%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX161^1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:36 AM UTC 2026
% Result : Theorem 13.65s 2.31s
% Output : Refutation 13.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX161^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:12:34 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.26 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
% 0.77/0.40 % (3714364)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.77/0.40 % (3714373)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1952105606:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.77/0.40 % (3714375)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.77/0.40 % (3714375)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
% 0.77/0.40 % (3714373)Instruction limit reached!
% 0.77/0.40 % (3714373)------------------------------
% 0.77/0.40 % (3714373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.40 % (3714373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.40 % (3714373)CaDiCaL version: 2.1.3
% 0.77/0.40 % (3714373)Termination reason: Instruction limit
% 0.77/0.40 % (3714373)Termination phase: Property scanning
% 0.77/0.40 % (3714373)Time elapsed: 0.006 s
% 0.77/0.40 % (3714373)Peak memory usage: 10 MB
% 0.77/0.40 % (3714373)Instructions burned: 27 (million)
% 0.77/0.40 % (3714371)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3830625913:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.77/0.40 % (3714370)lrs+10_16_si=on:nwc=1.5:random_seed=336672353:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.77/0.40 % (3714369)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4083779406:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.77/0.40 % (3714375)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=2829977300:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.77/0.40 % (3714372)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=1718080627: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)
% 0.77/0.40 % (3714374)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=263587293:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.77/0.40 % (3714371)Instruction limit reached!
% 0.77/0.40 % (3714371)------------------------------
% 0.77/0.40 % (3714371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.40 % (3714371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.40 % (3714371)CaDiCaL version: 2.1.3
% 0.77/0.40 % (3714371)Termination reason: Instruction limit
% 0.77/0.40 % (3714371)Termination phase: shuffling
% 0.77/0.40 % (3714371)Time elapsed: 0.002 s
% 0.77/0.40 % (3714371)Peak memory usage: 9 MB
% 0.77/0.40 % (3714371)Instructions burned: 4 (million)
% 0.77/0.40 % (3714370)Instruction limit reached!
% 0.77/0.40 % (3714370)------------------------------
% 0.77/0.40 % (3714370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.40 % (3714370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.40 % (3714370)CaDiCaL version: 2.1.3
% 0.77/0.40 % (3714370)Termination reason: Instruction limit
% 0.77/0.40 % (3714370)Termination phase: shuffling
% 0.77/0.40 % (3714370)Time elapsed: 0.009 s
% 0.77/0.40 % (3714370)Peak memory usage: 10 MB
% 0.77/0.40 % (3714370)Instructions burned: 20 (million)
% 0.77/0.40 % (3714380)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=928654674:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.40 % (3714380)Instruction limit reached!
% 0.77/0.40 % (3714380)------------------------------
% 0.77/0.40 % (3714380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.40 % (3714380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.40 % (3714380)CaDiCaL version: 2.1.3
% 0.77/0.40 % (3714380)Termination reason: Instruction limit
% 0.77/0.40 % (3714380)Termination phase: shuffling
% 0.77/0.40 % (3714380)Time elapsed: 0.002 s
% 0.77/0.40 % (3714380)Peak memory usage: 10 MB
% 0.77/0.40 % (3714380)Instructions burned: 7 (million)
% 0.77/0.40 % (3714384)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=684703959:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.77/0.43 % (3714387)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3895809071:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.77/0.43 % (3714384)Instruction limit reached!
% 0.77/0.43 % (3714384)------------------------------
% 0.77/0.43 % (3714384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (3714385)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.43 % (3714384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (3714384)CaDiCaL version: 2.1.3
% 0.77/0.43 % (3714384)Termination reason: Instruction limit
% 0.77/0.43 % (3714384)Termination phase: shuffling
% 0.77/0.43 % (3714384)Time elapsed: 0.003 s
% 0.77/0.43 % (3714384)Peak memory usage: 10 MB
% 0.77/0.43 % (3714384)Instructions burned: 6 (million)
% 0.77/0.43 % (3714387)Instruction limit reached!
% 0.77/0.43 % (3714387)------------------------------
% 0.77/0.43 % (3714387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (3714387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (3714387)CaDiCaL version: 2.1.3
% 0.77/0.43 % (3714387)Termination reason: Instruction limit
% 0.77/0.43 % (3714387)Termination phase: shuffling
% 0.77/0.43 % (3714387)Time elapsed: 0.003 s
% 0.77/0.43 % (3714387)Peak memory usage: 10 MB
% 0.77/0.43 % (3714387)Instructions burned: 15 (million)
% 0.77/0.43 % (3714385)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3369530959:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.77/0.43 % (3714385)Instruction limit reached!
% 0.77/0.43 % (3714385)------------------------------
% 0.77/0.43 % (3714385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (3714385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (3714385)CaDiCaL version: 2.1.3
% 0.77/0.43 % (3714385)Termination reason: Instruction limit
% 0.77/0.43 % (3714385)Termination phase: shuffling
% 0.77/0.43 % (3714385)Time elapsed: 0.004 s
% 0.77/0.43 % (3714385)Peak memory usage: 9 MB
% 0.77/0.43 % (3714385)Instructions burned: 9 (million)
% 0.77/0.43 % (3714374)Instruction limit reached!
% 0.77/0.43 % (3714374)------------------------------
% 0.77/0.43 % (3714374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (3714374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.43 % (3714374)CaDiCaL version: 2.1.3
% 0.77/0.43 % (3714374)Termination reason: Instruction limit
% 0.77/0.43 % (3714374)Termination phase: Preprocessing 3
% 0.77/0.43 % (3714374)Time elapsed: 0.034 s
% 0.77/0.43 % (3714374)Peak memory usage: 12 MB
% 0.77/0.43 % (3714374)Instructions burned: 77 (million)
% 0.77/0.43 % (3714391)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=2731327533:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.77/0.43 % (3714390)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
% 0.77/0.43 % (3714390)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.77/0.43 % (3714390)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3031588500:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.77/0.43 % (3714394)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.77/0.43 % (3714393)lrs+10_1_si=on:cs=on:random_seed=953068697:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.77/0.43 % (3714394)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=1779966983:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.77/0.43 % (3714394)Instruction limit reached!
% 0.77/0.43 % (3714394)------------------------------
% 0.77/0.43 % (3714394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.43 % (3714394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714394)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714394)Termination reason: Instruction limit
% 0.77/0.46 % (3714394)Termination phase: shuffling
% 0.77/0.46 % (3714393)Instruction limit reached!
% 0.77/0.46 % (3714393)------------------------------
% 0.77/0.46 % (3714393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714394)Time elapsed: 0.001 s
% 0.77/0.46 % (3714394)Peak memory usage: 10 MB
% 0.77/0.46 % (3714394)Instructions burned: 2 (million)
% 0.77/0.46 % (3714393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714393)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714393)Termination reason: Instruction limit
% 0.77/0.46 % (3714393)Termination phase: shuffling
% 0.77/0.46 % (3714393)Time elapsed: 0.004 s
% 0.77/0.46 % (3714393)Peak memory usage: 10 MB
% 0.77/0.46 % (3714393)Instructions burned: 9 (million)
% 0.77/0.46 % (3714390)Instruction limit reached!
% 0.77/0.46 % (3714390)------------------------------
% 0.77/0.46 % (3714390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714390)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714390)Termination reason: Instruction limit
% 0.77/0.46 % (3714390)Termination phase: shuffling
% 0.77/0.46 % (3714390)Time elapsed: 0.013 s
% 0.77/0.46 % (3714390)Peak memory usage: 10 MB
% 0.77/0.46 % (3714390)Instructions burned: 30 (million)
% 0.77/0.46 % (3714391)Instruction limit reached!
% 0.77/0.46 % (3714391)------------------------------
% 0.77/0.46 % (3714391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714391)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714391)Termination reason: Instruction limit
% 0.77/0.46 % (3714391)Termination phase: Saturation
% 0.77/0.46 % (3714391)Time elapsed: 0.019 s
% 0.77/0.46 % (3714391)Peak memory usage: 12 MB
% 0.77/0.46 % (3714391)Instructions burned: 88 (million)
% 0.77/0.46 % (3714369)Instruction limit reached!
% 0.77/0.46 % (3714369)------------------------------
% 0.77/0.46 % (3714369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714369)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714369)Termination reason: Instruction limit
% 0.77/0.46 % (3714369)Termination phase: Preprocessing 3
% 0.77/0.46 % (3714369)Time elapsed: 0.063 s
% 0.77/0.46 % (3714369)Peak memory usage: 12 MB
% 0.77/0.46 % (3714369)Instructions burned: 87 (million)
% 0.77/0.46 % (3714375)Instruction limit reached!
% 0.77/0.46 % (3714375)------------------------------
% 0.77/0.46 % (3714375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714375)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714375)Termination reason: Instruction limit
% 0.77/0.46 % (3714375)Termination phase: Property scanning
% 0.77/0.46 % (3714375)Time elapsed: 0.068 s
% 0.77/0.46 % (3714375)Peak memory usage: 13 MB
% 0.77/0.46 % (3714375)Instructions burned: 157 (million)
% 0.77/0.46 % (3714402)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3779788932:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.77/0.46 % (3714402)Instruction limit reached!
% 0.77/0.46 % (3714402)------------------------------
% 0.77/0.46 % (3714402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.46 % (3714402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.46 % (3714402)CaDiCaL version: 2.1.3
% 0.77/0.46 % (3714402)Termination reason: Instruction limit
% 0.77/0.46 % (3714402)Termination phase: shuffling
% 0.77/0.46 % (3714402)Time elapsed: 0.004 s
% 0.77/0.46 % (3714402)Peak memory usage: 10 MB
% 0.77/0.46 % (3714402)Instructions burned: 18 (million)
% 0.77/0.46 % (3714401)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2178968915:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.77/0.46 % (3714399)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4169460541:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.77/0.46 % (3714400)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3250366973:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.47/0.53 % (3714403)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3281163749:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.47/0.53 % (3714406)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2128547505: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)
% 1.47/0.53 % (3714406)Instruction limit reached!
% 1.47/0.53 % (3714406)------------------------------
% 1.47/0.53 % (3714406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (3714406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (3714406)CaDiCaL version: 2.1.3
% 1.47/0.53 % (3714406)Termination reason: Instruction limit
% 1.47/0.53 % (3714406)Termination phase: shuffling
% 1.47/0.53 % (3714406)Time elapsed: 0.001 s
% 1.47/0.53 % (3714406)Peak memory usage: 10 MB
% 1.47/0.53 % (3714406)Instructions burned: 5 (million)
% 1.47/0.53 % (3714405)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1346575103:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.47/0.53 % (3714401)Instruction limit reached!
% 1.47/0.53 % (3714401)------------------------------
% 1.47/0.53 % (3714401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (3714401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (3714401)CaDiCaL version: 2.1.3
% 1.47/0.53 % (3714401)Termination reason: Instruction limit
% 1.47/0.53 % (3714401)Termination phase: Property scanning
% 1.47/0.53 % (3714401)Time elapsed: 0.011 s
% 1.47/0.53 % (3714401)Peak memory usage: 10 MB
% 1.47/0.53 % (3714401)Instructions burned: 26 (million)
% 1.47/0.53 % (3714405)Instruction limit reached!
% 1.47/0.53 % (3714405)------------------------------
% 1.47/0.53 % (3714405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (3714405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (3714405)CaDiCaL version: 2.1.3
% 1.47/0.53 % (3714405)Termination reason: Instruction limit
% 1.47/0.53 % (3714405)Termination phase: shuffling
% 1.47/0.53 % (3714405)Time elapsed: 0.006 s
% 1.47/0.53 % (3714405)Peak memory usage: 10 MB
% 1.47/0.53 % (3714405)Instructions burned: 14 (million)
% 1.47/0.53 % (3714412)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2495725657:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.47/0.53 % (3714399)Refutation not found, incomplete strategy
% 1.47/0.53 % (3714399)------------------------------
% 1.47/0.53 % (3714399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (3714399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (3714399)CaDiCaL version: 2.1.3
% 1.47/0.53 % (3714399)Termination reason: Refutation not found, incomplete strategy
% 1.47/0.53 % (3714399)Time elapsed: 0.016 s
% 1.47/0.53 % (3714399)Peak memory usage: 13 MB
% 1.47/0.53 % (3714399)Instructions burned: 36 (million)
% 1.47/0.53 % (3714399)------------------------------
% 1.47/0.53 % (3714399)------------------------------
% 1.47/0.53 % (3714412)Instruction limit reached!
% 1.47/0.53 % (3714412)------------------------------
% 1.47/0.53 % (3714412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.53 % (3714412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.53 % (3714412)CaDiCaL version: 2.1.3
% 1.47/0.53 % (3714412)Termination reason: Instruction limit
% 1.47/0.53 % (3714412)Termination phase: shuffling
% 1.47/0.53 % (3714412)Time elapsed: 0.007 s
% 1.47/0.53 % (3714412)Peak memory usage: 10 MB
% 1.47/0.53 % (3714412)Instructions burned: 29 (million)
% 1.47/0.53 % (3714414)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1870736467:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.47/0.53 % (3714418)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.47/0.53 % (3714415)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2597756389:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.47/0.53 % (3714417)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.47/0.57 % (3714417)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.47/0.57 % (3714418)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=2193023763:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.47/0.57 % (3714418)Instruction limit reached!
% 1.47/0.57 % (3714418)------------------------------
% 1.47/0.57 % (3714418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714418)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714418)Termination reason: Instruction limit
% 1.47/0.57 % (3714418)Termination phase: shuffling
% 1.47/0.57 % (3714418)Time elapsed: 0.002 s
% 1.47/0.57 % (3714418)Peak memory usage: 10 MB
% 1.47/0.57 % (3714418)Instructions burned: 11 (million)
% 1.47/0.57 % (3714417)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=3075028239:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.47/0.57 % (3714414)Instruction limit reached!
% 1.47/0.57 % (3714414)------------------------------
% 1.47/0.57 % (3714414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714414)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714414)Termination reason: Instruction limit
% 1.47/0.57 % (3714414)Termination phase: Property scanning
% 1.47/0.57 % (3714414)Time elapsed: 0.010 s
% 1.47/0.57 % (3714414)Peak memory usage: 10 MB
% 1.47/0.57 % (3714414)Instructions burned: 24 (million)
% 1.47/0.57 % (3714417)Instruction limit reached!
% 1.47/0.57 % (3714417)------------------------------
% 1.47/0.57 % (3714417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714417)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714417)Termination reason: Instruction limit
% 1.47/0.57 % (3714417)Termination phase: shuffling
% 1.47/0.57 % (3714417)Time elapsed: 0.006 s
% 1.47/0.57 % (3714417)Peak memory usage: 10 MB
% 1.47/0.57 % (3714417)Instructions burned: 14 (million)
% 1.47/0.57 % (3714422)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=209133623:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.47/0.57 % (3714422)Instruction limit reached!
% 1.47/0.57 % (3714422)------------------------------
% 1.47/0.57 % (3714422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714422)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714422)Termination reason: Instruction limit
% 1.47/0.57 % (3714422)Termination phase: Property scanning
% 1.47/0.57 % (3714422)Time elapsed: 0.008 s
% 1.47/0.57 % (3714422)Peak memory usage: 10 MB
% 1.47/0.57 % (3714422)Instructions burned: 34 (million)
% 1.47/0.57 % (3714424)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1952529096:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.47/0.57 % (3714424)Instruction limit reached!
% 1.47/0.57 % (3714424)------------------------------
% 1.47/0.57 % (3714424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714424)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714424)Termination reason: Instruction limit
% 1.47/0.57 % (3714424)Termination phase: shuffling
% 1.47/0.57 % (3714424)Time elapsed: 0.003 s
% 1.47/0.57 % (3714424)Peak memory usage: 9 MB
% 1.47/0.57 % (3714424)Instructions burned: 7 (million)
% 1.47/0.57 % (3714415)Instruction limit reached!
% 1.47/0.57 % (3714415)------------------------------
% 1.47/0.57 % (3714415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.47/0.57 % (3714415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.47/0.57 % (3714415)CaDiCaL version: 2.1.3
% 1.47/0.57 % (3714415)Termination reason: Instruction limit
% 1.47/0.57 % (3714415)Termination phase: Preprocessing 3
% 2.20/0.67 % (3714415)Time elapsed: 0.027 s
% 2.20/0.67 % (3714415)Peak memory usage: 11 MB
% 2.20/0.67 % (3714415)Instructions burned: 62 (million)
% 2.20/0.67 % (3714425)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1672282613:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.20/0.67 % (3714427)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3739312677:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.20/0.67 % (3714427)Instruction limit reached!
% 2.20/0.67 % (3714427)------------------------------
% 2.20/0.67 % (3714427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.67 % (3714427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.67 % (3714427)CaDiCaL version: 2.1.3
% 2.20/0.67 % (3714427)Termination reason: Instruction limit
% 2.20/0.67 % (3714427)Termination phase: shuffling
% 2.20/0.67 % (3714427)Time elapsed: 0.005 s
% 2.20/0.67 % (3714427)Peak memory usage: 10 MB
% 2.20/0.67 % (3714427)Instructions burned: 23 (million)
% 2.20/0.67 % (3714425)Instruction limit reached!
% 2.20/0.67 % (3714425)------------------------------
% 2.20/0.67 % (3714425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.67 % (3714425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.67 % (3714425)CaDiCaL version: 2.1.3
% 2.20/0.67 % (3714425)Termination reason: Instruction limit
% 2.20/0.67 % (3714425)Termination phase: shuffling
% 2.20/0.67 % (3714425)Time elapsed: 0.011 s
% 2.20/0.67 % (3714425)Peak memory usage: 10 MB
% 2.20/0.67 % (3714425)Instructions burned: 25 (million)
% 2.20/0.67 % (3714429)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1306588965:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.20/0.67 % (3714430)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3113148739:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.20/0.67 % (3714433)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1093085500:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.20/0.67 % (3714434)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=251638452:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.20/0.67 % (3714434)Instruction limit reached!
% 2.20/0.67 % (3714434)------------------------------
% 2.20/0.67 % (3714434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.67 % (3714434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.67 % (3714434)CaDiCaL version: 2.1.3
% 2.20/0.67 % (3714434)Termination reason: Instruction limit
% 2.20/0.67 % (3714434)Termination phase: Naming
% 2.20/0.67 % (3714434)Time elapsed: 0.019 s
% 2.20/0.67 % (3714434)Peak memory usage: 11 MB
% 2.20/0.67 % (3714434)Instructions burned: 43 (million)
% 2.20/0.67 % (3714433)Instruction limit reached!
% 2.20/0.67 % (3714433)------------------------------
% 2.20/0.67 % (3714433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.67 % (3714433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.67 % (3714433)CaDiCaL version: 2.1.3
% 2.20/0.67 % (3714433)Termination reason: Instruction limit
% 2.20/0.67 % (3714433)Termination phase: Saturation
% 2.20/0.67 % (3714433)Time elapsed: 0.044 s
% 2.20/0.67 % (3714433)Peak memory usage: 14 MB
% 2.20/0.67 % (3714433)Instructions burned: 197 (million)
% 2.20/0.67 % (3714439)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.20/0.67 % (3714439)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=949368217:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.20/0.67 % (3714440)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2603629481:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.20/0.67 % (3714439)Instruction limit reached!
% 2.20/0.67 % (3714439)------------------------------
% 2.20/0.67 % (3714439)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.67 % (3714439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.67 % (3714439)CaDiCaL version: 2.1.3
% 2.20/0.67 % (3714439)Termination reason: Instruction limit
% 2.67/0.77 % (3714439)Termination phase: shuffling
% 2.67/0.77 % (3714439)Time elapsed: 0.004 s
% 2.67/0.77 % (3714439)Peak memory usage: 9 MB
% 2.67/0.77 % (3714439)Instructions burned: 9 (million)
% 2.67/0.77 % (3714430)Instruction limit reached!
% 2.67/0.77 % (3714430)------------------------------
% 2.67/0.77 % (3714430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714430)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714430)Termination reason: Instruction limit
% 2.67/0.77 % (3714430)Termination phase: Property scanning
% 2.67/0.77 % (3714430)Time elapsed: 0.063 s
% 2.67/0.77 % (3714430)Peak memory usage: 13 MB
% 2.67/0.77 % (3714430)Instructions burned: 147 (million)
% 2.67/0.77 % (3714400)Instruction limit reached!
% 2.67/0.77 % (3714400)------------------------------
% 2.67/0.77 % (3714400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714400)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714400)Termination reason: Instruction limit
% 2.67/0.77 % (3714400)Termination phase: Saturation
% 2.67/0.77 % (3714400)Time elapsed: 0.144 s
% 2.67/0.77 % (3714400)Peak memory usage: 15 MB
% 2.67/0.77 % (3714400)Instructions burned: 250 (million)
% 2.67/0.77 % (3714440)Refutation not found, incomplete strategy
% 2.67/0.77 % (3714440)------------------------------
% 2.67/0.77 % (3714440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714440)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714440)Termination reason: Refutation not found, incomplete strategy
% 2.67/0.77 % (3714440)Time elapsed: 0.009 s
% 2.67/0.77 % (3714440)Peak memory usage: 13 MB
% 2.67/0.77 % (3714440)Instructions burned: 37 (million)
% 2.67/0.77 % (3714440)------------------------------
% 2.67/0.77 % (3714440)------------------------------
% 2.67/0.77 % (3714403)Instruction limit reached!
% 2.67/0.77 % (3714403)------------------------------
% 2.67/0.77 % (3714403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714403)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714403)Termination reason: Instruction limit
% 2.67/0.77 % (3714403)Termination phase: Saturation
% 2.67/0.77 % (3714403)Time elapsed: 0.147 s
% 2.67/0.77 % (3714403)Peak memory usage: 16 MB
% 2.67/0.77 % (3714403)Instructions burned: 329 (million)
% 2.67/0.77 % (3714446)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=587996182:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.67/0.77 % (3714443)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=3750441278:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.67/0.77 % (3714444)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.67/0.77 % (3714444)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3537251063:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.67/0.77 % (3714446)Instruction limit reached!
% 2.67/0.77 % (3714446)------------------------------
% 2.67/0.77 % (3714446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714446)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714446)Termination reason: Instruction limit
% 2.67/0.77 % (3714446)Termination phase: shuffling
% 2.67/0.77 % (3714446)Time elapsed: 0.009 s
% 2.67/0.77 % (3714446)Peak memory usage: 10 MB
% 2.67/0.77 % (3714446)Instructions burned: 20 (million)
% 2.67/0.77 % (3714444)Instruction limit reached!
% 2.67/0.77 % (3714444)------------------------------
% 2.67/0.77 % (3714444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.67/0.77 % (3714444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/0.77 % (3714444)CaDiCaL version: 2.1.3
% 2.67/0.77 % (3714444)Termination reason: Instruction limit
% 2.67/0.77 % (3714444)Termination phase: shuffling
% 2.67/0.77 % (3714444)Time elapsed: 0.006 s
% 3.13/0.84 % (3714444)Peak memory usage: 10 MB
% 3.13/0.84 % (3714444)Instructions burned: 7 (million)
% 3.13/0.84 % (3714445)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2581838198:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 3.13/0.84 % (3714447)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=3872653580:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.13/0.84 % (3714451)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=3914821505:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.13/0.84 % (3714452)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=3938490057:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.13/0.84 % (3714445)Instruction limit reached!
% 3.13/0.84 % (3714445)------------------------------
% 3.13/0.84 % (3714445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.84 % (3714445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.84 % (3714445)CaDiCaL version: 2.1.3
% 3.13/0.84 % (3714445)Termination reason: Instruction limit
% 3.13/0.84 % (3714445)Termination phase: shuffling
% 3.13/0.84 % (3714445)Time elapsed: 0.040 s
% 3.13/0.84 % (3714445)Peak memory usage: 10 MB
% 3.13/0.84 % (3714445)Instructions burned: 23 (million)
% 3.13/0.84 % (3714452)Instruction limit reached!
% 3.13/0.84 % (3714452)------------------------------
% 3.13/0.84 % (3714452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.84 % (3714452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.84 % (3714452)CaDiCaL version: 2.1.3
% 3.13/0.84 % (3714452)Termination reason: Instruction limit
% 3.13/0.84 % (3714452)Termination phase: SInE selection
% 3.13/0.84 % (3714452)Time elapsed: 0.022 s
% 3.13/0.84 % (3714452)Peak memory usage: 10 MB
% 3.13/0.84 % (3714452)Instructions burned: 45 (million)
% 3.13/0.84 % (3714457)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2179021903:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.13/0.84 % (3714458)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3477386148:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.13/0.84 % (3714443)Instruction limit reached!
% 3.13/0.84 % (3714443)------------------------------
% 3.13/0.84 % (3714443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.84 % (3714443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.84 % (3714443)CaDiCaL version: 2.1.3
% 3.13/0.84 % (3714443)Termination reason: Instruction limit
% 3.13/0.84 % (3714443)Termination phase: Property scanning
% 3.13/0.84 % (3714443)Time elapsed: 0.098 s
% 3.13/0.84 % (3714443)Peak memory usage: 13 MB
% 3.13/0.84 % (3714443)Instructions burned: 171 (million)
% 3.13/0.84 % (3714458)Instruction limit reached!
% 3.13/0.84 % (3714458)------------------------------
% 3.13/0.84 % (3714458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.84 % (3714458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.84 % (3714458)CaDiCaL version: 2.1.3
% 3.13/0.84 % (3714458)Termination reason: Instruction limit
% 3.13/0.84 % (3714458)Termination phase: shuffling
% 3.13/0.84 % (3714458)Time elapsed: 0.010 s
% 3.13/0.84 % (3714458)Peak memory usage: 10 MB
% 3.13/0.84 % (3714458)Instructions burned: 23 (million)
% 3.13/0.84 % (3714372)Instruction limit reached!
% 3.13/0.84 % (3714372)------------------------------
% 3.13/0.84 % (3714372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.13/0.84 % (3714372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/0.84 % (3714372)CaDiCaL version: 2.1.3
% 3.13/0.84 % (3714372)Termination reason: Instruction limit
% 3.13/0.84 % (3714372)Termination phase: Saturation
% 3.13/0.84 % (3714372)Time elapsed: 0.351 s
% 3.13/0.84 % (3714372)Peak memory usage: 19 MB
% 3.13/0.84 % (3714372)Instructions burned: 635 (million)
% 3.13/0.84 % (3714461)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 4.08/0.91 % (3714461)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3075919416:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 4.08/0.91 % (3714462)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3369675056:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 4.08/0.91 % (3714462)Instruction limit reached!
% 4.08/0.91 % (3714462)------------------------------
% 4.08/0.91 % (3714462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.91 % (3714462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.91 % (3714462)CaDiCaL version: 2.1.3
% 4.08/0.91 % (3714462)Termination reason: Instruction limit
% 4.08/0.91 % (3714462)Termination phase: shuffling
% 4.08/0.91 % (3714462)Time elapsed: 0.006 s
% 4.08/0.91 % (3714462)Peak memory usage: 10 MB
% 4.08/0.91 % (3714462)Instructions burned: 14 (million)
% 4.08/0.91 % (3714463)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=1967317871:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.08/0.91 % (3714466)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2035354043:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 4.08/0.91 % (3714463)Instruction limit reached!
% 4.08/0.91 % (3714463)------------------------------
% 4.08/0.91 % (3714463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.91 % (3714463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.91 % (3714463)CaDiCaL version: 2.1.3
% 4.08/0.91 % (3714463)Termination reason: Instruction limit
% 4.08/0.91 % (3714463)Termination phase: Property scanning
% 4.08/0.91 % (3714463)Time elapsed: 0.028 s
% 4.08/0.91 % (3714463)Peak memory usage: 11 MB
% 4.08/0.91 % (3714463)Instructions burned: 67 (million)
% 4.08/0.91 % (3714466)Instruction limit reached!
% 4.08/0.91 % (3714466)------------------------------
% 4.08/0.91 % (3714466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.91 % (3714466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.91 % (3714466)CaDiCaL version: 2.1.3
% 4.08/0.91 % (3714466)Termination reason: Instruction limit
% 4.08/0.91 % (3714466)Termination phase: Preprocessing 3
% 4.08/0.91 % (3714466)Time elapsed: 0.023 s
% 4.08/0.91 % (3714466)Peak memory usage: 11 MB
% 4.08/0.91 % (3714466)Instructions burned: 53 (million)
% 4.08/0.91 % (3714469)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2616267267:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 4.08/0.91 % (3714470)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2511706266:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.08/0.91 % (3714469)Instruction limit reached!
% 4.08/0.91 % (3714469)------------------------------
% 4.08/0.91 % (3714469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.91 % (3714469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.91 % (3714469)CaDiCaL version: 2.1.3
% 4.08/0.91 % (3714469)Termination reason: Instruction limit
% 4.08/0.91 % (3714469)Termination phase: Property scanning
% 4.08/0.91 % (3714469)Time elapsed: 0.014 s
% 4.08/0.91 % (3714469)Peak memory usage: 10 MB
% 4.08/0.91 % (3714469)Instructions burned: 31 (million)
% 4.08/0.91 % (3714461)Instruction limit reached!
% 4.08/0.91 % (3714461)------------------------------
% 4.08/0.91 % (3714461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/0.91 % (3714461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/0.91 % (3714461)CaDiCaL version: 2.1.3
% 4.08/0.91 % (3714461)Termination reason: Instruction limit
% 4.08/0.91 % (3714461)Termination phase: Saturation
% 4.08/0.91 % (3714461)Time elapsed: 0.085 s
% 4.08/0.91 % (3714461)Peak memory usage: 14 MB
% 4.08/0.91 % (3714461)Instructions burned: 201 (million)
% 4.08/0.91 % (3714473)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=3497979394:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.08/0.91 % (3714447)Instruction limit reached!
% 4.08/0.91 % (3714447)------------------------------
% 4.08/1.04 % (3714447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714447)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714447)Termination reason: Instruction limit
% 4.08/1.04 % (3714447)Termination phase: Saturation
% 4.08/1.04 % (3714447)Time elapsed: 0.195 s
% 4.08/1.04 % (3714447)Peak memory usage: 15 MB
% 4.08/1.04 % (3714447)Instructions burned: 316 (million)
% 4.08/1.04 % (3714474)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1858247225:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 4.08/1.04 % (3714473)Instruction limit reached!
% 4.08/1.04 % (3714473)------------------------------
% 4.08/1.04 % (3714473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714473)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714473)Termination reason: Instruction limit
% 4.08/1.04 % (3714473)Termination phase: Property scanning
% 4.08/1.04 % (3714473)Time elapsed: 0.015 s
% 4.08/1.04 % (3714473)Peak memory usage: 10 MB
% 4.08/1.04 % (3714473)Instructions burned: 34 (million)
% 4.08/1.04 % (3714476)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 4.08/1.04 % (3714476)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=4125527775:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 4.08/1.04 % (3714478)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=4194872968:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 4.08/1.04 % (3714470)Instruction limit reached!
% 4.08/1.04 % (3714470)------------------------------
% 4.08/1.04 % (3714470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714470)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714470)Termination reason: Instruction limit
% 4.08/1.04 % (3714470)Termination phase: Function definition elimination
% 4.08/1.04 % (3714470)Time elapsed: 0.061 s
% 4.08/1.04 % (3714470)Peak memory usage: 13 MB
% 4.08/1.04 % (3714470)Instructions burned: 138 (million)
% 4.08/1.04 % (3714474)Instruction limit reached!
% 4.08/1.04 % (3714474)------------------------------
% 4.08/1.04 % (3714474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714474)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714474)Termination reason: Instruction limit
% 4.08/1.04 % (3714474)Termination phase: Preprocessing 3
% 4.08/1.04 % (3714474)Time elapsed: 0.030 s
% 4.08/1.04 % (3714474)Peak memory usage: 12 MB
% 4.08/1.04 % (3714474)Instructions burned: 69 (million)
% 4.08/1.04 % (3714481)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2444040053:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 4.08/1.04 % (3714482)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3678323190:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 4.08/1.04 % (3714451)Instruction limit reached!
% 4.08/1.04 % (3714451)------------------------------
% 4.08/1.04 % (3714451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714451)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714451)Termination reason: Instruction limit
% 4.08/1.04 % (3714451)Termination phase: Saturation
% 4.08/1.04 % (3714451)Time elapsed: 0.246 s
% 4.08/1.04 % (3714451)Peak memory usage: 19 MB
% 4.08/1.04 % (3714451)Instructions burned: 855 (million)
% 4.08/1.04 % (3714485)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2885487202:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 4.08/1.04 % (3714457)Refutation not found, incomplete strategy
% 4.08/1.04 % (3714457)------------------------------
% 4.08/1.04 % (3714457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.08/1.04 % (3714457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.04 % (3714457)CaDiCaL version: 2.1.3
% 4.08/1.04 % (3714457)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.04 % (3714457)Time elapsed: 0.205 s
% 5.43/1.12 % (3714457)Peak memory usage: 16 MB
% 5.43/1.12 % (3714457)Instructions burned: 263 (million)
% 5.43/1.12 % (3714457)------------------------------
% 5.43/1.12 % (3714457)------------------------------
% 5.43/1.12 % (3714482)Refutation not found, incomplete strategy
% 5.43/1.12 % (3714482)------------------------------
% 5.43/1.12 % (3714482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714482)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714482)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.12 % (3714482)Time elapsed: 0.017 s
% 5.43/1.12 % (3714482)Peak memory usage: 13 MB
% 5.43/1.12 % (3714482)Instructions burned: 37 (million)
% 5.43/1.12 % (3714482)------------------------------
% 5.43/1.12 % (3714482)------------------------------
% 5.43/1.12 % (3714487)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1963776679:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 5.43/1.12 % (3714476)Instruction limit reached!
% 5.43/1.12 % (3714476)------------------------------
% 5.43/1.12 % (3714476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714476)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714488)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=4287462947:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.43/1.12 % (3714476)Termination reason: Instruction limit
% 5.43/1.12 % (3714476)Termination phase: Saturation
% 5.43/1.12 % (3714476)Time elapsed: 0.074 s
% 5.43/1.12 % (3714476)Peak memory usage: 12 MB
% 5.43/1.12 % (3714476)Instructions burned: 180 (million)
% 5.43/1.12 % (3714481)Instruction limit reached!
% 5.43/1.12 % (3714481)------------------------------
% 5.43/1.12 % (3714481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714481)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714481)Termination reason: Instruction limit
% 5.43/1.12 % (3714481)Termination phase: Property scanning
% 5.43/1.12 % (3714481)Time elapsed: 0.044 s
% 5.43/1.12 % (3714481)Peak memory usage: 12 MB
% 5.43/1.12 % (3714481)Instructions burned: 98 (million)
% 5.43/1.12 % (3714491)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3411634197:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.43/1.12 % (3714492)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=1943860174:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.43/1.12 % (3714488)Refutation not found, incomplete strategy
% 5.43/1.12 % (3714488)------------------------------
% 5.43/1.12 % (3714488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714488)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714488)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.12 % (3714488)Time elapsed: 0.028 s
% 5.43/1.12 % (3714488)Peak memory usage: 13 MB
% 5.43/1.12 % (3714488)Instructions burned: 65 (million)
% 5.43/1.12 % (3714488)------------------------------
% 5.43/1.12 % (3714488)------------------------------
% 5.43/1.12 % (3714491)Instruction limit reached!
% 5.43/1.12 % (3714491)------------------------------
% 5.43/1.12 % (3714491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714491)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714491)Termination reason: Instruction limit
% 5.43/1.12 % (3714491)Termination phase: Property scanning
% 5.43/1.12 % (3714491)Time elapsed: 0.019 s
% 5.43/1.12 % (3714491)Peak memory usage: 10 MB
% 5.43/1.12 % (3714491)Instructions burned: 46 (million)
% 5.43/1.12 % (3714478)Instruction limit reached!
% 5.43/1.12 % (3714478)------------------------------
% 5.43/1.12 % (3714478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.12 % (3714478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.12 % (3714478)CaDiCaL version: 2.1.3
% 5.43/1.12 % (3714478)Termination reason: Instruction limit
% 5.43/1.12 % (3714478)Termination phase: Saturation
% 5.43/1.12 % (3714478)Time elapsed: 0.108 s
% 5.43/1.12 % (3714478)Peak memory usage: 15 MB
% 6.22/1.20 % (3714478)Instructions burned: 249 (million)
% 6.22/1.20 % (3714495)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=3550545113:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 6.22/1.20 % (3714496)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1875395642:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 6.22/1.20 % (3714498)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=2811556207:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 6.22/1.20 % (3714496)Instruction limit reached!
% 6.22/1.20 % (3714496)------------------------------
% 6.22/1.20 % (3714496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.20 % (3714496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.20 % (3714496)CaDiCaL version: 2.1.3
% 6.22/1.20 % (3714496)Termination reason: Instruction limit
% 6.22/1.20 % (3714496)Termination phase: Property scanning
% 6.22/1.20 % (3714496)Time elapsed: 0.042 s
% 6.22/1.20 % (3714496)Peak memory usage: 13 MB
% 6.22/1.20 % (3714496)Instructions burned: 95 (million)
% 6.22/1.20 % (3714429)Instruction limit reached!
% 6.22/1.20 % (3714429)------------------------------
% 6.22/1.20 % (3714429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.20 % (3714429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.20 % (3714429)CaDiCaL version: 2.1.3
% 6.22/1.20 % (3714429)Termination reason: Instruction limit
% 6.22/1.20 % (3714429)Termination phase: Saturation
% 6.22/1.20 % (3714429)Time elapsed: 0.500 s
% 6.22/1.20 % (3714429)Peak memory usage: 13 MB
% 6.22/1.20 % (3714429)Instructions burned: 1241 (million)
% 6.22/1.20 % (3714498)Instruction limit reached!
% 6.22/1.20 % (3714498)------------------------------
% 6.22/1.20 % (3714498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.20 % (3714498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.20 % (3714498)CaDiCaL version: 2.1.3
% 6.22/1.20 % (3714498)Termination reason: Instruction limit
% 6.22/1.20 % (3714498)Termination phase: Property scanning
% 6.22/1.20 % (3714498)Time elapsed: 0.048 s
% 6.22/1.20 % (3714498)Peak memory usage: 11 MB
% 6.22/1.20 % (3714498)Instructions burned: 66 (million)
% 6.22/1.20 % (3714501)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=3772038622: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_2993 on theBenchmark for (2993ds/105Mi)
% 6.22/1.20 % (3714502)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=4002736511:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 6.22/1.20 % (3714504)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3456124490:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 6.22/1.20 % (3714501)Instruction limit reached!
% 6.22/1.20 % (3714501)------------------------------
% 6.22/1.20 % (3714501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.20 % (3714501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.20 % (3714501)CaDiCaL version: 2.1.3
% 6.22/1.20 % (3714501)Termination reason: Instruction limit
% 6.22/1.20 % (3714501)Termination phase: Saturation
% 6.22/1.20 % (3714501)Time elapsed: 0.044 s
% 6.22/1.20 % (3714501)Peak memory usage: 12 MB
% 6.22/1.20 % (3714501)Instructions burned: 108 (million)
% 6.22/1.20 % (3714492)Refutation not found, incomplete strategy
% 6.22/1.20 % (3714492)------------------------------
% 6.22/1.20 % (3714492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.22/1.20 % (3714492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.20 % (3714492)CaDiCaL version: 2.1.3
% 6.22/1.20 % (3714492)Termination reason: Refutation not found, incomplete strategy
% 6.22/1.20 % (3714492)Time elapsed: 0.153 s
% 6.22/1.20 % (3714492)Peak memory usage: 16 MB
% 6.22/1.20 % (3714492)Instructions burned: 332 (million)
% 6.22/1.20 % (3714492)------------------------------
% 6.64/1.32 % (3714492)------------------------------
% 6.64/1.32 % (3714507)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3069012002:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 6.64/1.32 % (3714508)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=993032595:cond=on:i=34:hud=10:nm=10:rtra=on_2992 on theBenchmark for (2992ds/34Mi)
% 6.64/1.32 % (3714485)Instruction limit reached!
% 6.64/1.32 % (3714485)------------------------------
% 6.64/1.32 % (3714485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714485)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714485)Termination reason: Instruction limit
% 6.64/1.32 % (3714485)Termination phase: Saturation
% 6.64/1.32 % (3714485)Time elapsed: 0.226 s
% 6.64/1.32 % (3714485)Peak memory usage: 18 MB
% 6.64/1.32 % (3714485)Instructions burned: 877 (million)
% 6.64/1.32 % (3714511)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3094028771:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 6.64/1.32 % (3714508)Instruction limit reached!
% 6.64/1.32 % (3714508)------------------------------
% 6.64/1.32 % (3714508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714508)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714508)Termination reason: Instruction limit
% 6.64/1.32 % (3714508)Termination phase: Property scanning
% 6.64/1.32 % (3714508)Time elapsed: 0.015 s
% 6.64/1.32 % (3714508)Peak memory usage: 10 MB
% 6.64/1.32 % (3714508)Instructions burned: 34 (million)
% 6.64/1.32 % (3714513)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3404491738:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2991 on theBenchmark for (2991ds/66Mi)
% 6.64/1.32 % (3714487)Instruction limit reached!
% 6.64/1.32 % (3714487)------------------------------
% 6.64/1.32 % (3714487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714487)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714487)Termination reason: Instruction limit
% 6.64/1.32 % (3714487)Termination phase: Saturation
% 6.64/1.32 % (3714487)Time elapsed: 0.239 s
% 6.64/1.32 % (3714487)Peak memory usage: 17 MB
% 6.64/1.32 % (3714487)Instructions burned: 517 (million)
% 6.64/1.32 % (3714511)Instruction limit reached!
% 6.64/1.32 % (3714511)------------------------------
% 6.64/1.32 % (3714511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714511)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714511)Termination reason: Instruction limit
% 6.64/1.32 % (3714511)Termination phase: Property scanning
% 6.64/1.32 % (3714511)Time elapsed: 0.022 s
% 6.64/1.32 % (3714511)Peak memory usage: 13 MB
% 6.64/1.32 % (3714511)Instructions burned: 94 (million)
% 6.64/1.32 % (3714516)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=445475796:i=338:bd=all:ins=4:rtra=on_2991 on theBenchmark for (2991ds/338Mi)
% 6.64/1.32 % (3714513)Refutation not found, incomplete strategy
% 6.64/1.32 % (3714513)------------------------------
% 6.64/1.32 % (3714513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714513)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714513)Termination reason: Refutation not found, incomplete strategy
% 6.64/1.32 % (3714513)Time elapsed: 0.016 s
% 6.64/1.32 % (3714513)Peak memory usage: 12 MB
% 6.64/1.32 % (3714513)Instructions burned: 36 (million)
% 6.64/1.32 % (3714513)------------------------------
% 6.64/1.32 % (3714513)------------------------------
% 6.64/1.32 % (3714495)Instruction limit reached!
% 6.64/1.32 % (3714495)------------------------------
% 6.64/1.32 % (3714495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.64/1.32 % (3714495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.32 % (3714495)CaDiCaL version: 2.1.3
% 6.64/1.32 % (3714495)Termination reason: Instruction limit
% 7.33/1.42 % (3714495)Termination phase: Saturation
% 7.33/1.42 % (3714495)Time elapsed: 0.205 s
% 7.33/1.42 % (3714495)Peak memory usage: 17 MB
% 7.33/1.42 % (3714495)Instructions burned: 450 (million)
% 7.33/1.42 % (3714515)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3505511145:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2991 on theBenchmark for (2991ds/22Mi)
% 7.33/1.42 % (3714515)Instruction limit reached!
% 7.33/1.42 % (3714515)------------------------------
% 7.33/1.42 % (3714515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.33/1.42 % (3714515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.33/1.42 % (3714515)CaDiCaL version: 2.1.3
% 7.33/1.42 % (3714515)Termination reason: Instruction limit
% 7.33/1.42 % (3714515)Termination phase: Property scanning
% 7.33/1.42 % (3714515)Time elapsed: 0.011 s
% 7.33/1.42 % (3714515)Peak memory usage: 10 MB
% 7.33/1.42 % (3714515)Instructions burned: 25 (million)
% 7.33/1.42 % (3714520)WARNING Broken Constraint: if avatar_split_queue_ratios(1,16) has been set then avatar_split_queue(off) is equal to on
% 7.33/1.42 % (3714518)lrs+10_1_sil=128000:si=on:urr=on:random_seed=2736770278:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/28Mi)
% 7.33/1.42 % (3714520)lrs+1010_2:13_to=kbo:sil=128000:cnfonf=lazy_not_gen:si=on:sp=const_min:uwa=interpreted_only:random_seed=761094716:i=137:add=off:avsqr=1,16:kws=inv_arity:bd=preordered:nm=0:rtra=on:ntd=on:rawr=on_2991 on theBenchmark for (2991ds/137Mi)
% 7.33/1.42 % (3714518)Instruction limit reached!
% 7.33/1.42 % (3714518)------------------------------
% 7.33/1.42 % (3714518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.33/1.42 % (3714518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.33/1.42 % (3714518)CaDiCaL version: 2.1.3
% 7.33/1.42 % (3714518)Termination reason: Instruction limit
% 7.33/1.42 % (3714518)Termination phase: Property scanning
% 7.33/1.42 % (3714518)Time elapsed: 0.013 s
% 7.33/1.42 % (3714518)Peak memory usage: 10 MB
% 7.33/1.42 % (3714518)Instructions burned: 30 (million)
% 7.33/1.42 % (3714521)dis+10_32_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=32,1:uwa=one_side_interpreted:nwc=1:random_seed=2749297121:hsq=on:hsqr=1,8:i=340:hsql=off:bd=preordered:av=off:rtra=on_2991 on theBenchmark for (2991ds/340Mi)
% 7.33/1.42 % (3714525)dis+1004_1_sil=128000:si=on:sos=on:uwa=one_side_interpreted:random_seed=195762715:i=227:sd=1:bd=all:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/227Mi)
% 7.33/1.42 % (3714525)Refutation not found, incomplete strategy
% 7.33/1.42 % (3714525)------------------------------
% 7.33/1.42 % (3714525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.33/1.42 % (3714525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.33/1.42 % (3714525)CaDiCaL version: 2.1.3
% 7.33/1.42 % (3714525)Termination reason: Refutation not found, incomplete strategy
% 7.33/1.42 % (3714525)Time elapsed: 0.017 s
% 7.33/1.42 % (3714525)Peak memory usage: 13 MB
% 7.33/1.42 % (3714525)Instructions burned: 37 (million)
% 7.33/1.42 % (3714525)------------------------------
% 7.33/1.42 % (3714525)------------------------------
% 7.33/1.42 % (3714516)Instruction limit reached!
% 7.33/1.42 % (3714516)------------------------------
% 7.33/1.42 % (3714516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.33/1.42 % (3714516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.33/1.42 % (3714516)CaDiCaL version: 2.1.3
% 7.33/1.42 % (3714516)Termination reason: Instruction limit
% 7.33/1.42 % (3714516)Termination phase: Saturation
% 7.33/1.42 % (3714516)Time elapsed: 0.082 s
% 7.33/1.42 % (3714516)Peak memory usage: 18 MB
% 7.33/1.42 % (3714516)Instructions burned: 342 (million)
% 7.33/1.42 % (3714520)Instruction limit reached!
% 7.33/1.42 % (3714520)------------------------------
% 7.33/1.42 % (3714520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.33/1.42 % (3714520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.33/1.42 % (3714520)CaDiCaL version: 2.1.3
% 7.33/1.42 % (3714520)Termination reason: Instruction limit
% 7.33/1.42 % (3714520)Termination phase: Saturation
% 7.33/1.42 % (3714520)Time elapsed: 0.057 s
% 7.33/1.42 % (3714520)Peak memory usage: 12 MB
% 7.33/1.42 % (3714520)Instructions burned: 138 (million)
% 7.33/1.42 % (3714527)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(1) has been set then sine_level_split_queue(off) is equal to on
% 8.03/1.57 % (3714528)lrs+10_64_anc=all_dependent:sil=128000:e2e=on:si=on:cbe=off:uwa=off:random_seed=172190688:i=116:ep=RSTC:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/116Mi)
% 8.03/1.57 % (3714527)dis+1010_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:nwc=2:slsqc=1:random_seed=2508673729:i=373:hud=10:nm=16:av=off:rtra=on:ntd=on_2990 on theBenchmark for (2990ds/373Mi)
% 8.03/1.57 % (3714504)Instruction limit reached!
% 8.03/1.57 % (3714504)------------------------------
% 8.03/1.57 % (3714504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.03/1.57 % (3714504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/1.57 % (3714504)CaDiCaL version: 2.1.3
% 8.03/1.57 % (3714504)Termination reason: Instruction limit
% 8.03/1.57 % (3714504)Termination phase: Saturation
% 8.03/1.57 % (3714504)Time elapsed: 0.195 s
% 8.03/1.57 % (3714504)Peak memory usage: 16 MB
% 8.03/1.57 % (3714504)Instructions burned: 375 (million)
% 8.03/1.57 % (3714529)lrs+10_1_sil=128000:drc=off:si=on:sos=on:erd=off:urr=on:uwa=interpreted_only:random_seed=4101030444:i=575:rtra=on_2990 on theBenchmark for (2990ds/575Mi)
% 8.03/1.57 % (3714532)dis+2_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:fdtod=off:sp=const_max:lma=off:random_seed=1565817400:cts=off:i=270:doe=on:hud=5:bs=unit_only:bd=preordered:nm=30:ins=25:rtra=on_2990 on theBenchmark for (2990ds/270Mi)
% 8.03/1.57 % (3714528)Instruction limit reached!
% 8.03/1.57 % (3714528)------------------------------
% 8.03/1.57 % (3714528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.03/1.57 % (3714528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/1.57 % (3714528)CaDiCaL version: 2.1.3
% 8.03/1.57 % (3714528)Termination reason: Instruction limit
% 8.03/1.57 % (3714528)Termination phase: Property scanning
% 8.03/1.57 % (3714528)Time elapsed: 0.027 s
% 8.03/1.57 % (3714528)Peak memory usage: 12 MB
% 8.03/1.57 % (3714528)Instructions burned: 118 (million)
% 8.03/1.57 % (3714535)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=903302937:hsq=on:hsqr=16,1:s2a=on:i=9840:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2990 on theBenchmark for (2990ds/9840Mi)
% 8.03/1.57 % (3714507)Instruction limit reached!
% 8.03/1.57 % (3714507)------------------------------
% 8.03/1.57 % (3714507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.03/1.57 % (3714507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/1.57 % (3714507)CaDiCaL version: 2.1.3
% 8.03/1.57 % (3714507)Termination reason: Instruction limit
% 8.03/1.57 % (3714507)Termination phase: Saturation
% 8.03/1.57 % (3714507)Time elapsed: 0.228 s
% 8.03/1.57 % (3714507)Peak memory usage: 16 MB
% 8.03/1.57 % (3714507)Instructions burned: 495 (million)
% 8.03/1.57 % (3714537)lrs+1010_1_sil=128000:si=on:sos=all:uwa=off:nwc=1:random_seed=2636258743:i=421:rtra=on:ss=axioms_2989 on theBenchmark for (2989ds/421Mi)
% 8.03/1.57 % (3714521)Instruction limit reached!
% 8.03/1.57 % (3714521)------------------------------
% 8.03/1.57 % (3714521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.03/1.57 % (3714521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/1.57 % (3714521)CaDiCaL version: 2.1.3
% 8.03/1.57 % (3714521)Termination reason: Instruction limit
% 8.03/1.57 % (3714521)Termination phase: Saturation
% 8.03/1.57 % (3714521)Time elapsed: 0.151 s
% 8.03/1.57 % (3714521)Peak memory usage: 17 MB
% 8.03/1.57 % (3714521)Instructions burned: 342 (million)
% 8.03/1.57 % (3714537)Refutation not found, incomplete strategy
% 8.03/1.57 % (3714537)------------------------------
% 8.03/1.57 % (3714537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.03/1.57 % (3714537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.03/1.57 % (3714537)CaDiCaL version: 2.1.3
% 8.03/1.57 % (3714537)Termination reason: Refutation not found, incomplete strategy
% 8.03/1.57 % (3714537)Time elapsed: 0.017 s
% 8.03/1.57 % (3714537)Peak memory usage: 12 MB
% 8.03/1.57 % (3714537)Instructions burned: 37 (million)
% 8.03/1.57 % (3714537)------------------------------
% 8.03/1.57 % (3714537)------------------------------
% 8.03/1.57 % (3714539)WARNING Broken Constraint: if sine_to_age_tolerance(3) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 8.80/1.78 % (3714539)lrs+10_40_sil=128000:tgt=full:cnfonf=off:si=on:sp=reverse_frequency:spb=goal_then_units:uwa=off:fd=preordered:nwc=1:random_seed=2794978973:avsq=on:i=270:s2at=3:avsqr=1,16:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/270Mi)
% 8.80/1.78 % (3714540)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2494728155:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2989 on theBenchmark for (2989ds/31Mi)
% 8.80/1.78 % (3714532)Instruction limit reached!
% 8.80/1.78 % (3714532)------------------------------
% 8.80/1.78 % (3714532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.80/1.78 % (3714532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.80/1.78 % (3714532)CaDiCaL version: 2.1.3
% 8.80/1.78 % (3714532)Termination reason: Instruction limit
% 8.80/1.78 % (3714532)Termination phase: Saturation
% 8.80/1.78 % (3714532)Time elapsed: 0.111 s
% 8.80/1.78 % (3714532)Peak memory usage: 12 MB
% 8.80/1.78 % (3714532)Instructions burned: 272 (million)
% 8.80/1.78 % (3714540)Instruction limit reached!
% 8.80/1.78 % (3714540)------------------------------
% 8.80/1.78 % (3714540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.80/1.78 % (3714540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.80/1.78 % (3714540)CaDiCaL version: 2.1.3
% 8.80/1.78 % (3714540)Termination reason: Instruction limit
% 8.80/1.78 % (3714540)Termination phase: Property scanning
% 8.80/1.78 % (3714540)Time elapsed: 0.014 s
% 8.80/1.78 % (3714540)Peak memory usage: 10 MB
% 8.80/1.78 % (3714540)Instructions burned: 32 (million)
% 8.80/1.78 % (3714527)Instruction limit reached!
% 8.80/1.78 % (3714527)------------------------------
% 8.80/1.78 % (3714527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.80/1.78 % (3714527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.80/1.78 % (3714527)CaDiCaL version: 2.1.3
% 8.80/1.78 % (3714527)Termination reason: Instruction limit
% 8.80/1.78 % (3714527)Termination phase: Saturation
% 8.80/1.78 % (3714527)Time elapsed: 0.147 s
% 8.80/1.78 % (3714543)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 8.80/1.78 % (3714527)Peak memory usage: 15 MB
% 8.80/1.78 % (3714527)Instructions burned: 373 (million)
% 8.80/1.78 % (3714543)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
% 8.80/1.78 % (3714543)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=822574672:hsqr=1,8:i=1440:s2at=5:add=on:nm=2:rtra=on_2989 on theBenchmark for (2989ds/1440Mi)
% 8.80/1.78 % (3714544)dis+10_2_sil=128000:si=on:random_seed=1525974823:s2a=on:i=339:av=off:rtra=on:fe=abstraction:ss=axioms:fsd=on:ntd=on_2989 on theBenchmark for (2989ds/339Mi)
% 8.80/1.78 % (3714545)lrs+2_16:1_si=on:cbe=off:uwa=interpreted_only:random_seed=3310128391:i=111:add=on:fgj=on:rtra=on:fdi=1024_2989 on theBenchmark for (2989ds/111Mi)
% 8.80/1.78 % (3714544)Refutation not found, incomplete strategy
% 8.80/1.78 % (3714544)------------------------------
% 8.80/1.78 % (3714544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.80/1.78 % (3714544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.80/1.78 % (3714544)CaDiCaL version: 2.1.3
% 8.80/1.78 % (3714544)Termination reason: Refutation not found, incomplete strategy
% 8.80/1.78 % (3714544)Time elapsed: 0.017 s
% 8.80/1.78 % (3714544)Peak memory usage: 12 MB
% 8.80/1.78 % (3714544)Instructions burned: 39 (million)
% 8.80/1.78 % (3714544)------------------------------
% 8.80/1.78 % (3714544)------------------------------
% 8.80/1.78 % (3714549)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=4294675076:st=3:avsq=on:i=122:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/122Mi)
% 8.80/1.78 % (3714545)Instruction limit reached!
% 8.80/1.78 % (3714545)------------------------------
% 8.80/1.78 % (3714545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.80/1.78 % (3714545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.80/1.78 % (3714545)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714545)Termination reason: Instruction limit
% 9.68/2.00 % (3714545)Termination phase: Property scanning
% 9.68/2.00 % (3714545)Time elapsed: 0.048 s
% 9.68/2.00 % (3714545)Peak memory usage: 12 MB
% 9.68/2.00 % (3714545)Instructions burned: 111 (million)
% 9.68/2.00 % (3714539)Instruction limit reached!
% 9.68/2.00 % (3714539)------------------------------
% 9.68/2.00 % (3714539)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/2.00 % (3714539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.00 % (3714539)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714539)Termination reason: Instruction limit
% 9.68/2.00 % (3714539)Termination phase: Saturation
% 9.68/2.00 % (3714539)Time elapsed: 0.118 s
% 9.68/2.00 % (3714539)Peak memory usage: 15 MB
% 9.68/2.00 % (3714539)Instructions burned: 271 (million)
% 9.68/2.00 % (3714551)dis+1010_3:2_anc=all_dependent:sil=128000:si=on:sos=on:lma=off:spb=goal_then_units:bce=on:fd=off:random_seed=181042066:uwa_fpi=on:avsq=on:i=136:avsqr=1,32:hud=15:nm=0:rtra=on:ntd=on_2988 on theBenchmark for (2988ds/136Mi)
% 9.68/2.00 % (3714553)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3335525550:hsq=on:st=2:i=232:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2988 on theBenchmark for (2988ds/232Mi)
% 9.68/2.00 % (3714549)Instruction limit reached!
% 9.68/2.00 % (3714549)------------------------------
% 9.68/2.00 % (3714549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/2.00 % (3714549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.00 % (3714549)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714549)Termination reason: Instruction limit
% 9.68/2.00 % (3714549)Termination phase: Property scanning
% 9.68/2.00 % (3714549)Time elapsed: 0.054 s
% 9.68/2.00 % (3714549)Peak memory usage: 13 MB
% 9.68/2.00 % (3714549)Instructions burned: 124 (million)
% 9.68/2.00 % (3714555)lrs+1010_8:1_sil=128000:tgt=ground:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sos=on:plsqr=256,1:uwa=off:random_seed=1832596392:i=1254:kws=precedence:bd=preordered:av=off:rtra=on_2988 on theBenchmark for (2988ds/1254Mi)
% 9.68/2.00 % (3714529)Instruction limit reached!
% 9.68/2.00 % (3714529)------------------------------
% 9.68/2.00 % (3714529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/2.00 % (3714529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.00 % (3714529)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714529)Termination reason: Instruction limit
% 9.68/2.00 % (3714529)Termination phase: Saturation
% 9.68/2.00 % (3714529)Time elapsed: 0.279 s
% 9.68/2.00 % (3714529)Peak memory usage: 18 MB
% 9.68/2.00 % (3714529)Instructions burned: 575 (million)
% 9.68/2.00 % (3714551)Instruction limit reached!
% 9.68/2.00 % (3714551)------------------------------
% 9.68/2.00 % (3714551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/2.00 % (3714551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.00 % (3714551)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714551)Termination reason: Instruction limit
% 9.68/2.00 % (3714551)Termination phase: Property scanning
% 9.68/2.00 % (3714551)Time elapsed: 0.061 s
% 9.68/2.00 % (3714551)Peak memory usage: 16 MB
% 9.68/2.00 % (3714551)Instructions burned: 137 (million)
% 9.68/2.00 % (3714557)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(discount) is equal to lrs
% 9.68/2.00 % (3714557)dis+1002_5:4_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_simp:si=on:plsqr=878,253:plsql=on:uwa=interpreted_only:lwlo=on:random_seed=765956982:s2a=on:i=281:add=on:rtra=on:fe=axiom:fdi=1024_2987 on theBenchmark for (2987ds/281Mi)
% 9.68/2.00 % (3714558)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=369937070:i=619:add=on:rtra=on_2987 on theBenchmark for (2987ds/619Mi)
% 9.68/2.00 % (3714553)Instruction limit reached!
