X342) => (! [X343 : term,X344 : (subst > term > subst > $o)] : ((X344 @ id @ (lam @ (sub @ X343 @ (push @ one @ sh))) @ id) | ~ ! [X345 : term] : ((X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id) | ~(X344 @ id @ X345 @ id)) | ~ ! [X346 : (subst > term > term)] : (~ ! [X347 : term] : (~(X344 @ id @ X347 @ id) | (X344 @ id @ (X346 @ id @ X347) @ id)) | (X344 @ id @ (lam @ (X346 @ sh @ one)) @ id) | ~ ! [X348 : subst,X349 : term,X350 : subst] : (((X346 @ (comp @ X348 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X346 @ X348 @ X349) @ X350))))) => ! [X351 : (subst > term > subst > $o),X352 : term] : (~ ! [X353 : (subst > term > term)] : ((X351 @ id @ (lam @ (X353 @ sh @ one)) @ id) | ~ ! [X354 : term] : (~(X351 @ id @ X354 @ id) | (X351 @ id @ (X353 @ id @ X354) @ id)) | ~ ! [X355 : subst,X356 : subst,X357 : term] : (((X353 @ (comp @ X356 @ X355) @ (sub @ X357 @ X355))) = ((sub @ (X353 @ X356 @ X357) @ X355)))) | (X351 @ id @ (lam @ X352) @ id) | ~ ! [X358 : term] : ((X351 @ id @ (sub @ X352 @ (push @ X358 @ id)) @ id) | ~(X351 @ id @ X358 @ id)))))) & ~ulamvar1 & apnotvar & axapp & ulamvarind & (! [X359 : term] : (((sub @ X359 @ id)) = X359) <=> termmset) & (! [X360 : term,X361 : (subst > term > term),X362 : term] : ((((lam @ (X361 @ sh @ one))) != ((ap @ (sub @ X360 @ id) @ X362))) | ~ ! [X363 : term,X364 : subst,X365 : subst] : (((X361 @ (comp @ X365 @ X364) @ (sub @ X363 @ X364))) = ((sub @ (X361 @ X365 @ X363) @ X364)))) <=> hoaslamnotap) & (axshiftcons <=> ! [X366 : term,X367 : subst] : (((comp @ sh @ (push @ X366 @ X367))) = X367)) & ~(var @ (d2term @ d_one)) & ! [X368 : d_subst,X369 : d_subst] : ((((d2subst @ X369)) = ((d2subst @ X368))) => (X368 = X369)) & (axidl <=> ! [X370 : subst] : (((comp @ id @ X370)) = X370)) & ! [X371 : d_term] : (d_one = X371) & (! [X372 : term,X373 : term,X374 : (subst > term > subst > $o)] : (~ ! [X375 : term,X376 : term] : (~(X374 @ id @ X376 @ id) | (X374 @ id @ (ap @ (sub @ X376 @ id) @ X375) @ id) | ~(X374 @ id @ X375 @ id)) | ~ ! [X377 : subst,X378 : subst,X379 : subst,X380 : term] : (~(X374 @ X378 @ X380 @ (comp @ X379 @ X377)) | (X374 @ (comp @ X378 @ X379) @ (sub @ X380 @ X379) @ X377)) | ~ ! [X381 : subst,X382 : subst,X383 : subst,X384 : term] : ((X374 @ X382 @ X384 @ (comp @ X383 @ X381)) | ~(X374 @ (comp @ X382 @ X383) @ (sub @ X384 @ X383) @ X381)) | (X374 @ id @ (ap @ X372 @ X373) @ id) | ~(X374 @ id @ X372 @ id) | ~(X374 @ id @ X373 @ id)) <=> hoasinduction_lem2) & hoasinduction_lem1_gthm & ! [X385 : term] : ? [X386 : d_term] : (((d2term @ X386)) = X385) & (! [X387 : term,X388 : (subst > term > subst > $o)] : (~ ! [X389 : (subst > term > term)] : ((X388 @ id @ (lam @ (X389 @ sh @ one)) @ id) | ~ ! [X390 : term] : ((X388 @ id @ (X389 @ id @ X390) @ id) | ~(X388 @ id @ X390 @ id)) | ~ ! [X391 : subst,X392 : term,X393 : subst] : (((X389 @ (comp @ X391 @ X393) @ (sub @ X392 @ X393))) = ((sub @ (X389 @ X391 @ X392) @ X393)))) | (X388 @ id @ (lam @ (sub @ X387 @ (push @ one @ sh))) @ id) | ~ ! [X394 : term] : ((X388 @ id @ (sub @ X387 @ (push @ X394 @ id)) @ id) | ~(X388 @ id @ X394 @ id))) <=> hoasinduction_lem3aa_lthm) & pushprop & axmap & hoasinduction_lem1v2 & hoasapinj1_gthm & ((! [X395 : subst] : (((comp @ id @ X395)) = X395) => (! [X396 : subst] : (((comp @ X396 @ id)) = X396) => (! [X397 : subst] : (((comp @ id @ X397)) = X397) & ! [X398 : subst] : (((comp @ X398 @ id)) = X398)))) <=> substmonoid_lthm) & hoasinduction_lem1_lthm & (pushprop_lem1_lthm <=> (! [X399 : term,X400 : subst] : (((sub @ one @ (push @ X399 @ X400))) = X399) => (! [X401 : subst,X402 : term] : (((comp @ sh @ (push @ X402 @ X401))) = X401) => ! [X403 : term,X404 : (term > $o),X405 : subst,X406 : term,X407 : (term > $o)] : (~(X404 @ X403) | (X407 @ (sub @ X403 @ (push @ X406 @ X405))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3 <=> ! [X408 : (subst > term > subst > $o),X409 : term] : (~ ! [X410 : term] : (~(X408 @ id @ X410 @ id) | (X408 @ id @ (sub @ X409 @ (push @ X410 @ id)) @ id)) | ~ ! [X411 : subst,X412 : term,X413 : subst,X414 : subst] : ((X408 @ X413 @ X412 @ (comp @ X414 @ X411)) | ~(X408 @ (comp @ X413 @ X414) @ (sub @ X412 @ X414) @ X411)) | ~ ! [X415 : (subst > term > term)] : (~ ! [X416 : term,X417 : subst,X418 : subst] : (((sub @ (X415 @ X417 @ X416) @ X418)) = ((X415 @ (comp @ X417 @ X418) @ (sub @ X416 @ X418)))) | (X408 @ id @ (lam @ (X415 @ sh @ one)) @ id) | ~ ! [X419 : term] : ((X408 @ id @ (X415 @ id @ X419) @ id) | ~(X408 @ id @ X419 @ id))) | ~ ! [X420 : subst,X421 : term,X422 : subst,X423 : subst] : ((X408 @ (comp @ X423 @ X422) @ (sub @ X421 @ X422) @ X420) | ~(X408 @ X423 @ X421 @ (comp @ X422 @ X420))) | (X408 @ id @ (lam @ X409) @ id))) & ((! [X424 : (subst > term > subst > $o)] : ~ ! [X425 : (term > $o)] : ~ ! [X426 : term] : (((X425 @ X426)) = ((X424 @ id @ X426 @ id))) => (! [X427 : (term > $o),X428 : term] : (~ ! [X429 : term] : (~ ! [X430 : term] : ((X427 @ (sub @ X429 @ (push @ X430 @ id))) | ~(X427 @ X430)) | (X427 @ (lam @ X429))) | ~ ! [X431 : term,X432 : term] : (~(X427 @ X431) | (X427 @ (ap @ X431 @ X432)) | ~(X427 @ X432)) | ~ ! [X433 : term] : (~(var @ X433) | (X427 @ X433)) | (X427 @ X428)) => (! [X434 : term] : (((sub @ X434 @ id)) = X434) => (! [X435 : (subst > term > subst > $o),X436 : (term > $o),X437 : term] : ((X436 @ (lam @ X437)) | ~ ! [X438 : (subst > term > term)] : (~ ! [X439 : subst,X440 : term,X441 : subst] : (((sub @ (X438 @ X439 @ X440) @ X441)) = ((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441)))) | (X435 @ id @ (lam @ (X438 @ sh @ one)) @ id) | ~ ! [X442 : term] : (~(X435 @ id @ X442 @ id) | (X435 @ id @ (X438 @ id @ X442) @ id))) | ~ ! [X443 : term] : (((X436 @ X443)) = ((X435 @ id @ X443 @ id))) | ~ ! [X444 : term] : (~(X436 @ X444) | (X436 @ (sub @ X437 @ (push @ X444 @ id))))) => ! [X445 : (subst > term > subst > $o),X446 : term] : (~ ! [X447 : term,X448 : term] : ((X445 @ id @ (ap @ (sub @ X447 @ id) @ X448) @ id) | ~(X445 @ id @ X448 @ id) | ~(X445 @ id @ X447 @ id)) | (X445 @ id @ X446 @ id) | ~ ! [X449 : (subst > term > term)] : (~ ! [X450 : term,X451 : subst,X452 : subst] : (((X449 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X449 @ X452 @ X450) @ X451))) | (X445 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~ ! [X453 : term] : (~(X445 @ id @ X453 @ id) | (X445 @ id @ (X449 @ id @ X453) @ id)))))))) <=> hoasinduction_no_psi_cond_lthm) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasapinj2 <=> ! [X454 : term,X455 : term,X456 : term,X457 : term] : ((X454 = X457) | (((ap @ (sub @ X456 @ id) @ X454)) != ((ap @ (sub @ X455 @ id) @ X457))))) & (! [X458 : term,X459 : (subst > term > subst > $o),X460 : (term > $o)] : (~ ! [X461 : (subst > term > term)] : ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id) | ~ ! [X462 : term] : ((X459 @ id @ (X461 @ id @ X462) @ id) | ~(X459 @ id @ X462 @ id)) | ~ ! [X463 : term,X464 : subst,X465 : subst] : (((X461 @ (comp @ X464 @ X465) @ (sub @ X463 @ X465))) = ((sub @ (X461 @ X464 @ X463) @ X465)))) | (X460 @ (lam @ X458)) | ~ ! [X466 : term] : ((X460 @ (sub @ X458 @ (push @ X466 @ id))) | ~(X460 @ X466)) | ~ ! [X467 : term] : (((X459 @ id @ X467 @ id)) = ((X460 @ X467)))) <=> hoasinduction_lem3v2a) & hoasapnotvar_lthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ~lamnotap & ((^[X468 : term, X469 : subst, X470 : (term > $o), X471 : (term > $o)] : (! [X472 : term] : (((X471 @ X472)) = ((X470 @ (sub @ X472 @ (push @ X468 @ X469))))))) = pushprop_p_and_p_prime) & (apinj2 <=> ! [X473 : term,X474 : term,X475 : term,X476 : term] : ((((ap @ X474 @ X475)) != ((ap @ X473 @ X476))) | (X475 = X476))) & axvarshift & (pushprop_lem1v2 <=> ! [X477 : (term > $o),X478 : subst,X479 : (term > $o),X480 : term] : (~(X479 @ X480) | (X477 @ one) | ~ ! [X481 : term] : (((X479 @ (sub @ X481 @ (push @ X480 @ X478)))) = ((X477 @ X481))))) & (! [X482 : term,X483 : (subst > term > subst > $o)] : (~ ! [X484 : term,X485 : subst,X486 : subst,X487 : subst] : ((X483 @ X487 @ X484 @ (comp @ X485 @ X486)) | ~(X483 @ (comp @ X487 @ X485) @ (sub @ X484 @ X485) @ X486)) | ~ ! [X488 : subst,X489 : term,X490 : subst,X491 : subst] : (~(X483 @ X490 @ X489 @ (comp @ X488 @ X491)) | (X483 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X491)) | ~ ! [X492 : (subst > term > term)] : ((X483 @ id @ (lam @ (X492 @ sh @ one)) @ id) | ~ ! [X493 : term] : (~(X483 @ id @ X493 @ id) | (X483 @ id @ (X492 @ id @ X493) @ id)) | ~ ! [X494 : subst,X495 : subst,X496 : term] : (((X492 @ (comp @ X495 @ X494) @ (sub @ X496 @ X494))) = ((sub @ (X492 @ X495 @ X496) @ X494)))) | ~ ! [X497 : term,X498 : term] : (~(X483 @ id @ X497 @ id) | ~(X483 @ id @ X498 @ id) | (X483 @ id @ (ap @ (sub @ X497 @ id) @ X498) @ id)) | (X483 @ id @ X482 @ id) | ~ ! [X499 : term] : (~(var @ (sub @ X499 @ id)) | (X483 @ id @ X499 @ id))) <=> hoasinduction) & (id = ((d2subst @ d_id))) & ! [X500 : d_subst] : (d_id = X500) & hoasinduction_lem1v2_gthm & (hoasinduction_lthm_3 <=> (! [X501 : (subst > term > subst > $o)] : ~ ! [X502 : (term > $o)] : ~ ! [X503 : term] : (((X502 @ X503)) = ((X501 @ id @ X503 @ id))) => (! [X504 : term,X505 : (term > $o)] : (~ ! [X506 : term] : ((X505 @ X506) | ~(var @ X506)) | (X505 @ X504) | ~ ! [X507 : term] : (~ ! [X508 : term] : (~(X505 @ X508) | (X505 @ (sub @ X507 @ (push @ X508 @ id)))) | (X505 @ (lam @ X507))) | ~ ! [X509 : term,X510 : term] : (~(X505 @ X510) | ~(X505 @ X509) | (X505 @ (ap @ X510 @ X509)))) => (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : (subst > term > subst > $o),X513 : term,X514 : (term > $o)] : (~ ! [X515 : term] : (((X512 @ id @ X515 @ id)) = ((X514 @ X515))) | ~ ! [X516 : term] : (~(X514 @ X516) | (X514 @ (sub @ X513 @ (push @ X516 @ id)))) | ~ ! [X517 : (subst > term > term)] : ((X512 @ id @ (lam @ (X517 @ sh @ one)) @ id) | ~ ! [X518 : term] : (~(X512 @ id @ X518 @ id) | (X512 @ id @ (X517 @ id @ X518) @ id)) | ~ ! [X519 : subst,X520 : subst,X521 : term] : (((sub @ (X517 @ X519 @ X521) @ X520)) = ((X517 @ (comp @ X519 @ X520) @ (sub @ X521 @ X520))))) | (X514 @ (lam @ X513))) => ! [X522 : (subst > term > subst > $o),X523 : term] : (~ ! [X524 : (subst > term > term)] : (~ ! [X525 : term] : ((X522 @ id @ (X524 @ id @ X525) @ id) | ~(X522 @ id @ X525 @ id)) | ~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X524 @ X527 @ X526) @ X528)) = ((X524 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528)))) | (X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)) | ~ ! [X529 : term,X530 : subst,X531 : subst,X532 : subst] : (~(X522 @ X530 @ X529 @ (comp @ X532 @ X531)) | (X522 @ (comp @ X530 @ X532) @ (sub @ X529 @ X532) @ X531)) | (X522 @ id @ X523 @ id) | ~ ! [X533 : term,X534 : term] : ((X522 @ id @ (ap @ (sub @ X534 @ id) @ X533) @ id) | ~(X522 @ id @ X533 @ id) | ~(X522 @ id @ X534 @ id)) | ~ ! [X535 : term] : (~(var @ (sub @ X535 @ id)) | (X522 @ id @ X535 @ id)) | ~ ! [X536 : subst,X537 : subst,X538 : subst,X539 : term] : ((X522 @ X538 @ X539 @ (comp @ X537 @ X536)) | ~(X522 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537) @ X536)))))))) & (! [X540 : term] : ~ ! [X541 : (subst > term > term)] : ~ ! [X542 : term,X543 : subst] : (((X541 @ X543 @ X542)) = ((sub @ X540 @ (push @ X542 @ X543)))) <=> hoasinduction_lem3v2_f) & ! [X544 : d_term,X545 : d_term] : ((((d2term @ X545)) = ((d2term @ X544))) => (X544 = X545)) & hoasinduction_gthm & pushprop_lem0_gthm & (! [X546 : (subst > term > subst > $o)] : ~ ! [X547 : (term > $o)] : ~ ! [X548 : term] : (((X546 @ id @ X548 @ id)) = ((X547 @ X548))) <=> hoasinduction_lem0_lthm) & (one = ((d2term @ d_one))) & hoasinduction_lem2v2_gthm & (axidr <=> ! [X549 : subst] : (((comp @ X549 @ id)) = X549))),
% 5.11/1.35 inference(rectify,[],[f1])).
% 5.11/1.35 thf(f7,plain,(
% 5.11/1.35 (axclos = $true) & (lamnotvar = $true) & (pushprop_lem2v2_gthm = $true) & (! [X0 : term,X1 : (term > $o)] : (($true = ((X1 @ X0))) | ~ ! [X2 : term,X3 : term] : (($true = ((X1 @ (ap @ X3 @ X2)))) | ~ ($true = ((X1 @ X3))) | ~ ($true = ((X1 @ X2)))) | ~ ! [X4 : term] : ((((X1 @ X4)) = $true) | ~ ($true = ((var @ X4)))) | ~ ! [X5 : term] : (($true = ((X1 @ (lam @ X5)))) | ~ (((X1 @ X5)) = $true))) <=> (induction = $true)) & ((! [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) = X7) => ! [X8 : term,X9 : (term > $o),X10 : subst,X11 : (term > $o)] : ((((X9 @ one)) = $true) | ~ ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))) | ~ ($true = ((X11 @ X8))))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & (hoaslamnotap_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem0 = $true) <=> ! [X19 : (term > $o),X18 : subst,X17 : term] : ~ ! [X20 : (term > $o)] : ~ ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21)))) & (induction2lem_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X22 : term] : ~ ! [X23 : (subst > term > term)] : ~ ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25)))) & (hoaslaminj_gthm = $true) & (! [X26 : subst,X27 : (term > $o),X28 : term] : (~ ! [X29 : term,X30 : term] : (~ ($true = ((X27 @ X29))) | ($true = ((X27 @ (ap @ X30 @ X29)))) | ~ ($true = ((X27 @ X30)))) | ~ ! [X31 : term] : ((((X27 @ (lam @ X31))) = $true) | ~ ! [X32 : term] : (($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id))))) | ~ ($true = ((X27 @ X32))))) | ~ ! [X33 : term] : (($true = ((X27 @ (sub @ X33 @ X26)))) | ~ ($true = ((var @ X33)))) | ($true = ((X27 @ (sub @ X28 @ X26))))) <=> (induction2lem = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X34 : term] : ~ ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & ((! [X41 : term,X39 : term,X40 : term,X38 : term] : ((((ap @ X38 @ X41)) != ((ap @ X40 @ X39))) | (X39 = X41)) => ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X47 : (subst > term > subst > $o),X48 : term] : (~ ! [X49 : (subst > term > term)] : (~ ! [X51 : subst,X52 : subst,X50 : term] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) = ((sub @ (X49 @ X52 @ X50) @ X51))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id))) | ~ ! [X53 : term] : (($true = ((X47 @ id @ (X49 @ id @ X53) @ id))) | ~ ($true = ((X47 @ id @ X53 @ id))))) | ($true = ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id))) | ~ ! [X54 : term] : (~ ($true = ((X47 @ id @ X54 @ id))) | ($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))))) => ! [X55 : (subst > term > subst > $o),X56 : term] : (~ ! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (~ ($true = ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60))) | ($true = ((X55 @ X59 @ X58 @ (comp @ X57 @ X60))))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ~ ! [X61 : term] : (~ ($true = ((X55 @ id @ X61 @ id))) | ($true = ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)))) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~ ($true = ((X55 @ id @ X63 @ id))) | ($true = ((X55 @ id @ (X62 @ id @ X63) @ id)))) | (((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true) | ~ ! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66))))) | ~ ! [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (~ ($true = ((X55 @ X67 @ X68 @ (comp @ X69 @ X70)))) | ($true = ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))))))) & (pushprop_lem1_gthm = $true) & (! [X71 : (subst > term > subst > $o)] : ~ ! [X72 : (term > $o)] : ~ ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & (substmonoid_gthm = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axabs = $true) & (pushprop_gthm = $true) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ((! [X77 : term] : (((sub @ X77 @ id)) = X77) => (! [X78 : (term > $o),X79 : subst,X80 : term] : (~ ! [X81 : term] : (~ ! [X82 : term] : (~ ($true = ((X78 @ X82))) | ($true = ((X78 @ (sub @ X81 @ (push @ X82 @ id)))))) | ($true = ((X78 @ (lam @ X81))))) | ($true = ((X78 @ (sub @ X80 @ X79)))) | ~ ! [X83 : term] : (($true = ((X78 @ (sub @ X83 @ X79)))) | ~ ($true = ((var @ X83)))) | ~ ! [X84 : term,X85 : term] : (~ ($true = ((X78 @ X84))) | ~ ($true = ((X78 @ X85))) | (((X78 @ (ap @ X84 @ X85))) = $true))) => ! [X86 : term,X87 : (term > $o)] : ((((X87 @ X86)) = $true) | ~ ! [X88 : term] : (~ ! [X89 : term] : (~ ($true = ((X87 @ X89))) | ($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id)))))) | ($true = ((X87 @ (lam @ X88))))) | ~ ! [X90 : term,X91 : term] : (($true = ((X87 @ (ap @ X91 @ X90)))) | ~ ($true = ((X87 @ X90))) | ~ ($true = ((X87 @ X91)))) | ~ ! [X92 : term] : (~ (((var @ X92)) = $true) | ($true = ((X87 @ X92))))))) <=> (induction2_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term] : (((sub @ X94 @ id)) = X94))) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2 = $true) & ((! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => (! [X100 : term,X101 : subst] : (((comp @ sh @ (push @ X100 @ X101))) = X101) => (! [X102 : term,X103 : term] : ((((lam @ X102)) != ((lam @ X103))) | (X102 = X103)) => ! [X104 : subst,X105 : (subst > term > term),X106 : (subst > term > term),X107 : term] : ((((lam @ (X105 @ sh @ one))) != ((lam @ (X106 @ sh @ one)))) | (((X105 @ X104 @ X107)) = ((X106 @ X104 @ X107))) | ~ ! [X108 : subst,X109 : subst,X110 : term] : (((X106 @ (comp @ X108 @ X109) @ (sub @ X110 @ X109))) = ((sub @ (X106 @ X108 @ X110) @ X109))) | ~ ! [X111 : term,X112 : subst,X113 : subst] : (((X105 @ (comp @ X112 @ X113) @ (sub @ X111 @ X113))) = ((sub @ (X105 @ X112 @ X111) @ X113))))))) <=> (hoaslaminj_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X114 : term,X115 : (term > $o),X116 : subst] : ~ ! [X117 : (term > $o)] : ~ ! [X118 : term] : (((X115 @ (sub @ X118 @ (push @ X114 @ X116)))) = ((X117 @ X118))) <=> (pushprop_lem0_lthm = $true)) & ((axvarcons = $true) <=> ! [X119 : subst,X120 : term] : (((sub @ one @ (push @ X120 @ X119))) = X120)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X123 : term,X124 : (term > $o),X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : ((((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id)) = $true) | ~ ! [X127 : subst,X128 : subst,X129 : term] : (((sub @ (X126 @ X127 @ X129) @ X128)) = ((X126 @ (comp @ X127 @ X128) @ (sub @ X129 @ X128)))) | ~ ! [X130 : term] : (~ ($true = ((X125 @ id @ X130 @ id))) | ($true = ((X125 @ id @ (X126 @ id @ X130) @ id))))) | ~ ! [X131 : subst,X132 : term,X133 : subst,X134 : subst] : (~ ($true = ((X125 @ (comp @ X131 @ X133) @ (sub @ X132 @ X133) @ X134))) | ($true = ((X125 @ X131 @ X132 @ (comp @ X133 @ X134))))) | ~ ! [X135 : term] : (((X124 @ X135)) = ((X125 @ id @ X135 @ id))) | ~ ! [X136 : subst,X137 : subst,X138 : subst,X139 : term] : (~ ($true = ((X125 @ X137 @ X139 @ (comp @ X136 @ X138)))) | ($true = ((X125 @ (comp @ X137 @ X136) @ (sub @ X139 @ X136) @ X138)))) | ~ ! [X140 : term] : ((((X124 @ (sub @ X123 @ (push @ X140 @ id)))) = $true) | ~ ($true = ((X124 @ X140)))) | ($true = ((X124 @ (lam @ X123)))))) & (pushprop_lem3v2_lthm = $true) & (! [X141 : term,X142 : (subst > term > subst > $o)] : (~ ! [X143 : term,X144 : term] : (~ ($true = ((X142 @ id @ X143 @ id))) | ($true = ((X142 @ id @ (ap @ (sub @ X143 @ id) @ X144) @ id))) | ~ ($true = ((X142 @ id @ X144 @ id)))) | ~ ! [X145 : (subst > term > term)] : (~ ! [X146 : subst,X147 : subst,X148 : term] : (((sub @ (X145 @ X147 @ X148) @ X146)) = ((X145 @ (comp @ X147 @ X146) @ (sub @ X148 @ X146)))) | ~ ! [X149 : term] : (~ ($true = ((X142 @ id @ X149 @ id))) | ($true = ((X142 @ id @ (X145 @ id @ X149) @ id)))) | ($true = ((X142 @ id @ (lam @ (X145 @ sh @ one)) @ id)))) | ($true = ((X142 @ id @ X141 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2 = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X150 : (term > $o),X151 : term] : (~ ! [X152 : term] : (($true = ((X150 @ (lam @ X152)))) | ~ ! [X153 : term] : (($true = ((X150 @ (sub @ X152 @ (push @ X153 @ id))))) | ~ ($true = ((X150 @ X153))))) | ($true = ((X150 @ X151))) | ~ ! [X154 : term,X155 : term] : (~ (((X150 @ X155)) = $true) | ($true = ((X150 @ (ap @ X155 @ X154)))) | ~ ($true = ((X150 @ X154)))) | ~ ! [X156 : term] : (($true = ((X150 @ X156))) | ~ ($true = ((var @ X156))))) <=> (induction2 = $true)) & (! [X157 : (term > $o),X158 : term,X159 : term,X160 : (subst > term > subst > $o)] : (~ ($true = ((X157 @ X159))) | ($true = ((X157 @ (ap @ X158 @ X159)))) | ~ ! [X161 : term,X162 : subst,X163 : subst,X164 : subst] : (~ ($true = ((X160 @ (comp @ X164 @ X162) @ (sub @ X161 @ X162) @ X163))) | ($true = ((X160 @ X164 @ X161 @ (comp @ X162 @ X163))))) | ~ ! [X165 : term,X166 : term] : (~ ($true = ((X160 @ id @ X166 @ id))) | ~ ($true = ((X160 @ id @ X165 @ id))) | (((X160 @ id @ (ap @ (sub @ X166 @ id) @ X165) @ id)) = $true)) | ~ ($true = ((X157 @ X158))) | ~ ! [X167 : subst,X168 : subst,X169 : subst,X170 : term] : (~ ($true = ((X160 @ X168 @ X170 @ (comp @ X167 @ X169)))) | ($true = ((X160 @ (comp @ X168 @ X167) @ (sub @ X170 @ X167) @ X169)))) | ~ ! [X171 : term] : (((X160 @ id @ X171 @ id)) = ((X157 @ X171)))) <=> (hoasinduction_lem2v2 = $true)) & (axassoc = $true) & ((induction2lem_lthm = $true) <=> (! [X172 : subst,X173 : term] : (((sub @ one @ (push @ X173 @ X172))) = X173) => (! [X174 : subst,X175 : term] : (((comp @ sh @ (push @ X175 @ X174))) = X174) => (! [X176 : subst] : (((comp @ X176 @ id)) = X176) => (! [X177 : term,X178 : (term > $o)] : (~ ! [X179 : term,X180 : term] : (~ ($true = ((X178 @ X180))) | ($true = ((X178 @ (ap @ X180 @ X179)))) | ~ ($true = ((X178 @ X179)))) | ~ ! [X181 : term] : (($true = ((X178 @ X181))) | ~ ($true = ((var @ X181)))) | ~ ! [X182 : term] : ((((X178 @ (lam @ X182))) = $true) | ~ ($true = ((X178 @ X182)))) | ($true = ((X178 @ X177)))) => ! [X183 : term,X184 : subst,X185 : (term > $o)] : (~ ! [X186 : term,X187 : term] : (($true = ((X185 @ (ap @ X187 @ X186)))) | ~ (((X185 @ X187)) = $true) | ~ ($true = ((X185 @ X186)))) | ~ ! [X188 : term] : (~ ($true = ((var @ X188))) | (((X185 @ (sub @ X188 @ X184))) = $true)) | ($true = ((X185 @ (sub @ X183 @ X184)))) | ~ ! [X189 : term] : (($true = ((X185 @ (lam @ X189)))) | ~ ! [X190 : term] : (~ ($true = ((X185 @ X190))) | (((X185 @ (sub @ X189 @ (push @ X190 @ id)))) = $true))))))))) & (! [X191 : term] : ~ ! [X192 : (subst > term > term)] : (((X192 @ sh @ one)) != ((sub @ X191 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((axscons = $true) <=> ! [X193 : subst] : (((push @ (sub @ one @ X193) @ (comp @ sh @ X193))) = X193)) & (hoasinduction_lem3a_gthm = $true) & ((! [X194 : term] : ~ ! [X195 : (subst > term > term)] : ~ ! [X196 : term,X197 : subst] : (((sub @ X194 @ (push @ X196 @ X197))) = ((X195 @ X197 @ X196))) => (! [X198 : term] : (((sub @ X198 @ id)) = X198) => ! [X199 : term,X200 : (term > $o),X201 : (subst > term > subst > $o)] : (~ ! [X202 : term] : (($true = ((X200 @ (sub @ X199 @ (push @ X202 @ id))))) | ~ (((X200 @ X202)) = $true)) | ~ ! [X203 : (subst > term > term)] : (($true = ((X201 @ id @ (lam @ (X203 @ sh @ one)) @ id))) | ~ ! [X204 : subst,X205 : subst,X206 : term] : (((sub @ (X203 @ X204 @ X206) @ X205)) = ((X203 @ (comp @ X204 @ X205) @ (sub @ X206 @ X205)))) | ~ ! [X207 : term] : (~ ($true = ((X201 @ id @ X207 @ id))) | ($true = ((X201 @ id @ (X203 @ id @ X207) @ id))))) | ($true = ((X200 @ (lam @ X199)))) | ~ ! [X208 : term] : (((X200 @ X208)) = ((X201 @ id @ X208 @ id)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X209 : term,X210 : term,X211 : term,X212 : term] : ((X209 = X211) | (((ap @ X211 @ X210)) != ((ap @ X209 @ X212))))) & ((laminj = $true) <=> ! [X213 : term,X214 : term] : ((((lam @ X214)) != ((lam @ X213))) | (X213 = X214))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (! [X215 : subst,X216 : (term > $o),X217 : (term > $o),X218 : term,X219 : term] : (~ ($true = ((X217 @ X219))) | (((X216 @ (sub @ X219 @ (push @ X218 @ X215)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((! [X220 : term] : (((sub @ X220 @ id)) = X220) => (! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X221 = X222) | (((ap @ X222 @ X223)) != ((ap @ X221 @ X224)))) => ! [X225 : term,X226 : term,X227 : term,X228 : term] : ((((ap @ (sub @ X227 @ id) @ X226)) != ((ap @ (sub @ X228 @ id) @ X225))) | (X227 = X228)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (! [X229 : (subst > term > subst > $o),X230 : term] : (~ ! [X231 : (subst > term > term)] : (($true = ((X229 @ id @ (lam @ (X231 @ sh @ one)) @ id))) | ~ ! [X232 : subst,X233 : subst,X234 : term] : (((sub @ (X231 @ X232 @ X234) @ X233)) = ((X231 @ (comp @ X232 @ X233) @ (sub @ X234 @ X233)))) | ~ ! [X235 : term] : (($true = ((X229 @ id @ (X231 @ id @ X235) @ id))) | ~ ($true = ((X229 @ id @ X235 @ id))))) | ($true = ((X229 @ id @ (lam @ (sub @ X230 @ (push @ one @ sh))) @ id))) | ~ ! [X236 : term] : (~ ($true = ((X229 @ id @ X236 @ id))) | ($true = ((X229 @ id @ (sub @ X230 @ (push @ X236 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X237 : (subst > term > subst > $o),X238 : term] : (($true = ((X237 @ id @ (lam @ X238) @ id))) | ~ ! [X239 : (subst > term > term)] : (~ ! [X240 : term] : ((((X237 @ id @ (X239 @ id @ X240) @ id)) = $true) | ~ ($true = ((X237 @ id @ X240 @ id)))) | ($true = ((X237 @ id @ (lam @ (X239 @ sh @ one)) @ id))) | ~ ! [X241 : term,X242 : subst,X243 : subst] : (((X239 @ (comp @ X242 @ X243) @ (sub @ X241 @ X243))) = ((sub @ (X239 @ X242 @ X241) @ X243)))) | ~ ! [X244 : term] : (~ ($true = ((X237 @ id @ X244 @ id))) | ($true = ((X237 @ id @ (sub @ X238 @ (push @ X244 @ id)) @ id)))))) & ((! [X245 : term] : (((sub @ X245 @ id)) = X245) => ! [X246 : (subst > term > subst > $o),X247 : (term > $o),X248 : term] : (~ ! [X249 : (subst > term > term)] : (~ ! [X250 : subst,X251 : term,X252 : subst] : (((sub @ (X249 @ X252 @ X251) @ X250)) = ((X249 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250)))) | ~ ! [X253 : term] : (($true = ((X246 @ id @ (X249 @ id @ X253) @ id))) | ~ ($true = ((X246 @ id @ X253 @ id)))) | ($true = ((X246 @ id @ (lam @ (X249 @ sh @ one)) @ id)))) | ~ ! [X254 : subst,X255 : term,X256 : subst,X257 : subst] : (($true = ((X246 @ (comp @ X257 @ X254) @ (sub @ X255 @ X254) @ X256))) | ~ ($true = ((X246 @ X257 @ X255 @ (comp @ X254 @ X256))))) | ($true = ((X247 @ (lam @ X248)))) | ~ ! [X258 : term] : (((X246 @ id @ X258 @ id)) = ((X247 @ X258))) | ~ ! [X259 : subst,X260 : subst,X261 : subst,X262 : term] : (($true = ((X246 @ X260 @ X262 @ (comp @ X261 @ X259)))) | ~ ($true = ((X246 @ (comp @ X260 @ X261) @ (sub @ X262 @ X261) @ X259)))) | ~ ! [X263 : term] : (($true = ((X247 @ (sub @ X248 @ (push @ X263 @ id))))) | ~ ($true = ((X247 @ X263)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (termmset_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X264 : (term > $o),X265 : term] : (($true = ((X264 @ X265))) | ~ ! [X266 : term,X267 : term] : (~ ($true = ((X264 @ X267))) | (((X264 @ (ap @ X267 @ X266))) = $true) | ~ ($true = ((X264 @ X266)))) | ~ ! [X268 : term] : (($true = ((X264 @ (lam @ X268)))) | ~ ! [X269 : term] : (~ ($true = ((X264 @ X269))) | (((X264 @ (sub @ X268 @ (push @ X269 @ id)))) = $true))) | ~ ! [X270 : term] : ((((X264 @ X270)) = $true) | ~ ($true = ((var @ X270))))) => (! [X271 : term,X272 : term,X273 : (subst > term > subst > $o)] : (~ ($true = ((X273 @ id @ X271 @ id))) | ~ ! [X274 : term,X275 : term] : (~ ($true = ((X273 @ id @ X275 @ id))) | ~ ($true = ((X273 @ id @ X274 @ id))) | (((X273 @ id @ (ap @ (sub @ X274 @ id) @ X275) @ id)) = $true)) | ($true = ((X273 @ id @ (ap @ X271 @ X272) @ id))) | ~ ! [X276 : subst,X277 : subst,X278 : term,X279 : subst] : (($true = ((X273 @ (comp @ X277 @ X279) @ (sub @ X278 @ X279) @ X276))) | ~ ($true = ((X273 @ X277 @ X278 @ (comp @ X279 @ X276))))) | ~ (((X273 @ id @ X272 @ id)) = $true) | ~ ! [X280 : term,X281 : subst,X282 : subst,X283 : subst] : (~ ($true = ((X273 @ (comp @ X282 @ X283) @ (sub @ X280 @ X283) @ X281))) | ($true = ((X273 @ X282 @ X280 @ (comp @ X283 @ X281)))))) => (! [X284 : (subst > term > subst > $o),X285 : term] : (~ ! [X286 : term] : (($true = ((X284 @ id @ (sub @ X285 @ (push @ X286 @ id)) @ id))) | ~ ($true = ((X284 @ id @ X286 @ id)))) | ~ ! [X287 : (subst > term > term)] : (($true = ((X284 @ id @ (lam @ (X287 @ sh @ one)) @ id))) | ~ ! [X288 : term] : (~ ($true = ((X284 @ id @ X288 @ id))) | ($true = ((X284 @ id @ (X287 @ id @ X288) @ id)))) | ~ ! [X289 : subst,X290 : term,X291 : subst] : (((sub @ (X287 @ X291 @ X290) @ X289)) = ((X287 @ (comp @ X291 @ X289) @ (sub @ X290 @ X289))))) | ~ ! [X292 : subst,X293 : term,X294 : subst,X295 : subst] : (~ ($true = ((X284 @ (comp @ X294 @ X295) @ (sub @ X293 @ X295) @ X292))) | ($true = ((X284 @ X294 @ X293 @ (comp @ X295 @ X292))))) | ($true = ((X284 @ id @ (lam @ X285) @ id))) | ~ ! [X296 : subst,X297 : subst,X298 : subst,X299 : term] : (~ ($true = ((X284 @ X298 @ X299 @ (comp @ X297 @ X296)))) | ($true = ((X284 @ (comp @ X298 @ X297) @ (sub @ X299 @ X297) @ X296))))) => ! [X300 : term,X301 : (subst > term > subst > $o)] : (~ ! [X302 : term] : ((((X301 @ id @ X302 @ id)) = $true) | ~ ($true = ((var @ (sub @ X302 @ id))))) | ~ ! [X303 : subst,X304 : subst,X305 : term,X306 : subst] : (($true = ((X301 @ (comp @ X303 @ X306) @ (sub @ X305 @ X306) @ X304))) | ~ ($true = ((X301 @ X303 @ X305 @ (comp @ X306 @ X304))))) | ~ ! [X307 : subst,X308 : term,X309 : subst,X310 : subst] : (~ (((X301 @ (comp @ X309 @ X307) @ (sub @ X308 @ X307) @ X310)) = $true) | ($true = ((X301 @ X309 @ X308 @ (comp @ X307 @ X310))))) | ~ ! [X311 : (subst > term > term)] : (~ ! [X312 : term] : (~ ($true = ((X301 @ id @ X312 @ id))) | ($true = ((X301 @ id @ (X311 @ id @ X312) @ id)))) | ~ ! [X313 : subst,X314 : term,X315 : subst] : (((sub @ (X311 @ X313 @ X314) @ X315)) = ((X311 @ (comp @ X313 @ X315) @ (sub @ X314 @ X315)))) | ($true = ((X301 @ id @ (lam @ (X311 @ sh @ one)) @ id)))) | ($true = ((X301 @ id @ X300 @ id))) | ~ ! [X316 : term,X317 : term] : (~ ($true = ((X301 @ id @ X317 @ id))) | ($true = ((X301 @ id @ (ap @ (sub @ X317 @ id) @ X316) @ id))) | ~ ($true = ((X301 @ id @ X316 @ id))))))))) & ((hoaslaminj = $true) <=> ! [X318 : subst,X319 : (subst > term > term),X320 : (subst > term > term),X321 : term] : ((((lam @ (X319 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | ~ ! [X322 : subst,X323 : term,X324 : subst] : (((sub @ (X319 @ X322 @ X323) @ X324)) = ((X319 @ (comp @ X322 @ X324) @ (sub @ X323 @ X324)))) | ~ ! [X325 : term,X326 : subst,X327 : subst] : (((sub @ (X320 @ X327 @ X325) @ X326)) = ((X320 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)))) | (((X319 @ X318 @ X321)) = ((X320 @ X318 @ X321))))) & (! [X328 : term,X329 : term] : ((X328 = X329) | (((sub @ X329 @ sh)) != ((sub @ X328 @ sh)))) <=> (shinj = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X330 : (subst > term > subst > $o),X331 : term] : (~ ! [X332 : (subst > term > term),X333 : term] : (($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ~ ! [X334 : term,X335 : subst,X336 : subst] : (((X332 @ (comp @ X335 @ X336) @ (sub @ X334 @ X336))) = ((sub @ X333 @ (push @ (sub @ X334 @ X336) @ (comp @ X335 @ X336))))) | ~ ! [X337 : term] : (($true = ((X330 @ id @ (X332 @ id @ X337) @ id))) | ~ (((X330 @ id @ X337 @ id)) = $true)) | ~ ! [X338 : subst,X339 : subst,X340 : term] : (((sub @ (X332 @ X339 @ X340) @ X338)) = ((sub @ (sub @ X333 @ (push @ X340 @ X339)) @ X338)))) | ~ ! [X341 : term] : (($true = ((X330 @ id @ (sub @ X331 @ (push @ X341 @ id)) @ id))) | ~ ($true = ((X330 @ id @ X341 @ id)))) | ($true = ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X342 : term] : (((sub @ X342 @ id)) = X342) => (! [X343 : term,X344 : (subst > term > subst > $o)] : (($true = ((X344 @ id @ (lam @ (sub @ X343 @ (push @ one @ sh))) @ id))) | ~ ! [X345 : term] : (($true = ((X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id))) | ~ ($true = ((X344 @ id @ X345 @ id)))) | ~ ! [X346 : (subst > term > term)] : (~ ! [X347 : term] : (~ ($true = ((X344 @ id @ X347 @ id))) | ($true = ((X344 @ id @ (X346 @ id @ X347) @ id)))) | ($true = ((X344 @ id @ (lam @ (X346 @ sh @ one)) @ id))) | ~ ! [X348 : subst,X349 : term,X350 : subst] : (((X346 @ (comp @ X348 @ X350) @ (sub @ X349 @ X350))) = ((sub @ (X346 @ X348 @ X349) @ X350))))) => ! [X351 : (subst > term > subst > $o),X352 : term] : (~ ! [X353 : (subst > term > term)] : (($true = ((X351 @ id @ (lam @ (X353 @ sh @ one)) @ id))) | ~ ! [X354 : term] : (~ ($true = ((X351 @ id @ X354 @ id))) | (((X351 @ id @ (X353 @ id @ X354) @ id)) = $true)) | ~ ! [X355 : subst,X356 : subst,X357 : term] : (((X353 @ (comp @ X356 @ X355) @ (sub @ X357 @ X355))) = ((sub @ (X353 @ X356 @ X357) @ X355)))) | ($true = ((X351 @ id @ (lam @ X352) @ id))) | ~ ! [X358 : term] : (($true = ((X351 @ id @ (sub @ X352 @ (push @ X358 @ id)) @ id))) | ~ ($true = ((X351 @ id @ X358 @ id)))))))) & ~ (ulamvar1 = $true) & (apnotvar = $true) & (axapp = $true) & (ulamvarind = $true) & (! [X359 : term] : (((sub @ X359 @ id)) = X359) <=> (termmset = $true)) & (! [X360 : term,X361 : (subst > term > term),X362 : term] : ((((lam @ (X361 @ sh @ one))) != ((ap @ (sub @ X360 @ id) @ X362))) | ~ ! [X363 : term,X364 : subst,X365 : subst] : (((X361 @ (comp @ X365 @ X364) @ (sub @ X363 @ X364))) = ((sub @ (X361 @ X365 @ X363) @ X364)))) <=> (hoaslamnotap = $true)) & ((axshiftcons = $true) <=> ! [X366 : term,X367 : subst] : (((comp @ sh @ (push @ X366 @ X367))) = X367)) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X368 : d_subst,X369 : d_subst] : ((((d2subst @ X369)) = ((d2subst @ X368))) => (X368 = X369)) & ((axidl = $true) <=> ! [X370 : subst] : (((comp @ id @ X370)) = X370)) & ! [X371 : d_term] : (d_one = X371) & (! [X372 : term,X373 : term,X374 : (subst > term > subst > $o)] : (~ ! [X375 : term,X376 : term] : (~ ($true = ((X374 @ id @ X376 @ id))) | ($true = ((X374 @ id @ (ap @ (sub @ X376 @ id) @ X375) @ id))) | ~ ($true = ((X374 @ id @ X375 @ id)))) | ~ ! [X377 : subst,X378 : subst,X379 : subst,X380 : term] : (~ ($true = ((X374 @ X378 @ X380 @ (comp @ X379 @ X377)))) | ($true = ((X374 @ (comp @ X378 @ X379) @ (sub @ X380 @ X379) @ X377)))) | ~ ! [X381 : subst,X382 : subst,X383 : subst,X384 : term] : (($true = ((X374 @ X382 @ X384 @ (comp @ X383 @ X381)))) | ~ (((X374 @ (comp @ X382 @ X383) @ (sub @ X384 @ X383) @ X381)) = $true)) | ($true = ((X374 @ id @ (ap @ X372 @ X373) @ id))) | ~ ($true = ((X374 @ id @ X372 @ id))) | ~ (((X374 @ id @ X373 @ id)) = $true)) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X385 : term] : ? [X386 : d_term] : (((d2term @ X386)) = X385) & (! [X387 : term,X388 : (subst > term > subst > $o)] : (~ ! [X389 : (subst > term > term)] : (($true = ((X388 @ id @ (lam @ (X389 @ sh @ one)) @ id))) | ~ ! [X390 : term] : (($true = ((X388 @ id @ (X389 @ id @ X390) @ id))) | ~ ($true = ((X388 @ id @ X390 @ id)))) | ~ ! [X391 : subst,X392 : term,X393 : subst] : (((X389 @ (comp @ X391 @ X393) @ (sub @ X392 @ X393))) = ((sub @ (X389 @ X391 @ X392) @ X393)))) | ($true = ((X388 @ id @ (lam @ (sub @ X387 @ (push @ one @ sh))) @ id))) | ~ ! [X394 : term] : (($true = ((X388 @ id @ (sub @ X387 @ (push @ X394 @ id)) @ id))) | ~ ($true = ((X388 @ id @ X394 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop = $true) & (axmap = $true) & (hoasinduction_lem1v2 = $true) & (hoasapinj1_gthm = $true) & ((! [X395 : subst] : (((comp @ id @ X395)) = X395) => (! [X396 : subst] : (((comp @ X396 @ id)) = X396) => (! [X397 : subst] : (((comp @ id @ X397)) = X397) & ! [X398 : subst] : (((comp @ X398 @ id)) = X398)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X399 : term,X400 : subst] : (((sub @ one @ (push @ X399 @ X400))) = X399) => (! [X401 : subst,X402 : term] : (((comp @ sh @ (push @ X402 @ X401))) = X401) => ! [X403 : term,X404 : (term > $o),X405 : subst,X406 : term,X407 : (term > $o)] : (~ ($true = ((X404 @ X403))) | ($true = ((X407 @ (sub @ X403 @ (push @ X406 @ X405))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3 = $true) <=> ! [X408 : (subst > term > subst > $o),X409 : term] : (~ ! [X410 : term] : (~ ($true = ((X408 @ id @ X410 @ id))) | ($true = ((X408 @ id @ (sub @ X409 @ (push @ X410 @ id)) @ id)))) | ~ ! [X411 : subst,X412 : term,X413 : subst,X414 : subst] : (($true = ((X408 @ X413 @ X412 @ (comp @ X414 @ X411)))) | ~ ($true = ((X408 @ (comp @ X413 @ X414) @ (sub @ X412 @ X414) @ X411)))) | ~ ! [X415 : (subst > term > term)] : (~ ! [X416 : term,X417 : subst,X418 : subst] : (((sub @ (X415 @ X417 @ X416) @ X418)) = ((X415 @ (comp @ X417 @ X418) @ (sub @ X416 @ X418)))) | ($true = ((X408 @ id @ (lam @ (X415 @ sh @ one)) @ id))) | ~ ! [X419 : term] : ((((X408 @ id @ (X415 @ id @ X419) @ id)) = $true) | ~ (((X408 @ id @ X419 @ id)) = $true))) | ~ ! [X420 : subst,X421 : term,X422 : subst,X423 : subst] : (($true = ((X408 @ (comp @ X423 @ X422) @ (sub @ X421 @ X422) @ X420))) | ~ ($true = ((X408 @ X423 @ X421 @ (comp @ X422 @ X420))))) | ($true = ((X408 @ id @ (lam @ X409) @ id))))) & ((! [X424 : (subst > term > subst > $o)] : ~ ! [X425 : (term > $o)] : ~ ! [X426 : term] : (((X425 @ X426)) = ((X424 @ id @ X426 @ id))) => (! [X427 : (term > $o),X428 : term] : (~ ! [X429 : term] : (~ ! [X430 : term] : (($true = ((X427 @ (sub @ X429 @ (push @ X430 @ id))))) | ~ ($true = ((X427 @ X430)))) | ($true = ((X427 @ (lam @ X429))))) | ~ ! [X431 : term,X432 : term] : (~ ($true = ((X427 @ X431))) | ($true = ((X427 @ (ap @ X431 @ X432)))) | ~ ($true = ((X427 @ X432)))) | ~ ! [X433 : term] : (~ ($true = ((var @ X433))) | ($true = ((X427 @ X433)))) | (((X427 @ X428)) = $true)) => (! [X434 : term] : (((sub @ X434 @ id)) = X434) => (! [X435 : (subst > term > subst > $o),X436 : (term > $o),X437 : term] : (($true = ((X436 @ (lam @ X437)))) | ~ ! [X438 : (subst > term > term)] : (~ ! [X439 : subst,X440 : term,X441 : subst] : (((sub @ (X438 @ X439 @ X440) @ X441)) = ((X438 @ (comp @ X439 @ X441) @ (sub @ X440 @ X441)))) | ($true = ((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id))) | ~ ! [X442 : term] : (~ ($true = ((X435 @ id @ X442 @ id))) | ($true = ((X435 @ id @ (X438 @ id @ X442) @ id))))) | ~ ! [X443 : term] : (((X436 @ X443)) = ((X435 @ id @ X443 @ id))) | ~ ! [X444 : term] : (~ ($true = ((X436 @ X444))) | ($true = ((X436 @ (sub @ X437 @ (push @ X444 @ id))))))) => ! [X445 : (subst > term > subst > $o),X446 : term] : (~ ! [X447 : term,X448 : term] : (($true = ((X445 @ id @ (ap @ (sub @ X447 @ id) @ X448) @ id))) | ~ ($true = ((X445 @ id @ X448 @ id))) | ~ ($true = ((X445 @ id @ X447 @ id)))) | ($true = ((X445 @ id @ X446 @ id))) | ~ ! [X449 : (subst > term > term)] : (~ ! [X450 : term,X451 : subst,X452 : subst] : (((X449 @ (comp @ X452 @ X451) @ (sub @ X450 @ X451))) = ((sub @ (X449 @ X452 @ X450) @ X451))) | ($true = ((X445 @ id @ (lam @ (X449 @ sh @ one)) @ id))) | ~ ! [X453 : term] : (~ ($true = ((X445 @ id @ X453 @ id))) | ($true = ((X445 @ id @ (X449 @ id @ X453) @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasapinj2 = $true) <=> ! [X454 : term,X455 : term,X456 : term,X457 : term] : ((X454 = X457) | (((ap @ (sub @ X456 @ id) @ X454)) != ((ap @ (sub @ X455 @ id) @ X457))))) & (! [X458 : term,X459 : (subst > term > subst > $o),X460 : (term > $o)] : (~ ! [X461 : (subst > term > term)] : (($true = ((X459 @ id @ (lam @ (X461 @ sh @ one)) @ id))) | ~ ! [X462 : term] : (($true = ((X459 @ id @ (X461 @ id @ X462) @ id))) | ~ ($true = ((X459 @ id @ X462 @ id)))) | ~ ! [X463 : term,X464 : subst,X465 : subst] : (((X461 @ (comp @ X464 @ X465) @ (sub @ X463 @ X465))) = ((sub @ (X461 @ X464 @ X463) @ X465)))) | ($true = ((X460 @ (lam @ X458)))) | ~ ! [X466 : term] : (($true = ((X460 @ (sub @ X458 @ (push @ X466 @ id))))) | ~ ($true = ((X460 @ X466)))) | ~ ! [X467 : term] : (((X459 @ id @ X467 @ id)) = ((X460 @ X467)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasapnotvar_lthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ~ (lamnotap = $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)))))))))))))) & ((apinj2 = $true) <=> ! [X473 : term,X474 : term,X475 : term,X476 : term] : ((((ap @ X474 @ X475)) != ((ap @ X473 @ X476))) | (X475 = X476))) & (axvarshift = $true) & ((pushprop_lem1v2 = $true) <=> ! [X477 : (term > $o),X478 : subst,X479 : (term > $o),X480 : term] : (~ ($true = ((X479 @ X480))) | (((X477 @ one)) = $true) | ~ ! [X481 : term] : (((X479 @ (sub @ X481 @ (push @ X480 @ X478)))) = ((X477 @ X481))))) & (! [X482 : term,X483 : (subst > term > subst > $o)] : (~ ! [X484 : term,X485 : subst,X486 : subst,X487 : subst] : (($true = ((X483 @ X487 @ X484 @ (comp @ X485 @ X486)))) | ~ ($true = ((X483 @ (comp @ X487 @ X485) @ (sub @ X484 @ X485) @ X486)))) | ~ ! [X488 : subst,X489 : term,X490 : subst,X491 : subst] : (~ ($true = ((X483 @ X490 @ X489 @ (comp @ X488 @ X491)))) | ($true = ((X483 @ (comp @ X490 @ X488) @ (sub @ X489 @ X488) @ X491)))) | ~ ! [X492 : (subst > term > term)] : (($true = ((X483 @ id @ (lam @ (X492 @ sh @ one)) @ id))) | ~ ! [X493 : term] : (~ ($true = ((X483 @ id @ X493 @ id))) | ($true = ((X483 @ id @ (X492 @ id @ X493) @ id)))) | ~ ! [X494 : subst,X495 : subst,X496 : term] : (((X492 @ (comp @ X495 @ X494) @ (sub @ X496 @ X494))) = ((sub @ (X492 @ X495 @ X496) @ X494)))) | ~ ! [X497 : term,X498 : term] : (~ ($true = ((X483 @ id @ X497 @ id))) | ~ (((X483 @ id @ X498 @ id)) = $true) | ($true = ((X483 @ id @ (ap @ (sub @ X497 @ id) @ X498) @ id)))) | ($true = ((X483 @ id @ X482 @ id))) | ~ ! [X499 : term] : (~ ($true = ((var @ (sub @ X499 @ id)))) | (((X483 @ id @ X499 @ id)) = $true))) <=> (hoasinduction = $true)) & (((d2subst @ d_id)) = id) & ! [X500 : d_subst] : (d_id = X500) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X501 : (subst > term > subst > $o)] : ~ ! [X502 : (term > $o)] : ~ ! [X503 : term] : (((X502 @ X503)) = ((X501 @ id @ X503 @ id))) => (! [X504 : term,X505 : (term > $o)] : (~ ! [X506 : term] : (($true = ((X505 @ X506))) | ~ ($true = ((var @ X506)))) | (((X505 @ X504)) = $true) | ~ ! [X507 : term] : (~ ! [X508 : term] : (~ ($true = ((X505 @ X508))) | ($true = ((X505 @ (sub @ X507 @ (push @ X508 @ id)))))) | ($true = ((X505 @ (lam @ X507))))) | ~ ! [X509 : term,X510 : term] : (~ ($true = ((X505 @ X510))) | ~ ($true = ((X505 @ X509))) | ($true = ((X505 @ (ap @ X510 @ X509)))))) => (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : (subst > term > subst > $o),X513 : term,X514 : (term > $o)] : (~ ! [X515 : term] : (((X512 @ id @ X515 @ id)) = ((X514 @ X515))) | ~ ! [X516 : term] : (~ ($true = ((X514 @ X516))) | ($true = ((X514 @ (sub @ X513 @ (push @ X516 @ id)))))) | ~ ! [X517 : (subst > term > term)] : (($true = ((X512 @ id @ (lam @ (X517 @ sh @ one)) @ id))) | ~ ! [X518 : term] : (~ ($true = ((X512 @ id @ X518 @ id))) | ($true = ((X512 @ id @ (X517 @ id @ X518) @ id)))) | ~ ! [X519 : subst,X520 : subst,X521 : term] : (((sub @ (X517 @ X519 @ X521) @ X520)) = ((X517 @ (comp @ X519 @ X520) @ (sub @ X521 @ X520))))) | ($true = ((X514 @ (lam @ X513))))) => ! [X522 : (subst > term > subst > $o),X523 : term] : (~ ! [X524 : (subst > term > term)] : (~ ! [X525 : term] : (($true = ((X522 @ id @ (X524 @ id @ X525) @ id))) | ~ ($true = ((X522 @ id @ X525 @ id)))) | ~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X524 @ X527 @ X526) @ X528)) = ((X524 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528)))) | ($true = ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id)))) | ~ ! [X529 : term,X530 : subst,X531 : subst,X532 : subst] : (~ ($true = ((X522 @ X530 @ X529 @ (comp @ X532 @ X531)))) | ($true = ((X522 @ (comp @ X530 @ X532) @ (sub @ X529 @ X532) @ X531)))) | (((X522 @ id @ X523 @ id)) = $true) | ~ ! [X533 : term,X534 : term] : (($true = ((X522 @ id @ (ap @ (sub @ X534 @ id) @ X533) @ id))) | ~ ($true = ((X522 @ id @ X533 @ id))) | ~ ($true = ((X522 @ id @ X534 @ id)))) | ~ ! [X535 : term] : (~ ($true = ((var @ (sub @ X535 @ id)))) | ($true = ((X522 @ id @ X535 @ id)))) | ~ ! [X536 : subst,X537 : subst,X538 : subst,X539 : term] : (($true = ((X522 @ X538 @ X539 @ (comp @ X537 @ X536)))) | ~ ($true = ((X522 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537) @ X536)))))))))) & (! [X540 : term] : ~ ! [X541 : (subst > term > term)] : ~ ! [X542 : term,X543 : subst] : (((X541 @ X543 @ X542)) = ((sub @ X540 @ (push @ X542 @ X543)))) <=> (hoasinduction_lem3v2_f = $true)) & ! [X544 : d_term,X545 : d_term] : ((((d2term @ X545)) = ((d2term @ X544))) => (X544 = X545)) & (hoasinduction_gthm = $true) & (pushprop_lem0_gthm = $true) & (! [X546 : (subst > term > subst > $o)] : ~ ! [X547 : (term > $o)] : ~ ! [X548 : term] : (((X546 @ id @ X548 @ id)) = ((X547 @ X548))) <=> (hoasinduction_lem0_lthm = $true)) & (one = ((d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) <=> ! [X549 : subst] : (((comp @ X549 @ id)) = X549))),
% 5.11/1.35 inference(fool_elimination,[],[f6])).
% 5.11/1.35 thf(f8,plain,(
% 5.11/1.35 (pushprop_lem1v2 != ((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => ((pushprop_p_and_p_prime @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))))))),
% 5.11/1.35 inference(flattening,[],[f5])).
% 5.11/1.35 thf(f9,plain,(
% 5.11/1.35 (axclos = $true) & (lamnotvar = $true) & (pushprop_lem2v2_gthm = $true) & (! [X0 : term,X1 : (term > $o)] : (($true = ((X1 @ X0))) | ~ ! [X2 : term,X3 : term] : (($true = ((X1 @ (ap @ X3 @ X2)))) | ~ ($true = ((X1 @ X3))) | ~ ($true = ((X1 @ X2)))) | ~ ! [X4 : term] : ((((X1 @ X4)) = $true) | ~ ($true = ((var @ X4)))) | ~ ! [X5 : term] : (($true = ((X1 @ (lam @ X5)))) | ~ (((X1 @ X5)) = $true))) <=> (induction = $true)) & ((! [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) = X7) => ! [X8 : term,X9 : (term > $o),X10 : subst,X11 : (term > $o)] : ((((X9 @ one)) = $true) | ~ ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))) | ~ ($true = ((X11 @ X8))))) <=> (pushprop_lem1v2_lthm = $true)) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & (hoaslamnotap_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem0 = $true) <=> ! [X19 : (term > $o),X18 : subst,X17 : term] : ~ ! [X20 : (term > $o)] : ~ ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21)))) & (induction2lem_gthm = $true) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X22 : term] : ~ ! [X23 : (subst > term > term)] : ~ ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25)))) & (hoaslaminj_gthm = $true) & (! [X26 : subst,X27 : (term > $o),X28 : term] : (~ ! [X29 : term,X30 : term] : (~ ($true = ((X27 @ X29))) | ($true = ((X27 @ (ap @ X30 @ X29)))) | ~ ($true = ((X27 @ X30)))) | ~ ! [X31 : term] : ((((X27 @ (lam @ X31))) = $true) | ~ ! [X32 : term] : (($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id))))) | ~ ($true = ((X27 @ X32))))) | ~ ! [X33 : term] : (($true = ((X27 @ (sub @ X33 @ X26)))) | ~ ($true = ((var @ X33)))) | ($true = ((X27 @ (sub @ X28 @ X26))))) <=> (induction2lem = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X34 : term] : ~ ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & ((! [X41 : term,X39 : term,X40 : term,X38 : term] : ((((ap @ X38 @ X41)) != ((ap @ X40 @ X39))) | (X39 = X41)) => ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X47 : (subst > term > subst > $o),X48 : term] : (~ ! [X49 : (subst > term > term)] : (~ ! [X51 : subst,X52 : subst,X50 : term] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) = ((sub @ (X49 @ X52 @ X50) @ X51))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id))) | ~ ! [X53 : term] : (($true = ((X47 @ id @ (X49 @ id @ X53) @ id))) | ~ ($true = ((X47 @ id @ X53 @ id))))) | ($true = ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id))) | ~ ! [X54 : term] : (~ ($true = ((X47 @ id @ X54 @ id))) | ($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))))) => ! [X55 : (subst > term > subst > $o),X56 : term] : (~ ! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (~ ($true = ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60))) | ($true = ((X55 @ X59 @ X58 @ (comp @ X57 @ X60))))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ~ ! [X61 : term] : (~ ($true = ((X55 @ id @ X61 @ id))) | ($true = ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)))) | ~ ! [X62 : (subst > term > term)] : (~ ! [X63 : term] : (~ ($true = ((X55 @ id @ X63 @ id))) | ($true = ((X55 @ id @ (X62 @ id @ X63) @ id)))) | (((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true) | ~ ! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66))))) | ~ ! [X67 : subst,X68 : term,X69 : subst,X70 : subst] : (~ ($true = ((X55 @ X67 @ X68 @ (comp @ X69 @ X70)))) | ($true = ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))))))) & (pushprop_lem1_gthm = $true) & (! [X71 : (subst > term > subst > $o)] : ~ ! [X72 : (term > $o)] : ~ ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & (substmonoid_gthm = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (hoaslamnotvar_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (axabs = $true) & (pushprop_gthm = $true) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ((! [X77 : term] : (((sub @ X77 @ id)) = X77) => (! [X78 : (term > $o),X79 : subst,X80 : term] : (~ ! [X81 : term] : (~ ! [X82 : term] : (~ ($true = ((X78 @ X82))) | ($true = ((X78 @ (sub @ X81 @ (push @ X82 @ id)))))) | ($true = ((X78 @ (lam @ X81))))) | ($true = ((X78 @ (sub @ X80 @ X79)))) | ~ ! [X83 : term] : (($true = ((X78 @ (sub @ X83 @ X79)))) | ~ ($true = ((var @ X83)))) | ~ ! [X84 : term,X85 : term] : (~ ($true = ((X78 @ X84))) | ~ ($true = ((X78 @ X85))) | (((X78 @ (ap @ X84 @ X85))) = $true))) => ! [X86 : term,X87 : (term > $o)] : ((((X87 @ X86)) = $true) | ~ ! [X88 : term] : (~ ! [X89 : term] : (~ ($true = ((X87 @ X89))) | ($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id)))))) | ($true = ((X87 @ (lam @ X88))))) | ~ ! [X90 : term,X91 : term] : (($true = ((X87 @ (ap @ X91 @ X90)))) | ~ ($true = ((X87 @ X90))) | ~ ($true = ((X87 @ X91)))) | ~ ! [X92 : term] : (~ (((var @ X92)) = $true) | ($true = ((X87 @ X92))))))) <=> (induction2_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term] : (((sub @ X94 @ id)) = X94))) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoasinduction_lem1 = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2 = $true) & ((! [X96 : term,X95 : subst] : (((sub @ one @ (push @ X96 @ X95))) = X96) => (! [X98 : subst,X97 : term] : (((comp @ sh @ (push @ X97 @ X98))) = X98) => (! [X100 : term,X99 : term] : ((((lam @ X99)) != ((lam @ X100))) | (X99 = X100)) => ! [X101 : subst,X104 : term,X103 : (subst > term > term),X102 : (subst > term > term)] : (~ ! [X110 : subst,X109 : subst,X108 : term] : (((X102 @ (comp @ X109 @ X110) @ (sub @ X108 @ X110))) = ((sub @ (X102 @ X109 @ X108) @ X110))) | ~ ! [X106 : subst,X105 : subst,X107 : term] : (((X103 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) = ((sub @ (X103 @ X105 @ X107) @ X106))) | (((X103 @ X101 @ X104)) = ((X102 @ X101 @ X104))) | (((lam @ (X102 @ sh @ one))) != ((lam @ (X103 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (hoaslamnotap_gthm = $true) & (! [X112 : (term > $o),X111 : term,X113 : subst] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) <=> (pushprop_lem0_lthm = $true)) & ((axvarcons = $true) <=> ! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117)) & (hoasapnotvar_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X118 : term,X119 : (term > $o),X120 : (subst > term > subst > $o)] : (~ ! [X121 : (subst > term > term)] : (($true = ((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id))) | ~ ! [X123 : subst,X124 : term,X122 : subst] : (((X121 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) = ((sub @ (X121 @ X122 @ X124) @ X123))) | ~ ! [X125 : term] : (~ ($true = ((X120 @ id @ X125 @ id))) | ($true = ((X120 @ id @ (X121 @ id @ X125) @ id))))) | ~ ! [X126 : subst,X127 : term,X128 : subst,X129 : subst] : (~ ($true = ((X120 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128) @ X129))) | ($true = ((X120 @ X126 @ X127 @ (comp @ X128 @ X129))))) | ~ ! [X130 : term] : (((X120 @ id @ X130 @ id)) = ((X119 @ X130))) | ~ ! [X131 : subst,X132 : subst,X133 : subst,X134 : term] : (~ (((X120 @ X132 @ X134 @ (comp @ X131 @ X133))) = $true) | ($true = ((X120 @ (comp @ X132 @ X131) @ (sub @ X134 @ X131) @ X133)))) | ~ ! [X135 : term] : (($true = ((X119 @ (sub @ X118 @ (push @ X135 @ id))))) | ~ ($true = ((X119 @ X135)))) | ($true = ((X119 @ (lam @ X118)))))) & (pushprop_lem3v2_lthm = $true) & (! [X136 : term,X137 : (subst > term > subst > $o)] : (~ ! [X138 : term,X139 : term] : (~ ($true = ((X137 @ id @ X138 @ id))) | ($true = ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id))) | ~ ($true = ((X137 @ id @ X139 @ id)))) | ~ ! [X140 : (subst > term > term)] : (~ ! [X143 : term,X142 : subst,X141 : subst] : (((sub @ (X140 @ X142 @ X143) @ X141)) = ((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141)))) | ~ ! [X144 : term] : (~ ($true = ((X137 @ id @ X144 @ id))) | ($true = ((X137 @ id @ (X140 @ id @ X144) @ id)))) | ($true = ((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)))) | ($true = ((X137 @ id @ X136 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem3v2 = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X145 : (term > $o),X146 : term] : (~ ! [X147 : term] : (($true = ((X145 @ (lam @ X147)))) | ~ ! [X148 : term] : (($true = ((X145 @ (sub @ X147 @ (push @ X148 @ id))))) | ~ ($true = ((X145 @ X148))))) | ($true = ((X145 @ X146))) | ~ ! [X149 : term,X150 : term] : (~ ($true = ((X145 @ X150))) | ($true = ((X145 @ (ap @ X150 @ X149)))) | ~ ($true = ((X145 @ X149)))) | ~ ! [X151 : term] : (($true = ((X145 @ X151))) | ~ ($true = ((var @ X151))))) <=> (induction2 = $true)) & (! [X152 : (term > $o),X153 : term,X154 : term,X155 : (subst > term > subst > $o)] : (~ ($true = ((X152 @ X154))) | ($true = ((X152 @ (ap @ X153 @ X154)))) | ~ ! [X156 : term,X157 : subst,X158 : subst,X159 : subst] : (~ ($true = ((X155 @ (comp @ X159 @ X157) @ (sub @ X156 @ X157) @ X158))) | ($true = ((X155 @ X159 @ X156 @ (comp @ X157 @ X158))))) | ~ ! [X160 : term,X161 : term] : (~ (((X155 @ id @ X161 @ id)) = $true) | ~ ($true = ((X155 @ id @ X160 @ id))) | ($true = ((X155 @ id @ (ap @ (sub @ X161 @ id) @ X160) @ id)))) | ~ ($true = ((X152 @ X153))) | ~ ! [X162 : subst,X163 : subst,X164 : subst,X165 : term] : (~ ($true = ((X155 @ X163 @ X165 @ (comp @ X162 @ X164)))) | ($true = ((X155 @ (comp @ X163 @ X162) @ (sub @ X165 @ X162) @ X164)))) | ~ ! [X166 : term] : (((X155 @ id @ X166 @ id)) = ((X152 @ X166)))) <=> (hoasinduction_lem2v2 = $true)) & (axassoc = $true) & ((induction2lem_lthm = $true) <=> (! [X168 : term,X167 : subst] : (((sub @ one @ (push @ X168 @ X167))) = X168) => (! [X169 : subst,X170 : term] : (((comp @ sh @ (push @ X170 @ X169))) = X169) => (! [X171 : subst] : (((comp @ X171 @ id)) = X171) => (! [X172 : term,X173 : (term > $o)] : (~ ! [X174 : term,X175 : term] : (~ ($true = ((X173 @ X175))) | ($true = ((X173 @ (ap @ X175 @ X174)))) | ~ ($true = ((X173 @ X174)))) | ~ ! [X176 : term] : (($true = ((X173 @ X176))) | ~ ($true = ((var @ X176)))) | ~ ! [X177 : term] : (($true = ((X173 @ (lam @ X177)))) | ~ ($true = ((X173 @ X177)))) | (((X173 @ X172)) = $true)) => ! [X178 : term,X179 : subst,X180 : (term > $o)] : (~ ! [X181 : term,X182 : term] : (($true = ((X180 @ (ap @ X182 @ X181)))) | ~ ($true = ((X180 @ X182))) | ~ ($true = ((X180 @ X181)))) | ~ ! [X183 : term] : (~ ($true = ((var @ X183))) | ($true = ((X180 @ (sub @ X183 @ X179))))) | ($true = ((X180 @ (sub @ X178 @ X179)))) | ~ ! [X184 : term] : (($true = ((X180 @ (lam @ X184)))) | ~ ! [X185 : term] : (~ ($true = ((X180 @ X185))) | ($true = ((X180 @ (sub @ X184 @ (push @ X185 @ id))))))))))))) & ((hoasinduction_lem3b = $true) <=> ! [X186 : term] : ~ ! [X187 : (subst > term > term)] : (((X187 @ sh @ one)) != ((sub @ X186 @ (push @ one @ sh))))) & ((axscons = $true) <=> ! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188)) & (hoasinduction_lem3a_gthm = $true) & ((! [X189 : term] : ~ ! [X190 : (subst > term > term)] : ~ ! [X191 : term,X192 : subst] : (((X190 @ X192 @ X191)) = ((sub @ X189 @ (push @ X191 @ X192)))) => (! [X193 : term] : (((sub @ X193 @ id)) = X193) => ! [X194 : term,X195 : (term > $o),X196 : (subst > term > subst > $o)] : (~ ! [X197 : term] : (($true = ((X195 @ (sub @ X194 @ (push @ X197 @ id))))) | ~ ($true = ((X195 @ X197)))) | ~ ! [X198 : (subst > term > term)] : (($true = ((X196 @ id @ (lam @ (X198 @ sh @ one)) @ id))) | ~ ! [X201 : term,X200 : subst,X199 : subst] : (((sub @ (X198 @ X199 @ X201) @ X200)) = ((X198 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200)))) | ~ ! [X202 : term] : (~ ($true = ((X196 @ id @ X202 @ id))) | ($true = ((X196 @ id @ (X198 @ id @ X202) @ id))))) | ($true = ((X195 @ (lam @ X194)))) | ~ ! [X203 : term] : (((X195 @ X203)) = ((X196 @ id @ X203 @ id)))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lthm = $true) & ((apinj1 = $true) <=> ! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205))))) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) <=> (laminj = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (! [X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term,X214 : term] : (~ ($true = ((X212 @ X214))) | ($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210)))))) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem3b_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X217 : term,X219 : term,X216 : term,X218 : term] : ((((ap @ X217 @ X218)) != ((ap @ X216 @ X219))) | (X216 = X217)) => ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (induction2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (pushprop_lthm_orig = $true) & (hoaslamnotvar = $true) & (! [X224 : (subst > term > subst > $o),X225 : term] : (~ ! [X226 : (subst > term > term)] : (($true = ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id))) | ~ ! [X228 : subst,X229 : term,X227 : subst] : (((X226 @ (comp @ X227 @ X228) @ (sub @ X229 @ X228))) = ((sub @ (X226 @ X227 @ X229) @ X228))) | ~ ! [X230 : term] : (($true = ((X224 @ id @ (X226 @ id @ X230) @ id))) | ~ ($true = ((X224 @ id @ X230 @ id))))) | ($true = ((X224 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id))) | ~ ! [X231 : term] : (~ ($true = ((X224 @ id @ X231 @ id))) | ($true = ((X224 @ id @ (sub @ X225 @ (push @ X231 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X232 : (subst > term > subst > $o),X233 : term] : (($true = ((X232 @ id @ (lam @ X233) @ id))) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (($true = ((X232 @ id @ (X234 @ id @ X235) @ id))) | ~ ($true = ((X232 @ id @ X235 @ id)))) | ($true = ((X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X237 : subst,X238 : subst,X236 : term] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ~ ! [X239 : term] : (~ ($true = ((X232 @ id @ X239 @ id))) | ($true = ((X232 @ id @ (sub @ X233 @ (push @ X239 @ id)) @ id)))))) & ((! [X240 : term] : (((sub @ X240 @ id)) = X240) => ! [X241 : (subst > term > subst > $o),X242 : (term > $o),X243 : term] : (~ ! [X244 : (subst > term > term)] : (~ ! [X247 : subst,X245 : subst,X246 : term] : (((sub @ (X244 @ X247 @ X246) @ X245)) = ((X244 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245)))) | ~ ! [X248 : term] : (($true = ((X241 @ id @ (X244 @ id @ X248) @ id))) | ~ ($true = ((X241 @ id @ X248 @ id)))) | ($true = ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id)))) | ~ ! [X249 : subst,X250 : term,X251 : subst,X252 : subst] : (($true = ((X241 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251))) | ~ ($true = ((X241 @ X252 @ X250 @ (comp @ X249 @ X251))))) | ($true = ((X242 @ (lam @ X243)))) | ~ ! [X253 : term] : (((X241 @ id @ X253 @ id)) = ((X242 @ X253))) | ~ ! [X254 : subst,X255 : subst,X256 : subst,X257 : term] : (($true = ((X241 @ X255 @ X257 @ (comp @ X256 @ X254)))) | ~ ($true = ((X241 @ (comp @ X255 @ X256) @ (sub @ X257 @ X256) @ X254)))) | ~ ! [X258 : term] : (($true = ((X242 @ (sub @ X243 @ (push @ X258 @ id))))) | ~ ($true = ((X242 @ X258)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (termmset_gthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X259 : (term > $o),X260 : term] : (($true = ((X259 @ X260))) | ~ ! [X261 : term,X262 : term] : (~ (((X259 @ X262)) = $true) | ($true = ((X259 @ (ap @ X262 @ X261)))) | ~ ($true = ((X259 @ X261)))) | ~ ! [X263 : term] : ((((X259 @ (lam @ X263))) = $true) | ~ ! [X264 : term] : (~ (((X259 @ X264)) = $true) | ($true = ((X259 @ (sub @ X263 @ (push @ X264 @ id))))))) | ~ ! [X265 : term] : (($true = ((X259 @ X265))) | ~ (((var @ X265)) = $true))) => (! [X266 : term,X267 : term,X268 : (subst > term > subst > $o)] : (~ ($true = ((X268 @ id @ X266 @ id))) | ~ ! [X269 : term,X270 : term] : (~ (((X268 @ id @ X270 @ id)) = $true) | ~ ($true = ((X268 @ id @ X269 @ id))) | ($true = ((X268 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)))) | ($true = ((X268 @ id @ (ap @ X266 @ X267) @ id))) | ~ ! [X271 : subst,X272 : subst,X273 : term,X274 : subst] : (($true = ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271))) | ~ ($true = ((X268 @ X272 @ X273 @ (comp @ X274 @ X271))))) | ~ ($true = ((X268 @ id @ X267 @ id))) | ~ ! [X275 : term,X276 : subst,X277 : subst,X278 : subst] : (~ (((X268 @ (comp @ X277 @ X278) @ (sub @ X275 @ X278) @ X276)) = $true) | ($true = ((X268 @ X277 @ X275 @ (comp @ X278 @ X276)))))) => (! [X279 : (subst > term > subst > $o),X280 : term] : (~ ! [X281 : term] : ((((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) = $true) | ~ ($true = ((X279 @ id @ X281 @ id)))) | ~ ! [X282 : (subst > term > term)] : (($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ~ ! [X283 : term] : (~ ($true = ((X279 @ id @ X283 @ id))) | (((X279 @ id @ (X282 @ id @ X283) @ id)) = $true)) | ~ ! [X286 : subst,X284 : subst,X285 : term] : (((X282 @ (comp @ X286 @ X284) @ (sub @ X285 @ X284))) = ((sub @ (X282 @ X286 @ X285) @ X284)))) | ~ ! [X287 : subst,X288 : term,X289 : subst,X290 : subst] : (~ ($true = ((X279 @ (comp @ X289 @ X290) @ (sub @ X288 @ X290) @ X287))) | ($true = ((X279 @ X289 @ X288 @ (comp @ X290 @ X287))))) | ($true = ((X279 @ id @ (lam @ X280) @ id))) | ~ ! [X291 : subst,X292 : subst,X293 : subst,X294 : term] : (~ ($true = ((X279 @ X293 @ X294 @ (comp @ X292 @ X291)))) | ($true = ((X279 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X291))))) => ! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X297 : term] : (($true = ((X296 @ id @ X297 @ id))) | ~ ($true = ((var @ (sub @ X297 @ id))))) | ~ ! [X298 : subst,X299 : subst,X300 : term,X301 : subst] : (($true = ((X296 @ (comp @ X298 @ X301) @ (sub @ X300 @ X301) @ X299))) | ~ ($true = ((X296 @ X298 @ X300 @ (comp @ X301 @ X299))))) | ~ ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~ ($true = ((X296 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302) @ X305))) | ($true = ((X296 @ X304 @ X303 @ (comp @ X302 @ X305))))) | ~ ! [X306 : (subst > term > term)] : (~ ! [X307 : term] : (~ ($true = ((X296 @ id @ X307 @ id))) | ($true = ((X296 @ id @ (X306 @ id @ X307) @ id)))) | ~ ! [X308 : subst,X310 : subst,X309 : term] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) | ($true = ((X296 @ id @ (lam @ (X306 @ sh @ one)) @ id)))) | ($true = ((X296 @ id @ X295 @ id))) | ~ ! [X311 : term,X312 : term] : (~ ($true = ((X296 @ id @ X312 @ id))) | ($true = ((X296 @ id @ (ap @ (sub @ X312 @ id) @ X311) @ id))) | ~ (((X296 @ id @ X311 @ id)) = $true))))))) & (! [X316 : term,X314 : (subst > term > term),X313 : subst,X315 : (subst > term > term)] : (~ ! [X319 : subst,X318 : term,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) = ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ~ ! [X320 : term,X321 : subst,X322 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321))) | (((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316)))) <=> (hoaslaminj = $true)) & ((shinj = $true) <=> ! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X325 : (subst > term > subst > $o),X326 : term] : (~ ! [X327 : (subst > term > term),X328 : term] : ((((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id)) = $true) | ~ ! [X330 : subst,X331 : subst,X329 : term] : (((sub @ X328 @ (push @ (sub @ X329 @ X331) @ (comp @ X330 @ X331)))) = ((X327 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331)))) | ~ ! [X332 : term] : (($true = ((X325 @ id @ (X327 @ id @ X332) @ id))) | ~ (((X325 @ id @ X332 @ id)) = $true)) | ~ ! [X335 : term,X333 : subst,X334 : subst] : (((sub @ (X327 @ X334 @ X335) @ X333)) = ((sub @ (sub @ X328 @ (push @ X335 @ X334)) @ X333)))) | ~ ! [X336 : term] : (($true = ((X325 @ id @ (sub @ X326 @ (push @ X336 @ id)) @ id))) | ~ (((X325 @ id @ X336 @ id)) = $true)) | ($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X337 : term] : (((sub @ X337 @ id)) = X337) => (! [X338 : term,X339 : (subst > term > subst > $o)] : (($true = ((X339 @ id @ (lam @ (sub @ X338 @ (push @ one @ sh))) @ id))) | ~ ! [X340 : term] : (($true = ((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id))) | ~ ($true = ((X339 @ id @ X340 @ id)))) | ~ ! [X341 : (subst > term > term)] : (~ ! [X342 : term] : (~ (((X339 @ id @ X342 @ id)) = $true) | ($true = ((X339 @ id @ (X341 @ id @ X342) @ id)))) | ($true = ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id))) | ~ ! [X345 : subst,X343 : subst,X344 : term] : (((X341 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345))) = ((sub @ (X341 @ X343 @ X344) @ X345))))) => ! [X346 : (subst > term > subst > $o),X347 : term] : (~ ! [X348 : (subst > term > term)] : (($true = ((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id))) | ~ ! [X349 : term] : (~ ($true = ((X346 @ id @ X349 @ id))) | ($true = ((X346 @ id @ (X348 @ id @ X349) @ id)))) | ~ ! [X351 : subst,X350 : subst,X352 : term] : (((sub @ (X348 @ X351 @ X352) @ X350)) = ((X348 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350))))) | ($true = ((X346 @ id @ (lam @ X347) @ id))) | ~ ! [X353 : term] : ((((X346 @ id @ (sub @ X347 @ (push @ X353 @ id)) @ id)) = $true) | ~ ($true = ((X346 @ id @ X353 @ id)))))))) & ~ (ulamvar1 = $true) & (apnotvar = $true) & (axapp = $true) & (ulamvarind = $true) & ((termmset = $true) <=> ! [X354 : term] : (((sub @ X354 @ id)) = X354)) & ((hoaslamnotap = $true) <=> ! [X357 : term,X356 : (subst > term > term),X355 : term] : (~ ! [X360 : subst,X359 : subst,X358 : term] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) = ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357))))) & ((axshiftcons = $true) <=> ! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362)) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) = ((d2subst @ X364))) => (X363 = X364)) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) <=> (axidl = $true)) & ! [X366 : d_term] : (d_one = X366) & (! [X367 : term,X368 : term,X369 : (subst > term > subst > $o)] : (~ ! [X370 : term,X371 : term] : (~ (((X369 @ id @ X371 @ id)) = $true) | ($true = ((X369 @ id @ (ap @ (sub @ X371 @ id) @ X370) @ id))) | ~ ($true = ((X369 @ id @ X370 @ id)))) | ~ ! [X372 : subst,X373 : subst,X374 : subst,X375 : term] : (~ ($true = ((X369 @ X373 @ X375 @ (comp @ X374 @ X372)))) | (((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) = $true)) | ~ ! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (($true = ((X369 @ X377 @ X379 @ (comp @ X378 @ X376)))) | ~ ($true = ((X369 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378) @ X376)))) | ($true = ((X369 @ id @ (ap @ X367 @ X368) @ id))) | ~ ($true = ((X369 @ id @ X367 @ id))) | ~ ($true = ((X369 @ id @ X368 @ id)))) <=> (hoasinduction_lem2 = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (! [X382 : term,X383 : (subst > term > subst > $o)] : (~ ! [X384 : (subst > term > term)] : (($true = ((X383 @ id @ (lam @ (X384 @ sh @ one)) @ id))) | ~ ! [X385 : term] : (($true = ((X383 @ id @ (X384 @ id @ X385) @ id))) | ~ ($true = ((X383 @ id @ X385 @ id)))) | ~ ! [X386 : subst,X388 : subst,X387 : term] : (((sub @ (X384 @ X386 @ X387) @ X388)) = ((X384 @ (comp @ X386 @ X388) @ (sub @ X387 @ X388))))) | ($true = ((X383 @ id @ (lam @ (sub @ X382 @ (push @ one @ sh))) @ id))) | ~ ! [X389 : term] : (($true = ((X383 @ id @ (sub @ X382 @ (push @ X389 @ id)) @ id))) | ~ ($true = ((X383 @ id @ X389 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop = $true) & (axmap = $true) & (hoasinduction_lem1v2 = $true) & (hoasapinj1_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X390 : subst] : (((comp @ id @ X390)) = X390) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393))))) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) = X394) => (! [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) = X396) => ! [X398 : term,X399 : (term > $o),X400 : subst,X401 : term,X402 : (term > $o)] : (~ ($true = ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3 = $true) <=> ! [X403 : (subst > term > subst > $o),X404 : term] : (~ ! [X405 : term] : (~ ($true = ((X403 @ id @ X405 @ id))) | ($true = ((X403 @ id @ (sub @ X404 @ (push @ X405 @ id)) @ id)))) | ~ ! [X406 : subst,X407 : term,X408 : subst,X409 : subst] : (($true = ((X403 @ X408 @ X407 @ (comp @ X409 @ X406)))) | ~ ($true = ((X403 @ (comp @ X408 @ X409) @ (sub @ X407 @ X409) @ X406)))) | ~ ! [X410 : (subst > term > term)] : (~ ! [X411 : term,X412 : subst,X413 : subst] : (((X410 @ (comp @ X412 @ X413) @ (sub @ X411 @ X413))) = ((sub @ (X410 @ X412 @ X411) @ X413))) | ($true = ((X403 @ id @ (lam @ (X410 @ sh @ one)) @ id))) | ~ ! [X414 : term] : (($true = ((X403 @ id @ (X410 @ id @ X414) @ id))) | ~ ($true = ((X403 @ id @ X414 @ id))))) | ~ ! [X415 : subst,X416 : term,X417 : subst,X418 : subst] : (($true = ((X403 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417) @ X415))) | ~ ($true = ((X403 @ X418 @ X416 @ (comp @ X417 @ X415))))) | ($true = ((X403 @ id @ (lam @ X404) @ id))))) & ((! [X419 : (subst > term > subst > $o)] : ~ ! [X420 : (term > $o)] : ~ ! [X421 : term] : (((X419 @ id @ X421 @ id)) = ((X420 @ X421))) => (! [X422 : (term > $o),X423 : term] : (~ ! [X424 : term] : (~ ! [X425 : term] : (($true = ((X422 @ (sub @ X424 @ (push @ X425 @ id))))) | ~ ($true = ((X422 @ X425)))) | (((X422 @ (lam @ X424))) = $true)) | ~ ! [X426 : term,X427 : term] : (~ ($true = ((X422 @ X426))) | ($true = ((X422 @ (ap @ X426 @ X427)))) | ~ ($true = ((X422 @ X427)))) | ~ ! [X428 : term] : (~ ($true = ((var @ X428))) | ($true = ((X422 @ X428)))) | ($true = ((X422 @ X423)))) => (! [X429 : term] : (((sub @ X429 @ id)) = X429) => (! [X430 : (subst > term > subst > $o),X431 : (term > $o),X432 : term] : ((((X431 @ (lam @ X432))) = $true) | ~ ! [X433 : (subst > term > term)] : (~ ! [X435 : term,X434 : subst,X436 : subst] : (((sub @ (X433 @ X434 @ X435) @ X436)) = ((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436)))) | ($true = ((X430 @ id @ (lam @ (X433 @ sh @ one)) @ id))) | ~ ! [X437 : term] : (~ ($true = ((X430 @ id @ X437 @ id))) | ($true = ((X430 @ id @ (X433 @ id @ X437) @ id))))) | ~ ! [X438 : term] : (((X430 @ id @ X438 @ id)) = ((X431 @ X438))) | ~ ! [X439 : term] : (~ ($true = ((X431 @ X439))) | ($true = ((X431 @ (sub @ X432 @ (push @ X439 @ id))))))) => ! [X440 : (subst > term > subst > $o),X441 : term] : (~ ! [X442 : term,X443 : term] : (($true = ((X440 @ id @ (ap @ (sub @ X442 @ id) @ X443) @ id))) | ~ ($true = ((X440 @ id @ X443 @ id))) | ~ ($true = ((X440 @ id @ X442 @ id)))) | ($true = ((X440 @ id @ X441 @ id))) | ~ ! [X444 : (subst > term > term)] : (~ ! [X447 : subst,X446 : subst,X445 : term] : (((X444 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X444 @ X447 @ X445) @ X446))) | ($true = ((X440 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ~ ! [X448 : term] : (~ (((X440 @ id @ X448 @ id)) = $true) | ($true = ((X440 @ id @ (X444 @ id @ X448) @ id)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) <=> (hoasapinj2 = $true)) & (! [X453 : term,X454 : (subst > term > subst > $o),X455 : (term > $o)] : (~ ! [X456 : (subst > term > term)] : (($true = ((X454 @ id @ (lam @ (X456 @ sh @ one)) @ id))) | ~ ! [X457 : term] : (($true = ((X454 @ id @ (X456 @ id @ X457) @ id))) | ~ ($true = ((X454 @ id @ X457 @ id)))) | ~ ! [X460 : subst,X458 : term,X459 : subst] : (((X456 @ (comp @ X459 @ X460) @ (sub @ X458 @ X460))) = ((sub @ (X456 @ X459 @ X458) @ X460)))) | ($true = ((X455 @ (lam @ X453)))) | ~ ! [X461 : term] : (($true = ((X455 @ (sub @ X453 @ (push @ X461 @ id))))) | ~ (((X455 @ X461)) = $true)) | ~ ! [X462 : term] : (((X454 @ id @ X462 @ id)) = ((X455 @ X462)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasapnotvar_lthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ~ (lamnotap = $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)))))))))))))) & ((apinj2 = $true) <=> ! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466))) & (axvarshift = $true) & ((pushprop_lem1v2 = $true) <=> ! [X467 : (term > $o),X468 : subst,X469 : (term > $o),X470 : term] : (~ ($true = ((X469 @ X470))) | ($true = ((X467 @ one))) | ~ ! [X471 : term] : (((X467 @ X471)) = ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))))) & (! [X472 : term,X473 : (subst > term > subst > $o)] : (~ ! [X474 : term,X475 : subst,X476 : subst,X477 : subst] : (($true = ((X473 @ X477 @ X474 @ (comp @ X475 @ X476)))) | ~ ($true = ((X473 @ (comp @ X477 @ X475) @ (sub @ X474 @ X475) @ X476)))) | ~ ! [X478 : subst,X479 : term,X480 : subst,X481 : subst] : (~ ($true = ((X473 @ X480 @ X479 @ (comp @ X478 @ X481)))) | ($true = ((X473 @ (comp @ X480 @ X478) @ (sub @ X479 @ X478) @ X481)))) | ~ ! [X482 : (subst > term > term)] : ((((X473 @ id @ (lam @ (X482 @ sh @ one)) @ id)) = $true) | ~ ! [X483 : term] : (~ ($true = ((X473 @ id @ X483 @ id))) | ($true = ((X473 @ id @ (X482 @ id @ X483) @ id)))) | ~ ! [X486 : term,X485 : subst,X484 : subst] : (((X482 @ (comp @ X485 @ X484) @ (sub @ X486 @ X484))) = ((sub @ (X482 @ X485 @ X486) @ X484)))) | ~ ! [X487 : term,X488 : term] : (~ ($true = ((X473 @ id @ X487 @ id))) | ~ ($true = ((X473 @ id @ X488 @ id))) | ($true = ((X473 @ id @ (ap @ (sub @ X487 @ id) @ X488) @ id)))) | ($true = ((X473 @ id @ X472 @ id))) | ~ ! [X489 : term] : (~ ($true = ((var @ (sub @ X489 @ id)))) | ($true = ((X473 @ id @ X489 @ id))))) <=> (hoasinduction = $true)) & (((d2subst @ d_id)) = id) & ! [X490 : d_subst] : (d_id = X490) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X491 : (subst > term > subst > $o)] : ~ ! [X492 : (term > $o)] : ~ ! [X493 : term] : (((X491 @ id @ X493 @ id)) = ((X492 @ X493))) => (! [X494 : term,X495 : (term > $o)] : (~ ! [X496 : term] : (($true = ((X495 @ X496))) | ~ ($true = ((var @ X496)))) | ($true = ((X495 @ X494))) | ~ ! [X497 : term] : (~ ! [X498 : term] : (~ ($true = ((X495 @ X498))) | ($true = ((X495 @ (sub @ X497 @ (push @ X498 @ id)))))) | ($true = ((X495 @ (lam @ X497))))) | ~ ! [X499 : term,X500 : term] : (~ ($true = ((X495 @ X500))) | ~ ($true = ((X495 @ X499))) | (((X495 @ (ap @ X500 @ X499))) = $true))) => (! [X501 : term] : (((sub @ X501 @ id)) = X501) => (! [X502 : (subst > term > subst > $o),X503 : term,X504 : (term > $o)] : (~ ! [X505 : term] : (((X504 @ X505)) = ((X502 @ id @ X505 @ id))) | ~ ! [X506 : term] : (~ ($true = ((X504 @ X506))) | ($true = ((X504 @ (sub @ X503 @ (push @ X506 @ id)))))) | ~ ! [X507 : (subst > term > term)] : (($true = ((X502 @ id @ (lam @ (X507 @ sh @ one)) @ id))) | ~ ! [X508 : term] : (~ (((X502 @ id @ X508 @ id)) = $true) | ($true = ((X502 @ id @ (X507 @ id @ X508) @ id)))) | ~ ! [X511 : term,X509 : subst,X510 : subst] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) = ((sub @ (X507 @ X509 @ X511) @ X510)))) | ($true = ((X504 @ (lam @ X503))))) => ! [X512 : (subst > term > subst > $o),X513 : term] : (~ ! [X514 : (subst > term > term)] : (~ ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | ~ ($true = ((X512 @ id @ X515 @ id)))) | ~ ! [X518 : subst,X516 : term,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) | ($true = ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id)))) | ~ ! [X519 : term,X520 : subst,X521 : subst,X522 : subst] : (~ ($true = ((X512 @ X520 @ X519 @ (comp @ X522 @ X521)))) | ($true = ((X512 @ (comp @ X520 @ X522) @ (sub @ X519 @ X522) @ X521)))) | ($true = ((X512 @ id @ X513 @ id))) | ~ ! [X523 : term,X524 : term] : (($true = ((X512 @ id @ (ap @ (sub @ X524 @ id) @ X523) @ id))) | ~ ($true = ((X512 @ id @ X523 @ id))) | ~ ($true = ((X512 @ id @ X524 @ id)))) | ~ ! [X525 : term] : (~ (((var @ (sub @ X525 @ id))) = $true) | ($true = ((X512 @ id @ X525 @ id)))) | ~ ! [X526 : subst,X527 : subst,X528 : subst,X529 : term] : (($true = ((X512 @ X528 @ X529 @ (comp @ X527 @ X526)))) | ~ ($true = ((X512 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527) @ X526)))))))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X530 : term] : ~ ! [X531 : (subst > term > term)] : ~ ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533))))) & ! [X535 : d_term,X534 : d_term] : ((((d2term @ X534)) = ((d2term @ X535))) => (X534 = X535)) & (hoasinduction_gthm = $true) & (pushprop_lem0_gthm = $true) & (! [X536 : (subst > term > subst > $o)] : ~ ! [X537 : (term > $o)] : ~ ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) <=> (hoasinduction_lem0_lthm = $true)) & (one = ((d2term @ d_one))) & (hoasinduction_lem2v2_gthm = $true) & ((axidr = $true) <=> ! [X539 : subst] : (((comp @ X539 @ id)) = X539))),
% 5.11/1.35 inference(rectify,[],[f7])).
