%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX162^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:36 AM UTC 2026
% Result : Theorem 5.43s 1.20s
% Output : Refutation 5.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX162^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n001.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 16:15:06 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running higher-order theorem proving
% 0.25/0.31 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
% 0.89/0.51 % (1435636)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.89/0.51 % (1435647)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=991069330: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)
% 0.89/0.51 % (1435644)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2583627360:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.89/0.51 % (1435650)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.89/0.51 % (1435650)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
% 0.89/0.51 % (1435646)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=707484360:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.89/0.51 % (1435648)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=839560808:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.89/0.51 % (1435649)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4250252555:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.89/0.51 % (1435650)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=177429138:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.89/0.51 % (1435646)Instruction limit reached!
% 0.89/0.51 % (1435646)------------------------------
% 0.89/0.51 % (1435646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.51 % (1435646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.51 % (1435646)CaDiCaL version: 2.1.3
% 0.89/0.51 % (1435646)Termination reason: Instruction limit
% 0.89/0.51 % (1435646)Termination phase: shuffling
% 0.89/0.51 % (1435646)Time elapsed: 0.003 s
% 0.89/0.51 % (1435646)Peak memory usage: 9 MB
% 0.89/0.51 % (1435646)Instructions burned: 3 (million)
% 0.89/0.51 % (1435645)lrs+10_16_si=on:nwc=1.5:random_seed=459794363:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.89/0.51 % (1435648)Instruction limit reached!
% 0.89/0.51 % (1435648)------------------------------
% 0.89/0.51 % (1435648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.51 % (1435648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.51 % (1435648)CaDiCaL version: 2.1.3
% 0.89/0.51 % (1435648)Termination reason: Instruction limit
% 0.89/0.51 % (1435648)Termination phase: shuffling
% 0.89/0.51 % (1435648)Time elapsed: 0.020 s
% 0.89/0.51 % (1435648)Peak memory usage: 10 MB
% 0.89/0.51 % (1435648)Instructions burned: 24 (million)
% 0.89/0.51 % (1435660)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1735494839:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.89/0.51 % (1435644)Instruction limit reached!
% 0.89/0.51 % (1435644)------------------------------
% 0.89/0.51 % (1435644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.51 % (1435644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.51 % (1435644)CaDiCaL version: 2.1.3
% 0.89/0.51 % (1435644)Termination reason: Instruction limit
% 0.89/0.51 % (1435644)Termination phase: Preprocessing 3
% 0.89/0.51 % (1435644)Time elapsed: 0.044 s
% 0.89/0.51 % (1435644)Peak memory usage: 13 MB
% 0.89/0.51 % (1435644)Instructions burned: 88 (million)
% 0.89/0.51 % (1435660)Instruction limit reached!
% 0.89/0.51 % (1435660)------------------------------
% 0.89/0.51 % (1435660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.51 % (1435660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.51 % (1435660)CaDiCaL version: 2.1.3
% 0.89/0.51 % (1435660)Termination reason: Instruction limit
% 0.89/0.51 % (1435660)Termination phase: shuffling
% 0.89/0.51 % (1435660)Time elapsed: 0.002 s
% 0.89/0.51 % (1435660)Peak memory usage: 10 MB
% 0.89/0.51 % (1435660)Instructions burned: 2 (million)
% 0.89/0.51 % (1435645)Instruction limit reached!
% 0.89/0.51 % (1435645)------------------------------
% 0.89/0.51 % (1435645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.58 % (1435645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.58 % (1435645)CaDiCaL version: 2.1.3
% 1.51/0.58 % (1435645)Termination reason: Instruction limit
% 1.51/0.58 % (1435645)Termination phase: shuffling
% 1.51/0.58 % (1435645)Time elapsed: 0.033 s
% 1.51/0.58 % (1435645)Peak memory usage: 10 MB
% 1.51/0.58 % (1435645)Instructions burned: 18 (million)
% 1.51/0.58 % (1435664)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.51/0.58 % (1435662)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=501850572:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.51/0.58 % (1435664)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2665439782:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.51/0.58 % (1435662)Instruction limit reached!
% 1.51/0.58 % (1435662)------------------------------
% 1.51/0.58 % (1435662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.58 % (1435662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.58 % (1435662)CaDiCaL version: 2.1.3
% 1.51/0.58 % (1435662)Termination reason: Instruction limit
% 1.51/0.58 % (1435662)Termination phase: shuffling
% 1.51/0.58 % (1435662)Time elapsed: 0.005 s
% 1.51/0.58 % (1435662)Peak memory usage: 9 MB
% 1.51/0.58 % (1435662)Instructions burned: 6 (million)
% 1.51/0.58 % (1435664)Instruction limit reached!
% 1.51/0.58 % (1435664)------------------------------
% 1.51/0.58 % (1435664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.58 % (1435664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.58 % (1435664)CaDiCaL version: 2.1.3
% 1.51/0.58 % (1435664)Termination reason: Instruction limit
% 1.51/0.58 % (1435664)Termination phase: shuffling
% 1.51/0.58 % (1435664)Time elapsed: 0.005 s
% 1.51/0.58 % (1435664)Peak memory usage: 9 MB
% 1.51/0.58 % (1435664)Instructions burned: 8 (million)
% 1.51/0.58 % (1435649)Instruction limit reached!
% 1.51/0.58 % (1435649)------------------------------
% 1.51/0.58 % (1435649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.58 % (1435649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.58 % (1435649)CaDiCaL version: 2.1.3
% 1.51/0.58 % (1435649)Termination reason: Instruction limit
% 1.51/0.58 % (1435649)Termination phase: Preprocessing 3
% 1.51/0.58 % (1435649)Time elapsed: 0.063 s
% 1.51/0.58 % (1435649)Peak memory usage: 12 MB
% 1.51/0.58 % (1435649)Instructions burned: 76 (million)
% 1.51/0.58 % (1435665)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3087088822:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.51/0.58 % (1435666)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.51/0.58 % (1435666)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.51/0.58 % (1435666)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2445347052:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.51/0.58 % (1435665)Instruction limit reached!
% 1.51/0.58 % (1435665)------------------------------
% 1.51/0.58 % (1435665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.58 % (1435665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.58 % (1435665)CaDiCaL version: 2.1.3
% 1.51/0.58 % (1435665)Termination reason: Instruction limit
% 1.51/0.58 % (1435665)Termination phase: shuffling
% 1.51/0.58 % (1435665)Time elapsed: 0.011 s
% 1.51/0.58 % (1435665)Peak memory usage: 10 MB
% 1.51/0.58 % (1435665)Instructions burned: 13 (million)
% 1.51/0.58 % (1435670)lrs+10_1_si=on:cs=on:random_seed=2926097641:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.51/0.58 % (1435669)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=2157803696:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.51/0.58 % (1435671)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.93/0.63 % (1435670)Instruction limit reached!
% 1.93/0.63 % (1435670)------------------------------
% 1.93/0.63 % (1435670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435670)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435670)Termination reason: Instruction limit
% 1.93/0.63 % (1435670)Termination phase: shuffling
% 1.93/0.63 % (1435670)Time elapsed: 0.007 s
% 1.93/0.63 % (1435670)Peak memory usage: 10 MB
% 1.93/0.63 % (1435670)Instructions burned: 8 (million)
% 1.93/0.63 % (1435666)Instruction limit reached!
% 1.93/0.63 % (1435666)------------------------------
% 1.93/0.63 % (1435666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435671)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=3314798288:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.93/0.63 % (1435666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435666)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435666)Termination reason: Instruction limit
% 1.93/0.63 % (1435666)Termination phase: shuffling
% 1.93/0.63 % (1435666)Time elapsed: 0.021 s
% 1.93/0.63 % (1435666)Peak memory usage: 10 MB
% 1.93/0.63 % (1435666)Instructions burned: 29 (million)
% 1.93/0.63 % (1435671)Instruction limit reached!
% 1.93/0.63 % (1435671)------------------------------
% 1.93/0.63 % (1435671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435671)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435671)Termination reason: Instruction limit
% 1.93/0.63 % (1435671)Termination phase: shuffling
% 1.93/0.63 % (1435671)Time elapsed: 0.002 s
% 1.93/0.63 % (1435671)Peak memory usage: 9 MB
% 1.93/0.63 % (1435671)Instructions burned: 2 (million)
% 1.93/0.63 % (1435675)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1949656498:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.93/0.63 % (1435678)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1835433535:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.93/0.63 % (1435680)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2059472710:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.93/0.63 % (1435650)Instruction limit reached!
% 1.93/0.63 % (1435650)------------------------------
% 1.93/0.63 % (1435650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435650)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435650)Termination reason: Instruction limit
% 1.93/0.63 % (1435650)Termination phase: Property scanning
% 1.93/0.63 % (1435650)Time elapsed: 0.130 s
% 1.93/0.63 % (1435650)Peak memory usage: 13 MB
% 1.93/0.63 % (1435650)Instructions burned: 157 (million)
% 1.93/0.63 % (1435681)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3613080024:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.93/0.63 % (1435675)Instruction limit reached!
% 1.93/0.63 % (1435675)------------------------------
% 1.93/0.63 % (1435675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435675)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435675)Termination reason: Instruction limit
% 1.93/0.63 % (1435675)Termination phase: Clausification
% 1.93/0.63 % (1435675)Time elapsed: 0.031 s
% 1.93/0.63 % (1435675)Peak memory usage: 11 MB
% 1.93/0.63 % (1435675)Instructions burned: 39 (million)
% 1.93/0.63 % (1435681)Instruction limit reached!
% 1.93/0.63 % (1435681)------------------------------
% 1.93/0.63 % (1435681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.93/0.63 % (1435681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.93/0.63 % (1435681)CaDiCaL version: 2.1.3
% 1.93/0.63 % (1435681)Termination reason: Instruction limit
% 1.93/0.63 % (1435681)Termination phase: shuffling
% 1.93/0.63 % (1435681)Time elapsed: 0.013 s
% 2.41/0.70 % (1435681)Peak memory usage: 10 MB
% 2.41/0.70 % (1435681)Instructions burned: 15 (million)
% 2.41/0.70 % (1435680)Instruction limit reached!
% 2.41/0.70 % (1435680)------------------------------
% 2.41/0.70 % (1435680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.70 % (1435680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.70 % (1435680)CaDiCaL version: 2.1.3
% 2.41/0.70 % (1435680)Termination reason: Instruction limit
% 2.41/0.70 % (1435680)Termination phase: Property scanning
% 2.41/0.70 % (1435680)Time elapsed: 0.021 s
% 2.41/0.70 % (1435680)Peak memory usage: 10 MB
% 2.41/0.70 % (1435680)Instructions burned: 25 (million)
% 2.41/0.70 % (1435669)Instruction limit reached!
% 2.41/0.70 % (1435669)------------------------------
% 2.41/0.70 % (1435669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.70 % (1435669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.70 % (1435669)CaDiCaL version: 2.1.3
% 2.41/0.70 % (1435669)Termination reason: Instruction limit
% 2.41/0.70 % (1435669)Termination phase: Saturation
% 2.41/0.70 % (1435669)Time elapsed: 0.069 s
% 2.41/0.70 % (1435669)Peak memory usage: 12 MB
% 2.41/0.70 % (1435669)Instructions burned: 87 (million)
% 2.41/0.70 % (1435687)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=279359887:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.41/0.70 % (1435689)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1404120054:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.41/0.70 % (1435691)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=764371666:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.41/0.70 % (1435690)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1787596688: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)
% 2.41/0.70 % (1435690)Instruction limit reached!
% 2.41/0.70 % (1435690)------------------------------
% 2.41/0.70 % (1435690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.70 % (1435690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.70 % (1435690)CaDiCaL version: 2.1.3
% 2.41/0.70 % (1435690)Termination reason: Instruction limit
% 2.41/0.70 % (1435690)Termination phase: shuffling
% 2.41/0.70 % (1435690)Time elapsed: 0.003 s
% 2.41/0.70 % (1435690)Peak memory usage: 10 MB
% 2.41/0.70 % (1435690)Instructions burned: 2 (million)
% 2.41/0.70 % (1435689)Instruction limit reached!
% 2.41/0.70 % (1435689)------------------------------
% 2.41/0.70 % (1435689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.70 % (1435689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.70 % (1435689)CaDiCaL version: 2.1.3
% 2.41/0.70 % (1435689)Termination reason: Instruction limit
% 2.41/0.70 % (1435689)Termination phase: shuffling
% 2.41/0.70 % (1435689)Time elapsed: 0.012 s
% 2.41/0.70 % (1435689)Peak memory usage: 10 MB
% 2.41/0.70 % (1435689)Instructions burned: 14 (million)
% 2.41/0.70 % (1435691)Instruction limit reached!
% 2.41/0.70 % (1435691)------------------------------
% 2.41/0.70 % (1435691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.41/0.70 % (1435691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/0.70 % (1435691)CaDiCaL version: 2.1.3
% 2.41/0.70 % (1435691)Termination reason: Instruction limit
% 2.41/0.70 % (1435691)Termination phase: shuffling
% 2.41/0.70 % (1435691)Time elapsed: 0.014 s
% 2.41/0.70 % (1435691)Peak memory usage: 10 MB
% 2.41/0.70 % (1435691)Instructions burned: 27 (million)
% 2.41/0.70 % (1435693)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3375486475:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.41/0.70 % (1435702)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.41/0.70 % (1435702)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=1583600236:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.41/0.70 % (1435700)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=221313327:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.63/0.79 % (1435693)Instruction limit reached!
% 2.63/0.79 % (1435693)------------------------------
% 2.63/0.79 % (1435693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435693)CaDiCaL version: 2.1.3
% 2.63/0.79 % (1435693)Termination reason: Instruction limit
% 2.63/0.79 % (1435693)Termination phase: shuffling
% 2.63/0.79 % (1435693)Time elapsed: 0.021 s
% 2.63/0.79 % (1435693)Peak memory usage: 10 MB
% 2.63/0.79 % (1435693)Instructions burned: 23 (million)
% 2.63/0.79 % (1435701)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.63/0.79 % (1435701)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.63/0.79 % (1435702)Instruction limit reached!
% 2.63/0.79 % (1435702)------------------------------
% 2.63/0.79 % (1435702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435702)CaDiCaL version: 2.1.3
% 2.63/0.79 % (1435702)Termination reason: Instruction limit
% 2.63/0.79 % (1435702)Termination phase: shuffling
% 2.63/0.79 % (1435702)Time elapsed: 0.008 s
% 2.63/0.79 % (1435702)Peak memory usage: 10 MB
% 2.63/0.79 % (1435702)Instructions burned: 8 (million)
% 2.63/0.79 % (1435701)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=570433761:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.63/0.79 % (1435701)Instruction limit reached!
% 2.63/0.79 % (1435701)------------------------------
% 2.63/0.79 % (1435701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435701)CaDiCaL version: 2.1.3
% 2.63/0.79 % (1435701)Termination reason: Instruction limit
% 2.63/0.79 % (1435701)Termination phase: shuffling
% 2.63/0.79 % (1435701)Time elapsed: 0.012 s
% 2.63/0.79 % (1435701)Peak memory usage: 10 MB
% 2.63/0.79 % (1435701)Instructions burned: 14 (million)
% 2.63/0.79 % (1435710)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=1327530412:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.63/0.79 % (1435712)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=218973850:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.63/0.79 % (1435713)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=913125916:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.63/0.79 % (1435712)Instruction limit reached!
% 2.63/0.79 % (1435712)------------------------------
% 2.63/0.79 % (1435712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435712)CaDiCaL version: 2.1.3
% 2.63/0.79 % (1435712)Termination reason: Instruction limit
% 2.63/0.79 % (1435712)Termination phase: shuffling
% 2.63/0.79 % (1435712)Time elapsed: 0.007 s
% 2.63/0.79 % (1435712)Peak memory usage: 10 MB
% 2.63/0.79 % (1435712)Instructions burned: 7 (million)
% 2.63/0.79 % (1435700)Instruction limit reached!
% 2.63/0.79 % (1435700)------------------------------
% 2.63/0.79 % (1435700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435700)CaDiCaL version: 2.1.3
% 2.63/0.79 % (1435700)Termination reason: Instruction limit
% 2.63/0.79 % (1435700)Termination phase: Preprocessing 3
% 2.63/0.79 % (1435700)Time elapsed: 0.051 s
% 2.63/0.79 % (1435700)Peak memory usage: 12 MB
% 2.63/0.79 % (1435700)Instructions burned: 60 (million)
% 2.63/0.79 % (1435710)Instruction limit reached!
% 2.63/0.79 % (1435710)------------------------------
% 2.63/0.79 % (1435710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.63/0.79 % (1435710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.79 % (1435710)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435710)Termination reason: Instruction limit
% 3.04/0.89 % (1435710)Termination phase: shuffling
% 3.04/0.89 % (1435710)Time elapsed: 0.016 s
% 3.04/0.89 % (1435710)Peak memory usage: 10 MB
% 3.04/0.89 % (1435710)Instructions burned: 31 (million)
% 3.04/0.89 % (1435713)Instruction limit reached!
% 3.04/0.89 % (1435713)------------------------------
% 3.04/0.89 % (1435713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.89 % (1435713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.89 % (1435713)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435713)Termination reason: Instruction limit
% 3.04/0.89 % (1435713)Termination phase: shuffling
% 3.04/0.89 % (1435713)Time elapsed: 0.018 s
% 3.04/0.89 % (1435713)Peak memory usage: 10 MB
% 3.04/0.89 % (1435713)Instructions burned: 24 (million)
% 3.04/0.89 % (1435647)Instruction limit reached!
% 3.04/0.89 % (1435647)------------------------------
% 3.04/0.89 % (1435647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.89 % (1435647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.89 % (1435647)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435647)Termination reason: Instruction limit
% 3.04/0.89 % (1435647)Termination phase: Saturation
% 3.04/0.89 % (1435647)Time elapsed: 0.299 s
% 3.04/0.89 % (1435647)Peak memory usage: 18 MB
% 3.04/0.89 % (1435647)Instructions burned: 635 (million)
% 3.04/0.89 % (1435722)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3009199853:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2996 on theBenchmark for (2996ds/143Mi)
% 3.04/0.89 % (1435719)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1786836554:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/20Mi)
% 3.04/0.89 % (1435721)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1418825688:i=1240:rtra=on:ixr=off_2996 on theBenchmark for (2996ds/1240Mi)
% 3.04/0.89 % (1435725)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1116609722:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 3.04/0.89 % (1435723)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=940895908:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/193Mi)
% 3.04/0.89 % (1435719)Instruction limit reached!
% 3.04/0.89 % (1435719)------------------------------
% 3.04/0.89 % (1435719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.89 % (1435719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.89 % (1435719)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435719)Termination reason: Instruction limit
% 3.04/0.89 % (1435719)Termination phase: shuffling
% 3.04/0.89 % (1435719)Time elapsed: 0.017 s
% 3.04/0.89 % (1435719)Peak memory usage: 10 MB
% 3.04/0.89 % (1435719)Instructions burned: 20 (million)
% 3.04/0.89 % (1435725)Instruction limit reached!
% 3.04/0.89 % (1435725)------------------------------
% 3.04/0.89 % (1435725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.89 % (1435725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.89 % (1435725)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435725)Termination reason: Instruction limit
% 3.04/0.89 % (1435725)Termination phase: Naming
% 3.04/0.89 % (1435725)Time elapsed: 0.021 s
% 3.04/0.89 % (1435725)Peak memory usage: 11 MB
% 3.04/0.89 % (1435725)Instructions burned: 44 (million)
% 3.04/0.89 % (1435732)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 3.04/0.89 % (1435732)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2441767976:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2996 on theBenchmark for (2996ds/7Mi)
% 3.04/0.89 % (1435678)Instruction limit reached!
% 3.04/0.89 % (1435678)------------------------------
% 3.04/0.89 % (1435678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.04/0.89 % (1435678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/0.89 % (1435678)CaDiCaL version: 2.1.3
% 3.04/0.89 % (1435678)Termination reason: Instruction limit
% 3.04/0.89 % (1435678)Termination phase: Saturation
% 3.04/0.89 % (1435678)Time elapsed: 0.208 s
% 3.04/0.89 % (1435678)Peak memory usage: 15 MB
% 3.04/0.89 % (1435678)Instructions burned: 249 (million)
% 3.04/0.89 % (1435732)Instruction limit reached!
% 3.04/0.89 % (1435732)------------------------------
% 3.04/0.89 % (1435732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.16/1.05 % (1435732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.05 % (1435732)CaDiCaL version: 2.1.3
% 5.16/1.05 % (1435732)Termination reason: Instruction limit
% 5.16/1.05 % (1435732)Termination phase: shuffling
% 5.16/1.05 % (1435732)Time elapsed: 0.003 s
% 5.16/1.05 % (1435732)Peak memory usage: 10 MB
% 5.16/1.05 % (1435732)Instructions burned: 7 (million)
% 5.16/1.05 % (1435734)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=378490428:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/181Mi)
% 5.16/1.05 % (1435737)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 5.16/1.05 % (1435736)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=4100770909:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2996 on theBenchmark for (2996ds/169Mi)
% 5.16/1.05 % (1435737)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3851293396:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 5.16/1.05 % (1435737)Instruction limit reached!
% 5.16/1.05 % (1435737)------------------------------
% 5.16/1.05 % (1435737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.16/1.05 % (1435737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.05 % (1435737)CaDiCaL version: 2.1.3
% 5.16/1.05 % (1435737)Termination reason: Instruction limit
% 5.16/1.05 % (1435737)Termination phase: shuffling
% 5.16/1.05 % (1435737)Time elapsed: 0.003 s
% 5.16/1.05 % (1435737)Peak memory usage: 9 MB
% 5.16/1.05 % (1435737)Instructions burned: 6 (million)
% 5.16/1.05 % (1435734)Refutation not found, incomplete strategy
% 5.16/1.05 % (1435734)------------------------------
% 5.16/1.05 % (1435734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.16/1.05 % (1435734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.05 % (1435734)CaDiCaL version: 2.1.3
% 5.16/1.05 % (1435734)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.05 % (1435734)Time elapsed: 0.026 s
% 5.16/1.05 % (1435734)Peak memory usage: 13 MB
% 5.16/1.05 % (1435734)Instructions burned: 49 (million)
% 5.16/1.05 % (1435734)------------------------------
% 5.16/1.05 % (1435734)------------------------------
% 5.16/1.05 % (1435722)Instruction limit reached!
% 5.16/1.05 % (1435722)------------------------------
% 5.16/1.05 % (1435722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.16/1.05 % (1435722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.05 % (1435722)CaDiCaL version: 2.1.3
% 5.16/1.05 % (1435722)Termination reason: Instruction limit
% 5.16/1.05 % (1435722)Termination phase: Function definition elimination
% 5.16/1.05 % (1435722)Time elapsed: 0.100 s
% 5.16/1.05 % (1435722)Peak memory usage: 12 MB
% 5.16/1.05 % (1435722)Instructions burned: 143 (million)
% 5.16/1.05 % (1435743)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3979188336:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2995 on theBenchmark for (2995ds/22Mi)
% 5.16/1.05 % (1435743)Instruction limit reached!
% 5.16/1.05 % (1435743)------------------------------
% 5.16/1.05 % (1435743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.16/1.05 % (1435743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.05 % (1435743)CaDiCaL version: 2.1.3
% 5.16/1.05 % (1435743)Termination reason: Instruction limit
% 5.16/1.05 % (1435743)Termination phase: shuffling
% 5.16/1.05 % (1435743)Time elapsed: 0.010 s
% 5.16/1.05 % (1435743)Peak memory usage: 10 MB
% 5.16/1.05 % (1435743)Instructions burned: 23 (million)
% 5.16/1.05 % (1435745)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2374962252:i=19:add=on:rtra=on_2995 on theBenchmark for (2995ds/19Mi)
% 5.16/1.05 % (1435748)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=3213348830:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/316Mi)
% 5.16/1.05 % (1435751)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=2648293037:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2995 on theBenchmark for (2995ds/853Mi)
% 5.63/1.16 % (1435745)Instruction limit reached!
% 5.63/1.16 % (1435745)------------------------------
% 5.63/1.16 % (1435745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.16 % (1435745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.16 % (1435745)CaDiCaL version: 2.1.3
% 5.63/1.16 % (1435745)Termination reason: Instruction limit
% 5.63/1.16 % (1435745)Termination phase: shuffling
% 5.63/1.16 % (1435745)Time elapsed: 0.016 s
% 5.63/1.16 % (1435745)Peak memory usage: 10 MB
% 5.63/1.16 % (1435745)Instructions burned: 20 (million)
% 5.63/1.16 % (1435687)Instruction limit reached!
% 5.63/1.16 % (1435687)------------------------------
% 5.63/1.16 % (1435687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.16 % (1435687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.16 % (1435687)CaDiCaL version: 2.1.3
% 5.63/1.16 % (1435687)Termination reason: Instruction limit
% 5.63/1.16 % (1435687)Termination phase: Saturation
% 5.63/1.16 % (1435687)Time elapsed: 0.272 s
% 5.63/1.16 % (1435687)Peak memory usage: 16 MB
% 5.63/1.16 % (1435687)Instructions burned: 327 (million)
% 5.63/1.16 % (1435759)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=586157916:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 5.63/1.16 % (1435723)Instruction limit reached!
% 5.63/1.16 % (1435723)------------------------------
% 5.63/1.16 % (1435723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.16 % (1435723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.16 % (1435723)CaDiCaL version: 2.1.3
% 5.63/1.16 % (1435723)Termination reason: Instruction limit
% 5.63/1.16 % (1435723)Termination phase: Property scanning
% 5.63/1.16 % (1435723)Time elapsed: 0.156 s
% 5.63/1.16 % (1435723)Peak memory usage: 13 MB
% 5.63/1.16 % (1435723)Instructions burned: 193 (million)
% 5.63/1.16 % (1435762)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3852151960:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 5.63/1.16 % (1435759)Instruction limit reached!
% 5.63/1.16 % (1435759)------------------------------
% 5.63/1.16 % (1435759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.16 % (1435759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.16 % (1435759)CaDiCaL version: 2.1.3
% 5.63/1.16 % (1435759)Termination reason: Instruction limit
% 5.63/1.16 % (1435759)Termination phase: SInE selection
% 5.63/1.16 % (1435759)Time elapsed: 0.036 s
% 5.63/1.16 % (1435759)Peak memory usage: 10 MB
% 5.63/1.16 % (1435759)Instructions burned: 45 (million)
% 5.63/1.16 % (1435736)Instruction limit reached!
% 5.63/1.16 % (1435736)------------------------------
% 5.63/1.16 % (1435736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.16 % (1435736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.16 % (1435736)CaDiCaL version: 2.1.3
% 5.63/1.16 % (1435736)Termination reason: Instruction limit
% 5.63/1.17 % (1435736)Termination phase: Property scanning
% 5.63/1.17 % (1435736)Time elapsed: 0.137 s
% 5.63/1.17 % (1435736)Peak memory usage: 13 MB
% 5.63/1.17 % (1435736)Instructions burned: 169 (million)
% 5.63/1.17 % (1435764)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=757559997:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2994 on theBenchmark for (2994ds/21Mi)
% 5.63/1.17 % (1435766)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 5.63/1.17 % (1435764)Instruction limit reached!
% 5.63/1.17 % (1435764)------------------------------
% 5.63/1.17 % (1435764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.63/1.17 % (1435764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.17 % (1435764)CaDiCaL version: 2.1.3
% 5.63/1.17 % (1435764)Termination reason: Instruction limit
% 5.63/1.17 % (1435764)Termination phase: shuffling
% 5.63/1.17 % (1435764)Time elapsed: 0.017 s
% 5.63/1.17 % (1435764)Peak memory usage: 10 MB
% 5.63/1.17 % (1435764)Instructions burned: 21 (million)
% 5.43/1.20 % (1435766)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3563496439:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/200Mi)
% 5.43/1.20 % (1435770)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1195216879:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2994 on theBenchmark for (2994ds/13Mi)
% 5.43/1.20 % (1435770)Instruction limit reached!
% 5.43/1.20 % (1435770)------------------------------
% 5.43/1.20 % (1435770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435770)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435770)Termination reason: Instruction limit
% 5.43/1.20 % (1435770)Termination phase: shuffling
% 5.43/1.20 % (1435770)Time elapsed: 0.015 s
% 5.43/1.20 % (1435770)Peak memory usage: 10 MB
% 5.43/1.20 % (1435770)Instructions burned: 14 (million)
% 5.43/1.20 % (1435771)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=564564822:i=66:s2at=3:nm=2:rtra=on:rawr=on_2994 on theBenchmark for (2994ds/66Mi)
% 5.43/1.20 % (1435777)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1875054733:i=51:fsr=off:rtra=on_2994 on theBenchmark for (2994ds/51Mi)
% 5.43/1.20 % (1435771)Instruction limit reached!
% 5.43/1.20 % (1435771)------------------------------
% 5.43/1.20 % (1435771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435771)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435771)Termination reason: Instruction limit
% 5.43/1.20 % (1435771)Termination phase: SInE selection
% 5.43/1.20 % (1435771)Time elapsed: 0.052 s
% 5.43/1.20 % (1435771)Peak memory usage: 11 MB
% 5.43/1.20 % (1435771)Instructions burned: 67 (million)
% 5.43/1.20 % (1435777)Instruction limit reached!
% 5.43/1.20 % (1435777)------------------------------
% 5.43/1.20 % (1435777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435777)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435777)Termination reason: Instruction limit
% 5.43/1.20 % (1435777)Termination phase: Preprocessing 3
% 5.43/1.20 % (1435777)Time elapsed: 0.043 s
% 5.43/1.20 % (1435777)Peak memory usage: 11 MB
% 5.43/1.20 % (1435777)Instructions burned: 52 (million)
% 5.43/1.20 % (1435748)Instruction limit reached!
% 5.43/1.20 % (1435748)------------------------------
% 5.43/1.20 % (1435748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435748)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435748)Termination reason: Instruction limit
% 5.43/1.20 % (1435748)Termination phase: Saturation
% 5.43/1.20 % (1435748)Time elapsed: 0.209 s
% 5.43/1.20 % (1435748)Peak memory usage: 15 MB
% 5.43/1.20 % (1435748)Instructions burned: 316 (million)
% 5.43/1.20 % (1435786)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2126491201:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/31Mi)
% 5.43/1.20 % (1435787)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2974248769:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2993 on theBenchmark for (2993ds/137Mi)
% 5.43/1.20 % (1435789)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=2630649713:cond=on:i=34:hud=10:nm=10:rtra=on_2993 on theBenchmark for (2993ds/34Mi)
% 5.43/1.20 % (1435786)Instruction limit reached!
% 5.43/1.20 % (1435786)------------------------------
% 5.43/1.20 % (1435786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435786)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435786)Termination reason: Instruction limit
% 5.43/1.20 % (1435786)Termination phase: shuffling
% 5.43/1.20 % (1435786)Time elapsed: 0.029 s
% 5.43/1.20 % (1435786)Peak memory usage: 10 MB
% 5.43/1.20 % (1435786)Instructions burned: 31 (million)
% 5.43/1.20 % (1435762)Refutation not found, incomplete strategy
% 5.43/1.20 % (1435762)------------------------------
% 5.43/1.20 % (1435762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435762)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435762)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.20 % (1435762)Time elapsed: 0.210 s
% 5.43/1.20 % (1435762)Peak memory usage: 16 MB
% 5.43/1.20 % (1435762)Instructions burned: 274 (million)
% 5.43/1.20 % (1435762)------------------------------
% 5.43/1.20 % (1435762)------------------------------
% 5.43/1.20 % (1435766)Instruction limit reached!
% 5.43/1.20 % (1435766)------------------------------
% 5.43/1.20 % (1435766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435766)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435766)Termination reason: Instruction limit
% 5.43/1.20 % (1435766)Termination phase: Saturation
% 5.43/1.20 % (1435766)Time elapsed: 0.157 s
% 5.43/1.20 % (1435766)Peak memory usage: 13 MB
% 5.43/1.20 % (1435766)Instructions burned: 200 (million)
% 5.43/1.20 % (1435789)Instruction limit reached!
% 5.43/1.20 % (1435789)------------------------------
% 5.43/1.20 % (1435789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435789)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435789)Termination reason: Instruction limit
% 5.43/1.20 % (1435789)Termination phase: Property scanning
% 5.43/1.20 % (1435789)Time elapsed: 0.027 s
% 5.43/1.20 % (1435789)Peak memory usage: 10 MB
% 5.43/1.20 % (1435789)Instructions burned: 34 (million)
% 5.43/1.20 % (1435796)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 5.43/1.20 % (1435795)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=4049341913:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2992 on theBenchmark for (2992ds/67Mi)
% 5.43/1.20 % (1435796)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3619466842:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2992 on theBenchmark for (2992ds/180Mi)
% 5.43/1.20 % (1435799)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2984566526:cond=on:i=96:bd=all:rtra=on_2992 on theBenchmark for (2992ds/96Mi)
% 5.43/1.20 % (1435798)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=2667826457:st=2:i=246:sd=3:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/246Mi)
% 5.43/1.20 % (1435751) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1435636-1435751"...
% 5.43/1.20 % (1435795)Instruction limit reached!
% 5.43/1.20 % (1435795)------------------------------
% 5.43/1.20 % (1435795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435795)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435795)Termination reason: Instruction limit
% 5.43/1.20 % (1435795)Termination phase: Preprocessing 3
% 5.43/1.20 % (1435795)Time elapsed: 0.057 s
% 5.43/1.20 % (1435795)Peak memory usage: 12 MB
% 5.43/1.20 % (1435795)Instructions burned: 68 (million)
% 5.43/1.20 % (1435787)Instruction limit reached!
% 5.43/1.20 % (1435787)------------------------------
% 5.43/1.20 % (1435787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435787)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435787)Termination reason: Instruction limit
% 5.43/1.20 % (1435787)Termination phase: Property scanning
% 5.43/1.20 % (1435787)Time elapsed: 0.112 s
% 5.43/1.20 % (1435787)Peak memory usage: 13 MB
% 5.43/1.20 % (1435787)Instructions burned: 137 (million)
% 5.43/1.20 % (1435807)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=1941567459:i=427:sd=1:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/427Mi)
% 5.43/1.20 % (1435799)Instruction limit reached!
% 5.43/1.20 % (1435799)------------------------------
% 5.43/1.20 % (1435799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435799)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435799)Termination reason: Instruction limit
% 5.43/1.20 % (1435799)Termination phase: Property scanning
% 5.43/1.20 % (1435799)Time elapsed: 0.080 s
% 5.43/1.20 % (1435799)Peak memory usage: 12 MB
% 5.43/1.20 % (1435799)Instructions burned: 96 (million)
% 5.43/1.20 % (1435810)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1326797999:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/874Mi)
% 5.43/1.20 % (1435796)Instruction limit reached!
% 5.43/1.20 % (1435796)------------------------------
% 5.43/1.20 % (1435796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.20 % (1435796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.20 % (1435796)CaDiCaL version: 2.1.3
% 5.43/1.20 % (1435796)Termination reason: Instruction limit
% 5.43/1.20 % (1435796)Termination phase: Saturation
% 5.43/1.20 % (1435796)Time elapsed: 0.098 s
% 5.43/1.20 % (1435796)Peak memory usage: 12 MB
% 5.43/1.20 % (1435796)Instructions burned: 182 (million)
% 5.43/1.20 % (1435813)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=2912009220:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/515Mi)
% 5.43/1.20 % (1435751)...printing done.
% 5.43/1.20 % (1435751)Refutation found. Thanks to Tanya!
% 5.43/1.20 % SZS status Theorem for theBenchmark
% 5.43/1.20 % SZS output start Proof for theBenchmark
% 5.43/1.20 thf(type_def_5, type, term: $tType).
% 5.43/1.20 thf(type_def_6, type, subst: $tType).
% 5.43/1.20 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 5.43/1.20 thf(type_def_8, type, d_term: $tType).
% 5.43/1.20 thf(type_def_9, type, d_subst: $tType).
% 5.43/1.20 thf(func_def_0, type, one: term).
% 5.43/1.20 thf(func_def_1, type, ap: (term > term > term)).
% 5.43/1.20 thf(func_def_2, type, lam: (term > term)).
% 5.43/1.20 thf(func_def_3, type, sub: (term > subst > term)).
% 5.43/1.20 thf(func_def_4, type, id: subst).
% 5.43/1.20 thf(func_def_5, type, sh: subst).
% 5.43/1.20 thf(func_def_6, type, push: (term > subst > subst)).
% 5.43/1.20 thf(func_def_7, type, comp: (subst > subst > subst)).
% 5.43/1.20 thf(func_def_8, type, var: (term > $o)).
% 5.43/1.20 thf(func_def_9, type, pushprop_lem1v2: $o).
% 5.43/1.20 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 5.43/1.20 thf(func_def_11, type, axmap: $o).
% 5.43/1.20 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 5.43/1.20 thf(func_def_13, type, shinj: $o).
% 5.43/1.20 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 5.43/1.20 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 5.43/1.20 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 5.43/1.20 thf(func_def_17, type, induction2lem: $o).
% 5.43/1.20 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 5.43/1.20 thf(func_def_19, type, axvarshift: $o).
% 5.43/1.20 thf(func_def_20, type, hoasapinj2: $o).
% 5.43/1.20 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 5.43/1.20 thf(func_def_22, type, hoasapinj1: $o).
% 5.43/1.20 thf(func_def_23, type, ulamvar1: $o).
% 5.43/1.20 thf(func_def_24, type, induction2lem_lthm: $o).
% 5.43/1.20 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 5.43/1.20 thf(func_def_26, type, apnotvar: $o).
% 5.43/1.20 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 5.43/1.20 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 5.43/1.20 thf(func_def_29, type, hoasinduction_lthm: $o).
% 5.43/1.20 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 5.43/1.20 thf(func_def_31, type, hoaslaminj: $o).
% 5.43/1.20 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 5.43/1.20 thf(func_def_33, type, induction2lem_gthm: $o).
% 5.43/1.20 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 5.43/1.20 thf(func_def_35, type, hoasinduction_lem3: $o).
% 5.43/1.20 thf(func_def_36, type, hoasinduction_lem2: $o).
% 5.43/1.20 thf(func_def_37, type, termmset_lthm: $o).
% 5.43/1.20 thf(func_def_38, type, hoasinduction_lem1: $o).
% 5.43/1.20 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 5.43/1.20 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 5.43/1.20 thf(func_def_41, type, hoasapnotvar: $o).
% 5.43/1.20 thf(func_def_42, type, hoasinduction_lem0: $o).
% 5.43/1.20 thf(func_def_43, type, hoasinduction: $o).
% 5.43/1.20 thf(func_def_44, type, hoasinduction_gthm: $o).
% 5.43/1.20 thf(func_def_45, type, axapp: $o).
% 5.43/1.20 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 5.43/1.20 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 5.43/1.20 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 5.43/1.20 thf(func_def_49, type, ulamvarind: $o).
% 5.43/1.20 thf(func_def_50, type, induction: $o).
% 5.43/1.20 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 5.43/1.20 thf(func_def_52, type, termmset_gthm: $o).
% 5.43/1.20 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 5.43/1.20 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 5.43/1.20 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 5.43/1.20 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 5.43/1.20 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 5.43/1.20 thf(func_def_58, type, pushprop_lem2v2: $o).
% 5.43/1.20 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 5.43/1.20 thf(func_def_60, type, axclos: $o).
% 5.43/1.20 thf(func_def_61, type, axassoc: $o).
% 5.43/1.20 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 5.43/1.20 thf(func_def_63, type, pushprop_lthm: $o).
% 5.43/1.20 thf(func_def_64, type, apinj2: $o).
% 5.43/1.20 thf(func_def_65, type, apinj1: $o).
% 5.43/1.20 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 5.43/1.20 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 5.43/1.20 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 5.43/1.20 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 5.43/1.20 thf(func_def_70, type, axvarcons: $o).
% 5.43/1.20 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 5.43/1.20 thf(func_def_72, type, axscons: $o).
% 5.43/1.20 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 5.43/1.20 thf(func_def_74, type, axidr: $o).
% 5.43/1.20 thf(func_def_75, type, pushprop_lem1: $o).
% 5.43/1.20 thf(func_def_76, type, laminj: $o).
% 5.43/1.20 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 5.43/1.20 thf(func_def_78, type, pushprop_lem0: $o).
% 5.43/1.20 thf(func_def_79, type, pushprop_gthm: $o).
% 5.43/1.20 thf(func_def_80, type, axabs: $o).
% 5.43/1.20 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 5.43/1.20 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 5.43/1.20 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 5.43/1.20 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 5.43/1.20 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 5.43/1.20 thf(func_def_86, type, lamnotap: $o).
% 5.43/1.20 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 5.43/1.20 thf(func_def_88, type, hoaslamnotvar: $o).
% 5.43/1.20 thf(func_def_89, type, axidl: $o).
% 5.43/1.20 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 5.43/1.20 thf(func_def_91, type, induction2_lthm: $o).
% 5.43/1.20 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 5.43/1.20 thf(func_def_93, type, substmonoid_lthm: $o).
% 5.43/1.20 thf(func_def_94, type, pushprop: $o).
% 5.43/1.20 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 5.43/1.20 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 5.43/1.20 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 5.43/1.20 thf(func_def_98, type, substmonoid: $o).
% 5.43/1.20 thf(func_def_99, type, lamnotvar: $o).
% 5.43/1.20 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 5.43/1.20 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 5.43/1.20 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 5.43/1.20 thf(func_def_103, type, induction2_gthm: $o).
% 5.43/1.20 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 5.43/1.20 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_106, type, hoaslamnotap: $o).
% 5.43/1.20 thf(func_def_107, type, substmonoid_gthm: $o).
% 5.43/1.20 thf(func_def_108, type, ulamvarsh: $o).
% 5.43/1.20 thf(func_def_109, type, induction2: $o).
% 5.43/1.20 thf(func_def_110, type, pushprop_lem3v2: $o).
% 5.43/1.20 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 5.43/1.20 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 5.43/1.20 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 5.43/1.20 thf(func_def_114, type, axshiftcons: $o).
% 5.43/1.20 thf(func_def_115, type, termmset: $o).
% 5.43/1.20 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 5.43/1.20 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 5.43/1.20 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 5.43/1.20 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 5.43/1.20 thf(func_def_120, type, axvarid: $o).
% 5.43/1.20 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 5.43/1.20 thf(func_def_122, type, d2term: (d_term > term)).
% 5.43/1.20 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 5.43/1.20 thf(func_def_124, type, d_one: d_term).
% 5.43/1.20 thf(func_def_125, type, d_id: d_subst).
% 5.43/1.20 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.43/1.20 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 5.43/1.20 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 5.43/1.20 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 5.43/1.20 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.43/1.20 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.43/1.20 thf(func_def_135, type, db4: !>[X0: $tType]:(X0)).
% 5.43/1.20 thf(func_def_136, type, db3: !>[X0: $tType]:(X0)).
% 5.43/1.20 thf(func_def_137, type, sP0: ((subst > term > subst > $o) > $o)).
% 5.43/1.20 thf(func_def_138, type, sP1: $o).
% 5.43/1.20 thf(func_def_139, type, sP2: $o).
% 5.43/1.20 thf(func_def_140, type, sP3: ((subst > term > subst > $o) > $o)).
% 5.43/1.20 thf(func_def_141, type, sP4: $o).
% 5.43/1.20 thf(func_def_142, type, sP5: $o).
% 5.43/1.20 thf(func_def_143, type, sP6: $o).
% 5.43/1.20 thf(func_def_144, type, sP7: ((subst > term > subst > $o) > $o)).
% 5.43/1.20 thf(func_def_145, type, sP8: $o).
% 5.43/1.20 thf(func_def_146, type, sP9: $o).
% 5.43/1.20 thf(func_def_147, type, sP10: $o).
% 5.43/1.20 thf(func_def_148, type, sK11: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_149, type, sK12: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_150, type, sK13: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_151, type, sK14: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_152, type, sK15: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_153, type, sK16: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_154, type, sK17: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_155, type, sK18: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_156, type, sK19: ((subst > term > subst > $o) > term > term)).
% 5.43/1.20 thf(func_def_157, type, sK20: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_158, type, sK21: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_159, type, sK22: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_160, type, sK23: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_161, type, sK24: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_162, type, sK25: term).
% 5.43/1.20 thf(func_def_163, type, sK26: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_164, type, sK27: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_165, type, sK28: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_166, type, sK29: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_167, type, sK30: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_168, type, sK31: (term > $o)).
% 5.43/1.20 thf(func_def_169, type, sK32: term).
% 5.43/1.20 thf(func_def_170, type, sK33: (term > term)).
% 5.43/1.20 thf(func_def_171, type, sK34: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_172, type, sK35: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_173, type, sK36: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_174, type, sK37: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_175, type, sK38: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_176, type, sK39: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_177, type, sK40: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_178, type, sK41: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_179, type, sK42: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_180, type, sK43: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_181, type, sK44: term).
% 5.43/1.20 thf(func_def_182, type, sK45: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_183, type, sK46: term).
% 5.43/1.20 thf(func_def_184, type, sK47: term).
% 5.43/1.20 thf(func_def_185, type, sK48: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_186, type, sK49: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_187, type, sK50: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_188, type, sK51: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_189, type, sK52: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_190, type, sK53: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_191, type, sK54: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_192, type, sK55: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_193, type, sK56: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_194, type, sK57: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_195, type, sK58: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_196, type, sK59: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_197, type, sK60: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_198, type, sK61: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_199, type, sK62: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_200, type, sK63: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_201, type, sK64: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_202, type, sK65: (term > $o)).
% 5.43/1.20 thf(func_def_203, type, sK66: term).
% 5.43/1.20 thf(func_def_204, type, sK67: (term > term)).
% 5.43/1.20 thf(func_def_205, type, sK68: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_206, type, sK69: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_207, type, sK70: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_208, type, sK71: (subst > (term > $o) > term)).
% 5.43/1.20 thf(func_def_209, type, sK72: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_210, type, sK73: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_211, type, sK74: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_212, type, sK75: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_213, type, sK76: term).
% 5.43/1.20 thf(func_def_214, type, sK77: (term > $o)).
% 5.43/1.20 thf(func_def_215, type, sK78: subst).
% 5.43/1.20 thf(func_def_216, type, sK79: (term > term)).
% 5.43/1.20 thf(func_def_217, type, sK80: term).
% 5.43/1.20 thf(func_def_218, type, sK81: term).
% 5.43/1.20 thf(func_def_219, type, sK82: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_220, type, sK83: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_221, type, sK84: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_222, type, sK85: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_223, type, sK86: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_224, type, sK87: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_225, type, sK88: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_226, type, sK89: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_227, type, sK90: term).
% 5.43/1.20 thf(func_def_228, type, sK91: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_229, type, sK92: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_230, type, sK93: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_231, type, sK94: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_232, type, sK95: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_233, type, sK96: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_234, type, sK97: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_235, type, sK98: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_236, type, sK99: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_237, type, sK100: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_238, type, sK101: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_239, type, sK102: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_240, type, sK103: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_241, type, sK104: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_242, type, sK105: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_243, type, sK106: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_244, type, sK107: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_245, type, sK108: term).
% 5.43/1.20 thf(func_def_246, type, sK109: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_247, type, sK110: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_248, type, sK111: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_249, type, sK112: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_250, type, sK113: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_251, type, sK114: ((subst > term > subst > $o) > term > term)).
% 5.43/1.20 thf(func_def_252, type, sK115: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_253, type, sK116: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_254, type, sK117: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_255, type, sK118: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_256, type, sK119: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_257, type, sK120: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_258, type, sK121: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_259, type, sK122: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_260, type, sK123: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_261, type, sK124: term).
% 5.43/1.20 thf(func_def_262, type, sK125: (term > $o)).
% 5.43/1.20 thf(func_def_263, type, sK126: subst).
% 5.43/1.20 thf(func_def_264, type, sK127: (term > term)).
% 5.43/1.20 thf(func_def_265, type, sK128: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_266, type, sK129: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_267, type, sK130: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_268, type, sK131: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_269, type, sK132: subst).
% 5.43/1.20 thf(func_def_270, type, sK133: term).
% 5.43/1.20 thf(func_def_271, type, sK134: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_272, type, sK135: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_273, type, sK136: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_274, type, sK137: (subst > (term > $o) > term)).
% 5.43/1.20 thf(func_def_275, type, sK138: (term > $o)).
% 5.43/1.20 thf(func_def_276, type, sK139: term).