% 9.68/2.00 % (3714553)------------------------------
% 9.68/2.00 % (3714553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 9.68/2.00 % (3714553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.00 % (3714553)CaDiCaL version: 2.1.3
% 9.68/2.00 % (3714553)Termination reason: Instruction limit
% 9.68/2.00 % (3714553)Termination phase: Saturation
% 9.68/2.00 % (3714553)Time elapsed: 0.101 s
% 9.68/2.00 % (3714553)Peak memory usage: 14 MB
% 9.68/2.00 % (3714553)Instructions burned: 234 (million)
% 9.68/2.00 % (3714555)Refutation not found, incomplete strategy
% 12.92/2.19 % (3714555)------------------------------
% 12.92/2.19 % (3714555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714555)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714555)Termination reason: Refutation not found, incomplete strategy
% 12.92/2.19 % (3714555)Time elapsed: 0.090 s
% 12.92/2.19 % (3714555)Peak memory usage: 15 MB
% 12.92/2.19 % (3714555)Instructions burned: 211 (million)
% 12.92/2.19 % (3714555)------------------------------
% 12.92/2.19 % (3714555)------------------------------
% 12.92/2.19 % (3714561)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=2772904448:i=865:bs=unit_only:ins=25:rtra=on:ntd=on_2987 on theBenchmark for (2987ds/865Mi)
% 12.92/2.19 % (3714562)lrs+10_1_sil=128000:si=on:urr=on:random_seed=1628753227:i=212:sd=1:rtra=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/212Mi)
% 12.92/2.19 % (3714557)Instruction limit reached!
% 12.92/2.19 % (3714557)------------------------------
% 12.92/2.19 % (3714557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714557)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714557)Termination reason: Instruction limit
% 12.92/2.19 % (3714557)Termination phase: Saturation
% 12.92/2.19 % (3714557)Time elapsed: 0.114 s
% 12.92/2.19 % (3714557)Peak memory usage: 12 MB
% 12.92/2.19 % (3714557)Instructions burned: 282 (million)
% 12.92/2.19 % (3714565)lrs+1010_64_sil=128000:si=on:avsql=on:uwa=off:random_seed=595631221:hsq=on:st=3:avsq=on:i=130:avsqr=1,16:sd=1:rtra=on:ss=axioms_2986 on theBenchmark for (2986ds/130Mi)
% 12.92/2.19 % (3714562)Instruction limit reached!
% 12.92/2.19 % (3714562)------------------------------
% 12.92/2.19 % (3714562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714562)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714562)Termination reason: Instruction limit
% 12.92/2.19 % (3714562)Termination phase: Saturation
% 12.92/2.19 % (3714562)Time elapsed: 0.090 s
% 12.92/2.19 % (3714562)Peak memory usage: 14 MB
% 12.92/2.19 % (3714562)Instructions burned: 213 (million)
% 12.92/2.19 % (3714567)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=1841766011:st=1.5:i=346:rtra=on:ss=axioms_2985 on theBenchmark for (2985ds/346Mi)
% 12.92/2.19 % (3714565)Instruction limit reached!
% 12.92/2.19 % (3714565)------------------------------
% 12.92/2.19 % (3714565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714565)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714565)Termination reason: Instruction limit
% 12.92/2.19 % (3714565)Termination phase: Property scanning
% 12.92/2.19 % (3714565)Time elapsed: 0.057 s
% 12.92/2.19 % (3714565)Peak memory usage: 13 MB
% 12.92/2.19 % (3714565)Instructions burned: 132 (million)
% 12.92/2.19 % (3714569)lrs+1010_3_sil=128000:si=on:slsq=on:random_seed=941560513:avsq=on:i=152:avsqr=8,1:hud=5:ins=1:fsr=off:rtra=on_2985 on theBenchmark for (2985ds/152Mi)
% 12.92/2.19 % (3714567)Refutation not found, incomplete strategy
% 12.92/2.19 % (3714567)------------------------------
% 12.92/2.19 % (3714567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714567)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714567)Termination reason: Refutation not found, incomplete strategy
% 12.92/2.19 % (3714567)Time elapsed: 0.028 s
% 12.92/2.19 % (3714567)Peak memory usage: 13 MB
% 12.92/2.19 % (3714567)Instructions burned: 65 (million)
% 12.92/2.19 % (3714567)------------------------------
% 12.92/2.19 % (3714567)------------------------------
% 12.92/2.19 % (3714571)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2752903193:i=75:ep=R:rtra=on:ntd=on_2985 on theBenchmark for (2985ds/75Mi)
% 12.92/2.19 % (3714571)Instruction limit reached!
% 12.92/2.19 % (3714571)------------------------------
% 12.92/2.19 % (3714571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 12.92/2.19 % (3714571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.92/2.19 % (3714571)CaDiCaL version: 2.1.3
% 12.92/2.19 % (3714571)Termination reason: Instruction limit
% 13.65/2.31 % (3714571)Termination phase: Property scanning
% 13.65/2.31 % (3714571)Time elapsed: 0.031 s
% 13.65/2.31 % (3714571)Peak memory usage: 11 MB
% 13.65/2.31 % (3714571)Instructions burned: 75 (million)
% 13.65/2.31 % (3714569)Instruction limit reached!
% 13.65/2.31 % (3714569)------------------------------
% 13.65/2.31 % (3714569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714569)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714569)Termination reason: Instruction limit
% 13.65/2.31 % (3714569)Termination phase: Inequality splitting
% 13.65/2.31 % (3714569)Time elapsed: 0.066 s
% 13.65/2.31 % (3714569)Peak memory usage: 13 MB
% 13.65/2.31 % (3714569)Instructions burned: 154 (million)
% 13.65/2.31 % (3714573)dis+10_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:nwc=5:random_seed=3287547370:st=2.5:i=387:sd=2:rtra=on:ss=axioms_2984 on theBenchmark for (2984ds/387Mi)
% 13.65/2.31 % (3714574)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=2350486570:uwa_fpi=on:i=148:doe=on:bd=preordered:rtra=on:fsd=on_2984 on theBenchmark for (2984ds/148Mi)
% 13.65/2.31 % (3714558)Instruction limit reached!
% 13.65/2.31 % (3714558)------------------------------
% 13.65/2.31 % (3714558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714558)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714558)Termination reason: Instruction limit
% 13.65/2.31 % (3714558)Termination phase: Saturation
% 13.65/2.31 % (3714558)Time elapsed: 0.311 s
% 13.65/2.31 % (3714558)Peak memory usage: 18 MB
% 13.65/2.31 % (3714558)Instructions burned: 620 (million)
% 13.65/2.31 % (3714577)dis+1010_3_si=on:uwa=one_side_interpreted:random_seed=2707342201:i=161:piset=and:rtra=on:ntd=on_2984 on theBenchmark for (2984ds/161Mi)
% 13.65/2.31 % (3714574)Instruction limit reached!
% 13.65/2.31 % (3714574)------------------------------
% 13.65/2.31 % (3714574)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714574)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714574)Termination reason: Instruction limit
% 13.65/2.31 % (3714574)Termination phase: Saturation
% 13.65/2.31 % (3714574)Time elapsed: 0.060 s
% 13.65/2.31 % (3714574)Peak memory usage: 12 MB
% 13.65/2.31 % (3714574)Instructions burned: 148 (million)
% 13.65/2.31 % (3714579)lrs+10_1_sil=128000:si=on:random_seed=2762646347:st=5:i=888:sd=3:bd=preordered:rtra=on:ss=axioms_2983 on theBenchmark for (2983ds/888Mi)
% 13.65/2.31 % (3714577)Instruction limit reached!
% 13.65/2.31 % (3714577)------------------------------
% 13.65/2.31 % (3714577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714577)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714577)Termination reason: Instruction limit
% 13.65/2.31 % (3714577)Termination phase: Property scanning
% 13.65/2.31 % (3714577)Time elapsed: 0.069 s
% 13.65/2.31 % (3714577)Peak memory usage: 13 MB
% 13.65/2.31 % (3714577)Instructions burned: 161 (million)
% 13.65/2.31 % (3714581)ott-1003_1_sil=128000:plsq=on:plsqc=1:si=on:sp=weighted_frequency:lma=off:plsqr=1,32:urr=on:cbe=off:random_seed=4162907196:i=136:add=on:ins=4:rtra=on:sup=off_2983 on theBenchmark for (2983ds/136Mi)
% 13.65/2.31 % (3714573)Instruction limit reached!
% 13.65/2.31 % (3714573)------------------------------
% 13.65/2.31 % (3714573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714573)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714573)Termination reason: Instruction limit
% 13.65/2.31 % (3714573)Termination phase: Saturation
% 13.65/2.31 % (3714573)Time elapsed: 0.156 s
% 13.65/2.31 % (3714573)Peak memory usage: 12 MB
% 13.65/2.31 % (3714573)Instructions burned: 388 (million)
% 13.65/2.31 % (3714583)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=2482343845:i=88:s2at=3:nm=2:rtra=on:rawr=on_2983 on theBenchmark for (2983ds/88Mi)
% 13.65/2.31 % (3714581)Instruction limit reached!
% 13.65/2.31 % (3714581)------------------------------
% 13.65/2.31 % (3714581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714581)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714581)Termination reason: Instruction limit
% 13.65/2.31 % (3714581)Termination phase: Function definition elimination
% 13.65/2.31 % (3714581)Time elapsed: 0.059 s
% 13.65/2.31 % (3714581)Peak memory usage: 12 MB
% 13.65/2.31 % (3714581)Instructions burned: 138 (million)
% 13.65/2.31 % (3714583)Instruction limit reached!
% 13.65/2.31 % (3714583)------------------------------
% 13.65/2.31 % (3714583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714583)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714583)Termination reason: Instruction limit
% 13.65/2.31 % (3714583)Termination phase: Property scanning
% 13.65/2.31 % (3714583)Time elapsed: 0.036 s
% 13.65/2.31 % (3714583)Peak memory usage: 11 MB
% 13.65/2.31 % (3714583)Instructions burned: 89 (million)
% 13.65/2.31 % (3714585)dis+1002_5:4_to=kbo:sil=128000:cnfonf=conj_eager:si=on:sp=reverse_arity:lma=off:hi=on:nwc=20:random_seed=2176259217:s2a=on:cond=on:i=93:add=on:bd=preordered:rtra=on:er=filter_2982 on theBenchmark for (2982ds/93Mi)
% 13.65/2.31 % (3714586)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2620277380:i=2186:rtra=on:ixr=off_2982 on theBenchmark for (2982ds/2186Mi)
% 13.65/2.31 % (3714585)Instruction limit reached!
% 13.65/2.31 % (3714585)------------------------------
% 13.65/2.31 % (3714585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714585)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714585)Termination reason: Instruction limit
% 13.65/2.31 % (3714585)Termination phase: Saturation
% 13.65/2.31 % (3714585)Time elapsed: 0.039 s
% 13.65/2.31 % (3714585)Peak memory usage: 12 MB
% 13.65/2.31 % (3714585)Instructions burned: 94 (million)
% 13.65/2.31 % (3714589)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=992022801:s2a=on:i=240:rtra=on:ntd=on_2982 on theBenchmark for (2982ds/240Mi)
% 13.65/2.31 % (3714561)Instruction limit reached!
% 13.65/2.31 % (3714561)------------------------------
% 13.65/2.31 % (3714561)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714561)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714561)Termination reason: Instruction limit
% 13.65/2.31 % (3714561)Termination phase: Saturation
% 13.65/2.31 % (3714561)Time elapsed: 0.518 s
% 13.65/2.31 % (3714561)Peak memory usage: 19 MB
% 13.65/2.31 % (3714561)Instructions burned: 865 (million)
% 13.65/2.31 % (3714543)Instruction limit reached!
% 13.65/2.31 % (3714543)------------------------------
% 13.65/2.31 % (3714543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714543)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714543)Termination reason: Instruction limit
% 13.65/2.31 % (3714543)Termination phase: Saturation
% 13.65/2.31 % (3714543)Time elapsed: 0.748 s
% 13.65/2.31 % (3714543)Peak memory usage: 20 MB
% 13.65/2.31 % (3714543)Instructions burned: 1441 (million)
% 13.65/2.31 % (3714591)dis+10_1_to=lpo:sil=128000:tgt=ground:si=on:urr=on:cbe=off:uwa=one_side_constant:nwc=5:random_seed=3851676020:i=805:aac=none:doe=on:piset=not:bd=all:rtra=on:fe=abstraction_2981 on theBenchmark for (2981ds/805Mi)
% 13.65/2.31 % (3714592)WARNING Broken Constraint: if avatar_split_queue_cutoffs(1) has been set then avatar_split_queue(off) is equal to on
% 13.65/2.31 % (3714592)dis+1002_1_to=lpo:sil=128000:cnfonf=conj_eager:si=on:sp=unary_first:spb=intro:urr=on:cbe=off:uwa=one_side_interpreted:rp=on:avsqc=1:random_seed=148839472:st=2:s2a=on:i=391:sd=4:bd=preordered:nm=16:rtra=on:ss=axioms:rawr=on_2981 on theBenchmark for (2981ds/391Mi)
% 13.65/2.31 % (3714589)Instruction limit reached!
% 13.65/2.31 % (3714589)------------------------------
% 13.65/2.31 % (3714589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714589)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714589)Termination reason: Instruction limit
% 13.65/2.31 % (3714589)Termination phase: Saturation
% 13.65/2.31 % (3714589)Time elapsed: 0.105 s
% 13.65/2.31 % (3714589)Peak memory usage: 15 MB
% 13.65/2.31 % (3714589)Instructions burned: 242 (million)
% 13.65/2.31 % (3714595)dis+10_1_sil=128000:si=on:urr=on:uwa=off:random_seed=3162373680:i=355:av=off:fsr=off:rtra=on:ixr=off_2980 on theBenchmark for (2980ds/355Mi)
% 13.65/2.31 % (3714579) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3714364-3714579"...
% 13.65/2.31 % (3714592)Instruction limit reached!
% 13.65/2.31 % (3714592)------------------------------
% 13.65/2.31 % (3714592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.31 % (3714592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.31 % (3714592)CaDiCaL version: 2.1.3
% 13.65/2.31 % (3714592)Termination reason: Instruction limit
% 13.65/2.31 % (3714592)Termination phase: Saturation
% 13.65/2.31 % (3714592)Time elapsed: 0.161 s
% 13.65/2.31 % (3714592)Peak memory usage: 12 MB
% 13.65/2.31 % (3714592)Instructions burned: 393 (million)
% 13.65/2.31 % (3714579)...printing done.
% 13.65/2.31 % (3714579)Refutation found. Thanks to Tanya!
% 13.65/2.31 % SZS status Theorem for theBenchmark
% 13.65/2.31 % SZS output start Proof for theBenchmark
% 13.65/2.31 thf(type_def_5, type, term: $tType).
% 13.65/2.31 thf(type_def_6, type, subst: $tType).
% 13.65/2.31 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 13.65/2.31 thf(type_def_8, type, d_term: $tType).
% 13.65/2.31 thf(type_def_9, type, d_subst: $tType).
% 13.65/2.31 thf(func_def_0, type, one: term).
% 13.65/2.31 thf(func_def_1, type, ap: (term > term > term)).
% 13.65/2.31 thf(func_def_2, type, lam: (term > term)).
% 13.65/2.31 thf(func_def_3, type, sub: (term > subst > term)).
% 13.65/2.31 thf(func_def_4, type, id: subst).
% 13.65/2.31 thf(func_def_5, type, sh: subst).
% 13.65/2.31 thf(func_def_6, type, push: (term > subst > subst)).
% 13.65/2.31 thf(func_def_7, type, comp: (subst > subst > subst)).
% 13.65/2.31 thf(func_def_8, type, var: (term > $o)).
% 13.65/2.31 thf(func_def_9, type, pushprop_lem1v2: $o).
% 13.65/2.31 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 13.65/2.31 thf(func_def_11, type, axmap: $o).
% 13.65/2.31 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 13.65/2.31 thf(func_def_13, type, shinj: $o).
% 13.65/2.31 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 13.65/2.31 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 13.65/2.31 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 13.65/2.31 thf(func_def_17, type, induction2lem: $o).
% 13.65/2.31 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 13.65/2.31 thf(func_def_19, type, axvarshift: $o).
% 13.65/2.31 thf(func_def_20, type, hoasapinj2: $o).
% 13.65/2.31 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 13.65/2.31 thf(func_def_22, type, hoasapinj1: $o).
% 13.65/2.31 thf(func_def_23, type, ulamvar1: $o).
% 13.65/2.31 thf(func_def_24, type, induction2lem_lthm: $o).
% 13.65/2.31 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 13.65/2.31 thf(func_def_26, type, apnotvar: $o).
% 13.65/2.31 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 13.65/2.31 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 13.65/2.31 thf(func_def_29, type, hoasinduction_lthm: $o).
% 13.65/2.31 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 13.65/2.31 thf(func_def_31, type, hoaslaminj: $o).
% 13.65/2.31 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 13.65/2.31 thf(func_def_33, type, induction2lem_gthm: $o).
% 13.65/2.31 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 13.65/2.31 thf(func_def_35, type, hoasinduction_lem3: $o).
% 13.65/2.31 thf(func_def_36, type, hoasinduction_lem2: $o).
% 13.65/2.31 thf(func_def_37, type, termmset_lthm: $o).
% 13.65/2.31 thf(func_def_38, type, hoasinduction_lem1: $o).
% 13.65/2.31 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 13.65/2.31 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 13.65/2.31 thf(func_def_41, type, hoasapnotvar: $o).
% 13.65/2.31 thf(func_def_42, type, hoasinduction_lem0: $o).
% 13.65/2.31 thf(func_def_43, type, hoasinduction: $o).
% 13.65/2.31 thf(func_def_44, type, hoasinduction_gthm: $o).
% 13.65/2.31 thf(func_def_45, type, axapp: $o).
% 13.65/2.31 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 13.65/2.31 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 13.65/2.31 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 13.65/2.31 thf(func_def_49, type, ulamvarind: $o).
% 13.65/2.31 thf(func_def_50, type, induction: $o).
% 13.65/2.31 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 13.65/2.31 thf(func_def_52, type, termmset_gthm: $o).
% 13.65/2.31 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 13.65/2.31 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 13.65/2.31 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 13.65/2.31 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 13.65/2.31 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 13.65/2.31 thf(func_def_58, type, pushprop_lem2v2: $o).
% 13.65/2.31 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 13.65/2.31 thf(func_def_60, type, axclos: $o).
% 13.65/2.31 thf(func_def_61, type, axassoc: $o).
% 13.65/2.31 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 13.65/2.31 thf(func_def_63, type, pushprop_lthm: $o).
% 13.65/2.31 thf(func_def_64, type, apinj2: $o).
% 13.65/2.31 thf(func_def_65, type, apinj1: $o).
% 13.65/2.31 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 13.65/2.31 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 13.65/2.31 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 13.65/2.31 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 13.65/2.31 thf(func_def_70, type, axvarcons: $o).
% 13.65/2.31 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 13.65/2.31 thf(func_def_72, type, axscons: $o).
% 13.65/2.31 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 13.65/2.31 thf(func_def_74, type, axidr: $o).
% 13.65/2.31 thf(func_def_75, type, pushprop_lem1: $o).
% 13.65/2.31 thf(func_def_76, type, laminj: $o).
% 13.65/2.31 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 13.65/2.31 thf(func_def_78, type, pushprop_lem0: $o).
% 13.65/2.31 thf(func_def_79, type, pushprop_gthm: $o).
% 13.65/2.31 thf(func_def_80, type, axabs: $o).
% 13.65/2.31 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 13.65/2.31 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 13.65/2.31 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 13.65/2.31 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 13.65/2.31 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 13.65/2.31 thf(func_def_86, type, lamnotap: $o).
% 13.65/2.31 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 13.65/2.31 thf(func_def_88, type, hoaslamnotvar: $o).
% 13.65/2.31 thf(func_def_89, type, axidl: $o).
% 13.65/2.31 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 13.65/2.31 thf(func_def_91, type, induction2_lthm: $o).
% 13.65/2.31 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 13.65/2.31 thf(func_def_93, type, substmonoid_lthm: $o).
% 13.65/2.31 thf(func_def_94, type, pushprop: $o).
% 13.65/2.31 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 13.65/2.31 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 13.65/2.31 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 13.65/2.31 thf(func_def_98, type, substmonoid: $o).
% 13.65/2.31 thf(func_def_99, type, lamnotvar: $o).
% 13.65/2.31 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 13.65/2.31 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 13.65/2.31 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 13.65/2.31 thf(func_def_103, type, induction2_gthm: $o).
% 13.65/2.31 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 13.65/2.31 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_106, type, hoaslamnotap: $o).
% 13.65/2.31 thf(func_def_107, type, substmonoid_gthm: $o).
% 13.65/2.31 thf(func_def_108, type, ulamvarsh: $o).
% 13.65/2.31 thf(func_def_109, type, induction2: $o).
% 13.65/2.31 thf(func_def_110, type, pushprop_lem3v2: $o).
% 13.65/2.31 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 13.65/2.31 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 13.65/2.31 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 13.65/2.31 thf(func_def_114, type, axshiftcons: $o).
% 13.65/2.31 thf(func_def_115, type, termmset: $o).
% 13.65/2.31 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 13.65/2.31 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 13.65/2.31 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 13.65/2.31 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 13.65/2.31 thf(func_def_120, type, axvarid: $o).
% 13.65/2.31 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 13.65/2.31 thf(func_def_122, type, d2term: (d_term > term)).
% 13.65/2.31 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 13.65/2.31 thf(func_def_124, type, d_one: d_term).
% 13.65/2.31 thf(func_def_125, type, d_id: d_subst).
% 13.65/2.31 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.65/2.31 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 13.65/2.31 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 13.65/2.31 thf(func_def_132, type, db4: !>[X0: $tType]:(X0)).
% 13.65/2.31 thf(func_def_133, type, db3: !>[X0: $tType]:(X0)).
% 13.65/2.31 thf(func_def_134, type, db1: !>[X0: $tType]:(X0)).
% 13.65/2.31 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 13.65/2.31 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 13.65/2.31 thf(func_def_137, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 13.65/2.31 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_139, type, sP1: $o).
% 13.65/2.31 thf(func_def_140, type, sP2: $o).
% 13.65/2.31 thf(func_def_141, type, sP3: $o).
% 13.65/2.31 thf(func_def_142, type, sP4: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_143, type, sP5: $o).
% 13.65/2.31 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_145, type, sP7: $o).
% 13.65/2.31 thf(func_def_146, type, sP8: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_147, type, sP9: $o).
% 13.65/2.31 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_149, type, sP11: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_150, type, sP12: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_151, type, sP13: $o).
% 13.65/2.31 thf(func_def_152, type, sP14: $o).
% 13.65/2.31 thf(func_def_153, type, sP15: $o).
% 13.65/2.31 thf(func_def_154, type, sP16: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_155, type, sP17: $o).
% 13.65/2.31 thf(func_def_156, type, sP18: $o).
% 13.65/2.31 thf(func_def_157, type, sP19: $o).
% 13.65/2.31 thf(func_def_158, type, sP20: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_159, type, sP21: $o).
% 13.65/2.31 thf(func_def_160, type, sP22: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_161, type, sP23: $o).
% 13.65/2.31 thf(func_def_162, type, sP24: $o).
% 13.65/2.31 thf(func_def_163, type, sP25: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_164, type, sP26: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_165, type, sP27: $o).
% 13.65/2.31 thf(func_def_166, type, sP28: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_168, type, sP30: $o).
% 13.65/2.31 thf(func_def_169, type, sP31: $o).
% 13.65/2.31 thf(func_def_170, type, sP32: $o).
% 13.65/2.31 thf(func_def_171, type, sP33: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_172, type, sP34: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_173, type, sP35: $o).
% 13.65/2.31 thf(func_def_174, type, sP36: $o).
% 13.65/2.31 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_176, type, sP38: $o).
% 13.65/2.31 thf(func_def_177, type, sP39: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_178, type, sP40: $o).
% 13.65/2.31 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_180, type, sP42: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_182, type, sP44: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_184, type, sP46: $o).
% 13.65/2.31 thf(func_def_185, type, sP47: $o).
% 13.65/2.31 thf(func_def_186, type, sP48: $o).
% 13.65/2.31 thf(func_def_187, type, sP49: $o).
% 13.65/2.31 thf(func_def_188, type, sP50: $o).
% 13.65/2.31 thf(func_def_189, type, sP51: $o).
% 13.65/2.31 thf(func_def_190, type, sP52: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_191, type, sP53: ((term > $o) > $o)).
% 13.65/2.31 thf(func_def_192, type, sP54: $o).
% 13.65/2.31 thf(func_def_193, type, sP55: $o).
% 13.65/2.31 thf(func_def_194, type, sP56: $o).
% 13.65/2.31 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 13.65/2.31 thf(func_def_196, type, sP58: $o).
% 13.65/2.31 thf(func_def_197, type, sK59: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_198, type, sK60: term).
% 13.65/2.31 thf(func_def_199, type, sK61: (term > $o)).
% 13.65/2.31 thf(func_def_200, type, sK62: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_201, type, sK63: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_202, type, sK64: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_203, type, sK65: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_204, type, sK66: ((term > $o) > term > term)).
% 13.65/2.31 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_206, type, sK68: ((term > $o) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_208, type, sK70: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_209, type, sK71: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_210, type, sK72: term).
% 13.65/2.31 thf(func_def_211, type, sK73: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_212, type, sK74: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_213, type, sK75: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_214, type, sK76: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_215, type, sK77: (term > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_216, type, sK78: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_217, type, sK79: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_218, type, sK80: ((term > $o) > subst > term)).
% 13.65/2.31 thf(func_def_219, type, sK81: subst).
% 13.65/2.31 thf(func_def_220, type, sK82: (term > $o)).
% 13.65/2.31 thf(func_def_221, type, sK83: term).
% 13.65/2.31 thf(func_def_222, type, sK84: (term > term)).
% 13.65/2.31 thf(func_def_223, type, sK85: term).
% 13.65/2.31 thf(func_def_224, type, sK86: term).
% 13.65/2.31 thf(func_def_225, type, sK87: (term > $o)).
% 13.65/2.31 thf(func_def_226, type, sK88: (term > term)).
% 13.65/2.31 thf(func_def_227, type, sK89: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_228, type, sK90: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_229, type, sK91: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_230, type, sK92: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_231, type, sK93: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_232, type, sK94: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_233, type, sK95: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_234, type, sK96: term).
% 13.65/2.31 thf(func_def_235, type, sK97: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_236, type, sK98: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_237, type, sK99: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_238, type, sK100: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_240, type, sK102: (term > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_241, type, sK103: term).
% 13.65/2.31 thf(func_def_242, type, sK104: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_243, type, sK105: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_244, type, sK106: ((subst > term > term) > term > term)).
% 13.65/2.31 thf(func_def_245, type, sK107: ((subst > term > term) > term > subst)).
% 13.65/2.31 thf(func_def_246, type, sK108: ((subst > term > term) > term > subst)).
% 13.65/2.31 thf(func_def_247, type, sK109: ((subst > term > term) > term > subst)).
% 13.65/2.31 thf(func_def_248, type, sK110: ((subst > term > term) > term > term)).
% 13.65/2.31 thf(func_def_249, type, sK111: ((subst > term > term) > term > subst)).
% 13.65/2.31 thf(func_def_250, type, sK112: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_251, type, sK113: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_252, type, sK114: ((subst > term > subst > $o) > term > term)).
% 13.65/2.31 thf(func_def_253, type, sK115: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_254, type, sK116: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_255, type, sK117: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_256, type, sK118: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_261, type, sK123: term).
% 13.65/2.31 thf(func_def_262, type, sK124: term).
% 13.65/2.31 thf(func_def_263, type, sK125: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_264, type, sK126: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_265, type, sK127: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_266, type, sK128: (term > $o)).
% 13.65/2.31 thf(func_def_267, type, sK129: term).
% 13.65/2.31 thf(func_def_268, type, sK130: (term > term)).
% 13.65/2.31 thf(func_def_269, type, sK131: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_270, type, sK132: term).
% 13.65/2.31 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_273, type, sK135: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_274, type, sK136: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_275, type, sK137: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_276, type, sK138: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_277, type, sK139: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_278, type, sK140: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_282, type, sK144: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_284, type, sK146: ((subst > term > subst > $o) > term > term)).
% 13.65/2.31 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_288, type, sK150: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_289, type, sK151: term).
% 13.65/2.31 thf(func_def_290, type, sK152: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_291, type, sK153: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_293, type, sK155: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_294, type, sK156: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_295, type, sK157: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_296, type, sK158: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_297, type, sK159: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_298, type, sK160: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_299, type, sK161: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_300, type, sK162: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_301, type, sK163: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_302, type, sK164: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_303, type, sK165: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_304, type, sK166: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_305, type, sK167: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_306, type, sK168: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_307, type, sK169: term).
% 13.65/2.31 thf(func_def_308, type, sK170: term).
% 13.65/2.31 thf(func_def_309, type, sK171: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_319, type, sK181: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_320, type, sK182: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_321, type, sK183: (term > $o)).
% 13.65/2.31 thf(func_def_322, type, sK184: term).
% 13.65/2.31 thf(func_def_323, type, sK185: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_324, type, sK186: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_325, type, sK187: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_327, type, sK189: ((term > $o) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_328, type, sK190: (term > (term > $o) > term)).
% 13.65/2.31 thf(func_def_329, type, sK191: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_330, type, sK192: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_331, type, sK193: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_332, type, sK194: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_333, type, sK195: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_334, type, sK196: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_335, type, sK197: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_336, type, sK198: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_337, type, sK199: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_338, type, sK200: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_339, type, sK201: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_340, type, sK202: (term > $o)).
% 13.65/2.31 thf(func_def_341, type, sK203: term).
% 13.65/2.31 thf(func_def_342, type, sK204: term).
% 13.65/2.31 thf(func_def_343, type, sK205: subst).
% 13.65/2.31 thf(func_def_344, type, sK206: term).
% 13.65/2.31 thf(func_def_345, type, sK207: subst).
% 13.65/2.31 thf(func_def_346, type, sK208: subst).
% 13.65/2.31 thf(func_def_347, type, sK209: term).
% 13.65/2.31 thf(func_def_348, type, sK210: (term > $o)).
% 13.65/2.31 thf(func_def_349, type, sK211: subst).
% 13.65/2.31 thf(func_def_350, type, sK212: (term > term)).
% 13.65/2.31 thf(func_def_351, type, sK213: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_352, type, sK214: (subst > (term > $o) > term)).
% 13.65/2.31 thf(func_def_353, type, sK215: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_354, type, sK216: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_355, type, sK217: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_356, type, sK218: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_357, type, sK219: term).
% 13.65/2.31 thf(func_def_358, type, sK220: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_359, type, sK221: ((subst > term > subst > $o) > term > $o)).
% 13.65/2.31 thf(func_def_360, type, sK222: term).
% 13.65/2.31 thf(func_def_361, type, sK223: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_362, type, sK224: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_363, type, sK225: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_364, type, sK226: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_365, type, sK227: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_366, type, sK228: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_367, type, sK229: (term > $o)).
% 13.65/2.31 thf(func_def_368, type, sK230: term).
% 13.65/2.31 thf(func_def_369, type, sK231: (term > term)).
% 13.65/2.31 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_371, type, sK233: ((term > $o) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_372, type, sK234: (term > (term > $o) > term)).
% 13.65/2.31 thf(func_def_373, type, sK235: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_374, type, sK236: (term > $o)).
% 13.65/2.31 thf(func_def_375, type, sK237: term).
% 13.65/2.31 thf(func_def_376, type, sK238: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_377, type, sK239: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_378, type, sK240: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_379, type, sK241: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_380, type, sK242: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_381, type, sK243: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_382, type, sK244: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_383, type, sK245: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_385, type, sK247: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_386, type, sK248: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_387, type, sK249: term).
% 13.65/2.31 thf(func_def_388, type, sK250: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_389, type, sK251: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_390, type, sK252: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_397, type, sK259: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_398, type, sK260: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_399, type, sK261: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_400, type, sK262: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_401, type, sK263: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_404, type, sK266: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_405, type, sK267: (subst > term > term)).
% 13.65/2.31 thf(func_def_406, type, sK268: subst).
% 13.65/2.31 thf(func_def_407, type, sK269: (subst > term > term)).
% 13.65/2.31 thf(func_def_408, type, sK270: term).
% 13.65/2.31 thf(func_def_409, type, sK271: term).
% 13.65/2.31 thf(func_def_410, type, sK272: term).
% 13.65/2.31 thf(func_def_411, type, sK273: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_412, type, sK274: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_413, type, sK275: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_414, type, sK276: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_415, type, sK277: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_416, type, sK278: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_417, type, sK279: subst).
% 13.65/2.31 thf(func_def_418, type, sK280: term).
% 13.65/2.31 thf(func_def_419, type, sK281: term).
% 13.65/2.31 thf(func_def_420, type, sK282: subst).
% 13.65/2.31 thf(func_def_421, type, sK283: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_422, type, sK284: term).
% 13.65/2.31 thf(func_def_423, type, sK285: (term > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_425, type, sK287: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_427, type, sK289: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_428, type, sK290: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_429, type, sK291: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_430, type, sK292: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_431, type, sK293: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_432, type, sK294: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_433, type, sK295: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_434, type, sK296: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_435, type, sK297: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_437, type, sK299: term).
% 13.65/2.31 thf(func_def_438, type, sK300: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_439, type, sK301: (term > $o)).
% 13.65/2.31 thf(func_def_440, type, sK302: term).
% 13.65/2.31 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_443, type, sK305: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_444, type, sK306: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_445, type, sK307: ((term > $o) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_446, type, sK308: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_447, type, sK309: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_449, type, sK311: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_450, type, sK312: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_451, type, sK313: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_452, type, sK314: term).
% 13.65/2.31 thf(func_def_453, type, sK315: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_454, type, sK316: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_455, type, sK317: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_456, type, sK318: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_457, type, sK319: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_458, type, sK320: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > term > term)).
% 13.65/2.31 thf(func_def_460, type, sK322: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_461, type, sK323: term).
% 13.65/2.31 thf(func_def_462, type, sK324: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_463, type, sK325: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_464, type, sK326: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_465, type, sK327: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_466, type, sK328: term).
% 13.65/2.31 thf(func_def_467, type, sK329: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_468, type, sK330: (term > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_469, type, sK331: (term > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_471, type, sK333: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_472, type, sK334: term).
% 13.65/2.31 thf(func_def_473, type, sK335: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_474, type, sK336: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_475, type, sK337: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_476, type, sK338: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_477, type, sK339: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_478, type, sK340: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_479, type, sK341: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_480, type, sK342: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_481, type, sK343: ((subst > term > subst > $o) > term > $o)).
% 13.65/2.31 thf(func_def_482, type, sK344: (term > $o)).
% 13.65/2.31 thf(func_def_483, type, sK345: term).
% 13.65/2.31 thf(func_def_484, type, sK346: (term > term)).
% 13.65/2.31 thf(func_def_485, type, sK347: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_486, type, sK348: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_487, type, sK349: term).
% 13.65/2.31 thf(func_def_488, type, sK350: (term > (term > $o) > term)).
% 13.65/2.31 thf(func_def_489, type, sK351: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_490, type, sK352: ((term > $o) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_491, type, sK353: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_492, type, sK354: (term > $o)).
% 13.65/2.31 thf(func_def_493, type, sK355: term).
% 13.65/2.31 thf(func_def_494, type, sK356: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_495, type, sK357: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_496, type, sK358: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_497, type, sK359: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_498, type, sK360: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_499, type, sK361: term).
% 13.65/2.31 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_503, type, sK365: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_509, type, sK371: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_510, type, sK372: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_513, type, sK375: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_514, type, sK376: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_515, type, sK377: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_516, type, sK378: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_518, type, sK380: term).
% 13.65/2.31 thf(func_def_519, type, sK381: (term > $o)).
% 13.65/2.31 thf(func_def_520, type, sK382: subst).
% 13.65/2.31 thf(func_def_521, type, sK383: (term > term)).
% 13.65/2.31 thf(func_def_522, type, sK384: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_523, type, sK385: (subst > (term > $o) > term)).
% 13.65/2.31 thf(func_def_524, type, sK386: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_525, type, sK387: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_526, type, sK388: term).
% 13.65/2.31 thf(func_def_527, type, sK389: (term > $o)).
% 13.65/2.31 thf(func_def_528, type, sK390: (term > term)).
% 13.65/2.31 thf(func_def_529, type, sK391: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_530, type, sK392: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_531, type, sK393: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_532, type, sK394: ((term > $o) > term)).
% 13.65/2.31 thf(func_def_533, type, sK395: (term > $o)).
% 13.65/2.31 thf(func_def_534, type, sK396: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_535, type, sK397: term).
% 13.65/2.31 thf(func_def_536, type, sK398: term).
% 13.65/2.31 thf(func_def_537, type, sK399: (term > (term > $o) > term)).
% 13.65/2.31 thf(func_def_538, type, sK400: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_539, type, sK401: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_541, type, sK403: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_544, type, sK406: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > (term > $o) > term)).
% 13.65/2.31 thf(func_def_547, type, sK409: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_548, type, sK410: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_549, type, sK411: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_550, type, sK412: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_552, type, sK414: (term > $o)).
% 13.65/2.31 thf(func_def_553, type, sK415: term).
% 13.65/2.31 thf(func_def_554, type, sK416: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_555, type, sK417: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_556, type, sK418: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_557, type, sK419: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_558, type, sK420: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_559, type, sK421: (term > subst > term > term)).
% 13.65/2.31 thf(func_def_560, type, sK422: (term > (term > $o) > term)).
% 13.65/2.31 thf(func_def_561, type, sK423: ((subst > term > subst > $o) > (term > $o) > term)).
% 13.65/2.31 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.31 thf(func_def_563, type, sK425: term).
% 13.65/2.31 thf(func_def_564, type, sK426: term).
% 13.65/2.31 thf(func_def_565, type, sK427: ((subst > term > term) > term)).
% 13.65/2.31 thf(func_def_566, type, sK428: ((subst > term > term) > subst)).
% 13.65/2.31 thf(func_def_567, type, sK429: term).
% 13.65/2.31 thf(func_def_568, type, sK430: (subst > term > subst > $o)).
% 13.65/2.31 thf(func_def_569, type, sK431: term).
% 13.65/2.31 thf(func_def_570, type, sK432: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_571, type, sK433: ((subst > term > subst > $o) > term)).
% 13.65/2.31 thf(func_def_572, type, sK434: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_573, type, sK435: ((subst > term > subst > $o) > subst)).
% 13.65/2.31 thf(func_def_574, type, sK436: ((subst > term > subst > $o) > subst)).
% 13.65/2.32 thf(func_def_575, type, sK437: ((subst > term > subst > $o) > term)).
% 13.65/2.32 thf(func_def_576, type, sK438: ((subst > term > subst > $o) > subst)).
% 13.65/2.32 thf(func_def_577, type, sK439: ((subst > term > subst > $o) > subst)).
% 13.65/2.32 thf(func_def_578, type, sK440: ((subst > term > subst > $o) > term > term)).
% 13.65/2.32 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.32 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > term > term)).
% 13.65/2.32 thf(func_def_581, type, sK443: term).
% 13.65/2.32 thf(func_def_582, type, sK444: (subst > term > subst > $o)).
% 13.65/2.32 thf(func_def_583, type, sK445: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_584, type, sK446: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_585, type, sK447: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_586, type, sK448: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_587, type, sK449: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_588, type, sK450: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_589, type, sK451: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_590, type, sK452: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 13.65/2.32 thf(func_def_591, type, sK453: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.32 thf(func_def_592, type, sK454: term).
% 13.65/2.32 thf(func_def_593, type, sK455: term).
% 13.65/2.32 thf(func_def_594, type, sK456: term).
% 13.65/2.32 thf(func_def_595, type, sK457: term).
% 13.65/2.32 thf(func_def_596, type, sK458: term).
% 13.65/2.32 thf(func_def_597, type, sK459: term).
% 13.65/2.32 thf(func_def_598, type, sK460: term).
% 13.65/2.32 thf(func_def_599, type, sK461: term).
% 13.65/2.32 thf(func_def_600, type, sK462: term).
% 13.65/2.32 thf(func_def_601, type, sK463: term).
% 13.65/2.32 thf(func_def_602, type, sK464: subst).
% 13.65/2.32 thf(func_def_603, type, sK465: subst).
% 13.65/2.32 thf(func_def_604, type, sK466: subst).
% 13.65/2.32 thf(func_def_605, type, sK467: subst).
% 13.65/2.32 thf(func_def_606, type, sK468: term).
% 13.65/2.32 thf(func_def_607, type, sK469: (subst > term > subst > $o)).
% 13.65/2.32 thf(func_def_608, type, sK470: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_609, type, sK471: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_610, type, sK472: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_611, type, sK473: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_612, type, sK474: ((subst > term > subst > $o) > subst > term > term)).
% 13.65/2.32 thf(func_def_613, type, sK475: term).
% 13.65/2.32 thf(func_def_614, type, sK476: term).
% 13.65/2.32 thf(func_def_615, type, sK477: term).
% 13.65/2.32 thf(func_def_616, type, sK478: term).
% 13.65/2.32 thf(func_def_617, type, sK479: term).
% 13.65/2.32 thf(func_def_618, type, sK480: term).
% 13.65/2.32 thf(func_def_619, type, sK481: term).
% 13.65/2.32 thf(func_def_620, type, sK482: term).
% 13.65/2.32 thf(func_def_621, type, sK483: ((term > $o) > subst > term > term > $o)).
% 13.65/2.32 thf(func_def_622, type, sK484: term).
% 13.65/2.32 thf(func_def_623, type, sK485: subst).
% 13.65/2.32 thf(func_def_624, type, sK486: (term > $o)).
% 13.65/2.32 thf(func_def_625, type, sK487: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_626, type, sK488: term).
% 13.65/2.32 thf(func_def_627, type, sK489: (term > subst > term > term)).
% 13.65/2.32 thf(func_def_628, type, sK490: term).
% 13.65/2.32 thf(func_def_629, type, sK491: term).
% 13.65/2.32 thf(func_def_630, type, sK492: (term > $o)).
% 13.65/2.32 thf(func_def_631, type, sK493: (term > $o)).
% 13.65/2.32 thf(func_def_632, type, sK494: subst).
% 13.65/2.32 thf(func_def_633, type, sK495: term).
% 13.65/2.32 thf(func_def_634, type, sK496: term).
% 13.65/2.32 thf(func_def_635, type, sK497: (subst > term > subst > $o)).
% 13.65/2.32 thf(func_def_636, type, sK498: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_637, type, sK499: ((subst > term > subst > $o) > term > $o)).
% 13.65/2.32 thf(func_def_638, type, sK500: subst).
% 13.65/2.32 thf(func_def_639, type, sK501: term).
% 13.65/2.32 thf(func_def_640, type, sK502: (term > $o)).
% 13.65/2.32 thf(func_def_641, type, sK503: subst).
% 13.65/2.32 thf(func_def_642, type, sK504: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_643, type, sK505: (subst > (term > $o) > term > term > $o)).
% 13.65/2.32 thf(func_def_644, type, sK506: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_645, type, sK507: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_646, type, sK508: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_647, type, sK509: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_648, type, sK510: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_649, type, sK511: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_650, type, sK512: subst).
% 13.65/2.32 thf(func_def_651, type, sK513: term).
% 13.65/2.32 thf(func_def_652, type, sK514: (subst > term > term)).
% 13.65/2.32 thf(func_def_653, type, sK515: (subst > term > term)).
% 13.65/2.32 thf(func_def_654, type, sK516: subst).
% 13.65/2.32 thf(func_def_655, type, sK517: term).
% 13.65/2.32 thf(func_def_656, type, sK518: term).
% 13.65/2.32 thf(func_def_657, type, sK519: subst).
% 13.65/2.32 thf(func_def_658, type, sK520: term).
% 13.65/2.32 thf(func_def_659, type, sK521: term).
% 13.65/2.32 thf(func_def_660, type, sK522: (term > $o)).
% 13.65/2.32 thf(func_def_661, type, sK523: subst).
% 13.65/2.32 thf(func_def_662, type, sK524: (term > $o)).
% 13.65/2.32 thf(func_def_663, type, sK525: term).
% 13.65/2.32 thf(func_def_664, type, sK526: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_665, type, sK527: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_666, type, sK528: (term > subst > term > term)).
% 13.65/2.32 thf(func_def_667, type, sK529: subst).
% 13.65/2.32 thf(func_def_668, type, sK530: subst).
% 13.65/2.32 thf(func_def_669, type, sK531: ((term > $o) > term > subst > (term > $o) > term)).
% 13.65/2.32 thf(func_def_670, type, sK532: term).
% 13.65/2.32 thf(func_def_671, type, sK533: subst).
% 13.65/2.32 thf(func_def_672, type, sK534: (term > $o)).
% 13.65/2.32 thf(func_def_673, type, sK535: subst).
% 13.65/2.32 thf(func_def_674, type, sK536: term).
% 13.65/2.32 thf(func_def_675, type, sK537: (term > $o)).
% 13.65/2.32 thf(func_def_676, type, sK538: subst).
% 13.65/2.32 thf(func_def_677, type, sK539: term).
% 13.65/2.32 thf(func_def_678, type, sK540: term).
% 13.65/2.32 thf(func_def_679, type, sK541: term).
% 13.65/2.32 thf(func_def_680, type, sK542: term).
% 13.65/2.32 thf(func_def_681, type, sK543: term).
% 13.65/2.32 thf(func_def_682, type, sK544: term).
% 13.65/2.32 thf(func_def_683, type, sK545: term).
% 13.65/2.32 thf(func_def_684, type, sK546: term).
% 13.65/2.32 thf(func_def_685, type, sK547: term).
% 13.65/2.32 thf(func_def_686, type, sK548: term).
% 13.65/2.32 thf(func_def_687, type, sK549: term).
% 13.65/2.32 thf(func_def_688, type, sK550: (term > d_term)).
% 13.65/2.32 thf(func_def_689, type, sK551: term).
% 13.65/2.32 thf(func_def_690, type, sK552: term).
% 13.65/2.32 thf(func_def_691, type, sK553: term).
% 13.65/2.32 thf(func_def_692, type, sK554: term).
% 13.65/2.32 thf(func_def_693, type, sK555: (term > subst > term > term)).
% 13.65/2.32 thf(func_def_694, type, sK556: term).
% 13.65/2.32 thf(func_def_695, type, sK557: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_696, type, sK558: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_697, type, sK559: subst).
% 13.65/2.32 thf(func_def_698, type, sK560: term).
% 13.65/2.32 thf(func_def_699, type, sK561: (term > $o)).
% 13.65/2.32 thf(func_def_700, type, sK562: (term > $o)).
% 13.65/2.32 thf(func_def_701, type, sK563: subst).
% 13.65/2.32 thf(func_def_702, type, sK564: (subst > (term > $o) > (term > $o) > term > term)).
% 13.65/2.32 thf(func_def_703, type, sK565: term).
% 13.65/2.32 thf(func_def_704, type, sK566: (term > $o)).
% 13.65/2.32 thf(func_def_705, type, sK567: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_706, type, sK568: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_707, type, sK569: subst).
% 13.65/2.32 thf(func_def_708, type, sK570: term).
% 13.65/2.32 thf(func_def_709, type, sK571: term).
% 13.65/2.32 thf(func_def_710, type, sK572: term).
% 13.65/2.32 thf(func_def_711, type, sK573: (subst > d_subst)).
% 13.65/2.32 thf(func_def_712, type, sK574: subst).
% 13.65/2.32 thf(func_def_713, type, sK575: term).
% 13.65/2.32 thf(func_def_714, type, sK576: term).
% 13.65/2.32 thf(func_def_715, type, sK577: term).
% 13.65/2.32 thf(func_def_716, type, sK578: term).
% 13.65/2.32 thf(func_def_717, type, sK579: term).
% 13.65/2.32 thf(func_def_718, type, sK580: term).
% 13.65/2.32 thf(func_def_719, type, sK581: (term > subst > term > term)).
% 13.65/2.32 thf(func_def_720, type, sK582: term).
% 13.65/2.32 thf(func_def_721, type, sK583: term).
% 13.65/2.32 thf(func_def_722, type, sK584: (subst > term > term)).
% 13.65/2.32 thf(func_def_723, type, sK585: ((subst > term > term) > term)).
% 13.65/2.32 thf(func_def_724, type, sK586: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_725, type, sK587: ((subst > term > term) > subst)).
% 13.65/2.32 thf(func_def_726, type, sK588: (subst > term > subst > $o)).
% 13.65/2.32 thf(func_def_727, type, sK589: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_728, type, sK590: ((subst > term > subst > $o) > term > $o)).
% 13.65/2.32 thf(func_def_729, type, vNOT: ($o > $o)).
% 13.65/2.32 thf(func_def_730, type, sK591: (subst > term > subst > $o)).
% 13.65/2.32 thf(func_def_731, type, sK592: ((term > $o) > term)).
% 13.65/2.32 thf(func_def_732, type, sK593: ((subst > term > subst > $o) > term > $o)).
% 13.65/2.32 thf(f1,axiom,(
% 13.65/2.32 (hoasinduction_lem3aaa <=> ! [X10 : (subst > term > subst > $o),X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & hoasinduction_lem3a_gthm & pushprop_lem3v2 & (id = ((d2subst @ d_id))) & (! [X13 : term,X19 : term,X20 : term,X15 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & (pushprop_lem1v2 <=> ! [X10 : (term > $o),X14 : subst,X11 : (term > $o),X13 : term] : (~(X10 @ X13) | (X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))) <=> induction2) & (! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction) & ~(var @ (d2term @ d_one)) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (apinj2 <=> ! [X19 : term,X15 : term,X13 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & (hoasinduction_lem2 <=> ! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : (~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id))) & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoasinduction_lem3v2_gthm & (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29))) <=> hoasinduction_lem3v2a) & pushprop_lem1v2_gthm & pushprop_lthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & hoasinduction_lem2_gthm & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & pushprop_lem1_gthm & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X13 : term,X14 : subst,X10 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13)))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & hoasinduction_lem1 & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)))))) & (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & axmap & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lthm_orig & (sh = ((d2subst @ d_id))) & ((! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) <=> substmonoid) & pushprop_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)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))))))) & pushprop_lem2v2_lthm & (hoasinduction_lem2v2 <=> ! [X45 : term,X11 : (term > $o),X10 : (subst > term > subst > $o),X44 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & hoasinduction_lem1_lthm & lamnotvar & pushprop_lem0_gthm & hoasinduction_lem1_gthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15))))) & hoasapnotvar_lthm & (hoasinduction_lthm <=> (! [X22 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22)) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~(X10 @ id @ X23 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))))))) & hoaslamnotvar & (induction2lem <=> ! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)))) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X33 : term,X18 : (subst > term > term),X32 : subst,X31 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem1v2_gthm & ! [X5 : d_subst] : (X5 = d_id) & (apinj1 <=> ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & hoasinduction_lem3_gthm & (! [X32 : subst,X33 : term,X31 : (subst > term > term),X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))) <=> hoaslaminj) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & hoasinduction_gthm & ~lamnotap & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [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))))) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))) <=> hoasinduction_lem3_lthm) & induction2_gthm & axapp & (pushprop_lem1 <=> ! [X10 : (term > $o),X13 : term,X26 : (term > $o),X14 : subst,X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & hoaslamnotap_lthm & hoasinduction_lem2v2_gthm & (hoasapinj2 <=> ! [X20 : term,X13 : term,X19 : term,X15 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & hoasapnotvar & axabs & (hoasinduction_lem3aa <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & hoasapnotvar_gthm & induction2lem_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction_lem3) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)))) <=> induction2_lthm) & hoaslamnotvar_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & pushprop_lem2v2_gthm & (laminj <=> ! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & axvarshift & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X26 : (term > $o),X10 : (term > $o),X14 : subst,X13 : term,X15 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)))) <=> pushprop_lem1_lthm) & axclos & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & axassoc & hoasinduction_lem2_lthm & (! [X13 : term,X10 : (term > $o),X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & hoasapinj2_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoasinduction_lem1v2 & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X21)) => ! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))))))) <=> induction2lem_lthm) & ulamvarsh & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop & (! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & apnotvar & hoasapinj1_gthm & (! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_lem3a) & hoaslaminj_gthm & substmonoid_gthm & ! [X1 : d_term] : (X1 = d_one) & pushprop_lem2v2 & ~ulamvar1 & hoasinduction_lem3b_gthm & ulamvarind & (! [X18 : (subst > term > term),X47 : term,X46 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) <=> hoaslamnotap) & ((! [X15 : term,X13 : term,X19 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj2_lthm) & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X13 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))))) & (hoasinduction_lem3v2 <=> ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X48)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & hoaslamnotap_gthm & termmset_gthm & pushprop_lem3v2_lthm & (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) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))))) & (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15))) <=> induction) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ((^[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) & (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & hoaslamnotvar_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id)))),
% 13.65/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 13.65/2.32 thf(f2,conjecture,(
% 13.65/2.32 (hoasinduction_lem0 = ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : (hoasinduction_p_and_p_prime @ X0 @ X1))),
% 13.65/2.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0)).
% 13.65/2.32 thf(f3,negated_conjecture,(
% 13.65/2.32 ~ (hoasinduction_lem0 = ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : (hoasinduction_p_and_p_prime @ X0 @ X1))),
% 13.65/2.32 inference(negated_conjecture,[status(cth)],[f2])).