% 5.11/1.35 thf(f10,plain,(
% 5.11/1.35 (hoasapnotvar_lthm = $true) & (hoaslamnotvar = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem1 = $true) & (one = ((d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axmap = $true) & ((induction2 = $true) <=> ! [X146 : term,X145 : (term > $o)] : (~ ! [X147 : term] : (~ ! [X148 : term] : (($true = ((X145 @ (sub @ X147 @ (push @ X148 @ id))))) | ($true != ((X145 @ X148)))) | ($true = ((X145 @ (lam @ X147))))) | ~ ! [X151 : term] : (($true = ((X145 @ X151))) | ($true != ((var @ X151)))) | ($true = ((X145 @ X146))) | ~ ! [X150 : term,X149 : term] : (($true != ((X145 @ X150))) | ($true != ((X145 @ X149))) | ($true = ((X145 @ (ap @ X150 @ X149))))))) & ((pushprop_lem0 = $true) <=> ! [X19 : (term > $o),X18 : subst,X17 : term] : ~ ! [X20 : (term > $o)] : ~ ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21)))) & ((termmset_lthm = $true) <=> (! [X93 : term] : (((sub @ X93 @ id)) = X93) => ! [X94 : term] : (((sub @ X94 @ id)) = X94))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (! [X382 : term,X383 : (subst > term > subst > $o)] : (~ ! [X384 : (subst > term > term)] : (~ ! [X386 : subst,X388 : subst,X387 : term] : (((sub @ (X384 @ X386 @ X387) @ X388)) = ((X384 @ (comp @ X386 @ X388) @ (sub @ X387 @ X388)))) | ~ ! [X385 : term] : (($true != ((X383 @ id @ X385 @ id))) | ($true = ((X383 @ id @ (X384 @ id @ X385) @ id)))) | ($true = ((X383 @ id @ (lam @ (X384 @ sh @ one)) @ id)))) | ($true = ((X383 @ id @ (lam @ (sub @ X382 @ (push @ one @ sh))) @ id))) | ~ ! [X389 : term] : (($true != ((X383 @ id @ X389 @ id))) | ($true = ((X383 @ id @ (sub @ X382 @ (push @ X389 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axvarcons = $true) <=> ! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117)) & (hoasinduction_lem2v2_gthm = $true) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X419 : (subst > term > subst > $o)] : ~ ! [X420 : (term > $o)] : ~ ! [X421 : term] : (((X419 @ id @ X421 @ id)) = ((X420 @ X421))) => (! [X422 : (term > $o),X423 : term] : (~ ! [X424 : term] : ((((X422 @ (lam @ X424))) = $true) | ~ ! [X425 : term] : (($true = ((X422 @ (sub @ X424 @ (push @ X425 @ id))))) | ($true != ((X422 @ X425))))) | ($true = ((X422 @ X423))) | ~ ! [X426 : term,X427 : term] : (($true = ((X422 @ (ap @ X426 @ X427)))) | ($true != ((X422 @ X426))) | ($true != ((X422 @ X427)))) | ~ ! [X428 : term] : (($true != ((var @ X428))) | ($true = ((X422 @ X428))))) => (! [X429 : term] : (((sub @ X429 @ id)) = X429) => (! [X431 : (term > $o),X430 : (subst > term > subst > $o),X432 : term] : (~ ! [X433 : (subst > term > term)] : (~ ! [X435 : term,X434 : subst,X436 : subst] : (((sub @ (X433 @ X434 @ X435) @ X436)) = ((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436)))) | ($true = ((X430 @ id @ (lam @ (X433 @ sh @ one)) @ id))) | ~ ! [X437 : term] : (($true != ((X430 @ id @ X437 @ id))) | ($true = ((X430 @ id @ (X433 @ id @ X437) @ id))))) | ~ ! [X438 : term] : (((X430 @ id @ X438 @ id)) = ((X431 @ X438))) | ~ ! [X439 : term] : (($true = ((X431 @ (sub @ X432 @ (push @ X439 @ id))))) | ($true != ((X431 @ X439)))) | (((X431 @ (lam @ X432))) = $true)) => ! [X441 : term,X440 : (subst > term > subst > $o)] : (($true = ((X440 @ id @ X441 @ id))) | ~ ! [X443 : term,X442 : term] : (($true = ((X440 @ id @ (ap @ (sub @ X442 @ id) @ X443) @ id))) | ($true != ((X440 @ id @ X443 @ id))) | ($true != ((X440 @ id @ X442 @ id)))) | ~ ! [X444 : (subst > term > term)] : (~ ! [X447 : subst,X446 : subst,X445 : term] : (((X444 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X444 @ X447 @ X445) @ X446))) | ($true = ((X440 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ~ ! [X448 : term] : (($true = ((X440 @ id @ (X444 @ id @ X448) @ id))) | (((X440 @ id @ X448 @ id)) != $true)))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (axabs = $true) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) <=> (hoasapinj2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X467 : (term > $o),X468 : subst,X470 : term,X469 : (term > $o)] : (~ ! [X471 : term] : (((X467 @ X471)) = ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) <=> (pushprop_lem1v2 = $true)) & (((var @ (d2term @ d_one))) != $true) & ((! [X41 : term,X39 : term,X40 : term,X38 : term] : ((((ap @ X38 @ X41)) != ((ap @ X40 @ X39))) | (X39 = X41)) => ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & ((! [X337 : term] : (((sub @ X337 @ id)) = X337) => (! [X339 : (subst > term > subst > $o),X338 : term] : (($true = ((X339 @ id @ (lam @ (sub @ X338 @ (push @ one @ sh))) @ id))) | ~ ! [X341 : (subst > term > term)] : (~ ! [X342 : term] : ((((X339 @ id @ X342 @ id)) != $true) | ($true = ((X339 @ id @ (X341 @ id @ X342) @ id)))) | ($true = ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id))) | ~ ! [X345 : subst,X343 : subst,X344 : term] : (((X341 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345))) = ((sub @ (X341 @ X343 @ X344) @ X345)))) | ~ ! [X340 : term] : (($true != ((X339 @ id @ X340 @ id))) | ($true = ((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id))))) => ! [X347 : term,X346 : (subst > term > subst > $o)] : (~ ! [X348 : (subst > term > term)] : (($true = ((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id))) | ~ ! [X351 : subst,X350 : subst,X352 : term] : (((sub @ (X348 @ X351 @ X352) @ X350)) = ((X348 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350)))) | ~ ! [X349 : term] : (($true != ((X346 @ id @ X349 @ id))) | ($true = ((X346 @ id @ (X348 @ id @ X349) @ id))))) | ($true = ((X346 @ id @ (lam @ X347) @ id))) | ~ ! [X353 : term] : ((((X346 @ id @ (sub @ X347 @ (push @ X353 @ id)) @ id)) = $true) | ($true != ((X346 @ id @ X353 @ id))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (lamnotvar = $true) & ((shinj = $true) <=> ! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh))))) & ((! [X96 : term,X95 : subst] : (((sub @ one @ (push @ X96 @ X95))) = X96) => (! [X98 : subst,X97 : term] : (((comp @ sh @ (push @ X97 @ X98))) = X98) => (! [X100 : term,X99 : term] : ((((lam @ X99)) != ((lam @ X100))) | (X99 = X100)) => ! [X101 : subst,X104 : term,X103 : (subst > term > term),X102 : (subst > term > term)] : (~ ! [X110 : subst,X109 : subst,X108 : term] : (((X102 @ (comp @ X109 @ X110) @ (sub @ X108 @ X110))) = ((sub @ (X102 @ X109 @ X108) @ X110))) | ~ ! [X106 : subst,X105 : subst,X107 : term] : (((X103 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) = ((sub @ (X103 @ X105 @ X107) @ X106))) | (((X103 @ X101 @ X104)) = ((X102 @ X101 @ X104))) | (((lam @ (X102 @ sh @ one))) != ((lam @ (X103 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (! [X136 : term,X137 : (subst > term > subst > $o)] : (~ ! [X138 : term,X139 : term] : (($true != ((X137 @ id @ X138 @ id))) | ($true != ((X137 @ id @ X139 @ id))) | ($true = ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ~ ! [X140 : (subst > term > term)] : (($true = ((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id))) | ~ ! [X143 : term,X142 : subst,X141 : subst] : (((sub @ (X140 @ X142 @ X143) @ X141)) = ((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141)))) | ~ ! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ($true != ((X137 @ id @ X144 @ id))))) | ($true = ((X137 @ id @ X136 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X112 : (term > $o),X111 : term,X113 : subst] : ~ ! [X114 : (term > $o)] : ~ ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) <=> (pushprop_lem0_lthm = $true)) & ((substmonoid_lthm = $true) <=> (! [X390 : subst] : (((comp @ id @ X390)) = X390) => (! [X391 : subst] : (((comp @ X391 @ id)) = X391) => (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393))))) & (lamnotap != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X325 : (subst > term > subst > $o),X326 : term] : (($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id))) | ~ ! [X328 : term,X327 : (subst > term > term)] : (~ ! [X332 : term] : ((((X325 @ id @ X332 @ id)) != $true) | ($true = ((X325 @ id @ (X327 @ id @ X332) @ id)))) | (((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id)) = $true) | ~ ! [X335 : term,X333 : subst,X334 : subst] : (((sub @ (X327 @ X334 @ X335) @ X333)) = ((sub @ (sub @ X328 @ (push @ X335 @ X334)) @ X333))) | ~ ! [X330 : subst,X331 : subst,X329 : term] : (((sub @ X328 @ (push @ (sub @ X329 @ X331) @ (comp @ X330 @ X331)))) = ((X327 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331))))) | ~ ! [X336 : term] : (($true = ((X325 @ id @ (sub @ X326 @ (push @ X336 @ id)) @ id))) | (((X325 @ id @ X336 @ id)) != $true)))) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X260 : term,X259 : (term > $o)] : (~ ! [X265 : term] : ((((var @ X265)) != $true) | ($true = ((X259 @ X265)))) | ~ ! [X262 : term,X261 : term] : ((((X259 @ X262)) != $true) | ($true != ((X259 @ X261))) | ($true = ((X259 @ (ap @ X262 @ X261))))) | ($true = ((X259 @ X260))) | ~ ! [X263 : term] : (~ ! [X264 : term] : ((((X259 @ X264)) != $true) | ($true = ((X259 @ (sub @ X263 @ (push @ X264 @ id)))))) | (((X259 @ (lam @ X263))) = $true))) => (! [X268 : (subst > term > subst > $o),X267 : term,X266 : term] : (~ ! [X271 : subst,X274 : subst,X272 : subst,X273 : term] : (($true = ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271))) | ($true != ((X268 @ X272 @ X273 @ (comp @ X274 @ X271))))) | ~ ! [X276 : subst,X277 : subst,X278 : subst,X275 : term] : (($true = ((X268 @ X277 @ X275 @ (comp @ X278 @ X276)))) | (((X268 @ (comp @ X277 @ X278) @ (sub @ X275 @ X278) @ X276)) != $true)) | ($true != ((X268 @ id @ X266 @ id))) | ($true != ((X268 @ id @ X267 @ id))) | ($true = ((X268 @ id @ (ap @ X266 @ X267) @ id))) | ~ ! [X270 : term,X269 : term] : (($true != ((X268 @ id @ X269 @ id))) | (((X268 @ id @ X270 @ id)) != $true) | ($true = ((X268 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id))))) => (! [X280 : term,X279 : (subst > term > subst > $o)] : (~ ! [X281 : term] : ((((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) = $true) | ($true != ((X279 @ id @ X281 @ id)))) | ~ ! [X293 : subst,X294 : term,X291 : subst,X292 : subst] : (($true = ((X279 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X291))) | ($true != ((X279 @ X293 @ X294 @ (comp @ X292 @ X291))))) | ($true = ((X279 @ id @ (lam @ X280) @ id))) | ~ ! [X282 : (subst > term > term)] : (~ ! [X286 : subst,X284 : subst,X285 : term] : (((X282 @ (comp @ X286 @ X284) @ (sub @ X285 @ X284))) = ((sub @ (X282 @ X286 @ X285) @ X284))) | ~ ! [X283 : term] : ((((X279 @ id @ (X282 @ id @ X283) @ id)) = $true) | ($true != ((X279 @ id @ X283 @ id)))) | ($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id)))) | ~ ! [X287 : subst,X290 : subst,X289 : subst,X288 : term] : (($true != ((X279 @ (comp @ X289 @ X290) @ (sub @ X288 @ X290) @ X287))) | ($true = ((X279 @ X289 @ X288 @ (comp @ X290 @ X287)))))) => ! [X295 : term,X296 : (subst > term > subst > $o)] : (~ ! [X297 : term] : (($true != ((var @ (sub @ X297 @ id)))) | ($true = ((X296 @ id @ X297 @ id)))) | ($true = ((X296 @ id @ X295 @ id))) | ~ ! [X301 : subst,X298 : subst,X300 : term,X299 : subst] : (($true = ((X296 @ (comp @ X298 @ X301) @ (sub @ X300 @ X301) @ X299))) | ($true != ((X296 @ X298 @ X300 @ (comp @ X301 @ X299))))) | ~ ! [X302 : subst,X304 : subst,X305 : subst,X303 : term] : (($true = ((X296 @ X304 @ X303 @ (comp @ X302 @ X305)))) | ($true != ((X296 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302) @ X305)))) | ~ ! [X312 : term,X311 : term] : ((((X296 @ id @ X311 @ id)) != $true) | ($true != ((X296 @ id @ X312 @ id))) | ($true = ((X296 @ id @ (ap @ (sub @ X312 @ id) @ X311) @ id)))) | ~ ! [X306 : (subst > term > term)] : (~ ! [X308 : subst,X310 : subst,X309 : term] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) | ($true = ((X296 @ id @ (lam @ (X306 @ sh @ one)) @ id))) | ~ ! [X307 : term] : (($true = ((X296 @ id @ (X306 @ id @ X307) @ id))) | ($true != ((X296 @ id @ X307 @ id)))))))))) & ((hoasinduction_lem3 = $true) <=> ! [X403 : (subst > term > subst > $o),X404 : term] : (~ ! [X410 : (subst > term > term)] : (($true = ((X403 @ id @ (lam @ (X410 @ sh @ one)) @ id))) | ~ ! [X414 : term] : (($true = ((X403 @ id @ (X410 @ id @ X414) @ id))) | ($true != ((X403 @ id @ X414 @ id)))) | ~ ! [X411 : term,X412 : subst,X413 : subst] : (((X410 @ (comp @ X412 @ X413) @ (sub @ X411 @ X413))) = ((sub @ (X410 @ X412 @ X411) @ X413)))) | ~ ! [X409 : subst,X406 : subst,X408 : subst,X407 : term] : (($true != ((X403 @ (comp @ X408 @ X409) @ (sub @ X407 @ X409) @ X406))) | ($true = ((X403 @ X408 @ X407 @ (comp @ X409 @ X406))))) | ($true = ((X403 @ id @ (lam @ X404) @ id))) | ~ ! [X405 : term] : (($true = ((X403 @ id @ (sub @ X404 @ (push @ X405 @ id)) @ id))) | ($true != ((X403 @ id @ X405 @ id)))) | ~ ! [X416 : term,X415 : subst,X418 : subst,X417 : subst] : (($true != ((X403 @ X418 @ X416 @ (comp @ X417 @ X415)))) | ($true = ((X403 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417) @ X415)))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X154 : term,X152 : (term > $o),X155 : (subst > term > subst > $o),X153 : term] : (($true != ((X152 @ X153))) | ~ ! [X164 : subst,X165 : term,X162 : subst,X163 : subst] : (($true = ((X155 @ (comp @ X163 @ X162) @ (sub @ X165 @ X162) @ X164))) | ($true != ((X155 @ X163 @ X165 @ (comp @ X162 @ X164))))) | ~ ! [X166 : term] : (((X155 @ id @ X166 @ id)) = ((X152 @ X166))) | ($true != ((X152 @ X154))) | ($true = ((X152 @ (ap @ X153 @ X154)))) | ~ ! [X157 : subst,X158 : subst,X156 : term,X159 : subst] : (($true != ((X155 @ (comp @ X159 @ X157) @ (sub @ X156 @ X157) @ X158))) | ($true = ((X155 @ X159 @ X156 @ (comp @ X157 @ X158))))) | ~ ! [X160 : term,X161 : term] : ((((X155 @ id @ X161 @ id)) != $true) | ($true = ((X155 @ id @ (ap @ (sub @ X161 @ id) @ X160) @ id))) | ($true != ((X155 @ id @ X160 @ id)))))) & ((hoasinduction_lem2 = $true) <=> ! [X367 : term,X369 : (subst > term > subst > $o),X368 : term] : (($true != ((X369 @ id @ X367 @ id))) | ~ ! [X375 : term,X374 : subst,X372 : subst,X373 : subst] : (($true != ((X369 @ X373 @ X375 @ (comp @ X374 @ X372)))) | (((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) = $true)) | ~ ! [X377 : subst,X376 : subst,X379 : term,X378 : subst] : (($true = ((X369 @ X377 @ X379 @ (comp @ X378 @ X376)))) | ($true != ((X369 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378) @ X376)))) | ($true != ((X369 @ id @ X368 @ id))) | ~ ! [X371 : term,X370 : term] : (($true != ((X369 @ id @ X370 @ id))) | ($true = ((X369 @ id @ (ap @ (sub @ X371 @ id) @ X370) @ id))) | (((X369 @ id @ X371 @ id)) != $true)) | ($true = ((X369 @ id @ (ap @ X367 @ X368) @ id))))) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) = ((d2subst @ X364))) => (X363 = X364)) & (ulamvar1 != $true) & ((induction = $true) <=> ! [X1 : (term > $o),X0 : term] : (~ ! [X5 : term] : (($true = ((X1 @ (lam @ X5)))) | (((X1 @ X5)) != $true)) | ($true = ((X1 @ X0))) | ~ ! [X3 : term,X2 : term] : (($true != ((X1 @ X2))) | ($true != ((X1 @ X3))) | ($true = ((X1 @ (ap @ X3 @ X2))))) | ~ ! [X4 : term] : (($true != ((var @ X4))) | (((X1 @ X4)) = $true)))) & ((! [X189 : term] : ~ ! [X190 : (subst > term > term)] : ~ ! [X191 : term,X192 : subst] : (((X190 @ X192 @ X191)) = ((sub @ X189 @ (push @ X191 @ X192)))) => (! [X193 : term] : (((sub @ X193 @ id)) = X193) => ! [X194 : term,X196 : (subst > term > subst > $o),X195 : (term > $o)] : (~ ! [X203 : term] : (((X195 @ X203)) = ((X196 @ id @ X203 @ id))) | ~ ! [X198 : (subst > term > term)] : (($true = ((X196 @ id @ (lam @ (X198 @ sh @ one)) @ id))) | ~ ! [X201 : term,X200 : subst,X199 : subst] : (((sub @ (X198 @ X199 @ X201) @ X200)) = ((X198 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200)))) | ~ ! [X202 : term] : (($true != ((X196 @ id @ X202 @ id))) | ($true = ((X196 @ id @ (X198 @ id @ X202) @ id))))) | ($true = ((X195 @ (lam @ X194)))) | ~ ! [X197 : term] : (($true != ((X195 @ X197))) | ($true = ((X195 @ (sub @ X194 @ (push @ X197 @ id))))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X232 : (subst > term > subst > $o),X233 : term] : (~ ! [X239 : term] : (($true = ((X232 @ id @ (sub @ X233 @ (push @ X239 @ id)) @ id))) | ($true != ((X232 @ id @ X239 @ id)))) | ($true = ((X232 @ id @ (lam @ X233) @ id))) | ~ ! [X234 : (subst > term > term)] : (($true = ((X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X235 : term] : (($true != ((X232 @ id @ X235 @ id))) | ($true = ((X232 @ id @ (X234 @ id @ X235) @ id)))) | ~ ! [X237 : subst,X238 : subst,X236 : term] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)))))) <=> (hoasinduction_lem3a = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X530 : term] : ~ ! [X531 : (subst > term > term)] : ~ ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533))))) & (induction2_gthm = $true) & (axclos = $true) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) <=> (axidl = $true)) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (hoasinduction_lem3_gthm = $true) & ! [X535 : d_term,X534 : d_term] : ((((d2term @ X534)) = ((d2term @ X535))) => (X534 = X535)) & (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)))))))))))))) & ! [X490 : d_subst] : (d_id = X490) & ((hoasinduction_lthm_3 = $true) <=> (! [X491 : (subst > term > subst > $o)] : ~ ! [X492 : (term > $o)] : ~ ! [X493 : term] : (((X491 @ id @ X493 @ id)) = ((X492 @ X493))) => (! [X494 : term,X495 : (term > $o)] : (($true = ((X495 @ X494))) | ~ ! [X500 : term,X499 : term] : (($true != ((X495 @ X499))) | (((X495 @ (ap @ X500 @ X499))) = $true) | ($true != ((X495 @ X500)))) | ~ ! [X497 : term] : (($true = ((X495 @ (lam @ X497)))) | ~ ! [X498 : term] : (($true = ((X495 @ (sub @ X497 @ (push @ X498 @ id))))) | ($true != ((X495 @ X498))))) | ~ ! [X496 : term] : (($true != ((var @ X496))) | ($true = ((X495 @ X496))))) => (! [X501 : term] : (((sub @ X501 @ id)) = X501) => (! [X503 : term,X502 : (subst > term > subst > $o),X504 : (term > $o)] : (($true = ((X504 @ (lam @ X503)))) | ~ ! [X506 : term] : (($true = ((X504 @ (sub @ X503 @ (push @ X506 @ id))))) | ($true != ((X504 @ X506)))) | ~ ! [X505 : term] : (((X504 @ X505)) = ((X502 @ id @ X505 @ id))) | ~ ! [X507 : (subst > term > term)] : (~ ! [X511 : term,X509 : subst,X510 : subst] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) = ((sub @ (X507 @ X509 @ X511) @ X510))) | ~ ! [X508 : term] : (($true = ((X502 @ id @ (X507 @ id @ X508) @ id))) | (((X502 @ id @ X508 @ id)) != $true)) | ($true = ((X502 @ id @ (lam @ (X507 @ sh @ one)) @ id))))) => ! [X513 : term,X512 : (subst > term > subst > $o)] : (($true = ((X512 @ id @ X513 @ id))) | ~ ! [X528 : subst,X529 : term,X527 : subst,X526 : subst] : (($true != ((X512 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527) @ X526))) | ($true = ((X512 @ X528 @ X529 @ (comp @ X527 @ X526))))) | ~ ! [X523 : term,X524 : term] : (($true != ((X512 @ id @ X523 @ id))) | ($true != ((X512 @ id @ X524 @ id))) | ($true = ((X512 @ id @ (ap @ (sub @ X524 @ id) @ X523) @ id)))) | ~ ! [X522 : subst,X520 : subst,X519 : term,X521 : subst] : (($true = ((X512 @ (comp @ X520 @ X522) @ (sub @ X519 @ X522) @ X521))) | ($true != ((X512 @ X520 @ X519 @ (comp @ X522 @ X521))))) | ~ ! [X525 : term] : ((((var @ (sub @ X525 @ id))) != $true) | ($true = ((X512 @ id @ X525 @ id)))) | ~ ! [X514 : (subst > term > term)] : (~ ! [X518 : subst,X516 : term,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) | ($true = ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | ($true != ((X512 @ id @ X515 @ id))))))))))) & ((! [X215 : term] : (((sub @ X215 @ id)) = X215) => (! [X217 : term,X219 : term,X216 : term,X218 : term] : ((((ap @ X217 @ X218)) != ((ap @ X216 @ X219))) | (X216 = X217)) => ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)))) <=> (hoasapinj1_lthm = $true)) & ((induction2_lthm = $true) <=> (! [X77 : term] : (((sub @ X77 @ id)) = X77) => (! [X79 : subst,X78 : (term > $o),X80 : term] : (($true = ((X78 @ (sub @ X80 @ X79)))) | ~ ! [X83 : term] : (($true != ((var @ X83))) | ($true = ((X78 @ (sub @ X83 @ X79))))) | ~ ! [X85 : term,X84 : term] : (($true != ((X78 @ X84))) | (((X78 @ (ap @ X84 @ X85))) = $true) | ($true != ((X78 @ X85)))) | ~ ! [X81 : term] : (~ ! [X82 : term] : (($true != ((X78 @ X82))) | ($true = ((X78 @ (sub @ X81 @ (push @ X82 @ id)))))) | ($true = ((X78 @ (lam @ X81)))))) => ! [X86 : term,X87 : (term > $o)] : (~ ! [X91 : term,X90 : term] : (($true = ((X87 @ (ap @ X91 @ X90)))) | ($true != ((X87 @ X91))) | ($true != ((X87 @ X90)))) | (((X87 @ X86)) = $true) | ~ ! [X92 : term] : ((((var @ X92)) != $true) | ($true = ((X87 @ X92)))) | ~ ! [X88 : term] : (($true = ((X87 @ (lam @ X88)))) | ~ ! [X89 : term] : (($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id))))) | ($true != ((X87 @ X89))))))))) & (ulamvarsh = $true) & (induction2lem_gthm = $true) & (! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) <=> (pushprop_lem1 = $true)) & (((d2subst @ d_id)) = sh) & ((axshiftcons = $true) <=> ! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362)) & (! [X34 : term] : ~ ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X455 : (term > $o),X453 : term,X454 : (subst > term > subst > $o)] : (~ ! [X456 : (subst > term > term)] : (~ ! [X457 : term] : (($true != ((X454 @ id @ X457 @ id))) | ($true = ((X454 @ id @ (X456 @ id @ X457) @ id)))) | ($true = ((X454 @ id @ (lam @ (X456 @ sh @ one)) @ id))) | ~ ! [X460 : subst,X458 : term,X459 : subst] : (((X456 @ (comp @ X459 @ X460) @ (sub @ X458 @ X460))) = ((sub @ (X456 @ X459 @ X458) @ X460)))) | ~ ! [X462 : term] : (((X454 @ id @ X462 @ id)) = ((X455 @ X462))) | ($true = ((X455 @ (lam @ X453)))) | ~ ! [X461 : term] : (($true = ((X455 @ (sub @ X453 @ (push @ X461 @ id))))) | (((X455 @ X461)) != $true))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & (pushprop = $true) & ((apinj1 = $true) <=> ! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205))))) & (hoasinduction_gthm = $true) & ((apinj2 = $true) <=> ! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466))) & (pushprop_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X22 : term] : ~ ! [X23 : (subst > term > term)] : ~ ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & ((axscons = $true) <=> ! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188)) & (hoasapinj1_gthm = $true) & ((termmset = $true) <=> ! [X354 : term] : (((sub @ X354 @ id)) = X354)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) = X394) => (! [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) = X396) => ! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400))))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X186 : term] : ~ ! [X187 : (subst > term > term)] : (((X187 @ sh @ one)) != ((sub @ X186 @ (push @ one @ sh))))) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) <=> (laminj = $true)) & (! [X536 : (subst > term > subst > $o)] : ~ ! [X537 : (term > $o)] : ~ ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) <=> (hoasinduction_lem0_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X357 : term,X356 : (subst > term > term),X355 : term] : (~ ! [X360 : subst,X359 : subst,X358 : term] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) = ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357))))) & (! [X119 : (term > $o),X118 : term,X120 : (subst > term > subst > $o)] : (~ ! [X121 : (subst > term > term)] : (~ ! [X125 : term] : (($true = ((X120 @ id @ (X121 @ id @ X125) @ id))) | ($true != ((X120 @ id @ X125 @ id)))) | ~ ! [X123 : subst,X124 : term,X122 : subst] : (((X121 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) = ((sub @ (X121 @ X122 @ X124) @ X123))) | ($true = ((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)))) | ~ ! [X130 : term] : (((X120 @ id @ X130 @ id)) = ((X119 @ X130))) | ~ ! [X135 : term] : (($true = ((X119 @ (sub @ X118 @ (push @ X135 @ id))))) | ($true != ((X119 @ X135)))) | ($true = ((X119 @ (lam @ X118)))) | ~ ! [X128 : subst,X126 : subst,X129 : subst,X127 : term] : (($true = ((X120 @ X126 @ X127 @ (comp @ X128 @ X129)))) | ($true != ((X120 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128) @ X129)))) | ~ ! [X131 : subst,X133 : subst,X132 : subst,X134 : term] : ((((X120 @ X132 @ X134 @ (comp @ X131 @ X133))) != $true) | ($true = ((X120 @ (comp @ X132 @ X131) @ (sub @ X134 @ X131) @ X133))))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem0_gthm = $true) & (apnotvar = $true) & (axapp = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) = X7) => ! [X9 : (term > $o),X8 : term,X11 : (term > $o),X10 : subst] : (($true != ((X11 @ X8))) | ~ ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))) | (((X9 @ one)) = $true)))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = id) & (! [X316 : term,X314 : (subst > term > term),X313 : subst,X315 : (subst > term > term)] : (~ ! [X319 : subst,X318 : term,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) = ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ~ ! [X320 : term,X321 : subst,X322 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321))) | (((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316)))) <=> (hoaslaminj = $true)) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ! [X366 : d_term] : (d_one = X366) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X472 : term,X473 : (subst > term > subst > $o)] : (~ ! [X482 : (subst > term > term)] : (~ ! [X483 : term] : (($true != ((X473 @ id @ X483 @ id))) | ($true = ((X473 @ id @ (X482 @ id @ X483) @ id)))) | ~ ! [X486 : term,X485 : subst,X484 : subst] : (((X482 @ (comp @ X485 @ X484) @ (sub @ X486 @ X484))) = ((sub @ (X482 @ X485 @ X486) @ X484))) | (((X473 @ id @ (lam @ (X482 @ sh @ one)) @ id)) = $true)) | ($true = ((X473 @ id @ X472 @ id))) | ~ ! [X489 : term] : (($true != ((var @ (sub @ X489 @ id)))) | ($true = ((X473 @ id @ X489 @ id)))) | ~ ! [X488 : term,X487 : term] : (($true = ((X473 @ id @ (ap @ (sub @ X487 @ id) @ X488) @ id))) | ($true != ((X473 @ id @ X487 @ id))) | ($true != ((X473 @ id @ X488 @ id)))) | ~ ! [X476 : subst,X475 : subst,X477 : subst,X474 : term] : (($true != ((X473 @ (comp @ X477 @ X475) @ (sub @ X474 @ X475) @ X476))) | ($true = ((X473 @ X477 @ X474 @ (comp @ X475 @ X476))))) | ~ ! [X480 : subst,X478 : subst,X481 : subst,X479 : term] : (($true != ((X473 @ X480 @ X479 @ (comp @ X478 @ X481)))) | ($true = ((X473 @ (comp @ X480 @ X478) @ (sub @ X479 @ X478) @ X481))))) <=> (hoasinduction = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotvar_gthm = $true) & (! [X224 : (subst > term > subst > $o),X225 : term] : (~ ! [X231 : term] : (($true = ((X224 @ id @ (sub @ X225 @ (push @ X231 @ id)) @ id))) | ($true != ((X224 @ id @ X231 @ id)))) | ($true = ((X224 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id))) | ~ ! [X226 : (subst > term > term)] : (~ ! [X228 : subst,X229 : term,X227 : subst] : (((X226 @ (comp @ X227 @ X228) @ (sub @ X229 @ X228))) = ((sub @ (X226 @ X227 @ X229) @ X228))) | ($true = ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id))) | ~ ! [X230 : term] : (($true = ((X224 @ id @ (X226 @ id @ X230) @ id))) | ($true != ((X224 @ id @ X230 @ id)))))) <=> (hoasinduction_lem3aa = $true)) & ((axidr = $true) <=> ! [X539 : subst] : (((comp @ X539 @ id)) = X539)) & (ulamvarind = $true) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X46 : term] : (((sub @ X46 @ id)) = X46) => (! [X47 : (subst > term > subst > $o),X48 : term] : (~ ! [X49 : (subst > term > term)] : (~ ! [X51 : subst,X52 : subst,X50 : term] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) = ((sub @ (X49 @ X52 @ X50) @ X51))) | ~ ! [X53 : term] : (($true != ((X47 @ id @ X53 @ id))) | ($true = ((X47 @ id @ (X49 @ id @ X53) @ id)))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id)))) | ~ ! [X54 : term] : (($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))) | ($true != ((X47 @ id @ X54 @ id)))) | ($true = ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id)))) => ! [X55 : (subst > term > subst > $o),X56 : term] : (~ ! [X62 : (subst > term > term)] : ((((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) = $true) | ~ ! [X63 : term] : (($true = ((X55 @ id @ (X62 @ id @ X63) @ id))) | ($true != ((X55 @ id @ X63 @ id)))) | ~ ! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66))))) | ~ ! [X61 : term] : (($true = ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id))) | ($true != ((X55 @ id @ X61 @ id)))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ~ ! [X67 : subst,X69 : subst,X68 : term,X70 : subst] : (($true = ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70))) | ($true != ((X55 @ X67 @ X68 @ (comp @ X69 @ X70))))) | ~ ! [X60 : subst,X59 : subst,X58 : term,X57 : subst] : (($true != ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60))) | ($true = ((X55 @ X59 @ X58 @ (comp @ X57 @ X60)))))))) <=> (hoasinduction_lem3_lthm = $true)) & ((! [X240 : term] : (((sub @ X240 @ id)) = X240) => ! [X241 : (subst > term > subst > $o),X242 : (term > $o),X243 : term] : (~ ! [X244 : (subst > term > term)] : (~ ! [X248 : term] : (($true != ((X241 @ id @ X248 @ id))) | ($true = ((X241 @ id @ (X244 @ id @ X248) @ id)))) | ~ ! [X247 : subst,X245 : subst,X246 : term] : (((sub @ (X244 @ X247 @ X246) @ X245)) = ((X244 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245)))) | ($true = ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id)))) | ~ ! [X257 : term,X255 : subst,X254 : subst,X256 : subst] : (($true = ((X241 @ X255 @ X257 @ (comp @ X256 @ X254)))) | ($true != ((X241 @ (comp @ X255 @ X256) @ (sub @ X257 @ X256) @ X254)))) | ~ ! [X253 : term] : (((X241 @ id @ X253 @ id)) = ((X242 @ X253))) | ~ ! [X258 : term] : (($true != ((X242 @ X258))) | ($true = ((X242 @ (sub @ X243 @ (push @ X258 @ id)))))) | ~ ! [X252 : subst,X249 : subst,X251 : subst,X250 : term] : (($true != ((X241 @ X252 @ X250 @ (comp @ X249 @ X251)))) | ($true = ((X241 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)))) | ($true = ((X242 @ (lam @ X243)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X27 : (term > $o),X28 : term,X26 : subst] : (~ ! [X29 : term,X30 : term] : (($true != ((X27 @ X29))) | ($true = ((X27 @ (ap @ X30 @ X29)))) | ($true != ((X27 @ X30)))) | ~ ! [X31 : term] : ((((X27 @ (lam @ X31))) = $true) | ~ ! [X32 : term] : (($true != ((X27 @ X32))) | ($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id))))))) | ($true = ((X27 @ (sub @ X28 @ X26)))) | ~ ! [X33 : term] : (($true != ((var @ X33))) | ($true = ((X27 @ (sub @ X33 @ X26)))))) <=> (induction2lem = $true)) & (! [X71 : (subst > term > subst > $o)] : ~ ! [X72 : (term > $o)] : ~ ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotap_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & (pushprop_lthm = $true) & (hoaslamnotap_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X168 : term,X167 : subst] : (((sub @ one @ (push @ X168 @ X167))) = X168) => (! [X169 : subst,X170 : term] : (((comp @ sh @ (push @ X170 @ X169))) = X169) => (! [X171 : subst] : (((comp @ X171 @ id)) = X171) => (! [X173 : (term > $o),X172 : term] : (~ ! [X177 : term] : (($true = ((X173 @ (lam @ X177)))) | ($true != ((X173 @ X177)))) | ~ ! [X174 : term,X175 : term] : (($true != ((X173 @ X175))) | ($true = ((X173 @ (ap @ X175 @ X174)))) | ($true != ((X173 @ X174)))) | ~ ! [X176 : term] : (($true = ((X173 @ X176))) | ($true != ((var @ X176)))) | (((X173 @ X172)) = $true)) => ! [X178 : term,X180 : (term > $o),X179 : subst] : (~ ! [X181 : term,X182 : term] : (($true = ((X180 @ (ap @ X182 @ X181)))) | ($true != ((X180 @ X181))) | ($true != ((X180 @ X182)))) | ($true = ((X180 @ (sub @ X178 @ X179)))) | ~ ! [X183 : term] : (($true = ((X180 @ (sub @ X183 @ X179)))) | ($true != ((var @ X183)))) | ~ ! [X184 : term] : (($true = ((X180 @ (lam @ X184)))) | ~ ! [X185 : term] : (($true = ((X180 @ (sub @ X184 @ (push @ X185 @ id))))) | ($true != ((X180 @ X185))))))))))) & (hoasinduction_lem1_gthm = $true) & (axassoc = $true)),
% 5.11/1.35 inference(flattening,[],[f9])).