% 5.43/1.20 thf(func_def_277, type, sK140: subst).
% 5.43/1.20 thf(func_def_278, type, sK141: term).
% 5.43/1.20 thf(func_def_279, type, sK142: subst).
% 5.43/1.20 thf(func_def_280, type, sK143: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_281, type, sK144: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_282, type, sK145: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_283, type, sK146: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_284, type, sK147: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_285, type, sK148: term).
% 5.43/1.20 thf(func_def_286, type, sK149: term).
% 5.43/1.20 thf(func_def_287, type, sK150: subst).
% 5.43/1.20 thf(func_def_288, type, sK151: (term > $o)).
% 5.43/1.20 thf(func_def_289, type, sK152: (term > $o)).
% 5.43/1.20 thf(func_def_290, type, sK153: term).
% 5.43/1.20 thf(func_def_291, type, sK154: term).
% 5.43/1.20 thf(func_def_292, type, sK155: subst).
% 5.43/1.20 thf(func_def_293, type, sK156: subst).
% 5.43/1.20 thf(func_def_294, type, sK157: term).
% 5.43/1.20 thf(func_def_295, type, sK158: ((subst > term > subst > $o) > term > term)).
% 5.43/1.20 thf(func_def_296, type, sK159: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_297, type, sK160: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_298, type, sK161: term).
% 5.43/1.20 thf(func_def_299, type, sK162: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_300, type, sK163: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_301, type, sK164: (term > (subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_302, type, sK165: (term > (subst > term > term) > term)).
% 5.43/1.20 thf(func_def_303, type, sK166: (term > (subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_304, type, sK167: (term > (subst > term > term) > term)).
% 5.43/1.20 thf(func_def_305, type, sK168: (term > (subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_306, type, sK169: (term > (subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_307, type, sK170: term).
% 5.43/1.20 thf(func_def_308, type, sK171: term).
% 5.43/1.20 thf(func_def_309, type, sK172: (term > (term > $o) > subst > (term > $o) > term)).
% 5.43/1.20 thf(func_def_310, type, sK173: (term > $o)).
% 5.43/1.20 thf(func_def_311, type, sK174: subst).
% 5.43/1.20 thf(func_def_312, type, sK175: (term > $o)).
% 5.43/1.20 thf(func_def_313, type, sK176: term).
% 5.43/1.20 thf(func_def_314, type, sK177: ((term > $o) > term > term)).
% 5.43/1.20 thf(func_def_315, type, sK178: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.43/1.20 thf(func_def_316, type, sK179: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_317, type, sK180: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_318, type, sK181: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_319, type, sK182: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_320, type, sK183: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_321, type, sK184: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_322, type, sK185: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_323, type, sK186: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_324, type, sK187: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_325, type, sK188: term).
% 5.43/1.20 thf(func_def_326, type, sK189: (term > $o)).
% 5.43/1.20 thf(func_def_327, type, sK190: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_328, type, sK191: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_329, type, sK192: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_330, type, sK193: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_331, type, sK194: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_332, type, sK195: subst).
% 5.43/1.20 thf(func_def_333, type, sK196: (term > $o)).
% 5.43/1.20 thf(func_def_334, type, sK197: term).
% 5.43/1.20 thf(func_def_335, type, sK198: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_336, type, sK199: (term > (term > $o) > subst > term > $o)).
% 5.43/1.20 thf(func_def_337, type, sK200: term).
% 5.43/1.20 thf(func_def_338, type, sK201: subst).
% 5.43/1.20 thf(func_def_339, type, sK202: subst).
% 5.43/1.20 thf(func_def_340, type, sK203: term).
% 5.43/1.20 thf(func_def_341, type, sK204: term).
% 5.43/1.20 thf(func_def_342, type, sK205: term).
% 5.43/1.20 thf(func_def_343, type, sK206: term).
% 5.43/1.20 thf(func_def_344, type, sK207: term).
% 5.43/1.20 thf(func_def_345, type, sK208: term).
% 5.43/1.20 thf(func_def_346, type, sK209: term).
% 5.43/1.20 thf(func_def_347, type, sK210: term).
% 5.43/1.20 thf(func_def_348, type, sK211: term).
% 5.43/1.20 thf(func_def_349, type, sK212: term).
% 5.43/1.20 thf(func_def_350, type, sK213: term).
% 5.43/1.20 thf(func_def_351, type, sK214: (term > $o)).
% 5.43/1.20 thf(func_def_352, type, sK215: subst).
% 5.43/1.20 thf(func_def_353, type, sK216: term).
% 5.43/1.20 thf(func_def_354, type, sK217: (term > term)).
% 5.43/1.20 thf(func_def_355, type, sK218: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_356, type, sK219: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_357, type, sK220: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_358, type, sK221: (subst > (term > $o) > term)).
% 5.43/1.20 thf(func_def_359, type, sK222: term).
% 5.43/1.20 thf(func_def_360, type, sK223: term).
% 5.43/1.20 thf(func_def_361, type, sK224: term).
% 5.43/1.20 thf(func_def_362, type, sK225: term).
% 5.43/1.20 thf(func_def_363, type, sK226: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_364, type, sK227: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_365, type, sK228: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_366, type, sK229: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_367, type, sK230: (term > $o)).
% 5.43/1.20 thf(func_def_368, type, sK231: term).
% 5.43/1.20 thf(func_def_369, type, sK232: term).
% 5.43/1.20 thf(func_def_370, type, sK233: term).
% 5.43/1.20 thf(func_def_371, type, sK234: term).
% 5.43/1.20 thf(func_def_372, type, sK235: term).
% 5.43/1.20 thf(func_def_373, type, sK236: term).
% 5.43/1.20 thf(func_def_374, type, sK237: term).
% 5.43/1.20 thf(func_def_375, type, sK238: term).
% 5.43/1.20 thf(func_def_376, type, sK239: term).
% 5.43/1.20 thf(func_def_377, type, sK240: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_378, type, sK241: term).
% 5.43/1.20 thf(func_def_379, type, sK242: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_380, type, sK243: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_381, type, sK244: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_382, type, sK245: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_383, type, sK246: (term > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_384, type, sK247: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_385, type, sK248: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_386, type, sK249: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_387, type, sK250: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_388, type, sK251: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_389, type, sK252: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_390, type, sK253: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_391, type, sK254: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_392, type, sK255: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_393, type, sK256: term).
% 5.43/1.20 thf(func_def_394, type, sK257: (term > subst > term > term)).
% 5.43/1.20 thf(func_def_395, type, sK258: term).
% 5.43/1.20 thf(func_def_396, type, sK259: (term > $o)).
% 5.43/1.20 thf(func_def_397, type, sK260: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_398, type, sK261: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_399, type, sK262: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_400, type, sK263: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_401, type, sK264: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_402, type, sK265: term).
% 5.43/1.20 thf(func_def_403, type, sK266: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.43/1.20 thf(func_def_404, type, sK267: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_405, type, sK268: ((term > $o) > term > term)).
% 5.43/1.20 thf(func_def_406, type, sK269: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_407, type, sK270: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_408, type, sK271: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_409, type, sK272: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_410, type, sK273: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_411, type, sK274: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_412, type, sK275: ((subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_413, type, sK276: ((subst > term > subst > $o) > subst)).
% 5.43/1.20 thf(func_def_414, type, sK277: subst).
% 5.43/1.20 thf(func_def_415, type, sK278: subst).
% 5.43/1.20 thf(func_def_416, type, sK279: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_417, type, sK280: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_418, type, sK281: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_419, type, sK282: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_420, type, sK283: ((subst > term > subst > $o) > term > $o)).
% 5.43/1.20 thf(func_def_421, type, sK284: ((term > $o) > term > term)).
% 5.43/1.20 thf(func_def_422, type, sK285: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_423, type, sK286: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_424, type, sK287: (term > $o)).
% 5.43/1.20 thf(func_def_425, type, sK288: term).
% 5.43/1.20 thf(func_def_426, type, sK289: (term > term)).
% 5.43/1.20 thf(func_def_427, type, sK290: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_428, type, sK291: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_429, type, sK292: term).
% 5.43/1.20 thf(func_def_430, type, sK293: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_431, type, sK294: (term > $o)).
% 5.43/1.20 thf(func_def_432, type, sK295: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_433, type, sK296: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_434, type, sK297: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_435, type, sK298: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_436, type, sK299: term).
% 5.43/1.20 thf(func_def_437, type, sK300: (term > $o)).
% 5.43/1.20 thf(func_def_438, type, sK301: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_439, type, sK302: term).
% 5.43/1.20 thf(func_def_440, type, sK303: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_441, type, sK304: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_442, type, sK305: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_443, type, sK306: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_444, type, sK307: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.43/1.20 thf(func_def_445, type, sK308: (term > (term > $o) > term)).
% 5.43/1.20 thf(func_def_446, type, sK309: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_447, type, sK310: term).
% 5.43/1.20 thf(func_def_448, type, sK311: term).
% 5.43/1.20 thf(func_def_449, type, sK312: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_450, type, sK313: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_451, type, sK314: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_452, type, sK315: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_453, type, sK316: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_454, type, sK317: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_455, type, sK318: subst).
% 5.43/1.20 thf(func_def_456, type, sK319: term).
% 5.43/1.20 thf(func_def_457, type, sK320: term).
% 5.43/1.20 thf(func_def_458, type, sK321: subst).
% 5.43/1.20 thf(func_def_459, type, sK322: (subst > term > term)).
% 5.43/1.20 thf(func_def_460, type, sK323: (subst > term > term)).
% 5.43/1.20 thf(func_def_461, type, sK324: subst).
% 5.43/1.20 thf(func_def_462, type, sK325: term).
% 5.43/1.20 thf(func_def_463, type, sK326: term).
% 5.43/1.20 thf(func_def_464, type, sK327: term).
% 5.43/1.20 thf(func_def_465, type, sK328: term).
% 5.43/1.20 thf(func_def_466, type, sK329: term).
% 5.43/1.20 thf(func_def_467, type, sK330: ((subst > term > subst > $o) > term > $o)).
% 5.43/1.20 thf(func_def_468, type, sK331: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_469, type, sK332: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_470, type, sK333: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_471, type, sK334: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_472, type, sK335: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_473, type, sK336: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_474, type, sK337: ((term > $o) > term > term)).
% 5.43/1.20 thf(func_def_475, type, sK338: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_476, type, sK339: ((term > $o) > term)).
% 5.43/1.20 thf(func_def_477, type, sK340: term).
% 5.43/1.20 thf(func_def_478, type, sK341: term).
% 5.43/1.20 thf(func_def_479, type, sK342: (term > $o)).
% 5.43/1.20 thf(func_def_480, type, sK343: (term > term)).
% 5.43/1.20 thf(func_def_481, type, sK344: term).
% 5.43/1.20 thf(func_def_482, type, sK345: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_483, type, sK346: (term > $o)).
% 5.43/1.20 thf(func_def_484, type, sK347: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_485, type, sK348: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_486, type, sK349: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_487, type, sK350: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_488, type, sK351: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_489, type, sK352: ((subst > term > subst > $o) > term > term)).
% 5.43/1.20 thf(func_def_490, type, sK353: term).
% 5.43/1.20 thf(func_def_491, type, sK354: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_492, type, sK355: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_493, type, sK356: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_494, type, sK357: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_495, type, sK358: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_496, type, sK359: (subst > term > subst > $o)).
% 5.43/1.20 thf(func_def_497, type, sK360: term).
% 5.43/1.20 thf(func_def_498, type, sK361: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_499, type, sK362: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_500, type, sK363: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_501, type, sK364: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_502, type, sK365: term).
% 5.43/1.20 thf(func_def_503, type, sK366: (term > (subst > term > subst > $o) > term)).
% 5.43/1.20 thf(func_def_504, type, sK367: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.20 thf(func_def_505, type, sK368: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_506, type, sK369: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_507, type, sK370: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_508, type, sK371: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_509, type, sK372: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_510, type, sK373: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_511, type, sK374: (subst > term > term)).
% 5.43/1.20 thf(func_def_512, type, sK375: (subst > term > term)).
% 5.43/1.20 thf(func_def_513, type, sK376: term).
% 5.43/1.20 thf(func_def_514, type, sK377: subst).
% 5.43/1.20 thf(func_def_515, type, sK378: (term > subst > term > term)).
% 5.43/1.20 thf(func_def_516, type, sK379: term).
% 5.43/1.20 thf(func_def_517, type, sK380: ((subst > term > term) > term)).
% 5.43/1.20 thf(func_def_518, type, sK381: ((subst > term > term) > subst)).
% 5.43/1.20 thf(func_def_519, type, sK382: term).
% 5.43/1.20 thf(func_def_520, type, sK383: term).
% 5.43/1.20 thf(func_def_521, type, sK384: (term > subst > term > term)).
% 5.43/1.20 thf(func_def_522, type, sK385: (term > subst > term > term)).
% 5.43/1.21 thf(func_def_523, type, sK386: term).
% 5.43/1.21 thf(func_def_524, type, sK387: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_525, type, sK388: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_526, type, sK389: term).
% 5.43/1.21 thf(func_def_527, type, sK390: subst).
% 5.43/1.21 thf(func_def_528, type, sK391: ((term > $o) > (subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_529, type, sK392: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_530, type, sK393: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_531, type, sK394: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_532, type, sK395: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_533, type, sK396: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_534, type, sK397: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_535, type, sK398: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_536, type, sK399: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_537, type, sK400: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_538, type, sK401: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_539, type, sK402: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_540, type, sK403: (term > $o)).
% 5.43/1.21 thf(func_def_541, type, sK404: term).
% 5.43/1.21 thf(func_def_542, type, sK405: term).
% 5.43/1.21 thf(func_def_543, type, sK406: (term > d_term)).
% 5.43/1.21 thf(func_def_544, type, sK407: subst).
% 5.43/1.21 thf(func_def_545, type, sK408: subst).
% 5.43/1.21 thf(func_def_546, type, sK409: subst).
% 5.43/1.21 thf(func_def_547, type, sK410: subst).
% 5.43/1.21 thf(func_def_548, type, sK411: term).
% 5.43/1.21 thf(func_def_549, type, sK412: term).
% 5.43/1.21 thf(func_def_550, type, sK413: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_551, type, sK414: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_552, type, sK415: ((subst > term > subst > $o) > term > $o)).
% 5.43/1.21 thf(func_def_553, type, sK416: (term > subst > term > term)).
% 5.43/1.21 thf(func_def_554, type, sK417: (term > $o)).
% 5.43/1.21 thf(func_def_555, type, sK418: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_556, type, sK419: term).
% 5.43/1.21 thf(func_def_557, type, sK420: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_558, type, sK421: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_559, type, sK422: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_560, type, sK423: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_561, type, sK424: term).
% 5.43/1.21 thf(func_def_562, type, sK425: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_563, type, sK426: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_564, type, sK427: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_565, type, sK428: (term > (term > $o) > term)).
% 5.43/1.21 thf(func_def_566, type, sK429: ((subst > term > subst > $o) > (term > $o) > term)).
% 5.43/1.21 thf(func_def_567, type, sK430: term).
% 5.43/1.21 thf(func_def_568, type, sK431: (subst > d_subst)).
% 5.43/1.21 thf(func_def_569, type, sK432: term).
% 5.43/1.21 thf(func_def_570, type, sK433: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_571, type, sK434: ((subst > term > subst > $o) > term > term)).
% 5.43/1.21 thf(func_def_572, type, sK435: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_573, type, sK436: term).
% 5.43/1.21 thf(func_def_574, type, sK437: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_575, type, sK438: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_576, type, sK439: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_577, type, sK440: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_578, type, sK441: term).
% 5.43/1.21 thf(func_def_579, type, sK442: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_580, type, sK443: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_581, type, sK444: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_582, type, sK445: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_583, type, sK446: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_584, type, sK447: (term > (subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_585, type, sK448: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_586, type, sK449: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_587, type, sK450: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_588, type, sK451: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_589, type, sK452: term).
% 5.43/1.21 thf(func_def_590, type, sK453: (subst > term > term)).
% 5.43/1.21 thf(func_def_591, type, sK454: term).
% 5.43/1.21 thf(func_def_592, type, sK455: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_593, type, sK456: ((subst > term > subst > $o) > term > term)).
% 5.43/1.21 thf(func_def_594, type, sK457: term).
% 5.43/1.21 thf(func_def_595, type, sK458: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_596, type, sK459: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_597, type, sK460: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_598, type, sK461: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_599, type, sK462: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_600, type, sK463: term).
% 5.43/1.21 thf(func_def_601, type, sK464: term).
% 5.43/1.21 thf(func_def_602, type, sK465: term).
% 5.43/1.21 thf(func_def_603, type, sK466: term).
% 5.43/1.21 thf(func_def_604, type, sK467: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_605, type, sK468: term).
% 5.43/1.21 thf(func_def_606, type, sK469: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_607, type, sK470: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_608, type, sK471: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_609, type, sK472: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_610, type, sK473: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_611, type, sK474: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_612, type, sK475: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_613, type, sK476: subst).
% 5.43/1.21 thf(func_def_614, type, sK477: term).
% 5.43/1.21 thf(func_def_615, type, sK478: (term > $o)).
% 5.43/1.21 thf(func_def_616, type, sK479: (term > term)).
% 5.43/1.21 thf(func_def_617, type, sK480: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_618, type, sK481: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_619, type, sK482: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_620, type, sK483: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_621, type, sK484: term).
% 5.43/1.21 thf(func_def_622, type, sK485: term).
% 5.43/1.21 thf(func_def_623, type, sK486: term).
% 5.43/1.21 thf(func_def_624, type, sK487: term).
% 5.43/1.21 thf(func_def_625, type, sK488: ((subst > term > subst > $o) > term > $o)).
% 5.43/1.21 thf(func_def_626, type, sK489: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_627, type, sK490: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_628, type, sK491: term).
% 5.43/1.21 thf(func_def_629, type, sK492: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_630, type, sK493: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_631, type, sK494: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_632, type, sK495: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_633, type, sK496: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_634, type, sK497: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_635, type, sK498: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_636, type, sK499: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_637, type, sK500: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_638, type, sK501: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_639, type, sK502: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_640, type, sK503: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_641, type, sK504: (term > $o)).
% 5.43/1.21 thf(func_def_642, type, sK505: term).
% 5.43/1.21 thf(func_def_643, type, sK506: term).
% 5.43/1.21 thf(func_def_644, type, sK507: (term > $o)).
% 5.43/1.21 thf(func_def_645, type, sK508: subst).
% 5.43/1.21 thf(func_def_646, type, sK509: (term > (term > $o) > subst > term > $o)).
% 5.43/1.21 thf(func_def_647, type, sK510: subst).
% 5.43/1.21 thf(func_def_648, type, sK511: (term > $o)).
% 5.43/1.21 thf(func_def_649, type, sK512: term).
% 5.43/1.21 thf(func_def_650, type, sK513: ((term > $o) > term)).
% 5.43/1.21 thf(func_def_651, type, sK514: subst).
% 5.43/1.21 thf(func_def_652, type, sK515: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_653, type, sK516: term).
% 5.43/1.21 thf(func_def_654, type, sK517: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_655, type, sK518: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_656, type, sK519: ((subst > term > term) > subst)).
% 5.43/1.21 thf(func_def_657, type, sK520: ((subst > term > term) > term)).
% 5.43/1.21 thf(func_def_658, type, sK521: ((subst > term > subst > $o) > subst > term > term)).
% 5.43/1.21 thf(func_def_659, type, sK522: (term > (subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_660, type, sK523: (term > $o)).
% 5.43/1.21 thf(func_def_661, type, sK524: term).
% 5.43/1.21 thf(func_def_662, type, sK525: subst).
% 5.43/1.21 thf(func_def_663, type, sK526: (term > $o)).
% 5.43/1.21 thf(func_def_664, type, sK527: ((term > $o) > subst > term > (term > $o) > term)).
% 5.43/1.21 thf(func_def_665, type, sK528: term).
% 5.43/1.21 thf(func_def_666, type, sK529: subst).
% 5.43/1.21 thf(func_def_667, type, sK530: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_668, type, sK531: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_669, type, sK532: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_670, type, sK533: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_671, type, sK534: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_672, type, sK535: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_673, type, sK536: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_674, type, sK537: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_675, type, sK538: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_676, type, sK539: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_677, type, sK540: term).
% 5.43/1.21 thf(func_def_678, type, sK541: term).
% 5.43/1.21 thf(func_def_679, type, sK542: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_680, type, sK543: (term > $o)).
% 5.43/1.21 thf(func_def_681, type, sK544: (subst > term > subst > $o)).
% 5.43/1.21 thf(func_def_682, type, sK545: term).
% 5.43/1.21 thf(func_def_683, type, sK546: term).
% 5.43/1.21 thf(func_def_684, type, sK547: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_685, type, sK548: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_686, type, sK549: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_687, type, sK550: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_688, type, sK551: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_689, type, sK552: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_690, type, sK553: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_691, type, sK554: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_692, type, sK555: ((subst > term > subst > $o) > term)).
% 5.43/1.21 thf(func_def_693, type, sK556: ((subst > term > subst > $o) > subst)).
% 5.43/1.21 thf(func_def_694, type, vNOT: ($o > $o)).
% 5.43/1.21 thf(f1,axiom,(
% 5.43/1.21 apnotvar & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & (! [X26 : (term > $o),X14 : subst,X13 : term,X15 : term,X10 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & pushprop_lem3v2_lthm & induction2lem_gthm & (hoaslamnotap <=> ! [X46 : term,X47 : term,X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & termmset_gthm & ((^[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) & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction_lem3v2) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasapinj2_lthm <=> (! [X15 : term,X19 : term,X13 : term,X20 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X19 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b_lthm) & (! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & pushprop & hoasinduction_lem2v2_gthm & ~(var @ (d2term @ d_one)) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (axidl <=> ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) & hoaslamnotap_lthm & ~lamnotap & ((! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22)) => (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X23 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(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)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) <=> hoasinduction_lthm) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X30 @ id))))))) & hoasinduction_gthm & pushprop_lem2v2_gthm & hoasinduction_lem1v2_gthm & (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & (! [X14 : subst,X11 : (term > $o),X13 : term,X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X33 : term,X18 : (subst > term > term),X32 : subst,X31 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & hoasapnotvar_lthm & pushprop_lem2v2 & (! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh)))) <=> shinj) & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id))) & (hoasapinj2 <=> ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ X43) @ id)) <=> hoasinduction_lem3a) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ~ulamvar1 & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & axmap & pushprop_lem0_gthm & hoasinduction_lem3v2_gthm & hoasinduction_lem1 & hoaslamnotvar & hoasinduction_lem3b_gthm & axclos & ! [X5 : d_subst] : (X5 = d_id) & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X26 : (term > $o),X14 : subst,X10 : (term > $o),X13 : term] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & ((! [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,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))))) <=> hoasinduction_lem3v2a_lthm) & (axvarcons <=> ! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (! [X31 : (subst > term > term),X18 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one))))) <=> hoaslaminj) & ! [X1 : d_term] : (X1 = d_one) & axapp & (! [X10 : (subst > term > subst > $o),X45 : term,X11 : (term > $o),X44 : term] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X44) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(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_lem2v2) & axassoc & hoasinduction_lem2_lthm & hoasinduction_lem3_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & hoasapnotvar & (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id))) <=> hoasinduction_lem2) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21)) => ! [X17 : subst,X16 : term,X10 : (term > $o)] : (~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17))))))) <=> induction2lem_lthm) & lamnotvar & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X20 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X15 : term,X19 : term,X13 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)))) <=> hoasapinj1_lthm) & (! [X14 : subst,X13 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & pushprop_lem2v2_lthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & hoasapinj1_gthm & pushprop_lem1_gthm & (hoasapinj1 <=> ! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (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_lem3v2a) & hoaslamnotvar_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [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] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & induction2_gthm & axabs & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & hoasapinj2_gthm & (sh = ((d2subst @ d_id))) & hoasapnotvar_gthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & (! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) <=> hoasinduction) & (! [X34 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X36 : subst,X37 : term,X38 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X39 : subst,X41 : subst,X40 : term] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem3aaa) & hoaslaminj_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X17 : subst,X10 : (term > $o),X16 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13))))) <=> induction2_lthm) & hoasinduction_lem1v2 & substmonoid_gthm & (apinj1 <=> ! [X13 : term,X19 : term,X15 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ 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)))))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [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] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))))) & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & ulamvarsh & (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) <=> laminj) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (id = ((d2subst @ d_id))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,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)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) <=> hoasinduction_lthm_3) & pushprop_gthm & pushprop_lem1v2_gthm & hoasinduction_lem1_lthm & (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & pushprop_lthm_orig & hoasinduction_lem2_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_lthm & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17)))) <=> induction2lem) & hoasinduction_lem1_gthm & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & pushprop_lem3v2 & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X30 @ id))) & hoasinduction_lem3a_gthm & axvarshift & hoaslamnotap_gthm & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))) & ulamvarind & pushprop_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem1v2_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X10 : (term > $o),X14 : subst,X13 : term,X11 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (one = ((d2term @ d_one))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)))) <=> hoasinduction_lem3v2_lthm) & (induction <=> ! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))))),
% 5.43/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 5.43/1.21 thf(f2,conjecture,(
% 5.43/1.21 (! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X4 : subst,X2 : subst,X3 : term,X5 : subst] : ((X0 @ X2 @ X3 @ (comp @ X5 @ X4)) => (X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4)) => (! [X5 : subst,X2 : subst,X4 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4) => (X0 @ X2 @ X3 @ (comp @ X5 @ X4))) => (! [X6 : term,X3 : term] : ((X0 @ id @ X3 @ id) => ((X0 @ id @ X6 @ id) => (X0 @ id @ (hoasap @ id @ X3 @ id @ X6) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X6 : term,X3 : term] : ((X1 @ X3) => ((X1 @ X6) => (X1 @ (ap @ X3 @ X6)))))))) = hoasinduction_lem2v2)),
% 5.43/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2)).
% 5.43/1.21 thf(f3,negated_conjecture,(
% 5.43/1.21 ~ (! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X4 : subst,X2 : subst,X3 : term,X5 : subst] : ((X0 @ X2 @ X3 @ (comp @ X5 @ X4)) => (X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4)) => (! [X5 : subst,X2 : subst,X4 : subst,X3 : term] : ((X0 @ (comp @ X2 @ X5) @ (sub @ X3 @ X5) @ X4) => (X0 @ X2 @ X3 @ (comp @ X5 @ X4))) => (! [X6 : term,X3 : term] : ((X0 @ id @ X3 @ id) => ((X0 @ id @ X6 @ id) => (X0 @ id @ (hoasap @ id @ X3 @ id @ X6) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X6 : term,X3 : term] : ((X1 @ X3) => ((X1 @ X6) => (X1 @ (ap @ X3 @ X6)))))))) = hoasinduction_lem2v2)),
% 5.43/1.21 inference(negated_conjecture,[status(cth)],[f2])).
% 5.43/1.21 thf(f4,plain,(
% 5.43/1.21 apnotvar & (! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) <=> hoasinduction_lem0_lthm) & (! [X3 : (term > $o),X4 : subst,X5 : term,X6 : term,X7 : (term > $o)] : (~(X7 @ X5) | (X3 @ (sub @ X5 @ (push @ X6 @ X4)))) <=> pushprop_lem1) & pushprop_lem3v2_lthm & induction2lem_gthm & (hoaslamnotap <=> ! [X8 : term,X9 : term,X10 : (subst > term > term)] : (~ ! [X11 : term,X12 : subst,X13 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12)))) | (((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))))) & ! [X14 : d_subst,X15 : d_subst] : ((((d2subst @ X15)) = ((d2subst @ X14))) => (X14 = X15)) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & termmset_gthm & ((^[X18 : term, X19 : subst, X20 : (term > $o), X21 : (term > $o)] : (! [X22 : term] : (((X20 @ (sub @ X22 @ (push @ X18 @ X19)))) = ((X21 @ X22))))) = pushprop_p_and_p_prime) & (! [X23 : (term > $o),X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X26 : term] : (((X24 @ id @ X26 @ id)) = ((X23 @ X26))) | ~ ! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : ((X24 @ X29 @ X30 @ (comp @ X28 @ X27)) | ~(X24 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28) @ X27)) | ~ ! [X31 : (subst > term > term)] : ((X24 @ id @ (lam @ (X31 @ sh @ one)) @ id) | ~ ! [X32 : subst,X33 : subst,X34 : term] : (((sub @ (X31 @ X33 @ X34) @ X32)) = ((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32)))) | ~ ! [X35 : term] : ((X24 @ id @ (X31 @ id @ X35) @ id) | ~(X24 @ id @ X35 @ id))) | ~ ! [X36 : term] : (~(X23 @ X36) | (X23 @ (sub @ X25 @ (push @ X36 @ id)))) | (X23 @ (lam @ X25)) | ~ ! [X37 : subst,X38 : term,X39 : subst,X40 : subst] : ((X24 @ (comp @ X37 @ X40) @ (sub @ X38 @ X40) @ X39) | ~(X24 @ X37 @ X38 @ (comp @ X40 @ X39)))) <=> hoasinduction_lem3v2) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & (hoasapinj2_lthm <=> (! [X41 : term,X42 : term,X43 : term,X44 : term] : ((X42 = X44) | (((ap @ X43 @ X42)) != ((ap @ X41 @ X44)))) => ! [X45 : term,X46 : term,X47 : term,X48 : term] : ((X47 = X48) | (((ap @ (sub @ X46 @ id) @ X48)) != ((ap @ (sub @ X45 @ id) @ X47)))))) & (! [X49 : term] : ~ ! [X50 : (subst > term > term)] : (((sub @ X49 @ (push @ one @ sh))) != ((X50 @ sh @ one))) <=> hoasinduction_lem3b_lthm) & (! [X51 : term,X52 : subst,X53 : (term > $o)] : ~ ! [X54 : (term > $o)] : ~ ! [X55 : term] : (((X54 @ X55)) = ((X53 @ (sub @ X55 @ (push @ X51 @ X52))))) <=> pushprop_lem0_lthm) & pushprop & hoasinduction_lem2v2_gthm & ~(var @ (d2term @ d_one)) & (! [X56 : term] : ~ ! [X57 : (subst > term > term)] : ~ ! [X58 : subst,X59 : term] : (((sub @ X56 @ (push @ X59 @ X58))) = ((X57 @ X58 @ X59))) <=> hoasinduction_lem3v2_f_lthm) & (substmonoid <=> (! [X60 : subst] : (((comp @ id @ X60)) = X60) & ! [X61 : subst] : (((comp @ X61 @ id)) = X61))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (axidl <=> ! [X62 : subst] : (((comp @ id @ X62)) = X62)) & hoaslamnotap_lthm & ~lamnotap & ((! [X63 : term,X64 : (term > $o)] : (~ ! [X65 : term] : (~(var @ X65) | (X64 @ X65)) | ~ ! [X66 : term,X67 : term] : (~(X64 @ X67) | (X64 @ (ap @ X66 @ X67)) | ~(X64 @ X66)) | ~ ! [X68 : term] : (~ ! [X69 : term] : ((X64 @ (sub @ X68 @ (push @ X69 @ id))) | ~(X64 @ X69)) | (X64 @ (lam @ X68))) | (X64 @ X63)) => (! [X70 : term,X71 : term,X72 : (subst > term > subst > $o)] : (~ ! [X73 : subst,X74 : subst,X75 : term,X76 : subst] : ((X72 @ X76 @ X75 @ (comp @ X73 @ X74)) | ~(X72 @ (comp @ X76 @ X73) @ (sub @ X75 @ X73) @ X74)) | ~ ! [X77 : subst,X78 : subst,X79 : term,X80 : subst] : ((X72 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77) @ X80) | ~(X72 @ X78 @ X79 @ (comp @ X77 @ X80))) | ~(X72 @ id @ X70 @ id) | (X72 @ id @ (ap @ X70 @ X71) @ id) | ~(X72 @ id @ X71 @ id) | ~ ! [X81 : term,X82 : term] : (~(X72 @ id @ X81 @ id) | (X72 @ id @ (ap @ (sub @ X81 @ id) @ X82) @ id) | ~(X72 @ id @ X82 @ id))) => (! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (~(X83 @ (comp @ X86 @ X88) @ (sub @ X85 @ X88) @ X87) | (X83 @ X86 @ X85 @ (comp @ X88 @ X87))) | ~ ! [X89 : term,X90 : subst,X91 : subst,X92 : subst] : (~(X83 @ X92 @ X89 @ (comp @ X90 @ X91)) | (X83 @ (comp @ X92 @ X90) @ (sub @ X89 @ X90) @ X91)) | ~ ! [X93 : term] : (~(X83 @ id @ X93 @ id) | (X83 @ id @ (sub @ X84 @ (push @ X93 @ id)) @ id)) | (X83 @ id @ (lam @ X84) @ id) | ~ ! [X94 : (subst > term > term)] : (~ ! [X95 : term] : ((X83 @ id @ (X94 @ id @ X95) @ id) | ~(X83 @ id @ X95 @ id)) | (X83 @ id @ (lam @ (X94 @ sh @ one)) @ id) | ~ ! [X96 : subst,X97 : subst,X98 : term] : (((X94 @ (comp @ X97 @ X96) @ (sub @ X98 @ X96))) = ((sub @ (X94 @ X97 @ X98) @ X96))))) => ! [X99 : (subst > term > subst > $o),X100 : term] : (~ ! [X101 : term,X102 : subst,X103 : subst,X104 : subst] : ((X99 @ (comp @ X104 @ X102) @ (sub @ X101 @ X102) @ X103) | ~(X99 @ X104 @ X101 @ (comp @ X102 @ X103))) | ~ ! [X105 : term] : ((X99 @ id @ X105 @ id) | ~(var @ (sub @ X105 @ id))) | (X99 @ id @ X100 @ id) | ~ ! [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (~(X99 @ (comp @ X108 @ X109) @ (sub @ X107 @ X109) @ X106) | (X99 @ X108 @ X107 @ (comp @ X109 @ X106))) | ~ ! [X110 : term,X111 : term] : (~(X99 @ id @ X110 @ id) | ~(X99 @ id @ X111 @ id) | (X99 @ id @ (ap @ (sub @ X111 @ id) @ X110) @ id)) | ~ ! [X112 : (subst > term > term)] : (~ ! [X113 : term] : (~(X99 @ id @ X113 @ id) | (X99 @ id @ (X112 @ id @ X113) @ id)) | (X99 @ id @ (lam @ (X112 @ sh @ one)) @ id) | ~ ! [X114 : term,X115 : subst,X116 : subst] : (((X112 @ (comp @ X116 @ X115) @ (sub @ X114 @ X115))) = ((sub @ (X112 @ X116 @ X114) @ X115)))))))) <=> hoasinduction_lthm) & (hoasinduction_no_psi_cond_lthm <=> (! [X117 : (subst > term > subst > $o)] : ~ ! [X118 : (term > $o)] : ~ ! [X119 : term] : (((X117 @ id @ X119 @ id)) = ((X118 @ X119))) => (! [X120 : (term > $o),X121 : term] : (~ ! [X122 : term] : ((X120 @ X122) | ~(var @ X122)) | (X120 @ X121) | ~ ! [X123 : term,X124 : term] : (~(X120 @ X124) | ~(X120 @ X123) | (X120 @ (ap @ X123 @ X124))) | ~ ! [X125 : term] : (~ ! [X126 : term] : ((X120 @ (sub @ X125 @ (push @ X126 @ id))) | ~(X120 @ X126)) | (X120 @ (lam @ X125)))) => (! [X127 : term] : (((sub @ X127 @ id)) = X127) => (! [X128 : term,X129 : (term > $o),X130 : (subst > term > subst > $o)] : ((X129 @ (lam @ X128)) | ~ ! [X131 : term] : (~(X129 @ X131) | (X129 @ (sub @ X128 @ (push @ X131 @ id)))) | ~ ! [X132 : (subst > term > term)] : ((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id) | ~ ! [X133 : subst,X134 : subst,X135 : term] : (((X132 @ (comp @ X134 @ X133) @ (sub @ X135 @ X133))) = ((sub @ (X132 @ X134 @ X135) @ X133))) | ~ ! [X136 : term] : ((X130 @ id @ (X132 @ id @ X136) @ id) | ~(X130 @ id @ X136 @ id))) | ~ ! [X137 : term] : (((X129 @ X137)) = ((X130 @ id @ X137 @ id)))) => ! [X138 : (subst > term > subst > $o),X139 : term] : (~ ! [X140 : (subst > term > term)] : ((X138 @ id @ (lam @ (X140 @ sh @ one)) @ id) | ~ ! [X141 : term] : (~(X138 @ id @ X141 @ id) | (X138 @ id @ (X140 @ id @ X141) @ id)) | ~ ! [X142 : subst,X143 : term,X144 : subst] : (((X140 @ (comp @ X144 @ X142) @ (sub @ X143 @ X142))) = ((sub @ (X140 @ X144 @ X143) @ X142)))) | ~ ! [X145 : term,X146 : term] : (~(X138 @ id @ X145 @ id) | (X138 @ id @ (ap @ (sub @ X146 @ id) @ X145) @ id) | ~(X138 @ id @ X146 @ id)) | (X138 @ id @ X139 @ id))))))) & hoasinduction_gthm & pushprop_lem2v2_gthm & hoasinduction_lem1v2_gthm & (! [X147 : term,X148 : term,X149 : term,X150 : term] : ((X147 = X148) | (((ap @ X149 @ X148)) != ((ap @ X150 @ X147)))) <=> apinj2) & (axscons <=> ! [X151 : subst] : (((push @ (sub @ one @ X151) @ (comp @ sh @ X151))) = X151)) & (hoaslam = (^[X152 : subst, X153 : (subst > term > term)] : ((d2term @ d_one)))) & (! [X154 : subst,X155 : (term > $o),X156 : term,X157 : (term > $o)] : ((X155 @ one) | ~(X157 @ X156) | ~ ! [X158 : term] : (((X155 @ X158)) = ((X157 @ (sub @ X158 @ (push @ X156 @ X154)))))) <=> pushprop_lem1v2) & ((! [X159 : term,X160 : subst] : (((sub @ one @ (push @ X159 @ X160))) = X159) => (! [X161 : subst,X162 : term] : (((comp @ sh @ (push @ X162 @ X161))) = X161) => (! [X163 : term,X164 : term] : ((((lam @ X164)) != ((lam @ X163))) | (X163 = X164)) => ! [X165 : term,X166 : (subst > term > term),X167 : subst,X168 : (subst > term > term)] : ((((X168 @ X167 @ X165)) = ((X166 @ X167 @ X165))) | ~ ! [X169 : subst,X170 : subst,X171 : term] : (((sub @ (X166 @ X169 @ X171) @ X170)) = ((X166 @ (comp @ X169 @ X170) @ (sub @ X171 @ X170)))) | (((lam @ (X168 @ sh @ one))) != ((lam @ (X166 @ sh @ one)))) | ~ ! [X172 : subst,X173 : term,X174 : subst] : (((sub @ (X168 @ X172 @ X173) @ X174)) = ((X168 @ (comp @ X172 @ X174) @ (sub @ X173 @ X174)))))))) <=> hoaslaminj_lthm) & hoasapnotvar_lthm & pushprop_lem2v2 & (! [X175 : term,X176 : term] : ((X175 = X176) | (((sub @ X176 @ sh)) != ((sub @ X175 @ sh)))) <=> shinj) & (hoasinduction_lem3aa <=> ! [X177 : (subst > term > subst > $o),X178 : term] : (~ ! [X179 : term] : ((X177 @ id @ (sub @ X178 @ (push @ X179 @ id)) @ id) | ~(X177 @ id @ X179 @ id)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term,X182 : subst,X183 : subst] : (((X180 @ (comp @ X182 @ X183) @ (sub @ X181 @ X183))) = ((sub @ (X180 @ X182 @ X181) @ X183))) | (X177 @ id @ (lam @ (X180 @ sh @ one)) @ id) | ~ ! [X184 : term] : (~(X177 @ id @ X184 @ id) | (X177 @ id @ (X180 @ id @ X184) @ id))) | (X177 @ id @ (lam @ (sub @ X178 @ (push @ one @ sh))) @ id))) & (hoasapinj2 <=> ! [X185 : term,X186 : term,X187 : term,X188 : term] : ((((ap @ (sub @ X188 @ id) @ X186)) != ((ap @ (sub @ X187 @ id) @ X185))) | (X185 = X186))) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X189 : (subst > term > subst > $o),X190 : term] : (~ ! [X191 : term] : ((X189 @ id @ (sub @ X190 @ (push @ X191 @ id)) @ id) | ~(X189 @ id @ X191 @ id)) | ~ ! [X192 : (subst > term > term)] : (~ ! [X193 : term,X194 : subst,X195 : subst] : (((X192 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X192 @ X194 @ X193) @ X195))) | (X189 @ id @ (lam @ (X192 @ sh @ one)) @ id) | ~ ! [X196 : term] : (~(X189 @ id @ X196 @ id) | (X189 @ id @ (X192 @ id @ X196) @ id))) | (X189 @ id @ (lam @ X190) @ id)) <=> hoasinduction_lem3a) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ~ulamvar1 & (hoasinduction_lem3aa_lthm <=> ! [X197 : (subst > term > subst > $o),X198 : term] : ((X197 @ id @ (lam @ (sub @ X198 @ (push @ one @ sh))) @ id) | ~ ! [X199 : term] : ((X197 @ id @ (sub @ X198 @ (push @ X199 @ id)) @ id) | ~(X197 @ id @ X199 @ id)) | ~ ! [X200 : (subst > term > term)] : ((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id) | ~ ! [X201 : subst,X202 : subst,X203 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X203 @ X202))) = ((sub @ (X200 @ X201 @ X203) @ X202))) | ~ ! [X204 : term] : ((X197 @ id @ (X200 @ id @ X204) @ id) | ~(X197 @ id @ X204 @ id))))) & axmap & pushprop_lem0_gthm & hoasinduction_lem3v2_gthm & hoasinduction_lem1 & hoaslamnotvar & hoasinduction_lem3b_gthm & axclos & ! [X205 : d_subst] : (d_id = X205) & (pushprop_lem1_lthm <=> (! [X206 : subst,X207 : term] : (((sub @ one @ (push @ X207 @ X206))) = X207) => (! [X208 : term,X209 : subst] : (((comp @ sh @ (push @ X208 @ X209))) = X209) => ! [X210 : term,X211 : (term > $o),X212 : subst,X213 : (term > $o),X214 : term] : ((X211 @ (sub @ X214 @ (push @ X210 @ X212))) | ~(X213 @ X214))))) & ((! [X215 : term] : ~ ! [X216 : (subst > term > term)] : ~ ! [X217 : subst,X218 : term] : (((sub @ X215 @ (push @ X218 @ X217))) = ((X216 @ X217 @ X218))) => (! [X219 : term] : (((sub @ X219 @ id)) = X219) => ! [X220 : term,X221 : (term > $o),X222 : (subst > term > subst > $o)] : ((X221 @ (lam @ X220)) | ~ ! [X223 : (subst > term > term)] : ((X222 @ id @ (lam @ (X223 @ sh @ one)) @ id) | ~ ! [X224 : term] : ((X222 @ id @ (X223 @ id @ X224) @ id) | ~(X222 @ id @ X224 @ id)) | ~ ! [X225 : term,X226 : subst,X227 : subst] : (((sub @ (X223 @ X227 @ X225) @ X226)) = ((X223 @ (comp @ X227 @ X226) @ (sub @ X225 @ X226))))) | ~ ! [X228 : term] : (((X221 @ X228)) = ((X222 @ id @ X228 @ id))) | ~ ! [X229 : term] : ((X221 @ (sub @ X220 @ (push @ X229 @ id))) | ~(X221 @ X229))))) <=> hoasinduction_lem3v2a_lthm) & (axvarcons <=> ! [X230 : subst,X231 : term] : (((sub @ one @ (push @ X231 @ X230))) = X231)) & (! [X232 : (subst > term > term),X233 : (subst > term > term),X234 : subst,X235 : term] : ((((X233 @ X234 @ X235)) = ((X232 @ X234 @ X235))) | ~ ! [X236 : term,X237 : subst,X238 : subst] : (((X232 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X232 @ X237 @ X236) @ X238))) | ~ ! [X239 : term,X240 : subst,X241 : subst] : (((X233 @ (comp @ X240 @ X241) @ (sub @ X239 @ X241))) = ((sub @ (X233 @ X240 @ X239) @ X241))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X232 @ sh @ one))))) <=> hoaslaminj) & ! [X242 : d_term] : (d_one = X242) & axapp & (! [X243 : (subst > term > subst > $o),X244 : term,X245 : (term > $o),X246 : term] : (~ ! [X247 : term] : (((X243 @ id @ X247 @ id)) = ((X245 @ X247))) | (X245 @ (ap @ X246 @ X244)) | ~(X245 @ X246) | ~ ! [X248 : subst,X249 : term,X250 : subst,X251 : subst] : (~(X243 @ (comp @ X248 @ X251) @ (sub @ X249 @ X251) @ X250) | (X243 @ X248 @ X249 @ (comp @ X251 @ X250))) | ~(X245 @ X244) | ~ ! [X252 : subst,X253 : subst,X254 : subst,X255 : term] : (~(X243 @ X252 @ X255 @ (comp @ X253 @ X254)) | (X243 @ (comp @ X252 @ X253) @ (sub @ X255 @ X253) @ X254)) | ~ ! [X256 : term,X257 : term] : (~(X243 @ id @ X256 @ id) | (X243 @ id @ (ap @ (sub @ X256 @ id) @ X257) @ id) | ~(X243 @ id @ X257 @ id))) <=> hoasinduction_lem2v2) & axassoc & hoasinduction_lem2_lthm & hoasinduction_lem3_gthm & ((! [X258 : term] : (((sub @ X258 @ id)) = X258) => ! [X259 : term] : (((sub @ X259 @ id)) = X259)) <=> termmset_lthm) & hoasapnotvar & (! [X260 : (subst > term > subst > $o),X261 : term,X262 : term] : (~ ! [X263 : subst,X264 : subst,X265 : subst,X266 : term] : (~(X260 @ X265 @ X266 @ (comp @ X263 @ X264)) | (X260 @ (comp @ X265 @ X263) @ (sub @ X266 @ X263) @ X264)) | (X260 @ id @ (ap @ X261 @ X262) @ id) | ~ ! [X267 : subst,X268 : subst,X269 : subst,X270 : term] : (~(X260 @ (comp @ X269 @ X267) @ (sub @ X270 @ X267) @ X268) | (X260 @ X269 @ X270 @ (comp @ X267 @ X268))) | ~(X260 @ id @ X262 @ id) | ~(X260 @ id @ X261 @ id) | ~ ! [X271 : term,X272 : term] : (~(X260 @ id @ X272 @ id) | ~(X260 @ id @ X271 @ id) | (X260 @ id @ (ap @ (sub @ X271 @ id) @ X272) @ id))) <=> hoasinduction_lem2) & ((! [X273 : subst,X274 : term] : (((sub @ one @ (push @ X274 @ X273))) = X274) => (! [X275 : term,X276 : subst] : (((comp @ sh @ (push @ X275 @ X276))) = X276) => (! [X277 : subst] : (((comp @ X277 @ id)) = X277) => (! [X278 : term,X279 : (term > $o)] : (~ ! [X280 : term] : (~(var @ X280) | (X279 @ X280)) | ~ ! [X281 : term,X282 : term] : (~(X279 @ X281) | ~(X279 @ X282) | (X279 @ (ap @ X282 @ X281))) | ~ ! [X283 : term] : (~(X279 @ X283) | (X279 @ (lam @ X283))) | (X279 @ X278)) => ! [X284 : subst,X285 : term,X286 : (term > $o)] : (~ ! [X287 : term] : ((X286 @ (sub @ X287 @ X284)) | ~(var @ X287)) | ~ ! [X288 : term] : (~ ! [X289 : term] : (~(X286 @ X289) | (X286 @ (sub @ X288 @ (push @ X289 @ id)))) | (X286 @ (lam @ X288))) | ~ ! [X290 : term,X291 : term] : ((X286 @ (ap @ X291 @ X290)) | ~(X286 @ X291) | ~(X286 @ X290)) | (X286 @ (sub @ X285 @ X284))))))) <=> induction2lem_lthm) & lamnotvar & ((! [X292 : term] : (((sub @ X292 @ id)) = X292) => (! [X293 : term,X294 : term,X295 : term,X296 : term] : ((((ap @ X295 @ X294)) != ((ap @ X293 @ X296))) | (X293 = X295)) => ! [X297 : term,X298 : term,X299 : term,X300 : term] : ((((ap @ (sub @ X299 @ id) @ X298)) != ((ap @ (sub @ X297 @ id) @ X300))) | (X297 = X299)))) <=> hoasapinj1_lthm) & (! [X301 : subst,X302 : term,X303 : (term > $o)] : ~ ! [X304 : (term > $o)] : ~ ! [X305 : term] : (((X303 @ (sub @ X305 @ (push @ X302 @ X301)))) = ((X304 @ X305))) <=> pushprop_lem0) & pushprop_lem2v2_lthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (termmset <=> ! [X306 : term] : (((sub @ X306 @ id)) = X306)) & (hoasinduction_lem3v2_f <=> ! [X307 : term] : ~ ! [X308 : (subst > term > term)] : ~ ! [X309 : term,X310 : subst] : (((X308 @ X310 @ X309)) = ((sub @ X307 @ (push @ X309 @ X310))))) & hoasapinj1_gthm & pushprop_lem1_gthm & (hoasapinj1 <=> ! [X311 : term,X312 : term,X313 : term,X314 : term] : ((((ap @ (sub @ X313 @ id) @ X311)) != ((ap @ (sub @ X314 @ id) @ X312))) | (X313 = X314))) & (hoasinduction_lem0 <=> ! [X315 : (subst > term > subst > $o)] : ~ ! [X316 : (term > $o)] : ~ ! [X317 : term] : (((X315 @ id @ X317 @ id)) = ((X316 @ X317)))) & (! [X318 : term,X319 : (term > $o),X320 : (subst > term > subst > $o)] : ((X319 @ (lam @ X318)) | ~ ! [X321 : term] : (~(X319 @ X321) | (X319 @ (sub @ X318 @ (push @ X321 @ id)))) | ~ ! [X322 : term] : (((X320 @ id @ X322 @ id)) = ((X319 @ X322))) | ~ ! [X323 : (subst > term > term)] : (~ ! [X324 : term] : ((X320 @ id @ (X323 @ id @ X324) @ id) | ~(X320 @ id @ X324 @ id)) | (X320 @ id @ (lam @ (X323 @ sh @ one)) @ id) | ~ ! [X325 : subst,X326 : term,X327 : subst] : (((sub @ (X323 @ X325 @ X326) @ X327)) = ((X323 @ (comp @ X325 @ X327) @ (sub @ X326 @ X327)))))) <=> hoasinduction_lem3v2a) & hoaslamnotvar_gthm & ((! [X328 : term] : (((sub @ X328 @ id)) = X328) => (! [X329 : (subst > term > subst > $o),X330 : term] : ((X329 @ id @ (lam @ (sub @ X330 @ (push @ one @ sh))) @ id) | ~ ! [X331 : term] : (~(X329 @ id @ X331 @ id) | (X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)) | ~ ! [X332 : (subst > term > term)] : ((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id) | ~ ! [X333 : term] : (~(X329 @ id @ X333 @ id) | (X329 @ id @ (X332 @ id @ X333) @ id)) | ~ ! [X334 : subst,X335 : term,X336 : subst] : (((sub @ (X332 @ X334 @ X335) @ X336)) = ((X332 @ (comp @ X334 @ X336) @ (sub @ X335 @ X336)))))) => ! [X337 : term,X338 : (subst > term > subst > $o)] : (~ ! [X339 : (subst > term > term)] : (~ ! [X340 : term] : (~(X338 @ id @ X340 @ id) | (X338 @ id @ (X339 @ id @ X340) @ id)) | ~ ! [X341 : subst,X342 : term,X343 : subst] : (((X339 @ (comp @ X343 @ X341) @ (sub @ X342 @ X341))) = ((sub @ (X339 @ X343 @ X342) @ X341))) | (X338 @ id @ (lam @ (X339 @ sh @ one)) @ id)) | ~ ! [X344 : term] : ((X338 @ id @ (sub @ X337 @ (push @ X344 @ id)) @ id) | ~(X338 @ id @ X344 @ id)) | (X338 @ id @ (lam @ X337) @ id)))) <=> hoasinduction_lem3a_lthm) & induction2_gthm & axabs & (! [X345 : term] : (((sub @ X345 @ id)) = X345) <=> axvarid) & hoasapinj2_gthm & (sh = ((d2subst @ d_id))) & hoasapnotvar_gthm & ((! [X346 : subst] : (((comp @ id @ X346)) = X346) => (! [X347 : subst] : (((comp @ X347 @ id)) = X347) => (! [X348 : subst] : (((comp @ id @ X348)) = X348) & ! [X349 : subst] : (((comp @ X349 @ id)) = X349)))) <=> substmonoid_lthm) & (! [X350 : (subst > term > subst > $o),X351 : term] : (~ ! [X352 : term,X353 : term] : (~(X350 @ id @ X352 @ id) | (X350 @ id @ (ap @ (sub @ X352 @ id) @ X353) @ id) | ~(X350 @ id @ X353 @ id)) | (X350 @ id @ X351 @ id) | ~ ! [X354 : (subst > term > term)] : (~ ! [X355 : subst,X356 : subst,X357 : term] : (((X354 @ (comp @ X355 @ X356) @ (sub @ X357 @ X356))) = ((sub @ (X354 @ X355 @ X357) @ X356))) | (X350 @ id @ (lam @ (X354 @ sh @ one)) @ id) | ~ ! [X358 : term] : (~(X350 @ id @ X358 @ id) | (X350 @ id @ (X354 @ id @ X358) @ id))) | ~ ! [X359 : term] : ((X350 @ id @ X359 @ id) | ~(var @ (sub @ X359 @ id))) | ~ ! [X360 : subst,X361 : subst,X362 : subst,X363 : term] : (~(X350 @ X360 @ X363 @ (comp @ X361 @ X362)) | (X350 @ (comp @ X360 @ X361) @ (sub @ X363 @ X361) @ X362)) | ~ ! [X364 : subst,X365 : term,X366 : subst,X367 : subst] : (~(X350 @ (comp @ X367 @ X364) @ (sub @ X365 @ X364) @ X366) | (X350 @ X367 @ X365 @ (comp @ X364 @ X366)))) <=> hoasinduction) & (! [X368 : term,X369 : (subst > term > subst > $o)] : ((X369 @ id @ (lam @ (sub @ X368 @ (push @ one @ sh))) @ id) | ~ ! [X370 : (subst > term > term),X371 : term] : ((X369 @ id @ (lam @ (X370 @ sh @ one)) @ id) | ~ ! [X372 : term] : (~(X369 @ id @ X372 @ id) | (X369 @ id @ (X370 @ id @ X372) @ id)) | ~ ! [X373 : subst,X374 : term,X375 : subst] : (((sub @ (sub @ X371 @ (push @ X374 @ X373)) @ X375)) = ((sub @ (X370 @ X373 @ X374) @ X375))) | ~ ! [X376 : subst,X377 : subst,X378 : term] : (((sub @ X371 @ (push @ (sub @ X378 @ X377) @ (comp @ X376 @ X377)))) = ((X370 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377))))) | ~ ! [X379 : term] : ((X369 @ id @ (sub @ X368 @ (push @ X379 @ id)) @ id) | ~(X369 @ id @ X379 @ id))) <=> hoasinduction_lem3aaa) & hoaslaminj_gthm & ((! [X380 : term] : (((sub @ X380 @ id)) = X380) => (! [X381 : subst,X382 : (term > $o),X383 : term] : (~ ! [X384 : term,X385 : term] : (~(X382 @ X384) | ~(X382 @ X385) | (X382 @ (ap @ X385 @ X384))) | (X382 @ (sub @ X383 @ X381)) | ~ ! [X386 : term] : (~(var @ X386) | (X382 @ (sub @ X386 @ X381))) | ~ ! [X387 : term] : (~ ! [X388 : term] : ((X382 @ (sub @ X387 @ (push @ X388 @ id))) | ~(X382 @ X388)) | (X382 @ (lam @ X387)))) => ! [X389 : (term > $o),X390 : term] : (~ ! [X391 : term] : (~ ! [X392 : term] : (~(X389 @ X392) | (X389 @ (sub @ X391 @ (push @ X392 @ id)))) | (X389 @ (lam @ X391))) | (X389 @ X390) | ~ ! [X393 : term,X394 : term] : (~(X389 @ X394) | (X389 @ (ap @ X393 @ X394)) | ~(X389 @ X393)) | ~ ! [X395 : term] : ((X389 @ X395) | ~(var @ X395))))) <=> induction2_lthm) & hoasinduction_lem1v2 & substmonoid_gthm & (apinj1 <=> ! [X396 : term,X397 : term,X398 : term,X399 : term] : ((X396 = X398) | (((ap @ X398 @ X399)) != ((ap @ X396 @ X397))))) & (hoasinduction_lem3_lthm <=> (! [X400 : term] : (((sub @ X400 @ id)) = X400) => (! [X401 : (subst > term > subst > $o),X402 : term] : ((X401 @ id @ (lam @ (sub @ X402 @ (push @ one @ sh))) @ id) | ~ ! [X403 : term] : (~(X401 @ id @ X403 @ id) | (X401 @ id @ (sub @ X402 @ (push @ X403 @ id)) @ id)) | ~ ! [X404 : (subst > term > term)] : ((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id) | ~ ! [X405 : term] : ((X401 @ id @ (X404 @ id @ X405) @ id) | ~(X401 @ id @ X405 @ id)) | ~ ! [X406 : subst,X407 : term,X408 : subst] : (((X404 @ (comp @ X408 @ X406) @ (sub @ X407 @ X406))) = ((sub @ (X404 @ X408 @ X407) @ X406))))) => ! [X409 : term,X410 : (subst > term > subst > $o)] : ((X410 @ id @ (lam @ X409) @ id) | ~ ! [X411 : subst,X412 : term,X413 : subst,X414 : subst] : (~(X410 @ X414 @ X412 @ (comp @ X411 @ X413)) | (X410 @ (comp @ X414 @ X411) @ (sub @ X412 @ X411) @ X413)) | ~ ! [X415 : subst,X416 : subst,X417 : subst,X418 : term] : ((X410 @ X416 @ X418 @ (comp @ X417 @ X415)) | ~(X410 @ (comp @ X416 @ X417) @ (sub @ X418 @ X417) @ X415)) | ~ ! [X419 : (subst > term > term)] : ((X410 @ id @ (lam @ (X419 @ sh @ one)) @ id) | ~ ! [X420 : subst,X421 : term,X422 : subst] : (((X419 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X419 @ X422 @ X421) @ X420))) | ~ ! [X423 : term] : (~(X410 @ id @ X423 @ id) | (X410 @ id @ (X419 @ id @ X423) @ id))) | ~ ! [X424 : term] : ((X410 @ id @ (sub @ X409 @ (push @ X424 @ id)) @ id) | ~(X410 @ id @ X424 @ id)))))) & (hoasinduction_lem3b <=> ! [X425 : term] : ~ ! [X426 : (subst > term > term)] : (((X426 @ sh @ one)) != ((sub @ X425 @ (push @ one @ sh))))) & ulamvarsh & (! [X427 : term,X428 : term] : ((((lam @ X428)) != ((lam @ X427))) | (X427 = X428)) <=> laminj) & (hoasinduction_p_and_p_prime = (^[X429 : (subst > term > subst > $o), X430 : (term > $o)] : (! [X431 : term] : (((X429 @ id @ X431 @ id)) = ((X430 @ X431)))))) & (id = ((d2subst @ d_id))) & ((! [X432 : (subst > term > subst > $o)] : ~ ! [X433 : (term > $o)] : ~ ! [X434 : term] : (((X432 @ id @ X434 @ id)) = ((X433 @ X434))) => (! [X435 : (term > $o),X436 : term] : ((X435 @ X436) | ~ ! [X437 : term,X438 : term] : (~(X435 @ X437) | ~(X435 @ X438) | (X435 @ (ap @ X437 @ X438))) | ~ ! [X439 : term] : (~(var @ X439) | (X435 @ X439)) | ~ ! [X440 : term] : ((X435 @ (lam @ X440)) | ~ ! [X441 : term] : (~(X435 @ X441) | (X435 @ (sub @ X440 @ (push @ X441 @ id)))))) => (! [X442 : term] : (((sub @ X442 @ id)) = X442) => (! [X443 : (term > $o),X444 : term,X445 : (subst > term > subst > $o)] : (~ ! [X446 : term] : (((X445 @ id @ X446 @ id)) = ((X443 @ X446))) | ~ ! [X447 : term] : ((X443 @ (sub @ X444 @ (push @ X447 @ id))) | ~(X443 @ X447)) | (X443 @ (lam @ X444)) | ~ ! [X448 : (subst > term > term)] : ((X445 @ id @ (lam @ (X448 @ sh @ one)) @ id) | ~ ! [X449 : term] : (~(X445 @ id @ X449 @ id) | (X445 @ id @ (X448 @ id @ X449) @ id)) | ~ ! [X450 : subst,X451 : term,X452 : subst] : (((X448 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) = ((sub @ (X448 @ X452 @ X451) @ X450))))) => ! [X453 : (subst > term > subst > $o),X454 : term] : (~ ! [X455 : term,X456 : term] : (~(X453 @ id @ X455 @ id) | (X453 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id) | ~(X453 @ id @ X456 @ id)) | ~ ! [X457 : (subst > term > term)] : (~ ! [X458 : subst,X459 : subst,X460 : term] : (((sub @ (X457 @ X458 @ X460) @ X459)) = ((X457 @ (comp @ X458 @ X459) @ (sub @ X460 @ X459)))) | (X453 @ id @ (lam @ (X457 @ sh @ one)) @ id) | ~ ! [X461 : term] : (~(X453 @ id @ X461 @ id) | (X453 @ id @ (X457 @ id @ X461) @ id))) | ~ ! [X462 : subst,X463 : term,X464 : subst,X465 : subst] : ((X453 @ (comp @ X465 @ X464) @ (sub @ X463 @ X464) @ X462) | ~(X453 @ X465 @ X463 @ (comp @ X464 @ X462))) | (X453 @ id @ X454 @ id) | ~ ! [X466 : term] : (~(var @ (sub @ X466 @ id)) | (X453 @ id @ X466 @ id)) | ~ ! [X467 : term,X468 : subst,X469 : subst,X470 : subst] : ((X453 @ X470 @ X467 @ (comp @ X469 @ X468)) | ~(X453 @ (comp @ X470 @ X469) @ (sub @ X467 @ X469) @ X468))))))) <=> hoasinduction_lthm_3) & pushprop_gthm & pushprop_lem1v2_gthm & hoasinduction_lem1_lthm & (! [X471 : subst,X472 : term] : (((comp @ sh @ (push @ X472 @ X471))) = X471) <=> axshiftcons) & pushprop_lthm_orig & hoasinduction_lem2_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_lthm & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (! [X475 : term,X476 : (term > $o),X477 : subst] : (~ ! [X478 : term,X479 : term] : (~(X476 @ X479) | (X476 @ (ap @ X479 @ X478)) | ~(X476 @ X478)) | ~ ! [X480 : term] : ((X476 @ (lam @ X480)) | ~ ! [X481 : term] : ((X476 @ (sub @ X480 @ (push @ X481 @ id))) | ~(X476 @ X481))) | (X476 @ (sub @ X475 @ X477)) | ~ ! [X482 : term] : (~(var @ X482) | (X476 @ (sub @ X482 @ X477)))) <=> induction2lem) & hoasinduction_lem1_gthm & (! [X483 : subst] : (((comp @ X483 @ id)) = X483) <=> axidr) & pushprop_lem3v2 & (hoasinduction_no_psi_cond <=> ! [X484 : (subst > term > subst > $o),X485 : term] : (~ ! [X486 : (subst > term > term)] : (~ ! [X487 : term] : ((X484 @ id @ (X486 @ id @ X487) @ id) | ~(X484 @ id @ X487 @ id)) | ~ ! [X488 : term,X489 : subst,X490 : subst] : (((sub @ (X486 @ X490 @ X488) @ X489)) = ((X486 @ (comp @ X490 @ X489) @ (sub @ X488 @ X489)))) | (X484 @ id @ (lam @ (X486 @ sh @ one)) @ id)) | ~ ! [X491 : term,X492 : term] : ((X484 @ id @ (ap @ (sub @ X491 @ id) @ X492) @ id) | ~(X484 @ id @ X492 @ id) | ~(X484 @ id @ X491 @ id)) | (X484 @ id @ X485 @ id))) & hoasinduction_lem3a_gthm & axvarshift & hoaslamnotap_gthm & (induction2 <=> ! [X493 : term,X494 : (term > $o)] : (~ ! [X495 : term] : ((X494 @ (lam @ X495)) | ~ ! [X496 : term] : ((X494 @ (sub @ X495 @ (push @ X496 @ id))) | ~(X494 @ X496))) | (X494 @ X493) | ~ ! [X497 : term] : ((X494 @ X497) | ~(var @ X497)) | ~ ! [X498 : term,X499 : term] : ((X494 @ (ap @ X498 @ X499)) | ~(X494 @ X499) | ~(X494 @ X498)))) & ulamvarind & pushprop_lthm & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & (pushprop_lem1v2_lthm <=> (! [X500 : term,X501 : subst] : (((sub @ one @ (push @ X500 @ X501))) = X500) => ! [X502 : (term > $o),X503 : subst,X504 : term,X505 : (term > $o)] : ((X505 @ one) | ~(X502 @ X504) | ~ ! [X506 : term] : (((X502 @ (sub @ X506 @ (push @ X504 @ X503)))) = ((X505 @ X506)))))) & (one = ((d2term @ d_one))) & ((! [X507 : term] : (((sub @ X507 @ id)) = X507) => ! [X508 : term,X509 : (term > $o),X510 : (subst > term > subst > $o)] : (~ ! [X511 : term,X512 : subst,X513 : subst,X514 : subst] : ((X510 @ (comp @ X514 @ X512) @ (sub @ X511 @ X512) @ X513) | ~(X510 @ X514 @ X511 @ (comp @ X512 @ X513))) | (X509 @ (lam @ X508)) | ~ ! [X515 : (subst > term > term)] : (~ ! [X516 : term] : (~(X510 @ id @ X516 @ id) | (X510 @ id @ (X515 @ id @ X516) @ id)) | ~ ! [X517 : subst,X518 : subst,X519 : term] : (((X515 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X515 @ X518 @ X519) @ X517))) | (X510 @ id @ (lam @ (X515 @ sh @ one)) @ id)) | ~ ! [X520 : term] : (((X510 @ id @ X520 @ id)) = ((X509 @ X520))) | ~ ! [X521 : subst,X522 : subst,X523 : subst,X524 : term] : ((X510 @ X521 @ X524 @ (comp @ X523 @ X522)) | ~(X510 @ (comp @ X521 @ X523) @ (sub @ X524 @ X523) @ X522)) | ~ ! [X525 : term] : ((X509 @ (sub @ X508 @ (push @ X525 @ id))) | ~(X509 @ X525)))) <=> hoasinduction_lem3v2_lthm) & (induction <=> ! [X526 : (term > $o),X527 : term] : ((X526 @ X527) | ~ ! [X528 : term] : (~(var @ X528) | (X526 @ X528)) | ~ ! [X529 : term,X530 : term] : (~(X526 @ X529) | (X526 @ (ap @ X529 @ X530)) | ~(X526 @ X530)) | ~ ! [X531 : term] : (~(X526 @ X531) | (X526 @ (lam @ X531))))) & ! [X532 : d_term,X533 : d_term] : ((((d2term @ X532)) = ((d2term @ X533))) => (X532 = X533)) & (hoasinduction_lem3 <=> ! [X534 : term,X535 : (subst > term > subst > $o)] : ((X535 @ id @ (lam @ X534) @ id) | ~ ! [X536 : subst,X537 : subst,X538 : term,X539 : subst] : (~(X535 @ X539 @ X538 @ (comp @ X536 @ X537)) | (X535 @ (comp @ X539 @ X536) @ (sub @ X538 @ X536) @ X537)) | ~ ! [X540 : (subst > term > term)] : (~ ! [X541 : term] : ((X535 @ id @ (X540 @ id @ X541) @ id) | ~(X535 @ id @ X541 @ id)) | (X535 @ id @ (lam @ (X540 @ sh @ one)) @ id) | ~ ! [X542 : subst,X543 : term,X544 : subst] : (((X540 @ (comp @ X544 @ X542) @ (sub @ X543 @ X542))) = ((sub @ (X540 @ X544 @ X543) @ X542)))) | ~ ! [X545 : term,X546 : subst,X547 : subst,X548 : subst] : (~(X535 @ (comp @ X548 @ X547) @ (sub @ X545 @ X547) @ X546) | (X535 @ X548 @ X545 @ (comp @ X547 @ X546))) | ~ ! [X549 : term] : ((X535 @ id @ (sub @ X534 @ (push @ X549 @ id)) @ id) | ~(X535 @ id @ X549 @ id))))),
% 5.43/1.21 inference(rectify,[],[f1])).
% 5.43/1.21 thf(f5,plain,(
% 5.43/1.21 (apnotvar = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (! [X3 : (term > $o),X4 : subst,X5 : term,X6 : term,X7 : (term > $o)] : (~ (((X7 @ X5)) = $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4)))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem3v2_lthm = $true) & (induction2lem_gthm = $true) & (! [X8 : term,X10 : (subst > term > term),X9 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ~ ! [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & ! [X14 : d_subst,X15 : d_subst] : ((((d2subst @ X15)) = ((d2subst @ X14))) => (X14 = X15)) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (termmset_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X23 : (term > $o),X24 : (subst > term > subst > $o),X25 : term] : (~ ! [X26 : term] : (((X24 @ id @ X26 @ id)) = ((X23 @ X26))) | ~ ! [X27 : subst,X28 : subst,X29 : subst,X30 : term] : ((((X24 @ X29 @ X30 @ (comp @ X28 @ X27))) = $true) | ~ (((X24 @ (comp @ X29 @ X28) @ (sub @ X30 @ X28) @ X27)) = $true)) | ~ ! [X31 : (subst > term > term)] : ((((X24 @ id @ (lam @ (X31 @ sh @ one)) @ id)) = $true) | ~ ! [X32 : subst,X33 : subst,X34 : term] : (((sub @ (X31 @ X33 @ X34) @ X32)) = ((X31 @ (comp @ X33 @ X32) @ (sub @ X34 @ X32)))) | ~ ! [X35 : term] : (($true = ((X24 @ id @ (X31 @ id @ X35) @ id))) | ~ (((X24 @ id @ X35 @ id)) = $true))) | ~ ! [X36 : term] : (~ (((X23 @ X36)) = $true) | ($true = ((X23 @ (sub @ X25 @ (push @ X36 @ id)))))) | ($true = ((X23 @ (lam @ X25)))) | ~ ! [X37 : subst,X38 : term,X39 : subst,X40 : subst] : ((((X24 @ (comp @ X37 @ X40) @ (sub @ X38 @ X40) @ X39)) = $true) | ~ ($true = ((X24 @ X37 @ X38 @ (comp @ X40 @ X39)))))) <=> (hoasinduction_lem3v2 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj2_lthm = $true) <=> (! [X41 : term,X42 : term,X43 : term,X44 : term] : ((X42 = X44) | (((ap @ X43 @ X42)) != ((ap @ X41 @ X44)))) => ! [X45 : term,X46 : term,X47 : term,X48 : term] : ((X47 = X48) | (((ap @ (sub @ X46 @ id) @ X48)) != ((ap @ (sub @ X45 @ id) @ X47)))))) & (! [X49 : term] : ~ ! [X50 : (subst > term > term)] : (((sub @ X49 @ (push @ one @ sh))) != ((X50 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X51 : term,X52 : subst,X53 : (term > $o)] : ~ ! [X54 : (term > $o)] : ~ ! [X55 : term] : (((X54 @ X55)) = ((X53 @ (sub @ X55 @ (push @ X51 @ X52))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop = $true) & (hoasinduction_lem2v2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X56 : term] : ~ ! [X57 : (subst > term > term)] : ~ ! [X58 : subst,X59 : term] : (((sub @ X56 @ (push @ X59 @ X58))) = ((X57 @ X58 @ X59))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((substmonoid = $true) <=> (! [X60 : subst] : (((comp @ id @ X60)) = X60) & ! [X61 : subst] : (((comp @ X61 @ id)) = X61))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((axidl = $true) <=> ! [X62 : subst] : (((comp @ id @ X62)) = X62)) & (hoaslamnotap_lthm = $true) & ~ (lamnotap = $true) & ((! [X63 : term,X64 : (term > $o)] : (~ ! [X65 : term] : (~ (((var @ X65)) = $true) | (((X64 @ X65)) = $true)) | ~ ! [X66 : term,X67 : term] : (~ (((X64 @ X67)) = $true) | ($true = ((X64 @ (ap @ X66 @ X67)))) | ~ ($true = ((X64 @ X66)))) | ~ ! [X68 : term] : (~ ! [X69 : term] : ((((X64 @ (sub @ X68 @ (push @ X69 @ id)))) = $true) | ~ ($true = ((X64 @ X69)))) | (((X64 @ (lam @ X68))) = $true)) | ($true = ((X64 @ X63)))) => (! [X70 : term,X71 : term,X72 : (subst > term > subst > $o)] : (~ ! [X73 : subst,X74 : subst,X75 : term,X76 : subst] : (($true = ((X72 @ X76 @ X75 @ (comp @ X73 @ X74)))) | ~ ($true = ((X72 @ (comp @ X76 @ X73) @ (sub @ X75 @ X73) @ X74)))) | ~ ! [X77 : subst,X78 : subst,X79 : term,X80 : subst] : ((((X72 @ (comp @ X78 @ X77) @ (sub @ X79 @ X77) @ X80)) = $true) | ~ ($true = ((X72 @ X78 @ X79 @ (comp @ X77 @ X80))))) | ~ (((X72 @ id @ X70 @ id)) = $true) | ($true = ((X72 @ id @ (ap @ X70 @ X71) @ id))) | ~ ($true = ((X72 @ id @ X71 @ id))) | ~ ! [X81 : term,X82 : term] : (~ (((X72 @ id @ X81 @ id)) = $true) | ($true = ((X72 @ id @ (ap @ (sub @ X81 @ id) @ X82) @ id))) | ~ ($true = ((X72 @ id @ X82 @ id))))) => (! [X83 : (subst > term > subst > $o),X84 : term] : (~ ! [X85 : term,X86 : subst,X87 : subst,X88 : subst] : (~ ($true = ((X83 @ (comp @ X86 @ X88) @ (sub @ X85 @ X88) @ X87))) | ($true = ((X83 @ X86 @ X85 @ (comp @ X88 @ X87))))) | ~ ! [X89 : term,X90 : subst,X91 : subst,X92 : subst] : (~ ($true = ((X83 @ X92 @ X89 @ (comp @ X90 @ X91)))) | ($true = ((X83 @ (comp @ X92 @ X90) @ (sub @ X89 @ X90) @ X91)))) | ~ ! [X93 : term] : (~ ($true = ((X83 @ id @ X93 @ id))) | (((X83 @ id @ (sub @ X84 @ (push @ X93 @ id)) @ id)) = $true)) | ($true = ((X83 @ id @ (lam @ X84) @ id))) | ~ ! [X94 : (subst > term > term)] : (~ ! [X95 : term] : ((((X83 @ id @ (X94 @ id @ X95) @ id)) = $true) | ~ (((X83 @ id @ X95 @ id)) = $true)) | (((X83 @ id @ (lam @ (X94 @ sh @ one)) @ id)) = $true) | ~ ! [X96 : subst,X97 : subst,X98 : term] : (((X94 @ (comp @ X97 @ X96) @ (sub @ X98 @ X96))) = ((sub @ (X94 @ X97 @ X98) @ X96))))) => ! [X99 : (subst > term > subst > $o),X100 : term] : (~ ! [X101 : term,X102 : subst,X103 : subst,X104 : subst] : (($true = ((X99 @ (comp @ X104 @ X102) @ (sub @ X101 @ X102) @ X103))) | ~ ($true = ((X99 @ X104 @ X101 @ (comp @ X102 @ X103))))) | ~ ! [X105 : term] : (($true = ((X99 @ id @ X105 @ id))) | ~ (((var @ (sub @ X105 @ id))) = $true)) | ($true = ((X99 @ id @ X100 @ id))) | ~ ! [X106 : subst,X107 : term,X108 : subst,X109 : subst] : (~ ($true = ((X99 @ (comp @ X108 @ X109) @ (sub @ X107 @ X109) @ X106))) | (((X99 @ X108 @ X107 @ (comp @ X109 @ X106))) = $true)) | ~ ! [X110 : term,X111 : term] : (~ ($true = ((X99 @ id @ X110 @ id))) | ~ ($true = ((X99 @ id @ X111 @ id))) | (((X99 @ id @ (ap @ (sub @ X111 @ id) @ X110) @ id)) = $true)) | ~ ! [X112 : (subst > term > term)] : (~ ! [X113 : term] : (~ (((X99 @ id @ X113 @ id)) = $true) | (((X99 @ id @ (X112 @ id @ X113) @ id)) = $true)) | ($true = ((X99 @ id @ (lam @ (X112 @ sh @ one)) @ id))) | ~ ! [X114 : term,X115 : subst,X116 : subst] : (((X112 @ (comp @ X116 @ X115) @ (sub @ X114 @ X115))) = ((sub @ (X112 @ X116 @ X114) @ X115)))))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X117 : (subst > term > subst > $o)] : ~ ! [X118 : (term > $o)] : ~ ! [X119 : term] : (((X117 @ id @ X119 @ id)) = ((X118 @ X119))) => (! [X120 : (term > $o),X121 : term] : (~ ! [X122 : term] : (($true = ((X120 @ X122))) | ~ ($true = ((var @ X122)))) | ($true = ((X120 @ X121))) | ~ ! [X123 : term,X124 : term] : (~ ($true = ((X120 @ X124))) | ~ (((X120 @ X123)) = $true) | ($true = ((X120 @ (ap @ X123 @ X124))))) | ~ ! [X125 : term] : (~ ! [X126 : term] : ((((X120 @ (sub @ X125 @ (push @ X126 @ id)))) = $true) | ~ ($true = ((X120 @ X126)))) | (((X120 @ (lam @ X125))) = $true))) => (! [X127 : term] : (((sub @ X127 @ id)) = X127) => (! [X128 : term,X129 : (term > $o),X130 : (subst > term > subst > $o)] : ((((X129 @ (lam @ X128))) = $true) | ~ ! [X131 : term] : (~ ($true = ((X129 @ X131))) | ($true = ((X129 @ (sub @ X128 @ (push @ X131 @ id)))))) | ~ ! [X132 : (subst > term > term)] : ((((X130 @ id @ (lam @ (X132 @ sh @ one)) @ id)) = $true) | ~ ! [X133 : subst,X134 : subst,X135 : term] : (((X132 @ (comp @ X134 @ X133) @ (sub @ X135 @ X133))) = ((sub @ (X132 @ X134 @ X135) @ X133))) | ~ ! [X136 : term] : (($true = ((X130 @ id @ (X132 @ id @ X136) @ id))) | ~ (((X130 @ id @ X136 @ id)) = $true))) | ~ ! [X137 : term] : (((X129 @ X137)) = ((X130 @ id @ X137 @ id)))) => ! [X138 : (subst > term > subst > $o),X139 : term] : (~ ! [X140 : (subst > term > term)] : (($true = ((X138 @ id @ (lam @ (X140 @ sh @ one)) @ id))) | ~ ! [X141 : term] : (~ ($true = ((X138 @ id @ X141 @ id))) | ($true = ((X138 @ id @ (X140 @ id @ X141) @ id)))) | ~ ! [X142 : subst,X143 : term,X144 : subst] : (((X140 @ (comp @ X144 @ X142) @ (sub @ X143 @ X142))) = ((sub @ (X140 @ X144 @ X143) @ X142)))) | ~ ! [X145 : term,X146 : term] : (~ ($true = ((X138 @ id @ X145 @ id))) | (((X138 @ id @ (ap @ (sub @ X146 @ id) @ X145) @ id)) = $true) | ~ ($true = ((X138 @ id @ X146 @ id)))) | (((X138 @ id @ X139 @ id)) = $true))))))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X147 : term,X148 : term,X149 : term,X150 : term] : ((X147 = X148) | (((ap @ X149 @ X148)) != ((ap @ X150 @ X147)))) <=> (apinj2 = $true)) & ((axscons = $true) <=> ! [X151 : subst] : (((push @ (sub @ one @ X151) @ (comp @ sh @ X151))) = X151)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X154 : subst,X155 : (term > $o),X156 : term,X157 : (term > $o)] : (($true = ((X155 @ one))) | ~ ($true = ((X157 @ X156))) | ~ ! [X158 : term] : (((X155 @ X158)) = ((X157 @ (sub @ X158 @ (push @ X156 @ X154)))))) <=> (pushprop_lem1v2 = $true)) & ((! [X159 : term,X160 : subst] : (((sub @ one @ (push @ X159 @ X160))) = X159) => (! [X161 : subst,X162 : term] : (((comp @ sh @ (push @ X162 @ X161))) = X161) => (! [X163 : term,X164 : term] : ((((lam @ X164)) != ((lam @ X163))) | (X163 = X164)) => ! [X165 : term,X166 : (subst > term > term),X167 : subst,X168 : (subst > term > term)] : ((((X168 @ X167 @ X165)) = ((X166 @ X167 @ X165))) | ~ ! [X169 : subst,X170 : subst,X171 : term] : (((sub @ (X166 @ X169 @ X171) @ X170)) = ((X166 @ (comp @ X169 @ X170) @ (sub @ X171 @ X170)))) | (((lam @ (X168 @ sh @ one))) != ((lam @ (X166 @ sh @ one)))) | ~ ! [X172 : subst,X173 : term,X174 : subst] : (((sub @ (X168 @ X172 @ X173) @ X174)) = ((X168 @ (comp @ X172 @ X174) @ (sub @ X173 @ X174)))))))) <=> (hoaslaminj_lthm = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem2v2 = $true) & (! [X175 : term,X176 : term] : ((X175 = X176) | (((sub @ X176 @ sh)) != ((sub @ X175 @ sh)))) <=> (shinj = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X177 : (subst > term > subst > $o),X178 : term] : (~ ! [X179 : term] : ((((X177 @ id @ (sub @ X178 @ (push @ X179 @ id)) @ id)) = $true) | ~ ($true = ((X177 @ id @ X179 @ id)))) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term,X182 : subst,X183 : subst] : (((X180 @ (comp @ X182 @ X183) @ (sub @ X181 @ X183))) = ((sub @ (X180 @ X182 @ X181) @ X183))) | (((X177 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true) | ~ ! [X184 : term] : (~ ($true = ((X177 @ id @ X184 @ id))) | ($true = ((X177 @ id @ (X180 @ id @ X184) @ id))))) | ($true = ((X177 @ id @ (lam @ (sub @ X178 @ (push @ one @ sh))) @ id))))) & ((hoasapinj2 = $true) <=> ! [X185 : term,X186 : term,X187 : term,X188 : term] : ((((ap @ (sub @ X188 @ id) @ X186)) != ((ap @ (sub @ X187 @ id) @ X185))) | (X185 = X186))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X189 : (subst > term > subst > $o),X190 : term] : (~ ! [X191 : term] : (($true = ((X189 @ id @ (sub @ X190 @ (push @ X191 @ id)) @ id))) | ~ (((X189 @ id @ X191 @ id)) = $true)) | ~ ! [X192 : (subst > term > term)] : (~ ! [X193 : term,X194 : subst,X195 : subst] : (((X192 @ (comp @ X194 @ X195) @ (sub @ X193 @ X195))) = ((sub @ (X192 @ X194 @ X193) @ X195))) | ($true = ((X189 @ id @ (lam @ (X192 @ sh @ one)) @ id))) | ~ ! [X196 : term] : (~ ($true = ((X189 @ id @ X196 @ id))) | ($true = ((X189 @ id @ (X192 @ id @ X196) @ id))))) | ($true = ((X189 @ id @ (lam @ X190) @ id)))) <=> (hoasinduction_lem3a = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ~ (ulamvar1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X197 : (subst > term > subst > $o),X198 : term] : ((((X197 @ id @ (lam @ (sub @ X198 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X199 : term] : ((((X197 @ id @ (sub @ X198 @ (push @ X199 @ id)) @ id)) = $true) | ~ (((X197 @ id @ X199 @ id)) = $true)) | ~ ! [X200 : (subst > term > term)] : (($true = ((X197 @ id @ (lam @ (X200 @ sh @ one)) @ id))) | ~ ! [X201 : subst,X202 : subst,X203 : term] : (((X200 @ (comp @ X201 @ X202) @ (sub @ X203 @ X202))) = ((sub @ (X200 @ X201 @ X203) @ X202))) | ~ ! [X204 : term] : (($true = ((X197 @ id @ (X200 @ id @ X204) @ id))) | ~ (((X197 @ id @ X204 @ id)) = $true))))) & (axmap = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1 = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (axclos = $true) & ! [X205 : d_subst] : (d_id = X205) & ((pushprop_lem1_lthm = $true) <=> (! [X206 : subst,X207 : term] : (((sub @ one @ (push @ X207 @ X206))) = X207) => (! [X208 : term,X209 : subst] : (((comp @ sh @ (push @ X208 @ X209))) = X209) => ! [X210 : term,X211 : (term > $o),X212 : subst,X213 : (term > $o),X214 : term] : (($true = ((X211 @ (sub @ X214 @ (push @ X210 @ X212))))) | ~ (((X213 @ X214)) = $true))))) & ((! [X215 : term] : ~ ! [X216 : (subst > term > term)] : ~ ! [X217 : subst,X218 : term] : (((sub @ X215 @ (push @ X218 @ X217))) = ((X216 @ X217 @ X218))) => (! [X219 : term] : (((sub @ X219 @ id)) = X219) => ! [X220 : term,X221 : (term > $o),X222 : (subst > term > subst > $o)] : (($true = ((X221 @ (lam @ X220)))) | ~ ! [X223 : (subst > term > term)] : (($true = ((X222 @ id @ (lam @ (X223 @ sh @ one)) @ id))) | ~ ! [X224 : term] : (($true = ((X222 @ id @ (X223 @ id @ X224) @ id))) | ~ (((X222 @ id @ X224 @ id)) = $true)) | ~ ! [X225 : term,X226 : subst,X227 : subst] : (((sub @ (X223 @ X227 @ X225) @ X226)) = ((X223 @ (comp @ X227 @ X226) @ (sub @ X225 @ X226))))) | ~ ! [X228 : term] : (((X221 @ X228)) = ((X222 @ id @ X228 @ id))) | ~ ! [X229 : term] : ((((X221 @ (sub @ X220 @ (push @ X229 @ id)))) = $true) | ~ ($true = ((X221 @ X229))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((axvarcons = $true) <=> ! [X230 : subst,X231 : term] : (((sub @ one @ (push @ X231 @ X230))) = X231)) & (! [X232 : (subst > term > term),X233 : (subst > term > term),X234 : subst,X235 : term] : ((((X233 @ X234 @ X235)) = ((X232 @ X234 @ X235))) | ~ ! [X236 : term,X237 : subst,X238 : subst] : (((X232 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X232 @ X237 @ X236) @ X238))) | ~ ! [X239 : term,X240 : subst,X241 : subst] : (((X233 @ (comp @ X240 @ X241) @ (sub @ X239 @ X241))) = ((sub @ (X233 @ X240 @ X239) @ X241))) | (((lam @ (X233 @ sh @ one))) != ((lam @ (X232 @ sh @ one))))) <=> (hoaslaminj = $true)) & ! [X242 : d_term] : (d_one = X242) & (axapp = $true) & (! [X243 : (subst > term > subst > $o),X244 : term,X245 : (term > $o),X246 : term] : (~ ! [X247 : term] : (((X243 @ id @ X247 @ id)) = ((X245 @ X247))) | (((X245 @ (ap @ X246 @ X244))) = $true) | ~ ($true = ((X245 @ X246))) | ~ ! [X248 : subst,X249 : term,X250 : subst,X251 : subst] : (~ ($true = ((X243 @ (comp @ X248 @ X251) @ (sub @ X249 @ X251) @ X250))) | ($true = ((X243 @ X248 @ X249 @ (comp @ X251 @ X250))))) | ~ ($true = ((X245 @ X244))) | ~ ! [X252 : subst,X253 : subst,X254 : subst,X255 : term] : (~ ($true = ((X243 @ X252 @ X255 @ (comp @ X253 @ X254)))) | ($true = ((X243 @ (comp @ X252 @ X253) @ (sub @ X255 @ X253) @ X254)))) | ~ ! [X256 : term,X257 : term] : (~ ($true = ((X243 @ id @ X256 @ id))) | (((X243 @ id @ (ap @ (sub @ X256 @ id) @ X257) @ id)) = $true) | ~ (((X243 @ id @ X257 @ id)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((! [X258 : term] : (((sub @ X258 @ id)) = X258) => ! [X259 : term] : (((sub @ X259 @ id)) = X259)) <=> (termmset_lthm = $true)) & (hoasapnotvar = $true) & (! [X260 : (subst > term > subst > $o),X261 : term,X262 : term] : (~ ! [X263 : subst,X264 : subst,X265 : subst,X266 : term] : (~ ($true = ((X260 @ X265 @ X266 @ (comp @ X263 @ X264)))) | (((X260 @ (comp @ X265 @ X263) @ (sub @ X266 @ X263) @ X264)) = $true)) | ($true = ((X260 @ id @ (ap @ X261 @ X262) @ id))) | ~ ! [X267 : subst,X268 : subst,X269 : subst,X270 : term] : (~ (((X260 @ (comp @ X269 @ X267) @ (sub @ X270 @ X267) @ X268)) = $true) | ($true = ((X260 @ X269 @ X270 @ (comp @ X267 @ X268))))) | ~ ($true = ((X260 @ id @ X262 @ id))) | ~ ($true = ((X260 @ id @ X261 @ id))) | ~ ! [X271 : term,X272 : term] : (~ ($true = ((X260 @ id @ X272 @ id))) | ~ ($true = ((X260 @ id @ X271 @ id))) | (((X260 @ id @ (ap @ (sub @ X271 @ id) @ X272) @ id)) = $true))) <=> (hoasinduction_lem2 = $true)) & ((! [X273 : subst,X274 : term] : (((sub @ one @ (push @ X274 @ X273))) = X274) => (! [X275 : term,X276 : subst] : (((comp @ sh @ (push @ X275 @ X276))) = X276) => (! [X277 : subst] : (((comp @ X277 @ id)) = X277) => (! [X278 : term,X279 : (term > $o)] : (~ ! [X280 : term] : (~ ($true = ((var @ X280))) | (((X279 @ X280)) = $true)) | ~ ! [X281 : term,X282 : term] : (~ (((X279 @ X281)) = $true) | ~ (((X279 @ X282)) = $true) | ($true = ((X279 @ (ap @ X282 @ X281))))) | ~ ! [X283 : term] : (~ ($true = ((X279 @ X283))) | (((X279 @ (lam @ X283))) = $true)) | ($true = ((X279 @ X278)))) => ! [X284 : subst,X285 : term,X286 : (term > $o)] : (~ ! [X287 : term] : (($true = ((X286 @ (sub @ X287 @ X284)))) | ~ ($true = ((var @ X287)))) | ~ ! [X288 : term] : (~ ! [X289 : term] : (~ ($true = ((X286 @ X289))) | ($true = ((X286 @ (sub @ X288 @ (push @ X289 @ id)))))) | ($true = ((X286 @ (lam @ X288))))) | ~ ! [X290 : term,X291 : term] : (($true = ((X286 @ (ap @ X291 @ X290)))) | ~ ($true = ((X286 @ X291))) | ~ ($true = ((X286 @ X290)))) | ($true = ((X286 @ (sub @ X285 @ X284))))))))) <=> (induction2lem_lthm = $true)) & (lamnotvar = $true) & ((! [X292 : term] : (((sub @ X292 @ id)) = X292) => (! [X293 : term,X294 : term,X295 : term,X296 : term] : ((((ap @ X295 @ X294)) != ((ap @ X293 @ X296))) | (X293 = X295)) => ! [X297 : term,X298 : term,X299 : term,X300 : term] : ((((ap @ (sub @ X299 @ id) @ X298)) != ((ap @ (sub @ X297 @ id) @ X300))) | (X297 = X299)))) <=> (hoasapinj1_lthm = $true)) & (! [X301 : subst,X302 : term,X303 : (term > $o)] : ~ ! [X304 : (term > $o)] : ~ ! [X305 : term] : (((X303 @ (sub @ X305 @ (push @ X302 @ X301)))) = ((X304 @ X305))) <=> (pushprop_lem0 = $true)) & (pushprop_lem2v2_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((termmset = $true) <=> ! [X306 : term] : (((sub @ X306 @ id)) = X306)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X307 : term] : ~ ! [X308 : (subst > term > term)] : ~ ! [X309 : term,X310 : subst] : (((X308 @ X310 @ X309)) = ((sub @ X307 @ (push @ X309 @ X310))))) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X311 : term,X312 : term,X313 : term,X314 : term] : ((((ap @ (sub @ X313 @ id) @ X311)) != ((ap @ (sub @ X314 @ id) @ X312))) | (X313 = X314))) & ((hoasinduction_lem0 = $true) <=> ! [X315 : (subst > term > subst > $o)] : ~ ! [X316 : (term > $o)] : ~ ! [X317 : term] : (((X315 @ id @ X317 @ id)) = ((X316 @ X317)))) & (! [X318 : term,X319 : (term > $o),X320 : (subst > term > subst > $o)] : (($true = ((X319 @ (lam @ X318)))) | ~ ! [X321 : term] : (~ ($true = ((X319 @ X321))) | ($true = ((X319 @ (sub @ X318 @ (push @ X321 @ id)))))) | ~ ! [X322 : term] : (((X320 @ id @ X322 @ id)) = ((X319 @ X322))) | ~ ! [X323 : (subst > term > term)] : (~ ! [X324 : term] : (($true = ((X320 @ id @ (X323 @ id @ X324) @ id))) | ~ (((X320 @ id @ X324 @ id)) = $true)) | ($true = ((X320 @ id @ (lam @ (X323 @ sh @ one)) @ id))) | ~ ! [X325 : subst,X326 : term,X327 : subst] : (((sub @ (X323 @ X325 @ X326) @ X327)) = ((X323 @ (comp @ X325 @ X327) @ (sub @ X326 @ X327)))))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & ((! [X328 : term] : (((sub @ X328 @ id)) = X328) => (! [X329 : (subst > term > subst > $o),X330 : term] : (($true = ((X329 @ id @ (lam @ (sub @ X330 @ (push @ one @ sh))) @ id))) | ~ ! [X331 : term] : (~ (((X329 @ id @ X331 @ id)) = $true) | ($true = ((X329 @ id @ (sub @ X330 @ (push @ X331 @ id)) @ id)))) | ~ ! [X332 : (subst > term > term)] : ((((X329 @ id @ (lam @ (X332 @ sh @ one)) @ id)) = $true) | ~ ! [X333 : term] : (~ (((X329 @ id @ X333 @ id)) = $true) | (((X329 @ id @ (X332 @ id @ X333) @ id)) = $true)) | ~ ! [X334 : subst,X335 : term,X336 : subst] : (((sub @ (X332 @ X334 @ X335) @ X336)) = ((X332 @ (comp @ X334 @ X336) @ (sub @ X335 @ X336)))))) => ! [X337 : term,X338 : (subst > term > subst > $o)] : (~ ! [X339 : (subst > term > term)] : (~ ! [X340 : term] : (~ ($true = ((X338 @ id @ X340 @ id))) | (((X338 @ id @ (X339 @ id @ X340) @ id)) = $true)) | ~ ! [X341 : subst,X342 : term,X343 : subst] : (((X339 @ (comp @ X343 @ X341) @ (sub @ X342 @ X341))) = ((sub @ (X339 @ X343 @ X342) @ X341))) | ($true = ((X338 @ id @ (lam @ (X339 @ sh @ one)) @ id)))) | ~ ! [X344 : term] : ((((X338 @ id @ (sub @ X337 @ (push @ X344 @ id)) @ id)) = $true) | ~ (((X338 @ id @ X344 @ id)) = $true)) | (((X338 @ id @ (lam @ X337) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (induction2_gthm = $true) & (axabs = $true) & (! [X345 : term] : (((sub @ X345 @ id)) = X345) <=> (axvarid = $true)) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoasapnotvar_gthm = $true) & ((! [X346 : subst] : (((comp @ id @ X346)) = X346) => (! [X347 : subst] : (((comp @ X347 @ id)) = X347) => (! [X348 : subst] : (((comp @ id @ X348)) = X348) & ! [X349 : subst] : (((comp @ X349 @ id)) = X349)))) <=> (substmonoid_lthm = $true)) & (! [X350 : (subst > term > subst > $o),X351 : term] : (~ ! [X352 : term,X353 : term] : (~ ($true = ((X350 @ id @ X352 @ id))) | (((X350 @ id @ (ap @ (sub @ X352 @ id) @ X353) @ id)) = $true) | ~ (((X350 @ id @ X353 @ id)) = $true)) | ($true = ((X350 @ id @ X351 @ id))) | ~ ! [X354 : (subst > term > term)] : (~ ! [X355 : subst,X356 : subst,X357 : term] : (((X354 @ (comp @ X355 @ X356) @ (sub @ X357 @ X356))) = ((sub @ (X354 @ X355 @ X357) @ X356))) | ($true = ((X350 @ id @ (lam @ (X354 @ sh @ one)) @ id))) | ~ ! [X358 : term] : (~ (((X350 @ id @ X358 @ id)) = $true) | ($true = ((X350 @ id @ (X354 @ id @ X358) @ id))))) | ~ ! [X359 : term] : ((((X350 @ id @ X359 @ id)) = $true) | ~ (((var @ (sub @ X359 @ id))) = $true)) | ~ ! [X360 : subst,X361 : subst,X362 : subst,X363 : term] : (~ (((X350 @ X360 @ X363 @ (comp @ X361 @ X362))) = $true) | (((X350 @ (comp @ X360 @ X361) @ (sub @ X363 @ X361) @ X362)) = $true)) | ~ ! [X364 : subst,X365 : term,X366 : subst,X367 : subst] : (~ (((X350 @ (comp @ X367 @ X364) @ (sub @ X365 @ X364) @ X366)) = $true) | (((X350 @ X367 @ X365 @ (comp @ X364 @ X366))) = $true))) <=> (hoasinduction = $true)) & (! [X368 : term,X369 : (subst > term > subst > $o)] : (($true = ((X369 @ id @ (lam @ (sub @ X368 @ (push @ one @ sh))) @ id))) | ~ ! [X370 : (subst > term > term),X371 : term] : ((((X369 @ id @ (lam @ (X370 @ sh @ one)) @ id)) = $true) | ~ ! [X372 : term] : (~ ($true = ((X369 @ id @ X372 @ id))) | ($true = ((X369 @ id @ (X370 @ id @ X372) @ id)))) | ~ ! [X373 : subst,X374 : term,X375 : subst] : (((sub @ (sub @ X371 @ (push @ X374 @ X373)) @ X375)) = ((sub @ (X370 @ X373 @ X374) @ X375))) | ~ ! [X376 : subst,X377 : subst,X378 : term] : (((sub @ X371 @ (push @ (sub @ X378 @ X377) @ (comp @ X376 @ X377)))) = ((X370 @ (comp @ X376 @ X377) @ (sub @ X378 @ X377))))) | ~ ! [X379 : term] : (($true = ((X369 @ id @ (sub @ X368 @ (push @ X379 @ id)) @ id))) | ~ ($true = ((X369 @ id @ X379 @ id))))) <=> (hoasinduction_lem3aaa = $true)) & (hoaslaminj_gthm = $true) & ((! [X380 : term] : (((sub @ X380 @ id)) = X380) => (! [X381 : subst,X382 : (term > $o),X383 : term] : (~ ! [X384 : term,X385 : term] : (~ (((X382 @ X384)) = $true) | ~ (((X382 @ X385)) = $true) | ($true = ((X382 @ (ap @ X385 @ X384))))) | ($true = ((X382 @ (sub @ X383 @ X381)))) | ~ ! [X386 : term] : (~ ($true = ((var @ X386))) | (((X382 @ (sub @ X386 @ X381))) = $true)) | ~ ! [X387 : term] : (~ ! [X388 : term] : (($true = ((X382 @ (sub @ X387 @ (push @ X388 @ id))))) | ~ ($true = ((X382 @ X388)))) | (((X382 @ (lam @ X387))) = $true))) => ! [X389 : (term > $o),X390 : term] : (~ ! [X391 : term] : (~ ! [X392 : term] : (~ (((X389 @ X392)) = $true) | (((X389 @ (sub @ X391 @ (push @ X392 @ id)))) = $true)) | ($true = ((X389 @ (lam @ X391))))) | ($true = ((X389 @ X390))) | ~ ! [X393 : term,X394 : term] : (~ (((X389 @ X394)) = $true) | (((X389 @ (ap @ X393 @ X394))) = $true) | ~ ($true = ((X389 @ X393)))) | ~ ! [X395 : term] : (($true = ((X389 @ X395))) | ~ (((var @ X395)) = $true))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & ((apinj1 = $true) <=> ! [X396 : term,X397 : term,X398 : term,X399 : term] : ((X396 = X398) | (((ap @ X398 @ X399)) != ((ap @ X396 @ X397))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X400 : term] : (((sub @ X400 @ id)) = X400) => (! [X401 : (subst > term > subst > $o),X402 : term] : ((((X401 @ id @ (lam @ (sub @ X402 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X403 : term] : (~ (((X401 @ id @ X403 @ id)) = $true) | ($true = ((X401 @ id @ (sub @ X402 @ (push @ X403 @ id)) @ id)))) | ~ ! [X404 : (subst > term > term)] : ((((X401 @ id @ (lam @ (X404 @ sh @ one)) @ id)) = $true) | ~ ! [X405 : term] : (($true = ((X401 @ id @ (X404 @ id @ X405) @ id))) | ~ (((X401 @ id @ X405 @ id)) = $true)) | ~ ! [X406 : subst,X407 : term,X408 : subst] : (((X404 @ (comp @ X408 @ X406) @ (sub @ X407 @ X406))) = ((sub @ (X404 @ X408 @ X407) @ X406))))) => ! [X409 : term,X410 : (subst > term > subst > $o)] : (($true = ((X410 @ id @ (lam @ X409) @ id))) | ~ ! [X411 : subst,X412 : term,X413 : subst,X414 : subst] : (~ ($true = ((X410 @ X414 @ X412 @ (comp @ X411 @ X413)))) | (((X410 @ (comp @ X414 @ X411) @ (sub @ X412 @ X411) @ X413)) = $true)) | ~ ! [X415 : subst,X416 : subst,X417 : subst,X418 : term] : (($true = ((X410 @ X416 @ X418 @ (comp @ X417 @ X415)))) | ~ ($true = ((X410 @ (comp @ X416 @ X417) @ (sub @ X418 @ X417) @ X415)))) | ~ ! [X419 : (subst > term > term)] : ((((X410 @ id @ (lam @ (X419 @ sh @ one)) @ id)) = $true) | ~ ! [X420 : subst,X421 : term,X422 : subst] : (((X419 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X419 @ X422 @ X421) @ X420))) | ~ ! [X423 : term] : (~ ($true = ((X410 @ id @ X423 @ id))) | ($true = ((X410 @ id @ (X419 @ id @ X423) @ id))))) | ~ ! [X424 : term] : (($true = ((X410 @ id @ (sub @ X409 @ (push @ X424 @ id)) @ id))) | ~ ($true = ((X410 @ id @ X424 @ id)))))))) & ((hoasinduction_lem3b = $true) <=> ! [X425 : term] : ~ ! [X426 : (subst > term > term)] : (((X426 @ sh @ one)) != ((sub @ X425 @ (push @ one @ sh))))) & (ulamvarsh = $true) & (! [X427 : term,X428 : term] : ((((lam @ X428)) != ((lam @ X427))) | (X427 = X428)) <=> (laminj = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((d2subst @ d_id)) = id) & ((! [X432 : (subst > term > subst > $o)] : ~ ! [X433 : (term > $o)] : ~ ! [X434 : term] : (((X432 @ id @ X434 @ id)) = ((X433 @ X434))) => (! [X435 : (term > $o),X436 : term] : (($true = ((X435 @ X436))) | ~ ! [X437 : term,X438 : term] : (~ ($true = ((X435 @ X437))) | ~ (((X435 @ X438)) = $true) | (((X435 @ (ap @ X437 @ X438))) = $true)) | ~ ! [X439 : term] : (~ ($true = ((var @ X439))) | (((X435 @ X439)) = $true)) | ~ ! [X440 : term] : ((((X435 @ (lam @ X440))) = $true) | ~ ! [X441 : term] : (~ ($true = ((X435 @ X441))) | ($true = ((X435 @ (sub @ X440 @ (push @ X441 @ id)))))))) => (! [X442 : term] : (((sub @ X442 @ id)) = X442) => (! [X443 : (term > $o),X444 : term,X445 : (subst > term > subst > $o)] : (~ ! [X446 : term] : (((X445 @ id @ X446 @ id)) = ((X443 @ X446))) | ~ ! [X447 : term] : ((((X443 @ (sub @ X444 @ (push @ X447 @ id)))) = $true) | ~ ($true = ((X443 @ X447)))) | ($true = ((X443 @ (lam @ X444)))) | ~ ! [X448 : (subst > term > term)] : ((((X445 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X449 : term] : (~ (((X445 @ id @ X449 @ id)) = $true) | ($true = ((X445 @ id @ (X448 @ id @ X449) @ id)))) | ~ ! [X450 : subst,X451 : term,X452 : subst] : (((X448 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) = ((sub @ (X448 @ X452 @ X451) @ X450))))) => ! [X453 : (subst > term > subst > $o),X454 : term] : (~ ! [X455 : term,X456 : term] : (~ ($true = ((X453 @ id @ X455 @ id))) | ($true = ((X453 @ id @ (ap @ (sub @ X456 @ id) @ X455) @ id))) | ~ ($true = ((X453 @ id @ X456 @ id)))) | ~ ! [X457 : (subst > term > term)] : (~ ! [X458 : subst,X459 : subst,X460 : term] : (((sub @ (X457 @ X458 @ X460) @ X459)) = ((X457 @ (comp @ X458 @ X459) @ (sub @ X460 @ X459)))) | ($true = ((X453 @ id @ (lam @ (X457 @ sh @ one)) @ id))) | ~ ! [X461 : term] : (~ (((X453 @ id @ X461 @ id)) = $true) | ($true = ((X453 @ id @ (X457 @ id @ X461) @ id))))) | ~ ! [X462 : subst,X463 : term,X464 : subst,X465 : subst] : (($true = ((X453 @ (comp @ X465 @ X464) @ (sub @ X463 @ X464) @ X462))) | ~ ($true = ((X453 @ X465 @ X463 @ (comp @ X464 @ X462))))) | ($true = ((X453 @ id @ X454 @ id))) | ~ ! [X466 : term] : (~ (((var @ (sub @ X466 @ id))) = $true) | (((X453 @ id @ X466 @ id)) = $true)) | ~ ! [X467 : term,X468 : subst,X469 : subst,X470 : subst] : (($true = ((X453 @ X470 @ X467 @ (comp @ X469 @ X468)))) | ~ ($true = ((X453 @ (comp @ X470 @ X469) @ (sub @ X467 @ X469) @ X468))))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & (! [X471 : subst,X472 : term] : (((comp @ sh @ (push @ X472 @ X471))) = X471) <=> (axshiftcons = $true)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X473 : subst] : ? [X474 : d_subst] : (((d2subst @ X474)) = X473) & (! [X475 : term,X476 : (term > $o),X477 : subst] : (~ ! [X478 : term,X479 : term] : (~ (((X476 @ X479)) = $true) | (((X476 @ (ap @ X479 @ X478))) = $true) | ~ ($true = ((X476 @ X478)))) | ~ ! [X480 : term] : (($true = ((X476 @ (lam @ X480)))) | ~ ! [X481 : term] : (($true = ((X476 @ (sub @ X480 @ (push @ X481 @ id))))) | ~ (((X476 @ X481)) = $true))) | ($true = ((X476 @ (sub @ X475 @ X477)))) | ~ ! [X482 : term] : (~ ($true = ((var @ X482))) | ($true = ((X476 @ (sub @ X482 @ X477)))))) <=> (induction2lem = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X483 : subst] : (((comp @ X483 @ id)) = X483) <=> (axidr = $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X484 : (subst > term > subst > $o),X485 : term] : (~ ! [X486 : (subst > term > term)] : (~ ! [X487 : term] : (($true = ((X484 @ id @ (X486 @ id @ X487) @ id))) | ~ (((X484 @ id @ X487 @ id)) = $true)) | ~ ! [X488 : term,X489 : subst,X490 : subst] : (((sub @ (X486 @ X490 @ X488) @ X489)) = ((X486 @ (comp @ X490 @ X489) @ (sub @ X488 @ X489)))) | (((X484 @ id @ (lam @ (X486 @ sh @ one)) @ id)) = $true)) | ~ ! [X491 : term,X492 : term] : (($true = ((X484 @ id @ (ap @ (sub @ X491 @ id) @ X492) @ id))) | ~ ($true = ((X484 @ id @ X492 @ id))) | ~ ($true = ((X484 @ id @ X491 @ id)))) | ($true = ((X484 @ id @ X485 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & ((induction2 = $true) <=> ! [X493 : term,X494 : (term > $o)] : (~ ! [X495 : term] : (($true = ((X494 @ (lam @ X495)))) | ~ ! [X496 : term] : ((((X494 @ (sub @ X495 @ (push @ X496 @ id)))) = $true) | ~ ($true = ((X494 @ X496))))) | ($true = ((X494 @ X493))) | ~ ! [X497 : term] : ((((X494 @ X497)) = $true) | ~ ($true = ((var @ X497)))) | ~ ! [X498 : term,X499 : term] : (($true = ((X494 @ (ap @ X498 @ X499)))) | ~ (((X494 @ X499)) = $true) | ~ (((X494 @ X498)) = $true)))) & (ulamvarind = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X500 : term,X501 : subst] : (((sub @ one @ (push @ X500 @ X501))) = X500) => ! [X502 : (term > $o),X503 : subst,X504 : term,X505 : (term > $o)] : (($true = ((X505 @ one))) | ~ (((X502 @ X504)) = $true) | ~ ! [X506 : term] : (((X502 @ (sub @ X506 @ (push @ X504 @ X503)))) = ((X505 @ X506)))))) & (one = ((d2term @ d_one))) & ((! [X507 : term] : (((sub @ X507 @ id)) = X507) => ! [X508 : term,X509 : (term > $o),X510 : (subst > term > subst > $o)] : (~ ! [X511 : term,X512 : subst,X513 : subst,X514 : subst] : (($true = ((X510 @ (comp @ X514 @ X512) @ (sub @ X511 @ X512) @ X513))) | ~ (((X510 @ X514 @ X511 @ (comp @ X512 @ X513))) = $true)) | (((X509 @ (lam @ X508))) = $true) | ~ ! [X515 : (subst > term > term)] : (~ ! [X516 : term] : (~ ($true = ((X510 @ id @ X516 @ id))) | ($true = ((X510 @ id @ (X515 @ id @ X516) @ id)))) | ~ ! [X517 : subst,X518 : subst,X519 : term] : (((X515 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X515 @ X518 @ X519) @ X517))) | ($true = ((X510 @ id @ (lam @ (X515 @ sh @ one)) @ id)))) | ~ ! [X520 : term] : (((X510 @ id @ X520 @ id)) = ((X509 @ X520))) | ~ ! [X521 : subst,X522 : subst,X523 : subst,X524 : term] : ((((X510 @ X521 @ X524 @ (comp @ X523 @ X522))) = $true) | ~ ($true = ((X510 @ (comp @ X521 @ X523) @ (sub @ X524 @ X523) @ X522)))) | ~ ! [X525 : term] : ((((X509 @ (sub @ X508 @ (push @ X525 @ id)))) = $true) | ~ (((X509 @ X525)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((induction = $true) <=> ! [X526 : (term > $o),X527 : term] : (($true = ((X526 @ X527))) | ~ ! [X528 : term] : (~ ($true = ((var @ X528))) | (((X526 @ X528)) = $true)) | ~ ! [X529 : term,X530 : term] : (~ (((X526 @ X529)) = $true) | ($true = ((X526 @ (ap @ X529 @ X530)))) | ~ ($true = ((X526 @ X530)))) | ~ ! [X531 : term] : (~ ($true = ((X526 @ X531))) | (((X526 @ (lam @ X531))) = $true)))) & ! [X532 : d_term,X533 : d_term] : ((((d2term @ X532)) = ((d2term @ X533))) => (X532 = X533)) & ((hoasinduction_lem3 = $true) <=> ! [X534 : term,X535 : (subst > term > subst > $o)] : (($true = ((X535 @ id @ (lam @ X534) @ id))) | ~ ! [X536 : subst,X537 : subst,X538 : term,X539 : subst] : (~ ($true = ((X535 @ X539 @ X538 @ (comp @ X536 @ X537)))) | (((X535 @ (comp @ X539 @ X536) @ (sub @ X538 @ X536) @ X537)) = $true)) | ~ ! [X540 : (subst > term > term)] : (~ ! [X541 : term] : (($true = ((X535 @ id @ (X540 @ id @ X541) @ id))) | ~ (((X535 @ id @ X541 @ id)) = $true)) | ($true = ((X535 @ id @ (lam @ (X540 @ sh @ one)) @ id))) | ~ ! [X542 : subst,X543 : term,X544 : subst] : (((X540 @ (comp @ X544 @ X542) @ (sub @ X543 @ X542))) = ((sub @ (X540 @ X544 @ X543) @ X542)))) | ~ ! [X545 : term,X546 : subst,X547 : subst,X548 : subst] : (~ ($true = ((X535 @ (comp @ X548 @ X547) @ (sub @ X545 @ X547) @ X546))) | ($true = ((X535 @ X548 @ X545 @ (comp @ X547 @ X546))))) | ~ ! [X549 : term] : (($true = ((X535 @ id @ (sub @ X534 @ (push @ X549 @ id)) @ id))) | ~ ($true = ((X535 @ id @ X549 @ id))))))),
% 5.43/1.21 inference(fool_elimination,[],[f4])).
% 5.43/1.21 thf(f6,plain,(
% 5.43/1.21 ~ (! [X0 : (subst > term > subst > $o),X1 : (term > $o)] : (! [X2 : subst,X3 : subst,X4 : term,X5 : subst] : ((X0 @ X3 @ X4 @ (comp @ X5 @ X2)) => (X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)) => (! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8) => (X0 @ X7 @ X9 @ (comp @ X6 @ X8))) => (! [X10 : term,X11 : term] : ((X0 @ id @ X11 @ id) => ((X0 @ id @ X10 @ id) => (X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id))) => ((hoasinduction_p_and_p_prime @ X0 @ X1) => ! [X12 : term,X13 : term] : ((X1 @ X13) => ((X1 @ X12) => (X1 @ (ap @ X13 @ X12)))))))) = hoasinduction_lem2v2)),
% 5.43/1.21 inference(rectify,[],[f3])).
% 5.43/1.21 thf(f7,plain,(
% 5.43/1.21 ~(! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : (! [X2 : subst,X3 : subst,X5 : subst,X4 : term] : ((((X0 @ X3 @ X4 @ (comp @ X5 @ X2))) = $true) => ($true = ((X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)))) => (! [X8 : subst,X6 : subst,X9 : term,X7 : subst] : ((((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8)) = $true) => ($true = ((X0 @ X7 @ X9 @ (comp @ X6 @ X8))))) => (! [X10 : term,X11 : term] : (($true = ((X0 @ id @ X11 @ id))) => ((((X0 @ id @ X10 @ id)) = $true) => ($true = ((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id))))) => ((((hoasinduction_p_and_p_prime @ X0 @ X1)) = $true) => ! [X12 : term,X13 : term] : ((((X1 @ X13)) = $true) => ((((X1 @ X12)) = $true) => ($true = ((X1 @ (ap @ X13 @ X12)))))))))) <=> (hoasinduction_lem2v2 = $true))),
% 5.43/1.21 inference(fool_elimination,[],[f6])).
% 5.43/1.21 thf(f8,plain,(
% 5.43/1.21 (apnotvar = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (! [X3 : (term > $o),X4 : subst,X5 : term,X6 : term,X7 : (term > $o)] : (~ (((X7 @ X5)) = $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4)))))) <=> (pushprop_lem1 = $true)) & (pushprop_lem3v2_lthm = $true) & (induction2lem_gthm = $true) & (! [X8 : term,X10 : (subst > term > term),X9 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ~ ! [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & ! [X14 : d_subst,X15 : d_subst] : ((((d2subst @ X15)) = ((d2subst @ X14))) => (X14 = X15)) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (termmset_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (! [X18 : (term > $o),X19 : (subst > term > subst > $o),X20 : term] : (~ ! [X21 : term] : (((X19 @ id @ X21 @ id)) = ((X18 @ X21))) | ~ ! [X22 : subst,X23 : subst,X24 : subst,X25 : term] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) = $true) | ~ ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22)))) | ~ ! [X26 : (subst > term > term)] : (($true = ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) | ~ ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) | ~ ! [X30 : term] : ((((X19 @ id @ (X26 @ id @ X30) @ id)) = $true) | ~ (((X19 @ id @ X30 @ id)) = $true))) | ~ ! [X31 : term] : (~ ($true = ((X18 @ X31))) | ($true = ((X18 @ (sub @ X20 @ (push @ X31 @ id)))))) | ($true = ((X18 @ (lam @ X20)))) | ~ ! [X32 : subst,X33 : term,X34 : subst,X35 : subst] : (($true = ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) | ~ ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34)))))) <=> (hoasinduction_lem3v2 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasapinj2_lthm = $true) <=> (! [X36 : term,X37 : term,X38 : term,X39 : term] : ((X37 = X39) | (((ap @ X38 @ X37)) != ((ap @ X36 @ X39)))) => ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)))) & (! [X44 : term] : ~ ! [X45 : (subst > term > term)] : (((X45 @ sh @ one)) != ((sub @ X44 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X47 : subst,X46 : term,X48 : (term > $o)] : ~ ! [X49 : (term > $o)] : ~ ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) <=> (pushprop_lem0_lthm = $true)) & (pushprop = $true) & (hoasinduction_lem2v2_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) <=> (substmonoid = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) <=> (axidl = $true)) & (hoaslamnotap_lthm = $true) & ~ (lamnotap = $true) & ((! [X58 : term,X59 : (term > $o)] : (~ ! [X60 : term] : (~ ($true = ((var @ X60))) | ($true = ((X59 @ X60)))) | ~ ! [X61 : term,X62 : term] : (~ ($true = ((X59 @ X62))) | ($true = ((X59 @ (ap @ X61 @ X62)))) | ~ (((X59 @ X61)) = $true)) | ~ ! [X63 : term] : (~ ! [X64 : term] : (($true = ((X59 @ (sub @ X63 @ (push @ X64 @ id))))) | ~ ($true = ((X59 @ X64)))) | (((X59 @ (lam @ X63))) = $true)) | ($true = ((X59 @ X58)))) => (! [X65 : term,X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : subst,X69 : subst,X70 : term,X71 : subst] : (($true = ((X67 @ X71 @ X70 @ (comp @ X68 @ X69)))) | ~ ($true = ((X67 @ (comp @ X71 @ X68) @ (sub @ X70 @ X68) @ X69)))) | ~ ! [X72 : subst,X73 : subst,X74 : term,X75 : subst] : (($true = ((X67 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72) @ X75))) | ~ ($true = ((X67 @ X73 @ X74 @ (comp @ X72 @ X75))))) | ~ (((X67 @ id @ X65 @ id)) = $true) | (((X67 @ id @ (ap @ X65 @ X66) @ id)) = $true) | ~ ($true = ((X67 @ id @ X66 @ id))) | ~ ! [X76 : term,X77 : term] : (~ ($true = ((X67 @ id @ X76 @ id))) | (((X67 @ id @ (ap @ (sub @ X76 @ id) @ X77) @ id)) = $true) | ~ ($true = ((X67 @ id @ X77 @ id))))) => (! [X78 : (subst > term > subst > $o),X79 : term] : (~ ! [X80 : term,X81 : subst,X82 : subst,X83 : subst] : (~ ($true = ((X78 @ (comp @ X81 @ X83) @ (sub @ X80 @ X83) @ X82))) | ($true = ((X78 @ X81 @ X80 @ (comp @ X83 @ X82))))) | ~ ! [X84 : term,X85 : subst,X86 : subst,X87 : subst] : (~ ($true = ((X78 @ X87 @ X84 @ (comp @ X85 @ X86)))) | ($true = ((X78 @ (comp @ X87 @ X85) @ (sub @ X84 @ X85) @ X86)))) | ~ ! [X88 : term] : (~ ($true = ((X78 @ id @ X88 @ id))) | ($true = ((X78 @ id @ (sub @ X79 @ (push @ X88 @ id)) @ id)))) | ($true = ((X78 @ id @ (lam @ X79) @ id))) | ~ ! [X89 : (subst > term > term)] : (~ ! [X90 : term] : ((((X78 @ id @ (X89 @ id @ X90) @ id)) = $true) | ~ ($true = ((X78 @ id @ X90 @ id)))) | ($true = ((X78 @ id @ (lam @ (X89 @ sh @ one)) @ id))) | ~ ! [X91 : subst,X92 : subst,X93 : term] : (((X89 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X89 @ X92 @ X93) @ X91))))) => ! [X94 : (subst > term > subst > $o),X95 : term] : (~ ! [X96 : term,X97 : subst,X98 : subst,X99 : subst] : (($true = ((X94 @ (comp @ X99 @ X97) @ (sub @ X96 @ X97) @ X98))) | ~ ($true = ((X94 @ X99 @ X96 @ (comp @ X97 @ X98))))) | ~ ! [X100 : term] : ((((X94 @ id @ X100 @ id)) = $true) | ~ ($true = ((var @ (sub @ X100 @ id))))) | ($true = ((X94 @ id @ X95 @ id))) | ~ ! [X101 : subst,X102 : term,X103 : subst,X104 : subst] : (~ (((X94 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104) @ X101)) = $true) | ($true = ((X94 @ X103 @ X102 @ (comp @ X104 @ X101))))) | ~ ! [X105 : term,X106 : term] : (~ (((X94 @ id @ X105 @ id)) = $true) | ~ (((X94 @ id @ X106 @ id)) = $true) | ($true = ((X94 @ id @ (ap @ (sub @ X106 @ id) @ X105) @ id)))) | ~ ! [X107 : (subst > term > term)] : (~ ! [X108 : term] : (~ (((X94 @ id @ X108 @ id)) = $true) | ($true = ((X94 @ id @ (X107 @ id @ X108) @ id)))) | ($true = ((X94 @ id @ (lam @ (X107 @ sh @ one)) @ id))) | ~ ! [X110 : subst,X111 : subst,X109 : term] : (((X107 @ (comp @ X111 @ X110) @ (sub @ X109 @ X110))) = ((sub @ (X107 @ X111 @ X109) @ X110)))))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X112 : (subst > term > subst > $o)] : ~ ! [X113 : (term > $o)] : ~ ! [X114 : term] : (((X113 @ X114)) = ((X112 @ id @ X114 @ id))) => (! [X115 : (term > $o),X116 : term] : (~ ! [X117 : term] : (($true = ((X115 @ X117))) | ~ ($true = ((var @ X117)))) | ($true = ((X115 @ X116))) | ~ ! [X118 : term,X119 : term] : (~ ($true = ((X115 @ X119))) | ~ (((X115 @ X118)) = $true) | ($true = ((X115 @ (ap @ X118 @ X119))))) | ~ ! [X120 : term] : (~ ! [X121 : term] : (($true = ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) | ~ (((X115 @ X121)) = $true)) | ($true = ((X115 @ (lam @ X120)))))) => (! [X122 : term] : (((sub @ X122 @ id)) = X122) => (! [X123 : term,X124 : (term > $o),X125 : (subst > term > subst > $o)] : (($true = ((X124 @ (lam @ X123)))) | ~ ! [X126 : term] : (~ ($true = ((X124 @ X126))) | (((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true)) | ~ ! [X127 : (subst > term > term)] : ((((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ~ ! [X130 : term,X129 : subst,X128 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) = ((sub @ (X127 @ X129 @ X130) @ X128))) | ~ ! [X131 : term] : (($true = ((X125 @ id @ (X127 @ id @ X131) @ id))) | ~ ($true = ((X125 @ id @ X131 @ id))))) | ~ ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id)))) => ! [X133 : (subst > term > subst > $o),X134 : term] : (~ ! [X135 : (subst > term > term)] : ((((X133 @ id @ (lam @ (X135 @ sh @ one)) @ id)) = $true) | ~ ! [X136 : term] : (~ ($true = ((X133 @ id @ X136 @ id))) | ($true = ((X133 @ id @ (X135 @ id @ X136) @ id)))) | ~ ! [X137 : subst,X139 : subst,X138 : term] : (((sub @ (X135 @ X139 @ X138) @ X137)) = ((X135 @ (comp @ X139 @ X137) @ (sub @ X138 @ X137))))) | ~ ! [X140 : term,X141 : term] : (~ ($true = ((X133 @ id @ X140 @ id))) | (((X133 @ id @ (ap @ (sub @ X141 @ id) @ X140) @ id)) = $true) | ~ (((X133 @ id @ X141 @ id)) = $true)) | ($true = ((X133 @ id @ X134 @ id))))))))) & (hoasinduction_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) <=> (apinj2 = $true)) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) <=> (axscons = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X147 : subst,X148 : (term > $o),X149 : term,X150 : (term > $o)] : (($true = ((X148 @ one))) | ~ (((X150 @ X149)) = $true) | ~ ! [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) = ((X148 @ X151)))) <=> (pushprop_lem1v2 = $true)) & ((! [X153 : subst,X152 : term] : (((sub @ one @ (push @ X152 @ X153))) = X152) => (! [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) = X154) => (! [X156 : term,X157 : term] : ((X156 = X157) | (((lam @ X156)) != ((lam @ X157)))) => ! [X160 : subst,X158 : term,X159 : (subst > term > term),X161 : (subst > term > term)] : (~ ! [X164 : term,X162 : subst,X163 : subst] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) = ((sub @ (X159 @ X162 @ X164) @ X163))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ~ ! [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) = ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))))))) <=> (hoaslaminj_lthm = $true)) & (hoasapnotvar_lthm = $true) & (pushprop_lem2v2 = $true) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) <=> (shinj = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X170 : (subst > term > subst > $o),X171 : term] : (~ ! [X172 : term] : (($true = ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) | ~ (((X170 @ id @ X172 @ id)) = $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) | (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : (~ ($true = ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true))) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) <=> (hoasapinj2 = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X182 : (subst > term > subst > $o),X183 : term] : (~ ! [X184 : term] : (($true = ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))) | ~ ($true = ((X182 @ id @ X184 @ id)))) | ~ ! [X185 : (subst > term > term)] : (~ ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188))) | (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true) | ~ ! [X189 : term] : (~ (((X182 @ id @ X189 @ id)) = $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true))) | ($true = ((X182 @ id @ (lam @ X183) @ id)))) <=> (hoasinduction_lem3a = $true)) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & ~ (ulamvar1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X190 : (subst > term > subst > $o),X191 : term] : ((((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X192 : term] : (($true = ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) | ~ (((X190 @ id @ X192 @ id)) = $true)) | ~ ! [X193 : (subst > term > term)] : ((((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) = $true) | ~ ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195))) | ~ ! [X197 : term] : (($true = ((X190 @ id @ (X193 @ id @ X197) @ id))) | ~ (((X190 @ id @ X197 @ id)) = $true))))) & (axmap = $true) & (pushprop_lem0_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1 = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & (axclos = $true) & ! [X198 : d_subst] : (d_id = X198) & ((pushprop_lem1_lthm = $true) <=> (! [X200 : term,X199 : subst] : (((sub @ one @ (push @ X200 @ X199))) = X200) => (! [X202 : subst,X201 : term] : (((comp @ sh @ (push @ X201 @ X202))) = X202) => ! [X203 : term,X204 : (term > $o),X205 : subst,X206 : (term > $o),X207 : term] : (($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205))))) | ~ ($true = ((X206 @ X207))))))) & ((! [X208 : term] : ~ ! [X209 : (subst > term > term)] : ~ ! [X210 : subst,X211 : term] : (((X209 @ X210 @ X211)) = ((sub @ X208 @ (push @ X211 @ X210)))) => (! [X212 : term] : (((sub @ X212 @ id)) = X212) => ! [X213 : term,X214 : (term > $o),X215 : (subst > term > subst > $o)] : (($true = ((X214 @ (lam @ X213)))) | ~ ! [X216 : (subst > term > term)] : ((((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ~ ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ~ ($true = ((X215 @ id @ X217 @ id)))) | ~ ! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219)))) | ~ ! [X221 : term] : (((X214 @ X221)) = ((X215 @ id @ X221 @ id))) | ~ ! [X222 : term] : (($true = ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) | ~ ($true = ((X214 @ X222))))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((axvarcons = $true) <=> ! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224)) & (! [X225 : (subst > term > term),X226 : (subst > term > term),X227 : subst,X228 : term] : (~ ! [X233 : subst,X234 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) = ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | ~ ! [X231 : subst,X229 : term,X230 : subst] : (((sub @ (X225 @ X230 @ X229) @ X231)) = ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) <=> (hoaslaminj = $true)) & ! [X235 : d_term] : (d_one = X235) & (axapp = $true) & (! [X236 : (subst > term > subst > $o),X237 : term,X238 : (term > $o),X239 : term] : (~ ! [X240 : term] : (((X236 @ id @ X240 @ id)) = ((X238 @ X240))) | ($true = ((X238 @ (ap @ X239 @ X237)))) | ~ ($true = ((X238 @ X239))) | ~ ! [X241 : subst,X242 : term,X243 : subst,X244 : subst] : (~ ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243))) | (((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) = $true)) | ~ ($true = ((X238 @ X237))) | ~ ! [X245 : subst,X246 : subst,X247 : subst,X248 : term] : (~ (((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) | ($true = ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247)))) | ~ ! [X249 : term,X250 : term] : (~ ($true = ((X236 @ id @ X249 @ id))) | ($true = ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id))) | ~ ($true = ((X236 @ id @ X250 @ id))))) <=> (hoasinduction_lem2v2 = $true)) & (axassoc = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem3_gthm = $true) & ((termmset_lthm = $true) <=> (! [X251 : term] : (((sub @ X251 @ id)) = X251) => ! [X252 : term] : (((sub @ X252 @ id)) = X252))) & (hoasapnotvar = $true) & (! [X253 : (subst > term > subst > $o),X254 : term,X255 : term] : (~ ! [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (~ ($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) | (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) = $true)) | (((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | ~ ! [X260 : subst,X261 : subst,X262 : subst,X263 : term] : (~ (((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) | (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) = $true)) | ~ (((X253 @ id @ X255 @ id)) = $true) | ~ ($true = ((X253 @ id @ X254 @ id))) | ~ ! [X264 : term,X265 : term] : (~ ($true = ((X253 @ id @ X265 @ id))) | ~ ($true = ((X253 @ id @ X264 @ id))) | ($true = ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))))) <=> (hoasinduction_lem2 = $true)) & ((! [X266 : subst,X267 : term] : (((sub @ one @ (push @ X267 @ X266))) = X267) => (! [X269 : subst,X268 : term] : (((comp @ sh @ (push @ X268 @ X269))) = X269) => (! [X270 : subst] : (((comp @ X270 @ id)) = X270) => (! [X271 : term,X272 : (term > $o)] : (~ ! [X273 : term] : (~ ($true = ((var @ X273))) | (((X272 @ X273)) = $true)) | ~ ! [X274 : term,X275 : term] : (~ ($true = ((X272 @ X274))) | ~ ($true = ((X272 @ X275))) | ($true = ((X272 @ (ap @ X275 @ X274))))) | ~ ! [X276 : term] : (~ (((X272 @ X276)) = $true) | ($true = ((X272 @ (lam @ X276))))) | (((X272 @ X271)) = $true)) => ! [X277 : subst,X278 : term,X279 : (term > $o)] : (~ ! [X280 : term] : ((((X279 @ (sub @ X280 @ X277))) = $true) | ~ ($true = ((var @ X280)))) | ~ ! [X281 : term] : (~ ! [X282 : term] : (~ (((X279 @ X282)) = $true) | ($true = ((X279 @ (sub @ X281 @ (push @ X282 @ id)))))) | (((X279 @ (lam @ X281))) = $true)) | ~ ! [X283 : term,X284 : term] : (($true = ((X279 @ (ap @ X284 @ X283)))) | ~ ($true = ((X279 @ X284))) | ~ ($true = ((X279 @ X283)))) | (((X279 @ (sub @ X278 @ X277))) = $true)))))) <=> (induction2lem_lthm = $true)) & (lamnotvar = $true) & ((hoasapinj1_lthm = $true) <=> (! [X285 : term] : (((sub @ X285 @ id)) = X285) => (! [X289 : term,X288 : term,X287 : term,X286 : term] : ((((ap @ X288 @ X287)) != ((ap @ X286 @ X289))) | (X286 = X288)) => ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292))))) & ((pushprop_lem0 = $true) <=> ! [X294 : subst,X296 : (term > $o),X295 : term] : ~ ! [X297 : (term > $o)] : ~ ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & (pushprop_lem2v2_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) <=> (termmset = $true)) & (! [X300 : term] : ~ ! [X301 : (subst > term > term)] : ~ ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X308 : (subst > term > subst > $o)] : ~ ! [X309 : (term > $o)] : ~ ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id)))) & (! [X311 : term,X312 : (term > $o),X313 : (subst > term > subst > $o)] : (($true = ((X312 @ (lam @ X311)))) | ~ ! [X314 : term] : (~ ($true = ((X312 @ X314))) | (((X312 @ (sub @ X311 @ (push @ X314 @ id)))) = $true)) | ~ ! [X315 : term] : (((X313 @ id @ X315 @ id)) = ((X312 @ X315))) | ~ ! [X316 : (subst > term > term)] : (~ ! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | ~ (((X313 @ id @ X317 @ id)) = $true)) | ($true = ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) | ~ ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320)))))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & ((! [X321 : term] : (((sub @ X321 @ id)) = X321) => (! [X322 : (subst > term > subst > $o),X323 : term] : (($true = ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) | ~ ! [X324 : term] : (~ ($true = ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) | ~ ! [X325 : (subst > term > term)] : (($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id))) | ~ ! [X326 : term] : (~ ($true = ((X322 @ id @ X326 @ id))) | ($true = ((X322 @ id @ (X325 @ id @ X326) @ id)))) | ~ ! [X329 : subst,X327 : subst,X328 : term] : (((sub @ (X325 @ X327 @ X328) @ X329)) = ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))))) => ! [X330 : term,X331 : (subst > term > subst > $o)] : (~ ! [X332 : (subst > term > term)] : (~ ! [X333 : term] : (~ ($true = ((X331 @ id @ X333 @ id))) | (((X331 @ id @ (X332 @ id @ X333) @ id)) = $true)) | ~ ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334))) | (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) = $true)) | ~ ! [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) = $true) | ~ ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (induction2_gthm = $true) & (axabs = $true) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) <=> (axvarid = $true)) & (hoasapinj2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoasapnotvar_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X339 : subst] : (((comp @ id @ X339)) = X339) => (! [X340 : subst] : (((comp @ X340 @ id)) = X340) => (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341))))) & (! [X343 : (subst > term > subst > $o),X344 : term] : (~ ! [X345 : term,X346 : term] : (~ ($true = ((X343 @ id @ X345 @ id))) | ($true = ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) | ~ ($true = ((X343 @ id @ X346 @ id)))) | ($true = ((X343 @ id @ X344 @ id))) | ~ ! [X347 : (subst > term > term)] : (~ ! [X350 : term,X349 : subst,X348 : subst] : (((sub @ (X347 @ X348 @ X350) @ X349)) = ((X347 @ (comp @ X348 @ X349) @ (sub @ X350 @ X349)))) | (((X343 @ id @ (lam @ (X347 @ sh @ one)) @ id)) = $true) | ~ ! [X351 : term] : (~ ($true = ((X343 @ id @ X351 @ id))) | ($true = ((X343 @ id @ (X347 @ id @ X351) @ id))))) | ~ ! [X352 : term] : (($true = ((X343 @ id @ X352 @ id))) | ~ ($true = ((var @ (sub @ X352 @ id))))) | ~ ! [X353 : subst,X354 : subst,X355 : subst,X356 : term] : (~ ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355)))) | ($true = ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355)))) | ~ ! [X357 : subst,X358 : term,X359 : subst,X360 : subst] : (~ ($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) | ($true = ((X343 @ X360 @ X358 @ (comp @ X357 @ X359)))))) <=> (hoasinduction = $true)) & (! [X361 : term,X362 : (subst > term > subst > $o)] : ((((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X363 : (subst > term > term),X364 : term] : (($true = ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) | ~ ! [X365 : term] : (~ ($true = ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) | ~ ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368))) | ~ ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))))) | ~ ! [X372 : term] : (($true = ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id))) | ~ ($true = ((X362 @ id @ X372 @ id))))) <=> (hoasinduction_lem3aaa = $true)) & (hoaslaminj_gthm = $true) & ((! [X373 : term] : (((sub @ X373 @ id)) = X373) => (! [X374 : subst,X375 : (term > $o),X376 : term] : (~ ! [X377 : term,X378 : term] : (~ ($true = ((X375 @ X377))) | ~ (((X375 @ X378)) = $true) | (((X375 @ (ap @ X378 @ X377))) = $true)) | ($true = ((X375 @ (sub @ X376 @ X374)))) | ~ ! [X379 : term] : (~ (((var @ X379)) = $true) | (((X375 @ (sub @ X379 @ X374))) = $true)) | ~ ! [X380 : term] : (~ ! [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true) | ~ ($true = ((X375 @ X381)))) | ($true = ((X375 @ (lam @ X380)))))) => ! [X382 : (term > $o),X383 : term] : (~ ! [X384 : term] : (~ ! [X385 : term] : (~ (((X382 @ X385)) = $true) | ($true = ((X382 @ (sub @ X384 @ (push @ X385 @ id)))))) | (((X382 @ (lam @ X384))) = $true)) | ($true = ((X382 @ X383))) | ~ ! [X386 : term,X387 : term] : (~ (((X382 @ X387)) = $true) | (((X382 @ (ap @ X386 @ X387))) = $true) | ~ ($true = ((X382 @ X386)))) | ~ ! [X388 : term] : (($true = ((X382 @ X388))) | ~ ($true = ((var @ X388))))))) <=> (induction2_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (substmonoid_gthm = $true) & ((apinj1 = $true) <=> ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X393 : term] : (((sub @ X393 @ id)) = X393) => (! [X394 : (subst > term > subst > $o),X395 : term] : (($true = ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) | ~ ! [X396 : term] : (~ (((X394 @ id @ X396 @ id)) = $true) | ($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id)))) | ~ ! [X397 : (subst > term > term)] : ((((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true) | ~ ! [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) = $true) | ~ ($true = ((X394 @ id @ X398 @ id)))) | ~ ! [X400 : term,X401 : subst,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X397 @ X401 @ X400) @ X399))))) => ! [X402 : term,X403 : (subst > term > subst > $o)] : (($true = ((X403 @ id @ (lam @ X402) @ id))) | ~ ! [X404 : subst,X405 : term,X406 : subst,X407 : subst] : (~ ($true = ((X403 @ X407 @ X405 @ (comp @ X404 @ X406)))) | ($true = ((X403 @ (comp @ X407 @ X404) @ (sub @ X405 @ X404) @ X406)))) | ~ ! [X408 : subst,X409 : subst,X410 : subst,X411 : term] : (($true = ((X403 @ X409 @ X411 @ (comp @ X410 @ X408)))) | ~ (((X403 @ (comp @ X409 @ X410) @ (sub @ X411 @ X410) @ X408)) = $true)) | ~ ! [X412 : (subst > term > term)] : (($true = ((X403 @ id @ (lam @ (X412 @ sh @ one)) @ id))) | ~ ! [X413 : subst,X414 : term,X415 : subst] : (((X412 @ (comp @ X415 @ X413) @ (sub @ X414 @ X413))) = ((sub @ (X412 @ X415 @ X414) @ X413))) | ~ ! [X416 : term] : (~ ($true = ((X403 @ id @ X416 @ id))) | ($true = ((X403 @ id @ (X412 @ id @ X416) @ id))))) | ~ ! [X417 : term] : (($true = ((X403 @ id @ (sub @ X402 @ (push @ X417 @ id)) @ id))) | ~ ($true = ((X403 @ id @ X417 @ id)))))))) & ((hoasinduction_lem3b = $true) <=> ! [X418 : term] : ~ ! [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) != ((X419 @ sh @ one)))) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (((d2subst @ d_id)) = id) & ((! [X422 : (subst > term > subst > $o)] : ~ ! [X423 : (term > $o)] : ~ ! [X424 : term] : (((X423 @ X424)) = ((X422 @ id @ X424 @ id))) => (! [X425 : (term > $o),X426 : term] : (($true = ((X425 @ X426))) | ~ ! [X427 : term,X428 : term] : (~ (((X425 @ X427)) = $true) | ~ ($true = ((X425 @ X428))) | (((X425 @ (ap @ X427 @ X428))) = $true)) | ~ ! [X429 : term] : (~ (((var @ X429)) = $true) | ($true = ((X425 @ X429)))) | ~ ! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ~ ! [X431 : term] : (~ (((X425 @ X431)) = $true) | (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) = $true)))) => (! [X432 : term] : (((sub @ X432 @ id)) = X432) => (! [X433 : (term > $o),X434 : term,X435 : (subst > term > subst > $o)] : (~ ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) | ~ ! [X437 : term] : (($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id))))) | ~ ($true = ((X433 @ X437)))) | ($true = ((X433 @ (lam @ X434)))) | ~ ! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ~ ! [X439 : term] : (~ ($true = ((X435 @ id @ X439 @ id))) | ($true = ((X435 @ id @ (X438 @ id @ X439) @ id)))) | ~ ! [X441 : term,X440 : subst,X442 : subst] : (((sub @ (X438 @ X442 @ X441) @ X440)) = ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440)))))) => ! [X443 : (subst > term > subst > $o),X444 : term] : (~ ! [X445 : term,X446 : term] : (~ (((X443 @ id @ X445 @ id)) = $true) | (((X443 @ id @ (ap @ (sub @ X446 @ id) @ X445) @ id)) = $true) | ~ (((X443 @ id @ X446 @ id)) = $true)) | ~ ! [X447 : (subst > term > term)] : (~ ! [X449 : subst,X448 : subst,X450 : term] : (((sub @ (X447 @ X448 @ X450) @ X449)) = ((X447 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449)))) | (((X443 @ id @ (lam @ (X447 @ sh @ one)) @ id)) = $true) | ~ ! [X451 : term] : (~ (((X443 @ id @ X451 @ id)) = $true) | ($true = ((X443 @ id @ (X447 @ id @ X451) @ id))))) | ~ ! [X452 : subst,X453 : term,X454 : subst,X455 : subst] : ((((X443 @ (comp @ X455 @ X454) @ (sub @ X453 @ X454) @ X452)) = $true) | ~ ($true = ((X443 @ X455 @ X453 @ (comp @ X454 @ X452))))) | ($true = ((X443 @ id @ X444 @ id))) | ~ ! [X456 : term] : (~ (((var @ (sub @ X456 @ id))) = $true) | ($true = ((X443 @ id @ X456 @ id)))) | ~ ! [X457 : term,X458 : subst,X459 : subst,X460 : subst] : ((((X443 @ X460 @ X457 @ (comp @ X459 @ X458))) = $true) | ~ ($true = ((X443 @ (comp @ X460 @ X459) @ (sub @ X457 @ X459) @ X458))))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_lthm = $true) & ((axshiftcons = $true) <=> ! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461)) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (! [X465 : term,X466 : (term > $o),X467 : subst] : (~ ! [X468 : term,X469 : term] : (~ ($true = ((X466 @ X469))) | (((X466 @ (ap @ X469 @ X468))) = $true) | ~ ($true = ((X466 @ X468)))) | ~ ! [X470 : term] : ((((X466 @ (lam @ X470))) = $true) | ~ ! [X471 : term] : (($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))) | ~ (((X466 @ X471)) = $true))) | ($true = ((X466 @ (sub @ X465 @ X467)))) | ~ ! [X472 : term] : (~ (((var @ X472)) = $true) | ($true = ((X466 @ (sub @ X472 @ X467)))))) <=> (induction2lem = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) <=> (axidr = $true)) & (pushprop_lem3v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X474 : (subst > term > subst > $o),X475 : term] : (~ ! [X476 : (subst > term > term)] : (~ ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ~ ($true = ((X474 @ id @ X477 @ id)))) | ~ ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479))) | ($true = ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id)))) | ~ ! [X481 : term,X482 : term] : (($true = ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) | ~ ($true = ((X474 @ id @ X482 @ id))) | ~ ($true = ((X474 @ id @ X481 @ id)))) | ($true = ((X474 @ id @ X475 @ id))))) & (hoasinduction_lem3a_gthm = $true) & (axvarshift = $true) & (hoaslamnotap_gthm = $true) & ((induction2 = $true) <=> ! [X483 : term,X484 : (term > $o)] : (~ ! [X485 : term] : (($true = ((X484 @ (lam @ X485)))) | ~ ! [X486 : term] : (($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))) | ~ ($true = ((X484 @ X486))))) | (((X484 @ X483)) = $true) | ~ ! [X487 : term] : ((((X484 @ X487)) = $true) | ~ ($true = ((var @ X487)))) | ~ ! [X488 : term,X489 : term] : (($true = ((X484 @ (ap @ X488 @ X489)))) | ~ (((X484 @ X489)) = $true) | ~ ($true = ((X484 @ X488)))))) & (ulamvarind = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) = X490) => ! [X492 : (term > $o),X493 : subst,X494 : term,X495 : (term > $o)] : (($true = ((X495 @ one))) | ~ (((X492 @ X494)) = $true) | ~ ! [X496 : term] : (((X495 @ X496)) = ((X492 @ (sub @ X496 @ (push @ X494 @ X493)))))))) & (one = ((d2term @ d_one))) & ((! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (~ ! [X501 : term,X502 : subst,X503 : subst,X504 : subst] : ((((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) = $true) | ~ ($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503))))) | (((X499 @ (lam @ X498))) = $true) | ~ ! [X505 : (subst > term > term)] : (~ ! [X506 : term] : (~ ($true = ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id)))) | ~ ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) | (((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true)) | ~ ! [X510 : term] : (((X500 @ id @ X510 @ id)) = ((X499 @ X510))) | ~ ! [X511 : subst,X512 : subst,X513 : subst,X514 : term] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) = $true) | ~ (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true)) | ~ ! [X515 : term] : (($true = ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) | ~ (((X499 @ X515)) = $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & ((induction = $true) <=> ! [X516 : (term > $o),X517 : term] : (($true = ((X516 @ X517))) | ~ ! [X518 : term] : (~ ($true = ((var @ X518))) | ($true = ((X516 @ X518)))) | ~ ! [X519 : term,X520 : term] : (~ ($true = ((X516 @ X519))) | ($true = ((X516 @ (ap @ X519 @ X520)))) | ~ ($true = ((X516 @ X520)))) | ~ ! [X521 : term] : (~ ($true = ((X516 @ X521))) | (((X516 @ (lam @ X521))) = $true)))) & ! [X522 : d_term,X523 : d_term] : ((((d2term @ X523)) = ((d2term @ X522))) => (X522 = X523)) & ((hoasinduction_lem3 = $true) <=> ! [X524 : term,X525 : (subst > term > subst > $o)] : (($true = ((X525 @ id @ (lam @ X524) @ id))) | ~ ! [X526 : subst,X527 : subst,X528 : term,X529 : subst] : (~ ($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) | ($true = ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))) | ~ ! [X530 : (subst > term > term)] : (~ ! [X531 : term] : (($true = ((X525 @ id @ (X530 @ id @ X531) @ id))) | ~ ($true = ((X525 @ id @ X531 @ id)))) | (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) = $true) | ~ ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ~ ! [X535 : term,X536 : subst,X537 : subst,X538 : subst] : (~ (((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) | ($true = ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ~ ! [X539 : term] : (($true = ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id))) | ~ (((X525 @ id @ X539 @ id)) = $true))))),
% 5.43/1.21 inference(rectify,[],[f5])).