% 13.65/2.32 thf(f4,plain,(
% 13.65/2.32 (hoasinduction_lem3aaa <=> ! [X0 : (subst > term > subst > $o),X1 : term] : ((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id) | ~ ! [X2 : (subst > term > term),X3 : term] : (~ ! [X4 : term] : (~(X0 @ id @ X4 @ id) | (X0 @ id @ (X2 @ id @ X4) @ id)) | ~ ! [X5 : term,X6 : subst,X7 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) | (X0 @ id @ (lam @ (X2 @ sh @ one)) @ id) | ~ ! [X8 : term,X9 : subst,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9)))) | ~ ! [X11 : term] : ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id) | ~(X0 @ id @ X11 @ id)))) & hoasinduction_lem3a_gthm & pushprop_lem3v2 & (id = ((d2subst @ d_id))) & (! [X12 : term,X13 : term,X14 : term,X15 : term] : ((X12 = X15) | (((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13)))) <=> hoasapinj1) & (pushprop_lem1v2 <=> ! [X16 : (term > $o),X17 : subst,X18 : (term > $o),X19 : term] : (~(X16 @ X19) | (X18 @ one) | ~ ! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))))) & (! [X21 : (term > $o),X22 : term] : (~ ! [X23 : term,X24 : term] : ((X21 @ (ap @ X23 @ X24)) | ~(X21 @ X24) | ~(X21 @ X23)) | ~ ! [X25 : term] : (~ ! [X26 : term] : (~(X21 @ X26) | (X21 @ (sub @ X25 @ (push @ X26 @ id)))) | (X21 @ (lam @ X25))) | (X21 @ X22) | ~ ! [X27 : term] : ((X21 @ X27) | ~(var @ X27))) <=> induction2) & (! [X28 : (subst > term > subst > $o),X29 : term] : (~ ! [X30 : (subst > term > term)] : (~ ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32))) | ~ ! [X34 : term] : ((X28 @ id @ (X30 @ id @ X34) @ id) | ~(X28 @ id @ X34 @ id)) | (X28 @ id @ (lam @ (X30 @ sh @ one)) @ id)) | (X28 @ id @ X29 @ id) | ~ ! [X35 : term] : ((X28 @ id @ X35 @ id) | ~(var @ (sub @ X35 @ id))) | ~ ! [X36 : term,X37 : subst,X38 : subst,X39 : subst] : ((X28 @ X38 @ X36 @ (comp @ X39 @ X37)) | ~(X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37)) | ~ ! [X40 : term,X41 : term] : ((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id) | ~(X28 @ id @ X41 @ id) | ~(X28 @ id @ X40 @ id)) | ~ ! [X42 : subst,X43 : subst,X44 : term,X45 : subst] : (~(X28 @ X43 @ X44 @ (comp @ X45 @ X42)) | (X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42))) <=> hoasinduction) & ~(var @ (d2term @ d_one)) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (apinj2 <=> ! [X48 : term,X49 : term,X50 : term,X51 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51))) & (hoasinduction_lem2 <=> ! [X52 : term,X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)) | ~(X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)) | (X53 @ id @ (ap @ X54 @ X52) @ id) | ~(X53 @ id @ X54 @ id) | ~ ! [X59 : term,X60 : term] : ((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id) | ~(X53 @ id @ X59 @ id) | ~(X53 @ id @ X60 @ id)) | ~ ! [X61 : subst,X62 : term,X63 : subst,X64 : subst] : (~(X53 @ X61 @ X62 @ (comp @ X64 @ X63)) | (X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) | ~(X53 @ id @ X52 @ id))) & (hoasinduction_lem3aa_lthm <=> ! [X65 : (subst > term > subst > $o),X66 : term] : (~ ! [X67 : (subst > term > term)] : (~ ! [X68 : term] : (~(X65 @ id @ X68 @ id) | (X65 @ id @ (X67 @ id @ X68) @ id)) | ~ ! [X69 : subst,X70 : subst,X71 : term] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70)))) | (X65 @ id @ (lam @ (X67 @ sh @ one)) @ id)) | (X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id) | ~ ! [X72 : term] : ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id) | ~(X65 @ id @ X72 @ id)))) & (axidr <=> ! [X73 : subst] : (((comp @ X73 @ id)) = X73)) & hoasinduction_lem3v2_gthm & (! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (~ ! [X77 : term] : ((X76 @ (sub @ X75 @ (push @ X77 @ id))) | ~(X76 @ X77)) | ~ ! [X78 : term] : (((X74 @ id @ X78 @ id)) = ((X76 @ X78))) | ~ ! [X79 : (subst > term > term)] : ((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id) | ~ ! [X80 : subst,X81 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81))) | ~ ! [X83 : term] : (~(X74 @ id @ X83 @ id) | (X74 @ id @ (X79 @ id @ X83) @ id))) | (X76 @ (lam @ X75))) <=> hoasinduction_lem3v2a) & pushprop_lem1v2_gthm & pushprop_lthm & ((! [X84 : subst] : (((comp @ id @ X84)) = X84) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87)))) <=> substmonoid_lthm) & hoasinduction_lem2_gthm & (hoasinduction_no_psi_cond <=> ! [X88 : (subst > term > subst > $o),X89 : term] : ((X88 @ id @ X89 @ id) | ~ ! [X90 : term,X91 : term] : (~(X88 @ id @ X90 @ id) | ~(X88 @ id @ X91 @ id) | (X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) | ~ ! [X92 : (subst > term > term)] : ((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id) | ~ ! [X93 : subst,X94 : subst,X95 : term] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) | ~ ! [X96 : term] : (~(X88 @ id @ X96 @ id) | (X88 @ id @ (X92 @ id @ X96) @ id))))) & pushprop_lem1_gthm & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> axvarid) & (pushprop_lem1v2_lthm <=> (! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => ! [X100 : (term > $o),X101 : term,X102 : subst,X103 : (term > $o)] : (~ ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | (X100 @ one) | ~(X103 @ X101)))) & (termmset_lthm <=> (! [X105 : term] : (((sub @ X105 @ id)) = X105) => ! [X106 : term] : (((sub @ X106 @ id)) = X106))) & hoasinduction_lem1 & ((^[X107 : (subst > term > subst > $o), X108 : (term > $o)] : (! [X109 : term] : (((X107 @ id @ X109 @ id)) = ((X108 @ X109))))) = hoasinduction_p_and_p_prime) & (! [X110 : term] : ~ ! [X111 : (subst > term > term)] : (((sub @ X110 @ (push @ one @ sh))) != ((X111 @ sh @ one))) <=> hoasinduction_lem3b) & ! [X112 : d_term,X113 : d_term] : ((((d2term @ X112)) = ((d2term @ X113))) => (X112 = X113)) & (hoasinduction_lem3v2a_lthm <=> (! [X114 : term] : ~ ! [X115 : (subst > term > term)] : ~ ! [X116 : subst,X117 : term] : (((sub @ X114 @ (push @ X117 @ X116))) = ((X115 @ X116 @ X117))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => ! [X119 : term,X120 : (subst > term > subst > $o),X121 : (term > $o)] : (~ ! [X122 : term] : ((X121 @ (sub @ X119 @ (push @ X122 @ id))) | ~(X121 @ X122)) | ~ ! [X123 : term] : (((X120 @ id @ X123 @ id)) = ((X121 @ X123))) | ~ ! [X124 : (subst > term > term)] : (~ ! [X125 : subst,X126 : subst,X127 : term] : (((X124 @ (comp @ X126 @ X125) @ (sub @ X127 @ X125))) = ((sub @ (X124 @ X126 @ X127) @ X125))) | ~ ! [X128 : term] : ((X120 @ id @ (X124 @ id @ X128) @ id) | ~(X120 @ id @ X128 @ id)) | (X120 @ id @ (lam @ (X124 @ sh @ one)) @ id)) | (X121 @ (lam @ X119)))))) & (! [X129 : term,X130 : subst] : (((sub @ one @ (push @ X129 @ X130))) = X129) <=> axvarcons) & axmap & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lthm_orig & (sh = ((d2subst @ d_id))) & ((! [X131 : subst] : (((comp @ X131 @ id)) = X131) & ! [X132 : subst] : (((comp @ id @ X132)) = X132)) <=> substmonoid) & pushprop_gthm & (hoasinduction_lthm_3 <=> (! [X133 : (subst > term > subst > $o)] : ~ ! [X134 : (term > $o)] : ~ ! [X135 : term] : (((X134 @ X135)) = ((X133 @ id @ X135 @ id))) => (! [X136 : term,X137 : (term > $o)] : (~ ! [X138 : term] : ((X137 @ X138) | ~(var @ X138)) | ~ ! [X139 : term,X140 : term] : (~(X137 @ X140) | (X137 @ (ap @ X140 @ X139)) | ~(X137 @ X139)) | (X137 @ X136) | ~ ! [X141 : term] : (~ ! [X142 : term] : ((X137 @ (sub @ X141 @ (push @ X142 @ id))) | ~(X137 @ X142)) | (X137 @ (lam @ X141)))) => (! [X143 : term] : (((sub @ X143 @ id)) = X143) => (! [X144 : term,X145 : (subst > term > subst > $o),X146 : (term > $o)] : (~ ! [X147 : (subst > term > term)] : (~ ! [X148 : subst,X149 : subst,X150 : term] : (((sub @ (X147 @ X148 @ X150) @ X149)) = ((X147 @ (comp @ X148 @ X149) @ (sub @ X150 @ X149)))) | (X145 @ id @ (lam @ (X147 @ sh @ one)) @ id) | ~ ! [X151 : term] : ((X145 @ id @ (X147 @ id @ X151) @ id) | ~(X145 @ id @ X151 @ id))) | (X146 @ (lam @ X144)) | ~ ! [X152 : term] : (~(X146 @ X152) | (X146 @ (sub @ X144 @ (push @ X152 @ id)))) | ~ ! [X153 : term] : (((X145 @ id @ X153 @ id)) = ((X146 @ X153)))) => ! [X154 : (subst > term > subst > $o),X155 : term] : (~ ! [X156 : subst,X157 : subst,X158 : subst,X159 : term] : (~(X154 @ (comp @ X156 @ X158) @ (sub @ X159 @ X158) @ X157) | (X154 @ X156 @ X159 @ (comp @ X158 @ X157))) | ~ ! [X160 : subst,X161 : term,X162 : subst,X163 : subst] : (~(X154 @ X160 @ X161 @ (comp @ X162 @ X163)) | (X154 @ (comp @ X160 @ X162) @ (sub @ X161 @ X162) @ X163)) | ~ ! [X164 : term] : ((X154 @ id @ X164 @ id) | ~(var @ (sub @ X164 @ id))) | (X154 @ id @ X155 @ id) | ~ ! [X165 : (subst > term > term)] : (~ ! [X166 : term] : (~(X154 @ id @ X166 @ id) | (X154 @ id @ (X165 @ id @ X166) @ id)) | ~ ! [X167 : subst,X168 : term,X169 : subst] : (((X165 @ (comp @ X169 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X165 @ X169 @ X168) @ X167))) | (X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) | ~ ! [X170 : term,X171 : term] : (~(X154 @ id @ X170 @ id) | ~(X154 @ id @ X171 @ id) | (X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)))))))) & pushprop_lem2v2_lthm & (hoasinduction_lem2v2 <=> ! [X172 : term,X173 : (term > $o),X174 : (subst > term > subst > $o),X175 : term] : (~ ! [X176 : term] : (((X174 @ id @ X176 @ id)) = ((X173 @ X176))) | ~ ! [X177 : subst,X178 : subst,X179 : term,X180 : subst] : ((X174 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177) @ X180) | ~(X174 @ X178 @ X179 @ (comp @ X177 @ X180))) | ~(X173 @ X175) | (X173 @ (ap @ X175 @ X172)) | ~(X173 @ X172) | ~ ! [X181 : subst,X182 : subst,X183 : term,X184 : subst] : ((X174 @ X184 @ X183 @ (comp @ X182 @ X181)) | ~(X174 @ (comp @ X184 @ X182) @ (sub @ X183 @ X182) @ X181)) | ~ ! [X185 : term,X186 : term] : (~(X174 @ id @ X185 @ id) | (X174 @ id @ (ap @ (sub @ X185 @ id) @ X186) @ id) | ~(X174 @ id @ X186 @ id)))) & hoasinduction_lem1_lthm & lamnotvar & pushprop_lem0_gthm & hoasinduction_lem1_gthm & ((! [X187 : (subst > term > subst > $o)] : ~ ! [X188 : (term > $o)] : ~ ! [X189 : term] : (((X187 @ id @ X189 @ id)) = ((X188 @ X189))) => (! [X190 : (term > $o),X191 : term] : (~ ! [X192 : term] : (~(var @ X192) | (X190 @ X192)) | ~ ! [X193 : term] : ((X190 @ (lam @ X193)) | ~ ! [X194 : term] : ((X190 @ (sub @ X193 @ (push @ X194 @ id))) | ~(X190 @ X194))) | ~ ! [X195 : term,X196 : term] : (~(X190 @ X195) | ~(X190 @ X196) | (X190 @ (ap @ X195 @ X196))) | (X190 @ X191)) => (! [X197 : term] : (((sub @ X197 @ id)) = X197) => (! [X198 : term,X199 : (term > $o),X200 : (subst > term > subst > $o)] : (~ ! [X201 : term] : (((X200 @ id @ X201 @ id)) = ((X199 @ X201))) | ~ ! [X202 : term] : ((X199 @ (sub @ X198 @ (push @ X202 @ id))) | ~(X199 @ X202)) | (X199 @ (lam @ X198)) | ~ ! [X203 : (subst > term > term)] : ((X200 @ id @ (lam @ (X203 @ sh @ one)) @ id) | ~ ! [X204 : term] : (~(X200 @ id @ X204 @ id) | (X200 @ id @ (X203 @ id @ X204) @ id)) | ~ ! [X205 : term,X206 : subst,X207 : subst] : (((X203 @ (comp @ X207 @ X206) @ (sub @ X205 @ X206))) = ((sub @ (X203 @ X207 @ X205) @ X206))))) => ! [X208 : (subst > term > subst > $o),X209 : term] : (~ ! [X210 : (subst > term > term)] : ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id) | ~ ! [X211 : subst,X212 : term,X213 : subst] : (((X210 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211))) = ((sub @ (X210 @ X213 @ X212) @ X211))) | ~ ! [X214 : term] : (~(X208 @ id @ X214 @ id) | (X208 @ id @ (X210 @ id @ X214) @ id))) | ~ ! [X215 : term,X216 : term] : (~(X208 @ id @ X215 @ id) | ~(X208 @ id @ X216 @ id) | (X208 @ id @ (ap @ (sub @ X216 @ id) @ X215) @ id)) | (X208 @ id @ X209 @ id)))))) <=> hoasinduction_no_psi_cond_lthm) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & ((^[X217 : subst, X218 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (hoasinduction_lem3v2_lthm <=> (! [X219 : term] : (((sub @ X219 @ id)) = X219) => ! [X220 : (subst > term > subst > $o),X221 : term,X222 : (term > $o)] : (~ ! [X223 : (subst > term > term)] : (~ ! [X224 : term] : (~(X220 @ id @ X224 @ id) | (X220 @ id @ (X223 @ id @ X224) @ id)) | ~ ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226))) = ((sub @ (X223 @ X225 @ X227) @ X226))) | (X220 @ id @ (lam @ (X223 @ sh @ one)) @ id)) | (X222 @ (lam @ X221)) | ~ ! [X228 : term] : (((X222 @ X228)) = ((X220 @ id @ X228 @ id))) | ~ ! [X229 : subst,X230 : subst,X231 : term,X232 : subst] : ((X220 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232) @ X229) | ~(X220 @ X230 @ X231 @ (comp @ X232 @ X229))) | ~ ! [X233 : subst,X234 : subst,X235 : term,X236 : subst] : (~(X220 @ (comp @ X233 @ X234) @ (sub @ X235 @ X234) @ X236) | (X220 @ X233 @ X235 @ (comp @ X234 @ X236))) | ~ ! [X237 : term] : ((X222 @ (sub @ X221 @ (push @ X237 @ id))) | ~(X222 @ X237))))) & hoasapnotvar_lthm & (hoasinduction_lthm <=> (! [X238 : term,X239 : (term > $o)] : (~ ! [X240 : term,X241 : term] : ((X239 @ (ap @ X241 @ X240)) | ~(X239 @ X241) | ~(X239 @ X240)) | ~ ! [X242 : term] : (~ ! [X243 : term] : ((X239 @ (sub @ X242 @ (push @ X243 @ id))) | ~(X239 @ X243)) | (X239 @ (lam @ X242))) | ~ ! [X244 : term] : (~(var @ X244) | (X239 @ X244)) | (X239 @ X238)) => (! [X245 : (subst > term > subst > $o),X246 : term,X247 : term] : (~(X245 @ id @ X246 @ id) | ~ ! [X248 : term,X249 : term] : (~(X245 @ id @ X248 @ id) | (X245 @ id @ (ap @ (sub @ X249 @ id) @ X248) @ id) | ~(X245 @ id @ X249 @ id)) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : ((X245 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250) @ X253) | ~(X245 @ X252 @ X251 @ (comp @ X250 @ X253))) | (X245 @ id @ (ap @ X246 @ X247) @ id) | ~(X245 @ id @ X247 @ id) | ~ ! [X254 : subst,X255 : term,X256 : subst,X257 : subst] : ((X245 @ X254 @ X255 @ (comp @ X256 @ X257)) | ~(X245 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))) => (! [X258 : term,X259 : (subst > term > subst > $o)] : ((X259 @ id @ (lam @ X258) @ id) | ~ ! [X260 : subst,X261 : subst,X262 : subst,X263 : term] : ((X259 @ (comp @ X262 @ X261) @ (sub @ X263 @ X261) @ X260) | ~(X259 @ X262 @ X263 @ (comp @ X261 @ X260))) | ~ ! [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (~(X259 @ (comp @ X266 @ X265) @ (sub @ X264 @ X265) @ X267) | (X259 @ X266 @ X264 @ (comp @ X265 @ X267))) | ~ ! [X268 : term] : (~(X259 @ id @ X268 @ id) | (X259 @ id @ (sub @ X258 @ (push @ X268 @ id)) @ id)) | ~ ! [X269 : (subst > term > term)] : (~ ! [X270 : subst,X271 : subst,X272 : term] : (((sub @ (X269 @ X270 @ X272) @ X271)) = ((X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271)))) | ~ ! [X273 : term] : (~(X259 @ id @ X273 @ id) | (X259 @ id @ (X269 @ id @ X273) @ id)) | (X259 @ id @ (lam @ (X269 @ sh @ one)) @ id))) => ! [X274 : (subst > term > subst > $o),X275 : term] : (~ ! [X276 : subst,X277 : term,X278 : subst,X279 : subst] : (~(X274 @ X276 @ X277 @ (comp @ X279 @ X278)) | (X274 @ (comp @ X276 @ X279) @ (sub @ X277 @ X279) @ X278)) | ~ ! [X280 : term] : (~(var @ (sub @ X280 @ id)) | (X274 @ id @ X280 @ id)) | (X274 @ id @ X275 @ id) | ~ ! [X281 : (subst > term > term)] : ((X274 @ id @ (lam @ (X281 @ sh @ one)) @ id) | ~ ! [X282 : term] : (~(X274 @ id @ X282 @ id) | (X274 @ id @ (X281 @ id @ X282) @ id)) | ~ ! [X283 : term,X284 : subst,X285 : subst] : (((X281 @ (comp @ X285 @ X284) @ (sub @ X283 @ X284))) = ((sub @ (X281 @ X285 @ X283) @ X284)))) | ~ ! [X286 : subst,X287 : subst,X288 : subst,X289 : term] : (~(X274 @ (comp @ X288 @ X286) @ (sub @ X289 @ X286) @ X287) | (X274 @ X288 @ X289 @ (comp @ X286 @ X287))) | ~ ! [X290 : term,X291 : term] : (~(X274 @ id @ X290 @ id) | ~(X274 @ id @ X291 @ id) | (X274 @ id @ (ap @ (sub @ X291 @ id) @ X290) @ id))))))) & hoaslamnotvar & (induction2lem <=> ! [X292 : subst,X293 : term,X294 : (term > $o)] : (~ ! [X295 : term] : ((X294 @ (lam @ X295)) | ~ ! [X296 : term] : ((X294 @ (sub @ X295 @ (push @ X296 @ id))) | ~(X294 @ X296))) | ~ ! [X297 : term] : (~(var @ X297) | (X294 @ (sub @ X297 @ X292))) | (X294 @ (sub @ X293 @ X292)) | ~ ! [X298 : term,X299 : term] : (~(X294 @ X298) | (X294 @ (ap @ X298 @ X299)) | ~(X294 @ X299)))) & (hoaslaminj_lthm <=> (! [X300 : term,X301 : subst] : (((sub @ one @ (push @ X300 @ X301))) = X300) => (! [X302 : term,X303 : subst] : (((comp @ sh @ (push @ X302 @ X303))) = X303) => (! [X304 : term,X305 : term] : ((((lam @ X304)) != ((lam @ X305))) | (X304 = X305)) => ! [X306 : term,X307 : (subst > term > term),X308 : subst,X309 : (subst > term > term)] : (~ ! [X310 : subst,X311 : subst,X312 : term] : (((X307 @ (comp @ X311 @ X310) @ (sub @ X312 @ X310))) = ((sub @ (X307 @ X311 @ X312) @ X310))) | (((X307 @ X308 @ X306)) = ((X309 @ X308 @ X306))) | ~ ! [X313 : subst,X314 : term,X315 : subst] : (((sub @ (X309 @ X313 @ X314) @ X315)) = ((X309 @ (comp @ X313 @ X315) @ (sub @ X314 @ X315)))) | (((lam @ (X307 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))))))) & (! [X316 : term] : ~ ! [X317 : (subst > term > term)] : (((sub @ X316 @ (push @ one @ sh))) != ((X317 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem1v2_gthm & ! [X318 : d_subst] : (d_id = X318) & (apinj1 <=> ! [X319 : term,X320 : term,X321 : term,X322 : term] : ((X319 = X322) | (((ap @ X322 @ X320)) != ((ap @ X319 @ X321))))) & hoasinduction_lem3_gthm & (! [X323 : subst,X324 : term,X325 : (subst > term > term),X326 : (subst > term > term)] : (~ ! [X327 : subst,X328 : subst,X329 : term] : (((X325 @ (comp @ X327 @ X328) @ (sub @ X329 @ X328))) = ((sub @ (X325 @ X327 @ X329) @ X328))) | (((X326 @ X323 @ X324)) = ((X325 @ X323 @ X324))) | ~ ! [X330 : subst,X331 : term,X332 : subst] : (((X326 @ (comp @ X332 @ X330) @ (sub @ X331 @ X330))) = ((sub @ (X326 @ X332 @ X331) @ X330))) | (((lam @ (X326 @ sh @ one))) != ((lam @ (X325 @ sh @ one))))) <=> hoaslaminj) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X333 : term] : (((sub @ X333 @ id)) = X333) <=> termmset) & hoasinduction_gthm & ~lamnotap & ((! [X334 : term] : (((sub @ X334 @ id)) = X334) => (! [X335 : (subst > term > subst > $o),X336 : term] : ((X335 @ id @ (lam @ (sub @ X336 @ (push @ one @ sh))) @ id) | ~ ! [X337 : (subst > term > term)] : ((X335 @ id @ (lam @ (X337 @ sh @ one)) @ id) | ~ ! [X338 : term] : (~(X335 @ id @ X338 @ id) | (X335 @ id @ (X337 @ id @ X338) @ id)) | ~ ! [X339 : subst,X340 : term,X341 : subst] : (((X337 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339))) = ((sub @ (X337 @ X341 @ X340) @ X339)))) | ~ ! [X342 : term] : (~(X335 @ id @ X342 @ id) | (X335 @ id @ (sub @ X336 @ (push @ X342 @ id)) @ id))) => ! [X343 : term,X344 : (subst > term > subst > $o)] : ((X344 @ id @ (lam @ X343) @ id) | ~ ! [X345 : term] : (~(X344 @ id @ X345 @ id) | (X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id)) | ~ ! [X346 : subst,X347 : subst,X348 : term,X349 : subst] : (~(X344 @ (comp @ X349 @ X346) @ (sub @ X348 @ X346) @ X347) | (X344 @ X349 @ X348 @ (comp @ X346 @ X347))) | ~ ! [X350 : (subst > term > term)] : ((X344 @ id @ (lam @ (X350 @ sh @ one)) @ id) | ~ ! [X351 : term] : (~(X344 @ id @ X351 @ id) | (X344 @ id @ (X350 @ id @ X351) @ id)) | ~ ! [X352 : subst,X353 : subst,X354 : term] : (((X350 @ (comp @ X352 @ X353) @ (sub @ X354 @ X353))) = ((sub @ (X350 @ X352 @ X354) @ X353)))) | ~ ! [X355 : subst,X356 : subst,X357 : term,X358 : subst] : (~(X344 @ X356 @ X357 @ (comp @ X355 @ X358)) | (X344 @ (comp @ X356 @ X355) @ (sub @ X357 @ X355) @ X358))))) <=> hoasinduction_lem3_lthm) & induction2_gthm & axapp & (pushprop_lem1 <=> ! [X359 : (term > $o),X360 : term,X361 : (term > $o),X362 : subst,X363 : term] : (~(X359 @ X360) | (X361 @ (sub @ X360 @ (push @ X363 @ X362))))) & ! [X364 : d_subst,X365 : d_subst] : ((((d2subst @ X365)) = ((d2subst @ X364))) => (X364 = X365)) & hoaslamnotap_lthm & hoasinduction_lem2v2_gthm & (hoasapinj2 <=> ! [X366 : term,X367 : term,X368 : term,X369 : term] : ((X366 = X368) | (((ap @ (sub @ X367 @ id) @ X368)) != ((ap @ (sub @ X369 @ id) @ X366))))) & hoasapnotvar & axabs & (hoasinduction_lem3aa <=> ! [X370 : term,X371 : (subst > term > subst > $o)] : (~ ! [X372 : (subst > term > term)] : (~ ! [X373 : term] : ((X371 @ id @ (X372 @ id @ X373) @ id) | ~(X371 @ id @ X373 @ id)) | ~ ! [X374 : term,X375 : subst,X376 : subst] : (((sub @ (X372 @ X375 @ X374) @ X376)) = ((X372 @ (comp @ X375 @ X376) @ (sub @ X374 @ X376)))) | (X371 @ id @ (lam @ (X372 @ sh @ one)) @ id)) | (X371 @ id @ (lam @ (sub @ X370 @ (push @ one @ sh))) @ id) | ~ ! [X377 : term] : ((X371 @ id @ (sub @ X370 @ (push @ X377 @ id)) @ id) | ~(X371 @ id @ X377 @ id)))) & hoasapnotvar_gthm & induction2lem_gthm & (! [X378 : term] : ~ ! [X379 : (subst > term > term)] : ~ ! [X380 : subst,X381 : term] : (((X379 @ X380 @ X381)) = ((sub @ X378 @ (push @ X381 @ X380)))) <=> hoasinduction_lem3v2_f) & (! [X382 : term,X383 : (subst > term > subst > $o)] : (~ ! [X384 : term] : ((X383 @ id @ (sub @ X382 @ (push @ X384 @ id)) @ id) | ~(X383 @ id @ X384 @ id)) | (X383 @ id @ (lam @ X382) @ id) | ~ ! [X385 : (subst > term > term)] : (~ ! [X386 : term] : (~(X383 @ id @ X386 @ id) | (X383 @ id @ (X385 @ id @ X386) @ id)) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389))) = ((sub @ (X385 @ X388 @ X387) @ X389))) | (X383 @ id @ (lam @ (X385 @ sh @ one)) @ id)) | ~ ! [X390 : subst,X391 : term,X392 : subst,X393 : subst] : (~(X383 @ X392 @ X391 @ (comp @ X393 @ X390)) | (X383 @ (comp @ X392 @ X393) @ (sub @ X391 @ X393) @ X390)) | ~ ! [X394 : term,X395 : subst,X396 : subst,X397 : subst] : ((X383 @ X396 @ X394 @ (comp @ X397 @ X395)) | ~(X383 @ (comp @ X396 @ X397) @ (sub @ X394 @ X397) @ X395))) <=> hoasinduction_lem3) & ((! [X398 : term] : (((sub @ X398 @ id)) = X398) => (! [X399 : (term > $o),X400 : subst,X401 : term] : (~ ! [X402 : term,X403 : term] : (~(X399 @ X403) | ~(X399 @ X402) | (X399 @ (ap @ X403 @ X402))) | ~ ! [X404 : term] : (~ ! [X405 : term] : (~(X399 @ X405) | (X399 @ (sub @ X404 @ (push @ X405 @ id)))) | (X399 @ (lam @ X404))) | ~ ! [X406 : term] : ((X399 @ (sub @ X406 @ X400)) | ~(var @ X406)) | (X399 @ (sub @ X401 @ X400))) => ! [X407 : term,X408 : (term > $o)] : (~ ! [X409 : term] : (~ ! [X410 : term] : (~(X408 @ X410) | (X408 @ (sub @ X409 @ (push @ X410 @ id)))) | (X408 @ (lam @ X409))) | ~ ! [X411 : term,X412 : term] : (~(X408 @ X411) | (X408 @ (ap @ X411 @ X412)) | ~(X408 @ X412)) | ~ ! [X413 : term] : ((X408 @ X413) | ~(var @ X413)) | (X408 @ X407)))) <=> induction2_lthm) & hoaslamnotvar_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (one = ((d2term @ d_one))) & pushprop_lem2v2_gthm & (laminj <=> ! [X414 : term,X415 : term] : ((((lam @ X415)) != ((lam @ X414))) | (X414 = X415))) & axvarshift & ((! [X416 : term,X417 : subst] : (((sub @ one @ (push @ X416 @ X417))) = X416) => (! [X418 : term,X419 : subst] : (((comp @ sh @ (push @ X418 @ X419))) = X419) => ! [X420 : (term > $o),X421 : (term > $o),X422 : subst,X423 : term,X424 : term] : ((X420 @ (sub @ X423 @ (push @ X424 @ X422))) | ~(X421 @ X423)))) <=> pushprop_lem1_lthm) & axclos & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & axassoc & hoasinduction_lem2_lthm & (! [X425 : term,X426 : (term > $o),X427 : subst] : ~ ! [X428 : (term > $o)] : ~ ! [X429 : term] : (((X428 @ X429)) = ((X426 @ (sub @ X429 @ (push @ X425 @ X427))))) <=> pushprop_lem0_lthm) & hoasapinj2_gthm & (! [X430 : subst] : (((comp @ id @ X430)) = X430) <=> axidl) & (hoasinduction_lem0_lthm <=> ! [X431 : (subst > term > subst > $o)] : ~ ! [X432 : (term > $o)] : ~ ! [X433 : term] : (((X432 @ X433)) = ((X431 @ id @ X433 @ id)))) & hoasinduction_lem1v2 & ((! [X434 : term,X435 : subst] : (((sub @ one @ (push @ X434 @ X435))) = X434) => (! [X436 : subst,X437 : term] : (((comp @ sh @ (push @ X437 @ X436))) = X436) => (! [X438 : subst] : (((comp @ X438 @ id)) = X438) => (! [X439 : term,X440 : (term > $o)] : (~ ! [X441 : term] : (~(var @ X441) | (X440 @ X441)) | ~ ! [X442 : term] : (~(X440 @ X442) | (X440 @ (lam @ X442))) | ~ ! [X443 : term,X444 : term] : (~(X440 @ X443) | ~(X440 @ X444) | (X440 @ (ap @ X444 @ X443))) | (X440 @ X439)) => ! [X445 : (term > $o),X446 : term,X447 : subst] : (~ ! [X448 : term] : ((X445 @ (lam @ X448)) | ~ ! [X449 : term] : ((X445 @ (sub @ X448 @ (push @ X449 @ id))) | ~(X445 @ X449))) | ~ ! [X450 : term,X451 : term] : ((X445 @ (ap @ X450 @ X451)) | ~(X445 @ X451) | ~(X445 @ X450)) | ~ ! [X452 : term] : ((X445 @ (sub @ X452 @ X447)) | ~(var @ X452)) | (X445 @ (sub @ X446 @ X447))))))) <=> induction2lem_lthm) & ulamvarsh & ! [X453 : subst] : ? [X454 : d_subst] : (((d2subst @ X454)) = X453) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & pushprop & (! [X455 : term,X456 : term] : ((X455 = X456) | (((sub @ X456 @ sh)) != ((sub @ X455 @ sh)))) <=> shinj) & apnotvar & hoasapinj1_gthm & (! [X457 : term,X458 : (subst > term > subst > $o)] : ((X458 @ id @ (lam @ X457) @ id) | ~ ! [X459 : term] : ((X458 @ id @ (sub @ X457 @ (push @ X459 @ id)) @ id) | ~(X458 @ id @ X459 @ id)) | ~ ! [X460 : (subst > term > term)] : (~ ! [X461 : term] : (~(X458 @ id @ X461 @ id) | (X458 @ id @ (X460 @ id @ X461) @ id)) | (X458 @ id @ (lam @ (X460 @ sh @ one)) @ id) | ~ ! [X462 : subst,X463 : term,X464 : subst] : (((X460 @ (comp @ X462 @ X464) @ (sub @ X463 @ X464))) = ((sub @ (X460 @ X462 @ X463) @ X464))))) <=> hoasinduction_lem3a) & hoaslaminj_gthm & substmonoid_gthm & ! [X465 : d_term] : (d_one = X465) & pushprop_lem2v2 & ~ulamvar1 & hoasinduction_lem3b_gthm & ulamvarind & (! [X466 : (subst > term > term),X467 : term,X468 : term] : ((((lam @ (X466 @ sh @ one))) != ((ap @ (sub @ X468 @ id) @ X467))) | ~ ! [X469 : subst,X470 : term,X471 : subst] : (((sub @ (X466 @ X471 @ X470) @ X469)) = ((X466 @ (comp @ X471 @ X469) @ (sub @ X470 @ X469))))) <=> hoaslamnotap) & ((! [X472 : term,X473 : term,X474 : term,X475 : term] : ((((ap @ X472 @ X475)) != ((ap @ X473 @ X474))) | (X474 = X475)) => ! [X476 : term,X477 : term,X478 : term,X479 : term] : ((X478 = X479) | (((ap @ (sub @ X476 @ id) @ X478)) != ((ap @ (sub @ X477 @ id) @ X479))))) <=> hoasapinj2_lthm) & (! [X480 : subst] : (((push @ (sub @ one @ X480) @ (comp @ sh @ X480))) = X480) <=> axscons) & (hoasapinj1_lthm <=> (! [X481 : term] : (((sub @ X481 @ id)) = X481) => (! [X482 : term,X483 : term,X484 : term,X485 : term] : ((X483 = X484) | (((ap @ X484 @ X482)) != ((ap @ X483 @ X485)))) => ! [X486 : term,X487 : term,X488 : term,X489 : term] : ((X486 = X488) | (((ap @ (sub @ X486 @ id) @ X489)) != ((ap @ (sub @ X488 @ id) @ X487))))))) & (hoasinduction_lem3v2 <=> ! [X490 : term,X491 : (term > $o),X492 : (subst > term > subst > $o)] : (~ ! [X493 : (subst > term > term)] : (~ ! [X494 : term,X495 : subst,X496 : subst] : (((sub @ (X493 @ X495 @ X494) @ X496)) = ((X493 @ (comp @ X495 @ X496) @ (sub @ X494 @ X496)))) | (X492 @ id @ (lam @ (X493 @ sh @ one)) @ id) | ~ ! [X497 : term] : (~(X492 @ id @ X497 @ id) | (X492 @ id @ (X493 @ id @ X497) @ id))) | ~ ! [X498 : subst,X499 : term,X500 : subst,X501 : subst] : (~(X492 @ X498 @ X499 @ (comp @ X500 @ X501)) | (X492 @ (comp @ X498 @ X500) @ (sub @ X499 @ X500) @ X501)) | ~ ! [X502 : term] : (((X492 @ id @ X502 @ id)) = ((X491 @ X502))) | ~ ! [X503 : term] : ((X491 @ (sub @ X490 @ (push @ X503 @ id))) | ~(X491 @ X503)) | (X491 @ (lam @ X490)) | ~ ! [X504 : subst,X505 : subst,X506 : subst,X507 : term] : ((X492 @ X506 @ X507 @ (comp @ X505 @ X504)) | ~(X492 @ (comp @ X506 @ X505) @ (sub @ X507 @ X505) @ X504)))) & (hoasinduction_lem0 <=> ! [X508 : (subst > term > subst > $o)] : ~ ! [X509 : (term > $o)] : ~ ! [X510 : term] : (((X509 @ X510)) = ((X508 @ id @ X510 @ id)))) & hoaslamnotap_gthm & termmset_gthm & pushprop_lem3v2_lthm & (hoasinduction_lem3a_lthm <=> (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : term,X513 : (subst > term > subst > $o)] : ((X513 @ id @ (lam @ (sub @ X512 @ (push @ one @ sh))) @ id) | ~ ! [X514 : (subst > term > term)] : ((X513 @ id @ (lam @ (X514 @ sh @ one)) @ id) | ~ ! [X515 : term] : ((X513 @ id @ (X514 @ id @ X515) @ id) | ~(X513 @ id @ X515 @ id)) | ~ ! [X516 : subst,X517 : term,X518 : subst] : (((X514 @ (comp @ X518 @ X516) @ (sub @ X517 @ X516))) = ((sub @ (X514 @ X518 @ X517) @ X516)))) | ~ ! [X519 : term] : ((X513 @ id @ (sub @ X512 @ (push @ X519 @ id)) @ id) | ~(X513 @ id @ X519 @ id))) => ! [X520 : term,X521 : (subst > term > subst > $o)] : (~ ! [X522 : term] : ((X521 @ id @ (sub @ X520 @ (push @ X522 @ id)) @ id) | ~(X521 @ id @ X522 @ id)) | (X521 @ id @ (lam @ X520) @ id) | ~ ! [X523 : (subst > term > term)] : (~ ! [X524 : term] : (~(X521 @ id @ X524 @ id) | (X521 @ id @ (X523 @ id @ X524) @ id)) | ~ ! [X525 : subst,X526 : subst,X527 : term] : (((sub @ (X523 @ X526 @ X527) @ X525)) = ((X523 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | (X521 @ id @ (lam @ (X523 @ sh @ one)) @ id)))))) & (! [X528 : term,X529 : (term > $o)] : ((X529 @ X528) | ~ ! [X530 : term] : ((X529 @ (lam @ X530)) | ~(X529 @ X530)) | ~ ! [X531 : term] : (~(var @ X531) | (X529 @ X531)) | ~ ! [X532 : term,X533 : term] : (~(X529 @ X533) | (X529 @ (ap @ X533 @ X532)) | ~(X529 @ X532))) <=> induction) & (hoasinduction_lem3v2_f_lthm <=> ! [X534 : term] : ~ ! [X535 : (subst > term > term)] : ~ ! [X536 : subst,X537 : term] : (((sub @ X534 @ (push @ X537 @ X536))) = ((X535 @ X536 @ X537)))) & (! [X538 : subst,X539 : term,X540 : (term > $o)] : ~ ! [X541 : (term > $o)] : ~ ! [X542 : term] : (((X540 @ (sub @ X542 @ (push @ X539 @ X538)))) = ((X541 @ X542))) <=> pushprop_lem0) & ((^[X543 : term, X544 : subst, X545 : (term > $o), X546 : (term > $o)] : (! [X547 : term] : (((X545 @ (sub @ X547 @ (push @ X543 @ X544)))) = ((X546 @ X547))))) = pushprop_p_and_p_prime) & (! [X548 : term,X549 : subst] : (((comp @ sh @ (push @ X548 @ X549))) = X549) <=> axshiftcons) & hoaslamnotvar_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id)))),
% 13.65/2.32 inference(rectify,[],[f1])).
% 13.65/2.32 thf(f5,plain,(
% 13.65/2.32 ((hoasinduction_lem3aaa = $true) <=> ! [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X2 : (subst > term > term),X3 : term] : (~ ! [X4 : term] : (~ (((X0 @ id @ X4 @ id)) = $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) | ~ ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) | ($true = ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id))) | ~ ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9)))) | ~ ! [X11 : term] : (($true = ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) | ~ (((X0 @ id @ X11 @ id)) = $true)))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & (((d2subst @ d_id)) = id) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & ((pushprop_lem1v2 = $true) <=> ! [X16 : (term > $o),X17 : subst,X18 : (term > $o),X19 : term] : (~ ($true = ((X16 @ X19))) | ($true = ((X18 @ one))) | ~ ! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))))) & (! [X21 : (term > $o),X22 : term] : (~ ! [X23 : term,X24 : term] : ((((X21 @ (ap @ X23 @ X24))) = $true) | ~ ($true = ((X21 @ X24))) | ~ (((X21 @ X23)) = $true)) | ~ ! [X25 : term] : (~ ! [X26 : term] : (~ ($true = ((X21 @ X26))) | ($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id)))))) | ($true = ((X21 @ (lam @ X25))))) | ($true = ((X21 @ X22))) | ~ ! [X27 : term] : ((((X21 @ X27)) = $true) | ~ (((var @ X27)) = $true))) <=> (induction2 = $true)) & (! [X28 : (subst > term > subst > $o),X29 : term] : (~ ! [X30 : (subst > term > term)] : (~ ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32))) | ~ ! [X34 : term] : ((((X28 @ id @ (X30 @ id @ X34) @ id)) = $true) | ~ ($true = ((X28 @ id @ X34 @ id)))) | ($true = ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id)))) | (((X28 @ id @ X29 @ id)) = $true) | ~ ! [X35 : term] : ((((X28 @ id @ X35 @ id)) = $true) | ~ ($true = ((var @ (sub @ X35 @ id))))) | ~ ! [X36 : term,X37 : subst,X38 : subst,X39 : subst] : ((((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) = $true) | ~ ($true = ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37)))) | ~ ! [X40 : term,X41 : term] : ((((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) = $true) | ~ (((X28 @ id @ X41 @ id)) = $true) | ~ (((X28 @ id @ X40 @ id)) = $true)) | ~ ! [X42 : subst,X43 : subst,X44 : term,X45 : subst] : (~ (((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) = $true) | (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) = $true))) <=> (hoasinduction = $true)) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X52 : term,X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)))) | ~ ($true = ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)))) | ($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | ~ (((X53 @ id @ X54 @ id)) = $true) | ~ ! [X59 : term,X60 : term] : ((((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) = $true) | ~ ($true = ((X53 @ id @ X59 @ id))) | ~ (((X53 @ id @ X60 @ id)) = $true)) | ~ ! [X61 : subst,X62 : term,X63 : subst,X64 : subst] : (~ (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) = $true) | (((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) = $true)) | ~ (((X53 @ id @ X52 @ id)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X65 : (subst > term > subst > $o),X66 : term] : (~ ! [X67 : (subst > term > term)] : (~ ! [X68 : term] : (~ ($true = ((X65 @ id @ X68 @ id))) | (((X65 @ id @ (X67 @ id @ X68) @ id)) = $true)) | ~ ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70)))) | ($true = ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id)))) | ($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id))) | ~ ! [X72 : term] : (($true = ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id))) | ~ (((X65 @ id @ X72 @ id)) = $true)))) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (~ ! [X77 : term] : (($true = ((X76 @ (sub @ X75 @ (push @ X77 @ id))))) | ~ ($true = ((X76 @ X77)))) | ~ ! [X78 : term] : (((X74 @ id @ X78 @ id)) = ((X76 @ X78))) | ~ ! [X79 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) = $true) | ~ ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81))) | ~ ! [X83 : term] : (~ (((X74 @ id @ X83 @ id)) = $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true))) | (((X76 @ (lam @ X75))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop_lthm = $true) & ((substmonoid_lthm = $true) <=> (! [X84 : subst] : (((comp @ id @ X84)) = X84) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))))) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X88 : (subst > term > subst > $o),X89 : term] : ((((X88 @ id @ X89 @ id)) = $true) | ~ ! [X90 : term,X91 : term] : (~ (((X88 @ id @ X90 @ id)) = $true) | ~ ($true = ((X88 @ id @ X91 @ id))) | (((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) = $true)) | ~ ! [X92 : (subst > term > term)] : ((((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) = $true) | ~ ! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) | ~ ! [X96 : term] : (~ (((X88 @ id @ X96 @ id)) = $true) | (((X88 @ id @ (X92 @ id @ X96) @ id)) = $true))))) & (pushprop_lem1_gthm = $true) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => ! [X100 : (term > $o),X101 : term,X102 : subst,X103 : (term > $o)] : (~ ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | (((X100 @ one)) = $true) | ~ ($true = ((X103 @ X101)))))) & ((! [X105 : term] : (((sub @ X105 @ id)) = X105) => ! [X106 : term] : (((sub @ X106 @ id)) = X106)) <=> (termmset_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X110 : term] : ~ ! [X111 : (subst > term > term)] : (((sub @ X110 @ (push @ one @ sh))) != ((X111 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ! [X112 : d_term,X113 : d_term] : ((((d2term @ X112)) = ((d2term @ X113))) => (X112 = X113)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X114 : term] : ~ ! [X115 : (subst > term > term)] : ~ ! [X116 : subst,X117 : term] : (((sub @ X114 @ (push @ X117 @ X116))) = ((X115 @ X116 @ X117))) => (! [X118 : term] : (((sub @ X118 @ id)) = X118) => ! [X119 : term,X120 : (subst > term > subst > $o),X121 : (term > $o)] : (~ ! [X122 : term] : ((((X121 @ (sub @ X119 @ (push @ X122 @ id)))) = $true) | ~ ($true = ((X121 @ X122)))) | ~ ! [X123 : term] : (((X120 @ id @ X123 @ id)) = ((X121 @ X123))) | ~ ! [X124 : (subst > term > term)] : (~ ! [X125 : subst,X126 : subst,X127 : term] : (((X124 @ (comp @ X126 @ X125) @ (sub @ X127 @ X125))) = ((sub @ (X124 @ X126 @ X127) @ X125))) | ~ ! [X128 : term] : ((((X120 @ id @ (X124 @ id @ X128) @ id)) = $true) | ~ (((X120 @ id @ X128 @ id)) = $true)) | (((X120 @ id @ (lam @ (X124 @ sh @ one)) @ id)) = $true)) | ($true = ((X121 @ (lam @ X119)))))))) & (! [X129 : term,X130 : subst] : (((sub @ one @ (push @ X129 @ X130))) = X129) <=> (axvarcons = $true)) & (axmap = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ((! [X131 : subst] : (((comp @ X131 @ id)) = X131) & ! [X132 : subst] : (((comp @ id @ X132)) = X132)) <=> (substmonoid = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X133 : (subst > term > subst > $o)] : ~ ! [X134 : (term > $o)] : ~ ! [X135 : term] : (((X134 @ X135)) = ((X133 @ id @ X135 @ id))) => (! [X136 : term,X137 : (term > $o)] : (~ ! [X138 : term] : ((((X137 @ X138)) = $true) | ~ (((var @ X138)) = $true)) | ~ ! [X139 : term,X140 : term] : (~ ($true = ((X137 @ X140))) | ($true = ((X137 @ (ap @ X140 @ X139)))) | ~ ($true = ((X137 @ X139)))) | (((X137 @ X136)) = $true) | ~ ! [X141 : term] : (~ ! [X142 : term] : ((((X137 @ (sub @ X141 @ (push @ X142 @ id)))) = $true) | ~ ($true = ((X137 @ X142)))) | ($true = ((X137 @ (lam @ X141)))))) => (! [X143 : term] : (((sub @ X143 @ id)) = X143) => (! [X144 : term,X145 : (subst > term > subst > $o),X146 : (term > $o)] : (~ ! [X147 : (subst > term > term)] : (~ ! [X148 : subst,X149 : subst,X150 : term] : (((sub @ (X147 @ X148 @ X150) @ X149)) = ((X147 @ (comp @ X148 @ X149) @ (sub @ X150 @ X149)))) | ($true = ((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id))) | ~ ! [X151 : term] : ((((X145 @ id @ (X147 @ id @ X151) @ id)) = $true) | ~ ($true = ((X145 @ id @ X151 @ id))))) | (((X146 @ (lam @ X144))) = $true) | ~ ! [X152 : term] : (~ (((X146 @ X152)) = $true) | (((X146 @ (sub @ X144 @ (push @ X152 @ id)))) = $true)) | ~ ! [X153 : term] : (((X145 @ id @ X153 @ id)) = ((X146 @ X153)))) => ! [X154 : (subst > term > subst > $o),X155 : term] : (~ ! [X156 : subst,X157 : subst,X158 : subst,X159 : term] : (~ ($true = ((X154 @ (comp @ X156 @ X158) @ (sub @ X159 @ X158) @ X157))) | (((X154 @ X156 @ X159 @ (comp @ X158 @ X157))) = $true)) | ~ ! [X160 : subst,X161 : term,X162 : subst,X163 : subst] : (~ ($true = ((X154 @ X160 @ X161 @ (comp @ X162 @ X163)))) | ($true = ((X154 @ (comp @ X160 @ X162) @ (sub @ X161 @ X162) @ X163)))) | ~ ! [X164 : term] : ((((X154 @ id @ X164 @ id)) = $true) | ~ ($true = ((var @ (sub @ X164 @ id))))) | ($true = ((X154 @ id @ X155 @ id))) | ~ ! [X165 : (subst > term > term)] : (~ ! [X166 : term] : (~ ($true = ((X154 @ id @ X166 @ id))) | ($true = ((X154 @ id @ (X165 @ id @ X166) @ id)))) | ~ ! [X167 : subst,X168 : term,X169 : subst] : (((X165 @ (comp @ X169 @ X167) @ (sub @ X168 @ X167))) = ((sub @ (X165 @ X169 @ X168) @ X167))) | (((X154 @ id @ (lam @ (X165 @ sh @ one)) @ id)) = $true)) | ~ ! [X170 : term,X171 : term] : (~ (((X154 @ id @ X170 @ id)) = $true) | ~ (((X154 @ id @ X171 @ id)) = $true) | ($true = ((X154 @ id @ (ap @ (sub @ X171 @ id) @ X170) @ id)))))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X172 : term,X173 : (term > $o),X174 : (subst > term > subst > $o),X175 : term] : (~ ! [X176 : term] : (((X174 @ id @ X176 @ id)) = ((X173 @ X176))) | ~ ! [X177 : subst,X178 : subst,X179 : term,X180 : subst] : ((((X174 @ (comp @ X178 @ X177) @ (sub @ X179 @ X177) @ X180)) = $true) | ~ (((X174 @ X178 @ X179 @ (comp @ X177 @ X180))) = $true)) | ~ (((X173 @ X175)) = $true) | (((X173 @ (ap @ X175 @ X172))) = $true) | ~ (((X173 @ X172)) = $true) | ~ ! [X181 : subst,X182 : subst,X183 : term,X184 : subst] : (($true = ((X174 @ X184 @ X183 @ (comp @ X182 @ X181)))) | ~ (((X174 @ (comp @ X184 @ X182) @ (sub @ X183 @ X182) @ X181)) = $true)) | ~ ! [X185 : term,X186 : term] : (~ ($true = ((X174 @ id @ X185 @ id))) | (((X174 @ id @ (ap @ (sub @ X185 @ id) @ X186) @ id)) = $true) | ~ (((X174 @ id @ X186 @ id)) = $true)))) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X187 : (subst > term > subst > $o)] : ~ ! [X188 : (term > $o)] : ~ ! [X189 : term] : (((X187 @ id @ X189 @ id)) = ((X188 @ X189))) => (! [X190 : (term > $o),X191 : term] : (~ ! [X192 : term] : (~ ($true = ((var @ X192))) | (((X190 @ X192)) = $true)) | ~ ! [X193 : term] : ((((X190 @ (lam @ X193))) = $true) | ~ ! [X194 : term] : ((((X190 @ (sub @ X193 @ (push @ X194 @ id)))) = $true) | ~ ($true = ((X190 @ X194))))) | ~ ! [X195 : term,X196 : term] : (~ ($true = ((X190 @ X195))) | ~ (((X190 @ X196)) = $true) | (((X190 @ (ap @ X195 @ X196))) = $true)) | (((X190 @ X191)) = $true)) => (! [X197 : term] : (((sub @ X197 @ id)) = X197) => (! [X198 : term,X199 : (term > $o),X200 : (subst > term > subst > $o)] : (~ ! [X201 : term] : (((X200 @ id @ X201 @ id)) = ((X199 @ X201))) | ~ ! [X202 : term] : ((((X199 @ (sub @ X198 @ (push @ X202 @ id)))) = $true) | ~ (((X199 @ X202)) = $true)) | ($true = ((X199 @ (lam @ X198)))) | ~ ! [X203 : (subst > term > term)] : (($true = ((X200 @ id @ (lam @ (X203 @ sh @ one)) @ id))) | ~ ! [X204 : term] : (~ ($true = ((X200 @ id @ X204 @ id))) | (((X200 @ id @ (X203 @ id @ X204) @ id)) = $true)) | ~ ! [X205 : term,X206 : subst,X207 : subst] : (((X203 @ (comp @ X207 @ X206) @ (sub @ X205 @ X206))) = ((sub @ (X203 @ X207 @ X205) @ X206))))) => ! [X208 : (subst > term > subst > $o),X209 : term] : (~ ! [X210 : (subst > term > term)] : (($true = ((X208 @ id @ (lam @ (X210 @ sh @ one)) @ id))) | ~ ! [X211 : subst,X212 : term,X213 : subst] : (((X210 @ (comp @ X213 @ X211) @ (sub @ X212 @ X211))) = ((sub @ (X210 @ X213 @ X212) @ X211))) | ~ ! [X214 : term] : (~ (((X208 @ id @ X214 @ id)) = $true) | (((X208 @ id @ (X210 @ id @ X214) @ id)) = $true))) | ~ ! [X215 : term,X216 : term] : (~ ($true = ((X208 @ id @ X215 @ id))) | ~ (((X208 @ id @ X216 @ id)) = $true) | (((X208 @ id @ (ap @ (sub @ X216 @ id) @ X215) @ id)) = $true)) | (((X208 @ id @ X209 @ id)) = $true)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X219 : term] : (((sub @ X219 @ id)) = X219) => ! [X220 : (subst > term > subst > $o),X221 : term,X222 : (term > $o)] : (~ ! [X223 : (subst > term > term)] : (~ ! [X224 : term] : (~ (((X220 @ id @ X224 @ id)) = $true) | (((X220 @ id @ (X223 @ id @ X224) @ id)) = $true)) | ~ ! [X225 : subst,X226 : subst,X227 : term] : (((X223 @ (comp @ X225 @ X226) @ (sub @ X227 @ X226))) = ((sub @ (X223 @ X225 @ X227) @ X226))) | (((X220 @ id @ (lam @ (X223 @ sh @ one)) @ id)) = $true)) | ($true = ((X222 @ (lam @ X221)))) | ~ ! [X228 : term] : (((X222 @ X228)) = ((X220 @ id @ X228 @ id))) | ~ ! [X229 : subst,X230 : subst,X231 : term,X232 : subst] : (($true = ((X220 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232) @ X229))) | ~ (((X220 @ X230 @ X231 @ (comp @ X232 @ X229))) = $true)) | ~ ! [X233 : subst,X234 : subst,X235 : term,X236 : subst] : (~ (((X220 @ (comp @ X233 @ X234) @ (sub @ X235 @ X234) @ X236)) = $true) | (((X220 @ X233 @ X235 @ (comp @ X234 @ X236))) = $true)) | ~ ! [X237 : term] : (($true = ((X222 @ (sub @ X221 @ (push @ X237 @ id))))) | ~ ($true = ((X222 @ X237))))))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X238 : term,X239 : (term > $o)] : (~ ! [X240 : term,X241 : term] : ((((X239 @ (ap @ X241 @ X240))) = $true) | ~ (((X239 @ X241)) = $true) | ~ (((X239 @ X240)) = $true)) | ~ ! [X242 : term] : (~ ! [X243 : term] : (($true = ((X239 @ (sub @ X242 @ (push @ X243 @ id))))) | ~ (((X239 @ X243)) = $true)) | (((X239 @ (lam @ X242))) = $true)) | ~ ! [X244 : term] : (~ ($true = ((var @ X244))) | ($true = ((X239 @ X244)))) | ($true = ((X239 @ X238)))) => (! [X245 : (subst > term > subst > $o),X246 : term,X247 : term] : (~ (((X245 @ id @ X246 @ id)) = $true) | ~ ! [X248 : term,X249 : term] : (~ (((X245 @ id @ X248 @ id)) = $true) | (((X245 @ id @ (ap @ (sub @ X249 @ id) @ X248) @ id)) = $true) | ~ ($true = ((X245 @ id @ X249 @ id)))) | ~ ! [X250 : subst,X251 : term,X252 : subst,X253 : subst] : (($true = ((X245 @ (comp @ X252 @ X250) @ (sub @ X251 @ X250) @ X253))) | ~ (((X245 @ X252 @ X251 @ (comp @ X250 @ X253))) = $true)) | ($true = ((X245 @ id @ (ap @ X246 @ X247) @ id))) | ~ ($true = ((X245 @ id @ X247 @ id))) | ~ ! [X254 : subst,X255 : term,X256 : subst,X257 : subst] : (($true = ((X245 @ X254 @ X255 @ (comp @ X256 @ X257)))) | ~ ($true = ((X245 @ (comp @ X254 @ X256) @ (sub @ X255 @ X256) @ X257))))) => (! [X258 : term,X259 : (subst > term > subst > $o)] : ((((X259 @ id @ (lam @ X258) @ id)) = $true) | ~ ! [X260 : subst,X261 : subst,X262 : subst,X263 : term] : (($true = ((X259 @ (comp @ X262 @ X261) @ (sub @ X263 @ X261) @ X260))) | ~ (((X259 @ X262 @ X263 @ (comp @ X261 @ X260))) = $true)) | ~ ! [X264 : term,X265 : subst,X266 : subst,X267 : subst] : (~ (((X259 @ (comp @ X266 @ X265) @ (sub @ X264 @ X265) @ X267)) = $true) | ($true = ((X259 @ X266 @ X264 @ (comp @ X265 @ X267))))) | ~ ! [X268 : term] : (~ (((X259 @ id @ X268 @ id)) = $true) | (((X259 @ id @ (sub @ X258 @ (push @ X268 @ id)) @ id)) = $true)) | ~ ! [X269 : (subst > term > term)] : (~ ! [X270 : subst,X271 : subst,X272 : term] : (((sub @ (X269 @ X270 @ X272) @ X271)) = ((X269 @ (comp @ X270 @ X271) @ (sub @ X272 @ X271)))) | ~ ! [X273 : term] : (~ ($true = ((X259 @ id @ X273 @ id))) | ($true = ((X259 @ id @ (X269 @ id @ X273) @ id)))) | (((X259 @ id @ (lam @ (X269 @ sh @ one)) @ id)) = $true))) => ! [X274 : (subst > term > subst > $o),X275 : term] : (~ ! [X276 : subst,X277 : term,X278 : subst,X279 : subst] : (~ ($true = ((X274 @ X276 @ X277 @ (comp @ X279 @ X278)))) | ($true = ((X274 @ (comp @ X276 @ X279) @ (sub @ X277 @ X279) @ X278)))) | ~ ! [X280 : term] : (~ (((var @ (sub @ X280 @ id))) = $true) | (((X274 @ id @ X280 @ id)) = $true)) | (((X274 @ id @ X275 @ id)) = $true) | ~ ! [X281 : (subst > term > term)] : ((((X274 @ id @ (lam @ (X281 @ sh @ one)) @ id)) = $true) | ~ ! [X282 : term] : (~ (((X274 @ id @ X282 @ id)) = $true) | ($true = ((X274 @ id @ (X281 @ id @ X282) @ id)))) | ~ ! [X283 : term,X284 : subst,X285 : subst] : (((X281 @ (comp @ X285 @ X284) @ (sub @ X283 @ X284))) = ((sub @ (X281 @ X285 @ X283) @ X284)))) | ~ ! [X286 : subst,X287 : subst,X288 : subst,X289 : term] : (~ ($true = ((X274 @ (comp @ X288 @ X286) @ (sub @ X289 @ X286) @ X287))) | ($true = ((X274 @ X288 @ X289 @ (comp @ X286 @ X287))))) | ~ ! [X290 : term,X291 : term] : (~ (((X274 @ id @ X290 @ id)) = $true) | ~ (((X274 @ id @ X291 @ id)) = $true) | ($true = ((X274 @ id @ (ap @ (sub @ X291 @ id) @ X290) @ id))))))))) & (hoaslamnotvar = $true) & ((induction2lem = $true) <=> ! [X292 : subst,X293 : term,X294 : (term > $o)] : (~ ! [X295 : term] : ((((X294 @ (lam @ X295))) = $true) | ~ ! [X296 : term] : ((((X294 @ (sub @ X295 @ (push @ X296 @ id)))) = $true) | ~ (((X294 @ X296)) = $true))) | ~ ! [X297 : term] : (~ (((var @ X297)) = $true) | (((X294 @ (sub @ X297 @ X292))) = $true)) | (((X294 @ (sub @ X293 @ X292))) = $true) | ~ ! [X298 : term,X299 : term] : (~ (((X294 @ X298)) = $true) | (((X294 @ (ap @ X298 @ X299))) = $true) | ~ ($true = ((X294 @ X299)))))) & ((hoaslaminj_lthm = $true) <=> (! [X300 : term,X301 : subst] : (((sub @ one @ (push @ X300 @ X301))) = X300) => (! [X302 : term,X303 : subst] : (((comp @ sh @ (push @ X302 @ X303))) = X303) => (! [X304 : term,X305 : term] : ((((lam @ X304)) != ((lam @ X305))) | (X304 = X305)) => ! [X306 : term,X307 : (subst > term > term),X308 : subst,X309 : (subst > term > term)] : (~ ! [X310 : subst,X311 : subst,X312 : term] : (((X307 @ (comp @ X311 @ X310) @ (sub @ X312 @ X310))) = ((sub @ (X307 @ X311 @ X312) @ X310))) | (((X307 @ X308 @ X306)) = ((X309 @ X308 @ X306))) | ~ ! [X313 : subst,X314 : term,X315 : subst] : (((sub @ (X309 @ X313 @ X314) @ X315)) = ((X309 @ (comp @ X313 @ X315) @ (sub @ X314 @ X315)))) | (((lam @ (X307 @ sh @ one))) != ((lam @ (X309 @ sh @ one))))))))) & (! [X316 : term] : ~ ! [X317 : (subst > term > term)] : (((sub @ X316 @ (push @ one @ sh))) != ((X317 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & ! [X318 : d_subst] : (d_id = X318) & ((apinj1 = $true) <=> ! [X319 : term,X320 : term,X321 : term,X322 : term] : ((X319 = X322) | (((ap @ X322 @ X320)) != ((ap @ X319 @ X321))))) & (hoasinduction_lem3_gthm = $true) & (! [X323 : subst,X324 : term,X325 : (subst > term > term),X326 : (subst > term > term)] : (~ ! [X327 : subst,X328 : subst,X329 : term] : (((X325 @ (comp @ X327 @ X328) @ (sub @ X329 @ X328))) = ((sub @ (X325 @ X327 @ X329) @ X328))) | (((X326 @ X323 @ X324)) = ((X325 @ X323 @ X324))) | ~ ! [X330 : subst,X331 : term,X332 : subst] : (((X326 @ (comp @ X332 @ X330) @ (sub @ X331 @ X330))) = ((sub @ (X326 @ X332 @ X331) @ X330))) | (((lam @ (X326 @ sh @ one))) != ((lam @ (X325 @ sh @ one))))) <=> (hoaslaminj = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X333 : term] : (((sub @ X333 @ id)) = X333) <=> (termmset = $true)) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & ((! [X334 : term] : (((sub @ X334 @ id)) = X334) => (! [X335 : (subst > term > subst > $o),X336 : term] : ((((X335 @ id @ (lam @ (sub @ X336 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X337 : (subst > term > term)] : ((((X335 @ id @ (lam @ (X337 @ sh @ one)) @ id)) = $true) | ~ ! [X338 : term] : (~ (((X335 @ id @ X338 @ id)) = $true) | ($true = ((X335 @ id @ (X337 @ id @ X338) @ id)))) | ~ ! [X339 : subst,X340 : term,X341 : subst] : (((X337 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339))) = ((sub @ (X337 @ X341 @ X340) @ X339)))) | ~ ! [X342 : term] : (~ ($true = ((X335 @ id @ X342 @ id))) | ($true = ((X335 @ id @ (sub @ X336 @ (push @ X342 @ id)) @ id))))) => ! [X343 : term,X344 : (subst > term > subst > $o)] : (($true = ((X344 @ id @ (lam @ X343) @ id))) | ~ ! [X345 : term] : (~ ($true = ((X344 @ id @ X345 @ id))) | (((X344 @ id @ (sub @ X343 @ (push @ X345 @ id)) @ id)) = $true)) | ~ ! [X346 : subst,X347 : subst,X348 : term,X349 : subst] : (~ (((X344 @ (comp @ X349 @ X346) @ (sub @ X348 @ X346) @ X347)) = $true) | (((X344 @ X349 @ X348 @ (comp @ X346 @ X347))) = $true)) | ~ ! [X350 : (subst > term > term)] : ((((X344 @ id @ (lam @ (X350 @ sh @ one)) @ id)) = $true) | ~ ! [X351 : term] : (~ (((X344 @ id @ X351 @ id)) = $true) | ($true = ((X344 @ id @ (X350 @ id @ X351) @ id)))) | ~ ! [X352 : subst,X353 : subst,X354 : term] : (((X350 @ (comp @ X352 @ X353) @ (sub @ X354 @ X353))) = ((sub @ (X350 @ X352 @ X354) @ X353)))) | ~ ! [X355 : subst,X356 : subst,X357 : term,X358 : subst] : (~ ($true = ((X344 @ X356 @ X357 @ (comp @ X355 @ X358)))) | ($true = ((X344 @ (comp @ X356 @ X355) @ (sub @ X357 @ X355) @ X358))))))) <=> (hoasinduction_lem3_lthm = $true)) & (induction2_gthm = $true) & (axapp = $true) & ((pushprop_lem1 = $true) <=> ! [X359 : (term > $o),X360 : term,X361 : (term > $o),X362 : subst,X363 : term] : (~ (((X359 @ X360)) = $true) | ($true = ((X361 @ (sub @ X360 @ (push @ X363 @ X362))))))) & ! [X364 : d_subst,X365 : d_subst] : ((((d2subst @ X365)) = ((d2subst @ X364))) => (X364 = X365)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X366 : term,X367 : term,X368 : term,X369 : term] : ((X366 = X368) | (((ap @ (sub @ X367 @ id) @ X368)) != ((ap @ (sub @ X369 @ id) @ X366))))) & (hoasapnotvar = $true) & (axabs = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X370 : term,X371 : (subst > term > subst > $o)] : (~ ! [X372 : (subst > term > term)] : (~ ! [X373 : term] : ((((X371 @ id @ (X372 @ id @ X373) @ id)) = $true) | ~ ($true = ((X371 @ id @ X373 @ id)))) | ~ ! [X374 : term,X375 : subst,X376 : subst] : (((sub @ (X372 @ X375 @ X374) @ X376)) = ((X372 @ (comp @ X375 @ X376) @ (sub @ X374 @ X376)))) | (((X371 @ id @ (lam @ (X372 @ sh @ one)) @ id)) = $true)) | (((X371 @ id @ (lam @ (sub @ X370 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X377 : term] : ((((X371 @ id @ (sub @ X370 @ (push @ X377 @ id)) @ id)) = $true) | ~ (((X371 @ id @ X377 @ id)) = $true)))) & (hoasapnotvar_gthm = $true) & (induction2lem_gthm = $true) & (! [X378 : term] : ~ ! [X379 : (subst > term > term)] : ~ ! [X380 : subst,X381 : term] : (((X379 @ X380 @ X381)) = ((sub @ X378 @ (push @ X381 @ X380)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X382 : term,X383 : (subst > term > subst > $o)] : (~ ! [X384 : term] : ((((X383 @ id @ (sub @ X382 @ (push @ X384 @ id)) @ id)) = $true) | ~ ($true = ((X383 @ id @ X384 @ id)))) | ($true = ((X383 @ id @ (lam @ X382) @ id))) | ~ ! [X385 : (subst > term > term)] : (~ ! [X386 : term] : (~ ($true = ((X383 @ id @ X386 @ id))) | ($true = ((X383 @ id @ (X385 @ id @ X386) @ id)))) | ~ ! [X387 : term,X388 : subst,X389 : subst] : (((X385 @ (comp @ X388 @ X389) @ (sub @ X387 @ X389))) = ((sub @ (X385 @ X388 @ X387) @ X389))) | (((X383 @ id @ (lam @ (X385 @ sh @ one)) @ id)) = $true)) | ~ ! [X390 : subst,X391 : term,X392 : subst,X393 : subst] : (~ ($true = ((X383 @ X392 @ X391 @ (comp @ X393 @ X390)))) | ($true = ((X383 @ (comp @ X392 @ X393) @ (sub @ X391 @ X393) @ X390)))) | ~ ! [X394 : term,X395 : subst,X396 : subst,X397 : subst] : ((((X383 @ X396 @ X394 @ (comp @ X397 @ X395))) = $true) | ~ ($true = ((X383 @ (comp @ X396 @ X397) @ (sub @ X394 @ X397) @ X395))))) <=> (hoasinduction_lem3 = $true)) & ((! [X398 : term] : (((sub @ X398 @ id)) = X398) => (! [X399 : (term > $o),X400 : subst,X401 : term] : (~ ! [X402 : term,X403 : term] : (~ ($true = ((X399 @ X403))) | ~ (((X399 @ X402)) = $true) | (((X399 @ (ap @ X403 @ X402))) = $true)) | ~ ! [X404 : term] : (~ ! [X405 : term] : (~ (((X399 @ X405)) = $true) | ($true = ((X399 @ (sub @ X404 @ (push @ X405 @ id)))))) | (((X399 @ (lam @ X404))) = $true)) | ~ ! [X406 : term] : (($true = ((X399 @ (sub @ X406 @ X400)))) | ~ (((var @ X406)) = $true)) | (((X399 @ (sub @ X401 @ X400))) = $true)) => ! [X407 : term,X408 : (term > $o)] : (~ ! [X409 : term] : (~ ! [X410 : term] : (~ ($true = ((X408 @ X410))) | (((X408 @ (sub @ X409 @ (push @ X410 @ id)))) = $true)) | (((X408 @ (lam @ X409))) = $true)) | ~ ! [X411 : term,X412 : term] : (~ ($true = ((X408 @ X411))) | (((X408 @ (ap @ X411 @ X412))) = $true) | ~ ($true = ((X408 @ X412)))) | ~ ! [X413 : term] : ((((X408 @ X413)) = $true) | ~ ($true = ((var @ X413)))) | ($true = ((X408 @ X407)))))) <=> (induction2_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & ((laminj = $true) <=> ! [X414 : term,X415 : term] : ((((lam @ X415)) != ((lam @ X414))) | (X414 = X415))) & (axvarshift = $true) & ((! [X416 : term,X417 : subst] : (((sub @ one @ (push @ X416 @ X417))) = X416) => (! [X418 : term,X419 : subst] : (((comp @ sh @ (push @ X418 @ X419))) = X419) => ! [X420 : (term > $o),X421 : (term > $o),X422 : subst,X423 : term,X424 : term] : (($true = ((X420 @ (sub @ X423 @ (push @ X424 @ X422))))) | ~ ($true = ((X421 @ X423)))))) <=> (pushprop_lem1_lthm = $true)) & (axclos = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & (! [X425 : term,X426 : (term > $o),X427 : subst] : ~ ! [X428 : (term > $o)] : ~ ! [X429 : term] : (((X428 @ X429)) = ((X426 @ (sub @ X429 @ (push @ X425 @ X427))))) <=> (pushprop_lem0_lthm = $true)) & (hoasapinj2_gthm = $true) & (! [X430 : subst] : (((comp @ id @ X430)) = X430) <=> (axidl = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X431 : (subst > term > subst > $o)] : ~ ! [X432 : (term > $o)] : ~ ! [X433 : term] : (((X432 @ X433)) = ((X431 @ id @ X433 @ id)))) & (hoasinduction_lem1v2 = $true) & ((! [X434 : term,X435 : subst] : (((sub @ one @ (push @ X434 @ X435))) = X434) => (! [X436 : subst,X437 : term] : (((comp @ sh @ (push @ X437 @ X436))) = X436) => (! [X438 : subst] : (((comp @ X438 @ id)) = X438) => (! [X439 : term,X440 : (term > $o)] : (~ ! [X441 : term] : (~ (((var @ X441)) = $true) | ($true = ((X440 @ X441)))) | ~ ! [X442 : term] : (~ (((X440 @ X442)) = $true) | (((X440 @ (lam @ X442))) = $true)) | ~ ! [X443 : term,X444 : term] : (~ (((X440 @ X443)) = $true) | ~ ($true = ((X440 @ X444))) | ($true = ((X440 @ (ap @ X444 @ X443))))) | ($true = ((X440 @ X439)))) => ! [X445 : (term > $o),X446 : term,X447 : subst] : (~ ! [X448 : term] : (($true = ((X445 @ (lam @ X448)))) | ~ ! [X449 : term] : ((((X445 @ (sub @ X448 @ (push @ X449 @ id)))) = $true) | ~ ($true = ((X445 @ X449))))) | ~ ! [X450 : term,X451 : term] : (($true = ((X445 @ (ap @ X450 @ X451)))) | ~ ($true = ((X445 @ X451))) | ~ (((X445 @ X450)) = $true)) | ~ ! [X452 : term] : (($true = ((X445 @ (sub @ X452 @ X447)))) | ~ ($true = ((var @ X452)))) | (((X445 @ (sub @ X446 @ X447))) = $true)))))) <=> (induction2lem_lthm = $true)) & (ulamvarsh = $true) & ! [X453 : subst] : ? [X454 : d_subst] : (((d2subst @ X454)) = X453) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & (! [X455 : term,X456 : term] : ((X455 = X456) | (((sub @ X456 @ sh)) != ((sub @ X455 @ sh)))) <=> (shinj = $true)) & (apnotvar = $true) & (hoasapinj1_gthm = $true) & (! [X457 : term,X458 : (subst > term > subst > $o)] : ((((X458 @ id @ (lam @ X457) @ id)) = $true) | ~ ! [X459 : term] : ((((X458 @ id @ (sub @ X457 @ (push @ X459 @ id)) @ id)) = $true) | ~ ($true = ((X458 @ id @ X459 @ id)))) | ~ ! [X460 : (subst > term > term)] : (~ ! [X461 : term] : (~ (((X458 @ id @ X461 @ id)) = $true) | ($true = ((X458 @ id @ (X460 @ id @ X461) @ id)))) | ($true = ((X458 @ id @ (lam @ (X460 @ sh @ one)) @ id))) | ~ ! [X462 : subst,X463 : term,X464 : subst] : (((X460 @ (comp @ X462 @ X464) @ (sub @ X463 @ X464))) = ((sub @ (X460 @ X462 @ X463) @ X464))))) <=> (hoasinduction_lem3a = $true)) & (hoaslaminj_gthm = $true) & (substmonoid_gthm = $true) & ! [X465 : d_term] : (d_one = X465) & (pushprop_lem2v2 = $true) & ~ (ulamvar1 = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarind = $true) & (! [X466 : (subst > term > term),X467 : term,X468 : term] : ((((lam @ (X466 @ sh @ one))) != ((ap @ (sub @ X468 @ id) @ X467))) | ~ ! [X469 : subst,X470 : term,X471 : subst] : (((sub @ (X466 @ X471 @ X470) @ X469)) = ((X466 @ (comp @ X471 @ X469) @ (sub @ X470 @ X469))))) <=> (hoaslamnotap = $true)) & ((! [X472 : term,X473 : term,X474 : term,X475 : term] : ((((ap @ X472 @ X475)) != ((ap @ X473 @ X474))) | (X474 = X475)) => ! [X476 : term,X477 : term,X478 : term,X479 : term] : ((X478 = X479) | (((ap @ (sub @ X476 @ id) @ X478)) != ((ap @ (sub @ X477 @ id) @ X479))))) <=> (hoasapinj2_lthm = $true)) & (! [X480 : subst] : (((push @ (sub @ one @ X480) @ (comp @ sh @ X480))) = X480) <=> (axscons = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X481 : term] : (((sub @ X481 @ id)) = X481) => (! [X482 : term,X483 : term,X484 : term,X485 : term] : ((X483 = X484) | (((ap @ X484 @ X482)) != ((ap @ X483 @ X485)))) => ! [X486 : term,X487 : term,X488 : term,X489 : term] : ((X486 = X488) | (((ap @ (sub @ X486 @ id) @ X489)) != ((ap @ (sub @ X488 @ id) @ X487))))))) & ((hoasinduction_lem3v2 = $true) <=> ! [X490 : term,X491 : (term > $o),X492 : (subst > term > subst > $o)] : (~ ! [X493 : (subst > term > term)] : (~ ! [X494 : term,X495 : subst,X496 : subst] : (((sub @ (X493 @ X495 @ X494) @ X496)) = ((X493 @ (comp @ X495 @ X496) @ (sub @ X494 @ X496)))) | (((X492 @ id @ (lam @ (X493 @ sh @ one)) @ id)) = $true) | ~ ! [X497 : term] : (~ ($true = ((X492 @ id @ X497 @ id))) | (((X492 @ id @ (X493 @ id @ X497) @ id)) = $true))) | ~ ! [X498 : subst,X499 : term,X500 : subst,X501 : subst] : (~ ($true = ((X492 @ X498 @ X499 @ (comp @ X500 @ X501)))) | ($true = ((X492 @ (comp @ X498 @ X500) @ (sub @ X499 @ X500) @ X501)))) | ~ ! [X502 : term] : (((X492 @ id @ X502 @ id)) = ((X491 @ X502))) | ~ ! [X503 : term] : (($true = ((X491 @ (sub @ X490 @ (push @ X503 @ id))))) | ~ (((X491 @ X503)) = $true)) | (((X491 @ (lam @ X490))) = $true) | ~ ! [X504 : subst,X505 : subst,X506 : subst,X507 : term] : (($true = ((X492 @ X506 @ X507 @ (comp @ X505 @ X504)))) | ~ (((X492 @ (comp @ X506 @ X505) @ (sub @ X507 @ X505) @ X504)) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X508 : (subst > term > subst > $o)] : ~ ! [X509 : (term > $o)] : ~ ! [X510 : term] : (((X509 @ X510)) = ((X508 @ id @ X510 @ id)))) & (hoaslamnotap_gthm = $true) & (termmset_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X511 : term] : (((sub @ X511 @ id)) = X511) => (! [X512 : term,X513 : (subst > term > subst > $o)] : ((((X513 @ id @ (lam @ (sub @ X512 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X514 : (subst > term > term)] : (($true = ((X513 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X515 : term] : (($true = ((X513 @ id @ (X514 @ id @ X515) @ id))) | ~ ($true = ((X513 @ id @ X515 @ id)))) | ~ ! [X516 : subst,X517 : term,X518 : subst] : (((X514 @ (comp @ X518 @ X516) @ (sub @ X517 @ X516))) = ((sub @ (X514 @ X518 @ X517) @ X516)))) | ~ ! [X519 : term] : ((((X513 @ id @ (sub @ X512 @ (push @ X519 @ id)) @ id)) = $true) | ~ (((X513 @ id @ X519 @ id)) = $true))) => ! [X520 : term,X521 : (subst > term > subst > $o)] : (~ ! [X522 : term] : (($true = ((X521 @ id @ (sub @ X520 @ (push @ X522 @ id)) @ id))) | ~ (((X521 @ id @ X522 @ id)) = $true)) | (((X521 @ id @ (lam @ X520) @ id)) = $true) | ~ ! [X523 : (subst > term > term)] : (~ ! [X524 : term] : (~ (((X521 @ id @ X524 @ id)) = $true) | ($true = ((X521 @ id @ (X523 @ id @ X524) @ id)))) | ~ ! [X525 : subst,X526 : subst,X527 : term] : (((sub @ (X523 @ X526 @ X527) @ X525)) = ((X523 @ (comp @ X526 @ X525) @ (sub @ X527 @ X525)))) | (((X521 @ id @ (lam @ (X523 @ sh @ one)) @ id)) = $true)))))) & (! [X528 : term,X529 : (term > $o)] : ((((X529 @ X528)) = $true) | ~ ! [X530 : term] : (($true = ((X529 @ (lam @ X530)))) | ~ ($true = ((X529 @ X530)))) | ~ ! [X531 : term] : (~ ($true = ((var @ X531))) | ($true = ((X529 @ X531)))) | ~ ! [X532 : term,X533 : term] : (~ ($true = ((X529 @ X533))) | (((X529 @ (ap @ X533 @ X532))) = $true) | ~ (((X529 @ X532)) = $true))) <=> (induction = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X534 : term] : ~ ! [X535 : (subst > term > term)] : ~ ! [X536 : subst,X537 : term] : (((sub @ X534 @ (push @ X537 @ X536))) = ((X535 @ X536 @ X537)))) & (! [X538 : subst,X539 : term,X540 : (term > $o)] : ~ ! [X541 : (term > $o)] : ~ ! [X542 : term] : (((X540 @ (sub @ X542 @ (push @ X539 @ X538)))) = ((X541 @ X542))) <=> (pushprop_lem0 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X548 : term,X549 : subst] : (((comp @ sh @ (push @ X548 @ X549))) = X549) <=> (axshiftcons = $true)) & (hoaslamnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id))))),
% 13.65/2.32 inference(fool_elimination,[],[f4])).