% 5.11/1.35 thf(f11,plain,(
% 5.11/1.35 (hoasapnotvar_lthm = $true) & (hoaslamnotvar = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem1 = $true) & (one = ((d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (axmap = $true) & (! [X145 : (term > $o),X146 : term] : (? [X151 : term] : (($true = ((var @ X151))) & ($true != ((X145 @ X151)))) | ($true = ((X145 @ X146))) | ? [X147 : term] : (! [X148 : term] : (($true = ((X145 @ (sub @ X147 @ (push @ X148 @ id))))) | ($true != ((X145 @ X148)))) & ($true != ((X145 @ (lam @ X147))))) | ? [X149 : term,X150 : term] : (($true != ((X145 @ (ap @ X150 @ X149)))) & ($true = ((X145 @ X149))) & ($true = ((X145 @ X150))))) <=> (induction2 = $true)) & (! [X18 : subst,X19 : (term > $o),X17 : term] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21))) <=> (pushprop_lem0 = $true)) & ((! [X94 : term] : (((sub @ X94 @ id)) = X94) | ? [X93 : term] : (((sub @ X93 @ id)) != X93)) <=> (termmset_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (! [X383 : (subst > term > subst > $o),X382 : term] : (? [X384 : (subst > term > term)] : (! [X385 : term] : (($true != ((X383 @ id @ X385 @ id))) | ($true = ((X383 @ id @ (X384 @ id @ X385) @ id)))) & ($true != ((X383 @ id @ (lam @ (X384 @ sh @ one)) @ id))) & ! [X386 : subst,X388 : subst,X387 : term] : (((sub @ (X384 @ X386 @ X387) @ X388)) = ((X384 @ (comp @ X386 @ X388) @ (sub @ X387 @ X388))))) | ($true = ((X383 @ id @ (lam @ (sub @ X382 @ (push @ one @ sh))) @ id))) | ? [X389 : term] : (($true != ((X383 @ id @ (sub @ X382 @ (push @ X389 @ id)) @ id))) & ($true = ((X383 @ id @ X389 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((axvarcons = $true) <=> ! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117)) & (hoasinduction_lem2v2_gthm = $true) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((((! [X440 : (subst > term > subst > $o),X441 : term] : (? [X443 : term,X442 : term] : (($true = ((X440 @ id @ X442 @ id))) & ($true != ((X440 @ id @ (ap @ (sub @ X442 @ id) @ X443) @ id))) & ($true = ((X440 @ id @ X443 @ id)))) | ? [X444 : (subst > term > term)] : (! [X447 : subst,X446 : subst,X445 : term] : (((X444 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X444 @ X447 @ X445) @ X446))) & ($true != ((X440 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X440 @ id @ (X444 @ id @ X448) @ id))) | (((X440 @ id @ X448 @ id)) != $true))) | ($true = ((X440 @ id @ X441 @ id)))) | ? [X432 : term,X430 : (subst > term > subst > $o),X431 : (term > $o)] : (! [X439 : term] : (($true = ((X431 @ (sub @ X432 @ (push @ X439 @ id))))) | ($true != ((X431 @ X439)))) & (((X431 @ (lam @ X432))) != $true) & ! [X438 : term] : (((X430 @ id @ X438 @ id)) = ((X431 @ X438))) & ! [X433 : (subst > term > term)] : (? [X435 : term,X436 : subst,X434 : subst] : (((sub @ (X433 @ X434 @ X435) @ X436)) != ((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436)))) | ? [X437 : term] : (($true != ((X430 @ id @ (X433 @ id @ X437) @ id))) & ($true = ((X430 @ id @ X437 @ id)))) | ($true = ((X430 @ id @ (lam @ (X433 @ sh @ one)) @ id)))))) | ? [X429 : term] : (((sub @ X429 @ id)) != X429)) | ? [X423 : term,X422 : (term > $o)] : (($true != ((X422 @ X423))) & ! [X428 : term] : (($true != ((var @ X428))) | ($true = ((X422 @ X428)))) & ! [X426 : term,X427 : term] : (($true = ((X422 @ (ap @ X426 @ X427)))) | ($true != ((X422 @ X426))) | ($true != ((X422 @ X427)))) & ! [X424 : term] : (? [X425 : term] : (($true = ((X422 @ X425))) & ($true != ((X422 @ (sub @ X424 @ (push @ X425 @ id)))))) | (((X422 @ (lam @ X424))) = $true)))) | ? [X419 : (subst > term > subst > $o)] : ! [X420 : (term > $o)] : ? [X421 : term] : (((X419 @ id @ X421 @ id)) != ((X420 @ X421)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & (axabs = $true) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) <=> (hoasapinj2 = $true)) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem2v2 = $true) & (! [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (? [X471 : term] : (((X467 @ X471)) != ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) <=> (pushprop_lem1v2 = $true)) & (((var @ (d2term @ d_one))) != $true) & ((? [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 != X41) & (((ap @ X38 @ X41)) = ((ap @ X40 @ X39)))) | ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & (((! [X347 : term,X346 : (subst > term > subst > $o)] : (($true = ((X346 @ id @ (lam @ X347) @ id))) | ? [X353 : term] : (($true = ((X346 @ id @ X353 @ id))) & (((X346 @ id @ (sub @ X347 @ (push @ X353 @ id)) @ id)) != $true)) | ? [X348 : (subst > term > term)] : (($true != ((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id))) & ! [X351 : subst,X350 : subst,X352 : term] : (((sub @ (X348 @ X351 @ X352) @ X350)) = ((X348 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350)))) & ! [X349 : term] : (($true != ((X346 @ id @ X349 @ id))) | ($true = ((X346 @ id @ (X348 @ id @ X349) @ id)))))) | ? [X338 : term,X339 : (subst > term > subst > $o)] : (! [X340 : term] : (($true != ((X339 @ id @ X340 @ id))) | ($true = ((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)))) & ($true != ((X339 @ id @ (lam @ (sub @ X338 @ (push @ one @ sh))) @ id))) & ! [X341 : (subst > term > term)] : (($true = ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id))) | ? [X342 : term] : ((((X339 @ id @ X342 @ id)) = $true) & ($true != ((X339 @ id @ (X341 @ id @ X342) @ id)))) | ? [X344 : term,X345 : subst,X343 : subst] : (((X341 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345))) != ((sub @ (X341 @ X343 @ X344) @ X345)))))) | ? [X337 : term] : (((sub @ X337 @ id)) != X337)) <=> (hoasinduction_lem3a_lthm = $true)) & (lamnotvar = $true) & ((shinj = $true) <=> ! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh))))) & ((((! [X101 : subst,X102 : (subst > term > term),X104 : term,X103 : (subst > term > term)] : (? [X106 : subst,X105 : subst,X107 : term] : (((X103 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X103 @ X105 @ X107) @ X106))) | ? [X109 : subst,X108 : term,X110 : subst] : (((X102 @ (comp @ X109 @ X110) @ (sub @ X108 @ X110))) != ((sub @ (X102 @ X109 @ X108) @ X110))) | (((X103 @ X101 @ X104)) = ((X102 @ X101 @ X104))) | (((lam @ (X102 @ sh @ one))) != ((lam @ (X103 @ sh @ one))))) | ? [X99 : term,X100 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100))))) | ? [X97 : term,X98 : subst] : (((comp @ sh @ (push @ X97 @ X98))) != X98)) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96)) <=> (hoaslaminj_lthm = $true)) & (! [X137 : (subst > term > subst > $o),X136 : term] : (? [X139 : term,X138 : term] : (($true = ((X137 @ id @ X139 @ id))) & ($true = ((X137 @ id @ X138 @ id))) & ($true != ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ($true = ((X137 @ id @ X136 @ id))) | ? [X140 : (subst > term > term)] : (! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ($true != ((X137 @ id @ X144 @ id)))) & ! [X143 : term,X142 : subst,X141 : subst] : (((sub @ (X140 @ X142 @ X143) @ X141)) = ((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141)))) & ($true != ((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X111 : term,X113 : subst,X112 : (term > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) <=> (pushprop_lem0_lthm = $true)) & ((substmonoid_lthm = $true) <=> (((! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393)) | ? [X391 : subst] : (((comp @ X391 @ id)) != X391)) | ? [X390 : subst] : (((comp @ id @ X390)) != X390))) & (lamnotap != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X326 : term,X325 : (subst > term > subst > $o)] : (? [X327 : (subst > term > term),X328 : term] : (! [X335 : term,X333 : subst,X334 : subst] : (((sub @ (X327 @ X334 @ X335) @ X333)) = ((sub @ (sub @ X328 @ (push @ X335 @ X334)) @ X333))) & ! [X330 : subst,X331 : subst,X329 : term] : (((sub @ X328 @ (push @ (sub @ X329 @ X331) @ (comp @ X330 @ X331)))) = ((X327 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331)))) & ! [X332 : term] : ((((X325 @ id @ X332 @ id)) != $true) | ($true = ((X325 @ id @ (X327 @ id @ X332) @ id)))) & (((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id)) != $true)) | ? [X336 : term] : ((((X325 @ id @ X336 @ id)) = $true) & ($true != ((X325 @ id @ (sub @ X326 @ (push @ X336 @ id)) @ id)))) | ($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lthm = $true) <=> (((! [X296 : (subst > term > subst > $o),X295 : term] : (? [X311 : term,X312 : term] : ((((X296 @ id @ X311 @ id)) = $true) & ($true = ((X296 @ id @ X312 @ id))) & ($true != ((X296 @ id @ (ap @ (sub @ X312 @ id) @ X311) @ id)))) | ? [X300 : term,X299 : subst,X298 : subst,X301 : subst] : (($true = ((X296 @ X298 @ X300 @ (comp @ X301 @ X299)))) & ($true != ((X296 @ (comp @ X298 @ X301) @ (sub @ X300 @ X301) @ X299)))) | ? [X305 : subst,X304 : subst,X303 : term,X302 : subst] : (($true != ((X296 @ X304 @ X303 @ (comp @ X302 @ X305)))) & ($true = ((X296 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302) @ X305)))) | ? [X297 : term] : (($true != ((X296 @ id @ X297 @ id))) & ($true = ((var @ (sub @ X297 @ id))))) | ($true = ((X296 @ id @ X295 @ id))) | ? [X306 : (subst > term > term)] : (($true != ((X296 @ id @ (lam @ (X306 @ sh @ one)) @ id))) & ! [X308 : subst,X310 : subst,X309 : term] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) & ! [X307 : term] : (($true = ((X296 @ id @ (X306 @ id @ X307) @ id))) | ($true != ((X296 @ id @ X307 @ id)))))) | ? [X280 : term,X279 : (subst > term > subst > $o)] : (! [X282 : (subst > term > term)] : (($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ? [X286 : subst,X285 : term,X284 : subst] : (((X282 @ (comp @ X286 @ X284) @ (sub @ X285 @ X284))) != ((sub @ (X282 @ X286 @ X285) @ X284))) | ? [X283 : term] : ((((X279 @ id @ (X282 @ id @ X283) @ id)) != $true) & ($true = ((X279 @ id @ X283 @ id))))) & ! [X287 : subst,X290 : subst,X289 : subst,X288 : term] : (($true != ((X279 @ (comp @ X289 @ X290) @ (sub @ X288 @ X290) @ X287))) | ($true = ((X279 @ X289 @ X288 @ (comp @ X290 @ X287))))) & ! [X293 : subst,X294 : term,X291 : subst,X292 : subst] : (($true = ((X279 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X291))) | ($true != ((X279 @ X293 @ X294 @ (comp @ X292 @ X291))))) & ($true != ((X279 @ id @ (lam @ X280) @ id))) & ! [X281 : term] : ((((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) = $true) | ($true != ((X279 @ id @ X281 @ id)))))) | ? [X268 : (subst > term > subst > $o),X266 : term,X267 : term] : (! [X271 : subst,X274 : subst,X272 : subst,X273 : term] : (($true = ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271))) | ($true != ((X268 @ X272 @ X273 @ (comp @ X274 @ X271))))) & ($true = ((X268 @ id @ X266 @ id))) & ! [X276 : subst,X277 : subst,X278 : subst,X275 : term] : (($true = ((X268 @ X277 @ X275 @ (comp @ X278 @ X276)))) | (((X268 @ (comp @ X277 @ X278) @ (sub @ X275 @ X278) @ X276)) != $true)) & ($true != ((X268 @ id @ (ap @ X266 @ X267) @ id))) & ($true = ((X268 @ id @ X267 @ id))) & ! [X270 : term,X269 : term] : (($true != ((X268 @ id @ X269 @ id))) | (((X268 @ id @ X270 @ id)) != $true) | ($true = ((X268 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)))))) | ? [X259 : (term > $o),X260 : term] : (! [X263 : term] : ((((X259 @ (lam @ X263))) = $true) | ? [X264 : term] : ((((X259 @ X264)) = $true) & ($true != ((X259 @ (sub @ X263 @ (push @ X264 @ id))))))) & ($true != ((X259 @ X260))) & ! [X265 : term] : ((((var @ X265)) != $true) | ($true = ((X259 @ X265)))) & ! [X262 : term,X261 : term] : ((((X259 @ X262)) != $true) | ($true != ((X259 @ X261))) | ($true = ((X259 @ (ap @ X262 @ X261)))))))) & (! [X403 : (subst > term > subst > $o),X404 : term] : (? [X409 : subst,X406 : subst,X407 : term,X408 : subst] : (($true != ((X403 @ X408 @ X407 @ (comp @ X409 @ X406)))) & ($true = ((X403 @ (comp @ X408 @ X409) @ (sub @ X407 @ X409) @ X406)))) | ? [X405 : term] : (($true != ((X403 @ id @ (sub @ X404 @ (push @ X405 @ id)) @ id))) & ($true = ((X403 @ id @ X405 @ id)))) | ? [X417 : subst,X418 : subst,X415 : subst,X416 : term] : (($true = ((X403 @ X418 @ X416 @ (comp @ X417 @ X415)))) & ($true != ((X403 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417) @ X415)))) | ? [X410 : (subst > term > term)] : (! [X414 : term] : (($true = ((X403 @ id @ (X410 @ id @ X414) @ id))) | ($true != ((X403 @ id @ X414 @ id)))) & ! [X411 : term,X412 : subst,X413 : subst] : (((X410 @ (comp @ X412 @ X413) @ (sub @ X411 @ X413))) = ((sub @ (X410 @ X412 @ X411) @ X413))) & ($true != ((X403 @ id @ (lam @ (X410 @ sh @ one)) @ id)))) | ($true = ((X403 @ id @ (lam @ X404) @ id)))) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X152 : (term > $o),X153 : term,X155 : (subst > term > subst > $o),X154 : term] : (? [X166 : term] : (((X155 @ id @ X166 @ id)) != ((X152 @ X166))) | ? [X162 : subst,X163 : subst,X164 : subst,X165 : term] : (($true = ((X155 @ X163 @ X165 @ (comp @ X162 @ X164)))) & ($true != ((X155 @ (comp @ X163 @ X162) @ (sub @ X165 @ X162) @ X164)))) | ($true != ((X152 @ X154))) | ($true != ((X152 @ X153))) | ? [X159 : subst,X158 : subst,X157 : subst,X156 : term] : (($true != ((X155 @ X159 @ X156 @ (comp @ X157 @ X158)))) & ($true = ((X155 @ (comp @ X159 @ X157) @ (sub @ X156 @ X157) @ X158)))) | ? [X161 : term,X160 : term] : (($true != ((X155 @ id @ (ap @ (sub @ X161 @ id) @ X160) @ id))) & ($true = ((X155 @ id @ X160 @ id))) & (((X155 @ id @ X161 @ id)) = $true)) | ($true = ((X152 @ (ap @ X153 @ X154)))))) & (! [X367 : term,X369 : (subst > term > subst > $o),X368 : term] : (? [X376 : subst,X377 : subst,X379 : term,X378 : subst] : (($true = ((X369 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378) @ X376))) & ($true != ((X369 @ X377 @ X379 @ (comp @ X378 @ X376))))) | ($true != ((X369 @ id @ X367 @ id))) | ($true != ((X369 @ id @ X368 @ id))) | ? [X370 : term,X371 : term] : ((((X369 @ id @ X371 @ id)) = $true) & ($true != ((X369 @ id @ (ap @ (sub @ X371 @ id) @ X370) @ id))) & ($true = ((X369 @ id @ X370 @ id)))) | ? [X372 : subst,X375 : term,X374 : subst,X373 : subst] : ((((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) != $true) & ($true = ((X369 @ X373 @ X375 @ (comp @ X374 @ X372))))) | ($true = ((X369 @ id @ (ap @ X367 @ X368) @ id)))) <=> (hoasinduction_lem2 = $true)) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) != ((d2subst @ X364))) | (X363 = X364)) & (ulamvar1 != $true) & (! [X1 : (term > $o),X0 : term] : (($true = ((X1 @ X0))) | ? [X5 : term] : (($true != ((X1 @ (lam @ X5)))) & (((X1 @ X5)) = $true)) | ? [X2 : term,X3 : term] : (($true = ((X1 @ X3))) & ($true = ((X1 @ X2))) & ($true != ((X1 @ (ap @ X3 @ X2))))) | ? [X4 : term] : (($true = ((var @ X4))) & (((X1 @ X4)) != $true))) <=> (induction = $true)) & (((! [X195 : (term > $o),X196 : (subst > term > subst > $o),X194 : term] : (? [X203 : term] : (((X195 @ X203)) != ((X196 @ id @ X203 @ id))) | ? [X197 : term] : (($true != ((X195 @ (sub @ X194 @ (push @ X197 @ id))))) & ($true = ((X195 @ X197)))) | ? [X198 : (subst > term > term)] : (($true != ((X196 @ id @ (lam @ (X198 @ sh @ one)) @ id))) & ! [X202 : term] : (($true != ((X196 @ id @ X202 @ id))) | ($true = ((X196 @ id @ (X198 @ id @ X202) @ id)))) & ! [X201 : term,X200 : subst,X199 : subst] : (((sub @ (X198 @ X199 @ X201) @ X200)) = ((X198 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200))))) | ($true = ((X195 @ (lam @ X194))))) | ? [X193 : term] : (((sub @ X193 @ id)) != X193)) | ? [X189 : term] : ! [X190 : (subst > term > term)] : ? [X192 : subst,X191 : term] : (((X190 @ X192 @ X191)) != ((sub @ X189 @ (push @ X191 @ X192))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X233 : term,X232 : (subst > term > subst > $o)] : (($true = ((X232 @ id @ (lam @ X233) @ id))) | ? [X234 : (subst > term > term)] : (($true != ((X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) & ! [X235 : term] : (($true != ((X232 @ id @ X235 @ id))) | ($true = ((X232 @ id @ (X234 @ id @ X235) @ id)))) & ! [X237 : subst,X238 : subst,X236 : term] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ? [X239 : term] : (($true != ((X232 @ id @ (sub @ X233 @ (push @ X239 @ id)) @ id))) & ($true = ((X232 @ id @ X239 @ id)))))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X530 : term] : ? [X531 : (subst > term > term)] : ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533))))) & (induction2_gthm = $true) & (axclos = $true) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) <=> (axidl = $true)) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (hoasinduction_lem3_gthm = $true) & ! [X534 : d_term,X535 : d_term] : ((((d2term @ X534)) != ((d2term @ X535))) | (X534 = X535)) & (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)))))))))))))) & ! [X490 : d_subst] : (d_id = X490) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : (subst > term > term)] : (! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | ($true != ((X512 @ id @ X515 @ id)))) & ! [X518 : subst,X516 : term,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id)))) | ? [X524 : term,X523 : term] : (($true = ((X512 @ id @ X523 @ id))) & ($true = ((X512 @ id @ X524 @ id))) & ($true != ((X512 @ id @ (ap @ (sub @ X524 @ id) @ X523) @ id)))) | ? [X525 : term] : ((((var @ (sub @ X525 @ id))) = $true) & ($true != ((X512 @ id @ X525 @ id)))) | ? [X528 : subst,X527 : subst,X526 : subst,X529 : term] : (($true != ((X512 @ X528 @ X529 @ (comp @ X527 @ X526)))) & ($true = ((X512 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527) @ X526)))) | ($true = ((X512 @ id @ X513 @ id))) | ? [X522 : subst,X521 : subst,X519 : term,X520 : subst] : (($true != ((X512 @ (comp @ X520 @ X522) @ (sub @ X519 @ X522) @ X521))) & ($true = ((X512 @ X520 @ X519 @ (comp @ X522 @ X521)))))) | ? [X502 : (subst > term > subst > $o),X504 : (term > $o),X503 : term] : (($true != ((X504 @ (lam @ X503)))) & ! [X507 : (subst > term > term)] : (? [X508 : term] : ((((X502 @ id @ X508 @ id)) = $true) & ($true != ((X502 @ id @ (X507 @ id @ X508) @ id)))) | ($true = ((X502 @ id @ (lam @ (X507 @ sh @ one)) @ id))) | ? [X510 : subst,X509 : subst,X511 : term] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) != ((sub @ (X507 @ X509 @ X511) @ X510)))) & ! [X506 : term] : (($true = ((X504 @ (sub @ X503 @ (push @ X506 @ id))))) | ($true != ((X504 @ X506)))) & ! [X505 : term] : (((X504 @ X505)) = ((X502 @ id @ X505 @ id))))) | ? [X501 : term] : (((sub @ X501 @ id)) != X501)) | ? [X494 : term,X495 : (term > $o)] : (! [X496 : term] : (($true != ((var @ X496))) | ($true = ((X495 @ X496)))) & ($true != ((X495 @ X494))) & ! [X500 : term,X499 : term] : (($true != ((X495 @ X499))) | (((X495 @ (ap @ X500 @ X499))) = $true) | ($true != ((X495 @ X500)))) & ! [X497 : term] : (($true = ((X495 @ (lam @ X497)))) | ? [X498 : term] : (($true = ((X495 @ X498))) & ($true != ((X495 @ (sub @ X497 @ (push @ X498 @ id))))))))) | ? [X491 : (subst > term > subst > $o)] : ! [X492 : (term > $o)] : ? [X493 : term] : (((X491 @ id @ X493 @ id)) != ((X492 @ X493))))) & (((! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)) | ? [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) = ((ap @ X216 @ X219))) & (X216 != X217))) | ? [X215 : term] : (((sub @ X215 @ id)) != X215)) <=> (hoasapinj1_lthm = $true)) & ((induction2_lthm = $true) <=> ((! [X87 : (term > $o),X86 : term] : (? [X90 : term,X91 : term] : (($true != ((X87 @ (ap @ X91 @ X90)))) & ($true = ((X87 @ X90))) & ($true = ((X87 @ X91)))) | ? [X92 : term] : ((((var @ X92)) = $true) & ($true != ((X87 @ X92)))) | (((X87 @ X86)) = $true) | ? [X88 : term] : (($true != ((X87 @ (lam @ X88)))) & ! [X89 : term] : (($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id))))) | ($true != ((X87 @ X89)))))) | ? [X79 : subst,X78 : (term > $o),X80 : term] : (! [X81 : term] : (? [X82 : term] : (($true != ((X78 @ (sub @ X81 @ (push @ X82 @ id))))) & ($true = ((X78 @ X82)))) | ($true = ((X78 @ (lam @ X81))))) & ! [X83 : term] : (($true != ((var @ X83))) | ($true = ((X78 @ (sub @ X83 @ X79))))) & ! [X85 : term,X84 : term] : (($true != ((X78 @ X84))) | (((X78 @ (ap @ X84 @ X85))) = $true) | ($true != ((X78 @ X85)))) & ($true != ((X78 @ (sub @ X80 @ X79)))))) | ? [X77 : term] : (((sub @ X77 @ id)) != X77))) & (ulamvarsh = $true) & (induction2lem_gthm = $true) & (! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) <=> (pushprop_lem1 = $true)) & (((d2subst @ d_id)) = sh) & ((axshiftcons = $true) <=> ! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X34 : term] : ? [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) = ((X35 @ sh @ one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X454 : (subst > term > subst > $o),X455 : (term > $o),X453 : term] : (? [X456 : (subst > term > term)] : (($true != ((X454 @ id @ (lam @ (X456 @ sh @ one)) @ id))) & ! [X460 : subst,X458 : term,X459 : subst] : (((X456 @ (comp @ X459 @ X460) @ (sub @ X458 @ X460))) = ((sub @ (X456 @ X459 @ X458) @ X460))) & ! [X457 : term] : (($true != ((X454 @ id @ X457 @ id))) | ($true = ((X454 @ id @ (X456 @ id @ X457) @ id))))) | ? [X462 : term] : (((X454 @ id @ X462 @ id)) != ((X455 @ X462))) | ? [X461 : term] : ((((X455 @ X461)) = $true) & ($true != ((X455 @ (sub @ X453 @ (push @ X461 @ id)))))) | ($true = ((X455 @ (lam @ X453))))) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar = $true) & (pushprop = $true) & ((apinj1 = $true) <=> ! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205))))) & (hoasinduction_gthm = $true) & ((apinj2 = $true) <=> ! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466))) & (pushprop_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & (! [X22 : term] : ? [X23 : (subst > term > term)] : ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasapnotvar_gthm = $true) & (axvarshift = $true) & ((axscons = $true) <=> ! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188)) & (hoasapinj1_gthm = $true) & ((termmset = $true) <=> ! [X354 : term] : (((sub @ X354 @ id)) = X354)) & (hoasinduction_lem1_lthm = $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) | ? [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) != X396)) | ? [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) != X394))) & (pushprop_lem2v2_lthm = $true) & (! [X186 : term] : ? [X187 : (subst > term > term)] : (((X187 @ sh @ one)) = ((sub @ X186 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) <=> (laminj = $true)) & (! [X536 : (subst > term > subst > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) <=> (hoasinduction_lem0_lthm = $true)) & ((hoaslamnotap = $true) <=> ! [X357 : term,X355 : term,X356 : (subst > term > term)] : (? [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) != ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357))))) & (! [X120 : (subst > term > subst > $o),X118 : term,X119 : (term > $o)] : (($true = ((X119 @ (lam @ X118)))) | ? [X135 : term] : (($true != ((X119 @ (sub @ X118 @ (push @ X135 @ id))))) & ($true = ((X119 @ X135)))) | ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X120 @ id @ (X121 @ id @ X125) @ id))) | ($true != ((X120 @ id @ X125 @ id)))) & ($true != ((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id))) & ! [X123 : subst,X124 : term,X122 : subst] : (((X121 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) = ((sub @ (X121 @ X122 @ X124) @ X123)))) | ? [X130 : term] : (((X120 @ id @ X130 @ id)) != ((X119 @ X130))) | ? [X129 : subst,X126 : subst,X127 : term,X128 : subst] : (($true != ((X120 @ X126 @ X127 @ (comp @ X128 @ X129)))) & ($true = ((X120 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128) @ X129)))) | ? [X131 : subst,X132 : subst,X134 : term,X133 : subst] : (($true != ((X120 @ (comp @ X132 @ X131) @ (sub @ X134 @ X131) @ X133))) & (((X120 @ X132 @ X134 @ (comp @ X131 @ X133))) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_lem0_gthm = $true) & (apnotvar = $true) & (axapp = $true) & ((? [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) != X7) | ! [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) = $true) | ($true != ((X11 @ X8))) | ? [X12 : term] : (((X9 @ X12)) != ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((d2subst @ d_id)) = id) & (! [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316))) | ? [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) != ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ? [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X315 @ X322 @ X320) @ X321)))) <=> (hoaslaminj = $true)) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ! [X366 : d_term] : (d_one = X366) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X472 : term,X473 : (subst > term > subst > $o)] : (? [X487 : term,X488 : term] : (($true = ((X473 @ id @ X487 @ id))) & ($true != ((X473 @ id @ (ap @ (sub @ X487 @ id) @ X488) @ id))) & ($true = ((X473 @ id @ X488 @ id)))) | ? [X481 : subst,X479 : term,X480 : subst,X478 : subst] : (($true = ((X473 @ X480 @ X479 @ (comp @ X478 @ X481)))) & ($true != ((X473 @ (comp @ X480 @ X478) @ (sub @ X479 @ X478) @ X481)))) | ($true = ((X473 @ id @ X472 @ id))) | ? [X489 : term] : (($true = ((var @ (sub @ X489 @ id)))) & ($true != ((X473 @ id @ X489 @ id)))) | ? [X475 : subst,X474 : term,X476 : subst,X477 : subst] : (($true = ((X473 @ (comp @ X477 @ X475) @ (sub @ X474 @ X475) @ X476))) & ($true != ((X473 @ X477 @ X474 @ (comp @ X475 @ X476))))) | ? [X482 : (subst > term > term)] : (! [X483 : term] : (($true != ((X473 @ id @ X483 @ id))) | ($true = ((X473 @ id @ (X482 @ id @ X483) @ id)))) & (((X473 @ id @ (lam @ (X482 @ sh @ one)) @ id)) != $true) & ! [X486 : term,X485 : subst,X484 : subst] : (((X482 @ (comp @ X485 @ X484) @ (sub @ X486 @ X484))) = ((sub @ (X482 @ X485 @ X486) @ X484))))) <=> (hoasinduction = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotvar_gthm = $true) & (! [X225 : term,X224 : (subst > term > subst > $o)] : (? [X231 : term] : (($true != ((X224 @ id @ (sub @ X225 @ (push @ X231 @ id)) @ id))) & ($true = ((X224 @ id @ X231 @ id)))) | ? [X226 : (subst > term > term)] : (! [X228 : subst,X229 : term,X227 : subst] : (((X226 @ (comp @ X227 @ X228) @ (sub @ X229 @ X228))) = ((sub @ (X226 @ X227 @ X229) @ X228))) & ($true != ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id))) & ! [X230 : term] : (($true = ((X224 @ id @ (X226 @ id @ X230) @ id))) | ($true != ((X224 @ id @ X230 @ id))))) | ($true = ((X224 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & ((axidr = $true) <=> ! [X539 : subst] : (((comp @ X539 @ id)) = X539)) & (ulamvarind = $true) & (pushprop_lem3v2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((! [X55 : (subst > term > subst > $o),X56 : term] : (? [X61 : term] : (($true = ((X55 @ id @ X61 @ id))) & ($true != ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)))) | ? [X67 : subst,X69 : subst,X70 : subst,X68 : term] : (($true = ((X55 @ X67 @ X68 @ (comp @ X69 @ X70)))) & ($true != ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ? [X60 : subst,X58 : term,X59 : subst,X57 : subst] : (($true != ((X55 @ X59 @ X58 @ (comp @ X57 @ X60)))) & ($true = ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60)))) | ? [X62 : (subst > term > term)] : (! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & (((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true) & ! [X63 : term] : (($true = ((X55 @ id @ (X62 @ id @ X63) @ id))) | ($true != ((X55 @ id @ X63 @ id)))))) | ? [X48 : term,X47 : (subst > term > subst > $o)] : (! [X49 : (subst > term > term)] : (? [X53 : term] : (($true != ((X47 @ id @ (X49 @ id @ X53) @ id))) & ($true = ((X47 @ id @ X53 @ id)))) | ? [X50 : term,X52 : subst,X51 : subst] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) != ((sub @ (X49 @ X52 @ X50) @ X51))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id)))) & ($true != ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id))) & ! [X54 : term] : (($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))) | ($true != ((X47 @ id @ X54 @ id)))))) | ? [X46 : term] : (((sub @ X46 @ id)) != X46)) <=> (hoasinduction_lem3_lthm = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X240 : term] : (((sub @ X240 @ id)) != X240) | ! [X243 : term,X241 : (subst > term > subst > $o),X242 : (term > $o)] : (? [X253 : term] : (((X241 @ id @ X253 @ id)) != ((X242 @ X253))) | ? [X257 : term,X254 : subst,X255 : subst,X256 : subst] : (($true = ((X241 @ (comp @ X255 @ X256) @ (sub @ X257 @ X256) @ X254))) & ($true != ((X241 @ X255 @ X257 @ (comp @ X256 @ X254))))) | ? [X250 : term,X252 : subst,X249 : subst,X251 : subst] : (($true = ((X241 @ X252 @ X250 @ (comp @ X249 @ X251)))) & ($true != ((X241 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)))) | ? [X258 : term] : (($true != ((X242 @ (sub @ X243 @ (push @ X258 @ id))))) & ($true = ((X242 @ X258)))) | ? [X244 : (subst > term > term)] : (! [X248 : term] : (($true != ((X241 @ id @ X248 @ id))) | ($true = ((X241 @ id @ (X244 @ id @ X248) @ id)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id))) & ! [X247 : subst,X245 : subst,X246 : term] : (((sub @ (X244 @ X247 @ X246) @ X245)) = ((X244 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245))))) | ($true = ((X242 @ (lam @ X243))))))) & (! [X26 : subst,X28 : term,X27 : (term > $o)] : (? [X30 : term,X29 : term] : (($true = ((X27 @ X30))) & ($true = ((X27 @ X29))) & ($true != ((X27 @ (ap @ X30 @ X29))))) | ? [X31 : term] : (! [X32 : term] : (($true != ((X27 @ X32))) | ($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id)))))) & (((X27 @ (lam @ X31))) != $true)) | ? [X33 : term] : (($true != ((X27 @ (sub @ X33 @ X26)))) & ($true = ((var @ X33)))) | ($true = ((X27 @ (sub @ X28 @ X26))))) <=> (induction2lem = $true)) & (! [X71 : (subst > term > subst > $o)] : ? [X72 : (term > $o)] : ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotap_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (termmset_gthm = $true) & (pushprop_lthm = $true) & (hoaslamnotap_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X180 : (term > $o),X179 : subst,X178 : term] : (? [X184 : term] : (! [X185 : term] : (($true = ((X180 @ (sub @ X184 @ (push @ X185 @ id))))) | ($true != ((X180 @ X185)))) & ($true != ((X180 @ (lam @ X184))))) | ($true = ((X180 @ (sub @ X178 @ X179)))) | ? [X183 : term] : (($true = ((var @ X183))) & ($true != ((X180 @ (sub @ X183 @ X179))))) | ? [X181 : term,X182 : term] : (($true != ((X180 @ (ap @ X182 @ X181)))) & ($true = ((X180 @ X182))) & ($true = ((X180 @ X181))))) | ? [X173 : (term > $o),X172 : term] : ((((X173 @ X172)) != $true) & ! [X177 : term] : (($true = ((X173 @ (lam @ X177)))) | ($true != ((X173 @ X177)))) & ! [X176 : term] : (($true = ((X173 @ X176))) | ($true != ((var @ X176)))) & ! [X174 : term,X175 : term] : (($true != ((X173 @ X175))) | ($true = ((X173 @ (ap @ X175 @ X174)))) | ($true != ((X173 @ X174)))))) | ? [X171 : subst] : (((comp @ X171 @ id)) != X171)) | ? [X169 : subst,X170 : term] : (((comp @ sh @ (push @ X170 @ X169))) != X169)) | ? [X167 : subst,X168 : term] : (((sub @ one @ (push @ X168 @ X167))) != X168))) & (hoasinduction_lem1_gthm = $true) & (axassoc = $true)),
% 5.11/1.35 inference(ennf_transformation,[],[f10])).