% 5.43/1.21 thf(f9,plain,(
% 5.43/1.21 (hoaslamnotvar_lthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (! [X36 : term,X37 : term,X38 : term,X39 : term] : ((X37 = X39) | (((ap @ X38 @ X37)) != ((ap @ X36 @ X39)))) => ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)))) & (! [X474 : (subst > term > subst > $o),X475 : term] : (~ ! [X476 : (subst > term > term)] : (~ ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479))) | ~ ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) | ($true = ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id)))) | ~ ! [X481 : term,X482 : term] : (($true != ((X474 @ id @ X481 @ id))) | ($true != ((X474 @ id @ X482 @ id))) | ($true = ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id)))) | ($true = ((X474 @ id @ X475 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((laminj = $true) <=> ! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420))))) & (! [X44 : term] : ~ ! [X45 : (subst > term > term)] : (((X45 @ sh @ one)) != ((sub @ X44 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_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)))))))))))) & ((! [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) = X490) => ! [X495 : (term > $o),X493 : subst,X494 : term,X492 : (term > $o)] : ((((X492 @ X494)) != $true) | ~ ! [X496 : term] : (((X495 @ X496)) = ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one))))) <=> (pushprop_lem1v2_lthm = $true)) & (ulamvarind = $true) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) <=> (substmonoid = $true)) & (ulamvar1 != $true) & (axabs = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) <=> (hoasapinj1 = $true)) & ((! [X266 : subst,X267 : term] : (((sub @ one @ (push @ X267 @ X266))) = X267) => (! [X269 : subst,X268 : term] : (((comp @ sh @ (push @ X268 @ X269))) = X269) => (! [X270 : subst] : (((comp @ X270 @ id)) = X270) => (! [X271 : term,X272 : (term > $o)] : (~ ! [X276 : term] : (($true = ((X272 @ (lam @ X276)))) | (((X272 @ X276)) != $true)) | (((X272 @ X271)) = $true) | ~ ! [X274 : term,X275 : term] : (($true != ((X272 @ X274))) | ($true = ((X272 @ (ap @ X275 @ X274)))) | ($true != ((X272 @ X275)))) | ~ ! [X273 : term] : ((((X272 @ X273)) = $true) | ($true != ((var @ X273))))) => ! [X278 : term,X277 : subst,X279 : (term > $o)] : ((((X279 @ (sub @ X278 @ X277))) = $true) | ~ ! [X280 : term] : (($true != ((var @ X280))) | (((X279 @ (sub @ X280 @ X277))) = $true)) | ~ ! [X284 : term,X283 : term] : (($true != ((X279 @ X284))) | ($true != ((X279 @ X283))) | ($true = ((X279 @ (ap @ X284 @ X283))))) | ~ ! [X281 : term] : ((((X279 @ (lam @ X281))) = $true) | ~ ! [X282 : term] : ((((X279 @ X282)) != $true) | ($true = ((X279 @ (sub @ X281 @ (push @ X282 @ id)))))))))))) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X418 : term] : ~ ! [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) != ((X419 @ sh @ one)))) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X112 : (subst > term > subst > $o)] : ~ ! [X113 : (term > $o)] : ~ ! [X114 : term] : (((X113 @ X114)) = ((X112 @ id @ X114 @ id))) => (! [X115 : (term > $o),X116 : term] : (~ ! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) | ~ ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ~ ! [X121 : term] : (($true = ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) | (((X115 @ X121)) != $true))) | ($true = ((X115 @ X116))) | ~ ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117))))) => (! [X122 : term] : (((sub @ X122 @ id)) = X122) => (! [X125 : (subst > term > subst > $o),X124 : (term > $o),X123 : term] : (~ ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) | ~ ! [X127 : (subst > term > term)] : ((((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ~ ! [X130 : term,X129 : subst,X128 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) = ((sub @ (X127 @ X129 @ X130) @ X128))) | ~ ! [X131 : term] : (($true != ((X125 @ id @ X131 @ id))) | ($true = ((X125 @ id @ (X127 @ id @ X131) @ id))))) | ~ ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) | ($true = ((X124 @ (lam @ X123))))) => ! [X133 : (subst > term > subst > $o),X134 : term] : (~ ! [X135 : (subst > term > term)] : ((((X133 @ id @ (lam @ (X135 @ sh @ one)) @ id)) = $true) | ~ ! [X136 : term] : (($true = ((X133 @ id @ (X135 @ id @ X136) @ id))) | ($true != ((X133 @ id @ X136 @ id)))) | ~ ! [X137 : subst,X139 : subst,X138 : term] : (((sub @ (X135 @ X139 @ X138) @ X137)) = ((X135 @ (comp @ X139 @ X137) @ (sub @ X138 @ X137))))) | ~ ! [X141 : term,X140 : term] : ((((X133 @ id @ (ap @ (sub @ X141 @ id) @ X140) @ id)) = $true) | (((X133 @ id @ X141 @ id)) != $true) | ($true != ((X133 @ id @ X140 @ id)))) | ($true = ((X133 @ id @ X134 @ id))))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) <=> (axidl = $true)) & (((var @ (d2term @ d_one))) != $true) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) <=> (termmset = $true)) & (induction2_gthm = $true) & (! [X8 : term,X10 : (subst > term > term),X9 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ~ ! [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X294 : subst,X296 : (term > $o),X295 : term] : ~ ! [X297 : (term > $o)] : ~ ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & (one = ((d2term @ d_one))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X422 : (subst > term > subst > $o)] : ~ ! [X423 : (term > $o)] : ~ ! [X424 : term] : (((X423 @ X424)) = ((X422 @ id @ X424 @ id))) => (! [X426 : term,X425 : (term > $o)] : (~ ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true)) | ~ ! [X430 : term] : (~ ! [X431 : term] : ((((X425 @ X431)) != $true) | (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) = $true)) | ($true = ((X425 @ (lam @ X430))))) | ~ ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) | ($true = ((X425 @ X426)))) => (! [X432 : term] : (((sub @ X432 @ id)) = X432) => (! [X434 : term,X433 : (term > $o),X435 : (subst > term > subst > $o)] : (~ ! [X438 : (subst > term > term)] : (~ ! [X439 : term] : (($true = ((X435 @ id @ (X438 @ id @ X439) @ id))) | ($true != ((X435 @ id @ X439 @ id)))) | ~ ! [X441 : term,X440 : subst,X442 : subst] : (((sub @ (X438 @ X442 @ X441) @ X440)) = ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440)))) | (((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true)) | ($true = ((X433 @ (lam @ X434)))) | ~ ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) | ~ ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))) => ! [X444 : term,X443 : (subst > term > subst > $o)] : (~ ! [X454 : subst,X452 : subst,X453 : term,X455 : subst] : (($true != ((X443 @ X455 @ X453 @ (comp @ X454 @ X452)))) | (((X443 @ (comp @ X455 @ X454) @ (sub @ X453 @ X454) @ X452)) = $true)) | ~ ! [X445 : term,X446 : term] : ((((X443 @ id @ X445 @ id)) != $true) | (((X443 @ id @ X446 @ id)) != $true) | (((X443 @ id @ (ap @ (sub @ X446 @ id) @ X445) @ id)) = $true)) | ~ ! [X456 : term] : ((((var @ (sub @ X456 @ id))) != $true) | ($true = ((X443 @ id @ X456 @ id)))) | ~ ! [X447 : (subst > term > term)] : (~ ! [X449 : subst,X448 : subst,X450 : term] : (((sub @ (X447 @ X448 @ X450) @ X449)) = ((X447 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449)))) | (((X443 @ id @ (lam @ (X447 @ sh @ one)) @ id)) = $true) | ~ ! [X451 : term] : ((((X443 @ id @ X451 @ id)) != $true) | ($true = ((X443 @ id @ (X447 @ id @ X451) @ id))))) | ~ ! [X459 : subst,X458 : subst,X460 : subst,X457 : term] : ((((X443 @ X460 @ X457 @ (comp @ X459 @ X458))) = $true) | ($true != ((X443 @ (comp @ X460 @ X459) @ (sub @ X457 @ X459) @ X458)))) | ($true = ((X443 @ id @ X444 @ id))))))))) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) <=> (axvarid = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X182 : (subst > term > subst > $o),X183 : term] : (~ ! [X184 : term] : (($true = ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))) | ($true != ((X182 @ id @ X184 @ id)))) | ($true = ((X182 @ id @ (lam @ X183) @ id))) | ~ ! [X185 : (subst > term > term)] : (~ ! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) | ~ ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188))) | (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true)))) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (hoasinduction_lem1_lthm = $true) & (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axvarshift = $true) & (! [X47 : subst,X46 : term,X48 : (term > $o)] : ~ ! [X49 : (term > $o)] : ~ ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X285 : term] : (((sub @ X285 @ id)) = X285) => (! [X289 : term,X288 : term,X287 : term,X286 : term] : ((((ap @ X288 @ X287)) != ((ap @ X286 @ X289))) | (X286 = X288)) => ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292))))) & (lamnotap != $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lthm_orig = $true) & ! [X235 : d_term] : (d_one = X235) & (substmonoid_gthm = $true) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) <=> (hoasapinj2 = $true)) & ((! [X153 : subst,X152 : term] : (((sub @ one @ (push @ X152 @ X153))) = X152) => (! [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) = X154) => (! [X156 : term,X157 : term] : ((X156 = X157) | (((lam @ X156)) != ((lam @ X157)))) => ! [X160 : subst,X158 : term,X159 : (subst > term > term),X161 : (subst > term > term)] : (~ ! [X164 : term,X162 : subst,X163 : subst] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) = ((sub @ (X159 @ X162 @ X164) @ X163))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ~ ! [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) = ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))))))) <=> (hoaslaminj_lthm = $true)) & ((apinj1 = $true) <=> ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390))))) & ! [X198 : d_subst] : (d_id = X198) & (! [X362 : (subst > term > subst > $o),X361 : term] : (~ ! [X372 : term] : (($true = ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id))) | ($true != ((X362 @ id @ X372 @ id)))) | ~ ! [X364 : term,X363 : (subst > term > term)] : (~ ! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) | ($true = ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) | ~ ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368))) | ~ ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370))))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ~ ! [X1 : (term > $o)] : ~ ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (axapp = $true) & (ulamvarsh = $true) & ((axshiftcons = $true) <=> ! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461)) & (pushprop_lem1_gthm = $true) & (! [X171 : term,X170 : (subst > term > subst > $o)] : (~ ! [X172 : term] : (($true = ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) | (((X170 @ id @ X172 @ id)) != $true)) | ~ ! [X173 : (subst > term > term)] : (~ ! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) | (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ~ ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X150 : (term > $o),X147 : subst,X148 : (term > $o),X149 : term] : (~ ! [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) = ((X148 @ X151))) | (((X150 @ X149)) != $true) | ($true = ((X148 @ one))))) & ((pushprop_lem1 = $true) <=> ! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) <=> (apinj2 = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X225 : (subst > term > term),X226 : (subst > term > term),X227 : subst,X228 : term] : (~ ! [X233 : subst,X234 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) = ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | ~ ! [X231 : subst,X229 : term,X230 : subst] : (((sub @ (X225 @ X230 @ X229) @ X231)) = ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) <=> (hoaslaminj = $true)) & ! [X14 : d_subst,X15 : d_subst] : ((((d2subst @ X15)) = ((d2subst @ X14))) => (X14 = X15)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X239 : term,X236 : (subst > term > subst > $o),X237 : term,X238 : (term > $o)] : (~ ! [X240 : term] : (((X236 @ id @ X240 @ id)) = ((X238 @ X240))) | ~ ! [X246 : subst,X245 : subst,X248 : term,X247 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) != $true) | ($true = ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247)))) | ~ ! [X250 : term,X249 : term] : (($true != ((X236 @ id @ X250 @ id))) | ($true = ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id))) | ($true != ((X236 @ id @ X249 @ id)))) | ($true != ((X238 @ X239))) | ($true = ((X238 @ (ap @ X239 @ X237)))) | ~ ! [X243 : subst,X244 : subst,X242 : term,X241 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) = $true) | ($true != ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ($true != ((X238 @ X237))))) & (((d2subst @ d_id)) = id) & ((termmset_lthm = $true) <=> (! [X251 : term] : (((sub @ X251 @ id)) = X251) => ! [X252 : term] : (((sub @ X252 @ id)) = X252))) & ((pushprop_lem1_lthm = $true) <=> (! [X200 : term,X199 : subst] : (((sub @ one @ (push @ X200 @ X199))) = X200) => (! [X202 : subst,X201 : term] : (((comp @ sh @ (push @ X201 @ X202))) = X202) => ! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205))))))))) & ((hoasinduction_lem2 = $true) <=> ! [X254 : term,X253 : (subst > term > subst > $o),X255 : term] : (($true != ((X253 @ id @ X254 @ id))) | ~ ! [X262 : subst,X261 : subst,X260 : subst,X263 : term] : ((((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) = $true) | (((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) != $true)) | (((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ~ ! [X264 : term,X265 : term] : (($true = ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) | ($true != ((X253 @ id @ X265 @ id))) | ($true != ((X253 @ id @ X264 @ id)))) | ~ ! [X258 : subst,X256 : subst,X257 : subst,X259 : term] : ((((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) = $true) | ($true != ((X253 @ X258 @ X259 @ (comp @ X256 @ X257))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (! [X300 : term] : ~ ! [X301 : (subst > term > term)] : ~ ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X20 : term,X19 : (subst > term > subst > $o),X18 : (term > $o)] : (~ ! [X32 : subst,X35 : subst,X34 : subst,X33 : term] : (($true = ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) | ($true != ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ~ ! [X25 : term,X24 : subst,X22 : subst,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) = $true) | ($true != ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22)))) | ~ ! [X31 : term] : (($true != ((X18 @ X31))) | ($true = ((X18 @ (sub @ X20 @ (push @ X31 @ id)))))) | ($true = ((X18 @ (lam @ X20)))) | ~ ! [X26 : (subst > term > term)] : (($true = ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) | ~ ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) | ~ ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ~ ! [X21 : term] : (((X19 @ id @ X21 @ id)) = ((X18 @ X21)))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lthm = $true) <=> (! [X58 : term,X59 : (term > $o)] : (~ ! [X60 : term] : (($true = ((X59 @ X60))) | ($true != ((var @ X60)))) | ~ ! [X61 : term,X62 : term] : ((((X59 @ X61)) != $true) | ($true = ((X59 @ (ap @ X61 @ X62)))) | ($true != ((X59 @ X62)))) | ~ ! [X63 : term] : ((((X59 @ (lam @ X63))) = $true) | ~ ! [X64 : term] : (($true != ((X59 @ X64))) | ($true = ((X59 @ (sub @ X63 @ (push @ X64 @ id))))))) | ($true = ((X59 @ X58)))) => (! [X66 : term,X65 : term,X67 : (subst > term > subst > $o)] : (~ ! [X76 : term,X77 : term] : (($true != ((X67 @ id @ X77 @ id))) | (((X67 @ id @ (ap @ (sub @ X76 @ id) @ X77) @ id)) = $true) | ($true != ((X67 @ id @ X76 @ id)))) | ~ ! [X74 : term,X75 : subst,X73 : subst,X72 : subst] : (($true = ((X67 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72) @ X75))) | ($true != ((X67 @ X73 @ X74 @ (comp @ X72 @ X75))))) | ($true != ((X67 @ id @ X66 @ id))) | (((X67 @ id @ (ap @ X65 @ X66) @ id)) = $true) | (((X67 @ id @ X65 @ id)) != $true) | ~ ! [X68 : subst,X70 : term,X69 : subst,X71 : subst] : (($true = ((X67 @ X71 @ X70 @ (comp @ X68 @ X69)))) | ($true != ((X67 @ (comp @ X71 @ X68) @ (sub @ X70 @ X68) @ X69))))) => (! [X79 : term,X78 : (subst > term > subst > $o)] : (~ ! [X87 : subst,X85 : subst,X86 : subst,X84 : term] : (($true != ((X78 @ X87 @ X84 @ (comp @ X85 @ X86)))) | ($true = ((X78 @ (comp @ X87 @ X85) @ (sub @ X84 @ X85) @ X86)))) | ~ ! [X88 : term] : (($true = ((X78 @ id @ (sub @ X79 @ (push @ X88 @ id)) @ id))) | ($true != ((X78 @ id @ X88 @ id)))) | ($true = ((X78 @ id @ (lam @ X79) @ id))) | ~ ! [X82 : subst,X81 : subst,X83 : subst,X80 : term] : (($true != ((X78 @ (comp @ X81 @ X83) @ (sub @ X80 @ X83) @ X82))) | ($true = ((X78 @ X81 @ X80 @ (comp @ X83 @ X82))))) | ~ ! [X89 : (subst > term > term)] : (($true = ((X78 @ id @ (lam @ (X89 @ sh @ one)) @ id))) | ~ ! [X91 : subst,X92 : subst,X93 : term] : (((X89 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) = ((sub @ (X89 @ X92 @ X93) @ X91))) | ~ ! [X90 : term] : (($true != ((X78 @ id @ X90 @ id))) | (((X78 @ id @ (X89 @ id @ X90) @ id)) = $true)))) => ! [X94 : (subst > term > subst > $o),X95 : term] : (~ ! [X100 : term] : ((((X94 @ id @ X100 @ id)) = $true) | ($true != ((var @ (sub @ X100 @ id))))) | ~ ! [X107 : (subst > term > term)] : (~ ! [X110 : subst,X111 : subst,X109 : term] : (((X107 @ (comp @ X111 @ X110) @ (sub @ X109 @ X110))) = ((sub @ (X107 @ X111 @ X109) @ X110))) | ($true = ((X94 @ id @ (lam @ (X107 @ sh @ one)) @ id))) | ~ ! [X108 : term] : (($true = ((X94 @ id @ (X107 @ id @ X108) @ id))) | (((X94 @ id @ X108 @ id)) != $true))) | ~ ! [X97 : subst,X96 : term,X99 : subst,X98 : subst] : (($true = ((X94 @ (comp @ X99 @ X97) @ (sub @ X96 @ X97) @ X98))) | ($true != ((X94 @ X99 @ X96 @ (comp @ X97 @ X98))))) | ~ ! [X105 : term,X106 : term] : ((((X94 @ id @ X105 @ id)) != $true) | (((X94 @ id @ X106 @ id)) != $true) | ($true = ((X94 @ id @ (ap @ (sub @ X106 @ id) @ X105) @ id)))) | ($true = ((X94 @ id @ X95 @ id))) | ~ ! [X101 : subst,X102 : term,X104 : subst,X103 : subst] : (($true = ((X94 @ X103 @ X102 @ (comp @ X104 @ X101)))) | (((X94 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104) @ X101)) != $true))))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) <=> (axscons = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2 = $true) <=> ! [X484 : (term > $o),X483 : term] : (~ ! [X487 : term] : (($true != ((var @ X487))) | (((X484 @ X487)) = $true)) | ~ ! [X489 : term,X488 : term] : (($true = ((X484 @ (ap @ X488 @ X489)))) | (((X484 @ X489)) != $true) | ($true != ((X484 @ X488)))) | ~ ! [X485 : term] : (~ ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id)))))) | ($true = ((X484 @ (lam @ X485))))) | (((X484 @ X483)) = $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X339 : subst] : (((comp @ id @ X339)) = X339) => (! [X340 : subst] : (((comp @ X340 @ id)) = X340) => (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X393 : term] : (((sub @ X393 @ id)) = X393) => (! [X394 : (subst > term > subst > $o),X395 : term] : (($true = ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) | ~ ! [X397 : (subst > term > term)] : (~ ! [X400 : term,X401 : subst,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X397 @ X401 @ X400) @ X399))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true) | ~ ! [X398 : term] : (($true != ((X394 @ id @ X398 @ id))) | (((X394 @ id @ (X397 @ id @ X398) @ id)) = $true))) | ~ ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true))) => ! [X402 : term,X403 : (subst > term > subst > $o)] : (($true = ((X403 @ id @ (lam @ X402) @ id))) | ~ ! [X417 : term] : (($true = ((X403 @ id @ (sub @ X402 @ (push @ X417 @ id)) @ id))) | ($true != ((X403 @ id @ X417 @ id)))) | ~ ! [X404 : subst,X406 : subst,X407 : subst,X405 : term] : (($true != ((X403 @ X407 @ X405 @ (comp @ X404 @ X406)))) | ($true = ((X403 @ (comp @ X407 @ X404) @ (sub @ X405 @ X404) @ X406)))) | ~ ! [X409 : subst,X408 : subst,X410 : subst,X411 : term] : (($true = ((X403 @ X409 @ X411 @ (comp @ X410 @ X408)))) | (((X403 @ (comp @ X409 @ X410) @ (sub @ X411 @ X410) @ X408)) != $true)) | ~ ! [X412 : (subst > term > term)] : (($true = ((X403 @ id @ (lam @ (X412 @ sh @ one)) @ id))) | ~ ! [X416 : term] : (($true != ((X403 @ id @ X416 @ id))) | ($true = ((X403 @ id @ (X412 @ id @ X416) @ id)))) | ~ ! [X413 : subst,X414 : term,X415 : subst] : (((X412 @ (comp @ X415 @ X413) @ (sub @ X414 @ X413))) = ((sub @ (X412 @ X415 @ X414) @ X413)))))))) & (pushprop_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axassoc = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & (hoasinduction_gthm = $true) & (! [X516 : (term > $o),X517 : term] : (~ ! [X521 : term] : ((((X516 @ (lam @ X521))) = $true) | ($true != ((X516 @ X521)))) | ~ ! [X518 : term] : (($true != ((var @ X518))) | ($true = ((X516 @ X518)))) | ~ ! [X519 : term,X520 : term] : (($true != ((X516 @ X519))) | ($true != ((X516 @ X520))) | ($true = ((X516 @ (ap @ X519 @ X520))))) | ($true = ((X516 @ X517)))) <=> (induction = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & ((induction2lem = $true) <=> ! [X467 : subst,X465 : term,X466 : (term > $o)] : (~ ! [X468 : term,X469 : term] : ((((X466 @ (ap @ X469 @ X468))) = $true) | ($true != ((X466 @ X468))) | ($true != ((X466 @ X469)))) | ~ ! [X472 : term] : ((((var @ X472)) != $true) | ($true = ((X466 @ (sub @ X472 @ X467))))) | ($true = ((X466 @ (sub @ X465 @ X467)))) | ~ ! [X470 : term] : ((((X466 @ (lam @ X470))) = $true) | ~ ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))))) & (((d2subst @ d_id)) = sh) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X208 : term] : ~ ! [X209 : (subst > term > term)] : ~ ! [X210 : subst,X211 : term] : (((X209 @ X210 @ X211)) = ((sub @ X208 @ (push @ X211 @ X210)))) => (! [X212 : term] : (((sub @ X212 @ id)) = X212) => ! [X213 : term,X215 : (subst > term > subst > $o),X214 : (term > $o)] : (($true = ((X214 @ (lam @ X213)))) | ~ ! [X216 : (subst > term > term)] : ((((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ~ ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id)))) | ~ ! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219)))) | ~ ! [X222 : term] : (($true = ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) | ($true != ((X214 @ X222)))) | ~ ! [X221 : term] : (((X214 @ X221)) = ((X215 @ id @ X221 @ id))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X313 : (subst > term > subst > $o),X311 : term,X312 : (term > $o)] : (~ ! [X314 : term] : (($true != ((X312 @ X314))) | (((X312 @ (sub @ X311 @ (push @ X314 @ id)))) = $true)) | ~ ! [X316 : (subst > term > term)] : (~ ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320)))) | ($true = ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) | ~ ! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true))) | ($true = ((X312 @ (lam @ X311)))) | ~ ! [X315 : term] : (((X313 @ id @ X315 @ id)) = ((X312 @ X315))))) & (hoasapnotvar_gthm = $true) & ((axvarcons = $true) <=> ! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224)) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((! [X497 : term] : (((sub @ X497 @ id)) = X497) => ! [X499 : (term > $o),X500 : (subst > term > subst > $o),X498 : term] : ((((X499 @ (lam @ X498))) = $true) | ~ ! [X504 : subst,X502 : subst,X503 : subst,X501 : term] : ((((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) = $true) | ($true != ((X500 @ X504 @ X501 @ (comp @ X502 @ X503))))) | ~ ! [X510 : term] : (((X500 @ id @ X510 @ id)) = ((X499 @ X510))) | ~ ! [X505 : (subst > term > term)] : (~ ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id)))) | (((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true) | ~ ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507)))) | ~ ! [X511 : subst,X514 : term,X513 : subst,X512 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) = $true) | (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) != $true)) | ~ ! [X515 : term] : ((((X499 @ X515)) != $true) | ($true = ((X499 @ (sub @ X498 @ (push @ X515 @ id)))))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (! [X525 : (subst > term > subst > $o),X524 : term] : (~ ! [X530 : (subst > term > term)] : (~ ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532)))) | (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) = $true) | ~ ! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id))))) | ~ ! [X539 : term] : (($true = ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id))) | (((X525 @ id @ X539 @ id)) != $true)) | ~ ! [X528 : term,X527 : subst,X529 : subst,X526 : subst] : (($true != ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) | ($true = ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))) | ~ ! [X537 : subst,X538 : subst,X535 : term,X536 : subst] : (($true = ((X525 @ X538 @ X535 @ (comp @ X537 @ X536)))) | (((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) != $true)) | ($true = ((X525 @ id @ (lam @ X524) @ id)))) <=> (hoasinduction_lem3 = $true)) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) <=> (shinj = $true)) & ! [X522 : d_term,X523 : d_term] : ((((d2term @ X523)) = ((d2term @ X522))) => (X522 = X523)) & ((! [X373 : term] : (((sub @ X373 @ id)) = X373) => (! [X375 : (term > $o),X374 : subst,X376 : term] : (~ ! [X379 : term] : ((((var @ X379)) != $true) | (((X375 @ (sub @ X379 @ X374))) = $true)) | ~ ! [X380 : term] : (~ ! [X381 : term] : (($true != ((X375 @ X381))) | (((X375 @ (sub @ X380 @ (push @ X381 @ id)))) = $true)) | ($true = ((X375 @ (lam @ X380))))) | ($true = ((X375 @ (sub @ X376 @ X374)))) | ~ ! [X377 : term,X378 : term] : ((((X375 @ (ap @ X378 @ X377))) = $true) | ($true != ((X375 @ X377))) | (((X375 @ X378)) != $true))) => ! [X382 : (term > $o),X383 : term] : (~ ! [X384 : term] : (~ ! [X385 : term] : ((((X382 @ X385)) != $true) | ($true = ((X382 @ (sub @ X384 @ (push @ X385 @ id)))))) | (((X382 @ (lam @ X384))) = $true)) | ($true = ((X382 @ X383))) | ~ ! [X386 : term,X387 : term] : ((((X382 @ (ap @ X386 @ X387))) = $true) | ($true != ((X382 @ X386))) | (((X382 @ X387)) != $true)) | ~ ! [X388 : term] : (($true = ((X382 @ X388))) | ($true != ((var @ X388))))))) <=> (induction2_lthm = $true)) & (hoaslamnotvar = $true) & (lamnotvar = $true) & ((! [X321 : term] : (((sub @ X321 @ id)) = X321) => (! [X322 : (subst > term > subst > $o),X323 : term] : (~ ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) | ~ ! [X325 : (subst > term > term)] : (~ ! [X326 : term] : (($true = ((X322 @ id @ (X325 @ id @ X326) @ id))) | ($true != ((X322 @ id @ X326 @ id)))) | ~ ! [X329 : subst,X327 : subst,X328 : term] : (((sub @ (X325 @ X327 @ X328) @ X329)) = ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))) | ($true = ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id)))) => ! [X331 : (subst > term > subst > $o),X330 : term] : (~ ! [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) = $true) | ($true != ((X331 @ id @ X337 @ id)))) | ~ ! [X332 : (subst > term > term)] : (~ ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334))) | (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) = $true) | ~ ! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id))))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X308 : (subst > term > subst > $o)] : ~ ! [X309 : (term > $o)] : ~ ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id)))) & (! [X191 : term,X190 : (subst > term > subst > $o)] : ((((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X192 : term] : (($true = ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) | (((X190 @ id @ X192 @ id)) != $true)) | ~ ! [X193 : (subst > term > term)] : ((((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) = $true) | ~ ! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) | ~ ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) <=> (axidr = $true)) & ((hoasinduction = $true) <=> ! [X344 : term,X343 : (subst > term > subst > $o)] : (($true = ((X343 @ id @ X344 @ id))) | ~ ! [X347 : (subst > term > term)] : ((((X343 @ id @ (lam @ (X347 @ sh @ one)) @ id)) = $true) | ~ ! [X350 : term,X349 : subst,X348 : subst] : (((sub @ (X347 @ X348 @ X350) @ X349)) = ((X347 @ (comp @ X348 @ X349) @ (sub @ X350 @ X349)))) | ~ ! [X351 : term] : (($true = ((X343 @ id @ (X347 @ id @ X351) @ id))) | ($true != ((X343 @ id @ X351 @ id))))) | ~ ! [X352 : term] : (($true = ((X343 @ id @ X352 @ id))) | ($true != ((var @ (sub @ X352 @ id))))) | ~ ! [X357 : subst,X358 : term,X359 : subst,X360 : subst] : (($true = ((X343 @ X360 @ X358 @ (comp @ X357 @ X359)))) | ($true != ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359)))) | ~ ! [X353 : subst,X354 : subst,X356 : term,X355 : subst] : (($true = ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) | ($true != ((X343 @ X353 @ X356 @ (comp @ X354 @ X355))))) | ~ ! [X346 : term,X345 : term] : (($true = ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) | ($true != ((X343 @ id @ X345 @ id))) | ($true != ((X343 @ id @ X346 @ id))))))),
% 5.43/1.21 inference(flattening,[],[f8])).
% 5.43/1.21 thf(f10,plain,(
% 5.43/1.21 (hoaslamnotvar_lthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (apnotvar = $true) & ((hoasapinj2_lthm = $true) <=> (? [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 != X39) & (((ap @ X38 @ X37)) = ((ap @ X36 @ X39)))) | ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X474 : (subst > term > subst > $o),X475 : term] : (? [X482 : term,X481 : term] : (($true = ((X474 @ id @ X482 @ id))) & ($true != ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) & ($true = ((X474 @ id @ X481 @ id)))) | ? [X476 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) & ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) & ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479)))) | ($true = ((X474 @ id @ X475 @ id))))) & ((laminj = $true) <=> ! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X44 : term] : ? [X45 : (subst > term > term)] : (((X45 @ sh @ one)) = ((sub @ X44 @ (push @ one @ sh))))) & (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_lem1v2_lthm = $true) <=> (! [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) != $true) | ? [X496 : term] : (((X495 @ X496)) != ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one)))) | ? [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) != X490))) & (ulamvarind = $true) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) <=> (substmonoid = $true)) & (ulamvar1 != $true) & (axabs = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) <=> (hoasapinj1 = $true)) & (((((! [X278 : term,X279 : (term > $o),X277 : subst] : ((((X279 @ (sub @ X278 @ X277))) = $true) | ? [X281 : term] : ((((X279 @ (lam @ X281))) != $true) & ! [X282 : term] : ((((X279 @ X282)) != $true) | ($true = ((X279 @ (sub @ X281 @ (push @ X282 @ id))))))) | ? [X283 : term,X284 : term] : (($true = ((X279 @ X284))) & ($true != ((X279 @ (ap @ X284 @ X283)))) & ($true = ((X279 @ X283)))) | ? [X280 : term] : (($true = ((var @ X280))) & (((X279 @ (sub @ X280 @ X277))) != $true))) | ? [X272 : (term > $o),X271 : term] : (! [X276 : term] : (($true = ((X272 @ (lam @ X276)))) | (((X272 @ X276)) != $true)) & (((X272 @ X271)) != $true) & ! [X274 : term,X275 : term] : (($true != ((X272 @ X274))) | ($true = ((X272 @ (ap @ X275 @ X274)))) | ($true != ((X272 @ X275)))) & ! [X273 : term] : ((((X272 @ X273)) = $true) | ($true != ((var @ X273)))))) | ? [X270 : subst] : (((comp @ X270 @ id)) != X270)) | ? [X269 : subst,X268 : term] : (((comp @ sh @ (push @ X268 @ X269))) != X269)) | ? [X266 : subst,X267 : term] : (((sub @ one @ (push @ X267 @ X266))) != X267)) <=> (induction2lem_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X418 : term] : ? [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) = ((X419 @ sh @ one)))) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X134 : term,X133 : (subst > term > subst > $o)] : (? [X135 : (subst > term > term)] : (! [X137 : subst,X139 : subst,X138 : term] : (((sub @ (X135 @ X139 @ X138) @ X137)) = ((X135 @ (comp @ X139 @ X137) @ (sub @ X138 @ X137)))) & ! [X136 : term] : (($true = ((X133 @ id @ (X135 @ id @ X136) @ id))) | ($true != ((X133 @ id @ X136 @ id)))) & (((X133 @ id @ (lam @ (X135 @ sh @ one)) @ id)) != $true)) | ($true = ((X133 @ id @ X134 @ id))) | ? [X140 : term,X141 : term] : (($true = ((X133 @ id @ X140 @ id))) & (((X133 @ id @ (ap @ (sub @ X141 @ id) @ X140) @ id)) != $true) & (((X133 @ id @ X141 @ id)) = $true))) | ? [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true != ((X124 @ (lam @ X123)))) & ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) & ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) & ! [X127 : (subst > term > term)] : (? [X131 : term] : (($true != ((X125 @ id @ (X127 @ id @ X131) @ id))) & ($true = ((X125 @ id @ X131 @ id)))) | (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) != ((sub @ (X127 @ X129 @ X130) @ X128)))))) | ? [X122 : term] : (((sub @ X122 @ id)) != X122)) | ? [X115 : (term > $o),X116 : term] : (! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) & ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ? [X121 : term] : (($true != ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) & (((X115 @ X121)) = $true))) & ($true != ((X115 @ X116))) & ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117)))))) | ? [X112 : (subst > term > subst > $o)] : ! [X113 : (term > $o)] : ? [X114 : term] : (((X113 @ X114)) != ((X112 @ id @ X114 @ id))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) <=> (axidl = $true)) & (((var @ (d2term @ d_one))) != $true) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) <=> (termmset = $true)) & (induction2_gthm = $true) & (! [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ? [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) != ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X294 : subst,X296 : (term > $o),X295 : term] : ? [X297 : (term > $o)] : ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & (one = ((d2term @ d_one))) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X444 : term,X443 : (subst > term > subst > $o)] : (? [X456 : term] : ((((var @ (sub @ X456 @ id))) = $true) & ($true != ((X443 @ id @ X456 @ id)))) | ? [X445 : term,X446 : term] : ((((X443 @ id @ X446 @ id)) = $true) & (((X443 @ id @ (ap @ (sub @ X446 @ id) @ X445) @ id)) != $true) & (((X443 @ id @ X445 @ id)) = $true)) | ($true = ((X443 @ id @ X444 @ id))) | ? [X447 : (subst > term > term)] : (! [X451 : term] : ((((X443 @ id @ X451 @ id)) != $true) | ($true = ((X443 @ id @ (X447 @ id @ X451) @ id)))) & ! [X449 : subst,X448 : subst,X450 : term] : (((sub @ (X447 @ X448 @ X450) @ X449)) = ((X447 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449)))) & (((X443 @ id @ (lam @ (X447 @ sh @ one)) @ id)) != $true)) | ? [X457 : term,X460 : subst,X459 : subst,X458 : subst] : (($true = ((X443 @ (comp @ X460 @ X459) @ (sub @ X457 @ X459) @ X458))) & (((X443 @ X460 @ X457 @ (comp @ X459 @ X458))) != $true)) | ? [X452 : subst,X453 : term,X455 : subst,X454 : subst] : (($true = ((X443 @ X455 @ X453 @ (comp @ X454 @ X452)))) & (((X443 @ (comp @ X455 @ X454) @ (sub @ X453 @ X454) @ X452)) != $true))) | ? [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ? [X439 : term] : (($true != ((X435 @ id @ (X438 @ id @ X439) @ id))) & ($true = ((X435 @ id @ X439 @ id)))) | ? [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) != ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) & ($true != ((X433 @ (lam @ X434)))) & ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) & ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id)))))))) | ? [X432 : term] : (((sub @ X432 @ id)) != X432)) | ? [X426 : term,X425 : (term > $o)] : (! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ? [X431 : term] : ((((X425 @ X431)) = $true) & (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) != $true))) & ($true != ((X425 @ X426))) & ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) & ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true)))) | ? [X422 : (subst > term > subst > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X423 @ X424)) != ((X422 @ id @ X424 @ id))))) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) <=> (axvarid = $true)) & (! [X183 : term,X182 : (subst > term > subst > $o)] : (($true = ((X182 @ id @ (lam @ X183) @ id))) | ? [X185 : (subst > term > term)] : (! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) & (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188)))) | ? [X184 : term] : (($true = ((X182 @ id @ X184 @ id))) & ($true != ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (hoasinduction_lem1_lthm = $true) & (! [X51 : term] : ? [X52 : (subst > term > term)] : ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axvarshift = $true) & (! [X47 : subst,X48 : (term > $o),X46 : term] : ? [X49 : (term > $o)] : ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) <=> (pushprop_lem0_lthm = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292)) | ? [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 != X288) & (((ap @ X288 @ X287)) = ((ap @ X286 @ X289))))) | ? [X285 : term] : (((sub @ X285 @ id)) != X285))) & (lamnotap != $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (termmset_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoaslamnotap_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lthm_orig = $true) & ! [X235 : d_term] : (d_one = X235) & (substmonoid_gthm = $true) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) <=> (hoasapinj2 = $true)) & ((((! [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (? [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) != ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ? [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) != ((sub @ (X159 @ X162 @ X164) @ X163)))) | ? [X157 : term,X156 : term] : ((((lam @ X156)) = ((lam @ X157))) & (X156 != X157))) | ? [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) != X154)) | ? [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) != X152)) <=> (hoaslaminj_lthm = $true)) & ((apinj1 = $true) <=> ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390))))) & ! [X198 : d_subst] : (d_id = X198) & (! [X361 : term,X362 : (subst > term > subst > $o)] : (? [X372 : term] : (($true = ((X362 @ id @ X372 @ id))) & ($true != ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) | ? [X363 : (subst > term > term),X364 : term] : (! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) & ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) & ($true != ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) & ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368)))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (axapp = $true) & (ulamvarsh = $true) & ((axshiftcons = $true) <=> ! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461)) & (pushprop_lem1_gthm = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X170 : (subst > term > subst > $o),X171 : term] : (? [X173 : (subst > term > term)] : (! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) & (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | ? [X172 : term] : (($true != ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) & (((X170 @ id @ X172 @ id)) = $true)) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true))) & (! [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true = ((X148 @ one))) | ? [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) != ((X148 @ X151))) | (((X150 @ X149)) != $true)) <=> (pushprop_lem1v2 = $true)) & ((pushprop_lem1 = $true) <=> ! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (pushprop_lem1v2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (axmap = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) <=> (apinj2 = $true)) & (hoasinduction_lem3a_gthm = $true) & (! [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (? [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) != ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | ? [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) != ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) <=> (hoaslaminj = $true)) & ! [X15 : d_subst,X14 : d_subst] : ((X14 = X15) | (((d2subst @ X15)) != ((d2subst @ X14)))) & (hoaslamnotap_lthm = $true) & (! [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true = ((X238 @ (ap @ X239 @ X237)))) | ($true != ((X238 @ X239))) | ? [X240 : term] : (((X236 @ id @ X240 @ id)) != ((X238 @ X240))) | ? [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) != $true) & ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ? [X250 : term,X249 : term] : (($true = ((X236 @ id @ X250 @ id))) & ($true = ((X236 @ id @ X249 @ id))) & ($true != ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) | ($true != ((X238 @ X237))) | ? [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) & ($true != ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))) <=> (hoasinduction_lem2v2 = $true)) & (((d2subst @ d_id)) = id) & ((! [X252 : term] : (((sub @ X252 @ id)) = X252) | ? [X251 : term] : (((sub @ X251 @ id)) != X251)) <=> (termmset_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) | ? [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) != X202)) | ? [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) != X200))) & (! [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ($true != ((X253 @ id @ X254 @ id))) | ? [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) & (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) != $true)) | ? [X265 : term,X264 : term] : (($true = ((X253 @ id @ X265 @ id))) & ($true != ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) & ($true = ((X253 @ id @ X264 @ id)))) | ? [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) & (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) != $true))) <=> (hoasinduction_lem2 = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_gthm = $true) & (! [X300 : term] : ? [X301 : (subst > term > term)] : ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true = ((X18 @ (lam @ X20)))) | ? [X31 : term] : (($true != ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) & ($true = ((X18 @ X31)))) | ? [X21 : term] : (((X19 @ id @ X21 @ id)) != ((X18 @ X21))) | ? [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true != ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) & ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ? [X26 : (subst > term > term)] : (($true != ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) & ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) & ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) != $true) & ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lthm = $true) <=> (((! [X95 : term,X94 : (subst > term > subst > $o)] : (? [X100 : term] : ((((X94 @ id @ X100 @ id)) != $true) & ($true = ((var @ (sub @ X100 @ id))))) | ? [X105 : term,X106 : term] : ((((X94 @ id @ X106 @ id)) = $true) & ($true != ((X94 @ id @ (ap @ (sub @ X106 @ id) @ X105) @ id))) & (((X94 @ id @ X105 @ id)) = $true)) | ($true = ((X94 @ id @ X95 @ id))) | ? [X101 : subst,X102 : term,X104 : subst,X103 : subst] : ((((X94 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104) @ X101)) = $true) & ($true != ((X94 @ X103 @ X102 @ (comp @ X104 @ X101))))) | ? [X98 : subst,X97 : subst,X99 : subst,X96 : term] : (($true != ((X94 @ (comp @ X99 @ X97) @ (sub @ X96 @ X97) @ X98))) & ($true = ((X94 @ X99 @ X96 @ (comp @ X97 @ X98))))) | ? [X107 : (subst > term > term)] : (($true != ((X94 @ id @ (lam @ (X107 @ sh @ one)) @ id))) & ! [X110 : subst,X111 : subst,X109 : term] : (((X107 @ (comp @ X111 @ X110) @ (sub @ X109 @ X110))) = ((sub @ (X107 @ X111 @ X109) @ X110))) & ! [X108 : term] : (($true = ((X94 @ id @ (X107 @ id @ X108) @ id))) | (((X94 @ id @ X108 @ id)) != $true)))) | ? [X79 : term,X78 : (subst > term > subst > $o)] : (($true != ((X78 @ id @ (lam @ X79) @ id))) & ! [X82 : subst,X81 : subst,X83 : subst,X80 : term] : (($true != ((X78 @ (comp @ X81 @ X83) @ (sub @ X80 @ X83) @ X82))) | ($true = ((X78 @ X81 @ X80 @ (comp @ X83 @ X82))))) & ! [X87 : subst,X85 : subst,X86 : subst,X84 : term] : (($true != ((X78 @ X87 @ X84 @ (comp @ X85 @ X86)))) | ($true = ((X78 @ (comp @ X87 @ X85) @ (sub @ X84 @ X85) @ X86)))) & ! [X88 : term] : (($true = ((X78 @ id @ (sub @ X79 @ (push @ X88 @ id)) @ id))) | ($true != ((X78 @ id @ X88 @ id)))) & ! [X89 : (subst > term > term)] : (($true = ((X78 @ id @ (lam @ (X89 @ sh @ one)) @ id))) | ? [X92 : subst,X93 : term,X91 : subst] : (((X89 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X89 @ X92 @ X93) @ X91))) | ? [X90 : term] : ((((X78 @ id @ (X89 @ id @ X90) @ id)) != $true) & ($true = ((X78 @ id @ X90 @ id))))))) | ? [X65 : term,X67 : (subst > term > subst > $o),X66 : term] : (! [X68 : subst,X70 : term,X69 : subst,X71 : subst] : (($true = ((X67 @ X71 @ X70 @ (comp @ X68 @ X69)))) | ($true != ((X67 @ (comp @ X71 @ X68) @ (sub @ X70 @ X68) @ X69)))) & ! [X74 : term,X75 : subst,X73 : subst,X72 : subst] : (($true = ((X67 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72) @ X75))) | ($true != ((X67 @ X73 @ X74 @ (comp @ X72 @ X75))))) & (((X67 @ id @ (ap @ X65 @ X66) @ id)) != $true) & ($true = ((X67 @ id @ X66 @ id))) & ! [X76 : term,X77 : term] : (($true != ((X67 @ id @ X77 @ id))) | (((X67 @ id @ (ap @ (sub @ X76 @ id) @ X77) @ id)) = $true) | ($true != ((X67 @ id @ X76 @ id)))) & (((X67 @ id @ X65 @ id)) = $true))) | ? [X59 : (term > $o),X58 : term] : (($true != ((X59 @ X58))) & ! [X61 : term,X62 : term] : ((((X59 @ X61)) != $true) | ($true = ((X59 @ (ap @ X61 @ X62)))) | ($true != ((X59 @ X62)))) & ! [X60 : term] : (($true = ((X59 @ X60))) | ($true != ((var @ X60)))) & ! [X63 : term] : (? [X64 : term] : (($true = ((X59 @ X64))) & ($true != ((X59 @ (sub @ X63 @ (push @ X64 @ id)))))) | (((X59 @ (lam @ X63))) = $true))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) <=> (axscons = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2 = $true) <=> ! [X483 : term,X484 : (term > $o)] : (? [X485 : term] : (($true != ((X484 @ (lam @ X485)))) & ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) | ? [X487 : term] : (($true = ((var @ X487))) & (((X484 @ X487)) != $true)) | ? [X488 : term,X489 : term] : (($true = ((X484 @ X488))) & ($true != ((X484 @ (ap @ X488 @ X489)))) & (((X484 @ X489)) = $true)) | (((X484 @ X483)) = $true))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & ((substmonoid_lthm = $true) <=> (((! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341)) | ? [X340 : subst] : (((comp @ X340 @ id)) != X340)) | ? [X339 : subst] : (((comp @ id @ X339)) != X339))) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X402 : term,X403 : (subst > term > subst > $o)] : (? [X417 : term] : (($true != ((X403 @ id @ (sub @ X402 @ (push @ X417 @ id)) @ id))) & ($true = ((X403 @ id @ X417 @ id)))) | ($true = ((X403 @ id @ (lam @ X402) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X403 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X416 : term] : (($true != ((X403 @ id @ X416 @ id))) | ($true = ((X403 @ id @ (X412 @ id @ X416) @ id)))) & ! [X413 : subst,X414 : term,X415 : subst] : (((X412 @ (comp @ X415 @ X413) @ (sub @ X414 @ X413))) = ((sub @ (X412 @ X415 @ X414) @ X413)))) | ? [X406 : subst,X405 : term,X404 : subst,X407 : subst] : (($true != ((X403 @ (comp @ X407 @ X404) @ (sub @ X405 @ X404) @ X406))) & ($true = ((X403 @ X407 @ X405 @ (comp @ X404 @ X406))))) | ? [X410 : subst,X409 : subst,X408 : subst,X411 : term] : ((((X403 @ (comp @ X409 @ X410) @ (sub @ X411 @ X410) @ X408)) = $true) & ($true != ((X403 @ X409 @ X411 @ (comp @ X410 @ X408)))))) | ? [X394 : (subst > term > subst > $o),X395 : term] : (($true != ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) & ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true)) & ! [X397 : (subst > term > term)] : (? [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X397 @ X401 @ X400) @ X399))) | ? [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) != $true) & ($true = ((X394 @ id @ X398 @ id)))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true)))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393))) & (pushprop_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axassoc = $true) & (hoasapinj2_gthm = $true) & (axclos = $true) & (hoasinduction_gthm = $true) & (! [X516 : (term > $o),X517 : term] : (? [X518 : term] : (($true != ((X516 @ X518))) & ($true = ((var @ X518)))) | ($true = ((X516 @ X517))) | ? [X519 : term,X520 : term] : (($true != ((X516 @ (ap @ X519 @ X520)))) & ($true = ((X516 @ X519))) & ($true = ((X516 @ X520)))) | ? [X521 : term] : ((((X516 @ (lam @ X521))) != $true) & ($true = ((X516 @ X521))))) <=> (induction = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasapnotvar = $true) & ((induction2lem = $true) <=> ! [X466 : (term > $o),X467 : subst,X465 : term] : (? [X470 : term] : ((((X466 @ (lam @ X470))) != $true) & ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) | ? [X469 : term,X468 : term] : (($true = ((X466 @ X469))) & (((X466 @ (ap @ X469 @ X468))) != $true) & ($true = ((X466 @ X468)))) | ? [X472 : term] : (($true != ((X466 @ (sub @ X472 @ X467)))) & (((var @ X472)) = $true)) | ($true = ((X466 @ (sub @ X465 @ X467)))))) & (((d2subst @ d_id)) = sh) & (pushprop = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (? [X216 : (subst > term > term)] : (! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219))) & (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true) & ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id))))) | ($true = ((X214 @ (lam @ X213)))) | ? [X222 : term] : (($true != ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) & ($true = ((X214 @ X222)))) | ? [X221 : term] : (((X214 @ X221)) != ((X215 @ id @ X221 @ id)))) | ? [X212 : term] : (((sub @ X212 @ id)) != X212)) | ? [X208 : term] : ! [X209 : (subst > term > term)] : ? [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) != ((sub @ X208 @ (push @ X211 @ X210)))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (? [X315 : term] : (((X313 @ id @ X315 @ id)) != ((X312 @ X315))) | ($true = ((X312 @ (lam @ X311)))) | ? [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) != $true) & ($true = ((X312 @ X314)))) | ? [X316 : (subst > term > term)] : (! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true)) & ($true != ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) & ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))))))) & (hoasapnotvar_gthm = $true) & ((axvarcons = $true) <=> ! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224)) & (hoasapinj1_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X497 : term] : (((sub @ X497 @ id)) != X497) | ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (? [X510 : term] : (((X500 @ id @ X510 @ id)) != ((X499 @ X510))) | ? [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) != $true) & ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) & ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id))))) | (((X499 @ (lam @ X498))) = $true) | ? [X515 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) & (((X499 @ X515)) = $true)) | ? [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) & (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) != $true)) | ? [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) != $true) & (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true))))) & ((hoasinduction_lem3 = $true) <=> ! [X525 : (subst > term > subst > $o),X524 : term] : (? [X539 : term] : ((((X525 @ id @ X539 @ id)) = $true) & ($true != ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) | ($true = ((X525 @ id @ (lam @ X524) @ id))) | ? [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) & ($true != ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ? [X530 : (subst > term > term)] : (! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id)))) & (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) != $true) & ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ? [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) & ($true != ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))))) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) <=> (shinj = $true)) & ! [X522 : d_term,X523 : d_term] : ((X522 = X523) | (((d2term @ X523)) != ((d2term @ X522)))) & (((! [X382 : (term > $o),X383 : term] : (? [X387 : term,X386 : term] : (($true = ((X382 @ X386))) & (((X382 @ X387)) = $true) & (((X382 @ (ap @ X386 @ X387))) != $true)) | ($true = ((X382 @ X383))) | ? [X384 : term] : (! [X385 : term] : ((((X382 @ X385)) != $true) | ($true = ((X382 @ (sub @ X384 @ (push @ X385 @ id)))))) & (((X382 @ (lam @ X384))) != $true)) | ? [X388 : term] : (($true = ((var @ X388))) & ($true != ((X382 @ X388))))) | ? [X376 : term,X375 : (term > $o),X374 : subst] : (! [X380 : term] : (($true = ((X375 @ (lam @ X380)))) | ? [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) != $true) & ($true = ((X375 @ X381))))) & ($true != ((X375 @ (sub @ X376 @ X374)))) & ! [X377 : term,X378 : term] : ((((X375 @ (ap @ X378 @ X377))) = $true) | ($true != ((X375 @ X377))) | (((X375 @ X378)) != $true)) & ! [X379 : term] : ((((var @ X379)) != $true) | (((X375 @ (sub @ X379 @ X374))) = $true)))) | ? [X373 : term] : (((sub @ X373 @ id)) != X373)) <=> (induction2_lthm = $true)) & (hoaslamnotvar = $true) & (lamnotvar = $true) & (((! [X330 : term,X331 : (subst > term > subst > $o)] : (? [X332 : (subst > term > term)] : (! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id)))) & (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) != $true) & ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ? [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) != $true) & ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))) | ? [X322 : (subst > term > subst > $o),X323 : term] : (($true != ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) & ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) & ! [X325 : (subst > term > term)] : (? [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) != ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ? [X326 : term] : (($true != ((X322 @ id @ (X325 @ id @ X326) @ id))) & ($true = ((X322 @ id @ X326 @ id)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))))) | ? [X321 : term] : (((sub @ X321 @ id)) != X321)) <=> (hoasinduction_lem3a_lthm = $true)) & (pushprop_lem3v2 = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem1 = $true) & (! [X308 : (subst > term > subst > $o)] : ? [X309 : (term > $o)] : ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id))) <=> (hoasinduction_lem0 = $true)) & (! [X191 : term,X190 : (subst > term > subst > $o)] : (? [X193 : (subst > term > term)] : (! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) & (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) != $true) & ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195)))) | (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ? [X192 : term] : (($true != ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) & (((X190 @ id @ X192 @ id)) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) <=> (axidr = $true)) & ((hoasinduction = $true) <=> ! [X344 : term,X343 : (subst > term > subst > $o)] : (? [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) & ($true != ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) | ($true = ((X343 @ id @ X344 @ id))) | ? [X345 : term,X346 : term] : (($true != ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) & ($true = ((X343 @ id @ X346 @ id))) & ($true = ((X343 @ id @ X345 @ id)))) | ? [X347 : (subst > term > term)] : ((((X343 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X351 : term] : (($true = ((X343 @ id @ (X347 @ id @ X351) @ id))) | ($true != ((X343 @ id @ X351 @ id)))) & ! [X350 : term,X349 : subst,X348 : subst] : (((sub @ (X347 @ X348 @ X350) @ X349)) = ((X347 @ (comp @ X348 @ X349) @ (sub @ X350 @ X349))))) | ? [X352 : term] : (($true = ((var @ (sub @ X352 @ id)))) & ($true != ((X343 @ id @ X352 @ id)))) | ? [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true != ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) & ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355)))))))),
% 5.43/1.21 inference(ennf_transformation,[],[f9])).