% 13.65/2.32 thf(f6,plain,(
% 13.65/2.32 ~ (hoasinduction_lem0 = ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : (hoasinduction_p_and_p_prime @ X0 @ X1))),
% 13.65/2.32 inference(rectify,[],[f3])).
% 13.65/2.32 thf(f7,plain,(
% 13.65/2.32 ~ (hoasinduction_lem0 = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1)))))))),
% 13.65/2.32 inference(fool_elimination,[],[f6])).
% 13.65/2.32 thf(f8,plain,(
% 13.65/2.32 (hoasinduction_lem0 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1)))))))),
% 13.65/2.32 inference(flattening,[],[f7])).
% 13.65/2.32 thf(f9,plain,(
% 13.65/2.32 ((hoasinduction_lem3aaa = $true) <=> ! [X0 : (subst > term > subst > $o),X1 : term] : ((((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X2 : (subst > term > term),X3 : term] : (~ ! [X4 : term] : (~ (((X0 @ id @ X4 @ id)) = $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) | ~ ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) | ($true = ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id))) | ~ ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9)))) | ~ ! [X11 : term] : (($true = ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) | ~ (((X0 @ id @ X11 @ id)) = $true)))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2 = $true) & (((d2subst @ d_id)) = id) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & ((pushprop_lem1v2 = $true) <=> ! [X16 : (term > $o),X17 : subst,X18 : (term > $o),X19 : term] : (~ ($true = ((X16 @ X19))) | ($true = ((X18 @ one))) | ~ ! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))))) & (! [X21 : (term > $o),X22 : term] : (~ ! [X23 : term,X24 : term] : ((((X21 @ (ap @ X23 @ X24))) = $true) | ~ ($true = ((X21 @ X24))) | ~ (((X21 @ X23)) = $true)) | ~ ! [X25 : term] : (~ ! [X26 : term] : (~ ($true = ((X21 @ X26))) | ($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id)))))) | ($true = ((X21 @ (lam @ X25))))) | ($true = ((X21 @ X22))) | ~ ! [X27 : term] : ((((X21 @ X27)) = $true) | ~ (((var @ X27)) = $true))) <=> (induction2 = $true)) & (! [X28 : (subst > term > subst > $o),X29 : term] : (~ ! [X30 : (subst > term > term)] : (~ ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32))) | ~ ! [X34 : term] : ((((X28 @ id @ (X30 @ id @ X34) @ id)) = $true) | ~ ($true = ((X28 @ id @ X34 @ id)))) | ($true = ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id)))) | (((X28 @ id @ X29 @ id)) = $true) | ~ ! [X35 : term] : ((((X28 @ id @ X35 @ id)) = $true) | ~ ($true = ((var @ (sub @ X35 @ id))))) | ~ ! [X36 : term,X37 : subst,X38 : subst,X39 : subst] : ((((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) = $true) | ~ ($true = ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37)))) | ~ ! [X40 : term,X41 : term] : ((((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) = $true) | ~ (((X28 @ id @ X41 @ id)) = $true) | ~ (((X28 @ id @ X40 @ id)) = $true)) | ~ ! [X42 : subst,X43 : subst,X44 : term,X45 : subst] : (~ (((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) = $true) | (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) = $true))) <=> (hoasinduction = $true)) & ~ (((var @ (d2term @ d_one))) = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X52 : term,X53 : (subst > term > subst > $o),X54 : term] : (~ ! [X55 : term,X56 : subst,X57 : subst,X58 : subst] : (($true = ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)))) | ~ ($true = ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)))) | ($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | ~ (((X53 @ id @ X54 @ id)) = $true) | ~ ! [X59 : term,X60 : term] : ((((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) = $true) | ~ ($true = ((X53 @ id @ X59 @ id))) | ~ (((X53 @ id @ X60 @ id)) = $true)) | ~ ! [X61 : subst,X62 : term,X63 : subst,X64 : subst] : (~ (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) = $true) | (((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) = $true)) | ~ (((X53 @ id @ X52 @ id)) = $true))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X65 : (subst > term > subst > $o),X66 : term] : (~ ! [X67 : (subst > term > term)] : (~ ! [X68 : term] : (~ ($true = ((X65 @ id @ X68 @ id))) | (((X65 @ id @ (X67 @ id @ X68) @ id)) = $true)) | ~ ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70)))) | ($true = ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id)))) | ($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id))) | ~ ! [X72 : term] : (($true = ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id))) | ~ (((X65 @ id @ X72 @ id)) = $true)))) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (~ ! [X77 : term] : (($true = ((X76 @ (sub @ X75 @ (push @ X77 @ id))))) | ~ ($true = ((X76 @ X77)))) | ~ ! [X78 : term] : (((X74 @ id @ X78 @ id)) = ((X76 @ X78))) | ~ ! [X79 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) = $true) | ~ ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81))) | ~ ! [X83 : term] : (~ (((X74 @ id @ X83 @ id)) = $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true))) | (((X76 @ (lam @ X75))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lem1v2_gthm = $true) & (pushprop_lthm = $true) & ((substmonoid_lthm = $true) <=> (! [X84 : subst] : (((comp @ id @ X84)) = X84) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))))) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X88 : (subst > term > subst > $o),X89 : term] : ((((X88 @ id @ X89 @ id)) = $true) | ~ ! [X90 : term,X91 : term] : (~ (((X88 @ id @ X90 @ id)) = $true) | ~ ($true = ((X88 @ id @ X91 @ id))) | (((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) = $true)) | ~ ! [X92 : (subst > term > term)] : ((((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) = $true) | ~ ! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) | ~ ! [X96 : term] : (~ (((X88 @ id @ X96 @ id)) = $true) | (((X88 @ id @ (X92 @ id @ X96) @ id)) = $true))))) & (pushprop_lem1_gthm = $true) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => ! [X100 : (term > $o),X101 : term,X102 : subst,X103 : (term > $o)] : (~ ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | (((X100 @ one)) = $true) | ~ ($true = ((X103 @ X101)))))) & ((! [X105 : term] : (((sub @ X105 @ id)) = X105) => ! [X106 : term] : (((sub @ X106 @ id)) = X106)) <=> (termmset_lthm = $true)) & (hoasinduction_lem1 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X107 : term] : ~ ! [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) != ((X108 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ! [X110 : d_term,X109 : d_term] : ((((d2term @ X110)) = ((d2term @ X109))) => (X109 = X110)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X111 : term] : ~ ! [X112 : (subst > term > term)] : ~ ! [X113 : subst,X114 : term] : (((X112 @ X113 @ X114)) = ((sub @ X111 @ (push @ X114 @ X113)))) => (! [X115 : term] : (((sub @ X115 @ id)) = X115) => ! [X116 : term,X117 : (subst > term > subst > $o),X118 : (term > $o)] : (~ ! [X119 : term] : ((((X118 @ (sub @ X116 @ (push @ X119 @ id)))) = $true) | ~ ($true = ((X118 @ X119)))) | ~ ! [X120 : term] : (((X117 @ id @ X120 @ id)) = ((X118 @ X120))) | ~ ! [X121 : (subst > term > term)] : (~ ! [X122 : subst,X124 : term,X123 : subst] : (((X121 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122))) = ((sub @ (X121 @ X123 @ X124) @ X122))) | ~ ! [X125 : term] : (($true = ((X117 @ id @ (X121 @ id @ X125) @ id))) | ~ (((X117 @ id @ X125 @ id)) = $true)) | (((X117 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true)) | ($true = ((X118 @ (lam @ X116)))))))) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) <=> (axvarcons = $true)) & (axmap = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lthm_orig = $true) & (((d2subst @ d_id)) = sh) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) <=> (substmonoid = $true)) & (pushprop_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X130 : (subst > term > subst > $o)] : ~ ! [X131 : (term > $o)] : ~ ! [X132 : term] : (((X130 @ id @ X132 @ id)) = ((X131 @ X132))) => (! [X133 : term,X134 : (term > $o)] : (~ ! [X135 : term] : ((((X134 @ X135)) = $true) | ~ (((var @ X135)) = $true)) | ~ ! [X136 : term,X137 : term] : (~ ($true = ((X134 @ X137))) | (((X134 @ (ap @ X137 @ X136))) = $true) | ~ (((X134 @ X136)) = $true)) | (((X134 @ X133)) = $true) | ~ ! [X138 : term] : (~ ! [X139 : term] : ((((X134 @ (sub @ X138 @ (push @ X139 @ id)))) = $true) | ~ (((X134 @ X139)) = $true)) | ($true = ((X134 @ (lam @ X138)))))) => (! [X140 : term] : (((sub @ X140 @ id)) = X140) => (! [X141 : term,X142 : (subst > term > subst > $o),X143 : (term > $o)] : (~ ! [X144 : (subst > term > term)] : (~ ! [X145 : subst,X146 : subst,X147 : term] : (((X144 @ (comp @ X145 @ X146) @ (sub @ X147 @ X146))) = ((sub @ (X144 @ X145 @ X147) @ X146))) | (((X142 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ~ ! [X148 : term] : (($true = ((X142 @ id @ (X144 @ id @ X148) @ id))) | ~ ($true = ((X142 @ id @ X148 @ id))))) | ($true = ((X143 @ (lam @ X141)))) | ~ ! [X149 : term] : (~ (((X143 @ X149)) = $true) | ($true = ((X143 @ (sub @ X141 @ (push @ X149 @ id)))))) | ~ ! [X150 : term] : (((X143 @ X150)) = ((X142 @ id @ X150 @ id)))) => ! [X151 : (subst > term > subst > $o),X152 : term] : (~ ! [X153 : subst,X154 : subst,X155 : subst,X156 : term] : (~ (((X151 @ (comp @ X153 @ X155) @ (sub @ X156 @ X155) @ X154)) = $true) | ($true = ((X151 @ X153 @ X156 @ (comp @ X155 @ X154))))) | ~ ! [X157 : subst,X158 : term,X159 : subst,X160 : subst] : (~ (((X151 @ X157 @ X158 @ (comp @ X159 @ X160))) = $true) | ($true = ((X151 @ (comp @ X157 @ X159) @ (sub @ X158 @ X159) @ X160)))) | ~ ! [X161 : term] : ((((X151 @ id @ X161 @ id)) = $true) | ~ (((var @ (sub @ X161 @ id))) = $true)) | (((X151 @ id @ X152 @ id)) = $true) | ~ ! [X162 : (subst > term > term)] : (~ ! [X163 : term] : (~ (((X151 @ id @ X163 @ id)) = $true) | ($true = ((X151 @ id @ (X162 @ id @ X163) @ id)))) | ~ ! [X164 : subst,X166 : subst,X165 : term] : (((sub @ (X162 @ X166 @ X165) @ X164)) = ((X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))) | ($true = ((X151 @ id @ (lam @ (X162 @ sh @ one)) @ id)))) | ~ ! [X167 : term,X168 : term] : (~ ($true = ((X151 @ id @ X167 @ id))) | ~ (((X151 @ id @ X168 @ id)) = $true) | (((X151 @ id @ (ap @ (sub @ X168 @ id) @ X167) @ id)) = $true)))))))) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X169 : term,X170 : (term > $o),X171 : (subst > term > subst > $o),X172 : term] : (~ ! [X173 : term] : (((X170 @ X173)) = ((X171 @ id @ X173 @ id))) | ~ ! [X174 : subst,X175 : subst,X176 : term,X177 : subst] : ((((X171 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) = $true) | ~ (((X171 @ X175 @ X176 @ (comp @ X174 @ X177))) = $true)) | ~ (((X170 @ X172)) = $true) | (((X170 @ (ap @ X172 @ X169))) = $true) | ~ ($true = ((X170 @ X169))) | ~ ! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : ((((X171 @ X181 @ X180 @ (comp @ X179 @ X178))) = $true) | ~ ($true = ((X171 @ (comp @ X181 @ X179) @ (sub @ X180 @ X179) @ X178)))) | ~ ! [X182 : term,X183 : term] : (~ ($true = ((X171 @ id @ X182 @ id))) | (((X171 @ id @ (ap @ (sub @ X182 @ id) @ X183) @ id)) = $true) | ~ ($true = ((X171 @ id @ X183 @ id)))))) & (hoasinduction_lem1_lthm = $true) & (lamnotvar = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((! [X184 : (subst > term > subst > $o)] : ~ ! [X185 : (term > $o)] : ~ ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) => (! [X187 : (term > $o),X188 : term] : (~ ! [X189 : term] : (~ ($true = ((var @ X189))) | ($true = ((X187 @ X189)))) | ~ ! [X190 : term] : (($true = ((X187 @ (lam @ X190)))) | ~ ! [X191 : term] : ((((X187 @ (sub @ X190 @ (push @ X191 @ id)))) = $true) | ~ ($true = ((X187 @ X191))))) | ~ ! [X192 : term,X193 : term] : (~ ($true = ((X187 @ X192))) | ~ (((X187 @ X193)) = $true) | (((X187 @ (ap @ X192 @ X193))) = $true)) | (((X187 @ X188)) = $true)) => (! [X194 : term] : (((sub @ X194 @ id)) = X194) => (! [X195 : term,X196 : (term > $o),X197 : (subst > term > subst > $o)] : (~ ! [X198 : term] : (((X197 @ id @ X198 @ id)) = ((X196 @ X198))) | ~ ! [X199 : term] : (($true = ((X196 @ (sub @ X195 @ (push @ X199 @ id))))) | ~ (((X196 @ X199)) = $true)) | (((X196 @ (lam @ X195))) = $true) | ~ ! [X200 : (subst > term > term)] : ((((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true) | ~ ! [X201 : term] : (~ (((X197 @ id @ X201 @ id)) = $true) | (((X197 @ id @ (X200 @ id @ X201) @ id)) = $true)) | ~ ! [X202 : term,X204 : subst,X203 : subst] : (((sub @ (X200 @ X204 @ X202) @ X203)) = ((X200 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))))) => ! [X205 : (subst > term > subst > $o),X206 : term] : (~ ! [X207 : (subst > term > term)] : (($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id))) | ~ ! [X210 : subst,X208 : subst,X209 : term] : (((X207 @ (comp @ X210 @ X208) @ (sub @ X209 @ X208))) = ((sub @ (X207 @ X210 @ X209) @ X208))) | ~ ! [X211 : term] : (~ (((X205 @ id @ X211 @ id)) = $true) | (((X205 @ id @ (X207 @ id @ X211) @ id)) = $true))) | ~ ! [X212 : term,X213 : term] : (~ ($true = ((X205 @ id @ X212 @ id))) | ~ ($true = ((X205 @ id @ X213 @ id))) | (((X205 @ id @ (ap @ (sub @ X213 @ id) @ X212) @ id)) = $true)) | (((X205 @ id @ X206 @ id)) = $true)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X214 : term] : (((sub @ X214 @ id)) = X214) => ! [X215 : (subst > term > subst > $o),X216 : term,X217 : (term > $o)] : (~ ! [X218 : (subst > term > term)] : (~ ! [X219 : term] : (~ (((X215 @ id @ X219 @ id)) = $true) | (((X215 @ id @ (X218 @ id @ X219) @ id)) = $true)) | ~ ! [X220 : subst,X222 : term,X221 : subst] : (((sub @ (X218 @ X220 @ X222) @ X221)) = ((X218 @ (comp @ X220 @ X221) @ (sub @ X222 @ X221)))) | ($true = ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id)))) | ($true = ((X217 @ (lam @ X216)))) | ~ ! [X223 : term] : (((X217 @ X223)) = ((X215 @ id @ X223 @ id))) | ~ ! [X224 : subst,X225 : subst,X226 : term,X227 : subst] : ((((X215 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true) | ~ (((X215 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true)) | ~ ! [X228 : subst,X229 : subst,X230 : term,X231 : subst] : (~ (((X215 @ (comp @ X228 @ X229) @ (sub @ X230 @ X229) @ X231)) = $true) | ($true = ((X215 @ X228 @ X230 @ (comp @ X229 @ X231))))) | ~ ! [X232 : term] : (($true = ((X217 @ (sub @ X216 @ (push @ X232 @ id))))) | ~ ($true = ((X217 @ X232))))))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X233 : term,X234 : (term > $o)] : (~ ! [X235 : term,X236 : term] : ((((X234 @ (ap @ X236 @ X235))) = $true) | ~ (((X234 @ X236)) = $true) | ~ (((X234 @ X235)) = $true)) | ~ ! [X237 : term] : (~ ! [X238 : term] : (($true = ((X234 @ (sub @ X237 @ (push @ X238 @ id))))) | ~ ($true = ((X234 @ X238)))) | ($true = ((X234 @ (lam @ X237))))) | ~ ! [X239 : term] : (~ ($true = ((var @ X239))) | ($true = ((X234 @ X239)))) | (((X234 @ X233)) = $true)) => (! [X240 : (subst > term > subst > $o),X241 : term,X242 : term] : (~ ($true = ((X240 @ id @ X241 @ id))) | ~ ! [X243 : term,X244 : term] : (~ ($true = ((X240 @ id @ X243 @ id))) | (((X240 @ id @ (ap @ (sub @ X244 @ id) @ X243) @ id)) = $true) | ~ ($true = ((X240 @ id @ X244 @ id)))) | ~ ! [X245 : subst,X246 : term,X247 : subst,X248 : subst] : (($true = ((X240 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245) @ X248))) | ~ ($true = ((X240 @ X247 @ X246 @ (comp @ X245 @ X248))))) | (((X240 @ id @ (ap @ X241 @ X242) @ id)) = $true) | ~ (((X240 @ id @ X242 @ id)) = $true) | ~ ! [X249 : subst,X250 : term,X251 : subst,X252 : subst] : (($true = ((X240 @ X249 @ X250 @ (comp @ X251 @ X252)))) | ~ (((X240 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251) @ X252)) = $true))) => (! [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ (lam @ X253) @ id)) = $true) | ~ ! [X255 : subst,X256 : subst,X257 : subst,X258 : term] : ((((X254 @ (comp @ X257 @ X256) @ (sub @ X258 @ X256) @ X255)) = $true) | ~ (((X254 @ X257 @ X258 @ (comp @ X256 @ X255))) = $true)) | ~ ! [X259 : term,X260 : subst,X261 : subst,X262 : subst] : (~ (((X254 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260) @ X262)) = $true) | (((X254 @ X261 @ X259 @ (comp @ X260 @ X262))) = $true)) | ~ ! [X263 : term] : (~ (((X254 @ id @ X263 @ id)) = $true) | (((X254 @ id @ (sub @ X253 @ (push @ X263 @ id)) @ id)) = $true)) | ~ ! [X264 : (subst > term > term)] : (~ ! [X265 : subst,X266 : subst,X267 : term] : (((sub @ (X264 @ X265 @ X267) @ X266)) = ((X264 @ (comp @ X265 @ X266) @ (sub @ X267 @ X266)))) | ~ ! [X268 : term] : (~ (((X254 @ id @ X268 @ id)) = $true) | ($true = ((X254 @ id @ (X264 @ id @ X268) @ id)))) | (((X254 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true))) => ! [X269 : (subst > term > subst > $o),X270 : term] : (~ ! [X271 : subst,X272 : term,X273 : subst,X274 : subst] : (~ ($true = ((X269 @ X271 @ X272 @ (comp @ X274 @ X273)))) | (((X269 @ (comp @ X271 @ X274) @ (sub @ X272 @ X274) @ X273)) = $true)) | ~ ! [X275 : term] : (~ (((var @ (sub @ X275 @ id))) = $true) | ($true = ((X269 @ id @ X275 @ id)))) | (((X269 @ id @ X270 @ id)) = $true) | ~ ! [X276 : (subst > term > term)] : ((((X269 @ id @ (lam @ (X276 @ sh @ one)) @ id)) = $true) | ~ ! [X277 : term] : (~ ($true = ((X269 @ id @ X277 @ id))) | (((X269 @ id @ (X276 @ id @ X277) @ id)) = $true)) | ~ ! [X278 : term,X279 : subst,X280 : subst] : (((X276 @ (comp @ X280 @ X279) @ (sub @ X278 @ X279))) = ((sub @ (X276 @ X280 @ X278) @ X279)))) | ~ ! [X281 : subst,X282 : subst,X283 : subst,X284 : term] : (~ (((X269 @ (comp @ X283 @ X281) @ (sub @ X284 @ X281) @ X282)) = $true) | (((X269 @ X283 @ X284 @ (comp @ X281 @ X282))) = $true)) | ~ ! [X285 : term,X286 : term] : (~ ($true = ((X269 @ id @ X285 @ id))) | ~ ($true = ((X269 @ id @ X286 @ id))) | ($true = ((X269 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id))))))))) & (hoaslamnotvar = $true) & ((induction2lem = $true) <=> ! [X287 : subst,X288 : term,X289 : (term > $o)] : (~ ! [X290 : term] : ((((X289 @ (lam @ X290))) = $true) | ~ ! [X291 : term] : ((((X289 @ (sub @ X290 @ (push @ X291 @ id)))) = $true) | ~ ($true = ((X289 @ X291))))) | ~ ! [X292 : term] : (~ (((var @ X292)) = $true) | ($true = ((X289 @ (sub @ X292 @ X287))))) | ($true = ((X289 @ (sub @ X288 @ X287)))) | ~ ! [X293 : term,X294 : term] : (~ (((X289 @ X293)) = $true) | (((X289 @ (ap @ X293 @ X294))) = $true) | ~ ($true = ((X289 @ X294)))))) & ((hoaslaminj_lthm = $true) <=> (! [X296 : subst,X295 : term] : (((sub @ one @ (push @ X295 @ X296))) = X295) => (! [X297 : term,X298 : subst] : (((comp @ sh @ (push @ X297 @ X298))) = X298) => (! [X300 : term,X299 : term] : ((((lam @ X299)) != ((lam @ X300))) | (X299 = X300)) => ! [X301 : term,X302 : (subst > term > term),X303 : subst,X304 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((X304 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X304 @ X308 @ X309) @ X310))) | (((X302 @ X303 @ X301)) = ((X304 @ X303 @ X301))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ~ ! [X306 : subst,X305 : subst,X307 : term] : (((X302 @ (comp @ X306 @ X305) @ (sub @ X307 @ X305))) = ((sub @ (X302 @ X306 @ X307) @ X305)))))))) & (! [X311 : term] : ~ ! [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) != ((X312 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem1v2_gthm = $true) & ! [X313 : d_subst] : (d_id = X313) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) <=> (apinj1 = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoaslaminj = $true) <=> ! [X320 : (subst > term > term),X319 : term,X318 : subst,X321 : (subst > term > term)] : (~ ! [X325 : subst,X326 : term,X327 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) = ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325)))) | ~ ! [X323 : subst,X324 : term,X322 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) = ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & ((! [X329 : term] : (((sub @ X329 @ id)) = X329) => (! [X330 : (subst > term > subst > $o),X331 : term] : (($true = ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id))) | ~ ! [X332 : (subst > term > term)] : (($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ~ ! [X333 : term] : (~ (((X330 @ id @ X333 @ id)) = $true) | ($true = ((X330 @ id @ (X332 @ id @ X333) @ id)))) | ~ ! [X336 : subst,X335 : term,X334 : subst] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ~ ! [X337 : term] : (~ (((X330 @ id @ X337 @ id)) = $true) | ($true = ((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))))) => ! [X338 : term,X339 : (subst > term > subst > $o)] : (($true = ((X339 @ id @ (lam @ X338) @ id))) | ~ ! [X340 : term] : (~ ($true = ((X339 @ id @ X340 @ id))) | (((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)) = $true)) | ~ ! [X341 : subst,X342 : subst,X343 : term,X344 : subst] : (~ (((X339 @ (comp @ X344 @ X341) @ (sub @ X343 @ X341) @ X342)) = $true) | ($true = ((X339 @ X344 @ X343 @ (comp @ X341 @ X342))))) | ~ ! [X345 : (subst > term > term)] : ((((X339 @ id @ (lam @ (X345 @ sh @ one)) @ id)) = $true) | ~ ! [X346 : term] : (~ ($true = ((X339 @ id @ X346 @ id))) | (((X339 @ id @ (X345 @ id @ X346) @ id)) = $true)) | ~ ! [X347 : subst,X348 : subst,X349 : term] : (((X345 @ (comp @ X347 @ X348) @ (sub @ X349 @ X348))) = ((sub @ (X345 @ X347 @ X349) @ X348)))) | ~ ! [X350 : subst,X351 : subst,X352 : term,X353 : subst] : (~ (((X339 @ X351 @ X352 @ (comp @ X350 @ X353))) = $true) | ($true = ((X339 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350) @ X353))))))) <=> (hoasinduction_lem3_lthm = $true)) & (induction2_gthm = $true) & (axapp = $true) & ((pushprop_lem1 = $true) <=> ! [X354 : (term > $o),X355 : term,X356 : (term > $o),X357 : subst,X358 : term] : (~ (((X354 @ X355)) = $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357))))))) & ! [X359 : d_subst,X360 : d_subst] : ((((d2subst @ X359)) = ((d2subst @ X360))) => (X359 = X360)) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363))) & (hoasapnotvar = $true) & (axabs = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X365 : term,X366 : (subst > term > subst > $o)] : (~ ! [X367 : (subst > term > term)] : (~ ! [X368 : term] : ((((X366 @ id @ (X367 @ id @ X368) @ id)) = $true) | ~ ($true = ((X366 @ id @ X368 @ id)))) | ~ ! [X370 : subst,X371 : subst,X369 : term] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) | ($true = ((X366 @ id @ (lam @ (X367 @ sh @ one)) @ id)))) | (((X366 @ id @ (lam @ (sub @ X365 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X372 : term] : (($true = ((X366 @ id @ (sub @ X365 @ (push @ X372 @ id)) @ id))) | ~ (((X366 @ id @ X372 @ id)) = $true)))) & (hoasapnotvar_gthm = $true) & (induction2lem_gthm = $true) & (! [X373 : term] : ~ ! [X374 : (subst > term > term)] : ~ ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X377 : term,X378 : (subst > term > subst > $o)] : (~ ! [X379 : term] : ((((X378 @ id @ (sub @ X377 @ (push @ X379 @ id)) @ id)) = $true) | ~ ($true = ((X378 @ id @ X379 @ id)))) | (((X378 @ id @ (lam @ X377) @ id)) = $true) | ~ ! [X380 : (subst > term > term)] : (~ ! [X381 : term] : (~ (((X378 @ id @ X381 @ id)) = $true) | ($true = ((X378 @ id @ (X380 @ id @ X381) @ id)))) | ~ ! [X384 : subst,X383 : subst,X382 : term] : (((sub @ (X380 @ X383 @ X382) @ X384)) = ((X380 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384)))) | (((X378 @ id @ (lam @ (X380 @ sh @ one)) @ id)) = $true)) | ~ ! [X385 : subst,X386 : term,X387 : subst,X388 : subst] : (~ ($true = ((X378 @ X387 @ X386 @ (comp @ X388 @ X385)))) | (((X378 @ (comp @ X387 @ X388) @ (sub @ X386 @ X388) @ X385)) = $true)) | ~ ! [X389 : term,X390 : subst,X391 : subst,X392 : subst] : (($true = ((X378 @ X391 @ X389 @ (comp @ X392 @ X390)))) | ~ ($true = ((X378 @ (comp @ X391 @ X392) @ (sub @ X389 @ X392) @ X390))))) <=> (hoasinduction_lem3 = $true)) & ((! [X393 : term] : (((sub @ X393 @ id)) = X393) => (! [X394 : (term > $o),X395 : subst,X396 : term] : (~ ! [X397 : term,X398 : term] : (~ (((X394 @ X398)) = $true) | ~ (((X394 @ X397)) = $true) | ($true = ((X394 @ (ap @ X398 @ X397))))) | ~ ! [X399 : term] : (~ ! [X400 : term] : (~ ($true = ((X394 @ X400))) | ($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id)))))) | ($true = ((X394 @ (lam @ X399))))) | ~ ! [X401 : term] : ((((X394 @ (sub @ X401 @ X395))) = $true) | ~ (((var @ X401)) = $true)) | ($true = ((X394 @ (sub @ X396 @ X395))))) => ! [X402 : term,X403 : (term > $o)] : (~ ! [X404 : term] : (~ ! [X405 : term] : (~ (((X403 @ X405)) = $true) | (((X403 @ (sub @ X404 @ (push @ X405 @ id)))) = $true)) | (((X403 @ (lam @ X404))) = $true)) | ~ ! [X406 : term,X407 : term] : (~ ($true = ((X403 @ X406))) | ($true = ((X403 @ (ap @ X406 @ X407)))) | ~ (((X403 @ X407)) = $true)) | ~ ! [X408 : term] : (($true = ((X403 @ X408))) | ~ ($true = ((var @ X408)))) | (((X403 @ X402)) = $true)))) <=> (induction2_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2_gthm = $true) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) <=> (laminj = $true)) & (axvarshift = $true) & ((! [X411 : term,X412 : subst] : (((sub @ one @ (push @ X411 @ X412))) = X411) => (! [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) = X414) => ! [X415 : (term > $o),X416 : (term > $o),X417 : subst,X418 : term,X419 : term] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | ~ (((X416 @ X418)) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (axclos = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & (! [X421 : (term > $o),X420 : term,X422 : subst] : ~ ! [X423 : (term > $o)] : ~ ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) <=> (pushprop_lem0_lthm = $true)) & (hoasapinj2_gthm = $true) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) <=> (axidl = $true)) & (! [X426 : (subst > term > subst > $o)] : ~ ! [X427 : (term > $o)] : ~ ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem1v2 = $true) & ((! [X429 : term,X430 : subst] : (((sub @ one @ (push @ X429 @ X430))) = X429) => (! [X432 : term,X431 : subst] : (((comp @ sh @ (push @ X432 @ X431))) = X431) => (! [X433 : subst] : (((comp @ X433 @ id)) = X433) => (! [X434 : term,X435 : (term > $o)] : (~ ! [X436 : term] : (~ (((var @ X436)) = $true) | ($true = ((X435 @ X436)))) | ~ ! [X437 : term] : (~ (((X435 @ X437)) = $true) | ($true = ((X435 @ (lam @ X437))))) | ~ ! [X438 : term,X439 : term] : (~ ($true = ((X435 @ X438))) | ~ (((X435 @ X439)) = $true) | ($true = ((X435 @ (ap @ X439 @ X438))))) | ($true = ((X435 @ X434)))) => ! [X440 : (term > $o),X441 : term,X442 : subst] : (~ ! [X443 : term] : ((((X440 @ (lam @ X443))) = $true) | ~ ! [X444 : term] : (($true = ((X440 @ (sub @ X443 @ (push @ X444 @ id))))) | ~ ($true = ((X440 @ X444))))) | ~ ! [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) = $true) | ~ (((X440 @ X446)) = $true) | ~ (((X440 @ X445)) = $true)) | ~ ! [X447 : term] : (($true = ((X440 @ (sub @ X447 @ X442)))) | ~ (((var @ X447)) = $true)) | (((X440 @ (sub @ X441 @ X442))) = $true)))))) <=> (induction2lem_lthm = $true)) & (ulamvarsh = $true) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop = $true) & ((shinj = $true) <=> ! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451))) & (apnotvar = $true) & (hoasapinj1_gthm = $true) & (! [X452 : term,X453 : (subst > term > subst > $o)] : ((((X453 @ id @ (lam @ X452) @ id)) = $true) | ~ ! [X454 : term] : (($true = ((X453 @ id @ (sub @ X452 @ (push @ X454 @ id)) @ id))) | ~ (((X453 @ id @ X454 @ id)) = $true)) | ~ ! [X455 : (subst > term > term)] : (~ ! [X456 : term] : (~ (((X453 @ id @ X456 @ id)) = $true) | ($true = ((X453 @ id @ (X455 @ id @ X456) @ id)))) | (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X457 @ X458) @ X459)) = ((X455 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))))) <=> (hoasinduction_lem3a = $true)) & (hoaslaminj_gthm = $true) & (substmonoid_gthm = $true) & ! [X460 : d_term] : (d_one = X460) & (pushprop_lem2v2 = $true) & ~ (ulamvar1 = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarind = $true) & ((hoaslamnotap = $true) <=> ! [X462 : term,X461 : (subst > term > term),X463 : term] : (~ ! [X466 : subst,X465 : term,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462))))) & ((! [X467 : term,X469 : term,X468 : term,X470 : term] : ((((ap @ X467 @ X470)) != ((ap @ X468 @ X469))) | (X469 = X470)) => ! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473))))) <=> (hoasapinj2_lthm = $true)) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) <=> (axscons = $true)) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) => (! [X480 : term,X477 : term,X479 : term,X478 : term] : ((X478 = X479) | (((ap @ X479 @ X477)) != ((ap @ X478 @ X480)))) => ! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)))) <=> (hoasapinj1_lthm = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X485 : term,X486 : (term > $o),X487 : (subst > term > subst > $o)] : (~ ! [X488 : (subst > term > term)] : (~ ! [X490 : subst,X489 : term,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))) | (((X487 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X492 : term] : (~ (((X487 @ id @ X492 @ id)) = $true) | (((X487 @ id @ (X488 @ id @ X492) @ id)) = $true))) | ~ ! [X493 : subst,X494 : term,X495 : subst,X496 : subst] : (~ ($true = ((X487 @ X493 @ X494 @ (comp @ X495 @ X496)))) | ($true = ((X487 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)))) | ~ ! [X497 : term] : (((X486 @ X497)) = ((X487 @ id @ X497 @ id))) | ~ ! [X498 : term] : ((((X486 @ (sub @ X485 @ (push @ X498 @ id)))) = $true) | ~ ($true = ((X486 @ X498)))) | ($true = ((X486 @ (lam @ X485)))) | ~ ! [X499 : subst,X500 : subst,X501 : subst,X502 : term] : (($true = ((X487 @ X501 @ X502 @ (comp @ X500 @ X499)))) | ~ (((X487 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499)) = $true)))) & ((hoasinduction_lem0 = $true) <=> ! [X503 : (subst > term > subst > $o)] : ~ ! [X504 : (term > $o)] : ~ ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505)))) & (hoaslamnotap_gthm = $true) & (termmset_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X506 : term] : (((sub @ X506 @ id)) = X506) => (! [X507 : term,X508 : (subst > term > subst > $o)] : (($true = ((X508 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id))) | ~ ! [X509 : (subst > term > term)] : ((((X508 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true) | ~ ! [X510 : term] : (($true = ((X508 @ id @ (X509 @ id @ X510) @ id))) | ~ ($true = ((X508 @ id @ X510 @ id)))) | ~ ! [X511 : subst,X512 : term,X513 : subst] : (((sub @ (X509 @ X513 @ X512) @ X511)) = ((X509 @ (comp @ X513 @ X511) @ (sub @ X512 @ X511))))) | ~ ! [X514 : term] : ((((X508 @ id @ (sub @ X507 @ (push @ X514 @ id)) @ id)) = $true) | ~ ($true = ((X508 @ id @ X514 @ id))))) => ! [X515 : term,X516 : (subst > term > subst > $o)] : (~ ! [X517 : term] : ((((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)) = $true) | ~ ($true = ((X516 @ id @ X517 @ id)))) | ($true = ((X516 @ id @ (lam @ X515) @ id))) | ~ ! [X518 : (subst > term > term)] : (~ ! [X519 : term] : (~ ($true = ((X516 @ id @ X519 @ id))) | ($true = ((X516 @ id @ (X518 @ id @ X519) @ id)))) | ~ ! [X520 : subst,X521 : subst,X522 : term] : (((sub @ (X518 @ X521 @ X522) @ X520)) = ((X518 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520)))) | ($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id)))))))) & (! [X523 : term,X524 : (term > $o)] : ((((X524 @ X523)) = $true) | ~ ! [X525 : term] : ((((X524 @ (lam @ X525))) = $true) | ~ ($true = ((X524 @ X525)))) | ~ ! [X526 : term] : (~ (((var @ X526)) = $true) | ($true = ((X524 @ X526)))) | ~ ! [X527 : term,X528 : term] : (~ (((X524 @ X528)) = $true) | ($true = ((X524 @ (ap @ X528 @ X527)))) | ~ ($true = ((X524 @ X527))))) <=> (induction = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X529 : term] : ~ ! [X530 : (subst > term > term)] : ~ ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532)))) & ((pushprop_lem0 = $true) <=> ! [X534 : term,X533 : subst,X535 : (term > $o)] : ~ ! [X536 : (term > $o)] : ~ ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) <=> (axshiftcons = $true)) & (hoaslamnotvar_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id))))),
% 13.65/2.32 inference(rectify,[],[f5])).