% 5.11/1.35 thf(f12,plain,(
% 5.11/1.35 (axvarshift = $true) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X111 : term,X113 : subst,X112 : (term > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) <=> (pushprop_lem0_lthm = $true)) & (! [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316))) | ? [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) != ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ? [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X315 @ X322 @ X320) @ X321)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & ((? [X259 : (term > $o),X260 : term] : (! [X263 : term] : ((((X259 @ (lam @ X263))) = $true) | ? [X264 : term] : ((((X259 @ X264)) = $true) & ($true != ((X259 @ (sub @ X263 @ (push @ X264 @ id))))))) & ($true != ((X259 @ X260))) & ! [X265 : term] : ((((var @ X265)) != $true) | ($true = ((X259 @ X265)))) & ! [X262 : term,X261 : term] : ((((X259 @ X262)) != $true) | ($true != ((X259 @ X261))) | ($true = ((X259 @ (ap @ X262 @ X261)))))) | ? [X280 : term,X279 : (subst > term > subst > $o)] : (! [X282 : (subst > term > term)] : (($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ? [X286 : subst,X285 : term,X284 : subst] : (((X282 @ (comp @ X286 @ X284) @ (sub @ X285 @ X284))) != ((sub @ (X282 @ X286 @ X285) @ X284))) | ? [X283 : term] : ((((X279 @ id @ (X282 @ id @ X283) @ id)) != $true) & ($true = ((X279 @ id @ X283 @ id))))) & ! [X287 : subst,X290 : subst,X289 : subst,X288 : term] : (($true != ((X279 @ (comp @ X289 @ X290) @ (sub @ X288 @ X290) @ X287))) | ($true = ((X279 @ X289 @ X288 @ (comp @ X290 @ X287))))) & ! [X293 : subst,X294 : term,X291 : subst,X292 : subst] : (($true = ((X279 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X291))) | ($true != ((X279 @ X293 @ X294 @ (comp @ X292 @ X291))))) & ($true != ((X279 @ id @ (lam @ X280) @ id))) & ! [X281 : term] : ((((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) = $true) | ($true != ((X279 @ id @ X281 @ id))))) | ! [X296 : (subst > term > subst > $o),X295 : term] : (? [X311 : term,X312 : term] : ((((X296 @ id @ X311 @ id)) = $true) & ($true = ((X296 @ id @ X312 @ id))) & ($true != ((X296 @ id @ (ap @ (sub @ X312 @ id) @ X311) @ id)))) | ? [X300 : term,X299 : subst,X298 : subst,X301 : subst] : (($true = ((X296 @ X298 @ X300 @ (comp @ X301 @ X299)))) & ($true != ((X296 @ (comp @ X298 @ X301) @ (sub @ X300 @ X301) @ X299)))) | ? [X305 : subst,X304 : subst,X303 : term,X302 : subst] : (($true != ((X296 @ X304 @ X303 @ (comp @ X302 @ X305)))) & ($true = ((X296 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302) @ X305)))) | ? [X297 : term] : (($true != ((X296 @ id @ X297 @ id))) & ($true = ((var @ (sub @ X297 @ id))))) | ($true = ((X296 @ id @ X295 @ id))) | ? [X306 : (subst > term > term)] : (($true != ((X296 @ id @ (lam @ (X306 @ sh @ one)) @ id))) & ! [X308 : subst,X310 : subst,X309 : term] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) & ! [X307 : term] : (($true = ((X296 @ id @ (X306 @ id @ X307) @ id))) | ($true != ((X296 @ id @ X307 @ id)))))) | ? [X268 : (subst > term > subst > $o),X266 : term,X267 : term] : (! [X271 : subst,X274 : subst,X272 : subst,X273 : term] : (($true = ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271))) | ($true != ((X268 @ X272 @ X273 @ (comp @ X274 @ X271))))) & ($true = ((X268 @ id @ X266 @ id))) & ! [X276 : subst,X277 : subst,X278 : subst,X275 : term] : (($true = ((X268 @ X277 @ X275 @ (comp @ X278 @ X276)))) | (((X268 @ (comp @ X277 @ X278) @ (sub @ X275 @ X278) @ X276)) != $true)) & ($true != ((X268 @ id @ (ap @ X266 @ X267) @ id))) & ($true = ((X268 @ id @ X267 @ id))) & ! [X270 : term,X269 : term] : (($true != ((X268 @ id @ X269 @ id))) | (((X268 @ id @ X270 @ id)) != $true) | ($true = ((X268 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)))))) <=> (hoasinduction_lthm = $true)) & (! [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (? [X471 : term] : (((X467 @ X471)) != ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) <=> (pushprop_lem1v2 = $true)) & (hoasapinj2_gthm = $true) & ((! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) | ? [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) != X396) | ? [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) != X394)) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) <=> (hoasapinj2 = $true)) & (! [X536 : (subst > term > subst > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) <=> (hoasinduction_lem0_lthm = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & ((? [X494 : term,X495 : (term > $o)] : (! [X496 : term] : (($true != ((var @ X496))) | ($true = ((X495 @ X496)))) & ($true != ((X495 @ X494))) & ! [X500 : term,X499 : term] : (($true != ((X495 @ X499))) | (((X495 @ (ap @ X500 @ X499))) = $true) | ($true != ((X495 @ X500)))) & ! [X497 : term] : (($true = ((X495 @ (lam @ X497)))) | ? [X498 : term] : (($true = ((X495 @ X498))) & ($true != ((X495 @ (sub @ X497 @ (push @ X498 @ id)))))))) | ? [X491 : (subst > term > subst > $o)] : ! [X492 : (term > $o)] : ? [X493 : term] : (((X491 @ id @ X493 @ id)) != ((X492 @ X493))) | ! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : (subst > term > term)] : (! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | ($true != ((X512 @ id @ X515 @ id)))) & ! [X518 : subst,X516 : term,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id)))) | ? [X524 : term,X523 : term] : (($true = ((X512 @ id @ X523 @ id))) & ($true = ((X512 @ id @ X524 @ id))) & ($true != ((X512 @ id @ (ap @ (sub @ X524 @ id) @ X523) @ id)))) | ? [X525 : term] : ((((var @ (sub @ X525 @ id))) = $true) & ($true != ((X512 @ id @ X525 @ id)))) | ? [X528 : subst,X527 : subst,X526 : subst,X529 : term] : (($true != ((X512 @ X528 @ X529 @ (comp @ X527 @ X526)))) & ($true = ((X512 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527) @ X526)))) | ($true = ((X512 @ id @ X513 @ id))) | ? [X522 : subst,X521 : subst,X519 : term,X520 : subst] : (($true != ((X512 @ (comp @ X520 @ X522) @ (sub @ X519 @ X522) @ X521))) & ($true = ((X512 @ X520 @ X519 @ (comp @ X522 @ X521)))))) | ? [X502 : (subst > term > subst > $o),X504 : (term > $o),X503 : term] : (($true != ((X504 @ (lam @ X503)))) & ! [X507 : (subst > term > term)] : (? [X508 : term] : ((((X502 @ id @ X508 @ id)) = $true) & ($true != ((X502 @ id @ (X507 @ id @ X508) @ id)))) | ($true = ((X502 @ id @ (lam @ (X507 @ sh @ one)) @ id))) | ? [X510 : subst,X509 : subst,X511 : term] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) != ((sub @ (X507 @ X509 @ X511) @ X510)))) & ! [X506 : term] : (($true = ((X504 @ (sub @ X503 @ (push @ X506 @ id))))) | ($true != ((X504 @ X506)))) & ! [X505 : term] : (((X504 @ X505)) = ((X502 @ id @ X505 @ id)))) | ? [X501 : term] : (((sub @ X501 @ id)) != X501)) <=> (hoasinduction_lthm_3 = $true)) & ((termmset = $true) <=> ! [X354 : term] : (((sub @ X354 @ id)) = X354)) & (pushprop_lem0_gthm = $true) & (! [X454 : (subst > term > subst > $o),X455 : (term > $o),X453 : term] : (? [X456 : (subst > term > term)] : (($true != ((X454 @ id @ (lam @ (X456 @ sh @ one)) @ id))) & ! [X460 : subst,X458 : term,X459 : subst] : (((X456 @ (comp @ X459 @ X460) @ (sub @ X458 @ X460))) = ((sub @ (X456 @ X459 @ X458) @ X460))) & ! [X457 : term] : (($true != ((X454 @ id @ X457 @ id))) | ($true = ((X454 @ id @ (X456 @ id @ X457) @ id))))) | ? [X462 : term] : (((X454 @ id @ X462 @ id)) != ((X455 @ X462))) | ? [X461 : term] : ((((X455 @ X461)) = $true) & ($true != ((X455 @ (sub @ X453 @ (push @ X461 @ id)))))) | ($true = ((X455 @ (lam @ X453))))) <=> (hoasinduction_lem3v2a = $true)) & ((axscons = $true) <=> ! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & (! [X472 : term,X473 : (subst > term > subst > $o)] : (? [X487 : term,X488 : term] : (($true = ((X473 @ id @ X487 @ id))) & ($true != ((X473 @ id @ (ap @ (sub @ X487 @ id) @ X488) @ id))) & ($true = ((X473 @ id @ X488 @ id)))) | ? [X481 : subst,X479 : term,X480 : subst,X478 : subst] : (($true = ((X473 @ X480 @ X479 @ (comp @ X478 @ X481)))) & ($true != ((X473 @ (comp @ X480 @ X478) @ (sub @ X479 @ X478) @ X481)))) | ($true = ((X473 @ id @ X472 @ id))) | ? [X489 : term] : (($true = ((var @ (sub @ X489 @ id)))) & ($true != ((X473 @ id @ X489 @ id)))) | ? [X475 : subst,X474 : term,X476 : subst,X477 : subst] : (($true = ((X473 @ (comp @ X477 @ X475) @ (sub @ X474 @ X475) @ X476))) & ($true != ((X473 @ X477 @ X474 @ (comp @ X475 @ X476))))) | ? [X482 : (subst > term > term)] : (! [X483 : term] : (($true != ((X473 @ id @ X483 @ id))) | ($true = ((X473 @ id @ (X482 @ id @ X483) @ id)))) & (((X473 @ id @ (lam @ (X482 @ sh @ one)) @ id)) != $true) & ! [X486 : term,X485 : subst,X484 : subst] : (((X482 @ (comp @ X485 @ X484) @ (sub @ X486 @ X484))) = ((sub @ (X482 @ X485 @ X486) @ X484))))) <=> (hoasinduction = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X530 : term] : ? [X531 : (subst > term > term)] : ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533))))) & (! [X403 : (subst > term > subst > $o),X404 : term] : (? [X409 : subst,X406 : subst,X407 : term,X408 : subst] : (($true != ((X403 @ X408 @ X407 @ (comp @ X409 @ X406)))) & ($true = ((X403 @ (comp @ X408 @ X409) @ (sub @ X407 @ X409) @ X406)))) | ? [X405 : term] : (($true != ((X403 @ id @ (sub @ X404 @ (push @ X405 @ id)) @ id))) & ($true = ((X403 @ id @ X405 @ id)))) | ? [X417 : subst,X418 : subst,X415 : subst,X416 : term] : (($true = ((X403 @ X418 @ X416 @ (comp @ X417 @ X415)))) & ($true != ((X403 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417) @ X415)))) | ? [X410 : (subst > term > term)] : (! [X414 : term] : (($true = ((X403 @ id @ (X410 @ id @ X414) @ id))) | ($true != ((X403 @ id @ X414 @ id)))) & ! [X411 : term,X412 : subst,X413 : subst] : (((X410 @ (comp @ X412 @ X413) @ (sub @ X411 @ X413))) = ((sub @ (X410 @ X412 @ X411) @ X413))) & ($true != ((X403 @ id @ (lam @ (X410 @ sh @ one)) @ id)))) | ($true = ((X403 @ id @ (lam @ X404) @ id)))) <=> (hoasinduction_lem3 = $true)) & (! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (? [X48 : term,X47 : (subst > term > subst > $o)] : (! [X49 : (subst > term > term)] : (? [X53 : term] : (($true != ((X47 @ id @ (X49 @ id @ X53) @ id))) & ($true = ((X47 @ id @ X53 @ id)))) | ? [X50 : term,X52 : subst,X51 : subst] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) != ((sub @ (X49 @ X52 @ X50) @ X51))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id)))) & ($true != ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id))) & ! [X54 : term] : (($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))) | ($true != ((X47 @ id @ X54 @ id))))) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ! [X55 : (subst > term > subst > $o),X56 : term] : (? [X61 : term] : (($true = ((X55 @ id @ X61 @ id))) & ($true != ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)))) | ? [X67 : subst,X69 : subst,X70 : subst,X68 : term] : (($true = ((X55 @ X67 @ X68 @ (comp @ X69 @ X70)))) & ($true != ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ? [X60 : subst,X58 : term,X59 : subst,X57 : subst] : (($true != ((X55 @ X59 @ X58 @ (comp @ X57 @ X60)))) & ($true = ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60)))) | ? [X62 : (subst > term > term)] : (! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & (((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true) & ! [X63 : term] : (($true = ((X55 @ id @ (X62 @ id @ X63) @ id))) | ($true != ((X55 @ id @ X63 @ id)))))))) & ((hoasinduction_lem3a = $true) <=> ! [X233 : term,X232 : (subst > term > subst > $o)] : (($true = ((X232 @ id @ (lam @ X233) @ id))) | ? [X234 : (subst > term > term)] : (($true != ((X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) & ! [X235 : term] : (($true != ((X232 @ id @ X235 @ id))) | ($true = ((X232 @ id @ (X234 @ id @ X235) @ id)))) & ! [X237 : subst,X238 : subst,X236 : term] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ? [X239 : term] : (($true != ((X232 @ id @ (sub @ X233 @ (push @ X239 @ id)) @ id))) & ($true = ((X232 @ id @ X239 @ id)))))) & (axassoc = $true) & ! [X534 : d_term,X535 : d_term] : ((((d2term @ X534)) != ((d2term @ X535))) | (X534 = X535)) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X240 : term] : (((sub @ X240 @ id)) != X240) | ! [X243 : term,X241 : (subst > term > subst > $o),X242 : (term > $o)] : (? [X253 : term] : (((X241 @ id @ X253 @ id)) != ((X242 @ X253))) | ? [X257 : term,X254 : subst,X255 : subst,X256 : subst] : (($true = ((X241 @ (comp @ X255 @ X256) @ (sub @ X257 @ X256) @ X254))) & ($true != ((X241 @ X255 @ X257 @ (comp @ X256 @ X254))))) | ? [X250 : term,X252 : subst,X249 : subst,X251 : subst] : (($true = ((X241 @ X252 @ X250 @ (comp @ X249 @ X251)))) & ($true != ((X241 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)))) | ? [X258 : term] : (($true != ((X242 @ (sub @ X243 @ (push @ X258 @ id))))) & ($true = ((X242 @ X258)))) | ? [X244 : (subst > term > term)] : (! [X248 : term] : (($true != ((X241 @ id @ X248 @ id))) | ($true = ((X241 @ id @ (X244 @ id @ X248) @ id)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id))) & ! [X247 : subst,X245 : subst,X246 : term] : (((sub @ (X244 @ X247 @ X246) @ X245)) = ((X244 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245))))) | ($true = ((X242 @ (lam @ X243))))))) & ((hoaslaminj_lthm = $true) <=> (? [X97 : term,X98 : subst] : (((comp @ sh @ (push @ X97 @ X98))) != X98) | ! [X101 : subst,X102 : (subst > term > term),X104 : term,X103 : (subst > term > term)] : (? [X106 : subst,X105 : subst,X107 : term] : (((X103 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X103 @ X105 @ X107) @ X106))) | ? [X109 : subst,X108 : term,X110 : subst] : (((X102 @ (comp @ X109 @ X110) @ (sub @ X108 @ X110))) != ((sub @ (X102 @ X109 @ X108) @ X110))) | (((X103 @ X101 @ X104)) = ((X102 @ X101 @ X104))) | (((lam @ (X102 @ sh @ one))) != ((lam @ (X103 @ sh @ one))))) | ? [X99 : term,X100 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100)))) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96))) & (! [X1 : (term > $o),X0 : term] : (($true = ((X1 @ X0))) | ? [X5 : term] : (($true != ((X1 @ (lam @ X5)))) & (((X1 @ X5)) = $true)) | ? [X2 : term,X3 : term] : (($true = ((X1 @ X3))) & ($true = ((X1 @ X2))) & ($true != ((X1 @ (ap @ X3 @ X2))))) | ? [X4 : term] : (($true = ((var @ X4))) & (((X1 @ X4)) != $true))) <=> (induction = $true)) & ((hoasapinj1_lthm = $true) <=> (? [X215 : term] : (((sub @ X215 @ id)) != X215) | ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)) | ? [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) = ((ap @ X216 @ X219))) & (X216 != X217)))) & ((axvarcons = $true) <=> ! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X391 : subst] : (((comp @ X391 @ id)) != X391) | (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393)) | ? [X390 : subst] : (((comp @ id @ X390)) != X390)) <=> (substmonoid_lthm = $true)) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) <=> (laminj = $true)) & (! [X186 : term] : ? [X187 : (subst > term > term)] : (((X187 @ sh @ one)) = ((sub @ X186 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasapnotvar = $true) & (! [X137 : (subst > term > subst > $o),X136 : term] : (? [X139 : term,X138 : term] : (($true = ((X137 @ id @ X139 @ id))) & ($true = ((X137 @ id @ X138 @ id))) & ($true != ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ($true = ((X137 @ id @ X136 @ id))) | ? [X140 : (subst > term > term)] : (! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ($true != ((X137 @ id @ X144 @ id)))) & ! [X143 : term,X142 : subst,X141 : subst] : (((sub @ (X140 @ X142 @ X143) @ X141)) = ((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141)))) & ($true != ((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & ((axshiftcons = $true) <=> ! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X367 : term,X369 : (subst > term > subst > $o),X368 : term] : (? [X376 : subst,X377 : subst,X379 : term,X378 : subst] : (($true = ((X369 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378) @ X376))) & ($true != ((X369 @ X377 @ X379 @ (comp @ X378 @ X376))))) | ($true != ((X369 @ id @ X367 @ id))) | ($true != ((X369 @ id @ X368 @ id))) | ? [X370 : term,X371 : term] : ((((X369 @ id @ X371 @ id)) = $true) & ($true != ((X369 @ id @ (ap @ (sub @ X371 @ id) @ X370) @ id))) & ($true = ((X369 @ id @ X370 @ id)))) | ? [X372 : subst,X375 : term,X374 : subst,X373 : subst] : ((((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) != $true) & ($true = ((X369 @ X373 @ X375 @ (comp @ X374 @ X372))))) | ($true = ((X369 @ id @ (ap @ X367 @ X368) @ id)))) <=> (hoasinduction_lem2 = $true)) & (! [X26 : subst,X28 : term,X27 : (term > $o)] : (? [X30 : term,X29 : term] : (($true = ((X27 @ X30))) & ($true = ((X27 @ X29))) & ($true != ((X27 @ (ap @ X30 @ X29))))) | ? [X31 : term] : (! [X32 : term] : (($true != ((X27 @ X32))) | ($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id)))))) & (((X27 @ (lam @ X31))) != $true)) | ? [X33 : term] : (($true != ((X27 @ (sub @ X33 @ X26)))) & ($true = ((var @ X33)))) | ($true = ((X27 @ (sub @ X28 @ X26))))) <=> (induction2lem = $true)) & ((! [X94 : term] : (((sub @ X94 @ id)) = X94) | ? [X93 : term] : (((sub @ X93 @ id)) != X93)) <=> (termmset_lthm = $true)) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & ((? [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) != X7) | ! [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) = $true) | ($true != ((X11 @ X8))) | ? [X12 : term] : (((X9 @ X12)) != ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (! [X71 : (subst > term > subst > $o)] : ? [X72 : (term > $o)] : ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & ((induction2lem_lthm = $true) <=> (? [X171 : subst] : (((comp @ X171 @ id)) != X171) | ? [X167 : subst,X168 : term] : (((sub @ one @ (push @ X168 @ X167))) != X168) | ? [X169 : subst,X170 : term] : (((comp @ sh @ (push @ X170 @ X169))) != X169) | ! [X180 : (term > $o),X179 : subst,X178 : term] : (? [X184 : term] : (! [X185 : term] : (($true = ((X180 @ (sub @ X184 @ (push @ X185 @ id))))) | ($true != ((X180 @ X185)))) & ($true != ((X180 @ (lam @ X184))))) | ($true = ((X180 @ (sub @ X178 @ X179)))) | ? [X183 : term] : (($true = ((var @ X183))) & ($true != ((X180 @ (sub @ X183 @ X179))))) | ? [X181 : term,X182 : term] : (($true != ((X180 @ (ap @ X182 @ X181)))) & ($true = ((X180 @ X182))) & ($true = ((X180 @ X181))))) | ? [X173 : (term > $o),X172 : term] : ((((X173 @ X172)) != $true) & ! [X177 : term] : (($true = ((X173 @ (lam @ X177)))) | ($true != ((X173 @ X177)))) & ! [X176 : term] : (($true = ((X173 @ X176))) | ($true != ((var @ X176)))) & ! [X174 : term,X175 : term] : (($true != ((X173 @ X175))) | ($true = ((X173 @ (ap @ X175 @ X174)))) | ($true != ((X173 @ X174))))))) & (hoaslamnotvar_lthm = $true) & (! [X22 : term] : ? [X23 : (subst > term > term)] : ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((? [X189 : term] : ! [X190 : (subst > term > term)] : ? [X192 : subst,X191 : term] : (((X190 @ X192 @ X191)) != ((sub @ X189 @ (push @ X191 @ X192)))) | ! [X195 : (term > $o),X196 : (subst > term > subst > $o),X194 : term] : (? [X203 : term] : (((X195 @ X203)) != ((X196 @ id @ X203 @ id))) | ? [X197 : term] : (($true != ((X195 @ (sub @ X194 @ (push @ X197 @ id))))) & ($true = ((X195 @ X197)))) | ? [X198 : (subst > term > term)] : (($true != ((X196 @ id @ (lam @ (X198 @ sh @ one)) @ id))) & ! [X202 : term] : (($true != ((X196 @ id @ X202 @ id))) | ($true = ((X196 @ id @ (X198 @ id @ X202) @ id)))) & ! [X201 : term,X200 : subst,X199 : subst] : (((sub @ (X198 @ X199 @ X201) @ X200)) = ((X198 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200))))) | ($true = ((X195 @ (lam @ X194))))) | ? [X193 : term] : (((sub @ X193 @ id)) != X193)) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X145 : (term > $o),X146 : term] : (? [X151 : term] : (($true = ((var @ X151))) & ($true != ((X145 @ X151)))) | ($true = ((X145 @ X146))) | ? [X147 : term] : (! [X148 : term] : (($true = ((X145 @ (sub @ X147 @ (push @ X148 @ id))))) | ($true != ((X145 @ X148)))) & ($true != ((X145 @ (lam @ X147))))) | ? [X149 : term,X150 : term] : (($true != ((X145 @ (ap @ X150 @ X149)))) & ($true = ((X145 @ X149))) & ($true = ((X145 @ X150))))) <=> (induction2 = $true)) & ((? [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 != X41) & (((ap @ X38 @ X41)) = ((ap @ X40 @ X39)))) | ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & (! [X120 : (subst > term > subst > $o),X118 : term,X119 : (term > $o)] : (($true = ((X119 @ (lam @ X118)))) | ? [X135 : term] : (($true != ((X119 @ (sub @ X118 @ (push @ X135 @ id))))) & ($true = ((X119 @ X135)))) | ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X120 @ id @ (X121 @ id @ X125) @ id))) | ($true != ((X120 @ id @ X125 @ id)))) & ($true != ((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id))) & ! [X123 : subst,X124 : term,X122 : subst] : (((X121 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) = ((sub @ (X121 @ X122 @ X124) @ X123)))) | ? [X130 : term] : (((X120 @ id @ X130 @ id)) != ((X119 @ X130))) | ? [X129 : subst,X126 : subst,X127 : term,X128 : subst] : (($true != ((X120 @ X126 @ X127 @ (comp @ X128 @ X129)))) & ($true = ((X120 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128) @ X129)))) | ? [X131 : subst,X132 : subst,X134 : term,X133 : subst] : (($true != ((X120 @ (comp @ X132 @ X131) @ (sub @ X134 @ X131) @ X133))) & (((X120 @ X132 @ X134 @ (comp @ X131 @ X133))) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) != ((d2subst @ X364))) | (X363 = X364)) & ((? [X432 : term,X430 : (subst > term > subst > $o),X431 : (term > $o)] : (! [X439 : term] : (($true = ((X431 @ (sub @ X432 @ (push @ X439 @ id))))) | ($true != ((X431 @ X439)))) & (((X431 @ (lam @ X432))) != $true) & ! [X438 : term] : (((X430 @ id @ X438 @ id)) = ((X431 @ X438))) & ! [X433 : (subst > term > term)] : (? [X435 : term,X436 : subst,X434 : subst] : (((sub @ (X433 @ X434 @ X435) @ X436)) != ((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436)))) | ? [X437 : term] : (($true != ((X430 @ id @ (X433 @ id @ X437) @ id))) & ($true = ((X430 @ id @ X437 @ id)))) | ($true = ((X430 @ id @ (lam @ (X433 @ sh @ one)) @ id))))) | ! [X440 : (subst > term > subst > $o),X441 : term] : (? [X443 : term,X442 : term] : (($true = ((X440 @ id @ X442 @ id))) & ($true != ((X440 @ id @ (ap @ (sub @ X442 @ id) @ X443) @ id))) & ($true = ((X440 @ id @ X443 @ id)))) | ? [X444 : (subst > term > term)] : (! [X447 : subst,X446 : subst,X445 : term] : (((X444 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X444 @ X447 @ X445) @ X446))) & ($true != ((X440 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X440 @ id @ (X444 @ id @ X448) @ id))) | (((X440 @ id @ X448 @ id)) != $true))) | ($true = ((X440 @ id @ X441 @ id)))) | ? [X419 : (subst > term > subst > $o)] : ! [X420 : (term > $o)] : ? [X421 : term] : (((X419 @ id @ X421 @ id)) != ((X420 @ X421))) | ? [X423 : term,X422 : (term > $o)] : (($true != ((X422 @ X423))) & ! [X428 : term] : (($true != ((var @ X428))) | ($true = ((X422 @ X428)))) & ! [X426 : term,X427 : term] : (($true = ((X422 @ (ap @ X426 @ X427)))) | ($true != ((X422 @ X426))) | ($true != ((X422 @ X427)))) & ! [X424 : term] : (? [X425 : term] : (($true = ((X422 @ X425))) & ($true != ((X422 @ (sub @ X424 @ (push @ X425 @ id)))))) | (((X422 @ (lam @ X424))) = $true))) | ? [X429 : term] : (((sub @ X429 @ id)) != X429)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X383 : (subst > term > subst > $o),X382 : term] : (? [X384 : (subst > term > term)] : (! [X385 : term] : (($true != ((X383 @ id @ X385 @ id))) | ($true = ((X383 @ id @ (X384 @ id @ X385) @ id)))) & ($true != ((X383 @ id @ (lam @ (X384 @ sh @ one)) @ id))) & ! [X386 : subst,X388 : subst,X387 : term] : (((sub @ (X384 @ X386 @ X387) @ X388)) = ((X384 @ (comp @ X386 @ X388) @ (sub @ X387 @ X388))))) | ($true = ((X383 @ id @ (lam @ (sub @ X382 @ (push @ one @ sh))) @ id))) | ? [X389 : term] : (($true != ((X383 @ id @ (sub @ X382 @ (push @ X389 @ id)) @ id))) & ($true = ((X383 @ id @ X389 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X347 : term,X346 : (subst > term > subst > $o)] : (($true = ((X346 @ id @ (lam @ X347) @ id))) | ? [X353 : term] : (($true = ((X346 @ id @ X353 @ id))) & (((X346 @ id @ (sub @ X347 @ (push @ X353 @ id)) @ id)) != $true)) | ? [X348 : (subst > term > term)] : (($true != ((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id))) & ! [X351 : subst,X350 : subst,X352 : term] : (((sub @ (X348 @ X351 @ X352) @ X350)) = ((X348 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350)))) & ! [X349 : term] : (($true != ((X346 @ id @ X349 @ id))) | ($true = ((X346 @ id @ (X348 @ id @ X349) @ id)))))) | ? [X338 : term,X339 : (subst > term > subst > $o)] : (! [X340 : term] : (($true != ((X339 @ id @ X340 @ id))) | ($true = ((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)))) & ($true != ((X339 @ id @ (lam @ (sub @ X338 @ (push @ one @ sh))) @ id))) & ! [X341 : (subst > term > term)] : (($true = ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id))) | ? [X342 : term] : ((((X339 @ id @ X342 @ id)) = $true) & ($true != ((X339 @ id @ (X341 @ id @ X342) @ id)))) | ? [X344 : term,X345 : subst,X343 : subst] : (((X341 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345))) != ((sub @ (X341 @ X343 @ X344) @ X345))))) | ? [X337 : term] : (((sub @ X337 @ id)) != X337))) & ! [X490 : d_subst] : (d_id = X490) & (((d2subst @ d_id)) = id) & ((induction2_lthm = $true) <=> (! [X87 : (term > $o),X86 : term] : (? [X90 : term,X91 : term] : (($true != ((X87 @ (ap @ X91 @ X90)))) & ($true = ((X87 @ X90))) & ($true = ((X87 @ X91)))) | ? [X92 : term] : ((((var @ X92)) = $true) & ($true != ((X87 @ X92)))) | (((X87 @ X86)) = $true) | ? [X88 : term] : (($true != ((X87 @ (lam @ X88)))) & ! [X89 : term] : (($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id))))) | ($true != ((X87 @ X89)))))) | ? [X79 : subst,X78 : (term > $o),X80 : term] : (! [X81 : term] : (? [X82 : term] : (($true != ((X78 @ (sub @ X81 @ (push @ X82 @ id))))) & ($true = ((X78 @ X82)))) | ($true = ((X78 @ (lam @ X81))))) & ! [X83 : term] : (($true != ((var @ X83))) | ($true = ((X78 @ (sub @ X83 @ X79))))) & ! [X85 : term,X84 : term] : (($true != ((X78 @ X84))) | (((X78 @ (ap @ X84 @ X85))) = $true) | ($true != ((X78 @ X85)))) & ($true != ((X78 @ (sub @ X80 @ X79))))) | ? [X77 : term] : (((sub @ X77 @ id)) != X77))) & ((apinj2 = $true) <=> ! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466))) & (! [X225 : term,X224 : (subst > term > subst > $o)] : (? [X231 : term] : (($true != ((X224 @ id @ (sub @ X225 @ (push @ X231 @ id)) @ id))) & ($true = ((X224 @ id @ X231 @ id)))) | ? [X226 : (subst > term > term)] : (! [X228 : subst,X229 : term,X227 : subst] : (((X226 @ (comp @ X227 @ X228) @ (sub @ X229 @ X228))) = ((sub @ (X226 @ X227 @ X229) @ X228))) & ($true != ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id))) & ! [X230 : term] : (($true = ((X224 @ id @ (X226 @ id @ X230) @ id))) | ($true != ((X224 @ id @ X230 @ id))))) | ($true = ((X224 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa = $true)) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) <=> (axidl = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X34 : term] : ? [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) = ((X35 @ sh @ one)))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & ((apinj1 = $true) <=> ! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205))))) & (ulamvarsh = $true) & (! [X326 : term,X325 : (subst > term > subst > $o)] : (? [X327 : (subst > term > term),X328 : term] : (! [X335 : term,X333 : subst,X334 : subst] : (((sub @ (X327 @ X334 @ X335) @ X333)) = ((sub @ (sub @ X328 @ (push @ X335 @ X334)) @ X333))) & ! [X330 : subst,X331 : subst,X329 : term] : (((sub @ X328 @ (push @ (sub @ X329 @ X331) @ (comp @ X330 @ X331)))) = ((X327 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331)))) & ! [X332 : term] : ((((X325 @ id @ X332 @ id)) != $true) | ($true = ((X325 @ id @ (X327 @ id @ X332) @ id)))) & (((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id)) != $true)) | ? [X336 : term] : ((((X325 @ id @ X336 @ id)) = $true) & ($true != ((X325 @ id @ (sub @ X326 @ (push @ X336 @ id)) @ id)))) | ($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & ((hoaslamnotap = $true) <=> ! [X357 : term,X355 : term,X356 : (subst > term > term)] : (? [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) != ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357))))) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X18 : subst,X19 : (term > $o),X17 : term] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21))) <=> (pushprop_lem0 = $true)) & ! [X366 : d_term] : (d_one = X366) & ((hoasinduction_lem2v2 = $true) <=> ! [X152 : (term > $o),X153 : term,X155 : (subst > term > subst > $o),X154 : term] : (? [X166 : term] : (((X155 @ id @ X166 @ id)) != ((X152 @ X166))) | ? [X162 : subst,X163 : subst,X164 : subst,X165 : term] : (($true = ((X155 @ X163 @ X165 @ (comp @ X162 @ X164)))) & ($true != ((X155 @ (comp @ X163 @ X162) @ (sub @ X165 @ X162) @ X164)))) | ($true != ((X152 @ X154))) | ($true != ((X152 @ X153))) | ? [X159 : subst,X158 : subst,X157 : subst,X156 : term] : (($true != ((X155 @ X159 @ X156 @ (comp @ X157 @ X158)))) & ($true = ((X155 @ (comp @ X159 @ X157) @ (sub @ X156 @ X157) @ X158)))) | ? [X161 : term,X160 : term] : (($true != ((X155 @ id @ (ap @ (sub @ X161 @ id) @ X160) @ id))) & ($true = ((X155 @ id @ X160 @ id))) & (((X155 @ id @ X161 @ id)) = $true)) | ($true = ((X152 @ (ap @ X153 @ X154)))))) & ((axidr = $true) <=> ! [X539 : subst] : (((comp @ X539 @ id)) = X539)) & ((shinj = $true) <=> ! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh))))) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 inference(flattening,[],[f11])).
% 5.11/1.35 thf(f13,definition,(
% 5.11/1.35 ! [X155 : (subst > term > subst > $o)] : ((((sP0 @ X155)) = $true) <=> ? [X161 : term,X160 : term] : (($true != ((X155 @ id @ (ap @ (sub @ X161 @ id) @ X160) @ id))) & ($true = ((X155 @ id @ X160 @ id))) & (((X155 @ id @ X161 @ id)) = $true)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f14,definition,(
% 5.11/1.35 ($true = sP1) <=> ! [X152 : (term > $o),X153 : term,X155 : (subst > term > subst > $o),X154 : term] : (? [X166 : term] : (((X155 @ id @ X166 @ id)) != ((X152 @ X166))) | ? [X162 : subst,X163 : subst,X164 : subst,X165 : term] : (($true = ((X155 @ X163 @ X165 @ (comp @ X162 @ X164)))) & ($true != ((X155 @ (comp @ X163 @ X162) @ (sub @ X165 @ X162) @ X164)))) | ($true != ((X152 @ X154))) | ($true != ((X152 @ X153))) | ? [X159 : subst,X158 : subst,X157 : subst,X156 : term] : (($true != ((X155 @ X159 @ X156 @ (comp @ X157 @ X158)))) & ($true = ((X155 @ (comp @ X159 @ X157) @ (sub @ X156 @ X157) @ X158)))) | (((sP0 @ X155)) = $true) | ($true = ((X152 @ (ap @ X153 @ X154)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f15,definition,(
% 5.11/1.35 ($true = sP2) <=> ! [X326 : term,X325 : (subst > term > subst > $o)] : (? [X327 : (subst > term > term),X328 : term] : (! [X335 : term,X333 : subst,X334 : subst] : (((sub @ (X327 @ X334 @ X335) @ X333)) = ((sub @ (sub @ X328 @ (push @ X335 @ X334)) @ X333))) & ! [X330 : subst,X331 : subst,X329 : term] : (((sub @ X328 @ (push @ (sub @ X329 @ X331) @ (comp @ X330 @ X331)))) = ((X327 @ (comp @ X330 @ X331) @ (sub @ X329 @ X331)))) & ! [X332 : term] : ((((X325 @ id @ X332 @ id)) != $true) | ($true = ((X325 @ id @ (X327 @ id @ X332) @ id)))) & (((X325 @ id @ (lam @ (X327 @ sh @ one)) @ id)) != $true)) | ? [X336 : term] : ((((X325 @ id @ X336 @ id)) = $true) & ($true != ((X325 @ id @ (sub @ X326 @ (push @ X336 @ id)) @ id)))) | ($true = ((X325 @ id @ (lam @ (sub @ X326 @ (push @ one @ sh))) @ id))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f16,definition,(
% 5.11/1.35 ($true = sP3) <=> ! [X225 : term,X224 : (subst > term > subst > $o)] : (? [X231 : term] : (($true != ((X224 @ id @ (sub @ X225 @ (push @ X231 @ id)) @ id))) & ($true = ((X224 @ id @ X231 @ id)))) | ? [X226 : (subst > term > term)] : (! [X228 : subst,X229 : term,X227 : subst] : (((X226 @ (comp @ X227 @ X228) @ (sub @ X229 @ X228))) = ((sub @ (X226 @ X227 @ X229) @ X228))) & ($true != ((X224 @ id @ (lam @ (X226 @ sh @ one)) @ id))) & ! [X230 : term] : (($true = ((X224 @ id @ (X226 @ id @ X230) @ id))) | ($true != ((X224 @ id @ X230 @ id))))) | ($true = ((X224 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f17,definition,(
% 5.11/1.35 ! [X78 : (term > $o)] : ((((sP4 @ X78)) = $true) <=> ! [X85 : term,X84 : term] : (($true != ((X78 @ X84))) | (((X78 @ (ap @ X84 @ X85))) = $true) | ($true != ((X78 @ X85)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f18,definition,(
% 5.11/1.35 ! [X87 : (term > $o)] : ((((sP5 @ X87)) = $true) <=> ? [X90 : term,X91 : term] : (($true != ((X87 @ (ap @ X91 @ X90)))) & ($true = ((X87 @ X90))) & ($true = ((X87 @ X91)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f19,definition,(
% 5.11/1.35 ($true = sP6) <=> ! [X87 : (term > $o),X86 : term] : ((((sP5 @ X87)) = $true) | ? [X92 : term] : ((((var @ X92)) = $true) & ($true != ((X87 @ X92)))) | (((X87 @ X86)) = $true) | ? [X88 : term] : (($true != ((X87 @ (lam @ X88)))) & ! [X89 : term] : (($true = ((X87 @ (sub @ X88 @ (push @ X89 @ id))))) | ($true != ((X87 @ X89))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f20,definition,(
% 5.11/1.35 (sP7 = $true) <=> (($true = sP6) | ? [X79 : subst,X78 : (term > $o),X80 : term] : (! [X81 : term] : (? [X82 : term] : (($true != ((X78 @ (sub @ X81 @ (push @ X82 @ id))))) & ($true = ((X78 @ X82)))) | ($true = ((X78 @ (lam @ X81))))) & ! [X83 : term] : (($true != ((var @ X83))) | ($true = ((X78 @ (sub @ X83 @ X79))))) & (((sP4 @ X78)) = $true) & ($true != ((X78 @ (sub @ X80 @ X79))))) | ? [X77 : term] : (((sub @ X77 @ id)) != X77))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f21,definition,(
% 5.11/1.35 ($true = sP8) <=> ? [X338 : term,X339 : (subst > term > subst > $o)] : (! [X340 : term] : (($true != ((X339 @ id @ X340 @ id))) | ($true = ((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)))) & ($true != ((X339 @ id @ (lam @ (sub @ X338 @ (push @ one @ sh))) @ id))) & ! [X341 : (subst > term > term)] : (($true = ((X339 @ id @ (lam @ (X341 @ sh @ one)) @ id))) | ? [X342 : term] : ((((X339 @ id @ X342 @ id)) = $true) & ($true != ((X339 @ id @ (X341 @ id @ X342) @ id)))) | ? [X344 : term,X345 : subst,X343 : subst] : (((X341 @ (comp @ X343 @ X345) @ (sub @ X344 @ X345))) != ((sub @ (X341 @ X343 @ X344) @ X345)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f22,definition,(
% 5.11/1.35 (sP9 = $true) <=> (! [X347 : term,X346 : (subst > term > subst > $o)] : (($true = ((X346 @ id @ (lam @ X347) @ id))) | ? [X353 : term] : (($true = ((X346 @ id @ X353 @ id))) & (((X346 @ id @ (sub @ X347 @ (push @ X353 @ id)) @ id)) != $true)) | ? [X348 : (subst > term > term)] : (($true != ((X346 @ id @ (lam @ (X348 @ sh @ one)) @ id))) & ! [X351 : subst,X350 : subst,X352 : term] : (((sub @ (X348 @ X351 @ X352) @ X350)) = ((X348 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350)))) & ! [X349 : term] : (($true != ((X346 @ id @ X349 @ id))) | ($true = ((X346 @ id @ (X348 @ id @ X349) @ id)))))) | ($true = sP8) | ? [X337 : term] : (((sub @ X337 @ id)) != X337))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f23,definition,(
% 5.11/1.35 ($true = sP10) <=> ! [X383 : (subst > term > subst > $o),X382 : term] : (? [X384 : (subst > term > term)] : (! [X385 : term] : (($true != ((X383 @ id @ X385 @ id))) | ($true = ((X383 @ id @ (X384 @ id @ X385) @ id)))) & ($true != ((X383 @ id @ (lam @ (X384 @ sh @ one)) @ id))) & ! [X386 : subst,X388 : subst,X387 : term] : (((sub @ (X384 @ X386 @ X387) @ X388)) = ((X384 @ (comp @ X386 @ X388) @ (sub @ X387 @ X388))))) | ($true = ((X383 @ id @ (lam @ (sub @ X382 @ (push @ one @ sh))) @ id))) | ? [X389 : term] : (($true != ((X383 @ id @ (sub @ X382 @ (push @ X389 @ id)) @ id))) & ($true = ((X383 @ id @ X389 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f24,definition,(
% 5.11/1.35 ! [X422 : (term > $o)] : (($true = ((sP11 @ X422))) <=> ! [X426 : term,X427 : term] : (($true = ((X422 @ (ap @ X426 @ X427)))) | ($true != ((X422 @ X426))) | ($true != ((X422 @ X427)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f25,definition,(
% 5.11/1.35 ! [X440 : (subst > term > subst > $o)] : (($true = ((sP12 @ X440))) <=> ? [X444 : (subst > term > term)] : (! [X447 : subst,X446 : subst,X445 : term] : (((X444 @ (comp @ X447 @ X446) @ (sub @ X445 @ X446))) = ((sub @ (X444 @ X447 @ X445) @ X446))) & ($true != ((X440 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X440 @ id @ (X444 @ id @ X448) @ id))) | (((X440 @ id @ X448 @ id)) != $true))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f26,definition,(
% 5.11/1.35 (sP13 = $true) <=> ? [X432 : term,X430 : (subst > term > subst > $o),X431 : (term > $o)] : (! [X439 : term] : (($true = ((X431 @ (sub @ X432 @ (push @ X439 @ id))))) | ($true != ((X431 @ X439)))) & (((X431 @ (lam @ X432))) != $true) & ! [X438 : term] : (((X430 @ id @ X438 @ id)) = ((X431 @ X438))) & ! [X433 : (subst > term > term)] : (? [X435 : term,X436 : subst,X434 : subst] : (((sub @ (X433 @ X434 @ X435) @ X436)) != ((X433 @ (comp @ X434 @ X436) @ (sub @ X435 @ X436)))) | ? [X437 : term] : (($true != ((X430 @ id @ (X433 @ id @ X437) @ id))) & ($true = ((X430 @ id @ X437 @ id)))) | ($true = ((X430 @ id @ (lam @ (X433 @ sh @ one)) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f27,definition,(
% 5.11/1.35 ($true = sP14) <=> ? [X423 : term,X422 : (term > $o)] : (($true != ((X422 @ X423))) & ! [X428 : term] : (($true != ((var @ X428))) | ($true = ((X422 @ X428)))) & ($true = ((sP11 @ X422))) & ! [X424 : term] : (? [X425 : term] : (($true = ((X422 @ X425))) & ($true != ((X422 @ (sub @ X424 @ (push @ X425 @ id)))))) | (((X422 @ (lam @ X424))) = $true)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f28,definition,(
% 5.11/1.35 ($true = sP15) <=> ((sP13 = $true) | ! [X440 : (subst > term > subst > $o),X441 : term] : (? [X443 : term,X442 : term] : (($true = ((X440 @ id @ X442 @ id))) & ($true != ((X440 @ id @ (ap @ (sub @ X442 @ id) @ X443) @ id))) & ($true = ((X440 @ id @ X443 @ id)))) | ($true = ((sP12 @ X440))) | ($true = ((X440 @ id @ X441 @ id)))) | ? [X419 : (subst > term > subst > $o)] : ! [X420 : (term > $o)] : ? [X421 : term] : (((X419 @ id @ X421 @ id)) != ((X420 @ X421))) | ($true = sP14) | ? [X429 : term] : (((sub @ X429 @ id)) != X429))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f29,definition,(
% 5.11/1.35 ! [X120 : (subst > term > subst > $o)] : (($true = ((sP16 @ X120))) <=> ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X120 @ id @ (X121 @ id @ X125) @ id))) | ($true != ((X120 @ id @ X125 @ id)))) & ($true != ((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id))) & ! [X123 : subst,X124 : term,X122 : subst] : (((X121 @ (comp @ X122 @ X123) @ (sub @ X124 @ X123))) = ((sub @ (X121 @ X122 @ X124) @ X123)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f30,definition,(
% 5.11/1.35 (sP17 = $true) <=> ! [X120 : (subst > term > subst > $o),X118 : term,X119 : (term > $o)] : (($true = ((X119 @ (lam @ X118)))) | ? [X135 : term] : (($true != ((X119 @ (sub @ X118 @ (push @ X135 @ id))))) & ($true = ((X119 @ X135)))) | ($true = ((sP16 @ X120))) | ? [X130 : term] : (((X120 @ id @ X130 @ id)) != ((X119 @ X130))) | ? [X129 : subst,X126 : subst,X127 : term,X128 : subst] : (($true != ((X120 @ X126 @ X127 @ (comp @ X128 @ X129)))) & ($true = ((X120 @ (comp @ X126 @ X128) @ (sub @ X127 @ X128) @ X129)))) | ? [X131 : subst,X132 : subst,X134 : term,X133 : subst] : (($true != ((X120 @ (comp @ X132 @ X131) @ (sub @ X134 @ X131) @ X133))) & (((X120 @ X132 @ X134 @ (comp @ X131 @ X133))) = $true)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f31,definition,(
% 5.11/1.35 ! [X145 : (term > $o)] : (($true = ((sP18 @ X145))) <=> ? [X149 : term,X150 : term] : (($true != ((X145 @ (ap @ X150 @ X149)))) & ($true = ((X145 @ X149))) & ($true = ((X145 @ X150)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f32,definition,(
% 5.11/1.35 ($true = sP19) <=> ! [X145 : (term > $o),X146 : term] : (? [X151 : term] : (($true = ((var @ X151))) & ($true != ((X145 @ X151)))) | ($true = ((X145 @ X146))) | ? [X147 : term] : (! [X148 : term] : (($true = ((X145 @ (sub @ X147 @ (push @ X148 @ id))))) | ($true != ((X145 @ X148)))) & ($true != ((X145 @ (lam @ X147))))) | ($true = ((sP18 @ X145))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f33,definition,(