% 5.43/1.21 thf(f11,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) <=> (termmset = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) | ? [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) != X202) | ? [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) != X200))) & ! [X235 : d_term] : (d_one = X235) & (! [X361 : term,X362 : (subst > term > subst > $o)] : (? [X372 : term] : (($true = ((X362 @ id @ X372 @ id))) & ($true != ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) | ? [X363 : (subst > term > term),X364 : term] : (! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) & ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) & ($true != ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) & ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368)))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lthm = $true) <=> (? [X79 : term,X78 : (subst > term > subst > $o)] : (($true != ((X78 @ id @ (lam @ X79) @ id))) & ! [X82 : subst,X81 : subst,X83 : subst,X80 : term] : (($true != ((X78 @ (comp @ X81 @ X83) @ (sub @ X80 @ X83) @ X82))) | ($true = ((X78 @ X81 @ X80 @ (comp @ X83 @ X82))))) & ! [X87 : subst,X85 : subst,X86 : subst,X84 : term] : (($true != ((X78 @ X87 @ X84 @ (comp @ X85 @ X86)))) | ($true = ((X78 @ (comp @ X87 @ X85) @ (sub @ X84 @ X85) @ X86)))) & ! [X88 : term] : (($true = ((X78 @ id @ (sub @ X79 @ (push @ X88 @ id)) @ id))) | ($true != ((X78 @ id @ X88 @ id)))) & ! [X89 : (subst > term > term)] : (($true = ((X78 @ id @ (lam @ (X89 @ sh @ one)) @ id))) | ? [X92 : subst,X93 : term,X91 : subst] : (((X89 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X89 @ X92 @ X93) @ X91))) | ? [X90 : term] : ((((X78 @ id @ (X89 @ id @ X90) @ id)) != $true) & ($true = ((X78 @ id @ X90 @ id)))))) | ! [X95 : term,X94 : (subst > term > subst > $o)] : (? [X100 : term] : ((((X94 @ id @ X100 @ id)) != $true) & ($true = ((var @ (sub @ X100 @ id))))) | ? [X105 : term,X106 : term] : ((((X94 @ id @ X106 @ id)) = $true) & ($true != ((X94 @ id @ (ap @ (sub @ X106 @ id) @ X105) @ id))) & (((X94 @ id @ X105 @ id)) = $true)) | ($true = ((X94 @ id @ X95 @ id))) | ? [X101 : subst,X102 : term,X104 : subst,X103 : subst] : ((((X94 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104) @ X101)) = $true) & ($true != ((X94 @ X103 @ X102 @ (comp @ X104 @ X101))))) | ? [X98 : subst,X97 : subst,X99 : subst,X96 : term] : (($true != ((X94 @ (comp @ X99 @ X97) @ (sub @ X96 @ X97) @ X98))) & ($true = ((X94 @ X99 @ X96 @ (comp @ X97 @ X98))))) | ? [X107 : (subst > term > term)] : (($true != ((X94 @ id @ (lam @ (X107 @ sh @ one)) @ id))) & ! [X110 : subst,X111 : subst,X109 : term] : (((X107 @ (comp @ X111 @ X110) @ (sub @ X109 @ X110))) = ((sub @ (X107 @ X111 @ X109) @ X110))) & ! [X108 : term] : (($true = ((X94 @ id @ (X107 @ id @ X108) @ id))) | (((X94 @ id @ X108 @ id)) != $true)))) | ? [X59 : (term > $o),X58 : term] : (($true != ((X59 @ X58))) & ! [X61 : term,X62 : term] : ((((X59 @ X61)) != $true) | ($true = ((X59 @ (ap @ X61 @ X62)))) | ($true != ((X59 @ X62)))) & ! [X60 : term] : (($true = ((X59 @ X60))) | ($true != ((var @ X60)))) & ! [X63 : term] : (? [X64 : term] : (($true = ((X59 @ X64))) & ($true != ((X59 @ (sub @ X63 @ (push @ X64 @ id)))))) | (((X59 @ (lam @ X63))) = $true))) | ? [X65 : term,X67 : (subst > term > subst > $o),X66 : term] : (! [X68 : subst,X70 : term,X69 : subst,X71 : subst] : (($true = ((X67 @ X71 @ X70 @ (comp @ X68 @ X69)))) | ($true != ((X67 @ (comp @ X71 @ X68) @ (sub @ X70 @ X68) @ X69)))) & ! [X74 : term,X75 : subst,X73 : subst,X72 : subst] : (($true = ((X67 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72) @ X75))) | ($true != ((X67 @ X73 @ X74 @ (comp @ X72 @ X75))))) & (((X67 @ id @ (ap @ X65 @ X66) @ id)) != $true) & ($true = ((X67 @ id @ X66 @ id))) & ! [X76 : term,X77 : term] : (($true != ((X67 @ id @ X77 @ id))) | (((X67 @ id @ (ap @ (sub @ X76 @ id) @ X77) @ id)) = $true) | ($true != ((X67 @ id @ X76 @ id)))) & (((X67 @ id @ X65 @ id)) = $true)))) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) <=> (shinj = $true)) & (! [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true = ((X148 @ one))) | ? [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) != ((X148 @ X151))) | (((X150 @ X149)) != $true)) <=> (pushprop_lem1v2 = $true)) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & (! [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true = ((X18 @ (lam @ X20)))) | ? [X31 : term] : (($true != ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) & ($true = ((X18 @ X31)))) | ? [X21 : term] : (((X19 @ id @ X21 @ id)) != ((X18 @ X21))) | ? [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true != ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) & ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ? [X26 : (subst > term > term)] : (($true != ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) & ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) & ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) != $true) & ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))) <=> (hoasinduction_lem3v2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X294 : subst,X296 : (term > $o),X295 : term] : ? [X297 : (term > $o)] : ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & ((axvarcons = $true) <=> ! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224)) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) <=> (axscons = $true)) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1_lthm = $true) <=> (? [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 != X288) & (((ap @ X288 @ X287)) = ((ap @ X286 @ X289)))) | ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292)) | ? [X285 : term] : (((sub @ X285 @ id)) != X285))) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((laminj = $true) <=> ! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420))))) & ((induction2lem = $true) <=> ! [X466 : (term > $o),X467 : subst,X465 : term] : (? [X470 : term] : ((((X466 @ (lam @ X470))) != $true) & ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) | ? [X469 : term,X468 : term] : (($true = ((X466 @ X469))) & (((X466 @ (ap @ X469 @ X468))) != $true) & ($true = ((X466 @ X468)))) | ? [X472 : term] : (($true != ((X466 @ (sub @ X472 @ X467)))) & (((var @ X472)) = $true)) | ($true = ((X466 @ (sub @ X465 @ X467)))))) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) <=> (hoasapinj1 = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X516 : (term > $o),X517 : term] : (? [X518 : term] : (($true != ((X516 @ X518))) & ($true = ((var @ X518)))) | ($true = ((X516 @ X517))) | ? [X519 : term,X520 : term] : (($true != ((X516 @ (ap @ X519 @ X520)))) & ($true = ((X516 @ X519))) & ($true = ((X516 @ X520)))) | ? [X521 : term] : ((((X516 @ (lam @ X521))) != $true) & ($true = ((X516 @ X521))))) <=> (induction = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 != X39) & (((ap @ X38 @ X37)) = ((ap @ X36 @ X39)))) | ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)))) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) <=> ! [X525 : (subst > term > subst > $o),X524 : term] : (? [X539 : term] : ((((X525 @ id @ X539 @ id)) = $true) & ($true != ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) | ($true = ((X525 @ id @ (lam @ X524) @ id))) | ? [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) & ($true != ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ? [X530 : (subst > term > term)] : (! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id)))) & (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) != $true) & ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ? [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) & ($true != ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))))) & (hoasinduction_lem2_lthm = $true) & ((induction2_lthm = $true) <=> (! [X382 : (term > $o),X383 : term] : (? [X387 : term,X386 : term] : (($true = ((X382 @ X386))) & (((X382 @ X387)) = $true) & (((X382 @ (ap @ X386 @ X387))) != $true)) | ($true = ((X382 @ X383))) | ? [X384 : term] : (! [X385 : term] : ((((X382 @ X385)) != $true) | ($true = ((X382 @ (sub @ X384 @ (push @ X385 @ id)))))) & (((X382 @ (lam @ X384))) != $true)) | ? [X388 : term] : (($true = ((var @ X388))) & ($true != ((X382 @ X388))))) | ? [X376 : term,X375 : (term > $o),X374 : subst] : (! [X380 : term] : (($true = ((X375 @ (lam @ X380)))) | ? [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) != $true) & ($true = ((X375 @ X381))))) & ($true != ((X375 @ (sub @ X376 @ X374)))) & ! [X377 : term,X378 : term] : ((((X375 @ (ap @ X378 @ X377))) = $true) | ($true != ((X375 @ X377))) | (((X375 @ X378)) != $true)) & ! [X379 : term] : ((((var @ X379)) != $true) | (((X375 @ (sub @ X379 @ X374))) = $true))) | ? [X373 : term] : (((sub @ X373 @ id)) != X373))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3b = $true) <=> ! [X418 : term] : ? [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) = ((X419 @ sh @ one)))) & (pushprop_lthm = $true) & ! [X522 : d_term,X523 : d_term] : ((X522 = X523) | (((d2term @ X523)) != ((d2term @ X522)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X497 : term] : (((sub @ X497 @ id)) != X497) | ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (? [X510 : term] : (((X500 @ id @ X510 @ id)) != ((X499 @ X510))) | ? [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) != $true) & ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) & ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id))))) | (((X499 @ (lam @ X498))) = $true) | ? [X515 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) & (((X499 @ X515)) = $true)) | ? [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) & (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) != $true)) | ? [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) != $true) & (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true))))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) <=> (substmonoid = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X115 : (term > $o),X116 : term] : (! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) & ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ? [X121 : term] : (($true != ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) & (((X115 @ X121)) = $true))) & ($true != ((X115 @ X116))) & ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117))))) | ? [X112 : (subst > term > subst > $o)] : ! [X113 : (term > $o)] : ? [X114 : term] : (((X113 @ X114)) != ((X112 @ id @ X114 @ id))) | ? [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true != ((X124 @ (lam @ X123)))) & ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) & ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) & ! [X127 : (subst > term > term)] : (? [X131 : term] : (($true != ((X125 @ id @ (X127 @ id @ X131) @ id))) & ($true = ((X125 @ id @ X131 @ id)))) | (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) != ((sub @ (X127 @ X129 @ X130) @ X128))))) | ? [X122 : term] : (((sub @ X122 @ id)) != X122) | ! [X134 : term,X133 : (subst > term > subst > $o)] : (? [X135 : (subst > term > term)] : (! [X137 : subst,X139 : subst,X138 : term] : (((sub @ (X135 @ X139 @ X138) @ X137)) = ((X135 @ (comp @ X139 @ X137) @ (sub @ X138 @ X137)))) & ! [X136 : term] : (($true = ((X133 @ id @ (X135 @ id @ X136) @ id))) | ($true != ((X133 @ id @ X136 @ id)))) & (((X133 @ id @ (lam @ (X135 @ sh @ one)) @ id)) != $true)) | ($true = ((X133 @ id @ X134 @ id))) | ? [X140 : term,X141 : term] : (($true = ((X133 @ id @ X140 @ id))) & (((X133 @ id @ (ap @ (sub @ X141 @ id) @ X140) @ id)) != $true) & (((X133 @ id @ X141 @ id)) = $true))))) & ! [X15 : d_subst,X14 : d_subst] : ((X14 = X15) | (((d2subst @ X15)) != ((d2subst @ X14)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (? [X315 : term] : (((X313 @ id @ X315 @ id)) != ((X312 @ X315))) | ($true = ((X312 @ (lam @ X311)))) | ? [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) != $true) & ($true = ((X312 @ X314)))) | ? [X316 : (subst > term > term)] : (! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true)) & ($true != ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) & ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))))))) & ((? [X157 : term,X156 : term] : ((((lam @ X156)) = ((lam @ X157))) & (X156 != X157)) | ! [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (? [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) != ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ? [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) != ((sub @ (X159 @ X162 @ X164) @ X163)))) | ? [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) != X154) | ? [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) != X152)) <=> (hoaslaminj_lthm = $true)) & ((apinj1 = $true) <=> ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390))))) & ((hoasinduction_lthm_3 = $true) <=> (? [X422 : (subst > term > subst > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X423 @ X424)) != ((X422 @ id @ X424 @ id))) | ! [X444 : term,X443 : (subst > term > subst > $o)] : (? [X456 : term] : ((((var @ (sub @ X456 @ id))) = $true) & ($true != ((X443 @ id @ X456 @ id)))) | ? [X445 : term,X446 : term] : ((((X443 @ id @ X446 @ id)) = $true) & (((X443 @ id @ (ap @ (sub @ X446 @ id) @ X445) @ id)) != $true) & (((X443 @ id @ X445 @ id)) = $true)) | ($true = ((X443 @ id @ X444 @ id))) | ? [X447 : (subst > term > term)] : (! [X451 : term] : ((((X443 @ id @ X451 @ id)) != $true) | ($true = ((X443 @ id @ (X447 @ id @ X451) @ id)))) & ! [X449 : subst,X448 : subst,X450 : term] : (((sub @ (X447 @ X448 @ X450) @ X449)) = ((X447 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449)))) & (((X443 @ id @ (lam @ (X447 @ sh @ one)) @ id)) != $true)) | ? [X457 : term,X460 : subst,X459 : subst,X458 : subst] : (($true = ((X443 @ (comp @ X460 @ X459) @ (sub @ X457 @ X459) @ X458))) & (((X443 @ X460 @ X457 @ (comp @ X459 @ X458))) != $true)) | ? [X452 : subst,X453 : term,X455 : subst,X454 : subst] : (($true = ((X443 @ X455 @ X453 @ (comp @ X454 @ X452)))) & (((X443 @ (comp @ X455 @ X454) @ (sub @ X453 @ X454) @ X452)) != $true))) | ? [X432 : term] : (((sub @ X432 @ id)) != X432) | ? [X426 : term,X425 : (term > $o)] : (! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ? [X431 : term] : ((((X425 @ X431)) = $true) & (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) != $true))) & ($true != ((X425 @ X426))) & ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) & ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true))) | ? [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ? [X439 : term] : (($true != ((X435 @ id @ (X438 @ id @ X439) @ id))) & ($true = ((X435 @ id @ X439 @ id)))) | ? [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) != ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) & ($true != ((X433 @ (lam @ X434)))) & ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) & ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))))) & (hoasinduction_lem3v2_gthm = $true) & (! [X191 : term,X190 : (subst > term > subst > $o)] : (? [X193 : (subst > term > term)] : (! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) & (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) != $true) & ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195)))) | (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ? [X192 : term] : (($true != ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) & (((X190 @ id @ X192 @ id)) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((? [X394 : (subst > term > subst > $o),X395 : term] : (($true != ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) & ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true)) & ! [X397 : (subst > term > term)] : (? [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X397 @ X401 @ X400) @ X399))) | ? [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) != $true) & ($true = ((X394 @ id @ X398 @ id)))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393) | ! [X402 : term,X403 : (subst > term > subst > $o)] : (? [X417 : term] : (($true != ((X403 @ id @ (sub @ X402 @ (push @ X417 @ id)) @ id))) & ($true = ((X403 @ id @ X417 @ id)))) | ($true = ((X403 @ id @ (lam @ X402) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X403 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X416 : term] : (($true != ((X403 @ id @ X416 @ id))) | ($true = ((X403 @ id @ (X412 @ id @ X416) @ id)))) & ! [X413 : subst,X414 : term,X415 : subst] : (((X412 @ (comp @ X415 @ X413) @ (sub @ X414 @ X413))) = ((sub @ (X412 @ X415 @ X414) @ X413)))) | ? [X406 : subst,X405 : term,X404 : subst,X407 : subst] : (($true != ((X403 @ (comp @ X407 @ X404) @ (sub @ X405 @ X404) @ X406))) & ($true = ((X403 @ X407 @ X405 @ (comp @ X404 @ X406))))) | ? [X410 : subst,X409 : subst,X408 : subst,X411 : term] : ((((X403 @ (comp @ X409 @ X410) @ (sub @ X411 @ X410) @ X408)) = $true) & ($true != ((X403 @ X409 @ X411 @ (comp @ X410 @ X408))))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (? [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) != ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | ? [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) != ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) <=> (hoaslaminj = $true)) & (! [X51 : term] : ? [X52 : (subst > term > term)] : ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) <=> (axvarid = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X44 : term] : ? [X45 : (subst > term > term)] : (((X45 @ sh @ one)) = ((sub @ X44 @ (push @ one @ sh))))) & (! [X300 : term] : ? [X301 : (subst > term > term)] : ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotvar = $true) & (pushprop = $true) & ((axshiftcons = $true) <=> ! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461)) & (substmonoid_gthm = $true) & (! [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true = ((X238 @ (ap @ X239 @ X237)))) | ($true != ((X238 @ X239))) | ? [X240 : term] : (((X236 @ id @ X240 @ id)) != ((X238 @ X240))) | ? [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) != $true) & ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ? [X250 : term,X249 : term] : (($true = ((X236 @ id @ X250 @ id))) & ($true = ((X236 @ id @ X249 @ id))) & ($true != ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) | ($true != ((X238 @ X237))) | ? [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) & ($true != ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))) <=> (hoasinduction_lem2v2 = $true)) & (axvarshift = $true) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & ((substmonoid_lthm = $true) <=> (? [X340 : subst] : (((comp @ X340 @ id)) != X340) | ? [X339 : subst] : (((comp @ id @ X339)) != X339) | (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341)))) & ((! [X252 : term] : (((sub @ X252 @ id)) = X252) | ? [X251 : term] : (((sub @ X251 @ id)) != X251)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X208 : term] : ! [X209 : (subst > term > term)] : ? [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) != ((sub @ X208 @ (push @ X211 @ X210)))) | ! [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (? [X216 : (subst > term > term)] : (! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219))) & (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true) & ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id))))) | ($true = ((X214 @ (lam @ X213)))) | ? [X222 : term] : (($true != ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) & ($true = ((X214 @ X222)))) | ? [X221 : term] : (((X214 @ X221)) != ((X215 @ id @ X221 @ id)))) | ? [X212 : term] : (((sub @ X212 @ id)) != X212))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (hoasapnotvar_lthm = $true) & ((? [X321 : term] : (((sub @ X321 @ id)) != X321) | ! [X330 : term,X331 : (subst > term > subst > $o)] : (? [X332 : (subst > term > term)] : (! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id)))) & (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) != $true) & ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ? [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) != $true) & ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))) | ? [X322 : (subst > term > subst > $o),X323 : term] : (($true != ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) & ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) & ! [X325 : (subst > term > term)] : (? [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) != ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ? [X326 : term] : (($true != ((X322 @ id @ (X325 @ id @ X326) @ id))) & ($true = ((X322 @ id @ X326 @ id)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X198 : d_subst] : (d_id = X198) & (! [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ? [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) != ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X183 : term,X182 : (subst > term > subst > $o)] : (($true = ((X182 @ id @ (lam @ X183) @ id))) | ? [X185 : (subst > term > term)] : (! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) & (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188)))) | ? [X184 : term] : (($true = ((X182 @ id @ X184 @ id))) & ($true != ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (apnotvar = $true) & (induction2lem_gthm = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) <=> (apinj2 = $true)) & (axassoc = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X474 : (subst > term > subst > $o),X475 : term] : (? [X482 : term,X481 : term] : (($true = ((X474 @ id @ X482 @ id))) & ($true != ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) & ($true = ((X474 @ id @ X481 @ id)))) | ? [X476 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) & ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) & ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479)))) | ($true = ((X474 @ id @ X475 @ id))))) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) <=> (axidr = $true)) & ((induction2 = $true) <=> ! [X483 : term,X484 : (term > $o)] : (? [X485 : term] : (($true != ((X484 @ (lam @ X485)))) & ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) | ? [X487 : term] : (($true = ((var @ X487))) & (((X484 @ X487)) != $true)) | ? [X488 : term,X489 : term] : (($true = ((X484 @ X488))) & ($true != ((X484 @ (ap @ X488 @ X489)))) & (((X484 @ X489)) = $true)) | (((X484 @ X483)) = $true))) & (pushprop_lem3v2 = $true) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) <=> (hoasapinj2 = $true)) & (ulamvar1 != $true) & (lamnotap != $true) & (! [X308 : (subst > term > subst > $o)] : ? [X309 : (term > $o)] : ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & ((? [X266 : subst,X267 : term] : (((sub @ one @ (push @ X267 @ X266))) != X267) | ! [X278 : term,X279 : (term > $o),X277 : subst] : ((((X279 @ (sub @ X278 @ X277))) = $true) | ? [X281 : term] : ((((X279 @ (lam @ X281))) != $true) & ! [X282 : term] : ((((X279 @ X282)) != $true) | ($true = ((X279 @ (sub @ X281 @ (push @ X282 @ id))))))) | ? [X283 : term,X284 : term] : (($true = ((X279 @ X284))) & ($true != ((X279 @ (ap @ X284 @ X283)))) & ($true = ((X279 @ X283)))) | ? [X280 : term] : (($true = ((var @ X280))) & (((X279 @ (sub @ X280 @ X277))) != $true))) | ? [X272 : (term > $o),X271 : term] : (! [X276 : term] : (($true = ((X272 @ (lam @ X276)))) | (((X272 @ X276)) != $true)) & (((X272 @ X271)) != $true) & ! [X274 : term,X275 : term] : (($true != ((X272 @ X274))) | ($true = ((X272 @ (ap @ X275 @ X274)))) | ($true != ((X272 @ X275)))) & ! [X273 : term] : ((((X272 @ X273)) = $true) | ($true != ((var @ X273))))) | ? [X269 : subst,X268 : term] : (((comp @ sh @ (push @ X268 @ X269))) != X269) | ? [X270 : subst] : (((comp @ X270 @ id)) != X270)) <=> (induction2lem_lthm = $true)) & ((hoasinduction = $true) <=> ! [X344 : term,X343 : (subst > term > subst > $o)] : (? [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) & ($true != ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) | ($true = ((X343 @ id @ X344 @ id))) | ? [X345 : term,X346 : term] : (($true != ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) & ($true = ((X343 @ id @ X346 @ id))) & ($true = ((X343 @ id @ X345 @ id)))) | ? [X347 : (subst > term > term)] : ((((X343 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X351 : term] : (($true = ((X343 @ id @ (X347 @ id @ X351) @ id))) | ($true != ((X343 @ id @ X351 @ id)))) & ! [X350 : term,X349 : subst,X348 : subst] : (((sub @ (X347 @ X348 @ X350) @ X349)) = ((X347 @ (comp @ X348 @ X349) @ (sub @ X350 @ X349))))) | ? [X352 : term] : (($true = ((var @ (sub @ X352 @ id)))) & ($true != ((X343 @ id @ X352 @ id)))) | ? [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true != ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) & ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355))))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & ((pushprop_lem1 = $true) <=> ! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X47 : subst,X48 : (term > $o),X46 : term] : ? [X49 : (term > $o)] : ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) <=> (axidl = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) <=> ! [X170 : (subst > term > subst > $o),X171 : term] : (? [X173 : (subst > term > term)] : (! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) & (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | ? [X172 : term] : (($true != ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) & (((X170 @ id @ X172 @ id)) = $true)) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) != $true) | ? [X496 : term] : (((X495 @ X496)) != ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one)))) | ? [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) != X490))) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ($true != ((X253 @ id @ X254 @ id))) | ? [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) & (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) != $true)) | ? [X265 : term,X264 : term] : (($true = ((X253 @ id @ X265 @ id))) & ($true != ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) & ($true = ((X253 @ id @ X264 @ id)))) | ? [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) & (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) != $true))) <=> (hoasinduction_lem2 = $true))),
% 5.43/1.21 inference(flattening,[],[f10])).
% 5.43/1.21 thf(f12,plain,(
% 5.43/1.21 ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : ((((! [X12 : term,X13 : term] : ((($true = ((X1 @ (ap @ X13 @ X12)))) | (((X1 @ X12)) != $true)) | (((X1 @ X13)) != $true)) | (((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true)) | ? [X10 : term,X11 : term] : ((($true != ((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id))) & (((X0 @ id @ X10 @ id)) = $true)) & ($true = ((X0 @ id @ X11 @ id))))) | ? [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8)) = $true) & ($true != ((X0 @ X7 @ X9 @ (comp @ X6 @ X8)))))) | ? [X2 : subst,X5 : subst,X4 : term,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X5 @ X2))) = $true) & ($true != ((X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2))))) <~> (hoasinduction_lem2v2 = $true)),
% 5.43/1.21 inference(ennf_transformation,[],[f7])).
% 5.43/1.21 thf(f13,plain,(
% 5.43/1.21 (hoasinduction_lem2v2 = $true) <~> ! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : ((((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true) | ? [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8)) = $true) & ($true != ((X0 @ X7 @ X9 @ (comp @ X6 @ X8))))) | ? [X10 : term,X11 : term] : (($true = ((X0 @ id @ X11 @ id))) & (((X0 @ id @ X10 @ id)) = $true) & ($true != ((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)))) | ? [X2 : subst,X5 : subst,X4 : term,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X5 @ X2))) = $true) & ($true != ((X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)))) | ! [X12 : term,X13 : term] : (($true = ((X1 @ (ap @ X13 @ X12)))) | (((X1 @ X13)) != $true) | (((X1 @ X12)) != $true)))),
% 5.43/1.21 inference(flattening,[],[f12])).