% 13.65/2.32 thf(f10,plain,(
% 13.65/2.32 ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X84 : subst] : (((comp @ id @ X84)) = X84) => (! [X85 : subst] : (((comp @ X85 @ id)) = X85) => (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X111 : term] : ~ ! [X112 : (subst > term > term)] : ~ ! [X113 : subst,X114 : term] : (((X112 @ X113 @ X114)) = ((sub @ X111 @ (push @ X114 @ X113)))) => (! [X115 : term] : (((sub @ X115 @ id)) = X115) => ! [X117 : (subst > term > subst > $o),X118 : (term > $o),X116 : term] : (~ ! [X119 : term] : ((((X118 @ (sub @ X116 @ (push @ X119 @ id)))) = $true) | ($true != ((X118 @ X119)))) | ($true = ((X118 @ (lam @ X116)))) | ~ ! [X120 : term] : (((X117 @ id @ X120 @ id)) = ((X118 @ X120))) | ~ ! [X121 : (subst > term > term)] : (~ ! [X122 : subst,X124 : term,X123 : subst] : (((X121 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122))) = ((sub @ (X121 @ X123 @ X124) @ X122))) | (((X117 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ~ ! [X125 : term] : (($true = ((X117 @ id @ (X121 @ id @ X125) @ id))) | (((X117 @ id @ X125 @ id)) != $true))))))) & ((induction2 = $true) <=> ! [X21 : (term > $o),X22 : term] : (($true = ((X21 @ X22))) | ~ ! [X25 : term] : (($true = ((X21 @ (lam @ X25)))) | ~ ! [X26 : term] : (($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id))))) | ($true != ((X21 @ X26))))) | ~ ! [X24 : term,X23 : term] : ((((X21 @ X23)) != $true) | (((X21 @ (ap @ X23 @ X24))) = $true) | ($true != ((X21 @ X24)))) | ~ ! [X27 : term] : ((((X21 @ X27)) = $true) | (((var @ X27)) != $true)))) & ((hoaslamnotap = $true) <=> ! [X462 : term,X461 : (subst > term > term),X463 : term] : (~ ! [X466 : subst,X465 : term,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462))))) & ((induction2_lthm = $true) <=> (! [X393 : term] : (((sub @ X393 @ id)) = X393) => (! [X394 : (term > $o),X395 : subst,X396 : term] : (~ ! [X401 : term] : ((((var @ X401)) != $true) | (((X394 @ (sub @ X401 @ X395))) = $true)) | ~ ! [X399 : term] : (($true = ((X394 @ (lam @ X399)))) | ~ ! [X400 : term] : (($true = ((X394 @ (sub @ X399 @ (push @ X400 @ id))))) | ($true != ((X394 @ X400))))) | ~ ! [X398 : term,X397 : term] : (($true = ((X394 @ (ap @ X398 @ X397)))) | (((X394 @ X397)) != $true) | (((X394 @ X398)) != $true)) | ($true = ((X394 @ (sub @ X396 @ X395))))) => ! [X402 : term,X403 : (term > $o)] : ((((X403 @ X402)) = $true) | ~ ! [X407 : term,X406 : term] : (($true = ((X403 @ (ap @ X406 @ X407)))) | (((X403 @ X407)) != $true) | ($true != ((X403 @ X406)))) | ~ ! [X404 : term] : ((((X403 @ (lam @ X404))) = $true) | ~ ! [X405 : term] : ((((X403 @ X405)) != $true) | (((X403 @ (sub @ X404 @ (push @ X405 @ id)))) = $true))) | ~ ! [X408 : term] : (($true = ((X403 @ X408))) | ($true != ((var @ X408)))))))) & ((induction2lem_lthm = $true) <=> (! [X429 : term,X430 : subst] : (((sub @ one @ (push @ X429 @ X430))) = X429) => (! [X432 : term,X431 : subst] : (((comp @ sh @ (push @ X432 @ X431))) = X431) => (! [X433 : subst] : (((comp @ X433 @ id)) = X433) => (! [X435 : (term > $o),X434 : term] : (~ ! [X438 : term,X439 : term] : (($true != ((X435 @ X438))) | (((X435 @ X439)) != $true) | ($true = ((X435 @ (ap @ X439 @ X438))))) | ($true = ((X435 @ X434))) | ~ ! [X437 : term] : (($true = ((X435 @ (lam @ X437)))) | (((X435 @ X437)) != $true)) | ~ ! [X436 : term] : ((((var @ X436)) != $true) | ($true = ((X435 @ X436))))) => ! [X441 : term,X440 : (term > $o),X442 : subst] : (~ ! [X443 : term] : (~ ! [X444 : term] : (($true != ((X440 @ X444))) | ($true = ((X440 @ (sub @ X443 @ (push @ X444 @ id)))))) | (((X440 @ (lam @ X443))) = $true)) | ~ ! [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) = $true) | (((X440 @ X446)) != $true) | (((X440 @ X445)) != $true)) | (((X440 @ (sub @ X441 @ X442))) = $true) | ~ ! [X447 : term] : ((((var @ X447)) != $true) | ($true = ((X440 @ (sub @ X447 @ X442))))))))))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X452 : term,X453 : (subst > term > subst > $o)] : ((((X453 @ id @ (lam @ X452) @ id)) = $true) | ~ ! [X455 : (subst > term > term)] : ((((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true) | ~ ! [X456 : term] : ((((X453 @ id @ X456 @ id)) != $true) | ($true = ((X453 @ id @ (X455 @ id @ X456) @ id)))) | ~ ! [X459 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X457 @ X458) @ X459)) = ((X455 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459))))) | ~ ! [X454 : term] : ((((X453 @ id @ X454 @ id)) != $true) | ($true = ((X453 @ id @ (sub @ X452 @ (push @ X454 @ id)) @ id)))))) & (! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X1 : term,X0 : (subst > term > subst > $o)] : (~ ! [X2 : (subst > term > term),X3 : term] : (~ ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) | ($true = ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id))) | ~ ! [X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) | ~ ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9)))) | ~ ! [X11 : term] : (($true = ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) | (((X0 @ id @ X11 @ id)) != $true)) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true))) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X130 : (subst > term > subst > $o)] : ~ ! [X131 : (term > $o)] : ~ ! [X132 : term] : (((X130 @ id @ X132 @ id)) = ((X131 @ X132))) => (! [X133 : term,X134 : (term > $o)] : (~ ! [X135 : term] : ((((var @ X135)) != $true) | (((X134 @ X135)) = $true)) | ~ ! [X138 : term] : (($true = ((X134 @ (lam @ X138)))) | ~ ! [X139 : term] : ((((X134 @ X139)) != $true) | (((X134 @ (sub @ X138 @ (push @ X139 @ id)))) = $true))) | ~ ! [X137 : term,X136 : term] : (($true != ((X134 @ X137))) | (((X134 @ X136)) != $true) | (((X134 @ (ap @ X137 @ X136))) = $true)) | (((X134 @ X133)) = $true)) => (! [X140 : term] : (((sub @ X140 @ id)) = X140) => (! [X143 : (term > $o),X141 : term,X142 : (subst > term > subst > $o)] : (~ ! [X150 : term] : (((X143 @ X150)) = ((X142 @ id @ X150 @ id))) | ~ ! [X149 : term] : (($true = ((X143 @ (sub @ X141 @ (push @ X149 @ id))))) | (((X143 @ X149)) != $true)) | ~ ! [X144 : (subst > term > term)] : ((((X142 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ~ ! [X145 : subst,X146 : subst,X147 : term] : (((X144 @ (comp @ X145 @ X146) @ (sub @ X147 @ X146))) = ((sub @ (X144 @ X145 @ X147) @ X146))) | ~ ! [X148 : term] : (($true = ((X142 @ id @ (X144 @ id @ X148) @ id))) | ($true != ((X142 @ id @ X148 @ id))))) | ($true = ((X143 @ (lam @ X141))))) => ! [X151 : (subst > term > subst > $o),X152 : term] : (~ ! [X161 : term] : ((((X151 @ id @ X161 @ id)) = $true) | (((var @ (sub @ X161 @ id))) != $true)) | ~ ! [X168 : term,X167 : term] : (($true != ((X151 @ id @ X167 @ id))) | (((X151 @ id @ X168 @ id)) != $true) | (((X151 @ id @ (ap @ (sub @ X168 @ id) @ X167) @ id)) = $true)) | (((X151 @ id @ X152 @ id)) = $true) | ~ ! [X162 : (subst > term > term)] : (~ ! [X163 : term] : (($true = ((X151 @ id @ (X162 @ id @ X163) @ id))) | (((X151 @ id @ X163 @ id)) != $true)) | ~ ! [X164 : subst,X166 : subst,X165 : term] : (((sub @ (X162 @ X166 @ X165) @ X164)) = ((X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))) | ($true = ((X151 @ id @ (lam @ (X162 @ sh @ one)) @ id)))) | ~ ! [X154 : subst,X156 : term,X155 : subst,X153 : subst] : (($true = ((X151 @ X153 @ X156 @ (comp @ X155 @ X154)))) | (((X151 @ (comp @ X153 @ X155) @ (sub @ X156 @ X155) @ X154)) != $true)) | ~ ! [X160 : subst,X158 : term,X159 : subst,X157 : subst] : (($true = ((X151 @ (comp @ X157 @ X159) @ (sub @ X158 @ X159) @ X160))) | (((X151 @ X157 @ X158 @ (comp @ X159 @ X160))) != $true)))))))) & ((! [X98 : subst,X99 : term] : (((sub @ one @ (push @ X99 @ X98))) = X99) => ! [X101 : term,X102 : subst,X103 : (term > $o),X100 : (term > $o)] : (($true != ((X103 @ X101))) | (((X100 @ one)) = $true) | ~ ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (apnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasapnotvar = $true) & (pushprop_lthm_orig = $true) & ((! [X234 : (term > $o),X233 : term] : (~ ! [X237 : term] : (~ ! [X238 : term] : (($true != ((X234 @ X238))) | ($true = ((X234 @ (sub @ X237 @ (push @ X238 @ id)))))) | ($true = ((X234 @ (lam @ X237))))) | (((X234 @ X233)) = $true) | ~ ! [X236 : term,X235 : term] : ((((X234 @ X235)) != $true) | (((X234 @ (ap @ X236 @ X235))) = $true) | (((X234 @ X236)) != $true)) | ~ ! [X239 : term] : (($true = ((X234 @ X239))) | ($true != ((var @ X239))))) => (! [X241 : term,X242 : term,X240 : (subst > term > subst > $o)] : ((((X240 @ id @ X242 @ id)) != $true) | ~ ! [X246 : term,X247 : subst,X245 : subst,X248 : subst] : (($true != ((X240 @ X247 @ X246 @ (comp @ X245 @ X248)))) | ($true = ((X240 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245) @ X248)))) | ($true != ((X240 @ id @ X241 @ id))) | ~ ! [X251 : subst,X250 : term,X249 : subst,X252 : subst] : ((((X240 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251) @ X252)) != $true) | ($true = ((X240 @ X249 @ X250 @ (comp @ X251 @ X252))))) | (((X240 @ id @ (ap @ X241 @ X242) @ id)) = $true) | ~ ! [X243 : term,X244 : term] : ((((X240 @ id @ (ap @ (sub @ X244 @ id) @ X243) @ id)) = $true) | ($true != ((X240 @ id @ X243 @ id))) | ($true != ((X240 @ id @ X244 @ id))))) => (! [X253 : term,X254 : (subst > term > subst > $o)] : (~ ! [X258 : term,X255 : subst,X257 : subst,X256 : subst] : ((((X254 @ (comp @ X257 @ X256) @ (sub @ X258 @ X256) @ X255)) = $true) | (((X254 @ X257 @ X258 @ (comp @ X256 @ X255))) != $true)) | ~ ! [X264 : (subst > term > term)] : (~ ! [X268 : term] : (($true = ((X254 @ id @ (X264 @ id @ X268) @ id))) | (((X254 @ id @ X268 @ id)) != $true)) | (((X254 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true) | ~ ! [X265 : subst,X266 : subst,X267 : term] : (((sub @ (X264 @ X265 @ X267) @ X266)) = ((X264 @ (comp @ X265 @ X266) @ (sub @ X267 @ X266))))) | ~ ! [X263 : term] : ((((X254 @ id @ X263 @ id)) != $true) | (((X254 @ id @ (sub @ X253 @ (push @ X263 @ id)) @ id)) = $true)) | (((X254 @ id @ (lam @ X253) @ id)) = $true) | ~ ! [X260 : subst,X262 : subst,X259 : term,X261 : subst] : ((((X254 @ X261 @ X259 @ (comp @ X260 @ X262))) = $true) | (((X254 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260) @ X262)) != $true))) => ! [X270 : term,X269 : (subst > term > subst > $o)] : (~ ! [X273 : subst,X274 : subst,X272 : term,X271 : subst] : ((((X269 @ (comp @ X271 @ X274) @ (sub @ X272 @ X274) @ X273)) = $true) | ($true != ((X269 @ X271 @ X272 @ (comp @ X274 @ X273))))) | ~ ! [X276 : (subst > term > term)] : (~ ! [X278 : term,X279 : subst,X280 : subst] : (((X276 @ (comp @ X280 @ X279) @ (sub @ X278 @ X279))) = ((sub @ (X276 @ X280 @ X278) @ X279))) | ~ ! [X277 : term] : (($true != ((X269 @ id @ X277 @ id))) | (((X269 @ id @ (X276 @ id @ X277) @ id)) = $true)) | (((X269 @ id @ (lam @ (X276 @ sh @ one)) @ id)) = $true)) | ~ ! [X285 : term,X286 : term] : (($true = ((X269 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id))) | ($true != ((X269 @ id @ X285 @ id))) | ($true != ((X269 @ id @ X286 @ id)))) | ~ ! [X275 : term] : ((((var @ (sub @ X275 @ id))) != $true) | ($true = ((X269 @ id @ X275 @ id)))) | ~ ! [X284 : term,X281 : subst,X282 : subst,X283 : subst] : ((((X269 @ (comp @ X283 @ X281) @ (sub @ X284 @ X281) @ X282)) != $true) | (((X269 @ X283 @ X284 @ (comp @ X281 @ X282))) = $true)) | (((X269 @ id @ X270 @ id)) = $true))))) <=> (hoasinduction_lthm = $true)) & (one = ((d2term @ d_one))) & (hoaslamnotap_lthm = $true) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) <=> (substmonoid = $true)) & (hoaslamnotvar = $true) & (! [X486 : (term > $o),X485 : term,X487 : (subst > term > subst > $o)] : (~ ! [X493 : subst,X496 : subst,X494 : term,X495 : subst] : (($true = ((X487 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496))) | ($true != ((X487 @ X493 @ X494 @ (comp @ X495 @ X496))))) | ~ ! [X498 : term] : ((((X486 @ (sub @ X485 @ (push @ X498 @ id)))) = $true) | ($true != ((X486 @ X498)))) | ~ ! [X500 : subst,X499 : subst,X501 : subst,X502 : term] : ((((X487 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499)) != $true) | ($true = ((X487 @ X501 @ X502 @ (comp @ X500 @ X499))))) | ($true = ((X486 @ (lam @ X485)))) | ~ ! [X488 : (subst > term > term)] : (~ ! [X490 : subst,X489 : term,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491)))) | (((X487 @ id @ (lam @ (X488 @ sh @ one)) @ id)) = $true) | ~ ! [X492 : term] : ((((X487 @ id @ X492 @ id)) != $true) | (((X487 @ id @ (X488 @ id @ X492) @ id)) = $true))) | ~ ! [X497 : term] : (((X486 @ X497)) = ((X487 @ id @ X497 @ id)))) <=> (hoasinduction_lem3v2 = $true)) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X76 : (term > $o),X74 : (subst > term > subst > $o),X75 : term] : (~ ! [X77 : term] : (($true = ((X76 @ (sub @ X75 @ (push @ X77 @ id))))) | ($true != ((X76 @ X77)))) | ~ ! [X78 : term] : (((X74 @ id @ X78 @ id)) = ((X76 @ X78))) | ~ ! [X79 : (subst > term > term)] : (~ ! [X83 : term] : ((((X74 @ id @ X83 @ id)) != $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true)) | ~ ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81))) | (((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) = $true)) | (((X76 @ (lam @ X75))) = $true))) & (! [X311 : term] : ~ ! [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) != ((X312 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X373 : term] : ~ ! [X374 : (subst > term > term)] : ~ ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376))) <=> (hoasinduction_lem3v2_f = $true)) & (hoaslaminj_gthm = $true) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) <=> (axshiftcons = $true)) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & ! [X110 : d_term,X109 : d_term] : ((((d2term @ X110)) = ((d2term @ X109))) => (X109 = X110)) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X529 : term] : ~ ! [X530 : (subst > term > term)] : ~ ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532)))) & (! [X89 : term,X88 : (subst > term > subst > $o)] : (~ ! [X92 : (subst > term > term)] : (~ ! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) | (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) = $true) | ~ ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true))) | ~ ! [X90 : term,X91 : term] : (($true != ((X88 @ id @ X91 @ id))) | (((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) = $true) | (((X88 @ id @ X90 @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & (((var @ (d2term @ d_one))) != $true) & (! [X107 : term] : ~ ! [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) != ((X108 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X296 : subst,X295 : term] : (((sub @ one @ (push @ X295 @ X296))) = X295) => (! [X297 : term,X298 : subst] : (((comp @ sh @ (push @ X297 @ X298))) = X298) => (! [X300 : term,X299 : term] : ((((lam @ X299)) != ((lam @ X300))) | (X299 = X300)) => ! [X301 : term,X302 : (subst > term > term),X303 : subst,X304 : (subst > term > term)] : (~ ! [X308 : subst,X309 : term,X310 : subst] : (((X304 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) = ((sub @ (X304 @ X308 @ X309) @ X310))) | (((X302 @ X303 @ X301)) = ((X304 @ X303 @ X301))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ~ ! [X306 : subst,X305 : subst,X307 : term] : (((X302 @ (comp @ X306 @ X305) @ (sub @ X307 @ X305))) = ((sub @ (X302 @ X306 @ X307) @ X305)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X184 : (subst > term > subst > $o)] : ~ ! [X185 : (term > $o)] : ~ ! [X186 : term] : (((X184 @ id @ X186 @ id)) = ((X185 @ X186))) => (! [X187 : (term > $o),X188 : term] : ((((X187 @ X188)) = $true) | ~ ! [X192 : term,X193 : term] : ((((X187 @ X193)) != $true) | ($true != ((X187 @ X192))) | (((X187 @ (ap @ X192 @ X193))) = $true)) | ~ ! [X189 : term] : (($true != ((var @ X189))) | ($true = ((X187 @ X189)))) | ~ ! [X190 : term] : (~ ! [X191 : term] : (($true != ((X187 @ X191))) | (((X187 @ (sub @ X190 @ (push @ X191 @ id)))) = $true)) | ($true = ((X187 @ (lam @ X190)))))) => (! [X194 : term] : (((sub @ X194 @ id)) = X194) => (! [X197 : (subst > term > subst > $o),X196 : (term > $o),X195 : term] : ((((X196 @ (lam @ X195))) = $true) | ~ ! [X200 : (subst > term > term)] : (~ ! [X201 : term] : ((((X197 @ id @ (X200 @ id @ X201) @ id)) = $true) | (((X197 @ id @ X201 @ id)) != $true)) | (((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true) | ~ ! [X202 : term,X204 : subst,X203 : subst] : (((sub @ (X200 @ X204 @ X202) @ X203)) = ((X200 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203))))) | ~ ! [X198 : term] : (((X197 @ id @ X198 @ id)) = ((X196 @ X198))) | ~ ! [X199 : term] : ((((X196 @ X199)) != $true) | ($true = ((X196 @ (sub @ X195 @ (push @ X199 @ id))))))) => ! [X205 : (subst > term > subst > $o),X206 : term] : (~ ! [X213 : term,X212 : term] : ((((X205 @ id @ (ap @ (sub @ X213 @ id) @ X212) @ id)) = $true) | ($true != ((X205 @ id @ X213 @ id))) | ($true != ((X205 @ id @ X212 @ id)))) | (((X205 @ id @ X206 @ id)) = $true) | ~ ! [X207 : (subst > term > term)] : (~ ! [X210 : subst,X208 : subst,X209 : term] : (((X207 @ (comp @ X210 @ X208) @ (sub @ X209 @ X208))) = ((sub @ (X207 @ X210 @ X209) @ X208))) | ~ ! [X211 : term] : ((((X205 @ id @ (X207 @ id @ X211) @ id)) = $true) | (((X205 @ id @ X211 @ id)) != $true)) | ($true = ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id)))))))))) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X365 : term,X366 : (subst > term > subst > $o)] : ((((X366 @ id @ (lam @ (sub @ X365 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X367 : (subst > term > term)] : (~ ! [X370 : subst,X371 : subst,X369 : term] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371))) | ($true = ((X366 @ id @ (lam @ (X367 @ sh @ one)) @ id))) | ~ ! [X368 : term] : (($true != ((X366 @ id @ X368 @ id))) | (((X366 @ id @ (X367 @ id @ X368) @ id)) = $true))) | ~ ! [X372 : term] : ((((X366 @ id @ X372 @ id)) != $true) | ($true = ((X366 @ id @ (sub @ X365 @ (push @ X372 @ id)) @ id)))))) & (lamnotvar = $true) & ((! [X476 : term] : (((sub @ X476 @ id)) = X476) => (! [X480 : term,X477 : term,X479 : term,X478 : term] : ((X478 = X479) | (((ap @ X479 @ X477)) != ((ap @ X478 @ X480)))) => ! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)))) <=> (hoasapinj1_lthm = $true)) & (lamnotap != $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X17 : subst,X16 : (term > $o),X19 : term,X18 : (term > $o)] : (($true = ((X18 @ one))) | ~ ! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true != ((X16 @ X19))))) & (hoasapnotvar_lthm = $true) & (! [X29 : term,X28 : (subst > term > subst > $o)] : (~ ! [X35 : term] : (($true != ((var @ (sub @ X35 @ id)))) | (((X28 @ id @ X35 @ id)) = $true)) | (((X28 @ id @ X29 @ id)) = $true) | ~ ! [X30 : (subst > term > term)] : (($true = ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id))) | ~ ! [X34 : term] : (($true != ((X28 @ id @ X34 @ id))) | (((X28 @ id @ (X30 @ id @ X34) @ id)) = $true)) | ~ ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32)))) | ~ ! [X41 : term,X40 : term] : ((((X28 @ id @ X41 @ id)) != $true) | (((X28 @ id @ X40 @ id)) != $true) | (((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) = $true)) | ~ ! [X43 : subst,X42 : subst,X45 : subst,X44 : term] : ((((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) != $true) | (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) = $true)) | ~ ! [X39 : subst,X38 : subst,X36 : term,X37 : subst] : (($true != ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37))) | (((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) = $true))) <=> (hoasinduction = $true)) & ((hoaslaminj = $true) <=> ! [X320 : (subst > term > term),X319 : term,X318 : subst,X321 : (subst > term > term)] : (~ ! [X325 : subst,X326 : term,X327 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) = ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325)))) | ~ ! [X323 : subst,X324 : term,X322 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) = ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))))) & ((! [X214 : term] : (((sub @ X214 @ id)) = X214) => ! [X217 : (term > $o),X215 : (subst > term > subst > $o),X216 : term] : (~ ! [X225 : subst,X224 : subst,X226 : term,X227 : subst] : ((((X215 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) = $true) | (((X215 @ X225 @ X226 @ (comp @ X227 @ X224))) != $true)) | ~ ! [X231 : subst,X230 : term,X228 : subst,X229 : subst] : (($true = ((X215 @ X228 @ X230 @ (comp @ X229 @ X231)))) | (((X215 @ (comp @ X228 @ X229) @ (sub @ X230 @ X229) @ X231)) != $true)) | ($true = ((X217 @ (lam @ X216)))) | ~ ! [X218 : (subst > term > term)] : (($true = ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id))) | ~ ! [X219 : term] : ((((X215 @ id @ X219 @ id)) != $true) | (((X215 @ id @ (X218 @ id @ X219) @ id)) = $true)) | ~ ! [X220 : subst,X222 : term,X221 : subst] : (((sub @ (X218 @ X220 @ X222) @ X221)) = ((X218 @ (comp @ X220 @ X221) @ (sub @ X222 @ X221))))) | ~ ! [X232 : term] : (($true != ((X217 @ X232))) | ($true = ((X217 @ (sub @ X216 @ (push @ X232 @ id)))))) | ~ ! [X223 : term] : (((X217 @ X223)) = ((X215 @ id @ X223 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ((! [X411 : term,X412 : subst] : (((sub @ one @ (push @ X411 @ X412))) = X411) => (! [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) = X414) => ! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true)))) <=> (pushprop_lem1_lthm = $true)) & (! [X421 : (term > $o),X420 : term,X422 : subst] : ~ ! [X423 : (term > $o)] : ~ ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X65 : (subst > term > subst > $o),X66 : term] : (($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id))) | ~ ! [X67 : (subst > term > term)] : (~ ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70)))) | ($true = ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id))) | ~ ! [X68 : term] : ((((X65 @ id @ (X67 @ id @ X68) @ id)) = $true) | ($true != ((X65 @ id @ X68 @ id))))) | ~ ! [X72 : term] : ((((X65 @ id @ X72 @ id)) != $true) | ($true = ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id)))))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & (! [X54 : term,X53 : (subst > term > subst > $o),X52 : term] : (($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | ~ ! [X57 : subst,X56 : subst,X58 : subst,X55 : term] : (($true != ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56))) | ($true = ((X53 @ X58 @ X55 @ (comp @ X57 @ X56))))) | (((X53 @ id @ X52 @ id)) != $true) | (((X53 @ id @ X54 @ id)) != $true) | ~ ! [X59 : term,X60 : term] : ((((X53 @ id @ X60 @ id)) != $true) | (((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) = $true) | ($true != ((X53 @ id @ X59 @ id)))) | ~ ! [X63 : subst,X62 : term,X64 : subst,X61 : subst] : ((((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) = $true) | (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) != $true))) <=> (hoasinduction_lem2 = $true)) & (ulamvarind = $true) & (((d2subst @ d_id)) = id) & (! [X426 : (subst > term > subst > $o)] : ~ ! [X427 : (term > $o)] : ~ ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (axmap = $true) & ((pushprop_lem0 = $true) <=> ! [X534 : term,X533 : subst,X535 : (term > $o)] : ~ ! [X536 : (term > $o)] : ~ ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & ((! [X329 : term] : (((sub @ X329 @ id)) = X329) => (! [X331 : term,X330 : (subst > term > subst > $o)] : (~ ! [X332 : (subst > term > term)] : (~ ! [X333 : term] : (($true = ((X330 @ id @ (X332 @ id @ X333) @ id))) | (((X330 @ id @ X333 @ id)) != $true)) | ($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ~ ! [X336 : subst,X335 : term,X334 : subst] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ($true = ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id))) | ~ ! [X337 : term] : (($true = ((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))) | (((X330 @ id @ X337 @ id)) != $true))) => ! [X338 : term,X339 : (subst > term > subst > $o)] : (~ ! [X340 : term] : (($true != ((X339 @ id @ X340 @ id))) | (((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)) = $true)) | ~ ! [X345 : (subst > term > term)] : ((((X339 @ id @ (lam @ (X345 @ sh @ one)) @ id)) = $true) | ~ ! [X346 : term] : ((((X339 @ id @ (X345 @ id @ X346) @ id)) = $true) | ($true != ((X339 @ id @ X346 @ id)))) | ~ ! [X347 : subst,X348 : subst,X349 : term] : (((X345 @ (comp @ X347 @ X348) @ (sub @ X349 @ X348))) = ((sub @ (X345 @ X347 @ X349) @ X348)))) | ($true = ((X339 @ id @ (lam @ X338) @ id))) | ~ ! [X343 : term,X344 : subst,X342 : subst,X341 : subst] : ((((X339 @ (comp @ X344 @ X341) @ (sub @ X343 @ X341) @ X342)) != $true) | ($true = ((X339 @ X344 @ X343 @ (comp @ X341 @ X342))))) | ~ ! [X351 : subst,X350 : subst,X353 : subst,X352 : term] : (($true = ((X339 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350) @ X353))) | (((X339 @ X351 @ X352 @ (comp @ X350 @ X353))) != $true))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X313 : d_subst] : (d_id = X313) & ! [X359 : d_subst,X360 : d_subst] : ((((d2subst @ X359)) = ((d2subst @ X360))) => (X359 = X360)) & (hoaslamnotvar_gthm = $true) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) <=> (axidl = $true)) & ! [X460 : d_term] : (d_one = X460) & (axvarshift = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X506 : term] : (((sub @ X506 @ id)) = X506) => (! [X508 : (subst > term > subst > $o),X507 : term] : (~ ! [X514 : term] : ((((X508 @ id @ (sub @ X507 @ (push @ X514 @ id)) @ id)) = $true) | ($true != ((X508 @ id @ X514 @ id)))) | ($true = ((X508 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id))) | ~ ! [X509 : (subst > term > term)] : (~ ! [X510 : term] : (($true != ((X508 @ id @ X510 @ id))) | ($true = ((X508 @ id @ (X509 @ id @ X510) @ id)))) | ~ ! [X511 : subst,X512 : term,X513 : subst] : (((sub @ (X509 @ X513 @ X512) @ X511)) = ((X509 @ (comp @ X513 @ X511) @ (sub @ X512 @ X511)))) | (((X508 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true))) => ! [X515 : term,X516 : (subst > term > subst > $o)] : (~ ! [X517 : term] : ((((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)) = $true) | ($true != ((X516 @ id @ X517 @ id)))) | ($true = ((X516 @ id @ (lam @ X515) @ id))) | ~ ! [X518 : (subst > term > term)] : (($true = ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id))) | ~ ! [X519 : term] : (($true != ((X516 @ id @ X519 @ id))) | ($true = ((X516 @ id @ (X518 @ id @ X519) @ id)))) | ~ ! [X520 : subst,X521 : subst,X522 : term] : (((sub @ (X518 @ X521 @ X522) @ X520)) = ((X518 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520))))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem3v2_lthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (ulamvarsh = $true) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (pushprop = $true) & (! [X378 : (subst > term > subst > $o),X377 : term] : (~ ! [X385 : subst,X387 : subst,X388 : subst,X386 : term] : ((((X378 @ (comp @ X387 @ X388) @ (sub @ X386 @ X388) @ X385)) = $true) | ($true != ((X378 @ X387 @ X386 @ (comp @ X388 @ X385))))) | ~ ! [X379 : term] : (($true != ((X378 @ id @ X379 @ id))) | (((X378 @ id @ (sub @ X377 @ (push @ X379 @ id)) @ id)) = $true)) | (((X378 @ id @ (lam @ X377) @ id)) = $true) | ~ ! [X380 : (subst > term > term)] : (~ ! [X381 : term] : ((((X378 @ id @ X381 @ id)) != $true) | ($true = ((X378 @ id @ (X380 @ id @ X381) @ id)))) | ~ ! [X384 : subst,X383 : subst,X382 : term] : (((sub @ (X380 @ X383 @ X382) @ X384)) = ((X380 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384)))) | (((X378 @ id @ (lam @ (X380 @ sh @ one)) @ id)) = $true)) | ~ ! [X392 : subst,X389 : term,X390 : subst,X391 : subst] : (($true = ((X378 @ X391 @ X389 @ (comp @ X392 @ X390)))) | ($true != ((X378 @ (comp @ X391 @ X392) @ (sub @ X389 @ X392) @ X390))))) <=> (hoasinduction_lem3 = $true)) & ((shinj = $true) <=> ! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem0 = $true) <=> ! [X503 : (subst > term > subst > $o)] : ~ ! [X504 : (term > $o)] : ~ ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505)))) & (hoasapinj1_gthm = $true) & (axapp = $true) & (! [X523 : term,X524 : (term > $o)] : (~ ! [X527 : term,X528 : term] : ((((X524 @ X528)) != $true) | ($true = ((X524 @ (ap @ X528 @ X527)))) | ($true != ((X524 @ X527)))) | (((X524 @ X523)) = $true) | ~ ! [X525 : term] : ((((X524 @ (lam @ X525))) = $true) | ($true != ((X524 @ X525)))) | ~ ! [X526 : term] : ((((var @ X526)) != $true) | ($true = ((X524 @ X526))))) <=> (induction = $true)) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & (pushprop_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X289 : (term > $o),X287 : subst,X288 : term] : (($true = ((X289 @ (sub @ X288 @ X287)))) | ~ ! [X294 : term,X293 : term] : ((((X289 @ (ap @ X293 @ X294))) = $true) | (((X289 @ X293)) != $true) | ($true != ((X289 @ X294)))) | ~ ! [X292 : term] : (($true = ((X289 @ (sub @ X292 @ X287)))) | (((var @ X292)) != $true)) | ~ ! [X290 : term] : (~ ! [X291 : term] : ((((X289 @ (sub @ X290 @ (push @ X291 @ id)))) = $true) | ($true != ((X289 @ X291)))) | (((X289 @ (lam @ X290))) = $true))) <=> (induction2lem = $true)) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) <=> (axvarcons = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) <=> (axscons = $true)) & ((hoasapinj2 = $true) <=> ! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363))) & (hoasinduction_gthm = $true) & ((! [X105 : term] : (((sub @ X105 @ id)) = X105) => ! [X106 : term] : (((sub @ X106 @ id)) = X106)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X169 : term,X171 : (subst > term > subst > $o),X170 : (term > $o),X172 : term] : (~ ! [X180 : term,X181 : subst,X178 : subst,X179 : subst] : ((((X171 @ X181 @ X180 @ (comp @ X179 @ X178))) = $true) | ($true != ((X171 @ (comp @ X181 @ X179) @ (sub @ X180 @ X179) @ X178)))) | ~ ! [X173 : term] : (((X170 @ X173)) = ((X171 @ id @ X173 @ id))) | ~ ! [X182 : term,X183 : term] : (($true != ((X171 @ id @ X183 @ id))) | (((X171 @ id @ (ap @ (sub @ X182 @ id) @ X183) @ id)) = $true) | ($true != ((X171 @ id @ X182 @ id)))) | (((X170 @ (ap @ X172 @ X169))) = $true) | (((X170 @ X172)) != $true) | ~ ! [X175 : subst,X176 : term,X174 : subst,X177 : subst] : ((((X171 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) = $true) | (((X171 @ X175 @ X176 @ (comp @ X174 @ X177))) != $true)) | ($true != ((X170 @ X169))))) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) <=> (laminj = $true)) & ((! [X467 : term,X469 : term,X468 : term,X470 : term] : ((((ap @ X467 @ X470)) != ((ap @ X468 @ X469))) | (X469 = X470)) => ! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473))))) <=> (hoasapinj2_lthm = $true)) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) <=> (apinj1 = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2 = $true)),
% 13.65/2.32 inference(flattening,[],[f9])).
% 13.65/2.32 thf(f11,plain,(
% 13.65/2.32 ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (pushprop_lem2v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2_gthm = $true) & ((substmonoid_lthm = $true) <=> (((! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87)) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85)) | ? [X84 : subst] : (((comp @ id @ X84)) != X84))) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X118 : (term > $o),X116 : term,X117 : (subst > term > subst > $o)] : (? [X119 : term] : (($true = ((X118 @ X119))) & (((X118 @ (sub @ X116 @ (push @ X119 @ id)))) != $true)) | ? [X120 : term] : (((X117 @ id @ X120 @ id)) != ((X118 @ X120))) | ($true = ((X118 @ (lam @ X116)))) | ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X117 @ id @ (X121 @ id @ X125) @ id))) | (((X117 @ id @ X125 @ id)) != $true)) & ! [X122 : subst,X124 : term,X123 : subst] : (((X121 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122))) = ((sub @ (X121 @ X123 @ X124) @ X122))) & (((X117 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true))) | ? [X115 : term] : (((sub @ X115 @ id)) != X115)) | ? [X111 : term] : ! [X112 : (subst > term > term)] : ? [X114 : term,X113 : subst] : (((X112 @ X113 @ X114)) != ((sub @ X111 @ (push @ X114 @ X113)))))) & ((induction2 = $true) <=> ! [X22 : term,X21 : (term > $o)] : (($true = ((X21 @ X22))) | ? [X27 : term] : ((((var @ X27)) = $true) & (((X21 @ X27)) != $true)) | ? [X25 : term] : (($true != ((X21 @ (lam @ X25)))) & ! [X26 : term] : (($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id))))) | ($true != ((X21 @ X26))))) | ? [X23 : term,X24 : term] : ((((X21 @ (ap @ X23 @ X24))) != $true) & ($true = ((X21 @ X24))) & (((X21 @ X23)) = $true)))) & ((hoaslamnotap = $true) <=> ! [X462 : term,X463 : term,X461 : (subst > term > term)] : (? [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) != ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462))))) & ((induction2_lthm = $true) <=> ((! [X402 : term,X403 : (term > $o)] : (? [X406 : term,X407 : term] : ((((X403 @ X407)) = $true) & ($true != ((X403 @ (ap @ X406 @ X407)))) & ($true = ((X403 @ X406)))) | (((X403 @ X402)) = $true) | ? [X404 : term] : ((((X403 @ (lam @ X404))) != $true) & ! [X405 : term] : ((((X403 @ X405)) != $true) | (((X403 @ (sub @ X404 @ (push @ X405 @ id)))) = $true))) | ? [X408 : term] : (($true = ((var @ X408))) & ($true != ((X403 @ X408))))) | ? [X395 : subst,X394 : (term > $o),X396 : term] : (! [X399 : term] : (? [X400 : term] : (($true != ((X394 @ (sub @ X399 @ (push @ X400 @ id))))) & ($true = ((X394 @ X400)))) | ($true = ((X394 @ (lam @ X399))))) & ! [X401 : term] : ((((var @ X401)) != $true) | (((X394 @ (sub @ X401 @ X395))) = $true)) & ($true != ((X394 @ (sub @ X396 @ X395)))) & ! [X398 : term,X397 : term] : (($true = ((X394 @ (ap @ X398 @ X397)))) | (((X394 @ X397)) != $true) | (((X394 @ X398)) != $true)))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393))) & ((induction2lem_lthm = $true) <=> ((((! [X441 : term,X440 : (term > $o),X442 : subst] : (? [X443 : term] : ((((X440 @ (lam @ X443))) != $true) & ! [X444 : term] : (($true != ((X440 @ X444))) | ($true = ((X440 @ (sub @ X443 @ (push @ X444 @ id))))))) | ? [X447 : term] : (($true != ((X440 @ (sub @ X447 @ X442)))) & (((var @ X447)) = $true)) | ? [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) != $true) & (((X440 @ X446)) = $true) & (((X440 @ X445)) = $true)) | (((X440 @ (sub @ X441 @ X442))) = $true)) | ? [X435 : (term > $o),X434 : term] : (($true != ((X435 @ X434))) & ! [X438 : term,X439 : term] : (($true != ((X435 @ X438))) | (((X435 @ X439)) != $true) | ($true = ((X435 @ (ap @ X439 @ X438))))) & ! [X437 : term] : (($true = ((X435 @ (lam @ X437)))) | (((X435 @ X437)) != $true)) & ! [X436 : term] : ((((var @ X436)) != $true) | ($true = ((X435 @ X436)))))) | ? [X433 : subst] : (((comp @ X433 @ id)) != X433)) | ? [X432 : term,X431 : subst] : (((comp @ sh @ (push @ X432 @ X431))) != X431)) | ? [X429 : term,X430 : subst] : (((sub @ one @ (push @ X429 @ X430))) != X429))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X453 : (subst > term > subst > $o),X452 : term] : ((((X453 @ id @ (lam @ X452) @ id)) = $true) | ? [X454 : term] : (($true != ((X453 @ id @ (sub @ X452 @ (push @ X454 @ id)) @ id))) & (((X453 @ id @ X454 @ id)) = $true)) | ? [X455 : (subst > term > term)] : (! [X459 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X457 @ X458) @ X459)) = ((X455 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))) & ! [X456 : term] : ((((X453 @ id @ X456 @ id)) != $true) | ($true = ((X453 @ id @ (X455 @ id @ X456) @ id)))) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true)))) & (! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) <=> (pushprop_lem1 = $true)) & (! [X1 : term,X0 : (subst > term > subst > $o)] : (? [X3 : term,X2 : (subst > term > term)] : (! [X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) & ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) & ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9))) & ($true != ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)))) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true) | ? [X11 : term] : (($true != ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) & (((X0 @ id @ X11 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem3a_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X151 : (subst > term > subst > $o),X152 : term] : (? [X153 : subst,X155 : subst,X156 : term,X154 : subst] : (($true != ((X151 @ X153 @ X156 @ (comp @ X155 @ X154)))) & (((X151 @ (comp @ X153 @ X155) @ (sub @ X156 @ X155) @ X154)) = $true)) | ? [X160 : subst,X157 : subst,X158 : term,X159 : subst] : ((((X151 @ X157 @ X158 @ (comp @ X159 @ X160))) = $true) & ($true != ((X151 @ (comp @ X157 @ X159) @ (sub @ X158 @ X159) @ X160)))) | ? [X161 : term] : ((((var @ (sub @ X161 @ id))) = $true) & (((X151 @ id @ X161 @ id)) != $true)) | (((X151 @ id @ X152 @ id)) = $true) | ? [X167 : term,X168 : term] : ((((X151 @ id @ X168 @ id)) = $true) & (((X151 @ id @ (ap @ (sub @ X168 @ id) @ X167) @ id)) != $true) & ($true = ((X151 @ id @ X167 @ id)))) | ? [X162 : (subst > term > term)] : (($true != ((X151 @ id @ (lam @ (X162 @ sh @ one)) @ id))) & ! [X163 : term] : (($true = ((X151 @ id @ (X162 @ id @ X163) @ id))) | (((X151 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X166 : subst,X165 : term] : (((sub @ (X162 @ X166 @ X165) @ X164)) = ((X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))))) | ? [X142 : (subst > term > subst > $o),X143 : (term > $o),X141 : term] : (! [X149 : term] : (($true = ((X143 @ (sub @ X141 @ (push @ X149 @ id))))) | (((X143 @ X149)) != $true)) & ! [X144 : (subst > term > term)] : (? [X148 : term] : (($true != ((X142 @ id @ (X144 @ id @ X148) @ id))) & ($true = ((X142 @ id @ X148 @ id)))) | (((X142 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ? [X145 : subst,X146 : subst,X147 : term] : (((X144 @ (comp @ X145 @ X146) @ (sub @ X147 @ X146))) != ((sub @ (X144 @ X145 @ X147) @ X146)))) & ($true != ((X143 @ (lam @ X141)))) & ! [X150 : term] : (((X143 @ X150)) = ((X142 @ id @ X150 @ id))))) | ? [X140 : term] : (((sub @ X140 @ id)) != X140)) | ? [X134 : (term > $o),X133 : term] : (! [X137 : term,X136 : term] : (($true != ((X134 @ X137))) | (((X134 @ X136)) != $true) | (((X134 @ (ap @ X137 @ X136))) = $true)) & ! [X135 : term] : ((((var @ X135)) != $true) | (((X134 @ X135)) = $true)) & (((X134 @ X133)) != $true) & ! [X138 : term] : (? [X139 : term] : ((((X134 @ (sub @ X138 @ (push @ X139 @ id)))) != $true) & (((X134 @ X139)) = $true)) | ($true = ((X134 @ (lam @ X138))))))) | ? [X130 : (subst > term > subst > $o)] : ! [X131 : (term > $o)] : ? [X132 : term] : (((X130 @ id @ X132 @ id)) != ((X131 @ X132))))) & ((! [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) = $true) | ? [X104 : term] : (((X100 @ X104)) != ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | ($true != ((X103 @ X101)))) | ? [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) != X99)) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (apnotvar = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasapnotvar = $true) & (pushprop_lthm_orig = $true) & ((((! [X269 : (subst > term > subst > $o),X270 : term] : (? [X276 : (subst > term > term)] : ((((X269 @ id @ (lam @ (X276 @ sh @ one)) @ id)) != $true) & ! [X277 : term] : (($true != ((X269 @ id @ X277 @ id))) | (((X269 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X278 : term,X279 : subst,X280 : subst] : (((X276 @ (comp @ X280 @ X279) @ (sub @ X278 @ X279))) = ((sub @ (X276 @ X280 @ X278) @ X279)))) | ? [X281 : subst,X284 : term,X283 : subst,X282 : subst] : ((((X269 @ X283 @ X284 @ (comp @ X281 @ X282))) != $true) & (((X269 @ (comp @ X283 @ X281) @ (sub @ X284 @ X281) @ X282)) = $true)) | ? [X273 : subst,X272 : term,X274 : subst,X271 : subst] : ((((X269 @ (comp @ X271 @ X274) @ (sub @ X272 @ X274) @ X273)) != $true) & ($true = ((X269 @ X271 @ X272 @ (comp @ X274 @ X273))))) | ? [X285 : term,X286 : term] : (($true = ((X269 @ id @ X285 @ id))) & ($true != ((X269 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id))) & ($true = ((X269 @ id @ X286 @ id)))) | ? [X275 : term] : ((((var @ (sub @ X275 @ id))) = $true) & ($true != ((X269 @ id @ X275 @ id)))) | (((X269 @ id @ X270 @ id)) = $true)) | ? [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ (lam @ X253) @ id)) != $true) & ! [X260 : subst,X262 : subst,X259 : term,X261 : subst] : ((((X254 @ X261 @ X259 @ (comp @ X260 @ X262))) = $true) | (((X254 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260) @ X262)) != $true)) & ! [X264 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true) | ? [X265 : subst,X266 : subst,X267 : term] : (((sub @ (X264 @ X265 @ X267) @ X266)) != ((X264 @ (comp @ X265 @ X266) @ (sub @ X267 @ X266)))) | ? [X268 : term] : ((((X254 @ id @ X268 @ id)) = $true) & ($true != ((X254 @ id @ (X264 @ id @ X268) @ id))))) & ! [X263 : term] : ((((X254 @ id @ X263 @ id)) != $true) | (((X254 @ id @ (sub @ X253 @ (push @ X263 @ id)) @ id)) = $true)) & ! [X258 : term,X255 : subst,X257 : subst,X256 : subst] : ((((X254 @ (comp @ X257 @ X256) @ (sub @ X258 @ X256) @ X255)) = $true) | (((X254 @ X257 @ X258 @ (comp @ X256 @ X255))) != $true)))) | ? [X242 : term,X241 : term,X240 : (subst > term > subst > $o)] : ((((X240 @ id @ (ap @ X241 @ X242) @ id)) != $true) & ! [X246 : term,X247 : subst,X245 : subst,X248 : subst] : (($true != ((X240 @ X247 @ X246 @ (comp @ X245 @ X248)))) | ($true = ((X240 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245) @ X248)))) & ! [X243 : term,X244 : term] : ((((X240 @ id @ (ap @ (sub @ X244 @ id) @ X243) @ id)) = $true) | ($true != ((X240 @ id @ X243 @ id))) | ($true != ((X240 @ id @ X244 @ id)))) & ! [X251 : subst,X250 : term,X249 : subst,X252 : subst] : ((((X240 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251) @ X252)) != $true) | ($true = ((X240 @ X249 @ X250 @ (comp @ X251 @ X252))))) & ($true = ((X240 @ id @ X241 @ id))) & (((X240 @ id @ X242 @ id)) = $true))) | ? [X234 : (term > $o),X233 : term] : ((((X234 @ X233)) != $true) & ! [X237 : term] : (? [X238 : term] : (($true != ((X234 @ (sub @ X237 @ (push @ X238 @ id))))) & ($true = ((X234 @ X238)))) | ($true = ((X234 @ (lam @ X237))))) & ! [X239 : term] : (($true = ((X234 @ X239))) | ($true != ((var @ X239)))) & ! [X236 : term,X235 : term] : ((((X234 @ X235)) != $true) | (((X234 @ (ap @ X236 @ X235))) = $true) | (((X234 @ X236)) != $true)))) <=> (hoasinduction_lthm = $true)) & (one = ((d2term @ d_one))) & (hoaslamnotap_lthm = $true) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) <=> (substmonoid = $true)) & (hoaslamnotvar = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X487 : (subst > term > subst > $o),X486 : (term > $o),X485 : term] : (? [X496 : subst,X495 : subst,X494 : term,X493 : subst] : (($true = ((X487 @ X493 @ X494 @ (comp @ X495 @ X496)))) & ($true != ((X487 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)))) | ? [X497 : term] : (((X486 @ X497)) != ((X487 @ id @ X497 @ id))) | ? [X498 : term] : (($true = ((X486 @ X498))) & (((X486 @ (sub @ X485 @ (push @ X498 @ id)))) != $true)) | ($true = ((X486 @ (lam @ X485)))) | ? [X488 : (subst > term > term)] : (! [X492 : term] : ((((X487 @ id @ X492 @ id)) != $true) | (((X487 @ id @ (X488 @ id @ X492) @ id)) = $true)) & (((X487 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X489 : term,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491))))) | ? [X502 : term,X499 : subst,X501 : subst,X500 : subst] : (($true != ((X487 @ X501 @ X502 @ (comp @ X500 @ X499)))) & (((X487 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499)) = $true)))) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (? [X77 : term] : (($true = ((X76 @ X77))) & ($true != ((X76 @ (sub @ X75 @ (push @ X77 @ id)))))) | ? [X79 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) != $true) & ! [X83 : term] : ((((X74 @ id @ X83 @ id)) != $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true)) & ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81)))) | ? [X78 : term] : (((X74 @ id @ X78 @ id)) != ((X76 @ X78))) | (((X76 @ (lam @ X75))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X311 : term] : ? [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) = ((X312 @ sh @ one)))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X373 : term] : ? [X374 : (subst > term > term)] : ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376)))) & (hoaslaminj_gthm = $true) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) <=> (axshiftcons = $true)) & (pushprop_lem3v2 = $true) & (substmonoid_gthm = $true) & ! [X110 : d_term,X109 : d_term] : ((X109 = X110) | (((d2term @ X110)) != ((d2term @ X109)))) & (hoasapinj2_gthm = $true) & (! [X529 : term] : ? [X530 : (subst > term > term)] : ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X89 : term,X88 : (subst > term > subst > $o)] : (? [X92 : (subst > term > term)] : (! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) & ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true)) & (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true) | ? [X90 : term,X91 : term] : ((((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) != $true) & (((X88 @ id @ X90 @ id)) = $true) & ($true = ((X88 @ id @ X91 @ id)))))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3b = $true) <=> ! [X107 : term] : ? [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) = ((X108 @ sh @ one)))) & ((hoaslaminj_lthm = $true) <=> (((! [X302 : (subst > term > term),X303 : subst,X304 : (subst > term > term),X301 : term] : ((((X302 @ X303 @ X301)) = ((X304 @ X303 @ X301))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ? [X309 : term,X308 : subst,X310 : subst] : (((X304 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) != ((sub @ (X304 @ X308 @ X309) @ X310))) | ? [X307 : term,X305 : subst,X306 : subst] : (((X302 @ (comp @ X306 @ X305) @ (sub @ X307 @ X305))) != ((sub @ (X302 @ X306 @ X307) @ X305)))) | ? [X299 : term,X300 : term] : ((((lam @ X299)) = ((lam @ X300))) & (X299 != X300))) | ? [X298 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X298))) != X298)) | ? [X295 : term,X296 : subst] : (((sub @ one @ (push @ X295 @ X296))) != X295))) & (hoasinduction_lem1 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X206 : term,X205 : (subst > term > subst > $o)] : (? [X212 : term,X213 : term] : (($true = ((X205 @ id @ X212 @ id))) & ($true = ((X205 @ id @ X213 @ id))) & (((X205 @ id @ (ap @ (sub @ X213 @ id) @ X212) @ id)) != $true)) | ? [X207 : (subst > term > term)] : (! [X211 : term] : ((((X205 @ id @ (X207 @ id @ X211) @ id)) = $true) | (((X205 @ id @ X211 @ id)) != $true)) & ! [X210 : subst,X208 : subst,X209 : term] : (((X207 @ (comp @ X210 @ X208) @ (sub @ X209 @ X208))) = ((sub @ (X207 @ X210 @ X209) @ X208))) & ($true != ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id)))) | (((X205 @ id @ X206 @ id)) = $true)) | ? [X197 : (subst > term > subst > $o),X196 : (term > $o),X195 : term] : ((((X196 @ (lam @ X195))) != $true) & ! [X200 : (subst > term > term)] : (? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X200 @ X204 @ X202) @ X203)) != ((X200 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | (((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true) | ? [X201 : term] : ((((X197 @ id @ X201 @ id)) = $true) & (((X197 @ id @ (X200 @ id @ X201) @ id)) != $true))) & ! [X198 : term] : (((X197 @ id @ X198 @ id)) = ((X196 @ X198))) & ! [X199 : term] : ((((X196 @ X199)) != $true) | ($true = ((X196 @ (sub @ X195 @ (push @ X199 @ id)))))))) | ? [X194 : term] : (((sub @ X194 @ id)) != X194)) | ? [X187 : (term > $o),X188 : term] : ((((X187 @ X188)) != $true) & ! [X192 : term,X193 : term] : ((((X187 @ X193)) != $true) | ($true != ((X187 @ X192))) | (((X187 @ (ap @ X192 @ X193))) = $true)) & ! [X190 : term] : (($true = ((X187 @ (lam @ X190)))) | ? [X191 : term] : ((((X187 @ (sub @ X190 @ (push @ X191 @ id)))) != $true) & ($true = ((X187 @ X191))))) & ! [X189 : term] : (($true != ((var @ X189))) | ($true = ((X187 @ X189)))))) | ? [X184 : (subst > term > subst > $o)] : ! [X185 : (term > $o)] : ? [X186 : term] : (((X184 @ id @ X186 @ id)) != ((X185 @ X186))))) & (hoasapnotvar_gthm = $true) & (! [X365 : term,X366 : (subst > term > subst > $o)] : (? [X367 : (subst > term > term)] : (! [X368 : term] : (($true != ((X366 @ id @ X368 @ id))) | (((X366 @ id @ (X367 @ id @ X368) @ id)) = $true)) & ($true != ((X366 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X370 : subst,X371 : subst,X369 : term] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371)))) | (((X366 @ id @ (lam @ (sub @ X365 @ (push @ one @ sh))) @ id)) = $true) | ? [X372 : term] : (($true != ((X366 @ id @ (sub @ X365 @ (push @ X372 @ id)) @ id))) & (((X366 @ id @ X372 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (lamnotvar = $true) & (((! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)) | ? [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 != X479) & (((ap @ X479 @ X477)) = ((ap @ X478 @ X480))))) | ? [X476 : term] : (((sub @ X476 @ id)) != X476)) <=> (hoasapinj1_lthm = $true)) & (lamnotap != $true) & (hoasinduction_lem1v2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (? [X20 : term] : (((X18 @ X20)) != ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true = ((X18 @ one))) | ($true != ((X16 @ X19))))) & (hoasapnotvar_lthm = $true) & ((hoasinduction = $true) <=> ! [X29 : term,X28 : (subst > term > subst > $o)] : (? [X35 : term] : (($true = ((var @ (sub @ X35 @ id)))) & (((X28 @ id @ X35 @ id)) != $true)) | ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true != ((X28 @ id @ X34 @ id))) | (((X28 @ id @ (X30 @ id @ X34) @ id)) = $true)) & ($true != ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id))) & ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32)))) | ? [X36 : term,X39 : subst,X37 : subst,X38 : subst] : (($true = ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37))) & (((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) != $true)) | (((X28 @ id @ X29 @ id)) = $true) | ? [X41 : term,X40 : term] : ((((X28 @ id @ X41 @ id)) = $true) & (((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) != $true) & (((X28 @ id @ X40 @ id)) = $true)) | ? [X42 : subst,X43 : subst,X45 : subst,X44 : term] : ((((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) = $true) & (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) != $true)))) & (! [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (? [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) != ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))) | ? [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) != ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))) <=> (hoaslaminj = $true)) & ((? [X214 : term] : (((sub @ X214 @ id)) != X214) | ! [X217 : (term > $o),X215 : (subst > term > subst > $o),X216 : term] : (? [X218 : (subst > term > term)] : (! [X220 : subst,X222 : term,X221 : subst] : (((sub @ (X218 @ X220 @ X222) @ X221)) = ((X218 @ (comp @ X220 @ X221) @ (sub @ X222 @ X221)))) & ! [X219 : term] : ((((X215 @ id @ X219 @ id)) != $true) | (((X215 @ id @ (X218 @ id @ X219) @ id)) = $true)) & ($true != ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id)))) | ($true = ((X217 @ (lam @ X216)))) | ? [X232 : term] : (($true != ((X217 @ (sub @ X216 @ (push @ X232 @ id))))) & ($true = ((X217 @ X232)))) | ? [X228 : subst,X229 : subst,X231 : subst,X230 : term] : ((((X215 @ (comp @ X228 @ X229) @ (sub @ X230 @ X229) @ X231)) = $true) & ($true != ((X215 @ X228 @ X230 @ (comp @ X229 @ X231))))) | ? [X224 : subst,X227 : subst,X226 : term,X225 : subst] : ((((X215 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true) & (((X215 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) != $true)) | ? [X223 : term] : (((X217 @ X223)) != ((X215 @ id @ X223 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (((! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true)) | ? [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) != X414)) | ? [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) != X411)) <=> (pushprop_lem1_lthm = $true)) & (! [X420 : term,X422 : subst,X421 : (term > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X65 : (subst > term > subst > $o),X66 : term] : (? [X67 : (subst > term > term)] : (! [X68 : term] : ((((X65 @ id @ (X67 @ id @ X68) @ id)) = $true) | ($true != ((X65 @ id @ X68 @ id)))) & ($true != ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id))) & ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70))))) | ? [X72 : term] : (($true != ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id))) & (((X65 @ id @ X72 @ id)) = $true)) | ($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & (! [X54 : term,X52 : term,X53 : (subst > term > subst > $o)] : (? [X58 : subst,X55 : term,X56 : subst,X57 : subst] : (($true != ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)))) & ($true = ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)))) | ($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | ? [X60 : term,X59 : term] : (($true = ((X53 @ id @ X59 @ id))) & (((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) != $true) & (((X53 @ id @ X60 @ id)) = $true)) | (((X53 @ id @ X52 @ id)) != $true) | (((X53 @ id @ X54 @ id)) != $true) | ? [X61 : subst,X64 : subst,X62 : term,X63 : subst] : ((((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) != $true) & (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) = $true))) <=> (hoasinduction_lem2 = $true)) & (ulamvarind = $true) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem0_lthm = $true) <=> ! [X426 : (subst > term > subst > $o)] : ? [X427 : (term > $o)] : ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id)))) & (axmap = $true) & ((pushprop_lem0 = $true) <=> ! [X534 : term,X535 : (term > $o),X533 : subst] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (((! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X351 : subst,X352 : term,X353 : subst,X350 : subst] : (($true != ((X339 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350) @ X353))) & (((X339 @ X351 @ X352 @ (comp @ X350 @ X353))) = $true)) | ? [X341 : subst,X343 : term,X344 : subst,X342 : subst] : (($true != ((X339 @ X344 @ X343 @ (comp @ X341 @ X342)))) & (((X339 @ (comp @ X344 @ X341) @ (sub @ X343 @ X341) @ X342)) = $true)) | ($true = ((X339 @ id @ (lam @ X338) @ id))) | ? [X345 : (subst > term > term)] : (! [X347 : subst,X348 : subst,X349 : term] : (((X345 @ (comp @ X347 @ X348) @ (sub @ X349 @ X348))) = ((sub @ (X345 @ X347 @ X349) @ X348))) & ! [X346 : term] : ((((X339 @ id @ (X345 @ id @ X346) @ id)) = $true) | ($true != ((X339 @ id @ X346 @ id)))) & (((X339 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true)) | ? [X340 : term] : (($true = ((X339 @ id @ X340 @ id))) & (((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)) != $true))) | ? [X331 : term,X330 : (subst > term > subst > $o)] : (($true != ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id))) & ! [X332 : (subst > term > term)] : (($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ? [X333 : term] : (($true != ((X330 @ id @ (X332 @ id @ X333) @ id))) & (((X330 @ id @ X333 @ id)) = $true)) | ? [X334 : subst,X335 : term,X336 : subst] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) != ((sub @ (X332 @ X336 @ X335) @ X334)))) & ! [X337 : term] : (($true = ((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))) | (((X330 @ id @ X337 @ id)) != $true)))) | ? [X329 : term] : (((sub @ X329 @ id)) != X329)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X313 : d_subst] : (d_id = X313) & ! [X360 : d_subst,X359 : d_subst] : ((X359 = X360) | (((d2subst @ X359)) != ((d2subst @ X360)))) & (hoaslamnotvar_gthm = $true) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) <=> (axidl = $true)) & ! [X460 : d_term] : (d_one = X460) & (axvarshift = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X516 : (subst > term > subst > $o),X515 : term] : (($true = ((X516 @ id @ (lam @ X515) @ id))) | ? [X518 : (subst > term > term)] : (! [X519 : term] : (($true != ((X516 @ id @ X519 @ id))) | ($true = ((X516 @ id @ (X518 @ id @ X519) @ id)))) & ! [X520 : subst,X521 : subst,X522 : term] : (((sub @ (X518 @ X521 @ X522) @ X520)) = ((X518 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520)))) & ($true != ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id)))) | ? [X517 : term] : (($true = ((X516 @ id @ X517 @ id))) & (((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)) != $true))) | ? [X508 : (subst > term > subst > $o),X507 : term] : (! [X514 : term] : ((((X508 @ id @ (sub @ X507 @ (push @ X514 @ id)) @ id)) = $true) | ($true != ((X508 @ id @ X514 @ id)))) & ! [X509 : (subst > term > term)] : (? [X513 : subst,X512 : term,X511 : subst] : (((sub @ (X509 @ X513 @ X512) @ X511)) != ((X509 @ (comp @ X513 @ X511) @ (sub @ X512 @ X511)))) | (((X508 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true) | ? [X510 : term] : (($true = ((X508 @ id @ X510 @ id))) & ($true != ((X508 @ id @ (X509 @ id @ X510) @ id))))) & ($true != ((X508 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id))))) | ? [X506 : term] : (((sub @ X506 @ id)) != X506))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (pushprop_lem3v2_lthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (axassoc = $true) & (ulamvarsh = $true) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (axclos = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (pushprop = $true) & ((hoasinduction_lem3 = $true) <=> ! [X378 : (subst > term > subst > $o),X377 : term] : (? [X379 : term] : ((((X378 @ id @ (sub @ X377 @ (push @ X379 @ id)) @ id)) != $true) & ($true = ((X378 @ id @ X379 @ id)))) | ? [X380 : (subst > term > term)] : (! [X381 : term] : ((((X378 @ id @ X381 @ id)) != $true) | ($true = ((X378 @ id @ (X380 @ id @ X381) @ id)))) & ! [X384 : subst,X383 : subst,X382 : term] : (((sub @ (X380 @ X383 @ X382) @ X384)) = ((X380 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384)))) & (((X378 @ id @ (lam @ (X380 @ sh @ one)) @ id)) != $true)) | (((X378 @ id @ (lam @ X377) @ id)) = $true) | ? [X386 : term,X385 : subst,X388 : subst,X387 : subst] : ((((X378 @ (comp @ X387 @ X388) @ (sub @ X386 @ X388) @ X385)) != $true) & ($true = ((X378 @ X387 @ X386 @ (comp @ X388 @ X385))))) | ? [X391 : subst,X389 : term,X390 : subst,X392 : subst] : (($true != ((X378 @ X391 @ X389 @ (comp @ X392 @ X390)))) & ($true = ((X378 @ (comp @ X391 @ X392) @ (sub @ X389 @ X392) @ X390)))))) & ((shinj = $true) <=> ! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem0 = $true) <=> ! [X503 : (subst > term > subst > $o)] : ? [X504 : (term > $o)] : ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505)))) & (hoasapinj1_gthm = $true) & (axapp = $true) & ((induction = $true) <=> ! [X523 : term,X524 : (term > $o)] : (? [X526 : term] : (($true != ((X524 @ X526))) & (((var @ X526)) = $true)) | ? [X525 : term] : ((((X524 @ (lam @ X525))) != $true) & ($true = ((X524 @ X525)))) | ? [X527 : term,X528 : term] : (($true != ((X524 @ (ap @ X528 @ X527)))) & ($true = ((X524 @ X527))) & (((X524 @ X528)) = $true)) | (((X524 @ X523)) = $true))) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & (pushprop_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X288 : term,X289 : (term > $o),X287 : subst] : (? [X290 : term] : ((((X289 @ (lam @ X290))) != $true) & ! [X291 : term] : ((((X289 @ (sub @ X290 @ (push @ X291 @ id)))) = $true) | ($true != ((X289 @ X291))))) | ($true = ((X289 @ (sub @ X288 @ X287)))) | ? [X292 : term] : (($true != ((X289 @ (sub @ X292 @ X287)))) & (((var @ X292)) = $true)) | ? [X294 : term,X293 : term] : ((((X289 @ (ap @ X293 @ X294))) != $true) & ($true = ((X289 @ X294))) & (((X289 @ X293)) = $true))) <=> (induction2lem = $true)) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) <=> (axvarcons = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) <=> (axscons = $true)) & ((hoasapinj2 = $true) <=> ! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363))) & (hoasinduction_gthm = $true) & ((! [X106 : term] : (((sub @ X106 @ id)) = X106) | ? [X105 : term] : (((sub @ X105 @ id)) != X105)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X169 : term,X171 : (subst > term > subst > $o),X170 : (term > $o),X172 : term] : ((((X170 @ X172)) != $true) | ($true != ((X170 @ X169))) | ? [X175 : subst,X176 : term,X177 : subst,X174 : subst] : ((((X171 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) != $true) & (((X171 @ X175 @ X176 @ (comp @ X174 @ X177))) = $true)) | ? [X183 : term,X182 : term] : ((((X171 @ id @ (ap @ (sub @ X182 @ id) @ X183) @ id)) != $true) & ($true = ((X171 @ id @ X183 @ id))) & ($true = ((X171 @ id @ X182 @ id)))) | (((X170 @ (ap @ X172 @ X169))) = $true) | ? [X173 : term] : (((X170 @ X173)) != ((X171 @ id @ X173 @ id))) | ? [X180 : term,X179 : subst,X178 : subst,X181 : subst] : ((((X171 @ X181 @ X180 @ (comp @ X179 @ X178))) != $true) & ($true = ((X171 @ (comp @ X181 @ X179) @ (sub @ X180 @ X179) @ X178)))))) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) <=> (laminj = $true)) & ((! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473)))) | ? [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 != X470) & (((ap @ X467 @ X470)) = ((ap @ X468 @ X469))))) <=> (hoasapinj2_lthm = $true)) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) <=> (apinj1 = $true)) & (hoaslamnotvar_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & (hoasinduction_lem1v2 = $true)),
% 13.65/2.32 inference(ennf_transformation,[],[f10])).