% 5.11/1.35 (sP20 = $true) <=> (? [X189 : term] : ! [X190 : (subst > term > term)] : ? [X192 : subst,X191 : term] : (((X190 @ X192 @ X191)) != ((sub @ X189 @ (push @ X191 @ X192)))) | ! [X195 : (term > $o),X196 : (subst > term > subst > $o),X194 : term] : (? [X203 : term] : (((X195 @ X203)) != ((X196 @ id @ X203 @ id))) | ? [X197 : term] : (($true != ((X195 @ (sub @ X194 @ (push @ X197 @ id))))) & ($true = ((X195 @ X197)))) | ? [X198 : (subst > term > term)] : (($true != ((X196 @ id @ (lam @ (X198 @ sh @ one)) @ id))) & ! [X202 : term] : (($true != ((X196 @ id @ X202 @ id))) | ($true = ((X196 @ id @ (X198 @ id @ X202) @ id)))) & ! [X201 : term,X200 : subst,X199 : subst] : (((sub @ (X198 @ X199 @ X201) @ X200)) = ((X198 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200))))) | ($true = ((X195 @ (lam @ X194))))) | ? [X193 : term] : (((sub @ X193 @ id)) != X193))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f34,definition,(
% 5.11/1.35 ! [X173 : (term > $o)] : (($true = ((sP21 @ X173))) <=> ! [X174 : term,X175 : term] : (($true != ((X173 @ X175))) | ($true = ((X173 @ (ap @ X175 @ X174)))) | ($true != ((X173 @ X174)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f35,definition,(
% 5.11/1.35 ! [X180 : (term > $o)] : (($true = ((sP22 @ X180))) <=> ? [X181 : term,X182 : term] : (($true != ((X180 @ (ap @ X182 @ X181)))) & ($true = ((X180 @ X182))) & ($true = ((X180 @ X181)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f36,definition,(
% 5.11/1.35 ($true = sP23) <=> ! [X180 : (term > $o),X179 : subst,X178 : term] : (? [X184 : term] : (! [X185 : term] : (($true = ((X180 @ (sub @ X184 @ (push @ X185 @ id))))) | ($true != ((X180 @ X185)))) & ($true != ((X180 @ (lam @ X184))))) | ($true = ((X180 @ (sub @ X178 @ X179)))) | ? [X183 : term] : (($true = ((var @ X183))) & ($true != ((X180 @ (sub @ X183 @ X179))))) | ($true = ((sP22 @ X180))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f37,definition,(
% 5.11/1.35 (sP24 = $true) <=> (? [X171 : subst] : (((comp @ X171 @ id)) != X171) | ? [X167 : subst,X168 : term] : (((sub @ one @ (push @ X168 @ X167))) != X168) | ? [X169 : subst,X170 : term] : (((comp @ sh @ (push @ X170 @ X169))) != X169) | ($true = sP23) | ? [X173 : (term > $o),X172 : term] : ((((X173 @ X172)) != $true) & ! [X177 : term] : (($true = ((X173 @ (lam @ X177)))) | ($true != ((X173 @ X177)))) & ! [X176 : term] : (($true = ((X173 @ X176))) | ($true != ((var @ X176)))) & ($true = ((sP21 @ X173)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f38,definition,(
% 5.11/1.35 ! [X27 : (term > $o)] : (($true = ((sP25 @ X27))) <=> ? [X30 : term,X29 : term] : (($true = ((X27 @ X30))) & ($true = ((X27 @ X29))) & ($true != ((X27 @ (ap @ X30 @ X29))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f39,definition,(
% 5.11/1.35 ($true = sP26) <=> ! [X26 : subst,X28 : term,X27 : (term > $o)] : (($true = ((sP25 @ X27))) | ? [X31 : term] : (! [X32 : term] : (($true != ((X27 @ X32))) | ($true = ((X27 @ (sub @ X31 @ (push @ X32 @ id)))))) & (((X27 @ (lam @ X31))) != $true)) | ? [X33 : term] : (($true != ((X27 @ (sub @ X33 @ X26)))) & ($true = ((var @ X33)))) | ($true = ((X27 @ (sub @ X28 @ X26)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f40,definition,(
% 5.11/1.35 ! [X369 : (subst > term > subst > $o)] : ((((sP27 @ X369)) = $true) <=> ? [X370 : term,X371 : term] : ((((X369 @ id @ X371 @ id)) = $true) & ($true != ((X369 @ id @ (ap @ (sub @ X371 @ id) @ X370) @ id))) & ($true = ((X369 @ id @ X370 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f41,definition,(
% 5.11/1.35 ($true = sP28) <=> ! [X367 : term,X369 : (subst > term > subst > $o),X368 : term] : (? [X376 : subst,X377 : subst,X379 : term,X378 : subst] : (($true = ((X369 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378) @ X376))) & ($true != ((X369 @ X377 @ X379 @ (comp @ X378 @ X376))))) | ($true != ((X369 @ id @ X367 @ id))) | ($true != ((X369 @ id @ X368 @ id))) | (((sP27 @ X369)) = $true) | ? [X372 : subst,X375 : term,X374 : subst,X373 : subst] : ((((X369 @ (comp @ X373 @ X374) @ (sub @ X375 @ X374) @ X372)) != $true) & ($true = ((X369 @ X373 @ X375 @ (comp @ X374 @ X372))))) | ($true = ((X369 @ id @ (ap @ X367 @ X368) @ id))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f42,definition,(
% 5.11/1.35 ! [X137 : (subst > term > subst > $o)] : ((((sP29 @ X137)) = $true) <=> ? [X140 : (subst > term > term)] : (! [X144 : term] : (($true = ((X137 @ id @ (X140 @ id @ X144) @ id))) | ($true != ((X137 @ id @ X144 @ id)))) & ! [X143 : term,X142 : subst,X141 : subst] : (((sub @ (X140 @ X142 @ X143) @ X141)) = ((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141)))) & ($true != ((X137 @ id @ (lam @ (X140 @ sh @ one)) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f43,definition,(
% 5.11/1.35 ! [X1 : (term > $o)] : (($true = ((sP30 @ X1))) <=> ? [X2 : term,X3 : term] : (($true = ((X1 @ X3))) & ($true = ((X1 @ X2))) & ($true != ((X1 @ (ap @ X3 @ X2))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f44,definition,(
% 5.11/1.35 ($true = sP31) <=> (? [X97 : term,X98 : subst] : (((comp @ sh @ (push @ X97 @ X98))) != X98) | ! [X101 : subst,X102 : (subst > term > term),X104 : term,X103 : (subst > term > term)] : (? [X106 : subst,X105 : subst,X107 : term] : (((X103 @ (comp @ X105 @ X106) @ (sub @ X107 @ X106))) != ((sub @ (X103 @ X105 @ X107) @ X106))) | ? [X109 : subst,X108 : term,X110 : subst] : (((X102 @ (comp @ X109 @ X110) @ (sub @ X108 @ X110))) != ((sub @ (X102 @ X109 @ X108) @ X110))) | (((X103 @ X101 @ X104)) = ((X102 @ X101 @ X104))) | (((lam @ (X102 @ sh @ one))) != ((lam @ (X103 @ sh @ one))))) | ? [X99 : term,X100 : term] : ((X99 != X100) & (((lam @ X99)) = ((lam @ X100)))) | ? [X95 : subst,X96 : term] : (((sub @ one @ (push @ X96 @ X95))) != X96))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f45,definition,(
% 5.11/1.35 ! [X241 : (subst > term > subst > $o)] : (($true = ((sP32 @ X241))) <=> ? [X244 : (subst > term > term)] : (! [X248 : term] : (($true != ((X241 @ id @ X248 @ id))) | ($true = ((X241 @ id @ (X244 @ id @ X248) @ id)))) & ($true != ((X241 @ id @ (lam @ (X244 @ sh @ one)) @ id))) & ! [X247 : subst,X245 : subst,X246 : term] : (((sub @ (X244 @ X247 @ X246) @ X245)) = ((X244 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f46,definition,(
% 5.11/1.35 ($true = sP33) <=> (? [X240 : term] : (((sub @ X240 @ id)) != X240) | ! [X243 : term,X241 : (subst > term > subst > $o),X242 : (term > $o)] : (? [X253 : term] : (((X241 @ id @ X253 @ id)) != ((X242 @ X253))) | ? [X257 : term,X254 : subst,X255 : subst,X256 : subst] : (($true = ((X241 @ (comp @ X255 @ X256) @ (sub @ X257 @ X256) @ X254))) & ($true != ((X241 @ X255 @ X257 @ (comp @ X256 @ X254))))) | ? [X250 : term,X252 : subst,X249 : subst,X251 : subst] : (($true = ((X241 @ X252 @ X250 @ (comp @ X249 @ X251)))) & ($true != ((X241 @ (comp @ X252 @ X249) @ (sub @ X250 @ X249) @ X251)))) | ? [X258 : term] : (($true != ((X242 @ (sub @ X243 @ (push @ X258 @ id))))) & ($true = ((X242 @ X258)))) | ($true = ((sP32 @ X241))) | ($true = ((X242 @ (lam @ X243))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f47,definition,(
% 5.11/1.35 ($true = sP34) <=> ! [X233 : term,X232 : (subst > term > subst > $o)] : (($true = ((X232 @ id @ (lam @ X233) @ id))) | ? [X234 : (subst > term > term)] : (($true != ((X232 @ id @ (lam @ (X234 @ sh @ one)) @ id))) & ! [X235 : term] : (($true != ((X232 @ id @ X235 @ id))) | ($true = ((X232 @ id @ (X234 @ id @ X235) @ id)))) & ! [X237 : subst,X238 : subst,X236 : term] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ? [X239 : term] : (($true != ((X232 @ id @ (sub @ X233 @ (push @ X239 @ id)) @ id))) & ($true = ((X232 @ id @ X239 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f48,definition,(
% 5.11/1.35 ! [X55 : (subst > term > subst > $o)] : (($true = ((sP35 @ X55))) <=> ? [X62 : (subst > term > term)] : (! [X65 : subst,X64 : term,X66 : subst] : (((sub @ (X62 @ X65 @ X64) @ X66)) = ((X62 @ (comp @ X65 @ X66) @ (sub @ X64 @ X66)))) & (((X55 @ id @ (lam @ (X62 @ sh @ one)) @ id)) != $true) & ! [X63 : term] : (($true = ((X55 @ id @ (X62 @ id @ X63) @ id))) | ($true != ((X55 @ id @ X63 @ id))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f49,definition,(
% 5.11/1.35 ($true = sP36) <=> ? [X48 : term,X47 : (subst > term > subst > $o)] : (! [X49 : (subst > term > term)] : (? [X53 : term] : (($true != ((X47 @ id @ (X49 @ id @ X53) @ id))) & ($true = ((X47 @ id @ X53 @ id)))) | ? [X50 : term,X52 : subst,X51 : subst] : (((X49 @ (comp @ X52 @ X51) @ (sub @ X50 @ X51))) != ((sub @ (X49 @ X52 @ X50) @ X51))) | ($true = ((X47 @ id @ (lam @ (X49 @ sh @ one)) @ id)))) & ($true != ((X47 @ id @ (lam @ (sub @ X48 @ (push @ one @ sh))) @ id))) & ! [X54 : term] : (($true = ((X47 @ id @ (sub @ X48 @ (push @ X54 @ id)) @ id))) | ($true != ((X47 @ id @ X54 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f50,definition,(
% 5.11/1.35 ($true = sP37) <=> (($true = sP36) | ? [X46 : term] : (((sub @ X46 @ id)) != X46) | ! [X55 : (subst > term > subst > $o),X56 : term] : (? [X61 : term] : (($true = ((X55 @ id @ X61 @ id))) & ($true != ((X55 @ id @ (sub @ X56 @ (push @ X61 @ id)) @ id)))) | ? [X67 : subst,X69 : subst,X70 : subst,X68 : term] : (($true = ((X55 @ X67 @ X68 @ (comp @ X69 @ X70)))) & ($true != ((X55 @ (comp @ X67 @ X69) @ (sub @ X68 @ X69) @ X70)))) | ($true = ((X55 @ id @ (lam @ X56) @ id))) | ? [X60 : subst,X58 : term,X59 : subst,X57 : subst] : (($true != ((X55 @ X59 @ X58 @ (comp @ X57 @ X60)))) & ($true = ((X55 @ (comp @ X59 @ X57) @ (sub @ X58 @ X57) @ X60)))) | ($true = ((sP35 @ X55)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f51,definition,(
% 5.11/1.35 ! [X403 : (subst > term > subst > $o)] : (($true = ((sP38 @ X403))) <=> ? [X410 : (subst > term > term)] : (! [X414 : term] : (($true = ((X403 @ id @ (X410 @ id @ X414) @ id))) | ($true != ((X403 @ id @ X414 @ id)))) & ! [X411 : term,X412 : subst,X413 : subst] : (((X410 @ (comp @ X412 @ X413) @ (sub @ X411 @ X413))) = ((sub @ (X410 @ X412 @ X411) @ X413))) & ($true != ((X403 @ id @ (lam @ (X410 @ sh @ one)) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f52,definition,(
% 5.11/1.35 ($true = sP39) <=> ! [X403 : (subst > term > subst > $o),X404 : term] : (? [X409 : subst,X406 : subst,X407 : term,X408 : subst] : (($true != ((X403 @ X408 @ X407 @ (comp @ X409 @ X406)))) & ($true = ((X403 @ (comp @ X408 @ X409) @ (sub @ X407 @ X409) @ X406)))) | ? [X405 : term] : (($true != ((X403 @ id @ (sub @ X404 @ (push @ X405 @ id)) @ id))) & ($true = ((X403 @ id @ X405 @ id)))) | ? [X417 : subst,X418 : subst,X415 : subst,X416 : term] : (($true = ((X403 @ X418 @ X416 @ (comp @ X417 @ X415)))) & ($true != ((X403 @ (comp @ X418 @ X417) @ (sub @ X416 @ X417) @ X415)))) | ($true = ((sP38 @ X403))) | ($true = ((X403 @ id @ (lam @ X404) @ id))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f53,definition,(
% 5.11/1.35 ! [X473 : (subst > term > subst > $o)] : (($true = ((sP40 @ X473))) <=> ? [X482 : (subst > term > term)] : (! [X483 : term] : (($true != ((X473 @ id @ X483 @ id))) | ($true = ((X473 @ id @ (X482 @ id @ X483) @ id)))) & (((X473 @ id @ (lam @ (X482 @ sh @ one)) @ id)) != $true) & ! [X486 : term,X485 : subst,X484 : subst] : (((X482 @ (comp @ X485 @ X484) @ (sub @ X486 @ X484))) = ((sub @ (X482 @ X485 @ X486) @ X484)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f54,definition,(
% 5.11/1.35 ! [X473 : (subst > term > subst > $o)] : (($true = ((sP41 @ X473))) <=> ? [X487 : term,X488 : term] : (($true = ((X473 @ id @ X487 @ id))) & ($true != ((X473 @ id @ (ap @ (sub @ X487 @ id) @ X488) @ id))) & ($true = ((X473 @ id @ X488 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f55,definition,(
% 5.11/1.35 ($true = sP42) <=> ! [X472 : term,X473 : (subst > term > subst > $o)] : (($true = ((sP41 @ X473))) | ? [X481 : subst,X479 : term,X480 : subst,X478 : subst] : (($true = ((X473 @ X480 @ X479 @ (comp @ X478 @ X481)))) & ($true != ((X473 @ (comp @ X480 @ X478) @ (sub @ X479 @ X478) @ X481)))) | ($true = ((X473 @ id @ X472 @ id))) | ? [X489 : term] : (($true = ((var @ (sub @ X489 @ id)))) & ($true != ((X473 @ id @ X489 @ id)))) | ? [X475 : subst,X474 : term,X476 : subst,X477 : subst] : (($true = ((X473 @ (comp @ X477 @ X475) @ (sub @ X474 @ X475) @ X476))) & ($true != ((X473 @ X477 @ X474 @ (comp @ X475 @ X476))))) | ($true = ((sP40 @ X473))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f56,definition,(
% 5.11/1.35 ($true = sP43) <=> ! [X454 : (subst > term > subst > $o),X455 : (term > $o),X453 : term] : (? [X456 : (subst > term > term)] : (($true != ((X454 @ id @ (lam @ (X456 @ sh @ one)) @ id))) & ! [X460 : subst,X458 : term,X459 : subst] : (((X456 @ (comp @ X459 @ X460) @ (sub @ X458 @ X460))) = ((sub @ (X456 @ X459 @ X458) @ X460))) & ! [X457 : term] : (($true != ((X454 @ id @ X457 @ id))) | ($true = ((X454 @ id @ (X456 @ id @ X457) @ id))))) | ? [X462 : term] : (((X454 @ id @ X462 @ id)) != ((X455 @ X462))) | ? [X461 : term] : ((((X455 @ X461)) = $true) & ($true != ((X455 @ (sub @ X453 @ (push @ X461 @ id)))))) | ($true = ((X455 @ (lam @ X453)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f57,definition,(
% 5.11/1.35 ! [X512 : (subst > term > subst > $o)] : (($true = ((sP44 @ X512))) <=> ? [X524 : term,X523 : term] : (($true = ((X512 @ id @ X523 @ id))) & ($true = ((X512 @ id @ X524 @ id))) & ($true != ((X512 @ id @ (ap @ (sub @ X524 @ id) @ X523) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f58,definition,(
% 5.11/1.35 ! [X512 : (subst > term > subst > $o)] : (($true = ((sP45 @ X512))) <=> ? [X514 : (subst > term > term)] : (! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | ($true != ((X512 @ id @ X515 @ id)))) & ! [X518 : subst,X516 : term,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f59,definition,(
% 5.11/1.35 ! [X495 : (term > $o)] : (($true = ((sP46 @ X495))) <=> ! [X500 : term,X499 : term] : (($true != ((X495 @ X499))) | (((X495 @ (ap @ X500 @ X499))) = $true) | ($true != ((X495 @ X500)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f60,definition,(
% 5.11/1.35 ($true = sP47) <=> ? [X502 : (subst > term > subst > $o),X504 : (term > $o),X503 : term] : (($true != ((X504 @ (lam @ X503)))) & ! [X507 : (subst > term > term)] : (? [X508 : term] : ((((X502 @ id @ X508 @ id)) = $true) & ($true != ((X502 @ id @ (X507 @ id @ X508) @ id)))) | ($true = ((X502 @ id @ (lam @ (X507 @ sh @ one)) @ id))) | ? [X510 : subst,X509 : subst,X511 : term] : (((X507 @ (comp @ X509 @ X510) @ (sub @ X511 @ X510))) != ((sub @ (X507 @ X509 @ X511) @ X510)))) & ! [X506 : term] : (($true = ((X504 @ (sub @ X503 @ (push @ X506 @ id))))) | ($true != ((X504 @ X506)))) & ! [X505 : term] : (((X504 @ X505)) = ((X502 @ id @ X505 @ id))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f61,definition,(
% 5.11/1.35 ($true = sP48) <=> ! [X512 : (subst > term > subst > $o),X513 : term] : (($true = ((sP45 @ X512))) | ($true = ((sP44 @ X512))) | ? [X525 : term] : ((((var @ (sub @ X525 @ id))) = $true) & ($true != ((X512 @ id @ X525 @ id)))) | ? [X528 : subst,X527 : subst,X526 : subst,X529 : term] : (($true != ((X512 @ X528 @ X529 @ (comp @ X527 @ X526)))) & ($true = ((X512 @ (comp @ X528 @ X527) @ (sub @ X529 @ X527) @ X526)))) | ($true = ((X512 @ id @ X513 @ id))) | ? [X522 : subst,X521 : subst,X519 : term,X520 : subst] : (($true != ((X512 @ (comp @ X520 @ X522) @ (sub @ X519 @ X522) @ X521))) & ($true = ((X512 @ X520 @ X519 @ (comp @ X522 @ X521))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f62,definition,(
% 5.11/1.35 ($true = sP49) <=> (? [X494 : term,X495 : (term > $o)] : (! [X496 : term] : (($true != ((var @ X496))) | ($true = ((X495 @ X496)))) & ($true != ((X495 @ X494))) & ($true = ((sP46 @ X495))) & ! [X497 : term] : (($true = ((X495 @ (lam @ X497)))) | ? [X498 : term] : (($true = ((X495 @ X498))) & ($true != ((X495 @ (sub @ X497 @ (push @ X498 @ id)))))))) | ? [X491 : (subst > term > subst > $o)] : ! [X492 : (term > $o)] : ? [X493 : term] : (((X491 @ id @ X493 @ id)) != ((X492 @ X493))) | ($true = sP48) | ($true = sP47) | ? [X501 : term] : (((sub @ X501 @ id)) != X501))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f63,definition,(
% 5.11/1.35 ! [X268 : (subst > term > subst > $o)] : (($true = ((sP50 @ X268))) <=> ! [X270 : term,X269 : term] : (($true != ((X268 @ id @ X269 @ id))) | (((X268 @ id @ X270 @ id)) != $true) | ($true = ((X268 @ id @ (ap @ (sub @ X269 @ id) @ X270) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f64,definition,(
% 5.11/1.35 ! [X296 : (subst > term > subst > $o)] : (($true = ((sP51 @ X296))) <=> ? [X306 : (subst > term > term)] : (($true != ((X296 @ id @ (lam @ (X306 @ sh @ one)) @ id))) & ! [X308 : subst,X310 : subst,X309 : term] : (((X306 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X306 @ X308 @ X309) @ X310))) & ! [X307 : term] : (($true = ((X296 @ id @ (X306 @ id @ X307) @ id))) | ($true != ((X296 @ id @ X307 @ id))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f65,definition,(
% 5.11/1.35 ! [X296 : (subst > term > subst > $o)] : (($true = ((sP52 @ X296))) <=> ? [X311 : term,X312 : term] : ((((X296 @ id @ X311 @ id)) = $true) & ($true = ((X296 @ id @ X312 @ id))) & ($true != ((X296 @ id @ (ap @ (sub @ X312 @ id) @ X311) @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f66,definition,(
% 5.11/1.35 ! [X279 : (subst > term > subst > $o)] : (($true = ((sP53 @ X279))) <=> ! [X282 : (subst > term > term)] : (($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ? [X286 : subst,X285 : term,X284 : subst] : (((X282 @ (comp @ X286 @ X284) @ (sub @ X285 @ X284))) != ((sub @ (X282 @ X286 @ X285) @ X284))) | ? [X283 : term] : ((((X279 @ id @ (X282 @ id @ X283) @ id)) != $true) & ($true = ((X279 @ id @ X283 @ id))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f67,definition,(
% 5.11/1.35 ! [X259 : (term > $o)] : (($true = ((sP54 @ X259))) <=> ! [X262 : term,X261 : term] : ((((X259 @ X262)) != $true) | ($true != ((X259 @ X261))) | ($true = ((X259 @ (ap @ X262 @ X261))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f68,definition,(
% 5.11/1.35 ($true = sP55) <=> ? [X280 : term,X279 : (subst > term > subst > $o)] : (($true = ((sP53 @ X279))) & ! [X287 : subst,X290 : subst,X289 : subst,X288 : term] : (($true != ((X279 @ (comp @ X289 @ X290) @ (sub @ X288 @ X290) @ X287))) | ($true = ((X279 @ X289 @ X288 @ (comp @ X290 @ X287))))) & ! [X293 : subst,X294 : term,X291 : subst,X292 : subst] : (($true = ((X279 @ (comp @ X293 @ X292) @ (sub @ X294 @ X292) @ X291))) | ($true != ((X279 @ X293 @ X294 @ (comp @ X292 @ X291))))) & ($true != ((X279 @ id @ (lam @ X280) @ id))) & ! [X281 : term] : ((((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) = $true) | ($true != ((X279 @ id @ X281 @ id)))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f69,definition,(
% 5.11/1.35 (sP56 = $true) <=> ! [X296 : (subst > term > subst > $o),X295 : term] : (($true = ((sP52 @ X296))) | ? [X300 : term,X299 : subst,X298 : subst,X301 : subst] : (($true = ((X296 @ X298 @ X300 @ (comp @ X301 @ X299)))) & ($true != ((X296 @ (comp @ X298 @ X301) @ (sub @ X300 @ X301) @ X299)))) | ? [X305 : subst,X304 : subst,X303 : term,X302 : subst] : (($true != ((X296 @ X304 @ X303 @ (comp @ X302 @ X305)))) & ($true = ((X296 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302) @ X305)))) | ? [X297 : term] : (($true != ((X296 @ id @ X297 @ id))) & ($true = ((var @ (sub @ X297 @ id))))) | ($true = ((X296 @ id @ X295 @ id))) | ($true = ((sP51 @ X296))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f70,definition,(
% 5.11/1.35 ($true = sP57) <=> ? [X268 : (subst > term > subst > $o),X266 : term,X267 : term] : (! [X271 : subst,X274 : subst,X272 : subst,X273 : term] : (($true = ((X268 @ (comp @ X272 @ X274) @ (sub @ X273 @ X274) @ X271))) | ($true != ((X268 @ X272 @ X273 @ (comp @ X274 @ X271))))) & ($true = ((X268 @ id @ X266 @ id))) & ! [X276 : subst,X277 : subst,X278 : subst,X275 : term] : (($true = ((X268 @ X277 @ X275 @ (comp @ X278 @ X276)))) | (((X268 @ (comp @ X277 @ X278) @ (sub @ X275 @ X278) @ X276)) != $true)) & ($true != ((X268 @ id @ (ap @ X266 @ X267) @ id))) & ($true = ((X268 @ id @ X267 @ id))) & ($true = ((sP50 @ X268))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f71,definition,(
% 5.11/1.35 ($true = sP58) <=> (? [X259 : (term > $o),X260 : term] : (! [X263 : term] : ((((X259 @ (lam @ X263))) = $true) | ? [X264 : term] : ((((X259 @ X264)) = $true) & ($true != ((X259 @ (sub @ X263 @ (push @ X264 @ id))))))) & ($true != ((X259 @ X260))) & ! [X265 : term] : ((((var @ X265)) != $true) | ($true = ((X259 @ X265)))) & ($true = ((sP54 @ X259)))) | ($true = sP55) | (sP56 = $true) | ($true = sP57))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.11/1.35 thf(f72,plain,(
% 5.11/1.35 (axvarshift = $true) & ((substmonoid = $true) <=> (! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36))) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X111 : term,X113 : subst,X112 : (term > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) <=> (pushprop_lem0_lthm = $true)) & (! [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316))) | ? [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) != ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ? [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X315 @ X322 @ X320) @ X321)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) <=> (axvarid = $true)) & ((hoasapinj1 = $true) <=> ! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14))))) & (($true = sP58) <=> (hoasinduction_lthm = $true)) & (! [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (? [X471 : term] : (((X467 @ X471)) != ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) <=> (pushprop_lem1v2 = $true)) & (hoasapinj2_gthm = $true) & ((! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) | ? [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) != X396) | ? [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) != X394)) <=> (pushprop_lem1_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) <=> (hoasapinj2 = $true)) & (! [X536 : (subst > term > subst > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) <=> (hoasinduction_lem0_lthm = $true)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & (($true = sP49) <=> (hoasinduction_lthm_3 = $true)) & ((termmset = $true) <=> ! [X354 : term] : (((sub @ X354 @ id)) = X354)) & (pushprop_lem0_gthm = $true) & (($true = sP43) <=> (hoasinduction_lem3v2a = $true)) & ((axscons = $true) <=> ! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & (($true = sP42) <=> (hoasinduction = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X530 : term] : ? [X531 : (subst > term > term)] : ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533))))) & (($true = sP39) <=> (hoasinduction_lem3 = $true)) & (! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP37)) & ((hoasinduction_lem3a = $true) <=> ($true = sP34)) & (axassoc = $true) & ! [X534 : d_term,X535 : d_term] : ((((d2term @ X534)) != ((d2term @ X535))) | (X534 = X535)) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> ($true = sP33)) & ((hoaslaminj_lthm = $true) <=> ($true = sP31)) & (! [X1 : (term > $o),X0 : term] : (($true = ((X1 @ X0))) | ? [X5 : term] : (($true != ((X1 @ (lam @ X5)))) & (((X1 @ X5)) = $true)) | ($true = ((sP30 @ X1))) | ? [X4 : term] : (($true = ((var @ X4))) & (((X1 @ X4)) != $true))) <=> (induction = $true)) & ((hoasapinj1_lthm = $true) <=> (? [X215 : term] : (((sub @ X215 @ id)) != X215) | ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)) | ? [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) = ((ap @ X216 @ X219))) & (X216 != X217)))) & ((axvarcons = $true) <=> ! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((? [X391 : subst] : (((comp @ X391 @ id)) != X391) | (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393)) | ? [X390 : subst] : (((comp @ id @ X390)) != X390)) <=> (substmonoid_lthm = $true)) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) <=> (laminj = $true)) & (! [X186 : term] : ? [X187 : (subst > term > term)] : (((X187 @ sh @ one)) = ((sub @ X186 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (hoasapnotvar = $true) & (! [X137 : (subst > term > subst > $o),X136 : term] : (? [X139 : term,X138 : term] : (($true = ((X137 @ id @ X139 @ id))) & ($true = ((X137 @ id @ X138 @ id))) & ($true != ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ($true = ((X137 @ id @ X136 @ id))) | (((sP29 @ X137)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & ((axshiftcons = $true) <=> ! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (($true = sP28) <=> (hoasinduction_lem2 = $true)) & (($true = sP26) <=> (induction2lem = $true)) & ((! [X94 : term] : (((sub @ X94 @ id)) = X94) | ? [X93 : term] : (((sub @ X93 @ id)) != X93)) <=> (termmset_lthm = $true)) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & ((? [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) != X7) | ! [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) = $true) | ($true != ((X11 @ X8))) | ? [X12 : term] : (((X9 @ X12)) != ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))))) <=> (pushprop_lem1v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (! [X71 : (subst > term > subst > $o)] : ? [X72 : (term > $o)] : ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) <=> (hoasinduction_lem0 = $true)) & ((induction2lem_lthm = $true) <=> (sP24 = $true)) & (hoaslamnotvar_lthm = $true) & (! [X22 : term] : ? [X23 : (subst > term > term)] : ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((sP20 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (($true = sP19) <=> (induction2 = $true)) & ((? [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 != X41) & (((ap @ X38 @ X41)) = ((ap @ X40 @ X39)))) | ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) <=> (hoasapinj2_lthm = $true)) & ((sP17 = $true) <=> (hoasinduction_lem3v2 = $true)) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) != ((d2subst @ X364))) | (X363 = X364)) & (($true = sP15) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (($true = sP10) <=> (hoasinduction_lem3aa_lthm = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP9 = $true)) & ! [X490 : d_subst] : (d_id = X490) & (((d2subst @ d_id)) = id) & ((induction2_lthm = $true) <=> (sP7 = $true)) & ((apinj2 = $true) <=> ! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466))) & (($true = sP3) <=> (hoasinduction_lem3aa = $true)) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) <=> (axidl = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X34 : term] : ? [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) = ((X35 @ sh @ one)))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & ((apinj1 = $true) <=> ! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205))))) & (ulamvarsh = $true) & (($true = sP2) <=> (hoasinduction_lem3aaa = $true)) & ((hoaslamnotap = $true) <=> ! [X357 : term,X355 : term,X356 : (subst > term > term)] : (? [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) != ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357))))) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X18 : subst,X19 : (term > $o),X17 : term] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21))) <=> (pushprop_lem0 = $true)) & ! [X366 : d_term] : (d_one = X366) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP1)) & ((axidr = $true) <=> ! [X539 : subst] : (((comp @ X539 @ id)) = X539)) & ((shinj = $true) <=> ! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh))))) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 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])).
% 5.11/1.35 thf(f260,plain,(
% 5.11/1.35 (axvarshift = $true) & (((substmonoid = $true) | (? [X37 : subst] : (((comp @ id @ X37)) != X37) | ? [X36 : subst] : (((comp @ X36 @ id)) != X36))) & ((! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36)) | (substmonoid != $true))) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ((! [X111 : term,X113 : subst,X112 : (term > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X111 : term,X113 : subst,X112 : (term > $o)] : ! [X114 : (term > $o)] : ? [X115 : term] : (((X114 @ X115)) != ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))))) & ((! [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316))) | ? [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) != ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ? [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X315 @ X322 @ X320) @ X321)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) != ((X314 @ X313 @ X316))) & ! [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) = ((sub @ (X314 @ X317 @ X318) @ X319))) & (((lam @ (X314 @ sh @ one))) = ((lam @ (X315 @ sh @ one)))) & ! [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321)))))) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & ((! [X74 : term] : (((sub @ X74 @ id)) = X74) | (axvarid != $true)) & ((axvarid = $true) | ? [X74 : term] : (((sub @ X74 @ id)) != X74))) & (((hoasapinj1 = $true) | ? [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 != X16) & (((ap @ (sub @ X16 @ id) @ X13)) = ((ap @ (sub @ X15 @ id) @ X14))))) & (! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14)))) | (hoasapinj1 != $true))) & ((($true = sP58) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP58))) & ((! [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (? [X471 : term] : (((X467 @ X471)) != ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (! [X471 : term] : (((X467 @ X471)) = ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) & ($true = ((X469 @ X470))) & ($true != ((X467 @ one)))))) & (hoasapinj2_gthm = $true) & (((! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) | ? [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) != X396) | ? [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) != X394)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true = ((X399 @ X398))) & ($true != ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) & ! [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) = X396) & ! [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) = X394)))) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & ((! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 != X452) & (((ap @ (sub @ X450 @ id) @ X452)) = ((ap @ (sub @ X451 @ id) @ X449)))))) & ((! [X536 : (subst > term > subst > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X536 : (subst > term > subst > $o)] : ! [X537 : (term > $o)] : ? [X538 : term] : (((X536 @ id @ X538 @ id)) != ((X537 @ X538))))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & ((($true = sP49) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP49))) & (((termmset = $true) | ? [X354 : term] : (((sub @ X354 @ id)) != X354)) & (! [X354 : term] : (((sub @ X354 @ id)) = X354) | (termmset != $true))) & (pushprop_lem0_gthm = $true) & ((($true = sP43) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP43))) & (((axscons = $true) | ? [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) != X188)) & (! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188) | (axscons != $true))) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & ((($true = sP42) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP42))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X530 : term] : ! [X531 : (subst > term > term)] : ? [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) != ((sub @ X530 @ (push @ X532 @ X533))))) & (! [X530 : term] : ? [X531 : (subst > term > term)] : ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533)))) | (hoasinduction_lem3v2_f != $true))) & ((($true = sP39) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP39))) & ((! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true != ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) & ($true = ((X212 @ X214)))))) & (((hoasinduction_lem3_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3_lthm != $true))) & (((hoasinduction_lem3a = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem3a != $true))) & (axassoc = $true) & ! [X534 : d_term,X535 : d_term] : ((((d2term @ X534)) != ((d2term @ X535))) | (X534 = X535)) & (induction2_gthm = $true) & (((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true))) & (((hoaslaminj_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoaslaminj_lthm != $true))) & ((! [X1 : (term > $o),X0 : term] : (($true = ((X1 @ X0))) | ? [X5 : term] : (($true != ((X1 @ (lam @ X5)))) & (((X1 @ X5)) = $true)) | ($true = ((sP30 @ X1))) | ? [X4 : term] : (($true = ((var @ X4))) & (((X1 @ X4)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X1 : (term > $o),X0 : term] : (($true != ((X1 @ X0))) & ! [X5 : term] : (($true = ((X1 @ (lam @ X5)))) | (((X1 @ X5)) != $true)) & ($true != ((sP30 @ X1))) & ! [X4 : term] : (($true != ((var @ X4))) | (((X1 @ X4)) = $true))))) & (((hoasapinj1_lthm = $true) | (! [X215 : term] : (((sub @ X215 @ id)) = X215) & ? [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) = ((ap @ (sub @ X223 @ id) @ X220))) & (X222 != X223)) & ! [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) != ((ap @ X216 @ X219))) | (X216 = X217)))) & ((? [X215 : term] : (((sub @ X215 @ id)) != X215) | ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)) | ? [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) = ((ap @ X216 @ X219))) & (X216 != X217))) | (hoasapinj1_lthm != $true))) & (((axvarcons = $true) | ? [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) != X117)) & (! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117) | (axvarcons != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((? [X391 : subst] : (((comp @ X391 @ id)) != X391) | (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393)) | ? [X390 : subst] : (((comp @ id @ X390)) != X390)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X391 : subst] : (((comp @ X391 @ id)) = X391) & (? [X392 : subst] : (((comp @ id @ X392)) != X392) | ? [X393 : subst] : (((comp @ X393 @ id)) != X393)) & ! [X390 : subst] : (((comp @ id @ X390)) = X390)))) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & ((! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) | (laminj != $true)) & ((laminj = $true) | ? [X208 : term,X209 : term] : ((((lam @ X208)) = ((lam @ X209))) & (X208 != X209)))) & ((! [X186 : term] : ? [X187 : (subst > term > term)] : (((X187 @ sh @ one)) = ((sub @ X186 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X186 : term] : ! [X187 : (subst > term > term)] : (((X187 @ sh @ one)) != ((sub @ X186 @ (push @ one @ sh)))))) & (hoasapnotvar = $true) & ((! [X137 : (subst > term > subst > $o),X136 : term] : (? [X139 : term,X138 : term] : (($true = ((X137 @ id @ X139 @ id))) & ($true = ((X137 @ id @ X138 @ id))) & ($true != ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ($true = ((X137 @ id @ X136 @ id))) | (((sP29 @ X137)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X137 : (subst > term > subst > $o),X136 : term] : (! [X139 : term,X138 : term] : (($true != ((X137 @ id @ X139 @ id))) | ($true != ((X137 @ id @ X138 @ id))) | ($true = ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) & ($true != ((X137 @ id @ X136 @ id))) & (((sP29 @ X137)) != $true)))) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & (((axshiftcons = $true) | ? [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) != X362)) & (! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362) | (axshiftcons != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28))) & ((($true = sP26) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP26))) & (((! [X94 : term] : (((sub @ X94 @ id)) = X94) | ? [X93 : term] : (((sub @ X93 @ id)) != X93)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X94 : term] : (((sub @ X94 @ id)) != X94) & ! [X93 : term] : (((sub @ X93 @ id)) = X93)))) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & (((? [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) != X7) | ! [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) = $true) | ($true != ((X11 @ X8))) | ? [X12 : term] : (((X9 @ X12)) != ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) = X7) & ? [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) != $true) & ($true = ((X11 @ X8))) & ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10))))))))) & (pushprop_lem2v2_lthm = $true) & ((! [X71 : (subst > term > subst > $o)] : ? [X72 : (term > $o)] : ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X71 : (subst > term > subst > $o)] : ! [X72 : (term > $o)] : ? [X73 : term] : (((X71 @ id @ X73 @ id)) != ((X72 @ X73))))) & (((induction2lem_lthm = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem_lthm != $true))) & (hoaslamnotvar_lthm = $true) & ((! [X22 : term] : ? [X23 : (subst > term > term)] : ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X22 : term] : ! [X23 : (subst > term > term)] : ? [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) != ((X23 @ X24 @ X25))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((sP20 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP20 != $true))) & ((($true = sP19) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP19))) & (((? [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 != X41) & (((ap @ X38 @ X41)) = ((ap @ X40 @ X39)))) | ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 = X41) | (((ap @ X38 @ X41)) != ((ap @ X40 @ X39)))) & ? [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) = ((ap @ (sub @ X45 @ id) @ X44))) & (X43 != X44))))) & (((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true))) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) != ((d2subst @ X364))) | (X363 = X364)) & ((($true = sP15) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP15))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10))) & (((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true))) & ! [X490 : d_subst] : (d_id = X490) & (((d2subst @ d_id)) = id) & (((induction2_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2_lthm != $true))) & (((apinj2 = $true) | ? [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) = ((ap @ X463 @ X466))) & (X465 != X466))) & (! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466)) | (apinj2 != $true))) & ((($true = sP3) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP3))) & ((! [X365 : subst] : (((comp @ id @ X365)) = X365) | (axidl != $true)) & ((axidl = $true) | ? [X365 : subst] : (((comp @ id @ X365)) != X365))) & (((hoasinduction_lem3b_lthm = $true) | ? [X34 : term] : ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one)))) & (! [X34 : term] : ? [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) = ((X35 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & (((apinj1 = $true) | ? [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 != X206) & (((ap @ X204 @ X207)) = ((ap @ X206 @ X205))))) & (! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205)))) | (apinj1 != $true))) & (ulamvarsh = $true) & ((($true = sP2) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP2))) & (((hoaslamnotap = $true) | ? [X357 : term,X355 : term,X356 : (subst > term > term)] : (! [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) = ((sub @ (X356 @ X360 @ X358) @ X359))) & (((lam @ (X356 @ sh @ one))) = ((ap @ (sub @ X355 @ id) @ X357))))) & (! [X357 : term,X355 : term,X356 : (subst > term > term)] : (? [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) != ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357)))) | (hoaslamnotap != $true))) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X18 : subst,X19 : (term > $o),X17 : term] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X18 : subst,X19 : (term > $o),X17 : term] : ! [X20 : (term > $o)] : ? [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) != ((X20 @ X21))))) & ! [X366 : d_term] : (d_one = X366) & (((hoasinduction_lem2v2 = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem2v2 != $true))) & (((axidr = $true) | ? [X539 : subst] : (((comp @ X539 @ id)) != X539)) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) | (axidr != $true))) & (((shinj = $true) | ? [X323 : term,X324 : term] : ((X323 != X324) & (((sub @ X324 @ sh)) = ((sub @ X323 @ sh))))) & (! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh)))) | (shinj != $true))) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 inference(nnf_transformation,[],[f72])).