% 5.43/1.21 thf(f14,definition,(
% 5.43/1.21 ! [X343 : (subst > term > subst > $o)] : (($true = ((sP0 @ X343))) <=> ? [X347 : (subst > term > term)] : ((((X343 @ id @ (lam @ (X347 @ sh @ one)) @ id)) != $true) & ! [X351 : term] : (($true = ((X343 @ id @ (X347 @ id @ X351) @ id))) | ($true != ((X343 @ id @ X351 @ id)))) & ! [X350 : term,X349 : subst,X348 : subst] : (((sub @ (X347 @ X348 @ X350) @ X349)) = ((X347 @ (comp @ X348 @ X349) @ (sub @ X350 @ X349))))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f15,definition,(
% 5.43/1.21 ($true = sP1) <=> (? [X266 : subst,X267 : term] : (((sub @ one @ (push @ X267 @ X266))) != X267) | ! [X278 : term,X279 : (term > $o),X277 : subst] : ((((X279 @ (sub @ X278 @ X277))) = $true) | ? [X281 : term] : ((((X279 @ (lam @ X281))) != $true) & ! [X282 : term] : ((((X279 @ X282)) != $true) | ($true = ((X279 @ (sub @ X281 @ (push @ X282 @ id))))))) | ? [X283 : term,X284 : term] : (($true = ((X279 @ X284))) & ($true != ((X279 @ (ap @ X284 @ X283)))) & ($true = ((X279 @ X283)))) | ? [X280 : term] : (($true = ((var @ X280))) & (((X279 @ (sub @ X280 @ X277))) != $true))) | ? [X272 : (term > $o),X271 : term] : (! [X276 : term] : (($true = ((X272 @ (lam @ X276)))) | (((X272 @ X276)) != $true)) & (((X272 @ X271)) != $true) & ! [X274 : term,X275 : term] : (($true != ((X272 @ X274))) | ($true = ((X272 @ (ap @ X275 @ X274)))) | ($true != ((X272 @ X275)))) & ! [X273 : term] : ((((X272 @ X273)) = $true) | ($true != ((var @ X273))))) | ? [X269 : subst,X268 : term] : (((comp @ sh @ (push @ X268 @ X269))) != X269) | ? [X270 : subst] : (((comp @ X270 @ id)) != X270))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f16,definition,(
% 5.43/1.21 ($true = sP2) <=> ! [X402 : term,X403 : (subst > term > subst > $o)] : (? [X417 : term] : (($true != ((X403 @ id @ (sub @ X402 @ (push @ X417 @ id)) @ id))) & ($true = ((X403 @ id @ X417 @ id)))) | ($true = ((X403 @ id @ (lam @ X402) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X403 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X416 : term] : (($true != ((X403 @ id @ X416 @ id))) | ($true = ((X403 @ id @ (X412 @ id @ X416) @ id)))) & ! [X413 : subst,X414 : term,X415 : subst] : (((X412 @ (comp @ X415 @ X413) @ (sub @ X414 @ X413))) = ((sub @ (X412 @ X415 @ X414) @ X413)))) | ? [X406 : subst,X405 : term,X404 : subst,X407 : subst] : (($true != ((X403 @ (comp @ X407 @ X404) @ (sub @ X405 @ X404) @ X406))) & ($true = ((X403 @ X407 @ X405 @ (comp @ X404 @ X406))))) | ? [X410 : subst,X409 : subst,X408 : subst,X411 : term] : ((((X403 @ (comp @ X409 @ X410) @ (sub @ X411 @ X410) @ X408)) = $true) & ($true != ((X403 @ X409 @ X411 @ (comp @ X410 @ X408))))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f17,definition,(
% 5.43/1.21 ! [X443 : (subst > term > subst > $o)] : (($true = ((sP3 @ X443))) <=> ? [X447 : (subst > term > term)] : (! [X451 : term] : ((((X443 @ id @ X451 @ id)) != $true) | ($true = ((X443 @ id @ (X447 @ id @ X451) @ id)))) & ! [X449 : subst,X448 : subst,X450 : term] : (((sub @ (X447 @ X448 @ X450) @ X449)) = ((X447 @ (comp @ X448 @ X449) @ (sub @ X450 @ X449)))) & (((X443 @ id @ (lam @ (X447 @ sh @ one)) @ id)) != $true)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f18,definition,(
% 5.43/1.21 ($true = sP4) <=> ! [X444 : term,X443 : (subst > term > subst > $o)] : (? [X456 : term] : ((((var @ (sub @ X456 @ id))) = $true) & ($true != ((X443 @ id @ X456 @ id)))) | ? [X445 : term,X446 : term] : ((((X443 @ id @ X446 @ id)) = $true) & (((X443 @ id @ (ap @ (sub @ X446 @ id) @ X445) @ id)) != $true) & (((X443 @ id @ X445 @ id)) = $true)) | ($true = ((X443 @ id @ X444 @ id))) | ($true = ((sP3 @ X443))) | ? [X457 : term,X460 : subst,X459 : subst,X458 : subst] : (($true = ((X443 @ (comp @ X460 @ X459) @ (sub @ X457 @ X459) @ X458))) & (((X443 @ X460 @ X457 @ (comp @ X459 @ X458))) != $true)) | ? [X452 : subst,X453 : term,X455 : subst,X454 : subst] : (($true = ((X443 @ X455 @ X453 @ (comp @ X454 @ X452)))) & (((X443 @ (comp @ X455 @ X454) @ (sub @ X453 @ X454) @ X452)) != $true)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f19,definition,(
% 5.43/1.21 ($true = sP5) <=> ! [X134 : term,X133 : (subst > term > subst > $o)] : (? [X135 : (subst > term > term)] : (! [X137 : subst,X139 : subst,X138 : term] : (((sub @ (X135 @ X139 @ X138) @ X137)) = ((X135 @ (comp @ X139 @ X137) @ (sub @ X138 @ X137)))) & ! [X136 : term] : (($true = ((X133 @ id @ (X135 @ id @ X136) @ id))) | ($true != ((X133 @ id @ X136 @ id)))) & (((X133 @ id @ (lam @ (X135 @ sh @ one)) @ id)) != $true)) | ($true = ((X133 @ id @ X134 @ id))) | ? [X140 : term,X141 : term] : (($true = ((X133 @ id @ X140 @ id))) & (((X133 @ id @ (ap @ (sub @ X141 @ id) @ X140) @ id)) != $true) & (((X133 @ id @ X141 @ id)) = $true)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f20,definition,(
% 5.43/1.21 ($true = sP6) <=> (! [X382 : (term > $o),X383 : term] : (? [X387 : term,X386 : term] : (($true = ((X382 @ X386))) & (((X382 @ X387)) = $true) & (((X382 @ (ap @ X386 @ X387))) != $true)) | ($true = ((X382 @ X383))) | ? [X384 : term] : (! [X385 : term] : ((((X382 @ X385)) != $true) | ($true = ((X382 @ (sub @ X384 @ (push @ X385 @ id)))))) & (((X382 @ (lam @ X384))) != $true)) | ? [X388 : term] : (($true = ((var @ X388))) & ($true != ((X382 @ X388))))) | ? [X376 : term,X375 : (term > $o),X374 : subst] : (! [X380 : term] : (($true = ((X375 @ (lam @ X380)))) | ? [X381 : term] : ((((X375 @ (sub @ X380 @ (push @ X381 @ id)))) != $true) & ($true = ((X375 @ X381))))) & ($true != ((X375 @ (sub @ X376 @ X374)))) & ! [X377 : term,X378 : term] : ((((X375 @ (ap @ X378 @ X377))) = $true) | ($true != ((X375 @ X377))) | (((X375 @ X378)) != $true)) & ! [X379 : term] : ((((var @ X379)) != $true) | (((X375 @ (sub @ X379 @ X374))) = $true))) | ? [X373 : term] : (((sub @ X373 @ id)) != X373))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f21,definition,(
% 5.43/1.21 ! [X94 : (subst > term > subst > $o)] : (($true = ((sP7 @ X94))) <=> ? [X107 : (subst > term > term)] : (($true != ((X94 @ id @ (lam @ (X107 @ sh @ one)) @ id))) & ! [X110 : subst,X111 : subst,X109 : term] : (((X107 @ (comp @ X111 @ X110) @ (sub @ X109 @ X110))) = ((sub @ (X107 @ X111 @ X109) @ X110))) & ! [X108 : term] : (($true = ((X94 @ id @ (X107 @ id @ X108) @ id))) | (((X94 @ id @ X108 @ id)) != $true))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f22,definition,(
% 5.43/1.21 ($true = sP8) <=> ! [X95 : term,X94 : (subst > term > subst > $o)] : (? [X100 : term] : ((((X94 @ id @ X100 @ id)) != $true) & ($true = ((var @ (sub @ X100 @ id))))) | ? [X105 : term,X106 : term] : ((((X94 @ id @ X106 @ id)) = $true) & ($true != ((X94 @ id @ (ap @ (sub @ X106 @ id) @ X105) @ id))) & (((X94 @ id @ X105 @ id)) = $true)) | ($true = ((X94 @ id @ X95 @ id))) | ? [X101 : subst,X102 : term,X104 : subst,X103 : subst] : ((((X94 @ (comp @ X103 @ X104) @ (sub @ X102 @ X104) @ X101)) = $true) & ($true != ((X94 @ X103 @ X102 @ (comp @ X104 @ X101))))) | ? [X98 : subst,X97 : subst,X99 : subst,X96 : term] : (($true != ((X94 @ (comp @ X99 @ X97) @ (sub @ X96 @ X97) @ X98))) & ($true = ((X94 @ X99 @ X96 @ (comp @ X97 @ X98))))) | ($true = ((sP7 @ X94))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f23,definition,(
% 5.43/1.21 (sP9 = $true) <=> ? [X65 : term,X67 : (subst > term > subst > $o),X66 : term] : (! [X68 : subst,X70 : term,X69 : subst,X71 : subst] : (($true = ((X67 @ X71 @ X70 @ (comp @ X68 @ X69)))) | ($true != ((X67 @ (comp @ X71 @ X68) @ (sub @ X70 @ X68) @ X69)))) & ! [X74 : term,X75 : subst,X73 : subst,X72 : subst] : (($true = ((X67 @ (comp @ X73 @ X72) @ (sub @ X74 @ X72) @ X75))) | ($true != ((X67 @ X73 @ X74 @ (comp @ X72 @ X75))))) & (((X67 @ id @ (ap @ X65 @ X66) @ id)) != $true) & ($true = ((X67 @ id @ X66 @ id))) & ! [X76 : term,X77 : term] : (($true != ((X67 @ id @ X77 @ id))) | (((X67 @ id @ (ap @ (sub @ X76 @ id) @ X77) @ id)) = $true) | ($true != ((X67 @ id @ X76 @ id)))) & (((X67 @ id @ X65 @ id)) = $true))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f24,definition,(
% 5.43/1.21 ($true = sP10) <=> (? [X79 : term,X78 : (subst > term > subst > $o)] : (($true != ((X78 @ id @ (lam @ X79) @ id))) & ! [X82 : subst,X81 : subst,X83 : subst,X80 : term] : (($true != ((X78 @ (comp @ X81 @ X83) @ (sub @ X80 @ X83) @ X82))) | ($true = ((X78 @ X81 @ X80 @ (comp @ X83 @ X82))))) & ! [X87 : subst,X85 : subst,X86 : subst,X84 : term] : (($true != ((X78 @ X87 @ X84 @ (comp @ X85 @ X86)))) | ($true = ((X78 @ (comp @ X87 @ X85) @ (sub @ X84 @ X85) @ X86)))) & ! [X88 : term] : (($true = ((X78 @ id @ (sub @ X79 @ (push @ X88 @ id)) @ id))) | ($true != ((X78 @ id @ X88 @ id)))) & ! [X89 : (subst > term > term)] : (($true = ((X78 @ id @ (lam @ (X89 @ sh @ one)) @ id))) | ? [X92 : subst,X93 : term,X91 : subst] : (((X89 @ (comp @ X92 @ X91) @ (sub @ X93 @ X91))) != ((sub @ (X89 @ X92 @ X93) @ X91))) | ? [X90 : term] : ((((X78 @ id @ (X89 @ id @ X90) @ id)) != $true) & ($true = ((X78 @ id @ X90 @ id)))))) | ($true = sP8) | ? [X59 : (term > $o),X58 : term] : (($true != ((X59 @ X58))) & ! [X61 : term,X62 : term] : ((((X59 @ X61)) != $true) | ($true = ((X59 @ (ap @ X61 @ X62)))) | ($true != ((X59 @ X62)))) & ! [X60 : term] : (($true = ((X59 @ X60))) | ($true != ((var @ X60)))) & ! [X63 : term] : (? [X64 : term] : (($true = ((X59 @ X64))) & ($true != ((X59 @ (sub @ X63 @ (push @ X64 @ id)))))) | (((X59 @ (lam @ X63))) = $true))) | (sP9 = $true))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 5.43/1.21 thf(f25,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) <=> (termmset = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) | ? [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) != X202) | ? [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) != X200))) & ! [X235 : d_term] : (d_one = X235) & (! [X361 : term,X362 : (subst > term > subst > $o)] : (? [X372 : term] : (($true = ((X362 @ id @ X372 @ id))) & ($true != ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) | ? [X363 : (subst > term > term),X364 : term] : (! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) & ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) & ($true != ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) & ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368)))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aaa = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lthm = $true) <=> ($true = sP10)) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) <=> (shinj = $true)) & (! [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true = ((X148 @ one))) | ? [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) != ((X148 @ X151))) | (((X150 @ X149)) != $true)) <=> (pushprop_lem1v2 = $true)) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & (! [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true = ((X18 @ (lam @ X20)))) | ? [X31 : term] : (($true != ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) & ($true = ((X18 @ X31)))) | ? [X21 : term] : (((X19 @ id @ X21 @ id)) != ((X18 @ X21))) | ? [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true != ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) & ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ? [X26 : (subst > term > term)] : (($true != ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) & ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) & ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) != $true) & ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))) <=> (hoasinduction_lem3v2 = $true)) & ((pushprop_lem0 = $true) <=> ! [X294 : subst,X296 : (term > $o),X295 : term] : ? [X297 : (term > $o)] : ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & ((axvarcons = $true) <=> ! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224)) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) <=> (axscons = $true)) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1_lthm = $true) <=> (? [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 != X288) & (((ap @ X288 @ X287)) = ((ap @ X286 @ X289)))) | ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292)) | ? [X285 : term] : (((sub @ X285 @ id)) != X285))) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((laminj = $true) <=> ! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420))))) & ((induction2lem = $true) <=> ! [X466 : (term > $o),X467 : subst,X465 : term] : (? [X470 : term] : ((((X466 @ (lam @ X470))) != $true) & ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) | ? [X469 : term,X468 : term] : (($true = ((X466 @ X469))) & (((X466 @ (ap @ X469 @ X468))) != $true) & ($true = ((X466 @ X468)))) | ? [X472 : term] : (($true != ((X466 @ (sub @ X472 @ X467)))) & (((var @ X472)) = $true)) | ($true = ((X466 @ (sub @ X465 @ X467)))))) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) <=> (hoasapinj1 = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X516 : (term > $o),X517 : term] : (? [X518 : term] : (($true != ((X516 @ X518))) & ($true = ((var @ X518)))) | ($true = ((X516 @ X517))) | ? [X519 : term,X520 : term] : (($true != ((X516 @ (ap @ X519 @ X520)))) & ($true = ((X516 @ X519))) & ($true = ((X516 @ X520)))) | ? [X521 : term] : ((((X516 @ (lam @ X521))) != $true) & ($true = ((X516 @ X521))))) <=> (induction = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (? [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 != X39) & (((ap @ X38 @ X37)) = ((ap @ X36 @ X39)))) | ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)))) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) <=> ! [X525 : (subst > term > subst > $o),X524 : term] : (? [X539 : term] : ((((X525 @ id @ X539 @ id)) = $true) & ($true != ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) | ($true = ((X525 @ id @ (lam @ X524) @ id))) | ? [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) & ($true != ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ? [X530 : (subst > term > term)] : (! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id)))) & (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) != $true) & ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ? [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) & ($true != ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))))) & (hoasinduction_lem2_lthm = $true) & ((induction2_lthm = $true) <=> ($true = sP6)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3b = $true) <=> ! [X418 : term] : ? [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) = ((X419 @ sh @ one)))) & (pushprop_lthm = $true) & ! [X522 : d_term,X523 : d_term] : ((X522 = X523) | (((d2term @ X523)) != ((d2term @ X522)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X497 : term] : (((sub @ X497 @ id)) != X497) | ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (? [X510 : term] : (((X500 @ id @ X510 @ id)) != ((X499 @ X510))) | ? [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) != $true) & ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) & ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id))))) | (((X499 @ (lam @ X498))) = $true) | ? [X515 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) & (((X499 @ X515)) = $true)) | ? [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) & (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) != $true)) | ? [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) != $true) & (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true))))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) <=> (substmonoid = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X115 : (term > $o),X116 : term] : (! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) & ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ? [X121 : term] : (($true != ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) & (((X115 @ X121)) = $true))) & ($true != ((X115 @ X116))) & ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117))))) | ? [X112 : (subst > term > subst > $o)] : ! [X113 : (term > $o)] : ? [X114 : term] : (((X113 @ X114)) != ((X112 @ id @ X114 @ id))) | ? [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true != ((X124 @ (lam @ X123)))) & ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) & ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) & ! [X127 : (subst > term > term)] : (? [X131 : term] : (($true != ((X125 @ id @ (X127 @ id @ X131) @ id))) & ($true = ((X125 @ id @ X131 @ id)))) | (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) != ((sub @ (X127 @ X129 @ X130) @ X128))))) | ? [X122 : term] : (((sub @ X122 @ id)) != X122) | ($true = sP5))) & ! [X15 : d_subst,X14 : d_subst] : ((X14 = X15) | (((d2subst @ X15)) != ((d2subst @ X14)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (? [X315 : term] : (((X313 @ id @ X315 @ id)) != ((X312 @ X315))) | ($true = ((X312 @ (lam @ X311)))) | ? [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) != $true) & ($true = ((X312 @ X314)))) | ? [X316 : (subst > term > term)] : (! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true)) & ($true != ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) & ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))))))) & ((? [X157 : term,X156 : term] : ((((lam @ X156)) = ((lam @ X157))) & (X156 != X157)) | ! [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (? [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) != ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ? [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) != ((sub @ (X159 @ X162 @ X164) @ X163)))) | ? [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) != X154) | ? [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) != X152)) <=> (hoaslaminj_lthm = $true)) & ((apinj1 = $true) <=> ! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390))))) & ((hoasinduction_lthm_3 = $true) <=> (? [X422 : (subst > term > subst > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X423 @ X424)) != ((X422 @ id @ X424 @ id))) | ($true = sP4) | ? [X432 : term] : (((sub @ X432 @ id)) != X432) | ? [X426 : term,X425 : (term > $o)] : (! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ? [X431 : term] : ((((X425 @ X431)) = $true) & (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) != $true))) & ($true != ((X425 @ X426))) & ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) & ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true))) | ? [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ? [X439 : term] : (($true != ((X435 @ id @ (X438 @ id @ X439) @ id))) & ($true = ((X435 @ id @ X439 @ id)))) | ? [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) != ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) & ($true != ((X433 @ (lam @ X434)))) & ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) & ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))))) & (hoasinduction_lem3v2_gthm = $true) & (! [X191 : term,X190 : (subst > term > subst > $o)] : (? [X193 : (subst > term > term)] : (! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) & (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) != $true) & ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195)))) | (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ? [X192 : term] : (($true != ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) & (((X190 @ id @ X192 @ id)) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((? [X394 : (subst > term > subst > $o),X395 : term] : (($true != ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) & ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true)) & ! [X397 : (subst > term > term)] : (? [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X397 @ X401 @ X400) @ X399))) | ? [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) != $true) & ($true = ((X394 @ id @ X398 @ id)))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393) | ($true = sP2)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (? [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) != ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | ? [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) != ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) <=> (hoaslaminj = $true)) & (! [X51 : term] : ? [X52 : (subst > term > term)] : ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) <=> (axvarid = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X44 : term] : ? [X45 : (subst > term > term)] : (((X45 @ sh @ one)) = ((sub @ X44 @ (push @ one @ sh))))) & (! [X300 : term] : ? [X301 : (subst > term > term)] : ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) <=> (hoasinduction_lem3v2_f = $true)) & (lamnotvar = $true) & (pushprop = $true) & ((axshiftcons = $true) <=> ! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461)) & (substmonoid_gthm = $true) & (! [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true = ((X238 @ (ap @ X239 @ X237)))) | ($true != ((X238 @ X239))) | ? [X240 : term] : (((X236 @ id @ X240 @ id)) != ((X238 @ X240))) | ? [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) != $true) & ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ? [X250 : term,X249 : term] : (($true = ((X236 @ id @ X250 @ id))) & ($true = ((X236 @ id @ X249 @ id))) & ($true != ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) | ($true != ((X238 @ X237))) | ? [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) & ($true != ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))) <=> (hoasinduction_lem2v2 = $true)) & (axvarshift = $true) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & ((substmonoid_lthm = $true) <=> (? [X340 : subst] : (((comp @ X340 @ id)) != X340) | ? [X339 : subst] : (((comp @ id @ X339)) != X339) | (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341)))) & ((! [X252 : term] : (((sub @ X252 @ id)) = X252) | ? [X251 : term] : (((sub @ X251 @ id)) != X251)) <=> (termmset_lthm = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id)))) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (? [X208 : term] : ! [X209 : (subst > term > term)] : ? [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) != ((sub @ X208 @ (push @ X211 @ X210)))) | ! [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (? [X216 : (subst > term > term)] : (! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219))) & (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true) & ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id))))) | ($true = ((X214 @ (lam @ X213)))) | ? [X222 : term] : (($true != ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) & ($true = ((X214 @ X222)))) | ? [X221 : term] : (((X214 @ X221)) != ((X215 @ id @ X221 @ id)))) | ? [X212 : term] : (((sub @ X212 @ id)) != X212))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (hoasapnotvar_lthm = $true) & ((? [X321 : term] : (((sub @ X321 @ id)) != X321) | ! [X330 : term,X331 : (subst > term > subst > $o)] : (? [X332 : (subst > term > term)] : (! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id)))) & (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) != $true) & ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ? [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) != $true) & ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))) | ? [X322 : (subst > term > subst > $o),X323 : term] : (($true != ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) & ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) & ! [X325 : (subst > term > term)] : (? [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) != ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ? [X326 : term] : (($true != ((X322 @ id @ (X325 @ id @ X326) @ id))) & ($true = ((X322 @ id @ X326 @ id)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X198 : d_subst] : (d_id = X198) & (! [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ? [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) != ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) <=> (hoaslamnotap = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X183 : term,X182 : (subst > term > subst > $o)] : (($true = ((X182 @ id @ (lam @ X183) @ id))) | ? [X185 : (subst > term > term)] : (! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) & (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188)))) | ? [X184 : term] : (($true = ((X182 @ id @ X184 @ id))) & ($true != ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (apnotvar = $true) & (induction2lem_gthm = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) <=> (apinj2 = $true)) & (axassoc = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X474 : (subst > term > subst > $o),X475 : term] : (? [X482 : term,X481 : term] : (($true = ((X474 @ id @ X482 @ id))) & ($true != ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) & ($true = ((X474 @ id @ X481 @ id)))) | ? [X476 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) & ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) & ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479)))) | ($true = ((X474 @ id @ X475 @ id))))) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) <=> (axidr = $true)) & ((induction2 = $true) <=> ! [X483 : term,X484 : (term > $o)] : (? [X485 : term] : (($true != ((X484 @ (lam @ X485)))) & ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) | ? [X487 : term] : (($true = ((var @ X487))) & (((X484 @ X487)) != $true)) | ? [X488 : term,X489 : term] : (($true = ((X484 @ X488))) & ($true != ((X484 @ (ap @ X488 @ X489)))) & (((X484 @ X489)) = $true)) | (((X484 @ X483)) = $true))) & (pushprop_lem3v2 = $true) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) <=> (hoasapinj2 = $true)) & (ulamvar1 != $true) & (lamnotap != $true) & (! [X308 : (subst > term > subst > $o)] : ? [X309 : (term > $o)] : ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & (($true = sP1) <=> (induction2lem_lthm = $true)) & ((hoasinduction = $true) <=> ! [X344 : term,X343 : (subst > term > subst > $o)] : (? [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) & ($true != ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) | ($true = ((X343 @ id @ X344 @ id))) | ? [X345 : term,X346 : term] : (($true != ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) & ($true = ((X343 @ id @ X346 @ id))) & ($true = ((X343 @ id @ X345 @ id)))) | ($true = ((sP0 @ X343))) | ? [X352 : term] : (($true = ((var @ (sub @ X352 @ id)))) & ($true != ((X343 @ id @ X352 @ id)))) | ? [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true != ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) & ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355))))))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & ((pushprop_lem1 = $true) <=> ! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X47 : subst,X48 : (term > $o),X46 : term] : ? [X49 : (term > $o)] : ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) <=> (axidl = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) <=> ! [X170 : (subst > term > subst > $o),X171 : term] : (? [X173 : (subst > term > term)] : (! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) & (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | ? [X172 : term] : (($true != ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) & (((X170 @ id @ X172 @ id)) = $true)) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) != $true) | ? [X496 : term] : (((X495 @ X496)) != ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one)))) | ? [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) != X490))) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ($true != ((X253 @ id @ X254 @ id))) | ? [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) & (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) != $true)) | ? [X265 : term,X264 : term] : (($true = ((X253 @ id @ X265 @ id))) & ($true != ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) & ($true = ((X253 @ id @ X264 @ id)))) | ? [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) & (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) != $true))) <=> (hoasinduction_lem2 = $true))),
% 5.43/1.21 inference(definition_folding,[],[f11,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 5.43/1.21 thf(f62,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & ((! [X299 : term] : (((sub @ X299 @ id)) = X299) | (termmset != $true)) & ((termmset = $true) | ? [X299 : term] : (((sub @ X299 @ id)) != X299))) & (((pushprop_lem1_lthm = $true) | (? [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true = ((X206 @ X207))) & ($true != ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) & ! [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) = X202) & ! [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) = X200))) & ((! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) | ? [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) != X202) | ? [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) != X200)) | (pushprop_lem1_lthm != $true))) & ! [X235 : d_term] : (d_one = X235) & ((! [X361 : term,X362 : (subst > term > subst > $o)] : (? [X372 : term] : (($true = ((X362 @ id @ X372 @ id))) & ($true != ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) | ? [X363 : (subst > term > term),X364 : term] : (! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) & ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) & ($true != ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) & ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368)))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X361 : term,X362 : (subst > term > subst > $o)] : (! [X372 : term] : (($true != ((X362 @ id @ X372 @ id))) | ($true = ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) & ! [X363 : (subst > term > term),X364 : term] : (? [X365 : term] : (($true = ((X362 @ id @ X365 @ id))) & ($true != ((X362 @ id @ (X363 @ id @ X365) @ id)))) | ? [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) != ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) | ($true = ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) | ? [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) != ((sub @ (X363 @ X366 @ X367) @ X368)))) & (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) != $true)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & (((hoasinduction_lthm = $true) | ($true != sP10)) & (($true = sP10) | (hoasinduction_lthm != $true))) & ((! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) | (shinj != $true)) & ((shinj = $true) | ? [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) = ((sub @ X168 @ sh))) & (X168 != X169)))) & ((! [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true = ((X148 @ one))) | ? [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) != ((X148 @ X151))) | (((X150 @ X149)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true != ((X148 @ one))) & ! [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) = ((X148 @ X151))) & (((X150 @ X149)) = $true)))) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & ((! [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true = ((X18 @ (lam @ X20)))) | ? [X31 : term] : (($true != ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) & ($true = ((X18 @ X31)))) | ? [X21 : term] : (((X19 @ id @ X21 @ id)) != ((X18 @ X21))) | ? [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true != ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) & ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ? [X26 : (subst > term > term)] : (($true != ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) & ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) & ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) != $true) & ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true != ((X18 @ (lam @ X20)))) & ! [X31 : term] : (($true = ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) | ($true != ((X18 @ X31)))) & ! [X21 : term] : (((X19 @ id @ X21 @ id)) = ((X18 @ X21))) & ! [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true = ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) | ($true != ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) & ! [X26 : (subst > term > term)] : (($true = ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) | ? [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) != ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) | ? [X30 : term] : ((((X19 @ id @ X30 @ id)) = $true) & (((X19 @ id @ (X26 @ id @ X30) @ id)) != $true))) & ! [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) = $true) | ($true != ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))))) & (((pushprop_lem0 = $true) | ? [X294 : subst,X296 : (term > $o),X295 : term] : ! [X297 : (term > $o)] : ? [X298 : term] : (((X297 @ X298)) != ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & (! [X294 : subst,X296 : (term > $o),X295 : term] : ? [X297 : (term > $o)] : ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294))))) | (pushprop_lem0 != $true))) & (((axvarcons = $true) | ? [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) != X224)) & (! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224) | (axvarcons != $true))) & ((! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) | (axscons != $true)) & ((axscons = $true) | ? [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) != X146))) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasapinj1_lthm = $true) | (! [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 = X288) | (((ap @ X288 @ X287)) != ((ap @ X286 @ X289)))) & ? [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) = ((ap @ (sub @ X292 @ id) @ X291))) & (X290 != X292)) & ! [X285 : term] : (((sub @ X285 @ id)) = X285))) & ((? [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 != X288) & (((ap @ X288 @ X287)) = ((ap @ X286 @ X289)))) | ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292)) | ? [X285 : term] : (((sub @ X285 @ id)) != X285)) | (hoasapinj1_lthm != $true))) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((laminj = $true) | ? [X420 : term,X421 : term] : ((X420 != X421) & (((lam @ X421)) = ((lam @ X420))))) & (! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420)))) | (laminj != $true))) & (((induction2lem = $true) | ? [X466 : (term > $o),X467 : subst,X465 : term] : (! [X470 : term] : ((((X466 @ (lam @ X470))) = $true) | ? [X471 : term] : ((((X466 @ X471)) = $true) & ($true != ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) & ! [X469 : term,X468 : term] : (($true != ((X466 @ X469))) | (((X466 @ (ap @ X469 @ X468))) = $true) | ($true != ((X466 @ X468)))) & ! [X472 : term] : (($true = ((X466 @ (sub @ X472 @ X467)))) | (((var @ X472)) != $true)) & ($true != ((X466 @ (sub @ X465 @ X467)))))) & (! [X466 : (term > $o),X467 : subst,X465 : term] : (? [X470 : term] : ((((X466 @ (lam @ X470))) != $true) & ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) | ? [X469 : term,X468 : term] : (($true = ((X466 @ X469))) & (((X466 @ (ap @ X469 @ X468))) != $true) & ($true = ((X466 @ X468)))) | ? [X472 : term] : (($true != ((X466 @ (sub @ X472 @ X467)))) & (((var @ X472)) = $true)) | ($true = ((X466 @ (sub @ X465 @ X467))))) | (induction2lem != $true))) & ((! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 != X307) & (((ap @ (sub @ X306 @ id) @ X304)) = ((ap @ (sub @ X307 @ id) @ X305)))))) & (pushprop_lem3v2_lthm = $true) & ((! [X516 : (term > $o),X517 : term] : (? [X518 : term] : (($true != ((X516 @ X518))) & ($true = ((var @ X518)))) | ($true = ((X516 @ X517))) | ? [X519 : term,X520 : term] : (($true != ((X516 @ (ap @ X519 @ X520)))) & ($true = ((X516 @ X519))) & ($true = ((X516 @ X520)))) | ? [X521 : term] : ((((X516 @ (lam @ X521))) != $true) & ($true = ((X516 @ X521))))) | (induction != $true)) & ((induction = $true) | ? [X516 : (term > $o),X517 : term] : (! [X518 : term] : (($true = ((X516 @ X518))) | ($true != ((var @ X518)))) & ($true != ((X516 @ X517))) & ! [X519 : term,X520 : term] : (($true = ((X516 @ (ap @ X519 @ X520)))) | ($true != ((X516 @ X519))) | ($true != ((X516 @ X520)))) & ! [X521 : term] : ((((X516 @ (lam @ X521))) = $true) | ($true != ((X516 @ X521))))))) & (hoaslamnotvar_gthm = $true) & (((hoasapinj2_lthm = $true) | (! [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 = X39) | (((ap @ X38 @ X37)) != ((ap @ X36 @ X39)))) & ? [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) = ((ap @ (sub @ X41 @ id) @ X43))) & (X42 != X43)))) & ((? [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 != X39) & (((ap @ X38 @ X37)) = ((ap @ X36 @ X39)))) | ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43))) | (hoasapinj2_lthm != $true))) & (one = ((d2term @ d_one))) & (((hoasinduction_lem3 = $true) | ? [X525 : (subst > term > subst > $o),X524 : term] : (! [X539 : term] : ((((X525 @ id @ X539 @ id)) != $true) | ($true = ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) & ($true != ((X525 @ id @ (lam @ X524) @ id))) & ! [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) != $true) | ($true = ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) & ! [X530 : (subst > term > term)] : (? [X531 : term] : (($true = ((X525 @ id @ X531 @ id))) & ($true != ((X525 @ id @ (X530 @ id @ X531) @ id)))) | (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) = $true) | ? [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) != ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) & ! [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true != ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) | ($true = ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))))) & (! [X525 : (subst > term > subst > $o),X524 : term] : (? [X539 : term] : ((((X525 @ id @ X539 @ id)) = $true) & ($true != ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) | ($true = ((X525 @ id @ (lam @ X524) @ id))) | ? [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) & ($true != ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ? [X530 : (subst > term > term)] : (! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id)))) & (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) != $true) & ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ? [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) & ($true != ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527))))) | (hoasinduction_lem3 != $true))) & (hoasinduction_lem2_lthm = $true) & (((induction2_lthm = $true) | ($true != sP6)) & (($true = sP6) | (induction2_lthm != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasinduction_lem3b = $true) | ? [X418 : term] : ! [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) != ((X419 @ sh @ one)))) & (! [X418 : term] : ? [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) = ((X419 @ sh @ one))) | (hoasinduction_lem3b != $true))) & (pushprop_lthm = $true) & ! [X522 : d_term,X523 : d_term] : ((X522 = X523) | (((d2term @ X523)) != ((d2term @ X522)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (((hoasinduction_lem3v2_lthm = $true) | (! [X497 : term] : (((sub @ X497 @ id)) = X497) & ? [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (! [X510 : term] : (((X500 @ id @ X510 @ id)) = ((X499 @ X510))) & ! [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true) | ? [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) != ((sub @ (X505 @ X508 @ X509) @ X507))) | ? [X506 : term] : (($true = ((X500 @ id @ X506 @ id))) & ($true != ((X500 @ id @ (X505 @ id @ X506) @ id))))) & (((X499 @ (lam @ X498))) != $true) & ! [X515 : term] : (($true = ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) | (((X499 @ X515)) != $true)) & ! [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true != ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) | (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) = $true)) & ! [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) = $true) | (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) != $true))))) & ((? [X497 : term] : (((sub @ X497 @ id)) != X497) | ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (? [X510 : term] : (((X500 @ id @ X510 @ id)) != ((X499 @ X510))) | ? [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) != $true) & ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) & ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id))))) | (((X499 @ (lam @ X498))) = $true) | ? [X515 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) & (((X499 @ X515)) = $true)) | ? [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) & (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) != $true)) | ? [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) != $true) & (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true)))) | (hoasinduction_lem3v2_lthm != $true))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X56 : subst] : (((comp @ X56 @ id)) != X56) | ? [X55 : subst] : (((comp @ id @ X55)) != X55)))) & (((hoasinduction_no_psi_cond_lthm = $true) | (! [X115 : (term > $o),X116 : term] : (? [X119 : term,X118 : term] : (($true != ((X115 @ (ap @ X118 @ X119)))) & ($true = ((X115 @ X119))) & (((X115 @ X118)) = $true)) | ? [X120 : term] : (($true != ((X115 @ (lam @ X120)))) & ! [X121 : term] : (($true = ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) | (((X115 @ X121)) != $true))) | ($true = ((X115 @ X116))) | ? [X117 : term] : (($true = ((var @ X117))) & ($true != ((X115 @ X117))))) & ! [X112 : (subst > term > subst > $o)] : ? [X113 : (term > $o)] : ! [X114 : term] : (((X113 @ X114)) = ((X112 @ id @ X114 @ id))) & ! [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true = ((X124 @ (lam @ X123)))) | ? [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) != $true) & ($true = ((X124 @ X126)))) | ? [X132 : term] : (((X124 @ X132)) != ((X125 @ id @ X132 @ id))) | ? [X127 : (subst > term > term)] : (! [X131 : term] : (($true = ((X125 @ id @ (X127 @ id @ X131) @ id))) | ($true != ((X125 @ id @ X131 @ id)))) & (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) != $true) & ! [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) = ((sub @ (X127 @ X129 @ X130) @ X128))))) & ! [X122 : term] : (((sub @ X122 @ id)) = X122) & ($true != sP5))) & ((? [X115 : (term > $o),X116 : term] : (! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) & ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ? [X121 : term] : (($true != ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) & (((X115 @ X121)) = $true))) & ($true != ((X115 @ X116))) & ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117))))) | ? [X112 : (subst > term > subst > $o)] : ! [X113 : (term > $o)] : ? [X114 : term] : (((X113 @ X114)) != ((X112 @ id @ X114 @ id))) | ? [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true != ((X124 @ (lam @ X123)))) & ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) & ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) & ! [X127 : (subst > term > term)] : (? [X131 : term] : (($true != ((X125 @ id @ (X127 @ id @ X131) @ id))) & ($true = ((X125 @ id @ X131 @ id)))) | (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) != ((sub @ (X127 @ X129 @ X130) @ X128))))) | ? [X122 : term] : (((sub @ X122 @ id)) != X122) | ($true = sP5)) | (hoasinduction_no_psi_cond_lthm != $true))) & ! [X15 : d_subst,X14 : d_subst] : ((X14 = X15) | (((d2subst @ X15)) != ((d2subst @ X14)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & (((hoasinduction_lem3v2a = $true) | ? [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (! [X315 : term] : (((X313 @ id @ X315 @ id)) = ((X312 @ X315))) & ($true != ((X312 @ (lam @ X311)))) & ! [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) = $true) | ($true != ((X312 @ X314)))) & ! [X316 : (subst > term > term)] : (? [X317 : term] : (($true != ((X313 @ id @ (X316 @ id @ X317) @ id))) & (((X313 @ id @ X317 @ id)) = $true)) | ($true = ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) | ? [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) != ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))))))) & (! [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (? [X315 : term] : (((X313 @ id @ X315 @ id)) != ((X312 @ X315))) | ($true = ((X312 @ (lam @ X311)))) | ? [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) != $true) & ($true = ((X312 @ X314)))) | ? [X316 : (subst > term > term)] : (! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true)) & ($true != ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) & ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320)))))) | (hoasinduction_lem3v2a != $true))) & (((? [X157 : term,X156 : term] : ((((lam @ X156)) = ((lam @ X157))) & (X156 != X157)) | ! [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (? [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) != ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ? [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) != ((sub @ (X159 @ X162 @ X164) @ X163)))) | ? [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) != X154) | ? [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) != X152)) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (! [X157 : term,X156 : term] : ((((lam @ X156)) != ((lam @ X157))) | (X156 = X157)) & ? [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (! [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) = ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) & (((lam @ (X159 @ sh @ one))) = ((lam @ (X161 @ sh @ one)))) & (((X161 @ X160 @ X158)) != ((X159 @ X160 @ X158))) & ! [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) = ((sub @ (X159 @ X162 @ X164) @ X163)))) & ! [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) = X154) & ! [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) = X152)))) & (((apinj1 = $true) | ? [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 != X391) & (((ap @ X391 @ X392)) = ((ap @ X389 @ X390))))) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390)))) | (apinj1 != $true))) & (((hoasinduction_lthm_3 = $true) | (! [X422 : (subst > term > subst > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X423 @ X424)) = ((X422 @ id @ X424 @ id))) & ($true != sP4) & ! [X432 : term] : (((sub @ X432 @ id)) = X432) & ! [X426 : term,X425 : (term > $o)] : (? [X430 : term] : (($true != ((X425 @ (lam @ X430)))) & ! [X431 : term] : ((((X425 @ X431)) != $true) | (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) = $true))) | ($true = ((X425 @ X426))) | ? [X429 : term] : ((((var @ X429)) = $true) & ($true != ((X425 @ X429)))) | ? [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) != $true) & ($true = ((X425 @ X428))) & (((X425 @ X427)) = $true))) & ! [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (? [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) != $true) & ! [X439 : term] : (($true = ((X435 @ id @ (X438 @ id @ X439) @ id))) | ($true != ((X435 @ id @ X439 @ id)))) & ! [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) = ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) | ($true = ((X433 @ (lam @ X434)))) | ? [X436 : term] : (((X433 @ X436)) != ((X435 @ id @ X436 @ id))) | ? [X437 : term] : (($true = ((X433 @ X437))) & ($true != ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))))) & ((? [X422 : (subst > term > subst > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X423 @ X424)) != ((X422 @ id @ X424 @ id))) | ($true = sP4) | ? [X432 : term] : (((sub @ X432 @ id)) != X432) | ? [X426 : term,X425 : (term > $o)] : (! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ? [X431 : term] : ((((X425 @ X431)) = $true) & (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) != $true))) & ($true != ((X425 @ X426))) & ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) & ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true))) | ? [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ? [X439 : term] : (($true != ((X435 @ id @ (X438 @ id @ X439) @ id))) & ($true = ((X435 @ id @ X439 @ id)))) | ? [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) != ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) & ($true != ((X433 @ (lam @ X434)))) & ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) & ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id)))))))) | (hoasinduction_lthm_3 != $true))) & (hoasinduction_lem3v2_gthm = $true) & ((! [X191 : term,X190 : (subst > term > subst > $o)] : (? [X193 : (subst > term > term)] : (! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) & (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) != $true) & ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195)))) | (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ? [X192 : term] : (($true != ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) & (((X190 @ id @ X192 @ id)) = $true))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X191 : term,X190 : (subst > term > subst > $o)] : (! [X193 : (subst > term > term)] : (? [X197 : term] : ((((X190 @ id @ X197 @ id)) = $true) & ($true != ((X190 @ id @ (X193 @ id @ X197) @ id)))) | (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) = $true) | ? [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) != ((sub @ (X193 @ X194 @ X196) @ X195)))) & (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) != $true) & ! [X192 : term] : (($true = ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) | (((X190 @ id @ X192 @ id)) != $true))))) & (((? [X394 : (subst > term > subst > $o),X395 : term] : (($true != ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) & ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true)) & ! [X397 : (subst > term > term)] : (? [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X397 @ X401 @ X400) @ X399))) | ? [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) != $true) & ($true = ((X394 @ id @ X398 @ id)))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393) | ($true = sP2)) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X394 : (subst > term > subst > $o),X395 : term] : (($true = ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) | ? [X396 : term] : (($true != ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) & (((X394 @ id @ X396 @ id)) = $true)) | ? [X397 : (subst > term > term)] : (! [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X397 @ X401 @ X400) @ X399))) & ! [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) = $true) | ($true != ((X394 @ id @ X398 @ id)))) & (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) != $true))) & ! [X393 : term] : (((sub @ X393 @ id)) = X393) & ($true != sP2)))) & ((! [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (? [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) != ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | ? [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) != ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (! [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) = ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) & (((lam @ (X225 @ sh @ one))) = ((lam @ (X226 @ sh @ one)))) & ! [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) = ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) & (((X226 @ X227 @ X228)) != ((X225 @ X227 @ X228)))))) & ((! [X51 : term] : ? [X52 : (subst > term > term)] : ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) != ((X52 @ X53 @ X54))))) & ((! [X338 : term] : (((sub @ X338 @ id)) = X338) | (axvarid != $true)) & ((axvarid = $true) | ? [X338 : term] : (((sub @ X338 @ id)) != X338))) & (((hoasinduction_lem3b_lthm = $true) | ? [X44 : term] : ! [X45 : (subst > term > term)] : (((X45 @ sh @ one)) != ((sub @ X44 @ (push @ one @ sh))))) & (! [X44 : term] : ? [X45 : (subst > term > term)] : (((X45 @ sh @ one)) = ((sub @ X44 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true))) & ((! [X300 : term] : ? [X301 : (subst > term > term)] : ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X300 : term] : ! [X301 : (subst > term > term)] : ? [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) != ((X301 @ X303 @ X302))))) & (lamnotvar = $true) & (pushprop = $true) & (((axshiftcons = $true) | ? [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) != X461)) & (! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461) | (axshiftcons != $true))) & (substmonoid_gthm = $true) & ((! [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true = ((X238 @ (ap @ X239 @ X237)))) | ($true != ((X238 @ X239))) | ? [X240 : term] : (((X236 @ id @ X240 @ id)) != ((X238 @ X240))) | ? [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) != $true) & ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ? [X250 : term,X249 : term] : (($true = ((X236 @ id @ X250 @ id))) & ($true = ((X236 @ id @ X249 @ id))) & ($true != ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) | ($true != ((X238 @ X237))) | ? [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) & ($true != ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ? [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true != ((X238 @ (ap @ X239 @ X237)))) & ($true = ((X238 @ X239))) & ! [X240 : term] : (((X236 @ id @ X240 @ id)) = ((X238 @ X240))) & ! [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) = $true) | ($true != ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) & ! [X250 : term,X249 : term] : (($true != ((X236 @ id @ X250 @ id))) | ($true != ((X236 @ id @ X249 @ id))) | ($true = ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) & ($true = ((X238 @ X237))) & ! [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) != $true) | ($true = ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))))) & (axvarshift = $true) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & (((substmonoid_lthm = $true) | (! [X340 : subst] : (((comp @ X340 @ id)) = X340) & ! [X339 : subst] : (((comp @ id @ X339)) = X339) & (? [X342 : subst] : (((comp @ X342 @ id)) != X342) | ? [X341 : subst] : (((comp @ id @ X341)) != X341)))) & ((? [X340 : subst] : (((comp @ X340 @ id)) != X340) | ? [X339 : subst] : (((comp @ id @ X339)) != X339) | (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341))) | (substmonoid_lthm != $true))) & (((! [X252 : term] : (((sub @ X252 @ id)) = X252) | ? [X251 : term] : (((sub @ X251 @ id)) != X251)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X252 : term] : (((sub @ X252 @ id)) != X252) & ! [X251 : term] : (((sub @ X251 @ id)) = X251)))) & (((hoasinduction_lem0_lthm = $true) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id)))) & (! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) | (hoasinduction_lem0_lthm != $true))) & (hoasinduction_gthm = $true) & (((hoasinduction_lem3v2a_lthm = $true) | (! [X208 : term] : ? [X209 : (subst > term > term)] : ! [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) = ((sub @ X208 @ (push @ X211 @ X210)))) & ? [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (! [X216 : (subst > term > term)] : (? [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) != ((sub @ (X216 @ X220 @ X218) @ X219))) | (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ? [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) != $true) & ($true = ((X215 @ id @ X217 @ id))))) & ($true != ((X214 @ (lam @ X213)))) & ! [X222 : term] : (($true = ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) | ($true != ((X214 @ X222)))) & ! [X221 : term] : (((X214 @ X221)) = ((X215 @ id @ X221 @ id)))) & ! [X212 : term] : (((sub @ X212 @ id)) = X212))) & ((? [X208 : term] : ! [X209 : (subst > term > term)] : ? [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) != ((sub @ X208 @ (push @ X211 @ X210)))) | ! [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (? [X216 : (subst > term > term)] : (! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219))) & (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true) & ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id))))) | ($true = ((X214 @ (lam @ X213)))) | ? [X222 : term] : (($true != ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) & ($true = ((X214 @ X222)))) | ? [X221 : term] : (((X214 @ X221)) != ((X215 @ id @ X221 @ id)))) | ? [X212 : term] : (((sub @ X212 @ id)) != X212)) | (hoasinduction_lem3v2a_lthm != $true))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (hoasapnotvar_lthm = $true) & (((? [X321 : term] : (((sub @ X321 @ id)) != X321) | ! [X330 : term,X331 : (subst > term > subst > $o)] : (? [X332 : (subst > term > term)] : (! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id)))) & (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) != $true) & ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ? [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) != $true) & ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))) | ? [X322 : (subst > term > subst > $o),X323 : term] : (($true != ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) & ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) & ! [X325 : (subst > term > term)] : (? [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) != ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ? [X326 : term] : (($true != ((X322 @ id @ (X325 @ id @ X326) @ id))) & ($true = ((X322 @ id @ X326 @ id)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))))) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X321 : term] : (((sub @ X321 @ id)) = X321) & ? [X330 : term,X331 : (subst > term > subst > $o)] : (! [X332 : (subst > term > term)] : (? [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) != $true) & ($true = ((X331 @ id @ X333 @ id)))) | (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) = $true) | ? [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) != ((sub @ (X332 @ X336 @ X335) @ X334)))) & ! [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) = $true) | ($true != ((X331 @ id @ X337 @ id)))) & ($true != ((X331 @ id @ (lam @ X330) @ id)))) & ! [X322 : (subst > term > subst > $o),X323 : term] : (($true = ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) | ? [X324 : term] : (($true = ((X322 @ id @ X324 @ id))) & ($true != ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) | ? [X325 : (subst > term > term)] : (! [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) = ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) & ! [X326 : term] : (($true = ((X322 @ id @ (X325 @ id @ X326) @ id))) | ($true != ((X322 @ id @ X326 @ id)))) & ($true != ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id)))))))) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X198 : d_subst] : (d_id = X198) & ((! [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ? [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) != ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) = ((ap @ (sub @ X8 @ id) @ X9))) & ! [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X183 : term,X182 : (subst > term > subst > $o)] : (($true = ((X182 @ id @ (lam @ X183) @ id))) | ? [X185 : (subst > term > term)] : (! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) & (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188)))) | ? [X184 : term] : (($true = ((X182 @ id @ X184 @ id))) & ($true != ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X183 : term,X182 : (subst > term > subst > $o)] : (($true != ((X182 @ id @ (lam @ X183) @ id))) & ! [X185 : (subst > term > term)] : (? [X189 : term] : ((((X182 @ id @ X189 @ id)) = $true) & (((X182 @ id @ (X185 @ id @ X189) @ id)) != $true)) | (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true) | ? [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) != ((sub @ (X185 @ X187 @ X186) @ X188)))) & ! [X184 : term] : (($true != ((X182 @ id @ X184 @ id))) | ($true = ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))))) & (apnotvar = $true) & (induction2lem_gthm = $true) & ((! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) = ((ap @ X144 @ X143))) & (X142 != X143)))) & (axassoc = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X474 : (subst > term > subst > $o),X475 : term] : (! [X482 : term,X481 : term] : (($true != ((X474 @ id @ X482 @ id))) | ($true = ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) | ($true != ((X474 @ id @ X481 @ id)))) & ! [X476 : (subst > term > term)] : (($true = ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) | ? [X477 : term] : (($true != ((X474 @ id @ (X476 @ id @ X477) @ id))) & ($true = ((X474 @ id @ X477 @ id)))) | ? [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) != ((sub @ (X476 @ X480 @ X478) @ X479)))) & ($true != ((X474 @ id @ X475 @ id))))) & (! [X474 : (subst > term > subst > $o),X475 : term] : (? [X482 : term,X481 : term] : (($true = ((X474 @ id @ X482 @ id))) & ($true != ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) & ($true = ((X474 @ id @ X481 @ id)))) | ? [X476 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) & ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) & ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479)))) | ($true = ((X474 @ id @ X475 @ id)))) | (hoasinduction_no_psi_cond != $true))) & ((! [X473 : subst] : (((comp @ X473 @ id)) = X473) | (axidr != $true)) & ((axidr = $true) | ? [X473 : subst] : (((comp @ X473 @ id)) != X473))) & (((induction2 = $true) | ? [X483 : term,X484 : (term > $o)] : (! [X485 : term] : (($true = ((X484 @ (lam @ X485)))) | ? [X486 : term] : (($true = ((X484 @ X486))) & ($true != ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) & ! [X487 : term] : (($true != ((var @ X487))) | (((X484 @ X487)) = $true)) & ! [X488 : term,X489 : term] : (($true != ((X484 @ X488))) | ($true = ((X484 @ (ap @ X488 @ X489)))) | (((X484 @ X489)) != $true)) & (((X484 @ X483)) != $true))) & (! [X483 : term,X484 : (term > $o)] : (? [X485 : term] : (($true != ((X484 @ (lam @ X485)))) & ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) | ? [X487 : term] : (($true = ((var @ X487))) & (((X484 @ X487)) != $true)) | ? [X488 : term,X489 : term] : (($true = ((X484 @ X488))) & ($true != ((X484 @ (ap @ X488 @ X489)))) & (((X484 @ X489)) = $true)) | (((X484 @ X483)) = $true)) | (induction2 != $true))) & (pushprop_lem3v2 = $true) & ((! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) = ((ap @ (sub @ X180 @ id) @ X178))) & (X178 != X179)))) & (ulamvar1 != $true) & (lamnotap != $true) & ((! [X308 : (subst > term > subst > $o)] : ? [X309 : (term > $o)] : ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X308 : (subst > term > subst > $o)] : ! [X309 : (term > $o)] : ? [X310 : term] : (((X309 @ X310)) != ((X308 @ id @ X310 @ id))))) & (pushprop_lem1v2_gthm = $true) & ((($true = sP1) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP1))) & (((hoasinduction = $true) | ? [X344 : term,X343 : (subst > term > subst > $o)] : (! [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true != ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) | ($true = ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) & ($true != ((X343 @ id @ X344 @ id))) & ! [X345 : term,X346 : term] : (($true = ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) | ($true != ((X343 @ id @ X346 @ id))) | ($true != ((X343 @ id @ X345 @ id)))) & ($true != ((sP0 @ X343))) & ! [X352 : term] : (($true != ((var @ (sub @ X352 @ id)))) | ($true = ((X343 @ id @ X352 @ id)))) & ! [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true = ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) | ($true != ((X343 @ X353 @ X356 @ (comp @ X354 @ X355))))))) & (! [X344 : term,X343 : (subst > term > subst > $o)] : (? [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) & ($true != ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) | ($true = ((X343 @ id @ X344 @ id))) | ? [X345 : term,X346 : term] : (($true != ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) & ($true = ((X343 @ id @ X346 @ id))) & ($true = ((X343 @ id @ X345 @ id)))) | ($true = ((sP0 @ X343))) | ? [X352 : term] : (($true = ((var @ (sub @ X352 @ id)))) & ($true != ((X343 @ id @ X352 @ id)))) | ? [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true != ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) & ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355)))))) | (hoasinduction != $true))) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & (((pushprop_lem1 = $true) | ? [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) = $true) & ($true != ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4)))))) | (pushprop_lem1 != $true))) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & ((! [X47 : subst,X48 : (term > $o),X46 : term] : ? [X49 : (term > $o)] : ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X47 : subst,X48 : (term > $o),X46 : term] : ! [X49 : (term > $o)] : ? [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) != ((X49 @ X50))))) & (hoasinduction_lem3b_gthm = $true) & ((! [X57 : subst] : (((comp @ id @ X57)) = X57) | (axidl != $true)) & ((axidl = $true) | ? [X57 : subst] : (((comp @ id @ X57)) != X57))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoasinduction_lem3aa = $true) | ? [X170 : (subst > term > subst > $o),X171 : term] : (! [X173 : (subst > term > term)] : (? [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) != ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) | (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : (($true = ((X170 @ id @ X177 @ id))) & (((X170 @ id @ (X173 @ id @ X177) @ id)) != $true))) & ! [X172 : term] : (($true = ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) | (((X170 @ id @ X172 @ id)) != $true)) & (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) != $true))) & (! [X170 : (subst > term > subst > $o),X171 : term] : (? [X173 : (subst > term > term)] : (! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) & (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | ? [X172 : term] : (($true != ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) & (((X170 @ id @ X172 @ id)) = $true)) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true))) & (((pushprop_lem1v2_lthm = $true) | (? [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) = $true) & ! [X496 : term] : (((X495 @ X496)) = ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) & ($true != ((X495 @ one)))) & ! [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) = X490))) & ((! [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) != $true) | ? [X496 : term] : (((X495 @ X496)) != ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one)))) | ? [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) != X490)) | (pushprop_lem1v2_lthm != $true))) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((! [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ($true != ((X253 @ id @ X254 @ id))) | ? [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) & (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) != $true)) | ? [X265 : term,X264 : term] : (($true = ((X253 @ id @ X265 @ id))) & ($true != ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) & ($true = ((X253 @ id @ X264 @ id)))) | ? [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) & (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) != $true))) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ? [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) != $true) & (((X253 @ id @ X255 @ id)) = $true) & ($true = ((X253 @ id @ X254 @ id))) & ! [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true != ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) | (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) = $true)) & ! [X265 : term,X264 : term] : (($true != ((X253 @ id @ X265 @ id))) | ($true = ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) | ($true != ((X253 @ id @ X264 @ id)))) & ! [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) != $true) | (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) = $true)))))),
% 5.43/1.21 inference(nnf_transformation,[],[f25])).