% 13.65/2.32 thf(f12,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X313 : d_subst] : (d_id = X313) & ((! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473)))) | ? [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 != X470) & (((ap @ X467 @ X470)) = ((ap @ X468 @ X469))))) <=> (hoasapinj2_lthm = $true)) & ((shinj = $true) <=> ! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451))) & (axvarshift = $true) & (induction2lem_gthm = $true) & (! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (? [X77 : term] : (($true = ((X76 @ X77))) & ($true != ((X76 @ (sub @ X75 @ (push @ X77 @ id)))))) | ? [X79 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) != $true) & ! [X83 : term] : ((((X74 @ id @ X83 @ id)) != $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true)) & ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81)))) | ? [X78 : term] : (((X74 @ id @ X78 @ id)) != ((X76 @ X78))) | (((X76 @ (lam @ X75))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lthm_orig = $true) & ((? [X84 : subst] : (((comp @ id @ X84)) != X84) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85) | (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X89 : term,X88 : (subst > term > subst > $o)] : (? [X92 : (subst > term > term)] : (! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) & ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true)) & (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true) | ? [X90 : term,X91 : term] : ((((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) != $true) & (((X88 @ id @ X90 @ id)) = $true) & ($true = ((X88 @ id @ X91 @ id)))))) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3a = $true) <=> ! [X453 : (subst > term > subst > $o),X452 : term] : ((((X453 @ id @ (lam @ X452) @ id)) = $true) | ? [X454 : term] : (($true != ((X453 @ id @ (sub @ X452 @ (push @ X454 @ id)) @ id))) & (((X453 @ id @ X454 @ id)) = $true)) | ? [X455 : (subst > term > term)] : (! [X459 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X457 @ X458) @ X459)) = ((X455 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))) & ! [X456 : term] : ((((X453 @ id @ X456 @ id)) != $true) | ($true = ((X453 @ id @ (X455 @ id @ X456) @ id)))) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true)))) & (substmonoid_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363))) & (! [X420 : term,X422 : subst,X421 : (term > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) <=> (pushprop_lem0_lthm = $true)) & ((induction2_lthm = $true) <=> (? [X395 : subst,X394 : (term > $o),X396 : term] : (! [X399 : term] : (? [X400 : term] : (($true != ((X394 @ (sub @ X399 @ (push @ X400 @ id))))) & ($true = ((X394 @ X400)))) | ($true = ((X394 @ (lam @ X399))))) & ! [X401 : term] : ((((var @ X401)) != $true) | (((X394 @ (sub @ X401 @ X395))) = $true)) & ($true != ((X394 @ (sub @ X396 @ X395)))) & ! [X398 : term,X397 : term] : (($true = ((X394 @ (ap @ X398 @ X397)))) | (((X394 @ X397)) != $true) | (((X394 @ X398)) != $true))) | ! [X402 : term,X403 : (term > $o)] : (? [X406 : term,X407 : term] : ((((X403 @ X407)) = $true) & ($true != ((X403 @ (ap @ X406 @ X407)))) & ($true = ((X403 @ X406)))) | (((X403 @ X402)) = $true) | ? [X404 : term] : ((((X403 @ (lam @ X404))) != $true) & ! [X405 : term] : ((((X403 @ X405)) != $true) | (((X403 @ (sub @ X404 @ (push @ X405 @ id)))) = $true))) | ? [X408 : term] : (($true = ((var @ X408))) & ($true != ((X403 @ X408))))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393))) & ! [X460 : d_term] : (d_one = X460) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X311 : term] : ? [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) = ((X312 @ sh @ one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) <=> (pushprop_lem1 = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (! [X65 : (subst > term > subst > $o),X66 : term] : (? [X67 : (subst > term > term)] : (! [X68 : term] : ((((X65 @ id @ (X67 @ id @ X68) @ id)) = $true) | ($true != ((X65 @ id @ X68 @ id)))) & ($true != ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id))) & ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70))))) | ? [X72 : term] : (($true != ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id))) & (((X65 @ id @ X72 @ id)) = $true)) | ($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((! [X106 : term] : (((sub @ X106 @ id)) = X106) | ? [X105 : term] : (((sub @ X105 @ id)) != X105)) <=> (termmset_lthm = $true)) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X426 : (subst > term > subst > $o)] : ? [X427 : (term > $o)] : ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id)))) & (! [X1 : term,X0 : (subst > term > subst > $o)] : (? [X3 : term,X2 : (subst > term > term)] : (! [X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) & ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) & ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9))) & ($true != ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)))) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true) | ? [X11 : term] : (($true != ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) & (((X0 @ id @ X11 @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) <=> (axscons = $true)) & ((hoasinduction_lthm = $true) <=> (? [X242 : term,X241 : term,X240 : (subst > term > subst > $o)] : ((((X240 @ id @ (ap @ X241 @ X242) @ id)) != $true) & ! [X246 : term,X247 : subst,X245 : subst,X248 : subst] : (($true != ((X240 @ X247 @ X246 @ (comp @ X245 @ X248)))) | ($true = ((X240 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245) @ X248)))) & ! [X243 : term,X244 : term] : ((((X240 @ id @ (ap @ (sub @ X244 @ id) @ X243) @ id)) = $true) | ($true != ((X240 @ id @ X243 @ id))) | ($true != ((X240 @ id @ X244 @ id)))) & ! [X251 : subst,X250 : term,X249 : subst,X252 : subst] : ((((X240 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251) @ X252)) != $true) | ($true = ((X240 @ X249 @ X250 @ (comp @ X251 @ X252))))) & ($true = ((X240 @ id @ X241 @ id))) & (((X240 @ id @ X242 @ id)) = $true)) | ! [X269 : (subst > term > subst > $o),X270 : term] : (? [X276 : (subst > term > term)] : ((((X269 @ id @ (lam @ (X276 @ sh @ one)) @ id)) != $true) & ! [X277 : term] : (($true != ((X269 @ id @ X277 @ id))) | (((X269 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X278 : term,X279 : subst,X280 : subst] : (((X276 @ (comp @ X280 @ X279) @ (sub @ X278 @ X279))) = ((sub @ (X276 @ X280 @ X278) @ X279)))) | ? [X281 : subst,X284 : term,X283 : subst,X282 : subst] : ((((X269 @ X283 @ X284 @ (comp @ X281 @ X282))) != $true) & (((X269 @ (comp @ X283 @ X281) @ (sub @ X284 @ X281) @ X282)) = $true)) | ? [X273 : subst,X272 : term,X274 : subst,X271 : subst] : ((((X269 @ (comp @ X271 @ X274) @ (sub @ X272 @ X274) @ X273)) != $true) & ($true = ((X269 @ X271 @ X272 @ (comp @ X274 @ X273))))) | ? [X285 : term,X286 : term] : (($true = ((X269 @ id @ X285 @ id))) & ($true != ((X269 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id))) & ($true = ((X269 @ id @ X286 @ id)))) | ? [X275 : term] : ((((var @ (sub @ X275 @ id))) = $true) & ($true != ((X269 @ id @ X275 @ id)))) | (((X269 @ id @ X270 @ id)) = $true)) | ? [X234 : (term > $o),X233 : term] : ((((X234 @ X233)) != $true) & ! [X237 : term] : (? [X238 : term] : (($true != ((X234 @ (sub @ X237 @ (push @ X238 @ id))))) & ($true = ((X234 @ X238)))) | ($true = ((X234 @ (lam @ X237))))) & ! [X239 : term] : (($true = ((X234 @ X239))) | ($true != ((var @ X239)))) & ! [X236 : term,X235 : term] : ((((X234 @ X235)) != $true) | (((X234 @ (ap @ X236 @ X235))) = $true) | (((X234 @ X236)) != $true))) | ? [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ (lam @ X253) @ id)) != $true) & ! [X260 : subst,X262 : subst,X259 : term,X261 : subst] : ((((X254 @ X261 @ X259 @ (comp @ X260 @ X262))) = $true) | (((X254 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260) @ X262)) != $true)) & ! [X264 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true) | ? [X265 : subst,X266 : subst,X267 : term] : (((sub @ (X264 @ X265 @ X267) @ X266)) != ((X264 @ (comp @ X265 @ X266) @ (sub @ X267 @ X266)))) | ? [X268 : term] : ((((X254 @ id @ X268 @ id)) = $true) & ($true != ((X254 @ id @ (X264 @ id @ X268) @ id))))) & ! [X263 : term] : ((((X254 @ id @ X263 @ id)) != $true) | (((X254 @ id @ (sub @ X253 @ (push @ X263 @ id)) @ id)) = $true)) & ! [X258 : term,X255 : subst,X257 : subst,X256 : subst] : ((((X254 @ (comp @ X257 @ X256) @ (sub @ X258 @ X256) @ X255)) = $true) | (((X254 @ X257 @ X258 @ (comp @ X256 @ X255))) != $true))))) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & (! [X54 : term,X52 : term,X53 : (subst > term > subst > $o)] : (? [X58 : subst,X55 : term,X56 : subst,X57 : subst] : (($true != ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)))) & ($true = ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)))) | ($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | ? [X60 : term,X59 : term] : (($true = ((X53 @ id @ X59 @ id))) & (((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) != $true) & (((X53 @ id @ X60 @ id)) = $true)) | (((X53 @ id @ X52 @ id)) != $true) | (((X53 @ id @ X54 @ id)) != $true) | ? [X61 : subst,X64 : subst,X62 : term,X63 : subst] : ((((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) != $true) & (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) = $true))) <=> (hoasinduction_lem2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X534 : term,X535 : (term > $o),X533 : subst] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (axmap = $true) & (! [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (? [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) != ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))) | ? [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) != ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X487 : (subst > term > subst > $o),X486 : (term > $o),X485 : term] : (? [X496 : subst,X495 : subst,X494 : term,X493 : subst] : (($true = ((X487 @ X493 @ X494 @ (comp @ X495 @ X496)))) & ($true != ((X487 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)))) | ? [X497 : term] : (((X486 @ X497)) != ((X487 @ id @ X497 @ id))) | ? [X498 : term] : (($true = ((X486 @ X498))) & (((X486 @ (sub @ X485 @ (push @ X498 @ id)))) != $true)) | ($true = ((X486 @ (lam @ X485)))) | ? [X488 : (subst > term > term)] : (! [X492 : term] : ((((X487 @ id @ X492 @ id)) != $true) | (((X487 @ id @ (X488 @ id @ X492) @ id)) = $true)) & (((X487 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X489 : term,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491))))) | ? [X502 : term,X499 : subst,X501 : subst,X500 : subst] : (($true != ((X487 @ X501 @ X502 @ (comp @ X500 @ X499)))) & (((X487 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499)) = $true)))) & ((? [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) != X411) | ? [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) != X414) | ! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X373 : term] : ? [X374 : (subst > term > term)] : ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) <=> (substmonoid = $true)) & (axabs = $true) & ((? [X435 : (term > $o),X434 : term] : (($true != ((X435 @ X434))) & ! [X438 : term,X439 : term] : (($true != ((X435 @ X438))) | (((X435 @ X439)) != $true) | ($true = ((X435 @ (ap @ X439 @ X438))))) & ! [X437 : term] : (($true = ((X435 @ (lam @ X437)))) | (((X435 @ X437)) != $true)) & ! [X436 : term] : ((((var @ X436)) != $true) | ($true = ((X435 @ X436))))) | ? [X432 : term,X431 : subst] : (((comp @ sh @ (push @ X432 @ X431))) != X431) | ? [X429 : term,X430 : subst] : (((sub @ one @ (push @ X429 @ X430))) != X429) | ! [X441 : term,X440 : (term > $o),X442 : subst] : (? [X443 : term] : ((((X440 @ (lam @ X443))) != $true) & ! [X444 : term] : (($true != ((X440 @ X444))) | ($true = ((X440 @ (sub @ X443 @ (push @ X444 @ id))))))) | ? [X447 : term] : (($true != ((X440 @ (sub @ X447 @ X442)))) & (((var @ X447)) = $true)) | ? [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) != $true) & (((X440 @ X446)) = $true) & (((X440 @ X445)) = $true)) | (((X440 @ (sub @ X441 @ X442))) = $true)) | ? [X433 : subst] : (((comp @ X433 @ id)) != X433)) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X197 : (subst > term > subst > $o),X196 : (term > $o),X195 : term] : ((((X196 @ (lam @ X195))) != $true) & ! [X200 : (subst > term > term)] : (? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X200 @ X204 @ X202) @ X203)) != ((X200 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | (((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true) | ? [X201 : term] : ((((X197 @ id @ X201 @ id)) = $true) & (((X197 @ id @ (X200 @ id @ X201) @ id)) != $true))) & ! [X198 : term] : (((X197 @ id @ X198 @ id)) = ((X196 @ X198))) & ! [X199 : term] : ((((X196 @ X199)) != $true) | ($true = ((X196 @ (sub @ X195 @ (push @ X199 @ id))))))) | ? [X194 : term] : (((sub @ X194 @ id)) != X194) | ! [X206 : term,X205 : (subst > term > subst > $o)] : (? [X212 : term,X213 : term] : (($true = ((X205 @ id @ X212 @ id))) & ($true = ((X205 @ id @ X213 @ id))) & (((X205 @ id @ (ap @ (sub @ X213 @ id) @ X212) @ id)) != $true)) | ? [X207 : (subst > term > term)] : (! [X211 : term] : ((((X205 @ id @ (X207 @ id @ X211) @ id)) = $true) | (((X205 @ id @ X211 @ id)) != $true)) & ! [X210 : subst,X208 : subst,X209 : term] : (((X207 @ (comp @ X210 @ X208) @ (sub @ X209 @ X208))) = ((sub @ (X207 @ X210 @ X209) @ X208))) & ($true != ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id)))) | (((X205 @ id @ X206 @ id)) = $true)) | ? [X184 : (subst > term > subst > $o)] : ! [X185 : (term > $o)] : ? [X186 : term] : (((X184 @ id @ X186 @ id)) != ((X185 @ X186))) | ? [X187 : (term > $o),X188 : term] : ((((X187 @ X188)) != $true) & ! [X192 : term,X193 : term] : ((((X187 @ X193)) != $true) | ($true != ((X187 @ X192))) | (((X187 @ (ap @ X192 @ X193))) = $true)) & ! [X190 : term] : (($true = ((X187 @ (lam @ X190)))) | ? [X191 : term] : ((((X187 @ (sub @ X190 @ (push @ X191 @ id)))) != $true) & ($true = ((X187 @ X191))))) & ! [X189 : term] : (($true != ((var @ X189))) | ($true = ((X187 @ X189))))))) & ! [X360 : d_subst,X359 : d_subst] : ((X359 = X360) | (((d2subst @ X359)) != ((d2subst @ X360)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & ((! [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) = $true) | ? [X104 : term] : (((X100 @ X104)) != ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | ($true != ((X103 @ X101)))) | ? [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) != X99)) <=> (pushprop_lem1v2_lthm = $true)) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) <=> (axvarcons = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & ((hoasinduction = $true) <=> ! [X29 : term,X28 : (subst > term > subst > $o)] : (? [X35 : term] : (($true = ((var @ (sub @ X35 @ id)))) & (((X28 @ id @ X35 @ id)) != $true)) | ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true != ((X28 @ id @ X34 @ id))) | (((X28 @ id @ (X30 @ id @ X34) @ id)) = $true)) & ($true != ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id))) & ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32)))) | ? [X36 : term,X39 : subst,X37 : subst,X38 : subst] : (($true = ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37))) & (((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) != $true)) | (((X28 @ id @ X29 @ id)) = $true) | ? [X41 : term,X40 : term] : ((((X28 @ id @ X41 @ id)) = $true) & (((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) != $true) & (((X28 @ id @ X40 @ id)) = $true)) | ? [X42 : subst,X43 : subst,X45 : subst,X44 : term] : ((((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) = $true) & (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) != $true)))) & ((hoaslaminj_lthm = $true) <=> (? [X299 : term,X300 : term] : ((((lam @ X299)) = ((lam @ X300))) & (X299 != X300)) | ! [X302 : (subst > term > term),X303 : subst,X304 : (subst > term > term),X301 : term] : ((((X302 @ X303 @ X301)) = ((X304 @ X303 @ X301))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ? [X309 : term,X308 : subst,X310 : subst] : (((X304 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) != ((sub @ (X304 @ X308 @ X309) @ X310))) | ? [X307 : term,X305 : subst,X306 : subst] : (((X302 @ (comp @ X306 @ X305) @ (sub @ X307 @ X305))) != ((sub @ (X302 @ X306 @ X307) @ X305)))) | ? [X298 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X298))) != X298) | ? [X295 : term,X296 : subst] : (((sub @ one @ (push @ X295 @ X296))) != X295))) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X378 : (subst > term > subst > $o),X377 : term] : (? [X379 : term] : ((((X378 @ id @ (sub @ X377 @ (push @ X379 @ id)) @ id)) != $true) & ($true = ((X378 @ id @ X379 @ id)))) | ? [X380 : (subst > term > term)] : (! [X381 : term] : ((((X378 @ id @ X381 @ id)) != $true) | ($true = ((X378 @ id @ (X380 @ id @ X381) @ id)))) & ! [X384 : subst,X383 : subst,X382 : term] : (((sub @ (X380 @ X383 @ X382) @ X384)) = ((X380 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384)))) & (((X378 @ id @ (lam @ (X380 @ sh @ one)) @ id)) != $true)) | (((X378 @ id @ (lam @ X377) @ id)) = $true) | ? [X386 : term,X385 : subst,X388 : subst,X387 : subst] : ((((X378 @ (comp @ X387 @ X388) @ (sub @ X386 @ X388) @ X385)) != $true) & ($true = ((X378 @ X387 @ X386 @ (comp @ X388 @ X385))))) | ? [X391 : subst,X389 : term,X390 : subst,X392 : subst] : (($true != ((X378 @ X391 @ X389 @ (comp @ X392 @ X390)))) & ($true = ((X378 @ (comp @ X391 @ X392) @ (sub @ X389 @ X392) @ X390)))))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)) | ? [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 != X479) & (((ap @ X479 @ X477)) = ((ap @ X478 @ X480)))) | ? [X476 : term] : (((sub @ X476 @ id)) != X476))) & ((hoasinduction_lem2v2 = $true) <=> ! [X169 : term,X171 : (subst > term > subst > $o),X170 : (term > $o),X172 : term] : ((((X170 @ X172)) != $true) | ($true != ((X170 @ X169))) | ? [X175 : subst,X176 : term,X177 : subst,X174 : subst] : ((((X171 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) != $true) & (((X171 @ X175 @ X176 @ (comp @ X174 @ X177))) = $true)) | ? [X183 : term,X182 : term] : ((((X171 @ id @ (ap @ (sub @ X182 @ id) @ X183) @ id)) != $true) & ($true = ((X171 @ id @ X183 @ id))) & ($true = ((X171 @ id @ X182 @ id)))) | (((X170 @ (ap @ X172 @ X169))) = $true) | ? [X173 : term] : (((X170 @ X173)) != ((X171 @ id @ X173 @ id))) | ? [X180 : term,X179 : subst,X178 : subst,X181 : subst] : ((((X171 @ X181 @ X180 @ (comp @ X179 @ X178))) != $true) & ($true = ((X171 @ (comp @ X181 @ X179) @ (sub @ X180 @ X179) @ X178)))))) & (pushprop_lem1_gthm = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & (! [X365 : term,X366 : (subst > term > subst > $o)] : (? [X367 : (subst > term > term)] : (! [X368 : term] : (($true != ((X366 @ id @ X368 @ id))) | (((X366 @ id @ (X367 @ id @ X368) @ id)) = $true)) & ($true != ((X366 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X370 : subst,X371 : subst,X369 : term] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371)))) | (((X366 @ id @ (lam @ (sub @ X365 @ (push @ one @ sh))) @ id)) = $true) | ? [X372 : term] : (($true != ((X366 @ id @ (sub @ X365 @ (push @ X372 @ id)) @ id))) & (((X366 @ id @ X372 @ id)) = $true))) <=> (hoasinduction_lem3aa = $true)) & (lamnotvar = $true) & (! [X529 : term] : ? [X530 : (subst > term > term)] : ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (? [X20 : term] : (((X18 @ X20)) != ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true = ((X18 @ one))) | ($true != ((X16 @ X19))))) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X508 : (subst > term > subst > $o),X507 : term] : (! [X514 : term] : ((((X508 @ id @ (sub @ X507 @ (push @ X514 @ id)) @ id)) = $true) | ($true != ((X508 @ id @ X514 @ id)))) & ! [X509 : (subst > term > term)] : (? [X513 : subst,X512 : term,X511 : subst] : (((sub @ (X509 @ X513 @ X512) @ X511)) != ((X509 @ (comp @ X513 @ X511) @ (sub @ X512 @ X511)))) | (((X508 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true) | ? [X510 : term] : (($true = ((X508 @ id @ X510 @ id))) & ($true != ((X508 @ id @ (X509 @ id @ X510) @ id))))) & ($true != ((X508 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id)))) | ? [X506 : term] : (((sub @ X506 @ id)) != X506) | ! [X516 : (subst > term > subst > $o),X515 : term] : (($true = ((X516 @ id @ (lam @ X515) @ id))) | ? [X518 : (subst > term > term)] : (! [X519 : term] : (($true != ((X516 @ id @ X519 @ id))) | ($true = ((X516 @ id @ (X518 @ id @ X519) @ id)))) & ! [X520 : subst,X521 : subst,X522 : term] : (((sub @ (X518 @ X521 @ X522) @ X520)) = ((X518 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520)))) & ($true != ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id)))) | ? [X517 : term] : (($true = ((X516 @ id @ X517 @ id))) & (((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)) != $true))))) & ((induction = $true) <=> ! [X523 : term,X524 : (term > $o)] : (? [X526 : term] : (($true != ((X524 @ X526))) & (((var @ X526)) = $true)) | ? [X525 : term] : ((((X524 @ (lam @ X525))) != $true) & ($true = ((X524 @ X525)))) | ? [X527 : term,X528 : term] : (($true != ((X524 @ (ap @ X528 @ X527)))) & ($true = ((X524 @ X527))) & (((X524 @ X528)) = $true)) | (((X524 @ X523)) = $true))) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) <=> (axshiftcons = $true)) & (hoaslaminj_gthm = $true) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) <=> (laminj = $true)) & ((hoasinduction_lthm_3 = $true) <=> (? [X134 : (term > $o),X133 : term] : (! [X137 : term,X136 : term] : (($true != ((X134 @ X137))) | (((X134 @ X136)) != $true) | (((X134 @ (ap @ X137 @ X136))) = $true)) & ! [X135 : term] : ((((var @ X135)) != $true) | (((X134 @ X135)) = $true)) & (((X134 @ X133)) != $true) & ! [X138 : term] : (? [X139 : term] : ((((X134 @ (sub @ X138 @ (push @ X139 @ id)))) != $true) & (((X134 @ X139)) = $true)) | ($true = ((X134 @ (lam @ X138)))))) | ? [X130 : (subst > term > subst > $o)] : ! [X131 : (term > $o)] : ? [X132 : term] : (((X130 @ id @ X132 @ id)) != ((X131 @ X132))) | ? [X142 : (subst > term > subst > $o),X143 : (term > $o),X141 : term] : (! [X149 : term] : (($true = ((X143 @ (sub @ X141 @ (push @ X149 @ id))))) | (((X143 @ X149)) != $true)) & ! [X144 : (subst > term > term)] : (? [X148 : term] : (($true != ((X142 @ id @ (X144 @ id @ X148) @ id))) & ($true = ((X142 @ id @ X148 @ id)))) | (((X142 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ? [X145 : subst,X146 : subst,X147 : term] : (((X144 @ (comp @ X145 @ X146) @ (sub @ X147 @ X146))) != ((sub @ (X144 @ X145 @ X147) @ X146)))) & ($true != ((X143 @ (lam @ X141)))) & ! [X150 : term] : (((X143 @ X150)) = ((X142 @ id @ X150 @ id)))) | ! [X151 : (subst > term > subst > $o),X152 : term] : (? [X153 : subst,X155 : subst,X156 : term,X154 : subst] : (($true != ((X151 @ X153 @ X156 @ (comp @ X155 @ X154)))) & (((X151 @ (comp @ X153 @ X155) @ (sub @ X156 @ X155) @ X154)) = $true)) | ? [X160 : subst,X157 : subst,X158 : term,X159 : subst] : ((((X151 @ X157 @ X158 @ (comp @ X159 @ X160))) = $true) & ($true != ((X151 @ (comp @ X157 @ X159) @ (sub @ X158 @ X159) @ X160)))) | ? [X161 : term] : ((((var @ (sub @ X161 @ id))) = $true) & (((X151 @ id @ X161 @ id)) != $true)) | (((X151 @ id @ X152 @ id)) = $true) | ? [X167 : term,X168 : term] : ((((X151 @ id @ X168 @ id)) = $true) & (((X151 @ id @ (ap @ (sub @ X168 @ id) @ X167) @ id)) != $true) & ($true = ((X151 @ id @ X167 @ id)))) | ? [X162 : (subst > term > term)] : (($true != ((X151 @ id @ (lam @ (X162 @ sh @ one)) @ id))) & ! [X163 : term] : (($true = ((X151 @ id @ (X162 @ id @ X163) @ id))) | (((X151 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X166 : subst,X165 : term] : (((sub @ (X162 @ X166 @ X165) @ X164)) = ((X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))))) | ? [X140 : term] : (((sub @ X140 @ id)) != X140))) & (ulamvar1 != $true) & (! [X288 : term,X289 : (term > $o),X287 : subst] : (? [X290 : term] : ((((X289 @ (lam @ X290))) != $true) & ! [X291 : term] : ((((X289 @ (sub @ X290 @ (push @ X291 @ id)))) = $true) | ($true != ((X289 @ X291))))) | ($true = ((X289 @ (sub @ X288 @ X287)))) | ? [X292 : term] : (($true != ((X289 @ (sub @ X292 @ X287)))) & (((var @ X292)) = $true)) | ? [X294 : term,X293 : term] : ((((X289 @ (ap @ X293 @ X294))) != $true) & ($true = ((X289 @ X294))) & (((X289 @ X293)) = $true))) <=> (induction2lem = $true)) & ((induction2 = $true) <=> ! [X22 : term,X21 : (term > $o)] : (($true = ((X21 @ X22))) | ? [X27 : term] : ((((var @ X27)) = $true) & (((X21 @ X27)) != $true)) | ? [X25 : term] : (($true != ((X21 @ (lam @ X25)))) & ! [X26 : term] : (($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id))))) | ($true != ((X21 @ X26))))) | ? [X23 : term,X24 : term] : ((((X21 @ (ap @ X23 @ X24))) != $true) & ($true = ((X21 @ X24))) & (((X21 @ X23)) = $true)))) & (hoasinduction_lem1 = $true) & ((? [X214 : term] : (((sub @ X214 @ id)) != X214) | ! [X217 : (term > $o),X215 : (subst > term > subst > $o),X216 : term] : (? [X218 : (subst > term > term)] : (! [X220 : subst,X222 : term,X221 : subst] : (((sub @ (X218 @ X220 @ X222) @ X221)) = ((X218 @ (comp @ X220 @ X221) @ (sub @ X222 @ X221)))) & ! [X219 : term] : ((((X215 @ id @ X219 @ id)) != $true) | (((X215 @ id @ (X218 @ id @ X219) @ id)) = $true)) & ($true != ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id)))) | ($true = ((X217 @ (lam @ X216)))) | ? [X232 : term] : (($true != ((X217 @ (sub @ X216 @ (push @ X232 @ id))))) & ($true = ((X217 @ X232)))) | ? [X228 : subst,X229 : subst,X231 : subst,X230 : term] : ((((X215 @ (comp @ X228 @ X229) @ (sub @ X230 @ X229) @ X231)) = $true) & ($true != ((X215 @ X228 @ X230 @ (comp @ X229 @ X231))))) | ? [X224 : subst,X227 : subst,X226 : term,X225 : subst] : ((((X215 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true) & (((X215 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) != $true)) | ? [X223 : term] : (((X217 @ X223)) != ((X215 @ id @ X223 @ id))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & ((! [X118 : (term > $o),X116 : term,X117 : (subst > term > subst > $o)] : (? [X119 : term] : (($true = ((X118 @ X119))) & (((X118 @ (sub @ X116 @ (push @ X119 @ id)))) != $true)) | ? [X120 : term] : (((X117 @ id @ X120 @ id)) != ((X118 @ X120))) | ($true = ((X118 @ (lam @ X116)))) | ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X117 @ id @ (X121 @ id @ X125) @ id))) | (((X117 @ id @ X125 @ id)) != $true)) & ! [X122 : subst,X124 : term,X123 : subst] : (((X121 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122))) = ((sub @ (X121 @ X123 @ X124) @ X122))) & (((X117 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true))) | ? [X115 : term] : (((sub @ X115 @ id)) != X115) | ? [X111 : term] : ! [X112 : (subst > term > term)] : ? [X114 : term,X113 : subst] : (((X112 @ X113 @ X114)) != ((sub @ X111 @ (push @ X114 @ X113))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) <=> (apinj1 = $true)) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (? [X329 : term] : (((sub @ X329 @ id)) != X329) | ? [X331 : term,X330 : (subst > term > subst > $o)] : (($true != ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id))) & ! [X332 : (subst > term > term)] : (($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ? [X333 : term] : (($true != ((X330 @ id @ (X332 @ id @ X333) @ id))) & (((X330 @ id @ X333 @ id)) = $true)) | ? [X334 : subst,X335 : term,X336 : subst] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) != ((sub @ (X332 @ X336 @ X335) @ X334)))) & ! [X337 : term] : (($true = ((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))) | (((X330 @ id @ X337 @ id)) != $true))) | ! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X351 : subst,X352 : term,X353 : subst,X350 : subst] : (($true != ((X339 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350) @ X353))) & (((X339 @ X351 @ X352 @ (comp @ X350 @ X353))) = $true)) | ? [X341 : subst,X343 : term,X344 : subst,X342 : subst] : (($true != ((X339 @ X344 @ X343 @ (comp @ X341 @ X342)))) & (((X339 @ (comp @ X344 @ X341) @ (sub @ X343 @ X341) @ X342)) = $true)) | ($true = ((X339 @ id @ (lam @ X338) @ id))) | ? [X345 : (subst > term > term)] : (! [X347 : subst,X348 : subst,X349 : term] : (((X345 @ (comp @ X347 @ X348) @ (sub @ X349 @ X348))) = ((sub @ (X345 @ X347 @ X349) @ X348))) & ! [X346 : term] : ((((X339 @ id @ (X345 @ id @ X346) @ id)) = $true) | ($true != ((X339 @ id @ X346 @ id)))) & (((X339 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true)) | ? [X340 : term] : (($true = ((X339 @ id @ X340 @ id))) & (((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)) != $true))))) & (hoasapnotvar = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X107 : term] : ? [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) = ((X108 @ sh @ one)))) & ((hoaslamnotap = $true) <=> ! [X462 : term,X463 : term,X461 : (subst > term > term)] : (? [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) != ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462))))) & (pushprop = $true) & ((hoasinduction_lem0 = $true) <=> ! [X503 : (subst > term > subst > $o)] : ? [X504 : (term > $o)] : ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505)))) & (((d2subst @ d_id)) = id) & ! [X110 : d_term,X109 : d_term] : ((X109 = X110) | (((d2term @ X110)) != ((d2term @ X109)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 inference(flattening,[],[f11])).
% 13.65/2.32 thf(f13,definition,(
% 13.65/2.32 ! [X339 : (subst > term > subst > $o)] : ((((sP0 @ X339)) = $true) <=> ? [X345 : (subst > term > term)] : (! [X347 : subst,X348 : subst,X349 : term] : (((X345 @ (comp @ X347 @ X348) @ (sub @ X349 @ X348))) = ((sub @ (X345 @ X347 @ X349) @ X348))) & ! [X346 : term] : ((((X339 @ id @ (X345 @ id @ X346) @ id)) = $true) | ($true != ((X339 @ id @ X346 @ id)))) & (((X339 @ id @ (lam @ (X345 @ sh @ one)) @ id)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f14,definition,(
% 13.65/2.32 ($true = sP1) <=> ? [X331 : term,X330 : (subst > term > subst > $o)] : (($true != ((X330 @ id @ (lam @ (sub @ X331 @ (push @ one @ sh))) @ id))) & ! [X332 : (subst > term > term)] : (($true = ((X330 @ id @ (lam @ (X332 @ sh @ one)) @ id))) | ? [X333 : term] : (($true != ((X330 @ id @ (X332 @ id @ X333) @ id))) & (((X330 @ id @ X333 @ id)) = $true)) | ? [X334 : subst,X335 : term,X336 : subst] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) != ((sub @ (X332 @ X336 @ X335) @ X334)))) & ! [X337 : term] : (($true = ((X330 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))) | (((X330 @ id @ X337 @ id)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f15,definition,(
% 13.65/2.32 ($true = sP2) <=> (? [X329 : term] : (((sub @ X329 @ id)) != X329) | ($true = sP1) | ! [X338 : term,X339 : (subst > term > subst > $o)] : (? [X351 : subst,X352 : term,X353 : subst,X350 : subst] : (($true != ((X339 @ (comp @ X351 @ X350) @ (sub @ X352 @ X350) @ X353))) & (((X339 @ X351 @ X352 @ (comp @ X350 @ X353))) = $true)) | ? [X341 : subst,X343 : term,X344 : subst,X342 : subst] : (($true != ((X339 @ X344 @ X343 @ (comp @ X341 @ X342)))) & (((X339 @ (comp @ X344 @ X341) @ (sub @ X343 @ X341) @ X342)) = $true)) | ($true = ((X339 @ id @ (lam @ X338) @ id))) | (((sP0 @ X339)) = $true) | ? [X340 : term] : (($true = ((X339 @ id @ X340 @ id))) & (((X339 @ id @ (sub @ X338 @ (push @ X340 @ id)) @ id)) != $true))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f16,definition,(
% 13.65/2.32 (sP3 = $true) <=> (! [X118 : (term > $o),X116 : term,X117 : (subst > term > subst > $o)] : (? [X119 : term] : (($true = ((X118 @ X119))) & (((X118 @ (sub @ X116 @ (push @ X119 @ id)))) != $true)) | ? [X120 : term] : (((X117 @ id @ X120 @ id)) != ((X118 @ X120))) | ($true = ((X118 @ (lam @ X116)))) | ? [X121 : (subst > term > term)] : (! [X125 : term] : (($true = ((X117 @ id @ (X121 @ id @ X125) @ id))) | (((X117 @ id @ X125 @ id)) != $true)) & ! [X122 : subst,X124 : term,X123 : subst] : (((X121 @ (comp @ X123 @ X122) @ (sub @ X124 @ X122))) = ((sub @ (X121 @ X123 @ X124) @ X122))) & (((X117 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true))) | ? [X115 : term] : (((sub @ X115 @ id)) != X115) | ? [X111 : term] : ! [X112 : (subst > term > term)] : ? [X114 : term,X113 : subst] : (((X112 @ X113 @ X114)) != ((sub @ X111 @ (push @ X114 @ X113)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f17,definition,(
% 13.65/2.32 ! [X215 : (subst > term > subst > $o)] : (($true = ((sP4 @ X215))) <=> ? [X218 : (subst > term > term)] : (! [X220 : subst,X222 : term,X221 : subst] : (((sub @ (X218 @ X220 @ X222) @ X221)) = ((X218 @ (comp @ X220 @ X221) @ (sub @ X222 @ X221)))) & ! [X219 : term] : ((((X215 @ id @ X219 @ id)) != $true) | (((X215 @ id @ (X218 @ id @ X219) @ id)) = $true)) & ($true != ((X215 @ id @ (lam @ (X218 @ sh @ one)) @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f18,definition,(
% 13.65/2.32 (sP5 = $true) <=> (? [X214 : term] : (((sub @ X214 @ id)) != X214) | ! [X217 : (term > $o),X215 : (subst > term > subst > $o),X216 : term] : (($true = ((sP4 @ X215))) | ($true = ((X217 @ (lam @ X216)))) | ? [X232 : term] : (($true != ((X217 @ (sub @ X216 @ (push @ X232 @ id))))) & ($true = ((X217 @ X232)))) | ? [X228 : subst,X229 : subst,X231 : subst,X230 : term] : ((((X215 @ (comp @ X228 @ X229) @ (sub @ X230 @ X229) @ X231)) = $true) & ($true != ((X215 @ X228 @ X230 @ (comp @ X229 @ X231))))) | ? [X224 : subst,X227 : subst,X226 : term,X225 : subst] : ((((X215 @ X225 @ X226 @ (comp @ X227 @ X224))) = $true) & (((X215 @ (comp @ X225 @ X227) @ (sub @ X226 @ X227) @ X224)) != $true)) | ? [X223 : term] : (((X217 @ X223)) != ((X215 @ id @ X223 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f19,definition,(
% 13.65/2.32 ! [X21 : (term > $o)] : ((((sP6 @ X21)) = $true) <=> ? [X23 : term,X24 : term] : ((((X21 @ (ap @ X23 @ X24))) != $true) & ($true = ((X21 @ X24))) & (((X21 @ X23)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f20,definition,(
% 13.65/2.32 (sP7 = $true) <=> ! [X22 : term,X21 : (term > $o)] : (($true = ((X21 @ X22))) | ? [X27 : term] : ((((var @ X27)) = $true) & (((X21 @ X27)) != $true)) | ? [X25 : term] : (($true != ((X21 @ (lam @ X25)))) & ! [X26 : term] : (($true = ((X21 @ (sub @ X25 @ (push @ X26 @ id))))) | ($true != ((X21 @ X26))))) | (((sP6 @ X21)) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f21,definition,(
% 13.65/2.32 ! [X289 : (term > $o)] : (($true = ((sP8 @ X289))) <=> ? [X294 : term,X293 : term] : ((((X289 @ (ap @ X293 @ X294))) != $true) & ($true = ((X289 @ X294))) & (((X289 @ X293)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f22,definition,(
% 13.65/2.32 (sP9 = $true) <=> ! [X288 : term,X289 : (term > $o),X287 : subst] : (? [X290 : term] : ((((X289 @ (lam @ X290))) != $true) & ! [X291 : term] : ((((X289 @ (sub @ X290 @ (push @ X291 @ id)))) = $true) | ($true != ((X289 @ X291))))) | ($true = ((X289 @ (sub @ X288 @ X287)))) | ? [X292 : term] : (($true != ((X289 @ (sub @ X292 @ X287)))) & (((var @ X292)) = $true)) | ($true = ((sP8 @ X289))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f23,definition,(
% 13.65/2.32 ! [X151 : (subst > term > subst > $o)] : ((((sP10 @ X151)) = $true) <=> ? [X162 : (subst > term > term)] : (($true != ((X151 @ id @ (lam @ (X162 @ sh @ one)) @ id))) & ! [X163 : term] : (($true = ((X151 @ id @ (X162 @ id @ X163) @ id))) | (((X151 @ id @ X163 @ id)) != $true)) & ! [X164 : subst,X166 : subst,X165 : term] : (((sub @ (X162 @ X166 @ X165) @ X164)) = ((X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f24,definition,(
% 13.65/2.32 ! [X151 : (subst > term > subst > $o)] : ((((sP11 @ X151)) = $true) <=> ? [X167 : term,X168 : term] : ((((X151 @ id @ X168 @ id)) = $true) & (((X151 @ id @ (ap @ (sub @ X168 @ id) @ X167) @ id)) != $true) & ($true = ((X151 @ id @ X167 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f25,definition,(
% 13.65/2.32 ! [X134 : (term > $o)] : (($true = ((sP12 @ X134))) <=> ! [X137 : term,X136 : term] : (($true != ((X134 @ X137))) | (((X134 @ X136)) != $true) | (((X134 @ (ap @ X137 @ X136))) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f26,definition,(
% 13.65/2.32 (sP13 = $true) <=> ! [X151 : (subst > term > subst > $o),X152 : term] : (? [X153 : subst,X155 : subst,X156 : term,X154 : subst] : (($true != ((X151 @ X153 @ X156 @ (comp @ X155 @ X154)))) & (((X151 @ (comp @ X153 @ X155) @ (sub @ X156 @ X155) @ X154)) = $true)) | ? [X160 : subst,X157 : subst,X158 : term,X159 : subst] : ((((X151 @ X157 @ X158 @ (comp @ X159 @ X160))) = $true) & ($true != ((X151 @ (comp @ X157 @ X159) @ (sub @ X158 @ X159) @ X160)))) | ? [X161 : term] : ((((var @ (sub @ X161 @ id))) = $true) & (((X151 @ id @ X161 @ id)) != $true)) | (((X151 @ id @ X152 @ id)) = $true) | (((sP11 @ X151)) = $true) | (((sP10 @ X151)) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f27,definition,(
% 13.65/2.32 (sP14 = $true) <=> ? [X142 : (subst > term > subst > $o),X143 : (term > $o),X141 : term] : (! [X149 : term] : (($true = ((X143 @ (sub @ X141 @ (push @ X149 @ id))))) | (((X143 @ X149)) != $true)) & ! [X144 : (subst > term > term)] : (? [X148 : term] : (($true != ((X142 @ id @ (X144 @ id @ X148) @ id))) & ($true = ((X142 @ id @ X148 @ id)))) | (((X142 @ id @ (lam @ (X144 @ sh @ one)) @ id)) = $true) | ? [X145 : subst,X146 : subst,X147 : term] : (((X144 @ (comp @ X145 @ X146) @ (sub @ X147 @ X146))) != ((sub @ (X144 @ X145 @ X147) @ X146)))) & ($true != ((X143 @ (lam @ X141)))) & ! [X150 : term] : (((X143 @ X150)) = ((X142 @ id @ X150 @ id))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f28,definition,(
% 13.65/2.32 (sP15 = $true) <=> (? [X134 : (term > $o),X133 : term] : (($true = ((sP12 @ X134))) & ! [X135 : term] : ((((var @ X135)) != $true) | (((X134 @ X135)) = $true)) & (((X134 @ X133)) != $true) & ! [X138 : term] : (? [X139 : term] : ((((X134 @ (sub @ X138 @ (push @ X139 @ id)))) != $true) & (((X134 @ X139)) = $true)) | ($true = ((X134 @ (lam @ X138)))))) | ? [X130 : (subst > term > subst > $o)] : ! [X131 : (term > $o)] : ? [X132 : term] : (((X130 @ id @ X132 @ id)) != ((X131 @ X132))) | (sP14 = $true) | (sP13 = $true) | ? [X140 : term] : (((sub @ X140 @ id)) != X140))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f29,definition,(
% 13.65/2.32 ! [X524 : (term > $o)] : ((((sP16 @ X524)) = $true) <=> ? [X527 : term,X528 : term] : (($true != ((X524 @ (ap @ X528 @ X527)))) & ($true = ((X524 @ X527))) & (((X524 @ X528)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f30,definition,(
% 13.65/2.32 ($true = sP17) <=> ? [X508 : (subst > term > subst > $o),X507 : term] : (! [X514 : term] : ((((X508 @ id @ (sub @ X507 @ (push @ X514 @ id)) @ id)) = $true) | ($true != ((X508 @ id @ X514 @ id)))) & ! [X509 : (subst > term > term)] : (? [X513 : subst,X512 : term,X511 : subst] : (((sub @ (X509 @ X513 @ X512) @ X511)) != ((X509 @ (comp @ X513 @ X511) @ (sub @ X512 @ X511)))) | (((X508 @ id @ (lam @ (X509 @ sh @ one)) @ id)) = $true) | ? [X510 : term] : (($true = ((X508 @ id @ X510 @ id))) & ($true != ((X508 @ id @ (X509 @ id @ X510) @ id))))) & ($true != ((X508 @ id @ (lam @ (sub @ X507 @ (push @ one @ sh))) @ id))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f31,definition,(
% 13.65/2.32 (sP18 = $true) <=> (($true = sP17) | ? [X506 : term] : (((sub @ X506 @ id)) != X506) | ! [X516 : (subst > term > subst > $o),X515 : term] : (($true = ((X516 @ id @ (lam @ X515) @ id))) | ? [X518 : (subst > term > term)] : (! [X519 : term] : (($true != ((X516 @ id @ X519 @ id))) | ($true = ((X516 @ id @ (X518 @ id @ X519) @ id)))) & ! [X520 : subst,X521 : subst,X522 : term] : (((sub @ (X518 @ X521 @ X522) @ X520)) = ((X518 @ (comp @ X521 @ X520) @ (sub @ X522 @ X520)))) & ($true != ((X516 @ id @ (lam @ (X518 @ sh @ one)) @ id)))) | ? [X517 : term] : (($true = ((X516 @ id @ X517 @ id))) & (((X516 @ id @ (sub @ X515 @ (push @ X517 @ id)) @ id)) != $true))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f32,definition,(
% 13.65/2.32 (sP19 = $true) <=> ! [X365 : term,X366 : (subst > term > subst > $o)] : (? [X367 : (subst > term > term)] : (! [X368 : term] : (($true != ((X366 @ id @ X368 @ id))) | (((X366 @ id @ (X367 @ id @ X368) @ id)) = $true)) & ($true != ((X366 @ id @ (lam @ (X367 @ sh @ one)) @ id))) & ! [X370 : subst,X371 : subst,X369 : term] : (((X367 @ (comp @ X370 @ X371) @ (sub @ X369 @ X371))) = ((sub @ (X367 @ X370 @ X369) @ X371)))) | (((X366 @ id @ (lam @ (sub @ X365 @ (push @ one @ sh))) @ id)) = $true) | ? [X372 : term] : (($true != ((X366 @ id @ (sub @ X365 @ (push @ X372 @ id)) @ id))) & (((X366 @ id @ X372 @ id)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f33,definition,(
% 13.65/2.32 ! [X171 : (subst > term > subst > $o)] : ((((sP20 @ X171)) = $true) <=> ? [X183 : term,X182 : term] : ((((X171 @ id @ (ap @ (sub @ X182 @ id) @ X183) @ id)) != $true) & ($true = ((X171 @ id @ X183 @ id))) & ($true = ((X171 @ id @ X182 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f34,definition,(
% 13.65/2.32 (sP21 = $true) <=> ! [X169 : term,X171 : (subst > term > subst > $o),X170 : (term > $o),X172 : term] : ((((X170 @ X172)) != $true) | ($true != ((X170 @ X169))) | ? [X175 : subst,X176 : term,X177 : subst,X174 : subst] : ((((X171 @ (comp @ X175 @ X174) @ (sub @ X176 @ X174) @ X177)) != $true) & (((X171 @ X175 @ X176 @ (comp @ X174 @ X177))) = $true)) | (((sP20 @ X171)) = $true) | (((X170 @ (ap @ X172 @ X169))) = $true) | ? [X173 : term] : (((X170 @ X173)) != ((X171 @ id @ X173 @ id))) | ? [X180 : term,X179 : subst,X178 : subst,X181 : subst] : ((((X171 @ X181 @ X180 @ (comp @ X179 @ X178))) != $true) & ($true = ((X171 @ (comp @ X181 @ X179) @ (sub @ X180 @ X179) @ X178)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f35,definition,(
% 13.65/2.32 ! [X378 : (subst > term > subst > $o)] : (($true = ((sP22 @ X378))) <=> ? [X380 : (subst > term > term)] : (! [X381 : term] : ((((X378 @ id @ X381 @ id)) != $true) | ($true = ((X378 @ id @ (X380 @ id @ X381) @ id)))) & ! [X384 : subst,X383 : subst,X382 : term] : (((sub @ (X380 @ X383 @ X382) @ X384)) = ((X380 @ (comp @ X383 @ X384) @ (sub @ X382 @ X384)))) & (((X378 @ id @ (lam @ (X380 @ sh @ one)) @ id)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f36,definition,(
% 13.65/2.32 ($true = sP23) <=> ! [X378 : (subst > term > subst > $o),X377 : term] : (? [X379 : term] : ((((X378 @ id @ (sub @ X377 @ (push @ X379 @ id)) @ id)) != $true) & ($true = ((X378 @ id @ X379 @ id)))) | ($true = ((sP22 @ X378))) | (((X378 @ id @ (lam @ X377) @ id)) = $true) | ? [X386 : term,X385 : subst,X388 : subst,X387 : subst] : ((((X378 @ (comp @ X387 @ X388) @ (sub @ X386 @ X388) @ X385)) != $true) & ($true = ((X378 @ X387 @ X386 @ (comp @ X388 @ X385))))) | ? [X391 : subst,X389 : term,X390 : subst,X392 : subst] : (($true != ((X378 @ X391 @ X389 @ (comp @ X392 @ X390)))) & ($true = ((X378 @ (comp @ X391 @ X392) @ (sub @ X389 @ X392) @ X390)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f37,definition,(
% 13.65/2.32 ($true = sP24) <=> (? [X299 : term,X300 : term] : ((((lam @ X299)) = ((lam @ X300))) & (X299 != X300)) | ! [X302 : (subst > term > term),X303 : subst,X304 : (subst > term > term),X301 : term] : ((((X302 @ X303 @ X301)) = ((X304 @ X303 @ X301))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ? [X309 : term,X308 : subst,X310 : subst] : (((X304 @ (comp @ X308 @ X310) @ (sub @ X309 @ X310))) != ((sub @ (X304 @ X308 @ X309) @ X310))) | ? [X307 : term,X305 : subst,X306 : subst] : (((X302 @ (comp @ X306 @ X305) @ (sub @ X307 @ X305))) != ((sub @ (X302 @ X306 @ X307) @ X305)))) | ? [X298 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X298))) != X298) | ? [X295 : term,X296 : subst] : (((sub @ one @ (push @ X295 @ X296))) != X295))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f38,definition,(
% 13.65/2.32 ! [X28 : (subst > term > subst > $o)] : ((((sP25 @ X28)) = $true) <=> ? [X41 : term,X40 : term] : ((((X28 @ id @ X41 @ id)) = $true) & (((X28 @ id @ (ap @ (sub @ X40 @ id) @ X41) @ id)) != $true) & (((X28 @ id @ X40 @ id)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f39,definition,(
% 13.65/2.32 ! [X28 : (subst > term > subst > $o)] : ((((sP26 @ X28)) = $true) <=> ? [X30 : (subst > term > term)] : (! [X34 : term] : (($true != ((X28 @ id @ X34 @ id))) | (((X28 @ id @ (X30 @ id @ X34) @ id)) = $true)) & ($true != ((X28 @ id @ (lam @ (X30 @ sh @ one)) @ id))) & ! [X31 : term,X32 : subst,X33 : subst] : (((X30 @ (comp @ X33 @ X32) @ (sub @ X31 @ X32))) = ((sub @ (X30 @ X33 @ X31) @ X32)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f40,definition,(
% 13.65/2.32 ($true = sP27) <=> ! [X29 : term,X28 : (subst > term > subst > $o)] : (? [X35 : term] : (($true = ((var @ (sub @ X35 @ id)))) & (((X28 @ id @ X35 @ id)) != $true)) | (((sP26 @ X28)) = $true) | ? [X36 : term,X39 : subst,X37 : subst,X38 : subst] : (($true = ((X28 @ (comp @ X38 @ X39) @ (sub @ X36 @ X39) @ X37))) & (((X28 @ X38 @ X36 @ (comp @ X39 @ X37))) != $true)) | (((X28 @ id @ X29 @ id)) = $true) | (((sP25 @ X28)) = $true) | ? [X42 : subst,X43 : subst,X45 : subst,X44 : term] : ((((X28 @ X43 @ X44 @ (comp @ X45 @ X42))) = $true) & (((X28 @ (comp @ X43 @ X45) @ (sub @ X44 @ X45) @ X42)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f41,definition,(
% 13.65/2.32 ! [X187 : (term > $o)] : (($true = ((sP28 @ X187))) <=> ! [X192 : term,X193 : term] : ((((X187 @ X193)) != $true) | ($true != ((X187 @ X192))) | (((X187 @ (ap @ X192 @ X193))) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f42,definition,(
% 13.65/2.32 ! [X205 : (subst > term > subst > $o)] : ((((sP29 @ X205)) = $true) <=> ? [X207 : (subst > term > term)] : (! [X211 : term] : ((((X205 @ id @ (X207 @ id @ X211) @ id)) = $true) | (((X205 @ id @ X211 @ id)) != $true)) & ! [X210 : subst,X208 : subst,X209 : term] : (((X207 @ (comp @ X210 @ X208) @ (sub @ X209 @ X208))) = ((sub @ (X207 @ X210 @ X209) @ X208))) & ($true != ((X205 @ id @ (lam @ (X207 @ sh @ one)) @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f43,definition,(
% 13.65/2.32 (sP30 = $true) <=> ? [X197 : (subst > term > subst > $o),X196 : (term > $o),X195 : term] : ((((X196 @ (lam @ X195))) != $true) & ! [X200 : (subst > term > term)] : (? [X204 : subst,X203 : subst,X202 : term] : (((sub @ (X200 @ X204 @ X202) @ X203)) != ((X200 @ (comp @ X204 @ X203) @ (sub @ X202 @ X203)))) | (((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id)) = $true) | ? [X201 : term] : ((((X197 @ id @ X201 @ id)) = $true) & (((X197 @ id @ (X200 @ id @ X201) @ id)) != $true))) & ! [X198 : term] : (((X197 @ id @ X198 @ id)) = ((X196 @ X198))) & ! [X199 : term] : ((((X196 @ X199)) != $true) | ($true = ((X196 @ (sub @ X195 @ (push @ X199 @ id)))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f44,definition,(
% 13.65/2.32 ($true = sP31) <=> ? [X187 : (term > $o),X188 : term] : ((((X187 @ X188)) != $true) & ($true = ((sP28 @ X187))) & ! [X190 : term] : (($true = ((X187 @ (lam @ X190)))) | ? [X191 : term] : ((((X187 @ (sub @ X190 @ (push @ X191 @ id)))) != $true) & ($true = ((X187 @ X191))))) & ! [X189 : term] : (($true != ((var @ X189))) | ($true = ((X187 @ X189)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f45,definition,(
% 13.65/2.32 ($true = sP32) <=> ((sP30 = $true) | ? [X194 : term] : (((sub @ X194 @ id)) != X194) | ! [X206 : term,X205 : (subst > term > subst > $o)] : (? [X212 : term,X213 : term] : (($true = ((X205 @ id @ X212 @ id))) & ($true = ((X205 @ id @ X213 @ id))) & (((X205 @ id @ (ap @ (sub @ X213 @ id) @ X212) @ id)) != $true)) | (((sP29 @ X205)) = $true) | (((X205 @ id @ X206 @ id)) = $true)) | ? [X184 : (subst > term > subst > $o)] : ! [X185 : (term > $o)] : ? [X186 : term] : (((X184 @ id @ X186 @ id)) != ((X185 @ X186))) | ($true = sP31))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f46,definition,(
% 13.65/2.32 ! [X440 : (term > $o)] : (($true = ((sP33 @ X440))) <=> ? [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) != $true) & (((X440 @ X446)) = $true) & (((X440 @ X445)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f47,definition,(
% 13.65/2.32 ! [X435 : (term > $o)] : (($true = ((sP34 @ X435))) <=> ! [X438 : term,X439 : term] : (($true != ((X435 @ X438))) | (((X435 @ X439)) != $true) | ($true = ((X435 @ (ap @ X439 @ X438))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f48,definition,(
% 13.65/2.32 (sP35 = $true) <=> ! [X441 : term,X440 : (term > $o),X442 : subst] : (? [X443 : term] : ((((X440 @ (lam @ X443))) != $true) & ! [X444 : term] : (($true != ((X440 @ X444))) | ($true = ((X440 @ (sub @ X443 @ (push @ X444 @ id))))))) | ? [X447 : term] : (($true != ((X440 @ (sub @ X447 @ X442)))) & (((var @ X447)) = $true)) | ($true = ((sP33 @ X440))) | (((X440 @ (sub @ X441 @ X442))) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f49,definition,(
% 13.65/2.32 ($true = sP36) <=> (? [X435 : (term > $o),X434 : term] : (($true != ((X435 @ X434))) & ($true = ((sP34 @ X435))) & ! [X437 : term] : (($true = ((X435 @ (lam @ X437)))) | (((X435 @ X437)) != $true)) & ! [X436 : term] : ((((var @ X436)) != $true) | ($true = ((X435 @ X436))))) | ? [X432 : term,X431 : subst] : (((comp @ sh @ (push @ X432 @ X431))) != X431) | ? [X429 : term,X430 : subst] : (((sub @ one @ (push @ X429 @ X430))) != X429) | (sP35 = $true) | ? [X433 : subst] : (((comp @ X433 @ id)) != X433))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f50,definition,(
% 13.65/2.32 ! [X487 : (subst > term > subst > $o)] : ((((sP37 @ X487)) = $true) <=> ? [X488 : (subst > term > term)] : (! [X492 : term] : ((((X487 @ id @ X492 @ id)) != $true) | (((X487 @ id @ (X488 @ id @ X492) @ id)) = $true)) & (((X487 @ id @ (lam @ (X488 @ sh @ one)) @ id)) != $true) & ! [X490 : subst,X489 : term,X491 : subst] : (((sub @ (X488 @ X490 @ X489) @ X491)) = ((X488 @ (comp @ X490 @ X491) @ (sub @ X489 @ X491))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f51,definition,(
% 13.65/2.32 (sP38 = $true) <=> ! [X487 : (subst > term > subst > $o),X486 : (term > $o),X485 : term] : (? [X496 : subst,X495 : subst,X494 : term,X493 : subst] : (($true = ((X487 @ X493 @ X494 @ (comp @ X495 @ X496)))) & ($true != ((X487 @ (comp @ X493 @ X495) @ (sub @ X494 @ X495) @ X496)))) | ? [X497 : term] : (((X486 @ X497)) != ((X487 @ id @ X497 @ id))) | ? [X498 : term] : (($true = ((X486 @ X498))) & (((X486 @ (sub @ X485 @ (push @ X498 @ id)))) != $true)) | ($true = ((X486 @ (lam @ X485)))) | (((sP37 @ X487)) = $true) | ? [X502 : term,X499 : subst,X501 : subst,X500 : subst] : (($true != ((X487 @ X501 @ X502 @ (comp @ X500 @ X499)))) & (((X487 @ (comp @ X501 @ X500) @ (sub @ X502 @ X500) @ X499)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f52,definition,(
% 13.65/2.32 ! [X53 : (subst > term > subst > $o)] : ((((sP39 @ X53)) = $true) <=> ? [X60 : term,X59 : term] : (($true = ((X53 @ id @ X59 @ id))) & (((X53 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) != $true) & (((X53 @ id @ X60 @ id)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f53,definition,(
% 13.65/2.32 (sP40 = $true) <=> ! [X54 : term,X52 : term,X53 : (subst > term > subst > $o)] : (? [X58 : subst,X55 : term,X56 : subst,X57 : subst] : (($true != ((X53 @ X58 @ X55 @ (comp @ X57 @ X56)))) & ($true = ((X53 @ (comp @ X58 @ X57) @ (sub @ X55 @ X57) @ X56)))) | ($true = ((X53 @ id @ (ap @ X54 @ X52) @ id))) | (((sP39 @ X53)) = $true) | (((X53 @ id @ X52 @ id)) != $true) | (((X53 @ id @ X54 @ id)) != $true) | ? [X61 : subst,X64 : subst,X62 : term,X63 : subst] : ((((X53 @ (comp @ X61 @ X64) @ (sub @ X62 @ X64) @ X63)) != $true) & (((X53 @ X61 @ X62 @ (comp @ X64 @ X63))) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f54,definition,(
% 13.65/2.32 ! [X254 : (subst > term > subst > $o)] : (($true = ((sP41 @ X254))) <=> ! [X264 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X264 @ sh @ one)) @ id)) = $true) | ? [X265 : subst,X266 : subst,X267 : term] : (((sub @ (X264 @ X265 @ X267) @ X266)) != ((X264 @ (comp @ X265 @ X266) @ (sub @ X267 @ X266)))) | ? [X268 : term] : ((((X254 @ id @ X268 @ id)) = $true) & ($true != ((X254 @ id @ (X264 @ id @ X268) @ id))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f55,definition,(
% 13.65/2.32 ! [X234 : (term > $o)] : ((((sP42 @ X234)) = $true) <=> ! [X236 : term,X235 : term] : ((((X234 @ X235)) != $true) | (((X234 @ (ap @ X236 @ X235))) = $true) | (((X234 @ X236)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f56,definition,(
% 13.65/2.32 ! [X269 : (subst > term > subst > $o)] : (($true = ((sP43 @ X269))) <=> ? [X285 : term,X286 : term] : (($true = ((X269 @ id @ X285 @ id))) & ($true != ((X269 @ id @ (ap @ (sub @ X286 @ id) @ X285) @ id))) & ($true = ((X269 @ id @ X286 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f57,definition,(
% 13.65/2.32 ! [X269 : (subst > term > subst > $o)] : (($true = ((sP44 @ X269))) <=> ? [X276 : (subst > term > term)] : ((((X269 @ id @ (lam @ (X276 @ sh @ one)) @ id)) != $true) & ! [X277 : term] : (($true != ((X269 @ id @ X277 @ id))) | (((X269 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X278 : term,X279 : subst,X280 : subst] : (((X276 @ (comp @ X280 @ X279) @ (sub @ X278 @ X279))) = ((sub @ (X276 @ X280 @ X278) @ X279)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f58,definition,(
% 13.65/2.32 ! [X240 : (subst > term > subst > $o)] : (($true = ((sP45 @ X240))) <=> ! [X243 : term,X244 : term] : ((((X240 @ id @ (ap @ (sub @ X244 @ id) @ X243) @ id)) = $true) | ($true != ((X240 @ id @ X243 @ id))) | ($true != ((X240 @ id @ X244 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f59,definition,(
% 13.65/2.32 (sP46 = $true) <=> ? [X253 : term,X254 : (subst > term > subst > $o)] : ((((X254 @ id @ (lam @ X253) @ id)) != $true) & ! [X260 : subst,X262 : subst,X259 : term,X261 : subst] : ((((X254 @ X261 @ X259 @ (comp @ X260 @ X262))) = $true) | (((X254 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260) @ X262)) != $true)) & ($true = ((sP41 @ X254))) & ! [X263 : term] : ((((X254 @ id @ X263 @ id)) != $true) | (((X254 @ id @ (sub @ X253 @ (push @ X263 @ id)) @ id)) = $true)) & ! [X258 : term,X255 : subst,X257 : subst,X256 : subst] : ((((X254 @ (comp @ X257 @ X256) @ (sub @ X258 @ X256) @ X255)) = $true) | (((X254 @ X257 @ X258 @ (comp @ X256 @ X255))) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f60,definition,(
% 13.65/2.32 (sP47 = $true) <=> ! [X269 : (subst > term > subst > $o),X270 : term] : (($true = ((sP44 @ X269))) | ? [X281 : subst,X284 : term,X283 : subst,X282 : subst] : ((((X269 @ X283 @ X284 @ (comp @ X281 @ X282))) != $true) & (((X269 @ (comp @ X283 @ X281) @ (sub @ X284 @ X281) @ X282)) = $true)) | ? [X273 : subst,X272 : term,X274 : subst,X271 : subst] : ((((X269 @ (comp @ X271 @ X274) @ (sub @ X272 @ X274) @ X273)) != $true) & ($true = ((X269 @ X271 @ X272 @ (comp @ X274 @ X273))))) | ($true = ((sP43 @ X269))) | ? [X275 : term] : ((((var @ (sub @ X275 @ id))) = $true) & ($true != ((X269 @ id @ X275 @ id)))) | (((X269 @ id @ X270 @ id)) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f61,definition,(
% 13.65/2.32 (sP48 = $true) <=> ? [X234 : (term > $o),X233 : term] : ((((X234 @ X233)) != $true) & ! [X237 : term] : (? [X238 : term] : (($true != ((X234 @ (sub @ X237 @ (push @ X238 @ id))))) & ($true = ((X234 @ X238)))) | ($true = ((X234 @ (lam @ X237))))) & ! [X239 : term] : (($true = ((X234 @ X239))) | ($true != ((var @ X239)))) & (((sP42 @ X234)) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f62,definition,(
% 13.65/2.32 (sP49 = $true) <=> (? [X242 : term,X241 : term,X240 : (subst > term > subst > $o)] : ((((X240 @ id @ (ap @ X241 @ X242) @ id)) != $true) & ! [X246 : term,X247 : subst,X245 : subst,X248 : subst] : (($true != ((X240 @ X247 @ X246 @ (comp @ X245 @ X248)))) | ($true = ((X240 @ (comp @ X247 @ X245) @ (sub @ X246 @ X245) @ X248)))) & ($true = ((sP45 @ X240))) & ! [X251 : subst,X250 : term,X249 : subst,X252 : subst] : ((((X240 @ (comp @ X249 @ X251) @ (sub @ X250 @ X251) @ X252)) != $true) | ($true = ((X240 @ X249 @ X250 @ (comp @ X251 @ X252))))) & ($true = ((X240 @ id @ X241 @ id))) & (((X240 @ id @ X242 @ id)) = $true)) | (sP47 = $true) | (sP48 = $true) | (sP46 = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f63,definition,(
% 13.65/2.32 (sP50 = $true) <=> ! [X1 : term,X0 : (subst > term > subst > $o)] : (? [X3 : term,X2 : (subst > term > term)] : (! [X4 : term] : ((((X0 @ id @ X4 @ id)) != $true) | (((X0 @ id @ (X2 @ id @ X4) @ id)) = $true)) & ! [X5 : term,X7 : subst,X6 : subst] : (((sub @ X3 @ (push @ (sub @ X5 @ X7) @ (comp @ X6 @ X7)))) = ((X2 @ (comp @ X6 @ X7) @ (sub @ X5 @ X7)))) & ! [X9 : subst,X8 : term,X10 : subst] : (((sub @ (sub @ X3 @ (push @ X8 @ X10)) @ X9)) = ((sub @ (X2 @ X10 @ X8) @ X9))) & ($true != ((X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)))) | (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)) = $true) | ? [X11 : term] : (($true != ((X0 @ id @ (sub @ X1 @ (push @ X11 @ id)) @ id))) & (((X0 @ id @ X11 @ id)) = $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f64,definition,(
% 13.65/2.32 (sP51 = $true) <=> ! [X65 : (subst > term > subst > $o),X66 : term] : (? [X67 : (subst > term > term)] : (! [X68 : term] : ((((X65 @ id @ (X67 @ id @ X68) @ id)) = $true) | ($true != ((X65 @ id @ X68 @ id)))) & ($true != ((X65 @ id @ (lam @ (X67 @ sh @ one)) @ id))) & ! [X70 : subst,X71 : term,X69 : subst] : (((sub @ (X67 @ X69 @ X71) @ X70)) = ((X67 @ (comp @ X69 @ X70) @ (sub @ X71 @ X70))))) | ? [X72 : term] : (($true != ((X65 @ id @ (sub @ X66 @ (push @ X72 @ id)) @ id))) & (((X65 @ id @ X72 @ id)) = $true)) | ($true = ((X65 @ id @ (lam @ (sub @ X66 @ (push @ one @ sh))) @ id))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f65,definition,(
% 13.65/2.32 ! [X403 : (term > $o)] : (($true = ((sP52 @ X403))) <=> ? [X406 : term,X407 : term] : ((((X403 @ X407)) = $true) & ($true != ((X403 @ (ap @ X406 @ X407)))) & ($true = ((X403 @ X406)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f66,definition,(
% 13.65/2.32 ! [X394 : (term > $o)] : (($true = ((sP53 @ X394))) <=> ! [X398 : term,X397 : term] : (($true = ((X394 @ (ap @ X398 @ X397)))) | (((X394 @ X397)) != $true) | (((X394 @ X398)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f67,definition,(
% 13.65/2.32 ($true = sP54) <=> ! [X402 : term,X403 : (term > $o)] : (($true = ((sP52 @ X403))) | (((X403 @ X402)) = $true) | ? [X404 : term] : ((((X403 @ (lam @ X404))) != $true) & ! [X405 : term] : ((((X403 @ X405)) != $true) | (((X403 @ (sub @ X404 @ (push @ X405 @ id)))) = $true))) | ? [X408 : term] : (($true = ((var @ X408))) & ($true != ((X403 @ X408)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f68,definition,(
% 13.65/2.32 ($true = sP55) <=> (? [X395 : subst,X394 : (term > $o),X396 : term] : (! [X399 : term] : (? [X400 : term] : (($true != ((X394 @ (sub @ X399 @ (push @ X400 @ id))))) & ($true = ((X394 @ X400)))) | ($true = ((X394 @ (lam @ X399))))) & ! [X401 : term] : ((((var @ X401)) != $true) | (((X394 @ (sub @ X401 @ X395))) = $true)) & ($true != ((X394 @ (sub @ X396 @ X395)))) & ($true = ((sP53 @ X394)))) | ($true = sP54) | ? [X393 : term] : (((sub @ X393 @ id)) != X393))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f69,definition,(
% 13.65/2.32 ($true = sP56) <=> ! [X453 : (subst > term > subst > $o),X452 : term] : ((((X453 @ id @ (lam @ X452) @ id)) = $true) | ? [X454 : term] : (($true != ((X453 @ id @ (sub @ X452 @ (push @ X454 @ id)) @ id))) & (((X453 @ id @ X454 @ id)) = $true)) | ? [X455 : (subst > term > term)] : (! [X459 : subst,X457 : subst,X458 : term] : (((sub @ (X455 @ X457 @ X458) @ X459)) = ((X455 @ (comp @ X457 @ X459) @ (sub @ X458 @ X459)))) & ! [X456 : term] : ((((X453 @ id @ X456 @ id)) != $true) | ($true = ((X453 @ id @ (X455 @ id @ X456) @ id)))) & (((X453 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f70,definition,(
% 13.65/2.32 ! [X88 : (subst > term > subst > $o)] : (($true = ((sP57 @ X88))) <=> ? [X90 : term,X91 : term] : ((((X88 @ id @ (ap @ (sub @ X90 @ id) @ X91) @ id)) != $true) & (((X88 @ id @ X90 @ id)) = $true) & ($true = ((X88 @ id @ X91 @ id)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f71,definition,(
% 13.65/2.32 (sP58 = $true) <=> ! [X74 : (subst > term > subst > $o),X75 : term,X76 : (term > $o)] : (? [X77 : term] : (($true = ((X76 @ X77))) & ($true != ((X76 @ (sub @ X75 @ (push @ X77 @ id)))))) | ? [X79 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X79 @ sh @ one)) @ id)) != $true) & ! [X83 : term] : ((((X74 @ id @ X83 @ id)) != $true) | (((X74 @ id @ (X79 @ id @ X83) @ id)) = $true)) & ! [X81 : subst,X80 : subst,X82 : term] : (((X79 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81))) = ((sub @ (X79 @ X80 @ X82) @ X81)))) | ? [X78 : term] : (((X74 @ id @ X78 @ id)) != ((X76 @ X78))) | (((X76 @ (lam @ X75))) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 13.65/2.32 thf(f72,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X313 : d_subst] : (d_id = X313) & ((! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473)))) | ? [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 != X470) & (((ap @ X467 @ X470)) = ((ap @ X468 @ X469))))) <=> (hoasapinj2_lthm = $true)) & ((shinj = $true) <=> ! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451))) & (axvarshift = $true) & (induction2lem_gthm = $true) & ((sP58 = $true) <=> (hoasinduction_lem3v2a = $true)) & (pushprop_lthm_orig = $true) & ((? [X84 : subst] : (((comp @ id @ X84)) != X84) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85) | (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X89 : term,X88 : (subst > term > subst > $o)] : (? [X92 : (subst > term > term)] : (! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) & ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true)) & (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true) | ($true = ((sP57 @ X88))))) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) <=> (apinj2 = $true)) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3a = $true) <=> ($true = sP56)) & (substmonoid_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363))) & (! [X420 : term,X422 : subst,X421 : (term > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) <=> (pushprop_lem0_lthm = $true)) & ((induction2_lthm = $true) <=> ($true = sP55)) & ! [X460 : d_term] : (d_one = X460) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X311 : term] : ? [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) = ((X312 @ sh @ one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) <=> (pushprop_lem1 = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((sP51 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & ((! [X106 : term] : (((sub @ X106 @ id)) = X106) | ? [X105 : term] : (((sub @ X105 @ id)) != X105)) <=> (termmset_lthm = $true)) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X426 : (subst > term > subst > $o)] : ? [X427 : (term > $o)] : ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id)))) & ((sP50 = $true) <=> (hoasinduction_lem3aaa = $true)) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) <=> (axscons = $true)) & ((hoasinduction_lthm = $true) <=> (sP49 = $true)) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & ((sP40 = $true) <=> (hoasinduction_lem2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X534 : term,X535 : (term > $o),X533 : subst] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (axmap = $true) & (! [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (? [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) != ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))) | ? [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) != ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2 = $true) <=> (sP38 = $true)) & ((? [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) != X411) | ? [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) != X414) | ! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true))) <=> (pushprop_lem1_lthm = $true)) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X373 : term] : ? [X374 : (subst > term > term)] : ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376)))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) <=> (substmonoid = $true)) & (axabs = $true) & (($true = sP36) <=> (induction2lem_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP32)) & ! [X360 : d_subst,X359 : d_subst] : ((X359 = X360) | (((d2subst @ X359)) != ((d2subst @ X360)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & ((! [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) = $true) | ? [X104 : term] : (((X100 @ X104)) != ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | ($true != ((X103 @ X101)))) | ? [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) != X99)) <=> (pushprop_lem1v2_lthm = $true)) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) <=> (axvarcons = $true)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) <=> (termmset = $true)) & ((hoasinduction = $true) <=> ($true = sP27)) & ((hoaslaminj_lthm = $true) <=> ($true = sP24)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ($true = sP23)) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)) | ? [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 != X479) & (((ap @ X479 @ X477)) = ((ap @ X478 @ X480)))) | ? [X476 : term] : (((sub @ X476 @ id)) != X476))) & ((hoasinduction_lem2v2 = $true) <=> (sP21 = $true)) & (pushprop_lem1_gthm = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & ((hoasapinj1 = $true) <=> ! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15))) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((sP19 = $true) <=> (hoasinduction_lem3aa = $true)) & (lamnotvar = $true) & (! [X529 : term] : ? [X530 : (subst > term > term)] : ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) <=> (axidl = $true)) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) <=> ! [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (? [X20 : term] : (((X18 @ X20)) != ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true = ((X18 @ one))) | ($true != ((X16 @ X19))))) & ((hoasinduction_lem3a_lthm = $true) <=> (sP18 = $true)) & ((induction = $true) <=> ! [X523 : term,X524 : (term > $o)] : (? [X526 : term] : (($true != ((X524 @ X526))) & (((var @ X526)) = $true)) | ? [X525 : term] : ((((X524 @ (lam @ X525))) != $true) & ($true = ((X524 @ X525)))) | (((sP16 @ X524)) = $true) | (((X524 @ X523)) = $true))) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) <=> (axshiftcons = $true)) & (hoaslaminj_gthm = $true) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) <=> (laminj = $true)) & ((hoasinduction_lthm_3 = $true) <=> (sP15 = $true)) & (ulamvar1 != $true) & ((sP9 = $true) <=> (induction2lem = $true)) & ((induction2 = $true) <=> (sP7 = $true)) & (hoasinduction_lem1 = $true) & ((sP5 = $true) <=> (hoasinduction_lem3v2_lthm = $true)) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & ((sP3 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) <=> (axidr = $true)) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) <=> (axvarid = $true)) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) <=> (apinj1 = $true)) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP2)) & (hoasapnotvar = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X107 : term] : ? [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) = ((X108 @ sh @ one)))) & ((hoaslamnotap = $true) <=> ! [X462 : term,X463 : term,X461 : (subst > term > term)] : (? [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) != ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462))))) & (pushprop = $true) & ((hoasinduction_lem0 = $true) <=> ! [X503 : (subst > term > subst > $o)] : ? [X504 : (term > $o)] : ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505)))) & (((d2subst @ d_id)) = id) & ! [X110 : d_term,X109 : d_term] : ((X109 = X110) | (((d2term @ X110)) != ((d2term @ X109)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 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])).