% 5.11/1.35 thf(f261,plain,(
% 5.11/1.35 (axvarshift = $true) & ((substmonoid = $true) | ? [X37 : subst] : (((comp @ id @ X37)) != X37) | ? [X36 : subst] : (((comp @ X36 @ id)) != X36)) & ((! [X37 : subst] : (((comp @ id @ X37)) = X37) & ! [X36 : subst] : (((comp @ X36 @ id)) = X36)) | (substmonoid != $true)) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X111 : term,X113 : subst,X112 : (term > $o)] : ? [X114 : (term > $o)] : ! [X115 : term] : (((X114 @ X115)) = ((X112 @ (sub @ X115 @ (push @ X111 @ X113))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X111 : term,X113 : subst,X112 : (term > $o)] : ! [X114 : (term > $o)] : ? [X115 : term] : (((X114 @ X115)) != ((X112 @ (sub @ X115 @ (push @ X111 @ X113)))))) & (! [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) = ((X314 @ X313 @ X316))) | ? [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) != ((sub @ (X314 @ X317 @ X318) @ X319))) | (((lam @ (X314 @ sh @ one))) != ((lam @ (X315 @ sh @ one)))) | ? [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) != ((sub @ (X315 @ X322 @ X320) @ X321)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X315 : (subst > term > term),X316 : term,X313 : subst,X314 : (subst > term > term)] : ((((X315 @ X313 @ X316)) != ((X314 @ X313 @ X316))) & ! [X318 : term,X319 : subst,X317 : subst] : (((X314 @ (comp @ X317 @ X319) @ (sub @ X318 @ X319))) = ((sub @ (X314 @ X317 @ X318) @ X319))) & (((lam @ (X314 @ sh @ one))) = ((lam @ (X315 @ sh @ one)))) & ! [X320 : term,X322 : subst,X321 : subst] : (((X315 @ (comp @ X322 @ X321) @ (sub @ X320 @ X321))) = ((sub @ (X315 @ X322 @ X320) @ X321))))) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X380 : term] : ? [X381 : d_term] : (((d2term @ X381)) = X380) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & (! [X74 : term] : (((sub @ X74 @ id)) = X74) | (axvarid != $true)) & ((axvarid = $true) | ? [X74 : term] : (((sub @ X74 @ id)) != X74)) & ((hoasapinj1 = $true) | ? [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 != X16) & (((ap @ (sub @ X16 @ id) @ X13)) = ((ap @ (sub @ X15 @ id) @ X14))))) & (! [X16 : term,X14 : term,X15 : term,X13 : term] : ((X15 = X16) | (((ap @ (sub @ X16 @ id) @ X13)) != ((ap @ (sub @ X15 @ id) @ X14)))) | (hoasapinj1 != $true)) & (($true = sP58) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP58)) & (! [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (? [X471 : term] : (((X467 @ X471)) != ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) | ($true != ((X469 @ X470))) | ($true = ((X467 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X469 : (term > $o),X470 : term,X467 : (term > $o),X468 : subst] : (! [X471 : term] : (((X467 @ X471)) = ((X469 @ (sub @ X471 @ (push @ X470 @ X468))))) & ($true = ((X469 @ X470))) & ($true != ((X467 @ one))))) & (hoasapinj2_gthm = $true) & (! [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true != ((X399 @ X398))) | ($true = ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) | ? [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) != X396) | ? [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) != X394) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X401 : term,X399 : (term > $o),X398 : term,X400 : subst,X402 : (term > $o)] : (($true = ((X399 @ X398))) & ($true != ((X402 @ (sub @ X398 @ (push @ X401 @ X400)))))) & ! [X396 : subst,X397 : term] : (((comp @ sh @ (push @ X397 @ X396))) = X396) & ! [X394 : term,X395 : subst] : (((sub @ one @ (push @ X394 @ X395))) = X394))) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 = X452) | (((ap @ (sub @ X450 @ id) @ X452)) != ((ap @ (sub @ X451 @ id) @ X449)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X450 : term,X452 : term,X451 : term,X449 : term] : ((X449 != X452) & (((ap @ (sub @ X450 @ id) @ X452)) = ((ap @ (sub @ X451 @ id) @ X449))))) & (! [X536 : (subst > term > subst > $o)] : ? [X537 : (term > $o)] : ! [X538 : term] : (((X536 @ id @ X538 @ id)) = ((X537 @ X538))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X536 : (subst > term > subst > $o)] : ! [X537 : (term > $o)] : ? [X538 : term] : (((X536 @ id @ X538 @ id)) != ((X537 @ X538)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & (($true = sP49) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP49)) & ((termmset = $true) | ? [X354 : term] : (((sub @ X354 @ id)) != X354)) & (! [X354 : term] : (((sub @ X354 @ id)) = X354) | (termmset != $true)) & (pushprop_lem0_gthm = $true) & (($true = sP43) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP43)) & ((axscons = $true) | ? [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) != X188)) & (! [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) = X188) | (axscons != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & (($true = sP42) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X530 : term] : ! [X531 : (subst > term > term)] : ? [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) != ((sub @ X530 @ (push @ X532 @ X533))))) & (! [X530 : term] : ? [X531 : (subst > term > term)] : ! [X532 : term,X533 : subst] : (((X531 @ X533 @ X532)) = ((sub @ X530 @ (push @ X532 @ X533)))) | (hoasinduction_lem3v2_f != $true)) & (($true = sP39) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP39)) & (! [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) | ($true != ((X212 @ X214)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X214 : term,X210 : subst,X211 : (term > $o),X212 : (term > $o),X213 : term] : (($true != ((X211 @ (sub @ X214 @ (push @ X213 @ X210))))) & ($true = ((X212 @ X214))))) & ((hoasinduction_lem3_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem3a != $true)) & (axassoc = $true) & ! [X534 : d_term,X535 : d_term] : ((((d2term @ X534)) != ((d2term @ X535))) | (X534 = X535)) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoaslaminj_lthm != $true)) & (! [X1 : (term > $o),X0 : term] : (($true = ((X1 @ X0))) | ? [X5 : term] : (($true != ((X1 @ (lam @ X5)))) & (((X1 @ X5)) = $true)) | ($true = ((sP30 @ X1))) | ? [X4 : term] : (($true = ((var @ X4))) & (((X1 @ X4)) != $true))) | (induction != $true)) & ((induction = $true) | ? [X1 : (term > $o),X0 : term] : (($true != ((X1 @ X0))) & ! [X5 : term] : (($true = ((X1 @ (lam @ X5)))) | (((X1 @ X5)) != $true)) & ($true != ((sP30 @ X1))) & ! [X4 : term] : (($true != ((var @ X4))) | (((X1 @ X4)) = $true)))) & ((hoasapinj1_lthm = $true) | (! [X215 : term] : (((sub @ X215 @ id)) = X215) & ? [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) = ((ap @ (sub @ X223 @ id) @ X220))) & (X222 != X223)) & ! [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) != ((ap @ X216 @ X219))) | (X216 = X217)))) & (? [X215 : term] : (((sub @ X215 @ id)) != X215) | ! [X223 : term,X222 : term,X220 : term,X221 : term] : ((((ap @ (sub @ X222 @ id) @ X221)) != ((ap @ (sub @ X223 @ id) @ X220))) | (X222 = X223)) | ? [X219 : term,X216 : term,X217 : term,X218 : term] : ((((ap @ X217 @ X218)) = ((ap @ X216 @ X219))) & (X216 != X217)) | (hoasapinj1_lthm != $true)) & ((axvarcons = $true) | ? [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) != X117)) & (! [X117 : term,X116 : subst] : (((sub @ one @ (push @ X117 @ X116))) = X117) | (axvarcons != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (? [X391 : subst] : (((comp @ X391 @ id)) != X391) | (! [X392 : subst] : (((comp @ id @ X392)) = X392) & ! [X393 : subst] : (((comp @ X393 @ id)) = X393)) | ? [X390 : subst] : (((comp @ id @ X390)) != X390) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X391 : subst] : (((comp @ X391 @ id)) = X391) & (? [X392 : subst] : (((comp @ id @ X392)) != X392) | ? [X393 : subst] : (((comp @ X393 @ id)) != X393)) & ! [X390 : subst] : (((comp @ id @ X390)) = X390))) & ! [X75 : subst] : ? [X76 : d_subst] : (((d2subst @ X76)) = X75) & (! [X208 : term,X209 : term] : ((((lam @ X208)) != ((lam @ X209))) | (X208 = X209)) | (laminj != $true)) & ((laminj = $true) | ? [X208 : term,X209 : term] : ((((lam @ X208)) = ((lam @ X209))) & (X208 != X209))) & (! [X186 : term] : ? [X187 : (subst > term > term)] : (((X187 @ sh @ one)) = ((sub @ X186 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X186 : term] : ! [X187 : (subst > term > term)] : (((X187 @ sh @ one)) != ((sub @ X186 @ (push @ one @ sh))))) & (hoasapnotvar = $true) & (! [X137 : (subst > term > subst > $o),X136 : term] : (? [X139 : term,X138 : term] : (($true = ((X137 @ id @ X139 @ id))) & ($true = ((X137 @ id @ X138 @ id))) & ($true != ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) | ($true = ((X137 @ id @ X136 @ id))) | (((sP29 @ X137)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X137 : (subst > term > subst > $o),X136 : term] : (! [X139 : term,X138 : term] : (($true != ((X137 @ id @ X139 @ id))) | ($true != ((X137 @ id @ X138 @ id))) | ($true = ((X137 @ id @ (ap @ (sub @ X138 @ id) @ X139) @ id)))) & ($true != ((X137 @ id @ X136 @ id))) & (((sP29 @ X137)) != $true))) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & ((axshiftcons = $true) | ? [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) != X362)) & (! [X361 : term,X362 : subst] : (((comp @ sh @ (push @ X361 @ X362))) = X362) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP26)) & (! [X94 : term] : (((sub @ X94 @ id)) = X94) | ? [X93 : term] : (((sub @ X93 @ id)) != X93) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X94 : term] : (((sub @ X94 @ id)) != X94) & ! [X93 : term] : (((sub @ X93 @ id)) = X93))) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & (? [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) != X7) | ! [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) = $true) | ($true != ((X11 @ X8))) | ? [X12 : term] : (((X9 @ X12)) != ((X11 @ (sub @ X12 @ (push @ X8 @ X10)))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X7 : term,X6 : subst] : (((sub @ one @ (push @ X7 @ X6))) = X7) & ? [X10 : subst,X8 : term,X9 : (term > $o),X11 : (term > $o)] : ((((X9 @ one)) != $true) & ($true = ((X11 @ X8))) & ! [X12 : term] : (((X9 @ X12)) = ((X11 @ (sub @ X12 @ (push @ X8 @ X10)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X71 : (subst > term > subst > $o)] : ? [X72 : (term > $o)] : ! [X73 : term] : (((X71 @ id @ X73 @ id)) = ((X72 @ X73))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X71 : (subst > term > subst > $o)] : ! [X72 : (term > $o)] : ? [X73 : term] : (((X71 @ id @ X73 @ id)) != ((X72 @ X73)))) & ((induction2lem_lthm = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar_lthm = $true) & (! [X22 : term] : ? [X23 : (subst > term > term)] : ! [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) = ((X23 @ X24 @ X25))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X22 : term] : ! [X23 : (subst > term > term)] : ? [X25 : term,X24 : subst] : (((sub @ X22 @ (push @ X25 @ X24))) != ((X23 @ X24 @ X25)))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((sP20 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP20 != $true)) & (($true = sP19) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP19)) & (? [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 != X41) & (((ap @ X38 @ X41)) = ((ap @ X40 @ X39)))) | ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) != ((ap @ (sub @ X45 @ id) @ X44))) | (X43 = X44)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X41 : term,X38 : term,X39 : term,X40 : term] : ((X39 = X41) | (((ap @ X38 @ X41)) != ((ap @ X40 @ X39)))) & ? [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X43)) = ((ap @ (sub @ X45 @ id) @ X44))) & (X43 != X44)))) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X364 : d_subst,X363 : d_subst] : ((((d2subst @ X363)) != ((d2subst @ X364))) | (X363 = X364)) & (($true = sP15) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP15)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X490 : d_subst] : (d_id = X490) & (((d2subst @ d_id)) = id) & ((induction2_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2_lthm != $true)) & ((apinj2 = $true) | ? [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) = ((ap @ X463 @ X466))) & (X465 != X466))) & (! [X466 : term,X463 : term,X464 : term,X465 : term] : ((((ap @ X464 @ X465)) != ((ap @ X463 @ X466))) | (X465 = X466)) | (apinj2 != $true)) & (($true = sP3) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP3)) & (! [X365 : subst] : (((comp @ id @ X365)) = X365) | (axidl != $true)) & ((axidl = $true) | ? [X365 : subst] : (((comp @ id @ X365)) != X365)) & ((hoasinduction_lem3b_lthm = $true) | ? [X34 : term] : ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one)))) & (! [X34 : term] : ? [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) = ((X35 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & ((apinj1 = $true) | ? [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 != X206) & (((ap @ X204 @ X207)) = ((ap @ X206 @ X205))))) & (! [X207 : term,X204 : term,X205 : term,X206 : term] : ((X204 = X206) | (((ap @ X204 @ X207)) != ((ap @ X206 @ X205)))) | (apinj1 != $true)) & (ulamvarsh = $true) & (($true = sP2) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP2)) & ((hoaslamnotap = $true) | ? [X357 : term,X355 : term,X356 : (subst > term > term)] : (! [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) = ((sub @ (X356 @ X360 @ X358) @ X359))) & (((lam @ (X356 @ sh @ one))) = ((ap @ (sub @ X355 @ id) @ X357))))) & (! [X357 : term,X355 : term,X356 : (subst > term > term)] : (? [X358 : term,X359 : subst,X360 : subst] : (((X356 @ (comp @ X360 @ X359) @ (sub @ X358 @ X359))) != ((sub @ (X356 @ X360 @ X358) @ X359))) | (((lam @ (X356 @ sh @ one))) != ((ap @ (sub @ X355 @ id) @ X357)))) | (hoaslamnotap != $true)) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X18 : subst,X19 : (term > $o),X17 : term] : ? [X20 : (term > $o)] : ! [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) = ((X20 @ X21))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X18 : subst,X19 : (term > $o),X17 : term] : ! [X20 : (term > $o)] : ? [X21 : term] : (((X19 @ (sub @ X21 @ (push @ X17 @ X18)))) != ((X20 @ X21)))) & ! [X366 : d_term] : (d_one = X366) & ((hoasinduction_lem2v2 = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem2v2 != $true)) & ((axidr = $true) | ? [X539 : subst] : (((comp @ X539 @ id)) != X539)) & (! [X539 : subst] : (((comp @ X539 @ id)) = X539) | (axidr != $true)) & ((shinj = $true) | ? [X323 : term,X324 : term] : ((X323 != X324) & (((sub @ X324 @ sh)) = ((sub @ X323 @ sh))))) & (! [X323 : term,X324 : term] : ((X323 = X324) | (((sub @ X324 @ sh)) != ((sub @ X323 @ sh)))) | (shinj != $true)) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 inference(flattening,[],[f260])).
% 5.11/1.35 thf(f262,plain,(
% 5.11/1.35 (axvarshift = $true) & ((substmonoid = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0) | ? [X1 : subst] : (((comp @ X1 @ id)) != X1)) & ((! [X2 : subst] : (((comp @ id @ X2)) = X2) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | (substmonoid != $true)) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X4 : term,X5 : subst,X6 : (term > $o)] : ? [X7 : (term > $o)] : ! [X8 : term] : (((X7 @ X8)) = ((X6 @ (sub @ X8 @ (push @ X4 @ X5))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X9 : term,X10 : subst,X11 : (term > $o)] : ! [X12 : (term > $o)] : ? [X13 : term] : (((X12 @ X13)) != ((X11 @ (sub @ X13 @ (push @ X9 @ X10)))))) & (! [X14 : (subst > term > term),X15 : term,X16 : subst,X17 : (subst > term > term)] : ((((X14 @ X16 @ X15)) = ((X17 @ X16 @ X15))) | ? [X18 : term,X19 : subst,X20 : subst] : (((X17 @ (comp @ X20 @ X19) @ (sub @ X18 @ X19))) != ((sub @ (X17 @ X20 @ X18) @ X19))) | (((lam @ (X14 @ sh @ one))) != ((lam @ (X17 @ sh @ one)))) | ? [X21 : term,X22 : subst,X23 : subst] : (((sub @ (X14 @ X22 @ X21) @ X23)) != ((X14 @ (comp @ X22 @ X23) @ (sub @ X21 @ X23))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X24 : (subst > term > term),X25 : term,X26 : subst,X27 : (subst > term > term)] : ((((X27 @ X26 @ X25)) != ((X24 @ X26 @ X25))) & ! [X28 : term,X29 : subst,X30 : subst] : (((X27 @ (comp @ X30 @ X29) @ (sub @ X28 @ X29))) = ((sub @ (X27 @ X30 @ X28) @ X29))) & (((lam @ (X24 @ sh @ one))) = ((lam @ (X27 @ sh @ one)))) & ! [X31 : term,X32 : subst,X33 : subst] : (((sub @ (X24 @ X32 @ X31) @ X33)) = ((X24 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33)))))) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X34 : term] : ? [X35 : d_term] : (((d2term @ X35)) = X34) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & (! [X36 : term] : (((sub @ X36 @ id)) = X36) | (axvarid != $true)) & ((axvarid = $true) | ? [X37 : term] : (((sub @ X37 @ id)) != X37)) & ((hoasapinj1 = $true) | ? [X38 : term,X39 : term,X40 : term,X41 : term] : ((X38 != X40) & (((ap @ (sub @ X38 @ id) @ X41)) = ((ap @ (sub @ X40 @ id) @ X39))))) & (! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X44) | (((ap @ (sub @ X42 @ id) @ X45)) != ((ap @ (sub @ X44 @ id) @ X43)))) | (hoasapinj1 != $true)) & (($true = sP58) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP58)) & (! [X46 : (term > $o),X47 : term,X48 : (term > $o),X49 : subst] : (? [X50 : term] : (((X46 @ (sub @ X50 @ (push @ X47 @ X49)))) != ((X48 @ X50))) | ($true != ((X46 @ X47))) | ($true = ((X48 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X51 : (term > $o),X52 : term,X53 : (term > $o),X54 : subst] : (! [X55 : term] : (((X51 @ (sub @ X55 @ (push @ X52 @ X54)))) = ((X53 @ X55))) & ($true = ((X51 @ X52))) & (((X53 @ one)) != $true))) & (hoasapinj2_gthm = $true) & (! [X56 : term,X57 : (term > $o),X58 : term,X59 : subst,X60 : (term > $o)] : (($true != ((X57 @ X58))) | ($true = ((X60 @ (sub @ X58 @ (push @ X56 @ X59)))))) | ? [X61 : subst,X62 : term] : (((comp @ sh @ (push @ X62 @ X61))) != X61) | ? [X63 : term,X64 : subst] : (((sub @ one @ (push @ X63 @ X64))) != X63) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X65 : term,X66 : (term > $o),X67 : term,X68 : subst,X69 : (term > $o)] : (($true = ((X66 @ X67))) & ($true != ((X69 @ (sub @ X67 @ (push @ X65 @ X68)))))) & ! [X70 : subst,X71 : term] : (((comp @ sh @ (push @ X71 @ X70))) = X70) & ! [X72 : term,X73 : subst] : (((sub @ one @ (push @ X72 @ X73))) = X72))) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X74 : term,X75 : term,X76 : term,X77 : term] : ((X75 = X77) | (((ap @ (sub @ X76 @ id) @ X77)) != ((ap @ (sub @ X74 @ id) @ X75)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X78 : term,X79 : term,X80 : term,X81 : term] : ((X79 != X81) & (((ap @ (sub @ X80 @ id) @ X81)) = ((ap @ (sub @ X78 @ id) @ X79))))) & (! [X82 : (subst > term > subst > $o)] : ? [X83 : (term > $o)] : ! [X84 : term] : (((X83 @ X84)) = ((X82 @ id @ X84 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X85 : (subst > term > subst > $o)] : ! [X86 : (term > $o)] : ? [X87 : term] : (((X86 @ X87)) != ((X85 @ id @ X87 @ id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & (($true = sP49) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP49)) & ((termmset = $true) | ? [X88 : term] : (((sub @ X88 @ id)) != X88)) & (! [X89 : term] : (((sub @ X89 @ id)) = X89) | (termmset != $true)) & (pushprop_lem0_gthm = $true) & (($true = sP43) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP43)) & ((axscons = $true) | ? [X90 : subst] : (((push @ (sub @ one @ X90) @ (comp @ sh @ X90))) != X90)) & (! [X91 : subst] : (((push @ (sub @ one @ X91) @ (comp @ sh @ X91))) = X91) | (axscons != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & (($true = sP42) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X92 : term] : ! [X93 : (subst > term > term)] : ? [X94 : term,X95 : subst] : (((X93 @ X95 @ X94)) != ((sub @ X92 @ (push @ X94 @ X95))))) & (! [X96 : term] : ? [X97 : (subst > term > term)] : ! [X98 : term,X99 : subst] : (((X97 @ X99 @ X98)) = ((sub @ X96 @ (push @ X98 @ X99)))) | (hoasinduction_lem3v2_f != $true)) & (($true = sP39) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP39)) & (! [X100 : term,X101 : subst,X102 : (term > $o),X103 : (term > $o),X104 : term] : (($true = ((X102 @ (sub @ X100 @ (push @ X104 @ X101))))) | (((X103 @ X100)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X105 : term,X106 : subst,X107 : (term > $o),X108 : (term > $o),X109 : term] : (($true != ((X107 @ (sub @ X105 @ (push @ X109 @ X106))))) & ($true = ((X108 @ X105))))) & ((hoasinduction_lem3_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem3a != $true)) & (axassoc = $true) & ! [X110 : d_term,X111 : d_term] : ((((d2term @ X110)) != ((d2term @ X111))) | (X110 = X111)) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoaslaminj_lthm != $true)) & (! [X112 : (term > $o),X113 : term] : (($true = ((X112 @ X113))) | ? [X114 : term] : (($true != ((X112 @ (lam @ X114)))) & (((X112 @ X114)) = $true)) | ($true = ((sP30 @ X112))) | ? [X115 : term] : (($true = ((var @ X115))) & ($true != ((X112 @ X115))))) | (induction != $true)) & ((induction = $true) | ? [X116 : (term > $o),X117 : term] : (($true != ((X116 @ X117))) & ! [X118 : term] : (($true = ((X116 @ (lam @ X118)))) | ($true != ((X116 @ X118)))) & ($true != ((sP30 @ X116))) & ! [X119 : term] : (($true != ((var @ X119))) | ($true = ((X116 @ X119)))))) & ((hoasapinj1_lthm = $true) | (! [X120 : term] : (((sub @ X120 @ id)) = X120) & ? [X121 : term,X122 : term,X123 : term,X124 : term] : ((((ap @ (sub @ X121 @ id) @ X123)) = ((ap @ (sub @ X122 @ id) @ X124))) & (X121 != X122)) & ! [X125 : term,X126 : term,X127 : term,X128 : term] : ((((ap @ X126 @ X125)) != ((ap @ X127 @ X128))) | (X126 = X127)))) & (? [X129 : term] : (((sub @ X129 @ id)) != X129) | ! [X130 : term,X131 : term,X132 : term,X133 : term] : ((((ap @ (sub @ X131 @ id) @ X133)) != ((ap @ (sub @ X130 @ id) @ X132))) | (X130 = X131)) | ? [X134 : term,X135 : term,X136 : term,X137 : term] : ((((ap @ X136 @ X137)) = ((ap @ X135 @ X134))) & (X135 != X136)) | (hoasapinj1_lthm != $true)) & ((axvarcons = $true) | ? [X138 : term,X139 : subst] : (((sub @ one @ (push @ X138 @ X139))) != X138)) & (! [X140 : term,X141 : subst] : (((sub @ one @ (push @ X140 @ X141))) = X140) | (axvarcons != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (? [X142 : subst] : (((comp @ X142 @ id)) != X142) | (! [X143 : subst] : (((comp @ id @ X143)) = X143) & ! [X144 : subst] : (((comp @ X144 @ id)) = X144)) | ? [X145 : subst] : (((comp @ id @ X145)) != X145) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X146 : subst] : (((comp @ X146 @ id)) = X146) & (? [X147 : subst] : (((comp @ id @ X147)) != X147) | ? [X148 : subst] : (((comp @ X148 @ id)) != X148)) & ! [X149 : subst] : (((comp @ id @ X149)) = X149))) & ! [X150 : subst] : ? [X151 : d_subst] : (((d2subst @ X151)) = X150) & (! [X152 : term,X153 : term] : ((((lam @ X152)) != ((lam @ X153))) | (X152 = X153)) | (laminj != $true)) & ((laminj = $true) | ? [X154 : term,X155 : term] : ((((lam @ X154)) = ((lam @ X155))) & (X154 != X155))) & (! [X156 : term] : ? [X157 : (subst > term > term)] : (((sub @ X156 @ (push @ one @ sh))) = ((X157 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X158 : term] : ! [X159 : (subst > term > term)] : (((X159 @ sh @ one)) != ((sub @ X158 @ (push @ one @ sh))))) & (hoasapnotvar = $true) & (! [X160 : (subst > term > subst > $o),X161 : term] : (? [X162 : term,X163 : term] : ((((X160 @ id @ X162 @ id)) = $true) & ($true = ((X160 @ id @ X163 @ id))) & ($true != ((X160 @ id @ (ap @ (sub @ X163 @ id) @ X162) @ id)))) | (((X160 @ id @ X161 @ id)) = $true) | ($true = ((sP29 @ X160)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X164 : (subst > term > subst > $o),X165 : term] : (! [X166 : term,X167 : term] : (($true != ((X164 @ id @ X166 @ id))) | ($true != ((X164 @ id @ X167 @ id))) | ($true = ((X164 @ id @ (ap @ (sub @ X167 @ id) @ X166) @ id)))) & ($true != ((X164 @ id @ X165 @ id))) & ($true != ((sP29 @ X164))))) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & ((axshiftcons = $true) | ? [X168 : term,X169 : subst] : (((comp @ sh @ (push @ X168 @ X169))) != X169)) & (! [X170 : term,X171 : subst] : (((comp @ sh @ (push @ X170 @ X171))) = X171) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP26)) & (! [X172 : term] : (((sub @ X172 @ id)) = X172) | ? [X173 : term] : (((sub @ X173 @ id)) != X173) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X174 : term] : (((sub @ X174 @ id)) != X174) & ! [X175 : term] : (((sub @ X175 @ id)) = X175))) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & (? [X176 : term,X177 : subst] : (((sub @ one @ (push @ X176 @ X177))) != X176) | ! [X178 : subst,X179 : term,X180 : (term > $o),X181 : (term > $o)] : (($true = ((X180 @ one))) | ($true != ((X181 @ X179))) | ? [X182 : term] : (((X181 @ (sub @ X182 @ (push @ X179 @ X178)))) != ((X180 @ X182)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X183 : term,X184 : subst] : (((sub @ one @ (push @ X183 @ X184))) = X183) & ? [X185 : subst,X186 : term,X187 : (term > $o),X188 : (term > $o)] : (($true != ((X187 @ one))) & ($true = ((X188 @ X186))) & ! [X189 : term] : (((X188 @ (sub @ X189 @ (push @ X186 @ X185)))) = ((X187 @ X189)))))) & (pushprop_lem2v2_lthm = $true) & (! [X190 : (subst > term > subst > $o)] : ? [X191 : (term > $o)] : ! [X192 : term] : (((X191 @ X192)) = ((X190 @ id @ X192 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X193 : (subst > term > subst > $o)] : ! [X194 : (term > $o)] : ? [X195 : term] : (((X193 @ id @ X195 @ id)) != ((X194 @ X195)))) & ((induction2lem_lthm = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar_lthm = $true) & (! [X196 : term] : ? [X197 : (subst > term > term)] : ! [X198 : term,X199 : subst] : (((sub @ X196 @ (push @ X198 @ X199))) = ((X197 @ X199 @ X198))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X200 : term] : ! [X201 : (subst > term > term)] : ? [X202 : term,X203 : subst] : (((X201 @ X203 @ X202)) != ((sub @ X200 @ (push @ X202 @ X203))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((sP20 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP20 != $true)) & (($true = sP19) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP19)) & (? [X204 : term,X205 : term,X206 : term,X207 : term] : ((X204 != X206) & (((ap @ X205 @ X204)) = ((ap @ X207 @ X206)))) | ! [X208 : term,X209 : term,X210 : term,X211 : term] : ((((ap @ (sub @ X209 @ id) @ X208)) != ((ap @ (sub @ X210 @ id) @ X211))) | (X208 = X211)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((X212 = X214) | (((ap @ X213 @ X212)) != ((ap @ X215 @ X214)))) & ? [X216 : term,X217 : term,X218 : term,X219 : term] : ((((ap @ (sub @ X218 @ id) @ X219)) = ((ap @ (sub @ X217 @ id) @ X216))) & (X216 != X219)))) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X220 : d_subst,X221 : d_subst] : ((((d2subst @ X221)) != ((d2subst @ X220))) | (X220 = X221)) & (($true = sP15) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP15)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X222 : d_subst] : (d_id = X222) & (((d2subst @ d_id)) = id) & ((induction2_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2_lthm != $true)) & ((apinj2 = $true) | ? [X223 : term,X224 : term,X225 : term,X226 : term] : ((((ap @ X224 @ X223)) = ((ap @ X225 @ X226))) & (X223 != X226))) & (! [X227 : term,X228 : term,X229 : term,X230 : term] : ((((ap @ X228 @ X227)) != ((ap @ X229 @ X230))) | (X227 = X230)) | (apinj2 != $true)) & (($true = sP3) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP3)) & (! [X231 : subst] : (((comp @ id @ X231)) = X231) | (axidl != $true)) & ((axidl = $true) | ? [X232 : subst] : (((comp @ id @ X232)) != X232)) & ((hoasinduction_lem3b_lthm = $true) | ? [X233 : term] : ! [X234 : (subst > term > term)] : (((X234 @ sh @ one)) != ((sub @ X233 @ (push @ one @ sh))))) & (! [X235 : term] : ? [X236 : (subst > term > term)] : (((X236 @ sh @ one)) = ((sub @ X235 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & ((apinj1 = $true) | ? [X237 : term,X238 : term,X239 : term,X240 : term] : ((X238 != X240) & (((ap @ X240 @ X239)) = ((ap @ X238 @ X237))))) & (! [X241 : term,X242 : term,X243 : term,X244 : term] : ((X242 = X244) | (((ap @ X244 @ X243)) != ((ap @ X242 @ X241)))) | (apinj1 != $true)) & (ulamvarsh = $true) & (($true = sP2) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP2)) & ((hoaslamnotap = $true) | ? [X245 : term,X246 : term,X247 : (subst > term > term)] : (! [X248 : term,X249 : subst,X250 : subst] : (((sub @ (X247 @ X250 @ X248) @ X249)) = ((X247 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249)))) & (((lam @ (X247 @ sh @ one))) = ((ap @ (sub @ X246 @ id) @ X245))))) & (! [X251 : term,X252 : term,X253 : (subst > term > term)] : (? [X254 : term,X255 : subst,X256 : subst] : (((X253 @ (comp @ X256 @ X255) @ (sub @ X254 @ X255))) != ((sub @ (X253 @ X256 @ X254) @ X255))) | (((lam @ (X253 @ sh @ one))) != ((ap @ (sub @ X252 @ id) @ X251)))) | (hoaslamnotap != $true)) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X257 : subst,X258 : (term > $o),X259 : term] : ? [X260 : (term > $o)] : ! [X261 : term] : (((X260 @ X261)) = ((X258 @ (sub @ X261 @ (push @ X259 @ X257))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X262 : subst,X263 : (term > $o),X264 : term] : ! [X265 : (term > $o)] : ? [X266 : term] : (((X265 @ X266)) != ((X263 @ (sub @ X266 @ (push @ X264 @ X262)))))) & ! [X267 : d_term] : (d_one = X267) & ((hoasinduction_lem2v2 = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem2v2 != $true)) & ((axidr = $true) | ? [X268 : subst] : (((comp @ X268 @ id)) != X268)) & (! [X269 : subst] : (((comp @ X269 @ id)) = X269) | (axidr != $true)) & ((shinj = $true) | ? [X270 : term,X271 : term] : ((X270 != X271) & (((sub @ X270 @ sh)) = ((sub @ X271 @ sh))))) & (! [X272 : term,X273 : term] : ((X272 = X273) | (((sub @ X272 @ sh)) != ((sub @ X273 @ sh)))) | (shinj != $true)) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 inference(rectify,[],[f261])).
% 5.11/1.35 thf(f263,plain,(
% 5.11/1.35 (axvarshift = $true) & ((substmonoid = $true) | (((comp @ id @ sK457)) != sK457) | (sK458 != ((comp @ sK458 @ id)))) & ((! [X2 : subst] : (((comp @ id @ X2)) = X2) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | (substmonoid != $true)) & (hoasinduction_lem3b_gthm = $true) & (induction2lem_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X4 : term,X5 : subst,X6 : (term > $o)] : ! [X8 : term] : (((X6 @ (sub @ X8 @ (push @ X4 @ X5)))) = ((sK459 @ X6 @ X5 @ X4 @ X8))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X12 : (term > $o)] : (((sK462 @ (sub @ (sK463 @ X12) @ (push @ sK460 @ sK461)))) != ((X12 @ (sK463 @ X12))))) & (! [X14 : (subst > term > term),X15 : term,X16 : subst,X17 : (subst > term > term)] : ((((X14 @ X16 @ X15)) = ((X17 @ X16 @ X15))) | (((X17 @ (comp @ (sK466 @ X17) @ (sK465 @ X17)) @ (sub @ (sK464 @ X17) @ (sK465 @ X17)))) != ((sub @ (X17 @ (sK466 @ X17) @ (sK464 @ X17)) @ (sK465 @ X17)))) | (((lam @ (X14 @ sh @ one))) != ((lam @ (X17 @ sh @ one)))) | (((X14 @ (comp @ (sK468 @ X14) @ (sK469 @ X14)) @ (sub @ (sK467 @ X14) @ (sK469 @ X14)))) != ((sub @ (X14 @ (sK468 @ X14) @ (sK467 @ X14)) @ (sK469 @ X14))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((sK470 @ sK472 @ sK471)) != ((sK473 @ sK472 @ sK471))) & ! [X28 : term,X29 : subst,X30 : subst] : (((sK473 @ (comp @ X30 @ X29) @ (sub @ X28 @ X29))) = ((sub @ (sK473 @ X30 @ X28) @ X29))) & (((lam @ (sK470 @ sh @ one))) = ((lam @ (sK473 @ sh @ one)))) & ! [X31 : term,X32 : subst,X33 : subst] : (((sub @ (sK470 @ X32 @ X31) @ X33)) = ((sK470 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33)))))) & (hoasinduction_lem2v2_gthm = $true) & (axapp = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X34 : term] : (((d2term @ (sK474 @ X34))) = X34) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (ulamvarind = $true) & (! [X36 : term] : (((sub @ X36 @ id)) = X36) | (axvarid != $true)) & ((axvarid = $true) | (sK475 != ((sub @ sK475 @ id)))) & ((hoasapinj1 = $true) | ((sK478 != sK476) & (((ap @ (sub @ sK478 @ id) @ sK477)) = ((ap @ (sub @ sK476 @ id) @ sK479))))) & (! [X42 : term,X43 : term,X44 : term,X45 : term] : ((X42 = X44) | (((ap @ (sub @ X42 @ id) @ X45)) != ((ap @ (sub @ X44 @ id) @ X43)))) | (hoasapinj1 != $true)) & (($true = sP58) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP58)) & (! [X46 : (term > $o),X47 : term,X48 : (term > $o),X49 : subst] : ((((X46 @ (sub @ (sK480 @ X49 @ X48 @ X47 @ X46) @ (push @ X47 @ X49)))) != ((X48 @ (sK480 @ X49 @ X48 @ X47 @ X46)))) | ($true != ((X46 @ X47))) | ($true = ((X48 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X55 : term] : (((sK481 @ (sub @ X55 @ (push @ sK482 @ sK484)))) = ((sK483 @ X55))) & ($true = ((sK481 @ sK482))) & ($true != ((sK483 @ one))))) & (hoasapinj2_gthm = $true) & (! [X56 : term,X57 : (term > $o),X58 : term,X59 : subst,X60 : (term > $o)] : (($true != ((X57 @ X58))) | ($true = ((X60 @ (sub @ X58 @ (push @ X56 @ X59)))))) | (((comp @ sh @ (push @ sK486 @ sK485))) != sK485) | (((sub @ one @ (push @ sK487 @ sK488))) != sK487) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | ((($true = ((sK490 @ sK491))) & ($true != ((sK493 @ (sub @ sK491 @ (push @ sK489 @ sK492)))))) & ! [X70 : subst,X71 : term] : (((comp @ sh @ (push @ X71 @ X70))) = X70) & ! [X72 : term,X73 : subst] : (((sub @ one @ (push @ X72 @ X73))) = X72))) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & (! [X74 : term,X75 : term,X76 : term,X77 : term] : ((X75 = X77) | (((ap @ (sub @ X76 @ id) @ X77)) != ((ap @ (sub @ X74 @ id) @ X75)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((sK497 != sK495) & (((ap @ (sub @ sK494 @ id) @ sK495)) = ((ap @ (sub @ sK496 @ id) @ sK497))))) & (! [X82 : (subst > term > subst > $o)] : ! [X84 : term] : (((sK498 @ X82 @ X84)) = ((X82 @ id @ X84 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X86 : (term > $o)] : (((X86 @ (sK500 @ X86))) != ((sK499 @ id @ (sK500 @ X86) @ id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1_gthm = $true) & (($true = sP49) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP49)) & ((termmset = $true) | (((sub @ sK501 @ id)) != sK501)) & (! [X89 : term] : (((sub @ X89 @ id)) = X89) | (termmset != $true)) & (pushprop_lem0_gthm = $true) & (($true = sP43) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP43)) & ((axscons = $true) | (((push @ (sub @ one @ sK502) @ (comp @ sh @ sK502))) != sK502)) & (! [X91 : subst] : (((push @ (sub @ one @ X91) @ (comp @ sh @ X91))) = X91) | (axscons != $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm_orig = $true) & (axabs = $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 = $true) & (one = ((d2term @ d_one))) & (($true = sP42) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP42)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X93 : (subst > term > term)] : (((X93 @ (sK505 @ X93) @ (sK504 @ X93))) != ((sub @ sK503 @ (push @ (sK504 @ X93) @ (sK505 @ X93)))))) & (! [X96 : term] : ! [X98 : term,X99 : subst] : (((sub @ X96 @ (push @ X98 @ X99))) = ((sK506 @ X96 @ X99 @ X98))) | (hoasinduction_lem3v2_f != $true)) & (($true = sP39) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP39)) & (! [X100 : term,X101 : subst,X102 : (term > $o),X103 : (term > $o),X104 : term] : (($true = ((X102 @ (sub @ X100 @ (push @ X104 @ X101))))) | (((X103 @ X100)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | (($true != ((sK509 @ (sub @ sK507 @ (push @ sK511 @ sK508))))) & ($true = ((sK510 @ sK507))))) & ((hoasinduction_lem3_lthm = $true) | ($true != sP37)) & (($true = sP37) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP34)) & (($true = sP34) | (hoasinduction_lem3a != $true)) & (axassoc = $true) & ! [X110 : d_term,X111 : d_term] : ((((d2term @ X110)) != ((d2term @ X111))) | (X110 = X111)) & (induction2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) | ($true != sP33)) & (($true = sP33) | (hoasinduction_lem3v2_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP31)) & (($true = sP31) | (hoaslaminj_lthm != $true)) & (! [X112 : (term > $o),X113 : term] : (($true = ((X112 @ X113))) | (($true != ((X112 @ (lam @ (sK512 @ X112))))) & (((X112 @ (sK512 @ X112))) = $true)) | ($true = ((sP30 @ X112))) | (($true = ((var @ (sK513 @ X112)))) & ($true != ((X112 @ (sK513 @ X112)))))) | (induction != $true)) & ((induction = $true) | (($true != ((sK514 @ sK515))) & ! [X118 : term] : (($true = ((sK514 @ (lam @ X118)))) | ($true != ((sK514 @ X118)))) & ($true != ((sP30 @ sK514))) & ! [X119 : term] : (($true != ((var @ X119))) | ($true = ((sK514 @ X119)))))) & ((hoasapinj1_lthm = $true) | (! [X120 : term] : (((sub @ X120 @ id)) = X120) & ((((ap @ (sub @ sK517 @ id) @ sK519)) = ((ap @ (sub @ sK516 @ id) @ sK518))) & (sK517 != sK516)) & ! [X125 : term,X126 : term,X127 : term,X128 : term] : ((((ap @ X126 @ X125)) != ((ap @ X127 @ X128))) | (X126 = X127)))) & ((sK520 != ((sub @ sK520 @ id))) | ! [X130 : term,X131 : term,X132 : term,X133 : term] : ((((ap @ (sub @ X131 @ id) @ X133)) != ((ap @ (sub @ X130 @ id) @ X132))) | (X130 = X131)) | ((((ap @ sK522 @ sK521)) = ((ap @ sK523 @ sK524))) & (sK522 != sK523)) | (hoasapinj1_lthm != $true)) & ((axvarcons = $true) | (((sub @ one @ (push @ sK525 @ sK526))) != sK525)) & (! [X140 : term,X141 : subst] : (((sub @ one @ (push @ X140 @ X141))) = X140) | (axvarcons != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((((comp @ sK527 @ id)) != sK527) | (! [X143 : subst] : (((comp @ id @ X143)) = X143) & ! [X144 : subst] : (((comp @ X144 @ id)) = X144)) | (((comp @ id @ sK528)) != sK528) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X146 : subst] : (((comp @ X146 @ id)) = X146) & ((sK529 != ((comp @ id @ sK529))) | (((comp @ sK530 @ id)) != sK530)) & ! [X149 : subst] : (((comp @ id @ X149)) = X149))) & ! [X150 : subst] : (((d2subst @ (sK531 @ X150))) = X150) & (! [X152 : term,X153 : term] : ((((lam @ X152)) != ((lam @ X153))) | (X152 = X153)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK532)) = ((lam @ sK533))) & (sK532 != sK533))) & (! [X156 : term] : (((sub @ X156 @ (push @ one @ sh))) = ((sK534 @ X156 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X159 : (subst > term > term)] : (((sub @ sK535 @ (push @ one @ sh))) != ((X159 @ sh @ one)))) & (hoasapnotvar = $true) & (! [X160 : (subst > term > subst > $o),X161 : term] : ((($true = ((X160 @ id @ (sK536 @ X160) @ id))) & ($true = ((X160 @ id @ (sK537 @ X160) @ id))) & ($true != ((X160 @ id @ (ap @ (sub @ (sK537 @ X160) @ id) @ (sK536 @ X160)) @ id)))) | (((X160 @ id @ X161 @ id)) = $true) | ($true = ((sP29 @ X160)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X166 : term,X167 : term] : (($true != ((sK538 @ id @ X166 @ id))) | (((sK538 @ id @ X167 @ id)) != $true) | ($true = ((sK538 @ id @ (ap @ (sub @ X167 @ id) @ X166) @ id)))) & ($true != ((sK538 @ id @ sK539 @ id))) & ($true != ((sP29 @ sK538))))) & (hoasapnotvar_gthm = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (ulamvar1 != $true) & ((axshiftcons = $true) | (sK541 != ((comp @ sh @ (push @ sK540 @ sK541))))) & (! [X170 : term,X171 : subst] : (((comp @ sh @ (push @ X170 @ X171))) = X171) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & (($true = sP26) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP26)) & (! [X172 : term] : (((sub @ X172 @ id)) = X172) | (sK542 != ((sub @ sK542 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK543 @ id)) != sK543) & ! [X175 : term] : (((sub @ X175 @ id)) = X175))) & (pushprop_gthm = $true) & (hoaslaminj_gthm = $true) & ((((sub @ one @ (push @ sK544 @ sK545))) != sK544) | ! [X178 : subst,X179 : term,X180 : (term > $o),X181 : (term > $o)] : (($true = ((X180 @ one))) | ($true != ((X181 @ X179))) | (((X181 @ (sub @ (sK546 @ X181 @ X180 @ X179 @ X178) @ (push @ X179 @ X178)))) != ((X180 @ (sK546 @ X181 @ X180 @ X179 @ X178))))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (! [X183 : term,X184 : subst] : (((sub @ one @ (push @ X183 @ X184))) = X183) & (($true != ((sK549 @ one))) & ($true = ((sK550 @ sK548))) & ! [X189 : term] : (((sK549 @ X189)) = ((sK550 @ (sub @ X189 @ (push @ sK548 @ sK547)))))))) & (pushprop_lem2v2_lthm = $true) & (! [X190 : (subst > term > subst > $o)] : ! [X192 : term] : (((X190 @ id @ X192 @ id)) = ((sK551 @ X190 @ X192))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X194 : (term > $o)] : (((sK552 @ id @ (sK553 @ X194) @ id)) != ((X194 @ (sK553 @ X194))))) & ((induction2lem_lthm = $true) | (sP24 != $true)) & ((sP24 = $true) | (induction2lem_lthm != $true)) & (hoaslamnotvar_lthm = $true) & (! [X196 : term] : ! [X198 : term,X199 : subst] : (((sub @ X196 @ (push @ X198 @ X199))) = ((sK554 @ X196 @ X199 @ X198))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X201 : (subst > term > term)] : (((sub @ sK555 @ (push @ (sK556 @ X201) @ (sK557 @ X201)))) != ((X201 @ (sK557 @ X201) @ (sK556 @ X201))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((sP20 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP20 != $true)) & (($true = sP19) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP19)) & (((sK558 != sK560) & (((ap @ sK559 @ sK558)) = ((ap @ sK561 @ sK560)))) | ! [X208 : term,X209 : term,X210 : term,X211 : term] : ((((ap @ (sub @ X209 @ id) @ X208)) != ((ap @ (sub @ X210 @ id) @ X211))) | (X208 = X211)) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (! [X212 : term,X213 : term,X214 : term,X215 : term] : ((X212 = X214) | (((ap @ X213 @ X212)) != ((ap @ X215 @ X214)))) & ((((ap @ (sub @ sK564 @ id) @ sK565)) = ((ap @ (sub @ sK563 @ id) @ sK562))) & (sK565 != sK562)))) & ((sP17 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP17 != $true)) & (lamnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = sh) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1v2_gthm = $true) & (pushprop = $true) & ! [X220 : d_subst,X221 : d_subst] : ((((d2subst @ X221)) != ((d2subst @ X220))) | (X220 = X221)) & (($true = sP15) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP15)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ! [X222 : d_subst] : (d_id = X222) & (((d2subst @ d_id)) = id) & ((induction2_lthm = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2_lthm != $true)) & ((apinj2 = $true) | ((((ap @ sK567 @ sK566)) = ((ap @ sK568 @ sK569))) & (sK566 != sK569))) & (! [X227 : term,X228 : term,X229 : term,X230 : term] : ((((ap @ X228 @ X227)) != ((ap @ X229 @ X230))) | (X227 = X230)) | (apinj2 != $true)) & (($true = sP3) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP3)) & (! [X231 : subst] : (((comp @ id @ X231)) = X231) | (axidl != $true)) & ((axidl = $true) | (sK570 != ((comp @ id @ sK570)))) & ((hoasinduction_lem3b_lthm = $true) | ! [X234 : (subst > term > term)] : (((X234 @ sh @ one)) != ((sub @ sK571 @ (push @ one @ sh))))) & (! [X235 : term] : (((sub @ X235 @ (push @ one @ sh))) = ((sK572 @ X235 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (lamnotap != $true) & (hoasinduction_gthm = $true) & (axmap = $true) & ((apinj1 = $true) | ((sK576 != sK574) & (((ap @ sK576 @ sK575)) = ((ap @ sK574 @ sK573))))) & (! [X241 : term,X242 : term,X243 : term,X244 : term] : ((X242 = X244) | (((ap @ X244 @ X243)) != ((ap @ X242 @ X241)))) | (apinj1 != $true)) & (ulamvarsh = $true) & (($true = sP2) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP2)) & ((hoaslamnotap = $true) | (! [X248 : term,X249 : subst,X250 : subst] : (((sK579 @ (comp @ X250 @ X249) @ (sub @ X248 @ X249))) = ((sub @ (sK579 @ X250 @ X248) @ X249))) & (((ap @ (sub @ sK578 @ id) @ sK577)) = ((lam @ (sK579 @ sh @ one)))))) & (! [X251 : term,X252 : term,X253 : (subst > term > term)] : ((((X253 @ (comp @ (sK582 @ X253) @ (sK581 @ X253)) @ (sub @ (sK580 @ X253) @ (sK581 @ X253)))) != ((sub @ (X253 @ (sK582 @ X253) @ (sK580 @ X253)) @ (sK581 @ X253)))) | (((lam @ (X253 @ sh @ one))) != ((ap @ (sub @ X252 @ id) @ X251)))) | (hoaslamnotap != $true)) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X257 : subst,X258 : (term > $o),X259 : term] : ! [X261 : term] : (((X258 @ (sub @ X261 @ (push @ X259 @ X257)))) = ((sK583 @ X259 @ X258 @ X257 @ X261))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X265 : (term > $o)] : (((sK585 @ (sub @ (sK587 @ X265) @ (push @ sK586 @ sK584)))) != ((X265 @ (sK587 @ X265))))) & ! [X267 : d_term] : (d_one = X267) & ((hoasinduction_lem2v2 = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem2v2 != $true)) & ((axidr = $true) | (sK588 != ((comp @ sK588 @ id)))) & (! [X269 : subst] : (((comp @ X269 @ id)) = X269) | (axidr != $true)) & ((shinj = $true) | ((sK589 != sK590) & (((sub @ sK590 @ sh)) = ((sub @ sK589 @ sh))))) & (! [X272 : term,X273 : term] : ((X272 = X273) | (((sub @ X272 @ sh)) != ((sub @ X273 @ sh)))) | (shinj != $true)) & (pushprop_lthm = $true) & (termmset_gthm = $true)),
% 5.11/1.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,vAPP,sK460,sK461,sK462,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK470,sK471,sK472,sK473,vAPP,sK475,sK476,sK477,sK478,sK479,vAPP,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,sK499,vAPP,sK501,sK502,sK503,vAPP,vAPP,vAPP,sK507,sK508,sK509,sK510,sK511,vAPP,vAPP,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,vAPP,sK532,sK533,vAPP,sK535,vAPP,vAPP,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,vAPP,sK547,sK548,sK549,sK550,vAPP,sK552,vAPP,vAPP,sK555,vAPP,vAPP,sK558,sK559,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,sK571,vAPP,sK573,sK574,sK575,sK576,sK577,sK578,sK579,vAPP,vAPP,vAPP,vAPP,sK584,sK585,sK586,vAPP,sK588,sK589,sK590]),skolemize(X0,sK457),skolemize(X1,sK458),skolemize(X8,sK63 @ X7),skolemize(X9,sK460),skolemize(X10,sK461),skolemize(X11,sK462),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X24,sK470),skolemize(X25,sK471),skolemize(X26,sK472),skolemize(X27,sK473),skolemize(X8,sK63 @ X7),skolemize(X37,sK475),skolemize(X38,sK476),skolemize(X39,sK477),skolemize(X40,sK478),skolemize(X41,sK479),skolemize(X8,sK63 @ X7),skolemize(X51,sK481),skolemize(X52,sK482),skolemize(X53,sK483),skolemize(X54,sK484),skolemize(X61,sK485),skolemize(X62,sK486),skolemize(X63,sK487),skolemize(X64,sK488),skolemize(X65,sK489),skolemize(X66,sK490),skolemize(X67,sK491),skolemize(X68,sK492),skolemize(X69,sK493),skolemize(X78,sK494),skolemize(X79,sK495),skolemize(X80,sK496),skolemize(X81,sK497),skolemize(X8,sK63 @ X7),skolemize(X85,sK499),skolemize(X8,sK63 @ X7),skolemize(X88,sK501),skolemize(X90,sK502),skolemize(X92,sK503),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X105,sK507),skolemize(X106,sK508),skolemize(X107,sK509),skolemize(X108,sK510),skolemize(X109,sK511),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X116,sK514),skolemize(X117,sK515),skolemize(X121,sK516),skolemize(X122,sK517),skolemize(X123,sK518),skolemize(X124,sK519),skolemize(X129,sK520),skolemize(X134,sK521),skolemize(X135,sK522),skolemize(X136,sK523),skolemize(X137,sK524),skolemize(X138,sK525),skolemize(X139,sK526),skolemize(X142,sK527),skolemize(X145,sK528),skolemize(X147,sK529),skolemize(X148,sK530),skolemize(X8,sK63 @ X7),skolemize(X154,sK532),skolemize(X155,sK533),skolemize(X8,sK63 @ X7),skolemize(X158,sK535),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X164,sK538),skolemize(X165,sK539),skolemize(X168,sK540),skolemize(X169,sK541),skolemize(X173,sK542),skolemize(X174,sK543),skolemize(X176,sK544),skolemize(X177,sK545),skolemize(X8,sK63 @ X7),skolemize(X185,sK547),skolemize(X186,sK548),skolemize(X187,sK549),skolemize(X188,sK550),skolemize(X8,sK63 @ X7),skolemize(X193,sK552),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X200,sK555),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X204,sK558),skolemize(X205,sK559),skolemize(X206,sK560),skolemize(X207,sK561),skolemize(X216,sK562),skolemize(X217,sK563),skolemize(X218,sK564),skolemize(X219,sK565),skolemize(X223,sK566),skolemize(X224,sK567),skolemize(X225,sK568),skolemize(X226,sK569),skolemize(X232,sK570),skolemize(X233,sK571),skolemize(X8,sK63 @ X7),skolemize(X237,sK573),skolemize(X238,sK574),skolemize(X239,sK575),skolemize(X240,sK576),skolemize(X245,sK577),skolemize(X246,sK578),skolemize(X247,sK579),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X8,sK63 @ X7),skolemize(X262,sK584),skolemize(X263,sK585),skolemize(X264,sK586),skolemize(X8,sK63 @ X7),skolemize(X268,sK588),skolemize(X270,sK589),skolemize(X271,sK590)],[f262])).