% 13.65/2.32 thf(f151,plain,(
% 13.65/2.32 ! [X440 : (term > $o)] : ((($true = ((sP33 @ X440))) | ! [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) = $true) | (((X440 @ X446)) != $true) | (((X440 @ X445)) != $true))) & (? [X445 : term,X446 : term] : ((((X440 @ (ap @ X445 @ X446))) != $true) & (((X440 @ X446)) = $true) & (((X440 @ X445)) = $true)) | ($true != ((sP33 @ X440)))))),
% 13.65/2.32 inference(nnf_transformation,[],[f46])).
% 13.65/2.32 thf(f152,plain,(
% 13.65/2.32 ! [X0 : (term > $o)] : (((((sP33 @ X0)) = $true) | ! [X1 : term,X2 : term] : (($true = ((X0 @ (ap @ X1 @ X2)))) | (((X0 @ X2)) != $true) | (((X0 @ X1)) != $true))) & (? [X3 : term,X4 : term] : ((((X0 @ (ap @ X3 @ X4))) != $true) & ($true = ((X0 @ X4))) & (((X0 @ X3)) = $true)) | (((sP33 @ X0)) != $true)))),
% 13.65/2.32 inference(rectify,[],[f151])).
% 13.65/2.32 thf(f153,plain,(
% 13.65/2.32 ! [X0 : (term > $o)] : (((((sP33 @ X0)) = $true) | ! [X1 : term,X2 : term] : (($true = ((X0 @ (ap @ X1 @ X2)))) | (((X0 @ X2)) != $true) | (((X0 @ X1)) != $true))) & ((($true != ((X0 @ (ap @ (sK217 @ X0) @ (sK218 @ X0))))) & (((X0 @ (sK218 @ X0))) = $true) & (((X0 @ (sK217 @ X0))) = $true)) | (((sP33 @ X0)) != $true)))),
% 13.65/2.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10)],[f152])).
% 13.65/2.32 thf(f260,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X313 : d_subst] : (d_id = X313) & (((! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473)))) | ? [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 != X470) & (((ap @ X467 @ X470)) = ((ap @ X468 @ X469))))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 != X474) & (((ap @ (sub @ X472 @ id) @ X474)) = ((ap @ (sub @ X471 @ id) @ X473)))) & ! [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 = X470) | (((ap @ X467 @ X470)) != ((ap @ X468 @ X469))))))) & (((shinj = $true) | ? [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) = ((sub @ X451 @ sh))) & (X450 != X451))) & (! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451)) | (shinj != $true))) & (axvarshift = $true) & (induction2lem_gthm = $true) & (((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true))) & (pushprop_lthm_orig = $true) & (((? [X84 : subst] : (((comp @ id @ X84)) != X84) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85) | (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87))) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X84 : subst] : (((comp @ id @ X84)) = X84) & ! [X85 : subst] : (((comp @ X85 @ id)) = X85) & (? [X86 : subst] : (((comp @ X86 @ id)) != X86) | ? [X87 : subst] : (((comp @ id @ X87)) != X87))))) & (((hoasinduction_no_psi_cond = $true) | ? [X89 : term,X88 : (subst > term > subst > $o)] : (! [X92 : (subst > term > term)] : (? [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) != ((sub @ (X92 @ X93 @ X95) @ X94))) | ? [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) != $true) & (((X88 @ id @ X96 @ id)) = $true)) | (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) = $true)) & (((X88 @ id @ X89 @ id)) != $true) & ($true != ((sP57 @ X88))))) & (! [X89 : term,X88 : (subst > term > subst > $o)] : (? [X92 : (subst > term > term)] : (! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) & ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true)) & (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true) | ($true = ((sP57 @ X88)))) | (hoasinduction_no_psi_cond != $true))) & ((! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) = ((ap @ X49 @ X51))) & (X48 != X51)))) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & (((hoasinduction_lem3a = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3a != $true))) & (substmonoid_gthm = $true) & (((hoasapinj2 = $true) | ? [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) = ((ap @ (sub @ X362 @ id) @ X363))) & (X361 != X363))) & (! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363)) | (hoasapinj2 != $true))) & ((! [X420 : term,X422 : subst,X421 : (term > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X420 : term,X422 : subst,X421 : (term > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) != ((X423 @ X424))))) & (((induction2_lthm = $true) | ($true != sP55)) & (($true = sP55) | (induction2_lthm != $true))) & ! [X460 : d_term] : (d_one = X460) & (((hoasinduction_lem3b_lthm = $true) | ? [X311 : term] : ! [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) != ((X312 @ sh @ one)))) & (! [X311 : term] : ? [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) = ((X312 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) = $true) & ($true != ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))))) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (((sP51 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP51 != $true))) & (((! [X106 : term] : (((sub @ X106 @ id)) = X106) | ? [X105 : term] : (((sub @ X105 @ id)) != X105)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X106 : term] : (((sub @ X106 @ id)) != X106) & ! [X105 : term] : (((sub @ X105 @ id)) = X105)))) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & (((hoasinduction_lem0_lthm = $true) | ? [X426 : (subst > term > subst > $o)] : ! [X427 : (term > $o)] : ? [X428 : term] : (((X427 @ X428)) != ((X426 @ id @ X428 @ id)))) & (! [X426 : (subst > term > subst > $o)] : ? [X427 : (term > $o)] : ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id))) | (hoasinduction_lem0_lthm != $true))) & (((sP50 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP50 != $true))) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) | (axscons != $true)) & ((axscons = $true) | ? [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) != X475))) & (((hoasinduction_lthm = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction_lthm != $true))) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & (((sP40 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP40 != $true))) & (((pushprop_lem0 = $true) | ? [X534 : term,X535 : (term > $o),X533 : subst] : ! [X536 : (term > $o)] : ? [X537 : term] : (((X536 @ X537)) != ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (! [X534 : term,X535 : (term > $o),X533 : subst] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533))))) | (pushprop_lem0 != $true))) & (axmap = $true) & ((! [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (? [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) != ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))) | ? [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) != ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (! [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) = ((sub @ (X320 @ X322 @ X324) @ X323))) & (((lam @ (X321 @ sh @ one))) = ((lam @ (X320 @ sh @ one)))) & (((X320 @ X318 @ X319)) != ((X321 @ X318 @ X319))) & ! [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) = ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))))) & (((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true))) & (((? [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) != X411) | ? [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) != X414) | ! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) = X411) & ! [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) = X414) & ? [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) != $true) & (((X416 @ X418)) = $true))))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X373 : term] : ! [X374 : (subst > term > term)] : ? [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) != ((X374 @ X375 @ X376)))) & (! [X373 : term] : ? [X374 : (subst > term > term)] : ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376))) | (hoasinduction_lem3v2_f != $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & (((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X128 : subst] : (((comp @ X128 @ id)) != X128) | ? [X129 : subst] : (((comp @ id @ X129)) != X129)))) & (axabs = $true) & ((($true = sP36) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP36))) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_no_psi_cond_lthm != $true))) & ! [X360 : d_subst,X359 : d_subst] : ((X359 = X360) | (((d2subst @ X359)) != ((d2subst @ X360)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & (((! [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) = $true) | ? [X104 : term] : (((X100 @ X104)) != ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | ($true != ((X103 @ X101)))) | ? [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) != X99)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) != $true) & ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) & ($true = ((X103 @ X101)))) & ! [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) = X99)))) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) != X126))) & ((! [X328 : term] : (((sub @ X328 @ id)) = X328) | (termmset != $true)) & ((termmset = $true) | ? [X328 : term] : (((sub @ X328 @ id)) != X328))) & (((hoasinduction = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction != $true))) & (((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true))) & (pushprop_lem2v2_gthm = $true) & (((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true))) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((hoasapinj1_lthm = $true) | (? [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) = ((ap @ (sub @ X481 @ id) @ X484))) & (X481 != X483)) & ! [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 = X479) | (((ap @ X479 @ X477)) != ((ap @ X478 @ X480)))) & ! [X476 : term] : (((sub @ X476 @ id)) = X476))) & ((! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)) | ? [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 != X479) & (((ap @ X479 @ X477)) = ((ap @ X478 @ X480)))) | ? [X476 : term] : (((sub @ X476 @ id)) != X476)) | (hoasapinj1_lthm != $true))) & (((hoasinduction_lem2v2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction_lem2v2 != $true))) & (pushprop_lem1_gthm = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & (((hoasapinj1 = $true) | ? [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) = ((ap @ (sub @ X12 @ id) @ X13))) & (X12 != X15))) & (! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15)) | (hoasapinj1 != $true))) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & (((sP19 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP19 != $true))) & (lamnotvar = $true) & ((! [X529 : term] : ? [X530 : (subst > term > term)] : ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X529 : term] : ! [X530 : (subst > term > term)] : ? [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) != ((X530 @ X531 @ X532))))) & ((! [X425 : subst] : (((comp @ id @ X425)) = X425) | (axidl != $true)) & ((axidl = $true) | ? [X425 : subst] : (((comp @ id @ X425)) != X425))) & (hoasinduction_lem1v2 = $true) & (((pushprop_lem1v2 = $true) | ? [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) & ($true != ((X18 @ one))) & ($true = ((X16 @ X19))))) & (! [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (? [X20 : term] : (((X18 @ X20)) != ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true = ((X18 @ one))) | ($true != ((X16 @ X19)))) | (pushprop_lem1v2 != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3a_lthm != $true))) & (((induction = $true) | ? [X523 : term,X524 : (term > $o)] : (! [X526 : term] : (($true = ((X524 @ X526))) | (((var @ X526)) != $true)) & ! [X525 : term] : ((((X524 @ (lam @ X525))) = $true) | ($true != ((X524 @ X525)))) & (((sP16 @ X524)) != $true) & (((X524 @ X523)) != $true))) & (! [X523 : term,X524 : (term > $o)] : (? [X526 : term] : (($true != ((X524 @ X526))) & (((var @ X526)) = $true)) | ? [X525 : term] : ((((X524 @ (lam @ X525))) != $true) & ($true = ((X524 @ X525)))) | (((sP16 @ X524)) = $true) | (((X524 @ X523)) = $true)) | (induction != $true))) & ((! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) != X539))) & (hoaslaminj_gthm = $true) & ((! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) | (laminj != $true)) & ((laminj = $true) | ? [X410 : term,X409 : term] : ((((lam @ X410)) = ((lam @ X409))) & (X409 != X410)))) & (((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true))) & (ulamvar1 != $true) & (((sP9 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP9 != $true))) & (((induction2 = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2 != $true))) & (hoasinduction_lem1 = $true) & (((sP5 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP5 != $true))) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & (((sP3 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP3 != $true))) & (pushprop_lem3v2_lthm = $true) & ((! [X73 : subst] : (((comp @ X73 @ id)) = X73) | (axidr != $true)) & ((axidr = $true) | ? [X73 : subst] : (((comp @ X73 @ id)) != X73))) & ((! [X97 : term] : (((sub @ X97 @ id)) = X97) | (axvarid != $true)) & ((axvarid = $true) | ? [X97 : term] : (((sub @ X97 @ id)) != X97))) & ((! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 != X317) & (((ap @ X314 @ X316)) = ((ap @ X317 @ X315)))))) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & (((hoasinduction_lem3_lthm = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3_lthm != $true))) & (hoasapnotvar = $true) & (induction2_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X107 : term] : ! [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) != ((X108 @ sh @ one)))) & (! [X107 : term] : ? [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) = ((X108 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (((hoaslamnotap = $true) | ? [X462 : term,X463 : term,X461 : (subst > term > term)] : (! [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X461 @ X466 @ X465) @ X464))) & (((lam @ (X461 @ sh @ one))) = ((ap @ (sub @ X463 @ id) @ X462))))) & (! [X462 : term,X463 : term,X461 : (subst > term > term)] : (? [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) != ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462)))) | (hoaslamnotap != $true))) & (pushprop = $true) & (((hoasinduction_lem0 = $true) | ? [X503 : (subst > term > subst > $o)] : ! [X504 : (term > $o)] : ? [X505 : term] : (((X503 @ id @ X505 @ id)) != ((X504 @ X505)))) & (! [X503 : (subst > term > subst > $o)] : ? [X504 : (term > $o)] : ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505))) | (hoasinduction_lem0 != $true))) & (((d2subst @ d_id)) = id) & ! [X110 : d_term,X109 : d_term] : ((X109 = X110) | (((d2term @ X110)) != ((d2term @ X109)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 inference(nnf_transformation,[],[f72])).
% 13.65/2.32 thf(f261,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X313 : d_subst] : (d_id = X313) & (! [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 = X474) | (((ap @ (sub @ X472 @ id) @ X474)) != ((ap @ (sub @ X471 @ id) @ X473)))) | ? [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 != X470) & (((ap @ X467 @ X470)) = ((ap @ X468 @ X469)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X471 : term,X474 : term,X473 : term,X472 : term] : ((X473 != X474) & (((ap @ (sub @ X472 @ id) @ X474)) = ((ap @ (sub @ X471 @ id) @ X473)))) & ! [X470 : term,X467 : term,X468 : term,X469 : term] : ((X469 = X470) | (((ap @ X467 @ X470)) != ((ap @ X468 @ X469)))))) & ((shinj = $true) | ? [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) = ((sub @ X451 @ sh))) & (X450 != X451))) & (! [X450 : term,X451 : term] : ((((sub @ X450 @ sh)) != ((sub @ X451 @ sh))) | (X450 = X451)) | (shinj != $true)) & (axvarshift = $true) & (induction2lem_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (pushprop_lthm_orig = $true) & (? [X84 : subst] : (((comp @ id @ X84)) != X84) | ? [X85 : subst] : (((comp @ X85 @ id)) != X85) | (! [X86 : subst] : (((comp @ X86 @ id)) = X86) & ! [X87 : subst] : (((comp @ id @ X87)) = X87)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X84 : subst] : (((comp @ id @ X84)) = X84) & ! [X85 : subst] : (((comp @ X85 @ id)) = X85) & (? [X86 : subst] : (((comp @ X86 @ id)) != X86) | ? [X87 : subst] : (((comp @ id @ X87)) != X87)))) & ((hoasinduction_no_psi_cond = $true) | ? [X89 : term,X88 : (subst > term > subst > $o)] : (! [X92 : (subst > term > term)] : (? [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) != ((sub @ (X92 @ X93 @ X95) @ X94))) | ? [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) != $true) & (((X88 @ id @ X96 @ id)) = $true)) | (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) = $true)) & (((X88 @ id @ X89 @ id)) != $true) & ($true != ((sP57 @ X88))))) & (! [X89 : term,X88 : (subst > term > subst > $o)] : (? [X92 : (subst > term > term)] : (! [X95 : term,X94 : subst,X93 : subst] : (((X92 @ (comp @ X93 @ X94) @ (sub @ X95 @ X94))) = ((sub @ (X92 @ X93 @ X95) @ X94))) & ! [X96 : term] : ((((X88 @ id @ (X92 @ id @ X96) @ id)) = $true) | (((X88 @ id @ X96 @ id)) != $true)) & (((X88 @ id @ (lam @ (X92 @ sh @ one)) @ id)) != $true)) | (((X88 @ id @ X89 @ id)) = $true) | ($true = ((sP57 @ X88)))) | (hoasinduction_no_psi_cond != $true)) & (! [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) != ((ap @ X49 @ X51))) | (X48 = X51)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X51 : term,X49 : term,X50 : term,X48 : term] : ((((ap @ X50 @ X48)) = ((ap @ X49 @ X51))) & (X48 != X51))) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3a = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3a != $true)) & (substmonoid_gthm = $true) & ((hoasapinj2 = $true) | ? [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) = ((ap @ (sub @ X362 @ id) @ X363))) & (X361 != X363))) & (! [X363 : term,X361 : term,X364 : term,X362 : term] : ((((ap @ (sub @ X364 @ id) @ X361)) != ((ap @ (sub @ X362 @ id) @ X363))) | (X361 = X363)) | (hoasapinj2 != $true)) & (! [X420 : term,X422 : subst,X421 : (term > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) = ((X423 @ X424))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X420 : term,X422 : subst,X421 : (term > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X421 @ (sub @ X424 @ (push @ X420 @ X422)))) != ((X423 @ X424)))) & ((induction2_lthm = $true) | ($true != sP55)) & (($true = sP55) | (induction2_lthm != $true)) & ! [X460 : d_term] : (d_one = X460) & ((hoasinduction_lem3b_lthm = $true) | ? [X311 : term] : ! [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) != ((X312 @ sh @ one)))) & (! [X311 : term] : ? [X312 : (subst > term > term)] : (((sub @ X311 @ (push @ one @ sh))) = ((X312 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) != $true) | ($true = ((X356 @ (sub @ X355 @ (push @ X358 @ X357)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X355 : term,X358 : term,X356 : (term > $o),X354 : (term > $o),X357 : subst] : ((((X354 @ X355)) = $true) & ($true != ((X356 @ (sub @ X355 @ (push @ X358 @ X357))))))) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((sP51 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP51 != $true)) & (! [X106 : term] : (((sub @ X106 @ id)) = X106) | ? [X105 : term] : (((sub @ X105 @ id)) != X105) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X106 : term] : (((sub @ X106 @ id)) != X106) & ! [X105 : term] : (((sub @ X105 @ id)) = X105))) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X426 : (subst > term > subst > $o)] : ! [X427 : (term > $o)] : ? [X428 : term] : (((X427 @ X428)) != ((X426 @ id @ X428 @ id)))) & (! [X426 : (subst > term > subst > $o)] : ? [X427 : (term > $o)] : ! [X428 : term] : (((X427 @ X428)) = ((X426 @ id @ X428 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((sP50 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP50 != $true)) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) = X475) | (axscons != $true)) & ((axscons = $true) | ? [X475 : subst] : (((push @ (sub @ one @ X475) @ (comp @ sh @ X475))) != X475)) & ((hoasinduction_lthm = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & ((sP40 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP40 != $true)) & ((pushprop_lem0 = $true) | ? [X534 : term,X535 : (term > $o),X533 : subst] : ! [X536 : (term > $o)] : ? [X537 : term] : (((X536 @ X537)) != ((X535 @ (sub @ X537 @ (push @ X534 @ X533)))))) & (! [X534 : term,X535 : (term > $o),X533 : subst] : ? [X536 : (term > $o)] : ! [X537 : term] : (((X536 @ X537)) = ((X535 @ (sub @ X537 @ (push @ X534 @ X533))))) | (pushprop_lem0 != $true)) & (axmap = $true) & (! [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (? [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) != ((sub @ (X320 @ X322 @ X324) @ X323))) | (((lam @ (X321 @ sh @ one))) != ((lam @ (X320 @ sh @ one)))) | (((X320 @ X318 @ X319)) = ((X321 @ X318 @ X319))) | ? [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) != ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X318 : subst,X319 : term,X321 : (subst > term > term),X320 : (subst > term > term)] : (! [X322 : subst,X324 : term,X323 : subst] : (((X320 @ (comp @ X322 @ X323) @ (sub @ X324 @ X323))) = ((sub @ (X320 @ X322 @ X324) @ X323))) & (((lam @ (X321 @ sh @ one))) = ((lam @ (X320 @ sh @ one)))) & (((X320 @ X318 @ X319)) != ((X321 @ X318 @ X319))) & ! [X327 : subst,X326 : term,X325 : subst] : (((sub @ (X321 @ X327 @ X326) @ X325)) = ((X321 @ (comp @ X327 @ X325) @ (sub @ X326 @ X325)))))) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & (? [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) != X411) | ? [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) != X414) | ! [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) = $true) | (((X416 @ X418)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X412 : subst,X411 : term] : (((sub @ one @ (push @ X411 @ X412))) = X411) & ! [X413 : term,X414 : subst] : (((comp @ sh @ (push @ X413 @ X414))) = X414) & ? [X418 : term,X419 : term,X415 : (term > $o),X417 : subst,X416 : (term > $o)] : ((((X415 @ (sub @ X418 @ (push @ X419 @ X417)))) != $true) & (((X416 @ X418)) = $true)))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X373 : term] : ! [X374 : (subst > term > term)] : ? [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) != ((X374 @ X375 @ X376)))) & (! [X373 : term] : ? [X374 : (subst > term > term)] : ! [X375 : subst,X376 : term] : (((sub @ X373 @ (push @ X376 @ X375))) = ((X374 @ X375 @ X376))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & ((! [X128 : subst] : (((comp @ X128 @ id)) = X128) & ! [X129 : subst] : (((comp @ id @ X129)) = X129)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X128 : subst] : (((comp @ X128 @ id)) != X128) | ? [X129 : subst] : (((comp @ id @ X129)) != X129)) & (axabs = $true) & (($true = sP36) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP36)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X360 : d_subst,X359 : d_subst] : ((X359 = X360) | (((d2subst @ X359)) != ((d2subst @ X360)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & (! [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) = $true) | ? [X104 : term] : (((X100 @ X104)) != ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) | ($true != ((X103 @ X101)))) | ? [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) != X99) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X103 : (term > $o),X102 : subst,X101 : term,X100 : (term > $o)] : ((((X100 @ one)) != $true) & ! [X104 : term] : (((X100 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X102))))) & ($true = ((X103 @ X101)))) & ! [X99 : term,X98 : subst] : (((sub @ one @ (push @ X99 @ X98))) = X99))) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) = X126) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X127 : subst,X126 : term] : (((sub @ one @ (push @ X126 @ X127))) != X126)) & (! [X328 : term] : (((sub @ X328 @ id)) = X328) | (termmset != $true)) & ((termmset = $true) | ? [X328 : term] : (((sub @ X328 @ id)) != X328)) & ((hoasinduction = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) = ((ap @ (sub @ X481 @ id) @ X484))) & (X481 != X483)) & ! [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 = X479) | (((ap @ X479 @ X477)) != ((ap @ X478 @ X480)))) & ! [X476 : term] : (((sub @ X476 @ id)) = X476))) & (! [X481 : term,X482 : term,X483 : term,X484 : term] : ((((ap @ (sub @ X483 @ id) @ X482)) != ((ap @ (sub @ X481 @ id) @ X484))) | (X481 = X483)) | ? [X480 : term,X479 : term,X477 : term,X478 : term] : ((X478 != X479) & (((ap @ X479 @ X477)) = ((ap @ X478 @ X480)))) | ? [X476 : term] : (((sub @ X476 @ id)) != X476) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem2v2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop_lem1_gthm = $true) & ! [X46 : term] : ? [X47 : d_term] : (((d2term @ X47)) = X46) & ((hoasapinj1 = $true) | ? [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) = ((ap @ (sub @ X12 @ id) @ X13))) & (X12 != X15))) & (! [X14 : term,X15 : term,X13 : term,X12 : term] : ((((ap @ (sub @ X15 @ id) @ X14)) != ((ap @ (sub @ X12 @ id) @ X13))) | (X12 = X15)) | (hoasapinj1 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((sP19 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP19 != $true)) & (lamnotvar = $true) & (! [X529 : term] : ? [X530 : (subst > term > term)] : ! [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) = ((X530 @ X531 @ X532))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X529 : term] : ! [X530 : (subst > term > term)] : ? [X531 : subst,X532 : term] : (((sub @ X529 @ (push @ X532 @ X531))) != ((X530 @ X531 @ X532)))) & (! [X425 : subst] : (((comp @ id @ X425)) = X425) | (axidl != $true)) & ((axidl = $true) | ? [X425 : subst] : (((comp @ id @ X425)) != X425)) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) | ? [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (! [X20 : term] : (((X18 @ X20)) = ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) & ($true != ((X18 @ one))) & ($true = ((X16 @ X19))))) & (! [X19 : term,X18 : (term > $o),X16 : (term > $o),X17 : subst] : (? [X20 : term] : (((X18 @ X20)) != ((X16 @ (sub @ X20 @ (push @ X19 @ X17))))) | ($true = ((X18 @ one))) | ($true != ((X16 @ X19)))) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ? [X523 : term,X524 : (term > $o)] : (! [X526 : term] : (($true = ((X524 @ X526))) | (((var @ X526)) != $true)) & ! [X525 : term] : ((((X524 @ (lam @ X525))) = $true) | ($true != ((X524 @ X525)))) & (((sP16 @ X524)) != $true) & (((X524 @ X523)) != $true))) & (! [X523 : term,X524 : (term > $o)] : (? [X526 : term] : (($true != ((X524 @ X526))) & (((var @ X526)) = $true)) | ? [X525 : term] : ((((X524 @ (lam @ X525))) != $true) & ($true = ((X524 @ X525)))) | (((sP16 @ X524)) = $true) | (((X524 @ X523)) = $true)) | (induction != $true)) & (! [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) = X539) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X539 : subst,X538 : term] : (((comp @ sh @ (push @ X538 @ X539))) != X539)) & (hoaslaminj_gthm = $true) & (! [X410 : term,X409 : term] : ((((lam @ X410)) != ((lam @ X409))) | (X409 = X410)) | (laminj != $true)) & ((laminj = $true) | ? [X410 : term,X409 : term] : ((((lam @ X410)) = ((lam @ X409))) & (X409 != X410))) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (ulamvar1 != $true) & ((sP9 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP9 != $true)) & ((induction2 = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2 != $true)) & (hoasinduction_lem1 = $true) & ((sP5 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP5 != $true)) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X448 : subst] : ? [X449 : d_subst] : (((d2subst @ X449)) = X448) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & ((sP3 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP3 != $true)) & (pushprop_lem3v2_lthm = $true) & (! [X73 : subst] : (((comp @ X73 @ id)) = X73) | (axidr != $true)) & ((axidr = $true) | ? [X73 : subst] : (((comp @ X73 @ id)) != X73)) & (! [X97 : term] : (((sub @ X97 @ id)) = X97) | (axvarid != $true)) & ((axvarid = $true) | ? [X97 : term] : (((sub @ X97 @ id)) != X97)) & (! [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 = X317) | (((ap @ X314 @ X316)) != ((ap @ X317 @ X315)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X315 : term,X316 : term,X317 : term,X314 : term] : ((X314 != X317) & (((ap @ X314 @ X316)) = ((ap @ X317 @ X315))))) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X107 : term] : ! [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) != ((X108 @ sh @ one)))) & (! [X107 : term] : ? [X108 : (subst > term > term)] : (((sub @ X107 @ (push @ one @ sh))) = ((X108 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoaslamnotap = $true) | ? [X462 : term,X463 : term,X461 : (subst > term > term)] : (! [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) = ((sub @ (X461 @ X466 @ X465) @ X464))) & (((lam @ (X461 @ sh @ one))) = ((ap @ (sub @ X463 @ id) @ X462))))) & (! [X462 : term,X463 : term,X461 : (subst > term > term)] : (? [X465 : term,X466 : subst,X464 : subst] : (((X461 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464))) != ((sub @ (X461 @ X466 @ X465) @ X464))) | (((lam @ (X461 @ sh @ one))) != ((ap @ (sub @ X463 @ id) @ X462)))) | (hoaslamnotap != $true)) & (pushprop = $true) & ((hoasinduction_lem0 = $true) | ? [X503 : (subst > term > subst > $o)] : ! [X504 : (term > $o)] : ? [X505 : term] : (((X503 @ id @ X505 @ id)) != ((X504 @ X505)))) & (! [X503 : (subst > term > subst > $o)] : ? [X504 : (term > $o)] : ! [X505 : term] : (((X503 @ id @ X505 @ id)) = ((X504 @ X505))) | (hoasinduction_lem0 != $true)) & (((d2subst @ d_id)) = id) & ! [X110 : d_term,X109 : d_term] : ((X109 = X110) | (((d2term @ X110)) != ((d2term @ X109)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 inference(flattening,[],[f260])).
% 13.65/2.32 thf(f262,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X0 : d_subst] : (d_id = X0) & (! [X1 : term,X2 : term,X3 : term,X4 : term] : ((X2 = X3) | (((ap @ (sub @ X4 @ id) @ X2)) != ((ap @ (sub @ X1 @ id) @ X3)))) | ? [X5 : term,X6 : term,X7 : term,X8 : term] : ((X5 != X8) & (((ap @ X6 @ X5)) = ((ap @ X7 @ X8)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X9 : term,X10 : term,X11 : term,X12 : term] : ((X10 != X11) & (((ap @ (sub @ X12 @ id) @ X10)) = ((ap @ (sub @ X9 @ id) @ X11)))) & ! [X13 : term,X14 : term,X15 : term,X16 : term] : ((X13 = X16) | (((ap @ X14 @ X13)) != ((ap @ X15 @ X16)))))) & ((shinj = $true) | ? [X17 : term,X18 : term] : ((((sub @ X17 @ sh)) = ((sub @ X18 @ sh))) & (X17 != X18))) & (! [X19 : term,X20 : term] : ((((sub @ X20 @ sh)) != ((sub @ X19 @ sh))) | (X19 = X20)) | (shinj != $true)) & (axvarshift = $true) & (induction2lem_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (pushprop_lthm_orig = $true) & (? [X21 : subst] : (((comp @ id @ X21)) != X21) | ? [X22 : subst] : (((comp @ X22 @ id)) != X22) | (! [X23 : subst] : (((comp @ X23 @ id)) = X23) & ! [X24 : subst] : (((comp @ id @ X24)) = X24)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X25 : subst] : (((comp @ id @ X25)) = X25) & ! [X26 : subst] : (((comp @ X26 @ id)) = X26) & (? [X27 : subst] : (((comp @ X27 @ id)) != X27) | ? [X28 : subst] : (((comp @ id @ X28)) != X28)))) & ((hoasinduction_no_psi_cond = $true) | ? [X29 : term,X30 : (subst > term > subst > $o)] : (! [X31 : (subst > term > term)] : (? [X32 : term,X33 : subst,X34 : subst] : (((sub @ (X31 @ X34 @ X32) @ X33)) != ((X31 @ (comp @ X34 @ X33) @ (sub @ X32 @ X33)))) | ? [X35 : term] : ((((X30 @ id @ (X31 @ id @ X35) @ id)) != $true) & (((X30 @ id @ X35 @ id)) = $true)) | ($true = ((X30 @ id @ (lam @ (X31 @ sh @ one)) @ id)))) & (((X30 @ id @ X29 @ id)) != $true) & ($true != ((sP57 @ X30))))) & (! [X36 : term,X37 : (subst > term > subst > $o)] : (? [X38 : (subst > term > term)] : (! [X39 : term,X40 : subst,X41 : subst] : (((sub @ (X38 @ X41 @ X39) @ X40)) = ((X38 @ (comp @ X41 @ X40) @ (sub @ X39 @ X40)))) & ! [X42 : term] : (($true = ((X37 @ id @ (X38 @ id @ X42) @ id))) | ($true != ((X37 @ id @ X42 @ id)))) & (((X37 @ id @ (lam @ (X38 @ sh @ one)) @ id)) != $true)) | ($true = ((X37 @ id @ X36 @ id))) | (((sP57 @ X37)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X43 : term,X44 : term,X45 : term,X46 : term] : ((((ap @ X45 @ X46)) != ((ap @ X44 @ X43))) | (X43 = X46)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X47 : term,X48 : term,X49 : term,X50 : term] : ((((ap @ X49 @ X50)) = ((ap @ X48 @ X47))) & (X47 != X50))) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3a = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3a != $true)) & (substmonoid_gthm = $true) & ((hoasapinj2 = $true) | ? [X51 : term,X52 : term,X53 : term,X54 : term] : ((((ap @ (sub @ X53 @ id) @ X52)) = ((ap @ (sub @ X54 @ id) @ X51))) & (X51 != X52))) & (! [X55 : term,X56 : term,X57 : term,X58 : term] : ((((ap @ (sub @ X58 @ id) @ X55)) != ((ap @ (sub @ X57 @ id) @ X56))) | (X55 = X56)) | (hoasapinj2 != $true)) & (! [X59 : term,X60 : subst,X61 : (term > $o)] : ? [X62 : (term > $o)] : ! [X63 : term] : (((X62 @ X63)) = ((X61 @ (sub @ X63 @ (push @ X59 @ X60))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X64 : term,X65 : subst,X66 : (term > $o)] : ! [X67 : (term > $o)] : ? [X68 : term] : (((X66 @ (sub @ X68 @ (push @ X64 @ X65)))) != ((X67 @ X68)))) & ((induction2_lthm = $true) | ($true != sP55)) & (($true = sP55) | (induction2_lthm != $true)) & ! [X69 : d_term] : (d_one = X69) & ((hoasinduction_lem3b_lthm = $true) | ? [X70 : term] : ! [X71 : (subst > term > term)] : (((sub @ X70 @ (push @ one @ sh))) != ((X71 @ sh @ one)))) & (! [X72 : term] : ? [X73 : (subst > term > term)] : (((X73 @ sh @ one)) = ((sub @ X72 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X74 : term,X75 : term,X76 : (term > $o),X77 : (term > $o),X78 : subst] : (($true != ((X77 @ X74))) | (((X76 @ (sub @ X74 @ (push @ X75 @ X78)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X79 : term,X80 : term,X81 : (term > $o),X82 : (term > $o),X83 : subst] : ((((X82 @ X79)) = $true) & ($true != ((X81 @ (sub @ X79 @ (push @ X80 @ X83))))))) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((sP51 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP51 != $true)) & (! [X84 : term] : (((sub @ X84 @ id)) = X84) | ? [X85 : term] : (((sub @ X85 @ id)) != X85) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X86 : term] : (((sub @ X86 @ id)) != X86) & ! [X87 : term] : (((sub @ X87 @ id)) = X87))) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ? [X88 : (subst > term > subst > $o)] : ! [X89 : (term > $o)] : ? [X90 : term] : (((X88 @ id @ X90 @ id)) != ((X89 @ X90)))) & (! [X91 : (subst > term > subst > $o)] : ? [X92 : (term > $o)] : ! [X93 : term] : (((X92 @ X93)) = ((X91 @ id @ X93 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((sP50 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP50 != $true)) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X94 : subst] : (((push @ (sub @ one @ X94) @ (comp @ sh @ X94))) = X94) | (axscons != $true)) & ((axscons = $true) | ? [X95 : subst] : (((push @ (sub @ one @ X95) @ (comp @ sh @ X95))) != X95)) & ((hoasinduction_lthm = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & ((sP40 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP40 != $true)) & ((pushprop_lem0 = $true) | ? [X96 : term,X97 : (term > $o),X98 : subst] : ! [X99 : (term > $o)] : ? [X100 : term] : (((X99 @ X100)) != ((X97 @ (sub @ X100 @ (push @ X96 @ X98)))))) & (! [X101 : term,X102 : (term > $o),X103 : subst] : ? [X104 : (term > $o)] : ! [X105 : term] : (((X102 @ (sub @ X105 @ (push @ X101 @ X103)))) = ((X104 @ X105))) | (pushprop_lem0 != $true)) & (axmap = $true) & (! [X106 : subst,X107 : term,X108 : (subst > term > term),X109 : (subst > term > term)] : (? [X110 : subst,X111 : term,X112 : subst] : (((sub @ (X109 @ X110 @ X111) @ X112)) != ((X109 @ (comp @ X110 @ X112) @ (sub @ X111 @ X112)))) | (((lam @ (X109 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | (((X108 @ X106 @ X107)) = ((X109 @ X106 @ X107))) | ? [X113 : subst,X114 : term,X115 : subst] : (((sub @ (X108 @ X113 @ X114) @ X115)) != ((X108 @ (comp @ X113 @ X115) @ (sub @ X114 @ X115))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X116 : subst,X117 : term,X118 : (subst > term > term),X119 : (subst > term > term)] : (! [X120 : subst,X121 : term,X122 : subst] : (((X119 @ (comp @ X120 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X119 @ X120 @ X121) @ X122))) & (((lam @ (X118 @ sh @ one))) = ((lam @ (X119 @ sh @ one)))) & (((X118 @ X116 @ X117)) != ((X119 @ X116 @ X117))) & ! [X123 : subst,X124 : term,X125 : subst] : (((sub @ (X118 @ X123 @ X124) @ X125)) = ((X118 @ (comp @ X123 @ X125) @ (sub @ X124 @ X125)))))) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & (? [X126 : subst,X127 : term] : (((sub @ one @ (push @ X127 @ X126))) != X127) | ? [X128 : term,X129 : subst] : (((comp @ sh @ (push @ X128 @ X129))) != X129) | ! [X130 : term,X131 : term,X132 : (term > $o),X133 : subst,X134 : (term > $o)] : (($true = ((X132 @ (sub @ X130 @ (push @ X131 @ X133))))) | (((X134 @ X130)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X135 : subst,X136 : term] : (((sub @ one @ (push @ X136 @ X135))) = X136) & ! [X137 : term,X138 : subst] : (((comp @ sh @ (push @ X137 @ X138))) = X138) & ? [X139 : term,X140 : term,X141 : (term > $o),X142 : subst,X143 : (term > $o)] : (($true != ((X141 @ (sub @ X139 @ (push @ X140 @ X142))))) & ($true = ((X143 @ X139)))))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X144 : term] : ! [X145 : (subst > term > term)] : ? [X146 : subst,X147 : term] : (((X145 @ X146 @ X147)) != ((sub @ X144 @ (push @ X147 @ X146))))) & (! [X148 : term] : ? [X149 : (subst > term > term)] : ! [X150 : subst,X151 : term] : (((sub @ X148 @ (push @ X151 @ X150))) = ((X149 @ X150 @ X151))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & ((! [X152 : subst] : (((comp @ X152 @ id)) = X152) & ! [X153 : subst] : (((comp @ id @ X153)) = X153)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X154 : subst] : (((comp @ X154 @ id)) != X154) | ? [X155 : subst] : (((comp @ id @ X155)) != X155)) & (axabs = $true) & (($true = sP36) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP36)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X156 : d_subst,X157 : d_subst] : ((X156 = X157) | (((d2subst @ X157)) != ((d2subst @ X156)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & (! [X158 : (term > $o),X159 : subst,X160 : term,X161 : (term > $o)] : ((((X161 @ one)) = $true) | ? [X162 : term] : (((X161 @ X162)) != ((X158 @ (sub @ X162 @ (push @ X160 @ X159))))) | ($true != ((X158 @ X160)))) | ? [X163 : term,X164 : subst] : (((sub @ one @ (push @ X163 @ X164))) != X163) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X165 : (term > $o),X166 : subst,X167 : term,X168 : (term > $o)] : ((((X168 @ one)) != $true) & ! [X169 : term] : (((X168 @ X169)) = ((X165 @ (sub @ X169 @ (push @ X167 @ X166))))) & ($true = ((X165 @ X167)))) & ! [X170 : term,X171 : subst] : (((sub @ one @ (push @ X170 @ X171))) = X170))) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X172 : subst,X173 : term] : (((sub @ one @ (push @ X173 @ X172))) = X173) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X174 : subst,X175 : term] : (((sub @ one @ (push @ X175 @ X174))) != X175)) & (! [X176 : term] : (((sub @ X176 @ id)) = X176) | (termmset != $true)) & ((termmset = $true) | ? [X177 : term] : (((sub @ X177 @ id)) != X177)) & ((hoasinduction = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj1_lthm = $true) | (? [X178 : term,X179 : term,X180 : term,X181 : term] : ((((ap @ (sub @ X178 @ id) @ X181)) = ((ap @ (sub @ X180 @ id) @ X179))) & (X178 != X180)) & ! [X182 : term,X183 : term,X184 : term,X185 : term] : ((X183 = X185) | (((ap @ X183 @ X184)) != ((ap @ X185 @ X182)))) & ! [X186 : term] : (((sub @ X186 @ id)) = X186))) & (! [X187 : term,X188 : term,X189 : term,X190 : term] : ((((ap @ (sub @ X187 @ id) @ X190)) != ((ap @ (sub @ X189 @ id) @ X188))) | (X187 = X189)) | ? [X191 : term,X192 : term,X193 : term,X194 : term] : ((X192 != X194) & (((ap @ X192 @ X193)) = ((ap @ X194 @ X191)))) | ? [X195 : term] : (((sub @ X195 @ id)) != X195) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem2v2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop_lem1_gthm = $true) & ! [X196 : term] : ? [X197 : d_term] : (((d2term @ X197)) = X196) & ((hoasapinj1 = $true) | ? [X198 : term,X199 : term,X200 : term,X201 : term] : ((((ap @ (sub @ X201 @ id) @ X200)) = ((ap @ (sub @ X199 @ id) @ X198))) & (X199 != X201))) & (! [X202 : term,X203 : term,X204 : term,X205 : term] : ((((ap @ (sub @ X203 @ id) @ X202)) != ((ap @ (sub @ X205 @ id) @ X204))) | (X203 = X205)) | (hoasapinj1 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((sP19 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP19 != $true)) & (lamnotvar = $true) & (! [X206 : term] : ? [X207 : (subst > term > term)] : ! [X208 : subst,X209 : term] : (((X207 @ X208 @ X209)) = ((sub @ X206 @ (push @ X209 @ X208)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X210 : term] : ! [X211 : (subst > term > term)] : ? [X212 : subst,X213 : term] : (((sub @ X210 @ (push @ X213 @ X212))) != ((X211 @ X212 @ X213)))) & (! [X214 : subst] : (((comp @ id @ X214)) = X214) | (axidl != $true)) & ((axidl = $true) | ? [X215 : subst] : (((comp @ id @ X215)) != X215)) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) | ? [X216 : term,X217 : (term > $o),X218 : (term > $o),X219 : subst] : (! [X220 : term] : (((X218 @ (sub @ X220 @ (push @ X216 @ X219)))) = ((X217 @ X220))) & ($true != ((X217 @ one))) & (((X218 @ X216)) = $true))) & (! [X221 : term,X222 : (term > $o),X223 : (term > $o),X224 : subst] : (? [X225 : term] : (((X223 @ (sub @ X225 @ (push @ X221 @ X224)))) != ((X222 @ X225))) | (((X222 @ one)) = $true) | (((X223 @ X221)) != $true)) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | ? [X226 : term,X227 : (term > $o)] : (! [X228 : term] : ((((X227 @ X228)) = $true) | ($true != ((var @ X228)))) & ! [X229 : term] : (($true = ((X227 @ (lam @ X229)))) | (((X227 @ X229)) != $true)) & ($true != ((sP16 @ X227))) & (((X227 @ X226)) != $true))) & (! [X230 : term,X231 : (term > $o)] : (? [X232 : term] : ((((X231 @ X232)) != $true) & (((var @ X232)) = $true)) | ? [X233 : term] : ((((X231 @ (lam @ X233))) != $true) & ($true = ((X231 @ X233)))) | (((sP16 @ X231)) = $true) | (((X231 @ X230)) = $true)) | (induction != $true)) & (! [X234 : subst,X235 : term] : (((comp @ sh @ (push @ X235 @ X234))) = X234) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X236 : subst,X237 : term] : (((comp @ sh @ (push @ X237 @ X236))) != X236)) & (hoaslaminj_gthm = $true) & (! [X238 : term,X239 : term] : ((((lam @ X239)) != ((lam @ X238))) | (X238 = X239)) | (laminj != $true)) & ((laminj = $true) | ? [X240 : term,X241 : term] : ((((lam @ X240)) = ((lam @ X241))) & (X240 != X241))) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (ulamvar1 != $true) & ((sP9 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP9 != $true)) & ((induction2 = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2 != $true)) & (hoasinduction_lem1 = $true) & ((sP5 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP5 != $true)) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X242 : subst] : ? [X243 : d_subst] : (((d2subst @ X243)) = X242) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & ((sP3 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP3 != $true)) & (pushprop_lem3v2_lthm = $true) & (! [X244 : subst] : (((comp @ X244 @ id)) = X244) | (axidr != $true)) & ((axidr = $true) | ? [X245 : subst] : (((comp @ X245 @ id)) != X245)) & (! [X246 : term] : (((sub @ X246 @ id)) = X246) | (axvarid != $true)) & ((axvarid = $true) | ? [X247 : term] : (((sub @ X247 @ id)) != X247)) & (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X250 = X251) | (((ap @ X250 @ X248)) != ((ap @ X251 @ X249)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X252 : term,X253 : term,X254 : term,X255 : term] : ((X254 != X255) & (((ap @ X254 @ X252)) = ((ap @ X255 @ X253))))) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X256 : term] : ! [X257 : (subst > term > term)] : (((X257 @ sh @ one)) != ((sub @ X256 @ (push @ one @ sh))))) & (! [X258 : term] : ? [X259 : (subst > term > term)] : (((sub @ X258 @ (push @ one @ sh))) = ((X259 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoaslamnotap = $true) | ? [X260 : term,X261 : term,X262 : (subst > term > term)] : (! [X263 : term,X264 : subst,X265 : subst] : (((sub @ (X262 @ X264 @ X263) @ X265)) = ((X262 @ (comp @ X264 @ X265) @ (sub @ X263 @ X265)))) & (((lam @ (X262 @ sh @ one))) = ((ap @ (sub @ X261 @ id) @ X260))))) & (! [X266 : term,X267 : term,X268 : (subst > term > term)] : (? [X269 : term,X270 : subst,X271 : subst] : (((sub @ (X268 @ X270 @ X269) @ X271)) != ((X268 @ (comp @ X270 @ X271) @ (sub @ X269 @ X271)))) | (((lam @ (X268 @ sh @ one))) != ((ap @ (sub @ X267 @ id) @ X266)))) | (hoaslamnotap != $true)) & (pushprop = $true) & ((hoasinduction_lem0 = $true) | ? [X272 : (subst > term > subst > $o)] : ! [X273 : (term > $o)] : ? [X274 : term] : (((X272 @ id @ X274 @ id)) != ((X273 @ X274)))) & (! [X275 : (subst > term > subst > $o)] : ? [X276 : (term > $o)] : ! [X277 : term] : (((X276 @ X277)) = ((X275 @ id @ X277 @ id))) | (hoasinduction_lem0 != $true)) & (((d2subst @ d_id)) = id) & ! [X278 : d_term,X279 : d_term] : ((X278 = X279) | (((d2term @ X279)) != ((d2term @ X278)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 inference(rectify,[],[f261])).
% 13.65/2.32 thf(f263,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ! [X0 : d_subst] : (d_id = X0) & (! [X1 : term,X2 : term,X3 : term,X4 : term] : ((X2 = X3) | (((ap @ (sub @ X4 @ id) @ X2)) != ((ap @ (sub @ X1 @ id) @ X3)))) | ((sK457 != sK454) & (((ap @ sK455 @ sK454)) = ((ap @ sK456 @ sK457)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((sK459 != sK460) & (((ap @ (sub @ sK461 @ id) @ sK459)) = ((ap @ (sub @ sK458 @ id) @ sK460)))) & ! [X13 : term,X14 : term,X15 : term,X16 : term] : ((X13 = X16) | (((ap @ X14 @ X13)) != ((ap @ X15 @ X16)))))) & ((shinj = $true) | ((((sub @ sK463 @ sh)) = ((sub @ sK462 @ sh))) & (sK463 != sK462))) & (! [X19 : term,X20 : term] : ((((sub @ X20 @ sh)) != ((sub @ X19 @ sh))) | (X19 = X20)) | (shinj != $true)) & (axvarshift = $true) & (induction2lem_gthm = $true) & ((sP58 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP58 != $true)) & (pushprop_lthm_orig = $true) & ((((comp @ id @ sK464)) != sK464) | (((comp @ sK465 @ id)) != sK465) | (! [X23 : subst] : (((comp @ X23 @ id)) = X23) & ! [X24 : subst] : (((comp @ id @ X24)) = X24)) | (substmonoid_lthm != $true)) & ((substmonoid_lthm = $true) | (! [X25 : subst] : (((comp @ id @ X25)) = X25) & ! [X26 : subst] : (((comp @ X26 @ id)) = X26) & ((((comp @ sK466 @ id)) != sK466) | (sK467 != ((comp @ id @ sK467)))))) & ((hoasinduction_no_psi_cond = $true) | (! [X31 : (subst > term > term)] : ((((sub @ (X31 @ (sK472 @ X31) @ (sK470 @ X31)) @ (sK471 @ X31))) != ((X31 @ (comp @ (sK472 @ X31) @ (sK471 @ X31)) @ (sub @ (sK470 @ X31) @ (sK471 @ X31))))) | ((((sK469 @ id @ (X31 @ id @ (sK473 @ X31)) @ id)) != $true) & (((sK469 @ id @ (sK473 @ X31) @ id)) = $true)) | (((sK469 @ id @ (lam @ (X31 @ sh @ one)) @ id)) = $true)) & (((sK469 @ id @ sK468 @ id)) != $true) & (((sP57 @ sK469)) != $true))) & (! [X36 : term,X37 : (subst > term > subst > $o)] : ((! [X39 : term,X40 : subst,X41 : subst] : (((sK474 @ X37 @ (comp @ X41 @ X40) @ (sub @ X39 @ X40))) = ((sub @ (sK474 @ X37 @ X41 @ X39) @ X40))) & ! [X42 : term] : (($true = ((X37 @ id @ (sK474 @ X37 @ id @ X42) @ id))) | ($true != ((X37 @ id @ X42 @ id)))) & (((X37 @ id @ (lam @ (sK474 @ X37 @ sh @ one)) @ id)) != $true)) | ($true = ((X37 @ id @ X36 @ id))) | (((sP57 @ X37)) = $true)) | (hoasinduction_no_psi_cond != $true)) & (! [X43 : term,X44 : term,X45 : term,X46 : term] : ((((ap @ X45 @ X46)) != ((ap @ X44 @ X43))) | (X43 = X46)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK477 @ sK478)) = ((ap @ sK476 @ sK475))) & (sK475 != sK478))) & (hoaslamnotvar = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((var @ (d2term @ d_one))) != $true) & ((hoasinduction_lem3a = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3a != $true)) & (substmonoid_gthm = $true) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK482 @ id) @ sK479)) = ((ap @ (sub @ sK481 @ id) @ sK480))) & (sK479 != sK480))) & (! [X55 : term,X56 : term,X57 : term,X58 : term] : ((((ap @ (sub @ X58 @ id) @ X55)) != ((ap @ (sub @ X57 @ id) @ X56))) | (X55 = X56)) | (hoasapinj2 != $true)) & (! [X59 : term,X60 : subst,X61 : (term > $o)] : ! [X63 : term] : (((X61 @ (sub @ X63 @ (push @ X59 @ X60)))) = ((sK483 @ X61 @ X60 @ X59 @ X63))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X67 : (term > $o)] : (((X67 @ (sK487 @ X67))) != ((sK486 @ (sub @ (sK487 @ X67) @ (push @ sK484 @ sK485)))))) & ((induction2_lthm = $true) | ($true != sP55)) & (($true = sP55) | (induction2_lthm != $true)) & ! [X69 : d_term] : (d_one = X69) & ((hoasinduction_lem3b_lthm = $true) | ! [X71 : (subst > term > term)] : (((sub @ sK488 @ (push @ one @ sh))) != ((X71 @ sh @ one)))) & (! [X72 : term] : (((sK489 @ X72 @ sh @ one)) = ((sub @ X72 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X74 : term,X75 : term,X76 : (term > $o),X77 : (term > $o),X78 : subst] : (($true != ((X77 @ X74))) | (((X76 @ (sub @ X74 @ (push @ X75 @ X78)))) = $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK493 @ sK490)) = $true) & ($true != ((sK492 @ (sub @ sK490 @ (push @ sK491 @ sK494))))))) & (hoasapnotvar_lthm = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((sP51 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP51 != $true)) & (! [X84 : term] : (((sub @ X84 @ id)) = X84) | (sK495 != ((sub @ sK495 @ id))) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((sK496 != ((sub @ sK496 @ id))) & ! [X87 : term] : (((sub @ X87 @ id)) = X87))) & (axassoc = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (pushprop_gthm = $true) & ((hoasinduction_lem0_lthm = $true) | ! [X89 : (term > $o)] : (((X89 @ (sK498 @ X89))) != ((sK497 @ id @ (sK498 @ X89) @ id)))) & (! [X91 : (subst > term > subst > $o)] : ! [X93 : term] : (((X91 @ id @ X93 @ id)) = ((sK499 @ X91 @ X93))) | (hoasinduction_lem0_lthm != $true)) & ((sP50 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP50 != $true)) & (hoaslamnotvar_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (! [X94 : subst] : (((push @ (sub @ one @ X94) @ (comp @ sh @ X94))) = X94) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK500) @ (comp @ sh @ sK500))) != sK500)) & ((hoasinduction_lthm = $true) | (sP49 != $true)) & ((sP49 = $true) | (hoasinduction_lthm != $true)) & (hoasinduction_lem1_lthm = $true) & (apnotvar = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & ((sP40 = $true) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (sP40 != $true)) & ((pushprop_lem0 = $true) | ! [X99 : (term > $o)] : (((X99 @ (sK504 @ X99))) != ((sK502 @ (sub @ (sK504 @ X99) @ (push @ sK501 @ sK503)))))) & (! [X101 : term,X102 : (term > $o),X103 : subst] : ! [X105 : term] : (((sK505 @ X103 @ X102 @ X101 @ X105)) = ((X102 @ (sub @ X105 @ (push @ X101 @ X103))))) | (pushprop_lem0 != $true)) & (axmap = $true) & (! [X106 : subst,X107 : term,X108 : (subst > term > term),X109 : (subst > term > term)] : ((((sub @ (X109 @ (sK506 @ X109) @ (sK507 @ X109)) @ (sK508 @ X109))) != ((X109 @ (comp @ (sK506 @ X109) @ (sK508 @ X109)) @ (sub @ (sK507 @ X109) @ (sK508 @ X109))))) | (((lam @ (X109 @ sh @ one))) != ((lam @ (X108 @ sh @ one)))) | (((X108 @ X106 @ X107)) = ((X109 @ X106 @ X107))) | (((X108 @ (comp @ (sK509 @ X108) @ (sK511 @ X108)) @ (sub @ (sK510 @ X108) @ (sK511 @ X108)))) != ((sub @ (X108 @ (sK509 @ X108) @ (sK510 @ X108)) @ (sK511 @ X108))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X120 : subst,X121 : term,X122 : subst] : (((sub @ (sK515 @ X120 @ X121) @ X122)) = ((sK515 @ (comp @ X120 @ X122) @ (sub @ X121 @ X122)))) & (((lam @ (sK515 @ sh @ one))) = ((lam @ (sK514 @ sh @ one)))) & (((sK515 @ sK512 @ sK513)) != ((sK514 @ sK512 @ sK513))) & ! [X123 : subst,X124 : term,X125 : subst] : (((sK514 @ (comp @ X123 @ X125) @ (sub @ X124 @ X125))) = ((sub @ (sK514 @ X123 @ X124) @ X125))))) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & ((((sub @ one @ (push @ sK517 @ sK516))) != sK517) | (sK519 != ((comp @ sh @ (push @ sK518 @ sK519)))) | ! [X130 : term,X131 : term,X132 : (term > $o),X133 : subst,X134 : (term > $o)] : (($true = ((X132 @ (sub @ X130 @ (push @ X131 @ X133))))) | (((X134 @ X130)) != $true)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X135 : subst,X136 : term] : (((sub @ one @ (push @ X136 @ X135))) = X136) & ! [X137 : term,X138 : subst] : (((comp @ sh @ (push @ X137 @ X138))) = X138) & ((((sK522 @ (sub @ sK520 @ (push @ sK521 @ sK523)))) != $true) & (((sK524 @ sK520)) = $true)))) & (ulamvarind = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X145 : (subst > term > term)] : (((X145 @ (sK526 @ X145) @ (sK527 @ X145))) != ((sub @ sK525 @ (push @ (sK527 @ X145) @ (sK526 @ X145)))))) & (! [X148 : term] : ! [X150 : subst,X151 : term] : (((sub @ X148 @ (push @ X151 @ X150))) = ((sK528 @ X148 @ X150 @ X151))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (ulamvarsh = $true) & ((! [X152 : subst] : (((comp @ X152 @ id)) = X152) & ! [X153 : subst] : (((comp @ id @ X153)) = X153)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK529 @ id)) != sK529) | (((comp @ id @ sK530)) != sK530)) & (axabs = $true) & (($true = sP36) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP36)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X156 : d_subst,X157 : d_subst] : ((X156 = X157) | (((d2subst @ X157)) != ((d2subst @ X156)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (one = ((d2term @ d_one))) & (! [X158 : (term > $o),X159 : subst,X160 : term,X161 : (term > $o)] : ((((X161 @ one)) = $true) | (((X158 @ (sub @ (sK531 @ X161 @ X160 @ X159 @ X158) @ (push @ X160 @ X159)))) != ((X161 @ (sK531 @ X161 @ X160 @ X159 @ X158)))) | ($true != ((X158 @ X160)))) | (((sub @ one @ (push @ sK532 @ sK533))) != sK532) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (((((sK537 @ one)) != $true) & ! [X169 : term] : (((sK537 @ X169)) = ((sK534 @ (sub @ X169 @ (push @ sK536 @ sK535))))) & (((sK534 @ sK536)) = $true)) & ! [X170 : term,X171 : subst] : (((sub @ one @ (push @ X170 @ X171))) = X170))) & (((d2subst @ d_id)) = sh) & (axapp = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X172 : subst,X173 : term] : (((sub @ one @ (push @ X173 @ X172))) = X173) | (axvarcons != $true)) & ((axvarcons = $true) | (sK539 != ((sub @ one @ (push @ sK539 @ sK538))))) & (! [X176 : term] : (((sub @ X176 @ id)) = X176) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK540 @ id)) != sK540)) & ((hoasinduction = $true) | ($true != sP27)) & (($true = sP27) | (hoasinduction != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3 = $true) | ($true != sP23)) & (($true = sP23) | (hoasinduction_lem3 != $true)) & (hoasinduction_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj1_lthm = $true) | (((((ap @ (sub @ sK543 @ id) @ sK542)) = ((ap @ (sub @ sK541 @ id) @ sK544))) & (sK543 != sK541)) & ! [X182 : term,X183 : term,X184 : term,X185 : term] : ((X183 = X185) | (((ap @ X183 @ X184)) != ((ap @ X185 @ X182)))) & ! [X186 : term] : (((sub @ X186 @ id)) = X186))) & (! [X187 : term,X188 : term,X189 : term,X190 : term] : ((((ap @ (sub @ X187 @ id) @ X190)) != ((ap @ (sub @ X189 @ id) @ X188))) | (X187 = X189)) | ((sK548 != sK546) & (((ap @ sK546 @ sK547)) = ((ap @ sK548 @ sK545)))) | (sK549 != ((sub @ sK549 @ id))) | (hoasapinj1_lthm != $true)) & ((hoasinduction_lem2v2 = $true) | (sP21 != $true)) & ((sP21 = $true) | (hoasinduction_lem2v2 != $true)) & (pushprop_lem1_gthm = $true) & ! [X196 : term] : (((d2term @ (sK550 @ X196))) = X196) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK554 @ id) @ sK553)) = ((ap @ (sub @ sK552 @ id) @ sK551))) & (sK554 != sK552))) & (! [X202 : term,X203 : term,X204 : term,X205 : term] : ((((ap @ (sub @ X203 @ id) @ X202)) != ((ap @ (sub @ X205 @ id) @ X204))) | (X203 = X205)) | (hoasapinj1 != $true)) & (hoasinduction_lem3_gthm = $true) & (hoasapinj1_gthm = $true) & (termmset_gthm = $true) & ((sP19 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP19 != $true)) & (lamnotvar = $true) & (! [X206 : term] : ! [X208 : subst,X209 : term] : (((sK555 @ X206 @ X208 @ X209)) = ((sub @ X206 @ (push @ X209 @ X208)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X211 : (subst > term > term)] : (((sub @ sK556 @ (push @ (sK558 @ X211) @ (sK557 @ X211)))) != ((X211 @ (sK557 @ X211) @ (sK558 @ X211))))) & (! [X214 : subst] : (((comp @ id @ X214)) = X214) | (axidl != $true)) & ((axidl = $true) | (sK559 != ((comp @ id @ sK559)))) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2 = $true) | (! [X220 : term] : (((sK561 @ X220)) = ((sK562 @ (sub @ X220 @ (push @ sK560 @ sK563))))) & ($true != ((sK561 @ one))) & (((sK562 @ sK560)) = $true))) & (! [X221 : term,X222 : (term > $o),X223 : (term > $o),X224 : subst] : ((((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224)))) != ((X222 @ (sK564 @ X224 @ X223 @ X222 @ X221)))) | (((X222 @ one)) = $true) | (((X223 @ X221)) != $true)) | (pushprop_lem1v2 != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP18 != $true)) & ((sP18 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((induction = $true) | (! [X228 : term] : ((((sK566 @ X228)) = $true) | ($true != ((var @ X228)))) & ! [X229 : term] : ((((sK566 @ (lam @ X229))) = $true) | (((sK566 @ X229)) != $true)) & ($true != ((sP16 @ sK566))) & (((sK566 @ sK565)) != $true))) & (! [X230 : term,X231 : (term > $o)] : (((((X231 @ (sK567 @ X231))) != $true) & ($true = ((var @ (sK567 @ X231))))) | (($true != ((X231 @ (lam @ (sK568 @ X231))))) & ($true = ((X231 @ (sK568 @ X231))))) | (((sP16 @ X231)) = $true) | (((X231 @ X230)) = $true)) | (induction != $true)) & (! [X234 : subst,X235 : term] : (((comp @ sh @ (push @ X235 @ X234))) = X234) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK569 != ((comp @ sh @ (push @ sK570 @ sK569))))) & (hoaslaminj_gthm = $true) & (! [X238 : term,X239 : term] : ((((lam @ X239)) != ((lam @ X238))) | (X238 = X239)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK571)) = ((lam @ sK572))) & (sK572 != sK571))) & ((hoasinduction_lthm_3 = $true) | (sP15 != $true)) & ((sP15 = $true) | (hoasinduction_lthm_3 != $true)) & (ulamvar1 != $true) & ((sP9 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP9 != $true)) & ((induction2 = $true) | (sP7 != $true)) & ((sP7 = $true) | (induction2 != $true)) & (hoasinduction_lem1 = $true) & ((sP5 = $true) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (sP5 != $true)) & (lamnotap != $true) & (pushprop_lem1v2_gthm = $true) & ! [X242 : subst] : (((d2subst @ (sK573 @ X242))) = X242) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotap_lthm = $true) & ((sP3 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP3 != $true)) & (pushprop_lem3v2_lthm = $true) & (! [X244 : subst] : (((comp @ X244 @ id)) = X244) | (axidr != $true)) & ((axidr = $true) | (sK574 != ((comp @ sK574 @ id)))) & (! [X246 : term] : (((sub @ X246 @ id)) = X246) | (axvarid != $true)) & ((axvarid = $true) | (((sub @ sK575 @ id)) != sK575)) & (! [X248 : term,X249 : term,X250 : term,X251 : term] : ((X250 = X251) | (((ap @ X250 @ X248)) != ((ap @ X251 @ X249)))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK578 != sK579) & (((ap @ sK579 @ sK577)) = ((ap @ sK578 @ sK576))))) & (pushprop_lem2v2 = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP2)) & (($true = sP2) | (hoasinduction_lem3_lthm != $true)) & (hoasapnotvar = $true) & (induction2_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X257 : (subst > term > term)] : (((X257 @ sh @ one)) != ((sub @ sK580 @ (push @ one @ sh))))) & (! [X258 : term] : (((sub @ X258 @ (push @ one @ sh))) = ((sK581 @ X258 @ sh @ one))) | (hoasinduction_lem3b != $true)) & ((hoaslamnotap = $true) | (! [X263 : term,X264 : subst,X265 : subst] : (((sK584 @ (comp @ X264 @ X265) @ (sub @ X263 @ X265))) = ((sub @ (sK584 @ X264 @ X263) @ X265))) & (((lam @ (sK584 @ sh @ one))) = ((ap @ (sub @ sK583 @ id) @ sK582))))) & (! [X266 : term,X267 : term,X268 : (subst > term > term)] : ((((sub @ (X268 @ (sK586 @ X268) @ (sK585 @ X268)) @ (sK587 @ X268))) != ((X268 @ (comp @ (sK586 @ X268) @ (sK587 @ X268)) @ (sub @ (sK585 @ X268) @ (sK587 @ X268))))) | (((lam @ (X268 @ sh @ one))) != ((ap @ (sub @ X267 @ id) @ X266)))) | (hoaslamnotap != $true)) & (pushprop = $true) & ((hoasinduction_lem0 = $true) | ! [X273 : (term > $o)] : (((X273 @ (sK589 @ X273))) != ((sK588 @ id @ (sK589 @ X273) @ id)))) & (! [X275 : (subst > term > subst > $o)] : ! [X277 : term] : (((X275 @ id @ X277 @ id)) = ((sK590 @ X275 @ X277))) | (hoasinduction_lem0 != $true)) & (((d2subst @ d_id)) = id) & ! [X278 : d_term,X279 : d_term] : ((X278 = X279) | (((d2term @ X279)) != ((d2term @ X278)))) & (hoasapnotvar_gthm = $true)),
% 13.65/2.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,sK467,sK468,sK469,vAPP,vAPP,vAPP,vAPP,vAPP,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,vAPP,sK484,sK485,sK486,vAPP,sK488,vAPP,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,vAPP,vAPP,sK500,sK501,sK502,sK503,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,vAPP,vAPP,vAPP,sK529,sK530,vAPP,sK532,sK533,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,vAPP,sK551,sK552,sK553,sK554,vAPP,sK556,vAPP,vAPP,sK559,sK560,sK561,sK562,sK563,vAPP,sK565,sK566,vAPP,vAPP,sK569,sK570,sK571,sK572,vAPP,sK574,sK575,sK576,sK577,sK578,sK579,sK580,vAPP,sK582,sK583,sK584,vAPP,vAPP,vAPP,sK588,vAPP,vAPP]),skolemize(X5,sK454),skolemize(X6,sK455),skolemize(X7,sK456),skolemize(X8,sK457),skolemize(X9,sK458),skolemize(X10,sK459),skolemize(X11,sK460),skolemize(X12,sK461),skolemize(X17,sK462),skolemize(X18,sK463),skolemize(X21,sK464),skolemize(X22,sK465),skolemize(X27,sK466),skolemize(X28,sK467),skolemize(X29,sK468),skolemize(X30,sK469),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X47,sK475),skolemize(X48,sK476),skolemize(X49,sK477),skolemize(X50,sK478),skolemize(X51,sK479),skolemize(X52,sK480),skolemize(X53,sK481),skolemize(X54,sK482),skolemize(X19,sK68 @ X12 @ X10),skolemize(X64,sK484),skolemize(X65,sK485),skolemize(X66,sK486),skolemize(X19,sK68 @ X12 @ X10),skolemize(X70,sK488),skolemize(X19,sK68 @ X12 @ X10),skolemize(X79,sK490),skolemize(X80,sK491),skolemize(X81,sK492),skolemize(X82,sK493),skolemize(X83,sK494),skolemize(X85,sK495),skolemize(X86,sK496),skolemize(X88,sK497),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X95,sK500),skolemize(X96,sK501),skolemize(X97,sK502),skolemize(X98,sK503),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X116,sK512),skolemize(X117,sK513),skolemize(X118,sK514),skolemize(X119,sK515),skolemize(X126,sK516),skolemize(X127,sK517),skolemize(X128,sK518),skolemize(X129,sK519),skolemize(X139,sK520),skolemize(X140,sK521),skolemize(X141,sK522),skolemize(X142,sK523),skolemize(X143,sK524),skolemize(X144,sK525),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X154,sK529),skolemize(X155,sK530),skolemize(X19,sK68 @ X12 @ X10),skolemize(X163,sK532),skolemize(X164,sK533),skolemize(X165,sK534),skolemize(X166,sK535),skolemize(X167,sK536),skolemize(X168,sK537),skolemize(X174,sK538),skolemize(X175,sK539),skolemize(X177,sK540),skolemize(X178,sK541),skolemize(X179,sK542),skolemize(X180,sK543),skolemize(X181,sK544),skolemize(X191,sK545),skolemize(X192,sK546),skolemize(X193,sK547),skolemize(X194,sK548),skolemize(X195,sK549),skolemize(X19,sK68 @ X12 @ X10),skolemize(X198,sK551),skolemize(X199,sK552),skolemize(X200,sK553),skolemize(X201,sK554),skolemize(X19,sK68 @ X12 @ X10),skolemize(X210,sK556),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X215,sK559),skolemize(X216,sK560),skolemize(X217,sK561),skolemize(X218,sK562),skolemize(X219,sK563),skolemize(X19,sK68 @ X12 @ X10),skolemize(X226,sK565),skolemize(X227,sK566),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X236,sK569),skolemize(X237,sK570),skolemize(X240,sK571),skolemize(X241,sK572),skolemize(X19,sK68 @ X12 @ X10),skolemize(X245,sK574),skolemize(X247,sK575),skolemize(X252,sK576),skolemize(X253,sK577),skolemize(X254,sK578),skolemize(X255,sK579),skolemize(X256,sK580),skolemize(X19,sK68 @ X12 @ X10),skolemize(X260,sK582),skolemize(X261,sK583),skolemize(X262,sK584),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10),skolemize(X272,sK588),skolemize(X19,sK68 @ X12 @ X10),skolemize(X19,sK68 @ X12 @ X10)],[f262])).
% 13.65/2.32 thf(f468,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o)] : ((((sP33 @ X0)) != $true) | (((X0 @ (sK217 @ X0))) = $true)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f153])).
% 13.65/2.32 thf(f471,plain,(
% 13.65/2.32 ( ! [X2 : term,X0 : (term > $o),X1 : term] : ((((X0 @ X1)) != $true) | (((sP33 @ X0)) = $true) | (((X0 @ X2)) != $true) | ($true = ((X0 @ (ap @ X1 @ X2))))) )),
% 13.65/2.32 inference(cnf_transformation,[],[f153])).
% 13.65/2.32 thf(f754,plain,(
% 13.65/2.32 (((d2subst @ d_id)) = id)),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f756,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : ((((X273 @ (sK589 @ X273))) != ((sK588 @ id @ (sK589 @ X273) @ id))) | (hoasinduction_lem0 = $true)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f780,plain,(
% 13.65/2.32 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2))))))))),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f782,plain,(
% 13.65/2.32 ( ! [X242 : subst] : ((((d2subst @ (sK573 @ X242))) = X242)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f811,plain,(
% 13.65/2.32 ( ! [X224 : subst,X222 : (term > $o),X223 : (term > $o),X221 : term] : ((((X223 @ X221)) != $true) | (((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224)))) != ((X222 @ (sK564 @ X224 @ X223 @ X222 @ X221)))) | (((X222 @ one)) = $true) | (pushprop_lem1v2 != $true)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f812,plain,(
% 13.65/2.32 (((sK562 @ sK560)) = $true) | (pushprop_lem1v2 = $true)),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f829,plain,(
% 13.65/2.32 ( ! [X196 : term] : ((((d2term @ (sK550 @ X196))) = X196)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f861,plain,(
% 13.65/2.32 (one = ((d2term @ d_one)))),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f934,plain,(
% 13.65/2.32 ( ! [X69 : d_term] : ((d_one = X69)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f945,plain,(
% 13.65/2.32 (((var @ (d2term @ d_one))) != $true)),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f976,plain,(
% 13.65/2.32 ( ! [X0 : d_subst] : ((d_id = X0)) )),
% 13.65/2.32 inference(cnf_transformation,[],[f263])).
% 13.65/2.32 thf(f978,plain,(
% 13.65/2.32 (hoasinduction_lem0 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: (hoasinduction_p_and_p_prime @ Y0 @ Y1)))))))),
% 13.65/2.32 inference(cnf_transformation,[],[f8])).
% 13.65/2.32 thf(f980,definition,(
% 13.65/2.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 13.65/2.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 13.65/2.32 thf(f981,plain,(
% 13.65/2.32 (hoasinduction_lem0 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: ((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ id @ Y4 @ id) = (Y3 @ Y4))))))) @ Y0 @ Y1)))))))),
% 13.65/2.32 inference(definition_unfolding,[],[f978,f780])).
% 13.65/2.32 thf(f1018,plain,(
% 13.65/2.32 ( ! [X224 : subst,X222 : (term > $o),X223 : (term > $o),X221 : term] : ((((X222 @ one)) = $true) | ($true = ((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224))))) | ($true = ((X222 @ (sK564 @ X224 @ X223 @ X222 @ X221)))) | (pushprop_lem1v2 != $true) | (((X223 @ X221)) != $true)) )),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f811])).
% 13.65/2.32 thf(f1041,plain,(
% 13.65/2.32 ($false = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: ((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ id @ Y4 @ id) = (Y3 @ Y4))))))) @ Y0 @ Y1))))))) | (hoasinduction_lem0 = $false)),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f981])).
% 13.65/2.32 thf(f1042,plain,(
% 13.65/2.32 (hoasinduction_lem0 = $false) | ((((^[Y0 : subst > term > subst > $o]: (?? @ (term > $o) @ (^[Y1 : term > $o]: ((^[Y2 : subst > term > subst > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ id @ Y4 @ id) = (Y3 @ Y4))))))) @ Y0 @ Y1)))) @ sK591)) = $false)),
% 13.65/2.32 inference(sigma_proxy_clausification,[],[f1041])).
% 13.65/2.32 thf(f1043,plain,(
% 13.65/2.32 (hoasinduction_lem0 = $false) | (((?? @ (term > $o) @ (^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) = (Y0 @ Y1))))))) = $false)),
% 13.65/2.32 inference(beta-eta_normalization,[],[f1042])).
% 13.65/2.32 thf(f1044,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((hoasinduction_lem0 = $false) | ($false = (((^[Y0 : term > $o]: (!! @ term @ (^[Y1 : term]: ((sK591 @ id @ Y1 @ id) = (Y0 @ Y1))))) @ X1)))) )),
% 13.65/2.32 inference(pi_proxy_clausification,[],[f1043])).
% 13.65/2.32 thf(f1045,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = ((!! @ term @ (^[Y0 : term]: ((sK591 @ id @ Y0 @ id) = (X1 @ Y0)))))) | (hoasinduction_lem0 = $false)) )),
% 13.65/2.32 inference(beta-eta_normalization,[],[f1044])).
% 13.65/2.32 thf(f1046,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((hoasinduction_lem0 = $false) | ($false = (((^[Y0 : term]: ((sK591 @ id @ Y0 @ id) = (X1 @ Y0))) @ (sK592 @ X1))))) )),
% 13.65/2.32 inference(sigma_proxy_clausification,[],[f1045])).
% 13.65/2.32 thf(f1047,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = (((sK591 @ id @ (sK592 @ X1) @ id) = (X1 @ (sK592 @ X1))))) | (hoasinduction_lem0 = $false)) )),
% 13.65/2.32 inference(beta-eta_normalization,[],[f1046])).
% 13.65/2.32 thf(f1048,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((hoasinduction_lem0 = $false) | (((X1 @ (sK592 @ X1))) != ((sK591 @ id @ (sK592 @ X1) @ id)))) )),
% 13.65/2.32 inference(equality_proxy_clausification,[],[f1047])).
% 13.65/2.32 thf(f1049,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((hoasinduction_lem0 = $false) | ($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((X1 @ (sK592 @ X1))) = $true)) )),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f1048])).
% 13.65/2.32 thf(f1050,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((hoasinduction_lem0 = $false) | ($false = ((sK591 @ id @ (sK592 @ X1) @ id))) | ($false = ((X1 @ (sK592 @ X1))))) )),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f1048])).
% 13.65/2.32 thf(f1082,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($true = ((sK588 @ id @ (sK589 @ X273) @ id))) | (hoasinduction_lem0 = $true) | (((X273 @ (sK589 @ X273))) = $true)) )),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f756])).
% 13.65/2.32 thf(f1083,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($false = ((sK588 @ id @ (sK589 @ X273) @ id))) | (hoasinduction_lem0 = $true) | ($false = ((X273 @ (sK589 @ X273))))) )),
% 13.65/2.32 inference(xor_proxy_clausification,[],[f756])).
% 13.65/2.32 thf(f1772,definition,(
% 13.65/2.32 spl594_152 <=> (pushprop_lem1v2 = $true)),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_152])],[avatar_definition])).
% 13.65/2.32 thf(f1777,definition,(
% 13.65/2.32 spl594_153 <=> ! [X224 : subst,X223 : (term > $o),X221 : term,X222 : (term > $o)] : ((((X222 @ one)) = $true) | (((X223 @ X221)) != $true) | ($true = ((X222 @ (sK564 @ X224 @ X223 @ X222 @ X221)))) | ($true = ((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224))))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_153])],[avatar_definition])).
% 13.65/2.32 thf(f1778,plain,(
% 13.65/2.32 ( ! [X224 : subst,X222 : (term > $o),X223 : (term > $o),X221 : term] : (($true = ((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224))))) | (((X223 @ X221)) != $true) | ($true = ((X222 @ (sK564 @ X224 @ X223 @ X222 @ X221)))) | (((X222 @ one)) = $true)) ) | ~spl594_153),
% 13.65/2.32 inference(avatar_component_clause,[],[f1777])).
% 13.65/2.32 thf(f1779,plain,(
% 13.65/2.32 spl594_153 | ~spl594_152),
% 13.65/2.32 inference(avatar_split_clause,[],[f1018,f1772,f1777])).
% 13.65/2.32 thf(f1969,definition,(
% 13.65/2.32 spl594_198 <=> (((sK562 @ sK560)) = $true)),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_198])],[avatar_definition])).
% 13.65/2.32 thf(f1971,plain,(
% 13.65/2.32 (((sK562 @ sK560)) = $true) | ~spl594_198),
% 13.65/2.32 inference(avatar_component_clause,[],[f1969])).
% 13.65/2.32 thf(f1972,plain,(
% 13.65/2.32 spl594_152 | spl594_198),
% 13.65/2.32 inference(avatar_split_clause,[],[f812,f1969,f1772])).
% 13.65/2.32 thf(f2138,definition,(
% 13.65/2.32 spl594_237 <=> ! [X1 : (term > $o)] : (($false = ((sK591 @ id @ (sK592 @ X1) @ id))) | ($false = ((X1 @ (sK592 @ X1)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_237])],[avatar_definition])).
% 13.65/2.32 thf(f2139,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = ((X1 @ (sK592 @ X1)))) | ($false = ((sK591 @ id @ (sK592 @ X1) @ id)))) ) | ~spl594_237),
% 13.65/2.32 inference(avatar_component_clause,[],[f2138])).
% 13.65/2.32 thf(f2141,definition,(
% 13.65/2.32 spl594_238 <=> (hoasinduction_lem0 = $false)),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_238])],[avatar_definition])).
% 13.65/2.32 thf(f2143,plain,(
% 13.65/2.32 (hoasinduction_lem0 = $false) | ~spl594_238),
% 13.65/2.32 inference(avatar_component_clause,[],[f2141])).
% 13.65/2.32 thf(f2144,plain,(
% 13.65/2.32 spl594_237 | spl594_238),
% 13.65/2.32 inference(avatar_split_clause,[],[f1050,f2141,f2138])).
% 13.65/2.32 thf(f2146,definition,(
% 13.65/2.32 spl594_239 <=> ! [X1 : (term > $o)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((X1 @ (sK592 @ X1))) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_239])],[avatar_definition])).
% 13.65/2.32 thf(f2147,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($true = ((sK591 @ id @ (sK592 @ X1) @ id))) | (((X1 @ (sK592 @ X1))) = $true)) ) | ~spl594_239),
% 13.65/2.32 inference(avatar_component_clause,[],[f2146])).
% 13.65/2.32 thf(f2148,plain,(
% 13.65/2.32 spl594_239 | spl594_238),
% 13.65/2.32 inference(avatar_split_clause,[],[f1049,f2141,f2146])).
% 13.65/2.32 thf(f2150,definition,(
% 13.65/2.32 spl594_240 <=> (hoasinduction_lem0 = $true)),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_240])],[avatar_definition])).
% 13.65/2.32 thf(f2152,plain,(
% 13.65/2.32 (hoasinduction_lem0 = $true) | ~spl594_240),
% 13.65/2.32 inference(avatar_component_clause,[],[f2150])).
% 13.65/2.32 thf(f2693,definition,(
% 13.65/2.32 spl594_366 <=> ! [X273 : (term > $o)] : (($false = ((sK588 @ id @ (sK589 @ X273) @ id))) | ($false = ((X273 @ (sK589 @ X273)))))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_366])],[avatar_definition])).
% 13.65/2.32 thf(f2694,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($false = ((X273 @ (sK589 @ X273)))) | ($false = ((sK588 @ id @ (sK589 @ X273) @ id)))) ) | ~spl594_366),
% 13.65/2.32 inference(avatar_component_clause,[],[f2693])).
% 13.65/2.32 thf(f2695,plain,(
% 13.65/2.32 spl594_240 | spl594_366),
% 13.65/2.32 inference(avatar_split_clause,[],[f1083,f2693,f2150])).
% 13.65/2.32 thf(f2697,definition,(
% 13.65/2.32 spl594_367 <=> ! [X273 : (term > $o)] : (($true = ((sK588 @ id @ (sK589 @ X273) @ id))) | (((X273 @ (sK589 @ X273))) = $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_367])],[avatar_definition])).
% 13.65/2.32 thf(f2698,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($true = ((sK588 @ id @ (sK589 @ X273) @ id))) | (((X273 @ (sK589 @ X273))) = $true)) ) | ~spl594_367),
% 13.65/2.32 inference(avatar_component_clause,[],[f2697])).
% 13.65/2.32 thf(f2699,plain,(
% 13.65/2.32 spl594_240 | spl594_367),
% 13.65/2.32 inference(avatar_split_clause,[],[f1082,f2697,f2150])).
% 13.65/2.32 thf(f2737,plain,(
% 13.65/2.32 ( ! [X242 : subst] : ((((d2subst @ d_id)) = X242)) )),
% 13.65/2.32 inference(forward_demodulation,[],[f782,f976])).
% 13.65/2.32 thf(f2859,plain,(
% 13.65/2.32 ( ! [X196 : term] : ((((d2term @ d_one)) = X196)) )),
% 13.65/2.32 inference(forward_demodulation,[],[f829,f934])).
% 13.65/2.32 thf(f3072,plain,(
% 13.65/2.32 (((var @ one)) != $true)),
% 13.65/2.32 inference(backward_demodulation,[],[f945,f861])).
% 13.65/2.32 thf(f4033,plain,(
% 13.65/2.32 ( ! [X224 : subst,X222 : (term > $o),X223 : (term > $o),X221 : term] : (($true = ((X223 @ (sub @ (sK564 @ X224 @ X223 @ X222 @ X221) @ (push @ X221 @ X224))))) | (((X222 @ one)) = $true) | (((X223 @ X221)) != $true) | ($true = ((X222 @ (d2term @ d_one))))) ) | ~spl594_153),
% 13.65/2.32 inference(forward_demodulation,[],[f1778,f2859])).
% 13.65/2.32 thf(f4043,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($true = ((sK588 @ id @ (sK589 @ X273) @ id))) | (((X273 @ (d2term @ d_one))) = $true)) ) | ~spl594_367),
% 13.65/2.32 inference(forward_demodulation,[],[f2698,f2859])).
% 13.65/2.32 thf(f4123,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : ((((X273 @ (d2term @ d_one))) = $false) | ($false = ((sK588 @ id @ (sK589 @ X273) @ id)))) ) | ~spl594_366),
% 13.65/2.32 inference(forward_demodulation,[],[f2694,f2859])).
% 13.65/2.32 thf(f4181,plain,(
% 13.65/2.32 ( ! [X222 : (term > $o),X223 : (term > $o),X221 : term] : (($true = ((X223 @ (d2term @ d_one)))) | ($true = ((X222 @ (d2term @ d_one)))) | (((X223 @ X221)) != $true) | (((X222 @ one)) = $true)) ) | ~spl594_153),
% 13.65/2.32 inference(forward_demodulation,[],[f4033,f2859])).
% 13.65/2.32 thf(f4193,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : ((((X273 @ (d2term @ d_one))) = $true) | ($true = ((sK588 @ id @ (d2term @ d_one) @ id)))) ) | ~spl594_367),
% 13.65/2.32 inference(forward_demodulation,[],[f4043,f2859])).
% 13.65/2.32 thf(f4284,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($false = ((sK588 @ id @ (sK589 @ X273) @ id))) | ($false = ((X273 @ one)))) ) | ~spl594_366),
% 13.65/2.32 inference(forward_demodulation,[],[f4123,f861])).
% 13.65/2.32 thf(f4351,plain,(
% 13.65/2.32 ( ! [X222 : (term > $o),X223 : (term > $o),X221 : term] : ((((X223 @ X221)) != $true) | (((X222 @ one)) = $true) | ($true = ((X222 @ (d2term @ d_one)))) | (((X223 @ one)) = $true)) ) | ~spl594_153),
% 13.65/2.32 inference(forward_demodulation,[],[f4181,f861])).
% 13.65/2.32 thf(f4372,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($true = ((sK588 @ id @ (d2term @ d_one) @ id))) | (((X273 @ one)) = $true)) ) | ~spl594_367),
% 13.65/2.32 inference(forward_demodulation,[],[f4193,f861])).
% 13.65/2.32 thf(f4447,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($false = ((X273 @ one))) | ($false = ((sK588 @ id @ (d2term @ d_one) @ id)))) ) | ~spl594_366),
% 13.65/2.32 inference(forward_demodulation,[],[f4284,f2859])).
% 13.65/2.32 thf(f4449,definition,(
% 13.65/2.32 spl594_642 <=> ! [X77 : (term > $o),X74 : term] : ($true != ((X77 @ X74)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_642])],[avatar_definition])).
% 13.65/2.32 thf(f4450,plain,(
% 13.65/2.32 ( ! [X77 : (term > $o),X74 : term] : (($true != ((X77 @ X74)))) ) | ~spl594_642),
% 13.65/2.32 inference(avatar_component_clause,[],[f4449])).
% 13.65/2.32 thf(f4452,definition,(
% 13.65/2.32 spl594_643 <=> ! [X76 : (term > $o)] : (((X76 @ one)) = $true)),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_643])],[avatar_definition])).
% 13.65/2.32 thf(f4453,plain,(
% 13.65/2.32 ( ! [X76 : (term > $o)] : ((((X76 @ one)) = $true)) ) | ~spl594_643),
% 13.65/2.32 inference(avatar_component_clause,[],[f4452])).
% 13.65/2.32 thf(f4501,plain,(
% 13.65/2.32 ( ! [X222 : (term > $o),X223 : (term > $o),X221 : term] : ((((X223 @ one)) = $true) | (((X222 @ one)) = $true) | (((X223 @ X221)) != $true) | (((X222 @ one)) = $true)) ) | ~spl594_153),
% 13.65/2.32 inference(forward_demodulation,[],[f4351,f861])).
% 13.65/2.32 thf(f4508,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : ((((X273 @ one)) = $true) | ($true = ((sK588 @ id @ one @ id)))) ) | ~spl594_367),
% 13.65/2.32 inference(forward_demodulation,[],[f4372,f861])).
% 13.65/2.32 thf(f4553,plain,(
% 13.65/2.32 ( ! [X273 : (term > $o)] : (($false = ((sK588 @ id @ one @ id))) | ($false = ((X273 @ one)))) ) | ~spl594_366),
% 13.65/2.32 inference(forward_demodulation,[],[f4447,f861])).
% 13.65/2.32 thf(f4583,definition,(
% 13.65/2.32 spl594_648 <=> ! [X221 : term,X223 : (term > $o)] : ((((X223 @ one)) = $true) | (((X223 @ X221)) != $true))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_648])],[avatar_definition])).
% 13.65/2.32 thf(f4584,plain,(
% 13.65/2.32 ( ! [X223 : (term > $o),X221 : term] : ((((X223 @ X221)) != $true) | (((X223 @ one)) = $true)) ) | ~spl594_648),
% 13.65/2.32 inference(avatar_component_clause,[],[f4583])).
% 13.65/2.32 thf(f4594,definition,(
% 13.65/2.32 spl594_650 <=> ($true = ((sK588 @ id @ one @ id)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_650])],[avatar_definition])).
% 13.65/2.32 thf(f4596,plain,(
% 13.65/2.32 ($true = ((sK588 @ id @ one @ id))) | ~spl594_650),
% 13.65/2.32 inference(avatar_component_clause,[],[f4594])).
% 13.65/2.32 thf(f4597,plain,(
% 13.65/2.32 spl594_650 | spl594_643 | ~spl594_367),
% 13.65/2.32 inference(avatar_split_clause,[],[f4508,f2697,f4452,f4594])).
% 13.65/2.32 thf(f4611,definition,(
% 13.65/2.32 spl594_653 <=> ! [X99 : (term > $o)] : ($false = ((X99 @ one)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_653])],[avatar_definition])).
% 13.65/2.32 thf(f4612,plain,(
% 13.65/2.32 ( ! [X99 : (term > $o)] : (($false = ((X99 @ one)))) ) | ~spl594_653),
% 13.65/2.32 inference(avatar_component_clause,[],[f4611])).
% 13.65/2.32 thf(f4652,definition,(
% 13.65/2.32 spl594_655 <=> ($false = ((sK588 @ id @ one @ id)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_655])],[avatar_definition])).
% 13.65/2.32 thf(f4654,plain,(
% 13.65/2.32 ($false = ((sK588 @ id @ one @ id))) | ~spl594_655),
% 13.65/2.32 inference(avatar_component_clause,[],[f4652])).
% 13.65/2.32 thf(f4949,plain,(
% 13.65/2.32 ($false = $true) | (~spl594_238 | ~spl594_240)),
% 13.65/2.32 inference(forward_demodulation,[],[f2152,f2143])).
% 13.65/2.32 thf(f4950,plain,(
% 13.65/2.32 $false | (~spl594_238 | ~spl594_240)),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f4949])).
% 13.65/2.32 thf(f4951,plain,(
% 13.65/2.32 ~spl594_238 | ~spl594_240),
% 13.65/2.32 inference(avatar_contradiction_clause,[],[f4950])).
% 13.65/2.32 thf(f5707,plain,(
% 13.65/2.32 ( ! [X222 : (term > $o),X223 : (term > $o),X221 : term] : ((((X223 @ one)) = $true) | (((X223 @ X221)) != $true) | (((X222 @ one)) = $true)) ) | ~spl594_153),
% 13.65/2.32 inference(duplicate_literal_removal,[],[f4501])).
% 13.65/2.32 thf(f5726,plain,(
% 13.65/2.32 ($true != $true) | ~spl594_643),
% 13.65/2.32 inference(backward_demodulation,[],[f3072,f4453])).
% 13.65/2.32 thf(f5736,plain,(
% 13.65/2.32 $false | ~spl594_643),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f5726])).
% 13.65/2.32 thf(f5737,plain,(
% 13.65/2.32 ~spl594_643),
% 13.65/2.32 inference(avatar_contradiction_clause,[],[f5736])).
% 13.65/2.32 thf(f5814,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ (sK592 @ X1))) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) ) | ~spl594_239),
% 13.65/2.32 inference(forward_demodulation,[],[f2147,f2859])).
% 13.65/2.32 thf(f5823,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((sK591 @ id @ (d2term @ d_one) @ id)) = $false) | ($false = ((X1 @ (sK592 @ X1))))) ) | ~spl594_237),
% 13.65/2.32 inference(forward_demodulation,[],[f2139,f2859])).
% 13.65/2.32 thf(f5916,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = ((X1 @ (sK592 @ X1)))) | ($false = ((sK591 @ id @ one @ id)))) ) | ~spl594_237),
% 13.65/2.32 inference(forward_demodulation,[],[f5823,f861])).
% 13.65/2.32 thf(f5943,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = ((X1 @ (d2term @ d_one)))) | ($false = ((sK591 @ id @ one @ id)))) ) | ~spl594_237),
% 13.65/2.32 inference(forward_demodulation,[],[f5916,f2859])).
% 13.65/2.32 thf(f5953,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ (d2term @ d_one))) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) ) | ~spl594_239),
% 13.65/2.32 inference(forward_demodulation,[],[f5814,f2859])).
% 13.65/2.32 thf(f6024,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : (($false = ((sK591 @ id @ one @ id))) | (((X1 @ one)) = $false)) ) | ~spl594_237),
% 13.65/2.32 inference(forward_demodulation,[],[f5943,f861])).
% 13.65/2.32 thf(f6029,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ one)) = $true) | (((sK591 @ id @ (d2term @ d_one) @ id)) = $true)) ) | ~spl594_239),
% 13.65/2.32 inference(forward_demodulation,[],[f5953,f861])).
% 13.65/2.32 thf(f6082,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ one)) = $true) | ($true = ((sK591 @ id @ one @ id)))) ) | ~spl594_239),
% 13.65/2.32 inference(forward_demodulation,[],[f6029,f861])).
% 13.65/2.32 thf(f6120,definition,(
% 13.65/2.32 spl594_706 <=> ($true = ((sK591 @ id @ one @ id)))),
% 13.65/2.32 introduced(definition,[new_symbols(definition,[spl594_706])],[avatar_definition])).
% 13.65/2.32 thf(f6122,plain,(
% 13.65/2.32 ($true = ((sK591 @ id @ one @ id))) | ~spl594_706),
% 13.65/2.32 inference(avatar_component_clause,[],[f6120])).
% 13.65/2.32 thf(f6123,plain,(
% 13.65/2.32 spl594_643 | spl594_706 | ~spl594_239),
% 13.65/2.32 inference(avatar_split_clause,[],[f6082,f2146,f6120,f4452])).
% 13.65/2.32 thf(f6237,plain,(
% 13.65/2.32 ( ! [X223 : (term > $o),X221 : term] : ((((X223 @ X221)) != $true) | ($false = $true)) ) | (~spl594_648 | ~spl594_653)),
% 13.65/2.32 inference(backward_demodulation,[],[f4584,f4612])).
% 13.65/2.32 thf(f6251,plain,(
% 13.65/2.32 ( ! [X223 : (term > $o),X221 : term] : ((((X223 @ X221)) != $true)) ) | (~spl594_648 | ~spl594_653)),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f6237])).
% 13.65/2.32 thf(f6309,plain,(
% 13.65/2.32 spl594_642 | ~spl594_648 | ~spl594_653),
% 13.65/2.32 inference(avatar_split_clause,[],[f6251,f4611,f4583,f4449])).
% 13.65/2.32 thf(f6849,plain,(
% 13.65/2.32 ( ! [X0 : d_subst] : ((id = ((d2subst @ X0)))) )),
% 13.65/2.32 inference(constrained_superposition,[],[f754,f976])).
% 13.65/2.32 thf(f6850,plain,(
% 13.65/2.32 ( ! [X242 : subst] : ((id = X242)) )),
% 13.65/2.32 inference(backward_demodulation,[],[f2737,f6849])).
% 13.65/2.32 thf(f6853,plain,(
% 13.65/2.32 ( ! [X0 : subst] : ((((sK591 @ X0 @ one @ X0)) = $true)) ) | ~spl594_706),
% 13.65/2.32 inference(constrained_superposition,[],[f6122,f6850])).
% 13.65/2.32 thf(f6854,plain,(
% 13.65/2.32 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 13.65/2.32 inference(constrained_superposition,[],[f861,f934])).
% 13.65/2.32 thf(f6856,plain,(
% 13.65/2.32 ( ! [X196 : term] : ((one = X196)) )),
% 13.65/2.32 inference(backward_demodulation,[],[f2859,f6854])).
% 13.65/2.32 thf(f6858,plain,(
% 13.65/2.32 ( ! [X0 : term,X1 : subst] : (($true = ((sK591 @ X1 @ X0 @ X1)))) ) | ~spl594_706),
% 13.65/2.32 inference(constrained_superposition,[],[f6853,f6856])).
% 13.65/2.32 thf(f6906,plain,(
% 13.65/2.32 (((sK562 @ one)) = $true) | ~spl594_198),
% 13.65/2.32 inference(constrained_superposition,[],[f1971,f6856])).
% 13.65/2.32 thf(f6907,plain,(
% 13.65/2.32 ($false = $true) | (~spl594_198 | ~spl594_653)),
% 13.65/2.32 inference(forward_demodulation,[],[f6906,f4612])).
% 13.65/2.32 thf(f6908,plain,(
% 13.65/2.32 $false | (~spl594_198 | ~spl594_653)),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f6907])).
% 13.65/2.32 thf(f6909,plain,(
% 13.65/2.32 ~spl594_198 | ~spl594_653),
% 13.65/2.32 inference(avatar_contradiction_clause,[],[f6908])).
% 13.65/2.32 thf(f6949,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o),X1 : term] : (($false = ((X0 @ X1))) | ($true != $true)) ) | ~spl594_642),
% 13.65/2.32 inference(constrained_superposition,[],[f4450,f980])).
% 13.65/2.32 thf(f7000,plain,(
% 13.65/2.32 ( ! [X0 : $o] : (($true != X0) | ($false = X0)) ) | ~spl594_642),
% 13.65/2.32 inference(constrained_superposition,[],[f4450,f980])).
% 13.65/2.32 thf(f7123,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o),X1 : term] : (($false = ((X0 @ X1)))) ) | ~spl594_642),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f6949])).
% 13.65/2.32 thf(f7179,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o)] : (($false = $true) | (((sP33 @ X0)) != $true)) ) | ~spl594_642),
% 13.65/2.32 inference(backward_demodulation,[],[f468,f7123])).
% 13.65/2.32 thf(f7205,plain,(
% 13.65/2.32 ( ! [X2 : term,X0 : (term > $o),X1 : term] : ((((X0 @ X1)) != $true) | (((sP33 @ X0)) = $true) | (((X0 @ X2)) != $true) | ($false = $true)) ) | ~spl594_642),
% 13.65/2.32 inference(backward_demodulation,[],[f471,f7123])).
% 13.65/2.32 thf(f7240,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o)] : ((((sP33 @ X0)) != $true)) ) | ~spl594_642),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f7179])).
% 13.65/2.32 thf(f7279,plain,(
% 13.65/2.32 ( ! [X2 : term,X0 : (term > $o),X1 : term] : ((((X0 @ X1)) != $true) | (((X0 @ X2)) != $true) | (((sP33 @ X0)) = $true)) ) | ~spl594_642),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f7205])).
% 13.65/2.32 thf(f7281,plain,(
% 13.65/2.32 ( ! [X0 : $o] : (($false = X0)) ) | ~spl594_642),
% 13.65/2.32 inference(forward_subsumption_resolution,[],[f7000,f980])).
% 13.65/2.32 thf(f7427,plain,(
% 13.65/2.32 ( ! [X2 : term,X0 : (term > $o),X1 : term] : ((((X0 @ X2)) != $true) | (((X0 @ X1)) != $true)) ) | ~spl594_642),
% 13.65/2.32 inference(forward_subsumption_resolution,[],[f7279,f7240])).
% 13.65/2.32 thf(f7477,plain,(
% 13.65/2.32 ( ! [X2 : term,X0 : (term > $o),X1 : term] : ((((X0 @ X1)) != $true) | (((X0 @ X2)) != $false)) ) | ~spl594_642),
% 13.65/2.32 inference(forward_demodulation,[],[f7427,f7281])).
% 13.65/2.32 thf(f7502,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o),X1 : term] : ((((X0 @ X1)) != $true)) ) | ~spl594_642),
% 13.65/2.32 inference(forward_subsumption_resolution,[],[f7477,f7281])).
% 13.65/2.32 thf(f7513,plain,(
% 13.65/2.32 ( ! [X0 : (term > $o),X1 : term] : (($false != ((X0 @ X1)))) ) | ~spl594_642),
% 13.65/2.32 inference(forward_demodulation,[],[f7502,f7281])).
% 13.65/2.32 thf(f7519,plain,(
% 13.65/2.32 $false | ~spl594_642),
% 13.65/2.32 inference(forward_subsumption_resolution,[],[f7513,f7281])).
% 13.65/2.32 thf(f7520,plain,(
% 13.65/2.32 ~spl594_642),
% 13.65/2.32 inference(avatar_contradiction_clause,[],[f7519])).
% 13.65/2.32 thf(f7550,plain,(
% 13.65/2.32 spl594_648 | spl594_643 | ~spl594_153),
% 13.65/2.32 inference(avatar_split_clause,[],[f5707,f1777,f4452,f4583])).
% 13.65/2.32 thf(f7560,plain,(
% 13.65/2.32 spl594_655 | spl594_653 | ~spl594_366),
% 13.65/2.32 inference(avatar_split_clause,[],[f4553,f2693,f4611,f4652])).
% 13.65/2.32 thf(f7615,plain,(
% 13.65/2.32 ($false = $true) | (~spl594_650 | ~spl594_655)),
% 13.65/2.32 inference(backward_demodulation,[],[f4596,f4654])).
% 13.65/2.32 thf(f7616,plain,(
% 13.65/2.32 $false | (~spl594_650 | ~spl594_655)),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f7615])).
% 13.65/2.32 thf(f7617,plain,(
% 13.65/2.32 ~spl594_650 | ~spl594_655),
% 13.65/2.32 inference(avatar_contradiction_clause,[],[f7616])).
% 13.65/2.32 thf(f7822,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ one)) = $false) | ($false = $true)) ) | (~spl594_237 | ~spl594_706)),
% 13.65/2.32 inference(forward_demodulation,[],[f6024,f6858])).
% 13.65/2.32 thf(f7823,plain,(
% 13.65/2.32 ( ! [X1 : (term > $o)] : ((((X1 @ one)) = $false)) ) | (~spl594_237 | ~spl594_706)),
% 13.65/2.32 inference(trivial_inequality_removal,[],[f7822])).
% 13.65/2.32 thf(f7851,plain,(
% 13.65/2.32 spl594_653 | ~spl594_237 | ~spl594_706),
% 13.65/2.32 inference(avatar_split_clause,[],[f7823,f6120,f2138,f4611])).
% 13.65/2.32 cnf(s103, plain, ~spl594_152 | spl594_153, inference(sat_conversion,[],[f1779])).
% 13.65/2.32 cnf(s143, plain, spl594_152 | spl594_198, inference(sat_conversion,[],[f1972])).
% 13.65/2.32 cnf(s174, plain, spl594_237 | spl594_238, inference(sat_conversion,[],[f2144])).
% 13.65/2.32 cnf(s175, plain, spl594_238 | spl594_239, inference(sat_conversion,[],[f2148])).
% 13.65/2.32 cnf(s300, plain, spl594_240 | spl594_366, inference(sat_conversion,[],[f2695])).
% 13.65/2.32 cnf(s301, plain, spl594_240 | spl594_367, inference(sat_conversion,[],[f2699])).
% 13.65/2.32 cnf(s640, plain, ~spl594_367 | spl594_643 | spl594_650, inference(sat_conversion,[],[f4597])).
% 13.65/2.32 cnf(s666, plain, ~spl594_238 | ~spl594_240, inference(sat_conversion,[],[f4951])).
% 13.65/2.32 cnf(s689, plain, ~spl594_643, inference(sat_conversion,[],[f5737])).
% 13.65/2.32 cnf(s721, plain, ~spl594_239 | spl594_643 | spl594_706, inference(sat_conversion,[],[f6123])).
% 13.65/2.32 cnf(s736, plain, spl594_642 | ~spl594_648 | ~spl594_653, inference(sat_conversion,[],[f6309])).
% 13.65/2.32 cnf(s759, plain, ~spl594_198 | ~spl594_653, inference(sat_conversion,[],[f6909])).
% 13.65/2.32 cnf(s867, plain, ~spl594_642, inference(sat_conversion,[],[f7520])).
% 13.65/2.32 cnf(s870, plain, ~spl594_153 | spl594_643 | spl594_648, inference(sat_conversion,[],[f7550])).
% 13.65/2.32 cnf(s872, plain, ~spl594_366 | spl594_653 | spl594_655, inference(sat_conversion,[],[f7560])).
% 13.65/2.32 cnf(s874, plain, ~spl594_650 | ~spl594_655, inference(sat_conversion,[],[f7617])).
% 13.65/2.32 cnf(s909, plain, ~spl594_237 | spl594_653 | ~spl594_706, inference(sat_conversion,[],[f7851])).
% 13.65/2.32 cnf(s912, plain, ~spl594_648 | ~spl594_653, inference(rat,[],[s736,s867])).
% 13.65/2.32 cnf(s917, plain, ~spl594_367 | spl594_650, inference(rat,[],[s640,s689])).
% 13.65/2.32 cnf(s1070, plain, spl594_240 | spl594_653, inference(rat,[],[s874,s872,s917,s300,s301])).
% 13.65/2.32 cnf(s1071, plain, spl594_653, inference(rat,[],[s909,s721,s174,s175,s666,s1070,s689])).
% 13.65/2.32 cnf(s1072, plain, ~spl594_198, inference(rat,[],[s759,s1071])).
% 13.65/2.32 cnf(s1074, plain, ~spl594_648, inference(rat,[],[s912,s1071])).
% 13.65/2.32 cnf(s1075, plain, spl594_152, inference(rat,[],[s143,s1072])).
% 13.65/2.32 cnf(s1078, plain, ~spl594_153, inference(rat,[],[s870,s689,s1074])).
% 13.65/2.32 cnf(s1080, plain, $false, inference(rat,[],[s103,s1078,s1075])).
% 13.65/2.32 thf(f7862,plain,(
% 13.65/2.32 $false),
% 13.65/2.32 inference(avatar_sat_refutation,[],[s1080])).
% 13.65/2.32 % SZS output end Proof for theBenchmark
% 13.65/2.32 % (3714579)------------------------------
% 13.65/2.32 % (3714579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 13.65/2.32 % (3714579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.65/2.32 % (3714579)CaDiCaL version: 2.1.3
% 13.65/2.32 % (3714579)Termination reason: Refutation
% 13.65/2.32 % (3714579)Time elapsed: 0.412 s
% 13.65/2.32 % (3714579)Peak memory usage: 19 MB
% 13.65/2.32 % (3714579)Instructions burned: 889 (million)
% 13.65/2.32 % (3714364)Success in time 2.043 s
% 13.65/2.32 % Vampire exiting
%------------------------------------------------------------------------------