% 5.11/1.35 thf(f762,plain,(
% 5.11/1.35 ( ! [X267 : d_term] : ((d_one = X267)) )),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f821,plain,(
% 5.11/1.35 (((var @ (d2term @ d_one))) != $true)),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f913,plain,(
% 5.11/1.35 (one = ((d2term @ d_one)))),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f915,plain,(
% 5.11/1.35 (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))))))))))))))),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f945,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $true) | ($true != ((sK483 @ one)))),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f946,plain,(
% 5.11/1.35 ($true = ((sK481 @ sK482))) | (pushprop_lem1v2 = $true)),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f947,plain,(
% 5.11/1.35 ( ! [X55 : term] : ((pushprop_lem1v2 = $true) | (((sK481 @ (sub @ X55 @ (push @ sK482 @ sK484)))) = ((sK483 @ X55)))) )),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f951,plain,(
% 5.11/1.35 ( ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X45)) != ((ap @ (sub @ X44 @ id) @ X43))) | (hoasapinj1 != $true) | (X42 = X44)) )),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f953,plain,(
% 5.11/1.35 (sK478 != sK476) | (hoasapinj1 = $true)),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f958,plain,(
% 5.11/1.35 ( ! [X34 : term] : ((((d2term @ (sK474 @ X34))) = X34)) )),
% 5.11/1.35 inference(cnf_transformation,[],[f263])).
% 5.11/1.35 thf(f978,plain,(
% 5.11/1.35 (pushprop_lem1v2 != ((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => ((pushprop_p_and_p_prime @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))))))),
% 5.11/1.35 inference(cnf_transformation,[],[f8])).
% 5.11/1.35 thf(f981,plain,(
% 5.11/1.35 (pushprop_lem1v2 != ((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))))))),
% 5.11/1.35 inference(definition_unfolding,[],[f978,f915])).
% 5.11/1.35 thf(f1067,plain,(
% 5.11/1.35 ( ! [X55 : term] : ((pushprop_lem1v2 = $true) | ($true = ((sK483 @ X55))) | ($false = ((sK481 @ (sub @ X55 @ (push @ sK482 @ sK484)))))) )),
% 5.11/1.35 inference(iff_proxy_clausification,[],[f947])).
% 5.11/1.35 thf(f1122,plain,(
% 5.11/1.35 ($true = ((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one))))))))))))) | (pushprop_lem1v2 = $true)),
% 5.11/1.35 inference(xor_proxy_clausification,[],[f981])).
% 5.11/1.35 thf(f1123,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))))) = $false)),
% 5.11/1.35 inference(xor_proxy_clausification,[],[f981])).
% 5.11/1.35 thf(f1124,plain,(
% 5.11/1.35 ((((^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))) @ sK591)) = $false) | (pushprop_lem1v2 = $false)),
% 5.11/1.35 inference(sigma_proxy_clausification,[],[f1123])).
% 5.11/1.35 thf(f1125,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | (((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) = (Y0 @ (sub @ Y3 @ (push @ Y2 @ sK591)))))) => (Y1 @ one)))))))))) = $false)),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1124])).
% 5.11/1.35 thf(f1126,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ($false = (((^[Y0 : term > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) = (Y0 @ (sub @ Y3 @ (push @ Y2 @ sK591)))))) => (Y1 @ one)))))))) @ sK592)))),
% 5.11/1.35 inference(sigma_proxy_clausification,[],[f1125])).
% 5.11/1.35 thf(f1127,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (sK592 @ (sub @ Y2 @ (push @ Y1 @ sK591)))))) => (Y0 @ one)))))))))),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1126])).
% 5.11/1.35 thf(f1128,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ((((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK592 @ Y1) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (sK592 @ (sub @ Y2 @ (push @ Y1 @ sK591)))))) => (Y0 @ one)))))) @ sK593)) = $false)),
% 5.11/1.35 inference(sigma_proxy_clausification,[],[f1127])).
% 5.11/1.35 thf(f1129,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | (((!! @ term @ (^[Y0 : term]: ((sK592 @ Y0) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) = (sK592 @ (sub @ Y1 @ (push @ Y0 @ sK591)))))) => (sK593 @ one)))))) = $false)),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1128])).
% 5.11/1.35 thf(f1130,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ((((^[Y0 : term]: ((sK592 @ Y0) => ((!! @ term @ (^[Y1 : term]: ((sK593 @ Y1) = (sK592 @ (sub @ Y1 @ (push @ Y0 @ sK591)))))) => (sK593 @ one)))) @ sK594)) = $false)),
% 5.11/1.35 inference(sigma_proxy_clausification,[],[f1129])).
% 5.11/1.35 thf(f1131,plain,(
% 5.11/1.35 ((((sK592 @ sK594) => ((!! @ term @ (^[Y0 : term]: ((sK593 @ Y0) = (sK592 @ (sub @ Y0 @ (push @ sK594 @ sK591)))))) => (sK593 @ one)))) = $false) | (pushprop_lem1v2 = $false)),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1130])).
% 5.11/1.35 thf(f1132,plain,(
% 5.11/1.35 ((((!! @ term @ (^[Y0 : term]: ((sK593 @ Y0) = (sK592 @ (sub @ Y0 @ (push @ sK594 @ sK591)))))) => (sK593 @ one))) = $false) | (pushprop_lem1v2 = $false)),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1131])).
% 5.11/1.35 thf(f1133,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | (((sK592 @ sK594)) = $true)),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1131])).
% 5.11/1.35 thf(f1134,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ($false = ((sK593 @ one)))),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1132])).
% 5.11/1.35 thf(f1135,plain,(
% 5.11/1.35 ($true = ((!! @ term @ (^[Y0 : term]: ((sK593 @ Y0) = (sK592 @ (sub @ Y0 @ (push @ sK594 @ sK591)))))))) | (pushprop_lem1v2 = $false)),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1132])).
% 5.11/1.35 thf(f1136,plain,(
% 5.11/1.35 ( ! [X1 : term] : (($true = (((^[Y0 : term]: ((sK593 @ Y0) = (sK592 @ (sub @ Y0 @ (push @ sK594 @ sK591))))) @ X1))) | (pushprop_lem1v2 = $false)) )),
% 5.11/1.35 inference(pi_proxy_clausification,[],[f1135])).
% 5.11/1.35 thf(f1137,plain,(
% 5.11/1.35 ( ! [X1 : term] : ((pushprop_lem1v2 = $false) | ($true = (((sK593 @ X1) = (sK592 @ (sub @ X1 @ (push @ sK594 @ sK591))))))) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1136])).
% 5.11/1.35 thf(f1138,plain,(
% 5.11/1.35 ( ! [X1 : term] : ((((sK592 @ (sub @ X1 @ (push @ sK594 @ sK591)))) = ((sK593 @ X1))) | (pushprop_lem1v2 = $false)) )),
% 5.11/1.35 inference(equality_proxy_clausification,[],[f1137])).
% 5.11/1.35 thf(f1140,plain,(
% 5.11/1.35 ( ! [X1 : term] : ((pushprop_lem1v2 = $false) | (((sK592 @ (sub @ X1 @ (push @ sK594 @ sK591)))) = $false) | ($true = ((sK593 @ X1)))) )),
% 5.11/1.35 inference(iff_proxy_clausification,[],[f1138])).
% 5.11/1.35 thf(f1141,plain,(
% 5.11/1.35 ( ! [X1 : subst] : (($true = (((^[Y0 : subst]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ (term > $o) @ (^[Y2 : term > $o]: (!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) => (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y7 @ Y8) = (Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))))))))))))) @ Y3 @ Y0 @ Y1 @ Y2) => (Y2 @ one)))))))))) @ X1))) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(pi_proxy_clausification,[],[f1122])).
% 5.11/1.35 thf(f1142,plain,(
% 5.11/1.35 ( ! [X1 : subst] : (($true = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) = (Y0 @ (sub @ Y3 @ (push @ Y2 @ X1)))))) => (Y1 @ one))))))))))) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1141])).
% 5.11/1.35 thf(f1143,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X1 : subst] : ((pushprop_lem1v2 = $true) | ($true = (((^[Y0 : term > $o]: (!! @ (term > $o) @ (^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) => ((!! @ term @ (^[Y3 : term]: ((Y1 @ Y3) = (Y0 @ (sub @ Y3 @ (push @ Y2 @ X1)))))) => (Y1 @ one)))))))) @ X2)))) )),
% 5.11/1.35 inference(pi_proxy_clausification,[],[f1142])).
% 5.11/1.35 thf(f1144,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X1 : subst] : ((pushprop_lem1v2 = $true) | (((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (X2 @ (sub @ Y2 @ (push @ Y1 @ X1)))))) => (Y0 @ one)))))))) = $true)) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1143])).
% 5.11/1.35 thf(f1145,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst] : ((pushprop_lem1v2 = $true) | ($true = (((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((X2 @ Y1) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ Y2) = (X2 @ (sub @ Y2 @ (push @ Y1 @ X1)))))) => (Y0 @ one)))))) @ X3)))) )),
% 5.11/1.35 inference(pi_proxy_clausification,[],[f1144])).
% 5.11/1.35 thf(f1146,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst] : (($true = ((!! @ term @ (^[Y0 : term]: ((X2 @ Y0) => ((!! @ term @ (^[Y1 : term]: ((X3 @ Y1) = (X2 @ (sub @ Y1 @ (push @ Y0 @ X1)))))) => (X3 @ one))))))) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1145])).
% 5.11/1.35 thf(f1147,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : ((pushprop_lem1v2 = $true) | ($true = (((^[Y0 : term]: ((X2 @ Y0) => ((!! @ term @ (^[Y1 : term]: ((X3 @ Y1) = (X2 @ (sub @ Y1 @ (push @ Y0 @ X1)))))) => (X3 @ one)))) @ X4)))) )),
% 5.11/1.35 inference(pi_proxy_clausification,[],[f1146])).
% 5.11/1.35 thf(f1148,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($true = (((X2 @ X4) => ((!! @ term @ (^[Y0 : term]: ((X3 @ Y0) = (X2 @ (sub @ Y0 @ (push @ X4 @ X1)))))) => (X3 @ one))))) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1147])).
% 5.11/1.35 thf(f1149,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : ((pushprop_lem1v2 = $true) | ($true = (((!! @ term @ (^[Y0 : term]: ((X3 @ Y0) = (X2 @ (sub @ Y0 @ (push @ X4 @ X1)))))) => (X3 @ one)))) | ($false = ((X2 @ X4)))) )),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1148])).
% 5.11/1.35 thf(f1150,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($true = ((X3 @ one))) | ($false = ((X2 @ X4))) | (pushprop_lem1v2 = $true) | (((!! @ term @ (^[Y0 : term]: ((X3 @ Y0) = (X2 @ (sub @ Y0 @ (push @ X4 @ X1))))))) = $false)) )),
% 5.11/1.35 inference(imp_proxy_clausification,[],[f1149])).
% 5.11/1.35 thf(f1151,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($true = ((X3 @ one))) | ($false = ((X2 @ X4))) | ((((^[Y0 : term]: ((X3 @ Y0) = (X2 @ (sub @ Y0 @ (push @ X4 @ X1))))) @ (sK595 @ X3 @ X1 @ X4 @ X2))) = $false) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(sigma_proxy_clausification,[],[f1150])).
% 5.11/1.35 thf(f1152,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($false = (((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)) = (X2 @ (sub @ (sK595 @ X3 @ X1 @ X4 @ X2) @ (push @ X4 @ X1)))))) | ($false = ((X2 @ X4))) | ($true = ((X3 @ one))) | (pushprop_lem1v2 = $true)) )),
% 5.11/1.35 inference(beta-eta_normalization,[],[f1151])).
% 5.11/1.35 thf(f1153,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($false = ((X2 @ X4))) | (pushprop_lem1v2 = $true) | (((X2 @ (sub @ (sK595 @ X3 @ X1 @ X4 @ X2) @ (push @ X4 @ X1)))) != ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((X3 @ one)))) )),
% 5.11/1.35 inference(equality_proxy_clausification,[],[f1152])).
% 5.11/1.35 thf(f1154,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($false = ((X2 @ X4))) | (pushprop_lem1v2 = $true) | (((X2 @ (sub @ (sK595 @ X3 @ X1 @ X4 @ X2) @ (push @ X4 @ X1)))) = $true) | ($true = ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((X3 @ one)))) )),
% 5.11/1.35 inference(xor_proxy_clausification,[],[f1153])).
% 5.11/1.35 thf(f1426,definition,(
% 5.11/1.35 spl596_64 <=> (hoasapinj1 = $true)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_64])],[avatar_definition])).
% 5.11/1.35 thf(f1586,definition,(
% 5.11/1.35 spl596_101 <=> (pushprop_lem1v2 = $true)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_101])],[avatar_definition])).
% 5.11/1.35 thf(f1587,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $true) | ~spl596_101),
% 5.11/1.35 inference(avatar_component_clause,[],[f1586])).
% 5.11/1.35 thf(f2233,definition,(
% 5.11/1.35 spl596_253 <=> ! [X44 : term,X43 : term,X42 : term,X45 : term] : ((((ap @ (sub @ X42 @ id) @ X45)) != ((ap @ (sub @ X44 @ id) @ X43))) | (X42 = X44))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_253])],[avatar_definition])).
% 5.11/1.35 thf(f2234,plain,(
% 5.11/1.35 ( ! [X44 : term,X45 : term,X42 : term,X43 : term] : ((((ap @ (sub @ X42 @ id) @ X45)) != ((ap @ (sub @ X44 @ id) @ X43))) | (X42 = X44)) ) | ~spl596_253),
% 5.11/1.35 inference(avatar_component_clause,[],[f2233])).
% 5.11/1.35 thf(f2235,plain,(
% 5.11/1.35 spl596_253 | ~spl596_64),
% 5.11/1.35 inference(avatar_split_clause,[],[f951,f1426,f2233])).
% 5.11/1.35 thf(f3016,definition,(
% 5.11/1.35 spl596_433 <=> ! [X55 : term] : (($true = ((sK483 @ X55))) | ($false = ((sK481 @ (sub @ X55 @ (push @ sK482 @ sK484))))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_433])],[avatar_definition])).
% 5.11/1.35 thf(f3017,plain,(
% 5.11/1.35 ( ! [X55 : term] : (($true = ((sK483 @ X55))) | ($false = ((sK481 @ (sub @ X55 @ (push @ sK482 @ sK484)))))) ) | ~spl596_433),
% 5.11/1.35 inference(avatar_component_clause,[],[f3016])).
% 5.11/1.35 thf(f3018,plain,(
% 5.11/1.35 spl596_101 | spl596_433),
% 5.11/1.35 inference(avatar_split_clause,[],[f1067,f3016,f1586])).
% 5.11/1.35 thf(f3112,definition,(
% 5.11/1.35 spl596_455 <=> ($true = ((sK483 @ one)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_455])],[avatar_definition])).
% 5.11/1.35 thf(f3114,plain,(
% 5.11/1.35 ($true != ((sK483 @ one))) | spl596_455),
% 5.11/1.35 inference(avatar_component_clause,[],[f3112])).
% 5.11/1.35 thf(f3115,plain,(
% 5.11/1.35 ~spl596_455 | spl596_101),
% 5.11/1.35 inference(avatar_split_clause,[],[f945,f1586,f3112])).
% 5.11/1.35 thf(f3467,definition,(
% 5.11/1.35 spl596_536 <=> (sK478 = sK476)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_536])],[avatar_definition])).
% 5.11/1.35 thf(f3469,plain,(
% 5.11/1.35 (sK478 != sK476) | spl596_536),
% 5.11/1.35 inference(avatar_component_clause,[],[f3467])).
% 5.11/1.35 thf(f3470,plain,(
% 5.11/1.35 spl596_64 | ~spl596_536),
% 5.11/1.35 inference(avatar_split_clause,[],[f953,f3467,f1426])).
% 5.11/1.35 thf(f3632,definition,(
% 5.11/1.35 spl596_573 <=> ($true = ((sK481 @ sK482)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_573])],[avatar_definition])).
% 5.11/1.35 thf(f3634,plain,(
% 5.11/1.35 ($true = ((sK481 @ sK482))) | ~spl596_573),
% 5.11/1.35 inference(avatar_component_clause,[],[f3632])).
% 5.11/1.35 thf(f3635,plain,(
% 5.11/1.35 spl596_101 | spl596_573),
% 5.11/1.35 inference(avatar_split_clause,[],[f946,f3632,f1586])).
% 5.11/1.35 thf(f3723,definition,(
% 5.11/1.35 spl596_594 <=> (pushprop_lem1v2 = $false)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_594])],[avatar_definition])).
% 5.11/1.35 thf(f3725,plain,(
% 5.11/1.35 (pushprop_lem1v2 = $false) | ~spl596_594),
% 5.11/1.35 inference(avatar_component_clause,[],[f3723])).
% 5.11/1.35 thf(f3727,definition,(
% 5.11/1.35 spl596_595 <=> (((sK592 @ sK594)) = $true)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_595])],[avatar_definition])).
% 5.11/1.35 thf(f3729,plain,(
% 5.11/1.35 (((sK592 @ sK594)) = $true) | ~spl596_595),
% 5.11/1.35 inference(avatar_component_clause,[],[f3727])).
% 5.11/1.35 thf(f3730,plain,(
% 5.11/1.35 spl596_594 | spl596_595),
% 5.11/1.35 inference(avatar_split_clause,[],[f1133,f3727,f3723])).
% 5.11/1.35 thf(f3732,definition,(
% 5.11/1.35 spl596_596 <=> ! [X1 : term] : ((((sK592 @ (sub @ X1 @ (push @ sK594 @ sK591)))) = $false) | ($true = ((sK593 @ X1))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_596])],[avatar_definition])).
% 5.11/1.35 thf(f3733,plain,(
% 5.11/1.35 ( ! [X1 : term] : ((((sK592 @ (sub @ X1 @ (push @ sK594 @ sK591)))) = $false) | ($true = ((sK593 @ X1)))) ) | ~spl596_596),
% 5.11/1.35 inference(avatar_component_clause,[],[f3732])).
% 5.11/1.35 thf(f3734,plain,(
% 5.11/1.35 spl596_594 | spl596_596),
% 5.11/1.35 inference(avatar_split_clause,[],[f1140,f3732,f3723])).
% 5.11/1.35 thf(f3740,definition,(
% 5.11/1.35 spl596_598 <=> ($false = ((sK593 @ one)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_598])],[avatar_definition])).
% 5.11/1.35 thf(f3742,plain,(
% 5.11/1.35 ($false = ((sK593 @ one))) | ~spl596_598),
% 5.11/1.35 inference(avatar_component_clause,[],[f3740])).
% 5.11/1.35 thf(f3743,plain,(
% 5.11/1.35 spl596_594 | spl596_598),
% 5.11/1.35 inference(avatar_split_clause,[],[f1134,f3740,f3723])).
% 5.11/1.35 thf(f3749,definition,(
% 5.11/1.35 spl596_600 <=> ! [X4 : term,X3 : (term > $o),X2 : (term > $o),X1 : subst] : (($false = ((X2 @ X4))) | ($true = ((X3 @ one))) | ($true = ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)))) | (((X2 @ (sub @ (sK595 @ X3 @ X1 @ X4 @ X2) @ (push @ X4 @ X1)))) = $true))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_600])],[avatar_definition])).
% 5.11/1.35 thf(f3750,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($false = ((X2 @ X4))) | (((X2 @ (sub @ (sK595 @ X3 @ X1 @ X4 @ X2) @ (push @ X4 @ X1)))) = $true) | ($true = ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((X3 @ one)))) ) | ~spl596_600),
% 5.11/1.35 inference(avatar_component_clause,[],[f3749])).
% 5.11/1.35 thf(f3751,plain,(
% 5.11/1.35 spl596_101 | spl596_600),
% 5.11/1.35 inference(avatar_split_clause,[],[f1154,f3749,f1586])).
% 5.11/1.35 thf(f3975,plain,(
% 5.11/1.35 ($true = $false) | (~spl596_101 | ~spl596_594)),
% 5.11/1.35 inference(forward_demodulation,[],[f1587,f3725])).
% 5.11/1.35 thf(f3976,plain,(
% 5.11/1.35 $false | (~spl596_101 | ~spl596_594)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f3975])).
% 5.11/1.35 thf(f3977,plain,(
% 5.11/1.35 ~spl596_101 | ~spl596_594),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f3976])).
% 5.11/1.35 thf(f4006,plain,(
% 5.11/1.35 ($true != ((var @ one)))),
% 5.11/1.35 inference(forward_demodulation,[],[f821,f913])).
% 5.11/1.35 thf(f4032,plain,(
% 5.11/1.35 ( ! [X34 : term] : ((((d2term @ d_one)) = X34)) )),
% 5.11/1.35 inference(forward_demodulation,[],[f958,f762])).
% 5.11/1.35 thf(f4040,plain,(
% 5.11/1.35 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 5.11/1.35 inference(superposition,[],[f4032,f4032])).
% 5.11/1.35 thf(f4052,definition,(
% 5.11/1.35 spl596_633 <=> (((sK592 @ one)) = $false)),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_633])],[avatar_definition])).
% 5.11/1.35 thf(f4054,plain,(
% 5.11/1.35 (((sK592 @ one)) = $false) | ~spl596_633),
% 5.11/1.35 inference(avatar_component_clause,[],[f4052])).
% 5.11/1.35 thf(f4056,definition,(
% 5.11/1.35 spl596_634 <=> ! [X0 : term] : ($true = ((sK593 @ X0)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_634])],[avatar_definition])).
% 5.11/1.35 thf(f4057,plain,(
% 5.11/1.35 ( ! [X0 : term] : (($true = ((sK593 @ X0)))) ) | ~spl596_634),
% 5.11/1.35 inference(avatar_component_clause,[],[f4056])).
% 5.11/1.35 thf(f4060,definition,(
% 5.11/1.35 spl596_635 <=> ! [X0 : term] : ($false = ((sK593 @ X0)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_635])],[avatar_definition])).
% 5.11/1.35 thf(f4061,plain,(
% 5.11/1.35 ( ! [X0 : term] : (($false = ((sK593 @ X0)))) ) | ~spl596_635),
% 5.11/1.35 inference(avatar_component_clause,[],[f4060])).
% 5.11/1.35 thf(f4078,definition,(
% 5.11/1.35 spl596_637 <=> ! [X55 : term] : ($true = ((sK483 @ X55)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_637])],[avatar_definition])).
% 5.11/1.35 thf(f4079,plain,(
% 5.11/1.35 ( ! [X55 : term] : (($true = ((sK483 @ X55)))) ) | ~spl596_637),
% 5.11/1.35 inference(avatar_component_clause,[],[f4078])).
% 5.11/1.35 thf(f4081,definition,(
% 5.11/1.35 spl596_638 <=> ($false = ((sK481 @ one)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_638])],[avatar_definition])).
% 5.11/1.35 thf(f4083,plain,(
% 5.11/1.35 ($false = ((sK481 @ one))) | ~spl596_638),
% 5.11/1.35 inference(avatar_component_clause,[],[f4081])).
% 5.11/1.35 thf(f4099,definition,(
% 5.11/1.35 spl596_641 <=> ! [X3 : (term > $o)] : ($true = ((X3 @ one)))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_641])],[avatar_definition])).
% 5.11/1.35 thf(f4100,plain,(
% 5.11/1.35 ( ! [X3 : (term > $o)] : (($true = ((X3 @ one)))) ) | ~spl596_641),
% 5.11/1.35 inference(avatar_component_clause,[],[f4099])).
% 5.11/1.35 thf(f4102,definition,(
% 5.11/1.35 spl596_642 <=> ! [X2 : (term > $o),X4 : term] : (($true = ((X2 @ one))) | ($false = ((X2 @ X4))))),
% 5.11/1.35 introduced(definition,[new_symbols(definition,[spl596_642])],[avatar_definition])).
% 5.11/1.35 thf(f4103,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X4 : term] : (($true = ((X2 @ one))) | ($false = ((X2 @ X4)))) ) | ~spl596_642),
% 5.11/1.35 inference(avatar_component_clause,[],[f4102])).
% 5.11/1.35 thf(f4116,plain,(
% 5.11/1.35 ( ! [X1 : term] : (($false = ((sK592 @ (d2term @ d_one)))) | ($true = ((sK593 @ X1)))) ) | ~spl596_596),
% 5.11/1.35 inference(forward_demodulation,[],[f3733,f4032])).
% 5.11/1.35 thf(f4122,plain,(
% 5.11/1.35 ( ! [X1 : term] : (($true = ((sK593 @ X1))) | (((sK592 @ one)) = $false)) ) | ~spl596_596),
% 5.11/1.35 inference(forward_demodulation,[],[f4116,f913])).
% 5.11/1.35 thf(f4127,plain,(
% 5.11/1.35 spl596_634 | spl596_633 | ~spl596_596),
% 5.11/1.35 inference(avatar_split_clause,[],[f4122,f3732,f4052,f4056])).
% 5.11/1.35 thf(f4400,plain,(
% 5.11/1.35 ( ! [X44 : term,X45 : term,X42 : term] : ((((d2term @ d_one)) != ((ap @ (sub @ X42 @ id) @ X45))) | (X42 = X44)) ) | ~spl596_253),
% 5.11/1.35 inference(forward_demodulation,[],[f2234,f4032])).
% 5.11/1.35 thf(f4401,plain,(
% 5.11/1.35 ( ! [X44 : term,X42 : term] : ((X42 = X44)) ) | ~spl596_253),
% 5.11/1.35 inference(forward_subsumption_resolution,[],[f4400,f4032])).
% 5.11/1.35 thf(f4415,plain,(
% 5.11/1.35 ( ! [X0 : term] : (($true = ((sK592 @ X0)))) ) | (~spl596_253 | ~spl596_595)),
% 5.11/1.35 inference(superposition,[],[f3729,f4401])).
% 5.11/1.35 thf(f4660,plain,(
% 5.11/1.35 ( ! [X0 : term] : ((sK478 != X0)) ) | spl596_536),
% 5.11/1.35 inference(superposition,[],[f3469,f4040])).
% 5.11/1.35 thf(f4670,plain,(
% 5.11/1.35 ( ! [X0 : term] : (($false = ((sK593 @ X0)))) ) | ~spl596_598),
% 5.11/1.35 inference(superposition,[],[f3742,f4040])).
% 5.11/1.35 thf(f4707,plain,(
% 5.11/1.35 $false | spl596_536),
% 5.11/1.35 inference(forward_subsumption_resolution,[],[f4660,f4040])).
% 5.11/1.35 thf(f4708,plain,(
% 5.11/1.35 spl596_536),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f4707])).
% 5.11/1.35 thf(f4717,plain,(
% 5.11/1.35 ($true = $false) | (~spl596_253 | ~spl596_595 | ~spl596_633)),
% 5.11/1.35 inference(superposition,[],[f4415,f4054])).
% 5.11/1.35 thf(f4721,plain,(
% 5.11/1.35 $false | (~spl596_253 | ~spl596_595 | ~spl596_633)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f4717])).
% 5.11/1.35 thf(f4722,plain,(
% 5.11/1.35 ~spl596_253 | ~spl596_595 | ~spl596_633),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f4721])).
% 5.11/1.35 thf(f4724,plain,(
% 5.11/1.35 ($true = $false) | (~spl596_634 | ~spl596_635)),
% 5.11/1.35 inference(forward_demodulation,[],[f4057,f4061])).
% 5.11/1.35 thf(f4725,plain,(
% 5.11/1.35 $false | (~spl596_634 | ~spl596_635)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f4724])).
% 5.11/1.35 thf(f4726,plain,(
% 5.11/1.35 ~spl596_634 | ~spl596_635),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f4725])).
% 5.11/1.35 thf(f4729,plain,(
% 5.11/1.35 spl596_635 | ~spl596_598),
% 5.11/1.35 inference(avatar_split_clause,[],[f4670,f3740,f4060])).
% 5.11/1.35 thf(f4736,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($true = ((X2 @ (d2term @ d_one)))) | ($false = ((X2 @ X4))) | ($true = ((X3 @ one))) | ($true = ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2))))) ) | ~spl596_600),
% 5.11/1.35 inference(forward_demodulation,[],[f3750,f4032])).
% 5.11/1.35 thf(f4737,plain,(
% 5.11/1.35 ( ! [X55 : term] : (($true = ((sK483 @ X55))) | (((sK481 @ (d2term @ d_one))) = $false)) ) | ~spl596_433),
% 5.11/1.35 inference(forward_demodulation,[],[f3017,f4032])).
% 5.11/1.35 thf(f4739,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X1 : subst,X4 : term] : (($true = ((X3 @ (sK595 @ X3 @ X1 @ X4 @ X2)))) | ($true = ((X3 @ one))) | ($false = ((X2 @ X4))) | ($true = ((X2 @ one)))) ) | ~spl596_600),
% 5.11/1.35 inference(forward_demodulation,[],[f4736,f913])).
% 5.11/1.35 thf(f4740,plain,(
% 5.11/1.35 ( ! [X55 : term] : (($false = ((sK481 @ one))) | ($true = ((sK483 @ X55)))) ) | ~spl596_433),
% 5.11/1.35 inference(forward_demodulation,[],[f4737,f913])).
% 5.11/1.35 thf(f4742,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X4 : term] : (($false = ((X2 @ X4))) | ($true = ((X2 @ one))) | ($true = ((X3 @ (d2term @ d_one)))) | ($true = ((X3 @ one)))) ) | ~spl596_600),
% 5.11/1.35 inference(forward_demodulation,[],[f4739,f4032])).
% 5.11/1.35 thf(f4743,plain,(
% 5.11/1.35 spl596_638 | spl596_637 | ~spl596_433),
% 5.11/1.35 inference(avatar_split_clause,[],[f4740,f3016,f4078,f4081])).
% 5.11/1.35 thf(f4744,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X4 : term] : (($true = ((X2 @ one))) | ($true = ((X3 @ one))) | ($false = ((X2 @ X4))) | ($true = ((X3 @ one)))) ) | ~spl596_600),
% 5.11/1.35 inference(forward_demodulation,[],[f4742,f913])).
% 5.11/1.35 thf(f4745,plain,(
% 5.11/1.35 ( ! [X2 : (term > $o),X3 : (term > $o),X4 : term] : (($true = ((X2 @ one))) | ($true = ((X3 @ one))) | ($false = ((X2 @ X4)))) ) | ~spl596_600),
% 5.11/1.35 inference(duplicate_literal_removal,[],[f4744])).
% 5.11/1.35 thf(f4746,plain,(
% 5.11/1.35 spl596_642 | spl596_641 | ~spl596_600),
% 5.11/1.35 inference(avatar_split_clause,[],[f4745,f3749,f4099,f4102])).
% 5.11/1.35 thf(f4754,plain,(
% 5.11/1.35 ($true != $true) | ~spl596_641),
% 5.11/1.35 inference(superposition,[],[f4006,f4100])).
% 5.11/1.35 thf(f4766,plain,(
% 5.11/1.35 $false | ~spl596_641),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f4754])).
% 5.11/1.35 thf(f4767,plain,(
% 5.11/1.35 ~spl596_641),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f4766])).
% 5.11/1.35 thf(f5395,plain,(
% 5.11/1.35 ($true != $true) | (spl596_455 | ~spl596_637)),
% 5.11/1.35 inference(superposition,[],[f3114,f4079])).
% 5.11/1.35 thf(f5404,plain,(
% 5.11/1.35 $false | (spl596_455 | ~spl596_637)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f5395])).
% 5.11/1.35 thf(f5405,plain,(
% 5.11/1.35 spl596_455 | ~spl596_637),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f5404])).
% 5.11/1.35 thf(f5436,plain,(
% 5.11/1.35 ( ! [X0 : term] : (($true = $false) | (((sK481 @ X0)) = $false)) ) | (~spl596_638 | ~spl596_642)),
% 5.11/1.35 inference(superposition,[],[f4083,f4103])).
% 5.11/1.35 thf(f5445,plain,(
% 5.11/1.35 ( ! [X0 : term] : ((((sK481 @ X0)) = $false)) ) | (~spl596_638 | ~spl596_642)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f5436])).
% 5.11/1.35 thf(f5458,plain,(
% 5.11/1.35 ($true = $false) | (~spl596_573 | ~spl596_638 | ~spl596_642)),
% 5.11/1.35 inference(superposition,[],[f3634,f5445])).
% 5.11/1.35 thf(f5473,plain,(
% 5.11/1.35 $false | (~spl596_573 | ~spl596_638 | ~spl596_642)),
% 5.11/1.35 inference(trivial_inequality_removal,[],[f5458])).
% 5.11/1.35 thf(f5474,plain,(
% 5.11/1.35 ~spl596_573 | ~spl596_638 | ~spl596_642),
% 5.11/1.35 inference(avatar_contradiction_clause,[],[f5473])).
% 5.11/1.35 cnf(s191, plain, ~spl596_64 | spl596_253, inference(sat_conversion,[],[f2235])).
% 5.11/1.35 cnf(s377, plain, spl596_101 | spl596_433, inference(sat_conversion,[],[f3018])).
% 5.11/1.35 cnf(s398, plain, spl596_101 | ~spl596_455, inference(sat_conversion,[],[f3115])).
% 5.11/1.35 cnf(s494, plain, spl596_64 | ~spl596_536, inference(sat_conversion,[],[f3470])).
% 5.11/1.35 cnf(s541, plain, spl596_101 | spl596_573, inference(sat_conversion,[],[f3635])).
% 5.11/1.35 cnf(s566, plain, spl596_594 | spl596_595, inference(sat_conversion,[],[f3730])).
% 5.11/1.35 cnf(s567, plain, spl596_594 | spl596_596, inference(sat_conversion,[],[f3734])).
% 5.11/1.35 cnf(s569, plain, spl596_594 | spl596_598, inference(sat_conversion,[],[f3743])).
% 5.11/1.35 cnf(s571, plain, spl596_101 | spl596_600, inference(sat_conversion,[],[f3751])).
% 5.11/1.35 cnf(s608, plain, ~spl596_101 | ~spl596_594, inference(sat_conversion,[],[f3977])).
% 5.11/1.35 cnf(s623, plain, ~spl596_596 | spl596_633 | spl596_634, inference(sat_conversion,[],[f4127])).
% 5.11/1.35 cnf(s668, plain, spl596_536, inference(sat_conversion,[],[f4708])).
% 5.11/1.35 cnf(s676, plain, ~spl596_253 | ~spl596_595 | ~spl596_633, inference(sat_conversion,[],[f4722])).
% 5.11/1.35 cnf(s677, plain, ~spl596_634 | ~spl596_635, inference(sat_conversion,[],[f4726])).
% 5.11/1.35 cnf(s680, plain, ~spl596_598 | spl596_635, inference(sat_conversion,[],[f4729])).
% 5.11/1.35 cnf(s689, plain, ~spl596_433 | spl596_637 | spl596_638, inference(sat_conversion,[],[f4743])).
% 5.11/1.35 cnf(s690, plain, ~spl596_600 | spl596_641 | spl596_642, inference(sat_conversion,[],[f4746])).
% 5.11/1.35 cnf(s693, plain, ~spl596_641, inference(sat_conversion,[],[f4767])).
% 5.11/1.35 cnf(s745, plain, spl596_455 | ~spl596_637, inference(sat_conversion,[],[f5405])).
% 5.11/1.35 cnf(s747, plain, ~spl596_573 | ~spl596_638 | ~spl596_642, inference(sat_conversion,[],[f5474])).
% 5.11/1.35 cnf(s748, plain, ~spl596_600 | spl596_642, inference(rat,[],[s690,s693])).
% 5.11/1.35 cnf(s759, plain, spl596_64, inference(rat,[],[s494,s668])).
% 5.11/1.35 cnf(s786, plain, spl596_253, inference(rat,[],[s191,s759])).
% 5.11/1.35 cnf(s799, plain, spl596_594, inference(rat,[],[s623,s677,s676,s680,s566,s567,s569,s786])).
% 5.11/1.35 cnf(s800, plain, ~spl596_101, inference(rat,[],[s608,s799])).
% 5.11/1.35 cnf(s801, plain, spl596_600, inference(rat,[],[s571,s800])).
% 5.11/1.35 cnf(s803, plain, spl596_573, inference(rat,[],[s541,s800])).
% 5.11/1.35 cnf(s804, plain, ~spl596_455, inference(rat,[],[s398,s800])).
% 5.11/1.35 cnf(s806, plain, spl596_433, inference(rat,[],[s377,s800])).
% 5.11/1.35 cnf(s807, plain, spl596_642, inference(rat,[],[s748,s801])).
% 5.11/1.35 cnf(s808, plain, ~spl596_638, inference(rat,[],[s747,s807,s803])).
% 5.11/1.35 cnf(s809, plain, ~spl596_637, inference(rat,[],[s745,s804])).
% 5.11/1.35 cnf(s811, plain, $false, inference(rat,[],[s689,s808,s809,s806])).
% 5.11/1.35 thf(f5475,plain,(
% 5.11/1.35 $false),
% 5.11/1.35 inference(avatar_sat_refutation,[],[s811])).
% 5.11/1.35 % SZS output end Proof for theBenchmark
% 5.11/1.35 % (978149)------------------------------
% 5.11/1.35 % (978149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.35 % (978149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.35 % (978149)CaDiCaL version: 2.1.3
% 5.11/1.35 % (978149)Termination reason: Refutation
% 5.11/1.35 % (978149)Time elapsed: 0.296 s
% 5.11/1.35 % (978149)Peak memory usage: 17 MB
% 5.11/1.35 % (978149)Instructions burned: 502 (million)
% 5.11/1.35 % (978028)Success in time 1.048 s
% 5.11/1.35 % Vampire exiting
%------------------------------------------------------------------------------