% 5.43/1.21 thf(f63,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & (! [X299 : term] : (((sub @ X299 @ id)) = X299) | (termmset != $true)) & ((termmset = $true) | ? [X299 : term] : (((sub @ X299 @ id)) != X299)) & ((pushprop_lem1_lthm = $true) | (? [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true = ((X206 @ X207))) & ($true != ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) & ! [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) = X202) & ! [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) = X200))) & (! [X207 : term,X205 : subst,X206 : (term > $o),X204 : (term > $o),X203 : term] : (($true != ((X206 @ X207))) | ($true = ((X204 @ (sub @ X207 @ (push @ X203 @ X205)))))) | ? [X201 : term,X202 : subst] : (((comp @ sh @ (push @ X201 @ X202))) != X202) | ? [X199 : subst,X200 : term] : (((sub @ one @ (push @ X200 @ X199))) != X200) | (pushprop_lem1_lthm != $true)) & ! [X235 : d_term] : (d_one = X235) & (! [X361 : term,X362 : (subst > term > subst > $o)] : (? [X372 : term] : (($true = ((X362 @ id @ X372 @ id))) & ($true != ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) | ? [X363 : (subst > term > term),X364 : term] : (! [X365 : term] : (($true != ((X362 @ id @ X365 @ id))) | ($true = ((X362 @ id @ (X363 @ id @ X365) @ id)))) & ! [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) = ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) & ($true != ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) & ! [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) = ((sub @ (X363 @ X366 @ X367) @ X368)))) | (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X361 : term,X362 : (subst > term > subst > $o)] : (! [X372 : term] : (($true != ((X362 @ id @ X372 @ id))) | ($true = ((X362 @ id @ (sub @ X361 @ (push @ X372 @ id)) @ id)))) & ! [X363 : (subst > term > term),X364 : term] : (? [X365 : term] : (($true = ((X362 @ id @ X365 @ id))) & ($true != ((X362 @ id @ (X363 @ id @ X365) @ id)))) | ? [X369 : subst,X371 : term,X370 : subst] : (((sub @ X364 @ (push @ (sub @ X371 @ X370) @ (comp @ X369 @ X370)))) != ((X363 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)))) | ($true = ((X362 @ id @ (lam @ (X363 @ sh @ one)) @ id))) | ? [X367 : term,X368 : subst,X366 : subst] : (((sub @ (sub @ X364 @ (push @ X367 @ X366)) @ X368)) != ((sub @ (X363 @ X366 @ X367) @ X368)))) & (((X362 @ id @ (lam @ (sub @ X361 @ (push @ one @ sh))) @ id)) != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lthm = $true) | ($true != sP10)) & (($true = sP10) | (hoasinduction_lthm != $true)) & (! [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) != ((sub @ X168 @ sh))) | (X168 = X169)) | (shinj != $true)) & ((shinj = $true) | ? [X169 : term,X168 : term] : ((((sub @ X169 @ sh)) = ((sub @ X168 @ sh))) & (X168 != X169))) & (! [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true = ((X148 @ one))) | ? [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) != ((X148 @ X151))) | (((X150 @ X149)) != $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X148 : (term > $o),X147 : subst,X150 : (term > $o),X149 : term] : (($true != ((X148 @ one))) & ! [X151 : term] : (((X150 @ (sub @ X151 @ (push @ X149 @ X147)))) = ((X148 @ X151))) & (((X150 @ X149)) = $true))) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & (! [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true = ((X18 @ (lam @ X20)))) | ? [X31 : term] : (($true != ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) & ($true = ((X18 @ X31)))) | ? [X21 : term] : (((X19 @ id @ X21 @ id)) != ((X18 @ X21))) | ? [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true != ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) & ($true = ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) | ? [X26 : (subst > term > term)] : (($true != ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) & ! [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) = ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) & ! [X30 : term] : ((((X19 @ id @ X30 @ id)) != $true) | (((X19 @ id @ (X26 @ id @ X30) @ id)) = $true))) | ? [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) != $true) & ($true = ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X20 : term,X18 : (term > $o),X19 : (subst > term > subst > $o)] : (($true != ((X18 @ (lam @ X20)))) & ! [X31 : term] : (($true = ((X18 @ (sub @ X20 @ (push @ X31 @ id))))) | ($true != ((X18 @ X31)))) & ! [X21 : term] : (((X19 @ id @ X21 @ id)) = ((X18 @ X21))) & ! [X32 : subst,X35 : subst,X33 : term,X34 : subst] : (($true = ((X19 @ (comp @ X32 @ X35) @ (sub @ X33 @ X35) @ X34))) | ($true != ((X19 @ X32 @ X33 @ (comp @ X35 @ X34))))) & ! [X26 : (subst > term > term)] : (($true = ((X19 @ id @ (lam @ (X26 @ sh @ one)) @ id))) | ? [X29 : term,X28 : subst,X27 : subst] : (((sub @ (X26 @ X28 @ X29) @ X27)) != ((X26 @ (comp @ X28 @ X27) @ (sub @ X29 @ X27)))) | ? [X30 : term] : ((((X19 @ id @ X30 @ id)) = $true) & (((X19 @ id @ (X26 @ id @ X30) @ id)) != $true))) & ! [X22 : subst,X24 : subst,X25 : term,X23 : subst] : ((((X19 @ X24 @ X25 @ (comp @ X23 @ X22))) = $true) | ($true != ((X19 @ (comp @ X24 @ X23) @ (sub @ X25 @ X23) @ X22)))))) & ((pushprop_lem0 = $true) | ? [X294 : subst,X296 : (term > $o),X295 : term] : ! [X297 : (term > $o)] : ? [X298 : term] : (((X297 @ X298)) != ((X296 @ (sub @ X298 @ (push @ X295 @ X294)))))) & (! [X294 : subst,X296 : (term > $o),X295 : term] : ? [X297 : (term > $o)] : ! [X298 : term] : (((X297 @ X298)) = ((X296 @ (sub @ X298 @ (push @ X295 @ X294))))) | (pushprop_lem0 != $true)) & ((axvarcons = $true) | ? [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) != X224)) & (! [X224 : term,X223 : subst] : (((sub @ one @ (push @ X224 @ X223))) = X224) | (axvarcons != $true)) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) | (axscons != $true)) & ((axscons = $true) | ? [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) != X146)) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1_lthm = $true) | (! [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 = X288) | (((ap @ X288 @ X287)) != ((ap @ X286 @ X289)))) & ? [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) = ((ap @ (sub @ X292 @ id) @ X291))) & (X290 != X292)) & ! [X285 : term] : (((sub @ X285 @ id)) = X285))) & (? [X288 : term,X289 : term,X286 : term,X287 : term] : ((X286 != X288) & (((ap @ X288 @ X287)) = ((ap @ X286 @ X289)))) | ! [X293 : term,X290 : term,X292 : term,X291 : term] : ((((ap @ (sub @ X290 @ id) @ X293)) != ((ap @ (sub @ X292 @ id) @ X291))) | (X290 = X292)) | ? [X285 : term] : (((sub @ X285 @ id)) != X285) | (hoasapinj1_lthm != $true)) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((laminj = $true) | ? [X420 : term,X421 : term] : ((X420 != X421) & (((lam @ X421)) = ((lam @ X420))))) & (! [X420 : term,X421 : term] : ((X420 = X421) | (((lam @ X421)) != ((lam @ X420)))) | (laminj != $true)) & ((induction2lem = $true) | ? [X466 : (term > $o),X467 : subst,X465 : term] : (! [X470 : term] : ((((X466 @ (lam @ X470))) = $true) | ? [X471 : term] : ((((X466 @ X471)) = $true) & ($true != ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) & ! [X469 : term,X468 : term] : (($true != ((X466 @ X469))) | (((X466 @ (ap @ X469 @ X468))) = $true) | ($true != ((X466 @ X468)))) & ! [X472 : term] : (($true = ((X466 @ (sub @ X472 @ X467)))) | (((var @ X472)) != $true)) & ($true != ((X466 @ (sub @ X465 @ X467)))))) & (! [X466 : (term > $o),X467 : subst,X465 : term] : (? [X470 : term] : ((((X466 @ (lam @ X470))) != $true) & ! [X471 : term] : ((((X466 @ X471)) != $true) | ($true = ((X466 @ (sub @ X470 @ (push @ X471 @ id))))))) | ? [X469 : term,X468 : term] : (($true = ((X466 @ X469))) & (((X466 @ (ap @ X469 @ X468))) != $true) & ($true = ((X466 @ X468)))) | ? [X472 : term] : (($true != ((X466 @ (sub @ X472 @ X467)))) & (((var @ X472)) = $true)) | ($true = ((X466 @ (sub @ X465 @ X467))))) | (induction2lem != $true)) & (! [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 = X307) | (((ap @ (sub @ X306 @ id) @ X304)) != ((ap @ (sub @ X307 @ id) @ X305)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X305 : term,X304 : term,X306 : term,X307 : term] : ((X306 != X307) & (((ap @ (sub @ X306 @ id) @ X304)) = ((ap @ (sub @ X307 @ id) @ X305))))) & (pushprop_lem3v2_lthm = $true) & (! [X516 : (term > $o),X517 : term] : (? [X518 : term] : (($true != ((X516 @ X518))) & ($true = ((var @ X518)))) | ($true = ((X516 @ X517))) | ? [X519 : term,X520 : term] : (($true != ((X516 @ (ap @ X519 @ X520)))) & ($true = ((X516 @ X519))) & ($true = ((X516 @ X520)))) | ? [X521 : term] : ((((X516 @ (lam @ X521))) != $true) & ($true = ((X516 @ X521))))) | (induction != $true)) & ((induction = $true) | ? [X516 : (term > $o),X517 : term] : (! [X518 : term] : (($true = ((X516 @ X518))) | ($true != ((var @ X518)))) & ($true != ((X516 @ X517))) & ! [X519 : term,X520 : term] : (($true = ((X516 @ (ap @ X519 @ X520)))) | ($true != ((X516 @ X519))) | ($true != ((X516 @ X520)))) & ! [X521 : term] : ((((X516 @ (lam @ X521))) = $true) | ($true != ((X516 @ X521)))))) & (hoaslamnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 = X39) | (((ap @ X38 @ X37)) != ((ap @ X36 @ X39)))) & ? [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) = ((ap @ (sub @ X41 @ id) @ X43))) & (X42 != X43)))) & (? [X39 : term,X37 : term,X38 : term,X36 : term] : ((X37 != X39) & (((ap @ X38 @ X37)) = ((ap @ X36 @ X39)))) | ! [X42 : term,X43 : term,X40 : term,X41 : term] : ((((ap @ (sub @ X40 @ id) @ X42)) != ((ap @ (sub @ X41 @ id) @ X43))) | (X42 = X43)) | (hoasapinj2_lthm != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) | ? [X525 : (subst > term > subst > $o),X524 : term] : (! [X539 : term] : ((((X525 @ id @ X539 @ id)) != $true) | ($true = ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) & ($true != ((X525 @ id @ (lam @ X524) @ id))) & ! [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) != $true) | ($true = ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) & ! [X530 : (subst > term > term)] : (? [X531 : term] : (($true = ((X525 @ id @ X531 @ id))) & ($true != ((X525 @ id @ (X530 @ id @ X531) @ id)))) | (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) = $true) | ? [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) != ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) & ! [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true != ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) | ($true = ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527)))))) & (! [X525 : (subst > term > subst > $o),X524 : term] : (? [X539 : term] : ((((X525 @ id @ X539 @ id)) = $true) & ($true != ((X525 @ id @ (sub @ X524 @ (push @ X539 @ id)) @ id)))) | ($true = ((X525 @ id @ (lam @ X524) @ id))) | ? [X538 : subst,X536 : subst,X537 : subst,X535 : term] : ((((X525 @ (comp @ X538 @ X537) @ (sub @ X535 @ X537) @ X536)) = $true) & ($true != ((X525 @ X538 @ X535 @ (comp @ X537 @ X536))))) | ? [X530 : (subst > term > term)] : (! [X531 : term] : (($true != ((X525 @ id @ X531 @ id))) | ($true = ((X525 @ id @ (X530 @ id @ X531) @ id)))) & (((X525 @ id @ (lam @ (X530 @ sh @ one)) @ id)) != $true) & ! [X534 : subst,X533 : term,X532 : subst] : (((sub @ (X530 @ X534 @ X533) @ X532)) = ((X530 @ (comp @ X534 @ X532) @ (sub @ X533 @ X532))))) | ? [X529 : subst,X528 : term,X527 : subst,X526 : subst] : (($true = ((X525 @ X529 @ X528 @ (comp @ X526 @ X527)))) & ($true != ((X525 @ (comp @ X529 @ X526) @ (sub @ X528 @ X526) @ X527))))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem2_lthm = $true) & ((induction2_lthm = $true) | ($true != sP6)) & (($true = sP6) | (induction2_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3b = $true) | ? [X418 : term] : ! [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) != ((X419 @ sh @ one)))) & (! [X418 : term] : ? [X419 : (subst > term > term)] : (((sub @ X418 @ (push @ one @ sh))) = ((X419 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (pushprop_lthm = $true) & ! [X522 : d_term,X523 : d_term] : ((X522 = X523) | (((d2term @ X523)) != ((d2term @ X522)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3v2_lthm = $true) | (! [X497 : term] : (((sub @ X497 @ id)) = X497) & ? [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (! [X510 : term] : (((X500 @ id @ X510 @ id)) = ((X499 @ X510))) & ! [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) = $true) | ? [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) != ((sub @ (X505 @ X508 @ X509) @ X507))) | ? [X506 : term] : (($true = ((X500 @ id @ X506 @ id))) & ($true != ((X500 @ id @ (X505 @ id @ X506) @ id))))) & (((X499 @ (lam @ X498))) != $true) & ! [X515 : term] : (($true = ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) | (((X499 @ X515)) != $true)) & ! [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true != ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) | (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) = $true)) & ! [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) = $true) | (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) != $true))))) & (? [X497 : term] : (((sub @ X497 @ id)) != X497) | ! [X498 : term,X499 : (term > $o),X500 : (subst > term > subst > $o)] : (? [X510 : term] : (((X500 @ id @ X510 @ id)) != ((X499 @ X510))) | ? [X505 : (subst > term > term)] : ((((X500 @ id @ (lam @ (X505 @ sh @ one)) @ id)) != $true) & ! [X508 : subst,X509 : term,X507 : subst] : (((X505 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507))) = ((sub @ (X505 @ X508 @ X509) @ X507))) & ! [X506 : term] : (($true != ((X500 @ id @ X506 @ id))) | ($true = ((X500 @ id @ (X505 @ id @ X506) @ id))))) | (((X499 @ (lam @ X498))) = $true) | ? [X515 : term] : (($true != ((X499 @ (sub @ X498 @ (push @ X515 @ id))))) & (((X499 @ X515)) = $true)) | ? [X501 : term,X503 : subst,X504 : subst,X502 : subst] : (($true = ((X500 @ X504 @ X501 @ (comp @ X502 @ X503)))) & (((X500 @ (comp @ X504 @ X502) @ (sub @ X501 @ X502) @ X503)) != $true)) | ? [X512 : subst,X513 : subst,X514 : term,X511 : subst] : ((((X500 @ X511 @ X514 @ (comp @ X513 @ X512))) != $true) & (((X500 @ (comp @ X511 @ X513) @ (sub @ X514 @ X513) @ X512)) = $true))) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((! [X56 : subst] : (((comp @ X56 @ id)) = X56) & ! [X55 : subst] : (((comp @ id @ X55)) = X55)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X56 : subst] : (((comp @ X56 @ id)) != X56) | ? [X55 : subst] : (((comp @ id @ X55)) != X55)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X115 : (term > $o),X116 : term] : (? [X119 : term,X118 : term] : (($true != ((X115 @ (ap @ X118 @ X119)))) & ($true = ((X115 @ X119))) & (((X115 @ X118)) = $true)) | ? [X120 : term] : (($true != ((X115 @ (lam @ X120)))) & ! [X121 : term] : (($true = ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) | (((X115 @ X121)) != $true))) | ($true = ((X115 @ X116))) | ? [X117 : term] : (($true = ((var @ X117))) & ($true != ((X115 @ X117))))) & ! [X112 : (subst > term > subst > $o)] : ? [X113 : (term > $o)] : ! [X114 : term] : (((X113 @ X114)) = ((X112 @ id @ X114 @ id))) & ! [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true = ((X124 @ (lam @ X123)))) | ? [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) != $true) & ($true = ((X124 @ X126)))) | ? [X132 : term] : (((X124 @ X132)) != ((X125 @ id @ X132 @ id))) | ? [X127 : (subst > term > term)] : (! [X131 : term] : (($true = ((X125 @ id @ (X127 @ id @ X131) @ id))) | ($true != ((X125 @ id @ X131 @ id)))) & (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) != $true) & ! [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) = ((sub @ (X127 @ X129 @ X130) @ X128))))) & ! [X122 : term] : (((sub @ X122 @ id)) = X122) & ($true != sP5))) & (? [X115 : (term > $o),X116 : term] : (! [X119 : term,X118 : term] : (($true = ((X115 @ (ap @ X118 @ X119)))) | ($true != ((X115 @ X119))) | (((X115 @ X118)) != $true)) & ! [X120 : term] : (($true = ((X115 @ (lam @ X120)))) | ? [X121 : term] : (($true != ((X115 @ (sub @ X120 @ (push @ X121 @ id))))) & (((X115 @ X121)) = $true))) & ($true != ((X115 @ X116))) & ! [X117 : term] : (($true != ((var @ X117))) | ($true = ((X115 @ X117))))) | ? [X112 : (subst > term > subst > $o)] : ! [X113 : (term > $o)] : ? [X114 : term] : (((X113 @ X114)) != ((X112 @ id @ X114 @ id))) | ? [X123 : term,X125 : (subst > term > subst > $o),X124 : (term > $o)] : (($true != ((X124 @ (lam @ X123)))) & ! [X126 : term] : ((((X124 @ (sub @ X123 @ (push @ X126 @ id)))) = $true) | ($true != ((X124 @ X126)))) & ! [X132 : term] : (((X124 @ X132)) = ((X125 @ id @ X132 @ id))) & ! [X127 : (subst > term > term)] : (? [X131 : term] : (($true != ((X125 @ id @ (X127 @ id @ X131) @ id))) & ($true = ((X125 @ id @ X131 @ id)))) | (((X125 @ id @ (lam @ (X127 @ sh @ one)) @ id)) = $true) | ? [X130 : term,X128 : subst,X129 : subst] : (((X127 @ (comp @ X129 @ X128) @ (sub @ X130 @ X128))) != ((sub @ (X127 @ X129 @ X130) @ X128))))) | ? [X122 : term] : (((sub @ X122 @ id)) != X122) | ($true = sP5) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X15 : d_subst,X14 : d_subst] : ((X14 = X15) | (((d2subst @ X15)) != ((d2subst @ X14)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2a = $true) | ? [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (! [X315 : term] : (((X313 @ id @ X315 @ id)) = ((X312 @ X315))) & ($true != ((X312 @ (lam @ X311)))) & ! [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) = $true) | ($true != ((X312 @ X314)))) & ! [X316 : (subst > term > term)] : (? [X317 : term] : (($true != ((X313 @ id @ (X316 @ id @ X317) @ id))) & (((X313 @ id @ X317 @ id)) = $true)) | ($true = ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) | ? [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) != ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))))))) & (! [X312 : (term > $o),X313 : (subst > term > subst > $o),X311 : term] : (? [X315 : term] : (((X313 @ id @ X315 @ id)) != ((X312 @ X315))) | ($true = ((X312 @ (lam @ X311)))) | ? [X314 : term] : ((((X312 @ (sub @ X311 @ (push @ X314 @ id)))) != $true) & ($true = ((X312 @ X314)))) | ? [X316 : (subst > term > term)] : (! [X317 : term] : (($true = ((X313 @ id @ (X316 @ id @ X317) @ id))) | (((X313 @ id @ X317 @ id)) != $true)) & ($true != ((X313 @ id @ (lam @ (X316 @ sh @ one)) @ id))) & ! [X319 : term,X320 : subst,X318 : subst] : (((sub @ (X316 @ X318 @ X319) @ X320)) = ((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320)))))) | (hoasinduction_lem3v2a != $true)) & (? [X157 : term,X156 : term] : ((((lam @ X156)) = ((lam @ X157))) & (X156 != X157)) | ! [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (? [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) != ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) | (((lam @ (X159 @ sh @ one))) != ((lam @ (X161 @ sh @ one)))) | (((X161 @ X160 @ X158)) = ((X159 @ X160 @ X158))) | ? [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) != ((sub @ (X159 @ X162 @ X164) @ X163)))) | ? [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) != X154) | ? [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) != X152) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (! [X157 : term,X156 : term] : ((((lam @ X156)) != ((lam @ X157))) | (X156 = X157)) & ? [X159 : (subst > term > term),X161 : (subst > term > term),X160 : subst,X158 : term] : (! [X165 : subst,X167 : subst,X166 : term] : (((sub @ (X161 @ X165 @ X166) @ X167)) = ((X161 @ (comp @ X165 @ X167) @ (sub @ X166 @ X167)))) & (((lam @ (X159 @ sh @ one))) = ((lam @ (X161 @ sh @ one)))) & (((X161 @ X160 @ X158)) != ((X159 @ X160 @ X158))) & ! [X162 : subst,X163 : subst,X164 : term] : (((X159 @ (comp @ X162 @ X163) @ (sub @ X164 @ X163))) = ((sub @ (X159 @ X162 @ X164) @ X163)))) & ! [X154 : subst,X155 : term] : (((comp @ sh @ (push @ X155 @ X154))) = X154) & ! [X152 : term,X153 : subst] : (((sub @ one @ (push @ X152 @ X153))) = X152))) & ((apinj1 = $true) | ? [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 != X391) & (((ap @ X391 @ X392)) = ((ap @ X389 @ X390))))) & (! [X389 : term,X390 : term,X391 : term,X392 : term] : ((X389 = X391) | (((ap @ X391 @ X392)) != ((ap @ X389 @ X390)))) | (apinj1 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X422 : (subst > term > subst > $o)] : ? [X423 : (term > $o)] : ! [X424 : term] : (((X423 @ X424)) = ((X422 @ id @ X424 @ id))) & ($true != sP4) & ! [X432 : term] : (((sub @ X432 @ id)) = X432) & ! [X426 : term,X425 : (term > $o)] : (? [X430 : term] : (($true != ((X425 @ (lam @ X430)))) & ! [X431 : term] : ((((X425 @ X431)) != $true) | (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) = $true))) | ($true = ((X425 @ X426))) | ? [X429 : term] : ((((var @ X429)) = $true) & ($true != ((X425 @ X429)))) | ? [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) != $true) & ($true = ((X425 @ X428))) & (((X425 @ X427)) = $true))) & ! [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (? [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) != $true) & ! [X439 : term] : (($true = ((X435 @ id @ (X438 @ id @ X439) @ id))) | ($true != ((X435 @ id @ X439 @ id)))) & ! [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) = ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) | ($true = ((X433 @ (lam @ X434)))) | ? [X436 : term] : (((X433 @ X436)) != ((X435 @ id @ X436 @ id))) | ? [X437 : term] : (($true = ((X433 @ X437))) & ($true != ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))))) & (? [X422 : (subst > term > subst > $o)] : ! [X423 : (term > $o)] : ? [X424 : term] : (((X423 @ X424)) != ((X422 @ id @ X424 @ id))) | ($true = sP4) | ? [X432 : term] : (((sub @ X432 @ id)) != X432) | ? [X426 : term,X425 : (term > $o)] : (! [X430 : term] : (($true = ((X425 @ (lam @ X430)))) | ? [X431 : term] : ((((X425 @ X431)) = $true) & (((X425 @ (sub @ X430 @ (push @ X431 @ id)))) != $true))) & ($true != ((X425 @ X426))) & ! [X429 : term] : ((((var @ X429)) != $true) | ($true = ((X425 @ X429)))) & ! [X428 : term,X427 : term] : ((((X425 @ (ap @ X427 @ X428))) = $true) | ($true != ((X425 @ X428))) | (((X425 @ X427)) != $true))) | ? [X434 : term,X435 : (subst > term > subst > $o),X433 : (term > $o)] : (! [X438 : (subst > term > term)] : ((((X435 @ id @ (lam @ (X438 @ sh @ one)) @ id)) = $true) | ? [X439 : term] : (($true != ((X435 @ id @ (X438 @ id @ X439) @ id))) & ($true = ((X435 @ id @ X439 @ id)))) | ? [X442 : subst,X440 : subst,X441 : term] : (((sub @ (X438 @ X442 @ X441) @ X440)) != ((X438 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440))))) & ($true != ((X433 @ (lam @ X434)))) & ! [X436 : term] : (((X433 @ X436)) = ((X435 @ id @ X436 @ id))) & ! [X437 : term] : (($true != ((X433 @ X437))) | ($true = ((X433 @ (sub @ X434 @ (push @ X437 @ id))))))) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X191 : term,X190 : (subst > term > subst > $o)] : (? [X193 : (subst > term > term)] : (! [X197 : term] : ((((X190 @ id @ X197 @ id)) != $true) | ($true = ((X190 @ id @ (X193 @ id @ X197) @ id)))) & (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) != $true) & ! [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) = ((sub @ (X193 @ X194 @ X196) @ X195)))) | (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ? [X192 : term] : (($true != ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) & (((X190 @ id @ X192 @ id)) = $true))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X191 : term,X190 : (subst > term > subst > $o)] : (! [X193 : (subst > term > term)] : (? [X197 : term] : ((((X190 @ id @ X197 @ id)) = $true) & ($true != ((X190 @ id @ (X193 @ id @ X197) @ id)))) | (((X190 @ id @ (lam @ (X193 @ sh @ one)) @ id)) = $true) | ? [X196 : term,X195 : subst,X194 : subst] : (((X193 @ (comp @ X194 @ X195) @ (sub @ X196 @ X195))) != ((sub @ (X193 @ X194 @ X196) @ X195)))) & (((X190 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) != $true) & ! [X192 : term] : (($true = ((X190 @ id @ (sub @ X191 @ (push @ X192 @ id)) @ id))) | (((X190 @ id @ X192 @ id)) != $true)))) & (? [X394 : (subst > term > subst > $o),X395 : term] : (($true != ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) & ! [X396 : term] : (($true = ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) | (((X394 @ id @ X396 @ id)) != $true)) & ! [X397 : (subst > term > term)] : (? [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X397 @ X401 @ X400) @ X399))) | ? [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) != $true) & ($true = ((X394 @ id @ X398 @ id)))) | (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) = $true))) | ? [X393 : term] : (((sub @ X393 @ id)) != X393) | ($true = sP2) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X394 : (subst > term > subst > $o),X395 : term] : (($true = ((X394 @ id @ (lam @ (sub @ X395 @ (push @ one @ sh))) @ id))) | ? [X396 : term] : (($true != ((X394 @ id @ (sub @ X395 @ (push @ X396 @ id)) @ id))) & (((X394 @ id @ X396 @ id)) = $true)) | ? [X397 : (subst > term > term)] : (! [X401 : subst,X400 : term,X399 : subst] : (((X397 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X397 @ X401 @ X400) @ X399))) & ! [X398 : term] : ((((X394 @ id @ (X397 @ id @ X398) @ id)) = $true) | ($true != ((X394 @ id @ X398 @ id)))) & (((X394 @ id @ (lam @ (X397 @ sh @ one)) @ id)) != $true))) & ! [X393 : term] : (((sub @ X393 @ id)) = X393) & ($true != sP2))) & (! [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (? [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) != ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) | (((lam @ (X225 @ sh @ one))) != ((lam @ (X226 @ sh @ one)))) | ? [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) != ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) | (((X226 @ X227 @ X228)) = ((X225 @ X227 @ X228)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X226 : (subst > term > term),X225 : (subst > term > term),X228 : term,X227 : subst] : (! [X234 : subst,X233 : subst,X232 : term] : (((sub @ (X226 @ X233 @ X232) @ X234)) = ((X226 @ (comp @ X233 @ X234) @ (sub @ X232 @ X234)))) & (((lam @ (X225 @ sh @ one))) = ((lam @ (X226 @ sh @ one)))) & ! [X231 : subst,X230 : subst,X229 : term] : (((sub @ (X225 @ X230 @ X229) @ X231)) = ((X225 @ (comp @ X230 @ X231) @ (sub @ X229 @ X231)))) & (((X226 @ X227 @ X228)) != ((X225 @ X227 @ X228))))) & (! [X51 : term] : ? [X52 : (subst > term > term)] : ! [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) = ((X52 @ X53 @ X54))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X54 : term,X53 : subst] : (((sub @ X51 @ (push @ X54 @ X53))) != ((X52 @ X53 @ X54)))) & (! [X338 : term] : (((sub @ X338 @ id)) = X338) | (axvarid != $true)) & ((axvarid = $true) | ? [X338 : term] : (((sub @ X338 @ id)) != X338)) & ((hoasinduction_lem3b_lthm = $true) | ? [X44 : term] : ! [X45 : (subst > term > term)] : (((X45 @ sh @ one)) != ((sub @ X44 @ (push @ one @ sh))))) & (! [X44 : term] : ? [X45 : (subst > term > term)] : (((X45 @ sh @ one)) = ((sub @ X44 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (! [X300 : term] : ? [X301 : (subst > term > term)] : ! [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) = ((X301 @ X303 @ X302))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X300 : term] : ! [X301 : (subst > term > term)] : ? [X303 : subst,X302 : term] : (((sub @ X300 @ (push @ X302 @ X303))) != ((X301 @ X303 @ X302)))) & (lamnotvar = $true) & (pushprop = $true) & ((axshiftcons = $true) | ? [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) != X461)) & (! [X462 : term,X461 : subst] : (((comp @ sh @ (push @ X462 @ X461))) = X461) | (axshiftcons != $true)) & (substmonoid_gthm = $true) & (! [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true = ((X238 @ (ap @ X239 @ X237)))) | ($true != ((X238 @ X239))) | ? [X240 : term] : (((X236 @ id @ X240 @ id)) != ((X238 @ X240))) | ? [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) != $true) & ($true = ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) | ? [X250 : term,X249 : term] : (($true = ((X236 @ id @ X250 @ id))) & ($true = ((X236 @ id @ X249 @ id))) & ($true != ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) | ($true != ((X238 @ X237))) | ? [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) = $true) & ($true != ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247))))) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ? [X236 : (subst > term > subst > $o),X238 : (term > $o),X237 : term,X239 : term] : (($true != ((X238 @ (ap @ X239 @ X237)))) & ($true = ((X238 @ X239))) & ! [X240 : term] : (((X236 @ id @ X240 @ id)) = ((X238 @ X240))) & ! [X241 : subst,X243 : subst,X242 : term,X244 : subst] : ((((X236 @ X241 @ X242 @ (comp @ X244 @ X243))) = $true) | ($true != ((X236 @ (comp @ X241 @ X244) @ (sub @ X242 @ X244) @ X243)))) & ! [X250 : term,X249 : term] : (($true != ((X236 @ id @ X250 @ id))) | ($true != ((X236 @ id @ X249 @ id))) | ($true = ((X236 @ id @ (ap @ (sub @ X249 @ id) @ X250) @ id)))) & ($true = ((X238 @ X237))) & ! [X247 : subst,X245 : subst,X248 : term,X246 : subst] : ((((X236 @ X245 @ X248 @ (comp @ X246 @ X247))) != $true) | ($true = ((X236 @ (comp @ X245 @ X246) @ (sub @ X248 @ X246) @ X247)))))) & (axvarshift = $true) & ! [X16 : term] : ? [X17 : d_term] : (((d2term @ X17)) = X16) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & ((substmonoid_lthm = $true) | (! [X340 : subst] : (((comp @ X340 @ id)) = X340) & ! [X339 : subst] : (((comp @ id @ X339)) = X339) & (? [X342 : subst] : (((comp @ X342 @ id)) != X342) | ? [X341 : subst] : (((comp @ id @ X341)) != X341)))) & (? [X340 : subst] : (((comp @ X340 @ id)) != X340) | ? [X339 : subst] : (((comp @ id @ X339)) != X339) | (! [X342 : subst] : (((comp @ X342 @ id)) = X342) & ! [X341 : subst] : (((comp @ id @ X341)) = X341)) | (substmonoid_lthm != $true)) & (! [X252 : term] : (((sub @ X252 @ id)) = X252) | ? [X251 : term] : (((sub @ X251 @ id)) != X251) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X252 : term] : (((sub @ X252 @ id)) != X252) & ! [X251 : term] : (((sub @ X251 @ id)) = X251))) & ((hoasinduction_lem0_lthm = $true) | ? [X0 : (subst > term > subst > $o)] : ! [X1 : (term > $o)] : ? [X2 : term] : (((X1 @ X2)) != ((X0 @ id @ X2 @ id)))) & (! [X0 : (subst > term > subst > $o)] : ? [X1 : (term > $o)] : ! [X2 : term] : (((X1 @ X2)) = ((X0 @ id @ X2 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X208 : term] : ? [X209 : (subst > term > term)] : ! [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) = ((sub @ X208 @ (push @ X211 @ X210)))) & ? [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (! [X216 : (subst > term > term)] : (? [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) != ((sub @ (X216 @ X220 @ X218) @ X219))) | (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) = $true) | ? [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) != $true) & ($true = ((X215 @ id @ X217 @ id))))) & ($true != ((X214 @ (lam @ X213)))) & ! [X222 : term] : (($true = ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) | ($true != ((X214 @ X222)))) & ! [X221 : term] : (((X214 @ X221)) = ((X215 @ id @ X221 @ id)))) & ! [X212 : term] : (((sub @ X212 @ id)) = X212))) & (? [X208 : term] : ! [X209 : (subst > term > term)] : ? [X211 : term,X210 : subst] : (((X209 @ X210 @ X211)) != ((sub @ X208 @ (push @ X211 @ X210)))) | ! [X214 : (term > $o),X215 : (subst > term > subst > $o),X213 : term] : (? [X216 : (subst > term > term)] : (! [X220 : subst,X218 : term,X219 : subst] : (((X216 @ (comp @ X220 @ X219) @ (sub @ X218 @ X219))) = ((sub @ (X216 @ X220 @ X218) @ X219))) & (((X215 @ id @ (lam @ (X216 @ sh @ one)) @ id)) != $true) & ! [X217 : term] : ((((X215 @ id @ (X216 @ id @ X217) @ id)) = $true) | ($true != ((X215 @ id @ X217 @ id))))) | ($true = ((X214 @ (lam @ X213)))) | ? [X222 : term] : (($true != ((X214 @ (sub @ X213 @ (push @ X222 @ id))))) & ($true = ((X214 @ X222)))) | ? [X221 : term] : (((X214 @ X221)) != ((X215 @ id @ X221 @ id)))) | ? [X212 : term] : (((sub @ X212 @ id)) != X212) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X463 : subst] : ? [X464 : d_subst] : (((d2subst @ X464)) = X463) & (hoasapnotvar_lthm = $true) & (? [X321 : term] : (((sub @ X321 @ id)) != X321) | ! [X330 : term,X331 : (subst > term > subst > $o)] : (? [X332 : (subst > term > term)] : (! [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) = $true) | ($true != ((X331 @ id @ X333 @ id)))) & (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) != $true) & ! [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) = ((sub @ (X332 @ X336 @ X335) @ X334)))) | ? [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) != $true) & ($true = ((X331 @ id @ X337 @ id)))) | ($true = ((X331 @ id @ (lam @ X330) @ id)))) | ? [X322 : (subst > term > subst > $o),X323 : term] : (($true != ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) & ! [X324 : term] : (($true != ((X322 @ id @ X324 @ id))) | ($true = ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) & ! [X325 : (subst > term > term)] : (? [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) != ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) | ? [X326 : term] : (($true != ((X322 @ id @ (X325 @ id @ X326) @ id))) & ($true = ((X322 @ id @ X326 @ id)))) | ($true = ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id))))) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X321 : term] : (((sub @ X321 @ id)) = X321) & ? [X330 : term,X331 : (subst > term > subst > $o)] : (! [X332 : (subst > term > term)] : (? [X333 : term] : ((((X331 @ id @ (X332 @ id @ X333) @ id)) != $true) & ($true = ((X331 @ id @ X333 @ id)))) | (((X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) = $true) | ? [X336 : subst,X334 : subst,X335 : term] : (((X332 @ (comp @ X336 @ X334) @ (sub @ X335 @ X334))) != ((sub @ (X332 @ X336 @ X335) @ X334)))) & ! [X337 : term] : ((((X331 @ id @ (sub @ X330 @ (push @ X337 @ id)) @ id)) = $true) | ($true != ((X331 @ id @ X337 @ id)))) & ($true != ((X331 @ id @ (lam @ X330) @ id)))) & ! [X322 : (subst > term > subst > $o),X323 : term] : (($true = ((X322 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id))) | ? [X324 : term] : (($true = ((X322 @ id @ X324 @ id))) & ($true != ((X322 @ id @ (sub @ X323 @ (push @ X324 @ id)) @ id)))) | ? [X325 : (subst > term > term)] : (! [X327 : subst,X328 : term,X329 : subst] : (((sub @ (X325 @ X327 @ X328) @ X329)) = ((X325 @ (comp @ X327 @ X329) @ (sub @ X328 @ X329)))) & ! [X326 : term] : (($true = ((X322 @ id @ (X325 @ id @ X326) @ id))) | ($true != ((X322 @ id @ X326 @ id)))) & ($true != ((X322 @ id @ (lam @ (X325 @ sh @ one)) @ id))))))) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X198 : d_subst] : (d_id = X198) & (! [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) != ((ap @ (sub @ X8 @ id) @ X9))) | ? [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) != ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X9 : term,X10 : (subst > term > term),X8 : term] : ((((lam @ (X10 @ sh @ one))) = ((ap @ (sub @ X8 @ id) @ X9))) & ! [X11 : term,X13 : subst,X12 : subst] : (((sub @ (X10 @ X13 @ X11) @ X12)) = ((X10 @ (comp @ X13 @ X12) @ (sub @ X11 @ X12)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X183 : term,X182 : (subst > term > subst > $o)] : (($true = ((X182 @ id @ (lam @ X183) @ id))) | ? [X185 : (subst > term > term)] : (! [X189 : term] : ((((X182 @ id @ X189 @ id)) != $true) | (((X182 @ id @ (X185 @ id @ X189) @ id)) = $true)) & (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) = ((sub @ (X185 @ X187 @ X186) @ X188)))) | ? [X184 : term] : (($true = ((X182 @ id @ X184 @ id))) & ($true != ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id))))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X183 : term,X182 : (subst > term > subst > $o)] : (($true != ((X182 @ id @ (lam @ X183) @ id))) & ! [X185 : (subst > term > term)] : (? [X189 : term] : ((((X182 @ id @ X189 @ id)) = $true) & (((X182 @ id @ (X185 @ id @ X189) @ id)) != $true)) | (((X182 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true) | ? [X186 : term,X187 : subst,X188 : subst] : (((X185 @ (comp @ X187 @ X188) @ (sub @ X186 @ X188))) != ((sub @ (X185 @ X187 @ X186) @ X188)))) & ! [X184 : term] : (($true != ((X182 @ id @ X184 @ id))) | ($true = ((X182 @ id @ (sub @ X183 @ (push @ X184 @ id)) @ id)))))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (! [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) != ((ap @ X144 @ X143))) | (X142 = X143)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X142 : term,X144 : term,X143 : term,X145 : term] : ((((ap @ X145 @ X142)) = ((ap @ X144 @ X143))) & (X142 != X143))) & (axassoc = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X474 : (subst > term > subst > $o),X475 : term] : (! [X482 : term,X481 : term] : (($true != ((X474 @ id @ X482 @ id))) | ($true = ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) | ($true != ((X474 @ id @ X481 @ id)))) & ! [X476 : (subst > term > term)] : (($true = ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) | ? [X477 : term] : (($true != ((X474 @ id @ (X476 @ id @ X477) @ id))) & ($true = ((X474 @ id @ X477 @ id)))) | ? [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) != ((sub @ (X476 @ X480 @ X478) @ X479)))) & ($true != ((X474 @ id @ X475 @ id))))) & (! [X474 : (subst > term > subst > $o),X475 : term] : (? [X482 : term,X481 : term] : (($true = ((X474 @ id @ X482 @ id))) & ($true != ((X474 @ id @ (ap @ (sub @ X481 @ id) @ X482) @ id))) & ($true = ((X474 @ id @ X481 @ id)))) | ? [X476 : (subst > term > term)] : (($true != ((X474 @ id @ (lam @ (X476 @ sh @ one)) @ id))) & ! [X477 : term] : (($true = ((X474 @ id @ (X476 @ id @ X477) @ id))) | ($true != ((X474 @ id @ X477 @ id)))) & ! [X480 : subst,X479 : subst,X478 : term] : (((X476 @ (comp @ X480 @ X479) @ (sub @ X478 @ X479))) = ((sub @ (X476 @ X480 @ X478) @ X479)))) | ($true = ((X474 @ id @ X475 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (! [X473 : subst] : (((comp @ X473 @ id)) = X473) | (axidr != $true)) & ((axidr = $true) | ? [X473 : subst] : (((comp @ X473 @ id)) != X473)) & ((induction2 = $true) | ? [X483 : term,X484 : (term > $o)] : (! [X485 : term] : (($true = ((X484 @ (lam @ X485)))) | ? [X486 : term] : (($true = ((X484 @ X486))) & ($true != ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) & ! [X487 : term] : (($true != ((var @ X487))) | (((X484 @ X487)) = $true)) & ! [X488 : term,X489 : term] : (($true != ((X484 @ X488))) | ($true = ((X484 @ (ap @ X488 @ X489)))) | (((X484 @ X489)) != $true)) & (((X484 @ X483)) != $true))) & (! [X483 : term,X484 : (term > $o)] : (? [X485 : term] : (($true != ((X484 @ (lam @ X485)))) & ! [X486 : term] : (($true != ((X484 @ X486))) | ($true = ((X484 @ (sub @ X485 @ (push @ X486 @ id))))))) | ? [X487 : term] : (($true = ((var @ X487))) & (((X484 @ X487)) != $true)) | ? [X488 : term,X489 : term] : (($true = ((X484 @ X488))) & ($true != ((X484 @ (ap @ X488 @ X489)))) & (((X484 @ X489)) = $true)) | (((X484 @ X483)) = $true)) | (induction2 != $true)) & (pushprop_lem3v2 = $true) & (! [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) != ((ap @ (sub @ X180 @ id) @ X178))) | (X178 = X179)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X178 : term,X181 : term,X179 : term,X180 : term] : ((((ap @ (sub @ X181 @ id) @ X179)) = ((ap @ (sub @ X180 @ id) @ X178))) & (X178 != X179))) & (ulamvar1 != $true) & (lamnotap != $true) & (! [X308 : (subst > term > subst > $o)] : ? [X309 : (term > $o)] : ! [X310 : term] : (((X309 @ X310)) = ((X308 @ id @ X310 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X308 : (subst > term > subst > $o)] : ! [X309 : (term > $o)] : ? [X310 : term] : (((X309 @ X310)) != ((X308 @ id @ X310 @ id)))) & (pushprop_lem1v2_gthm = $true) & (($true = sP1) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & ((hoasinduction = $true) | ? [X344 : term,X343 : (subst > term > subst > $o)] : (! [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true != ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) | ($true = ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) & ($true != ((X343 @ id @ X344 @ id))) & ! [X345 : term,X346 : term] : (($true = ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) | ($true != ((X343 @ id @ X346 @ id))) | ($true != ((X343 @ id @ X345 @ id)))) & ($true != ((sP0 @ X343))) & ! [X352 : term] : (($true != ((var @ (sub @ X352 @ id)))) | ($true = ((X343 @ id @ X352 @ id)))) & ! [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true = ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) | ($true != ((X343 @ X353 @ X356 @ (comp @ X354 @ X355))))))) & (! [X344 : term,X343 : (subst > term > subst > $o)] : (? [X358 : term,X357 : subst,X359 : subst,X360 : subst] : (($true = ((X343 @ (comp @ X360 @ X357) @ (sub @ X358 @ X357) @ X359))) & ($true != ((X343 @ X360 @ X358 @ (comp @ X357 @ X359))))) | ($true = ((X343 @ id @ X344 @ id))) | ? [X345 : term,X346 : term] : (($true != ((X343 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id))) & ($true = ((X343 @ id @ X346 @ id))) & ($true = ((X343 @ id @ X345 @ id)))) | ($true = ((sP0 @ X343))) | ? [X352 : term] : (($true = ((var @ (sub @ X352 @ id)))) & ($true != ((X343 @ id @ X352 @ id)))) | ? [X354 : subst,X356 : term,X355 : subst,X353 : subst] : (($true != ((X343 @ (comp @ X353 @ X354) @ (sub @ X356 @ X354) @ X355))) & ($true = ((X343 @ X353 @ X356 @ (comp @ X354 @ X355)))))) | (hoasinduction != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & ((pushprop_lem1 = $true) | ? [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) = $true) & ($true != ((X3 @ (sub @ X5 @ (push @ X6 @ X4))))))) & (! [X7 : (term > $o),X5 : term,X6 : term,X3 : (term > $o),X4 : subst] : ((((X7 @ X5)) != $true) | ($true = ((X3 @ (sub @ X5 @ (push @ X6 @ X4)))))) | (pushprop_lem1 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X47 : subst,X48 : (term > $o),X46 : term] : ? [X49 : (term > $o)] : ! [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) = ((X49 @ X50))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X47 : subst,X48 : (term > $o),X46 : term] : ! [X49 : (term > $o)] : ? [X50 : term] : (((X48 @ (sub @ X50 @ (push @ X46 @ X47)))) != ((X49 @ X50)))) & (hoasinduction_lem3b_gthm = $true) & (! [X57 : subst] : (((comp @ id @ X57)) = X57) | (axidl != $true)) & ((axidl = $true) | ? [X57 : subst] : (((comp @ id @ X57)) != X57)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) | ? [X170 : (subst > term > subst > $o),X171 : term] : (! [X173 : (subst > term > term)] : (? [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) != ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) | (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) = $true) | ? [X177 : term] : (($true = ((X170 @ id @ X177 @ id))) & (((X170 @ id @ (X173 @ id @ X177) @ id)) != $true))) & ! [X172 : term] : (($true = ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) | (((X170 @ id @ X172 @ id)) != $true)) & (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) != $true))) & (! [X170 : (subst > term > subst > $o),X171 : term] : (? [X173 : (subst > term > term)] : (! [X174 : term,X175 : subst,X176 : subst] : (((sub @ (X173 @ X175 @ X174) @ X176)) = ((X173 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176)))) & (((X170 @ id @ (lam @ (X173 @ sh @ one)) @ id)) != $true) & ! [X177 : term] : (($true != ((X170 @ id @ X177 @ id))) | (((X170 @ id @ (X173 @ id @ X177) @ id)) = $true))) | ? [X172 : term] : (($true != ((X170 @ id @ (sub @ X171 @ (push @ X172 @ id)) @ id))) & (((X170 @ id @ X172 @ id)) = $true)) | (((X170 @ id @ (lam @ (sub @ X171 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) = $true) & ! [X496 : term] : (((X495 @ X496)) = ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) & ($true != ((X495 @ one)))) & ! [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) = X490))) & (! [X492 : (term > $o),X494 : term,X493 : subst,X495 : (term > $o)] : ((((X492 @ X494)) != $true) | ? [X496 : term] : (((X495 @ X496)) != ((X492 @ (sub @ X496 @ (push @ X494 @ X493))))) | ($true = ((X495 @ one)))) | ? [X490 : term,X491 : subst] : (((sub @ one @ (push @ X490 @ X491))) != X490) | (pushprop_lem1v2_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) = $true) | (((X253 @ id @ X255 @ id)) != $true) | ($true != ((X253 @ id @ X254 @ id))) | ? [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true = ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) & (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) != $true)) | ? [X265 : term,X264 : term] : (($true = ((X253 @ id @ X265 @ id))) & ($true != ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) & ($true = ((X253 @ id @ X264 @ id)))) | ? [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) = $true) & (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) != $true))) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ? [X255 : term,X254 : term,X253 : (subst > term > subst > $o)] : ((((X253 @ id @ (ap @ X254 @ X255) @ id)) != $true) & (((X253 @ id @ X255 @ id)) = $true) & ($true = ((X253 @ id @ X254 @ id))) & ! [X256 : subst,X257 : subst,X258 : subst,X259 : term] : (($true != ((X253 @ X258 @ X259 @ (comp @ X256 @ X257)))) | (((X253 @ (comp @ X258 @ X256) @ (sub @ X259 @ X256) @ X257)) = $true)) & ! [X265 : term,X264 : term] : (($true != ((X253 @ id @ X265 @ id))) | ($true = ((X253 @ id @ (ap @ (sub @ X264 @ id) @ X265) @ id))) | ($true != ((X253 @ id @ X264 @ id)))) & ! [X261 : subst,X260 : subst,X263 : term,X262 : subst] : ((((X253 @ (comp @ X262 @ X260) @ (sub @ X263 @ X260) @ X261)) != $true) | (((X253 @ X262 @ X263 @ (comp @ X260 @ X261))) = $true))))),
% 5.43/1.21 inference(flattening,[],[f62])).
% 5.43/1.21 thf(f64,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & (! [X0 : term] : (((sub @ X0 @ id)) = X0) | (termmset != $true)) & ((termmset = $true) | ? [X1 : term] : (((sub @ X1 @ id)) != X1)) & ((pushprop_lem1_lthm = $true) | (? [X2 : term,X3 : subst,X4 : (term > $o),X5 : (term > $o),X6 : term] : ((((X4 @ X2)) = $true) & (((X5 @ (sub @ X2 @ (push @ X6 @ X3)))) != $true)) & ! [X7 : term,X8 : subst] : (((comp @ sh @ (push @ X7 @ X8))) = X8) & ! [X9 : subst,X10 : term] : (((sub @ one @ (push @ X10 @ X9))) = X10))) & (! [X11 : term,X12 : subst,X13 : (term > $o),X14 : (term > $o),X15 : term] : (($true != ((X13 @ X11))) | (((X14 @ (sub @ X11 @ (push @ X15 @ X12)))) = $true)) | ? [X16 : term,X17 : subst] : (((comp @ sh @ (push @ X16 @ X17))) != X17) | ? [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) != X19) | (pushprop_lem1_lthm != $true)) & ! [X20 : d_term] : (d_one = X20) & (! [X21 : term,X22 : (subst > term > subst > $o)] : (? [X23 : term] : (($true = ((X22 @ id @ X23 @ id))) & ($true != ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) | ? [X24 : (subst > term > term),X25 : term] : (! [X26 : term] : ((((X22 @ id @ X26 @ id)) != $true) | ($true = ((X22 @ id @ (X24 @ id @ X26) @ id)))) & ! [X27 : subst,X28 : term,X29 : subst] : (((X24 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29))) = ((sub @ X25 @ (push @ (sub @ X28 @ X29) @ (comp @ X27 @ X29))))) & ($true != ((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id))) & ! [X30 : term,X31 : subst,X32 : subst] : (((sub @ (X24 @ X32 @ X30) @ X31)) = ((sub @ (sub @ X25 @ (push @ X30 @ X32)) @ X31)))) | (((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ? [X33 : term,X34 : (subst > term > subst > $o)] : (! [X35 : term] : ((((X34 @ id @ X35 @ id)) != $true) | (((X34 @ id @ (sub @ X33 @ (push @ X35 @ id)) @ id)) = $true)) & ! [X36 : (subst > term > term),X37 : term] : (? [X38 : term] : (($true = ((X34 @ id @ X38 @ id))) & ($true != ((X34 @ id @ (X36 @ id @ X38) @ id)))) | ? [X39 : subst,X40 : term,X41 : subst] : (((X36 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) != ((sub @ X37 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ($true = ((X34 @ id @ (lam @ (X36 @ sh @ one)) @ id))) | ? [X42 : term,X43 : subst,X44 : subst] : (((sub @ (X36 @ X44 @ X42) @ X43)) != ((sub @ (sub @ X37 @ (push @ X42 @ X44)) @ X43)))) & (((X34 @ id @ (lam @ (sub @ X33 @ (push @ one @ sh))) @ id)) != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lthm = $true) | ($true != sP10)) & (($true = sP10) | (hoasinduction_lthm != $true)) & (! [X45 : term,X46 : term] : ((((sub @ X45 @ sh)) != ((sub @ X46 @ sh))) | (X45 = X46)) | (shinj != $true)) & ((shinj = $true) | ? [X47 : term,X48 : term] : ((((sub @ X47 @ sh)) = ((sub @ X48 @ sh))) & (X47 != X48))) & (! [X49 : (term > $o),X50 : subst,X51 : (term > $o),X52 : term] : ((((X49 @ one)) = $true) | ? [X53 : term] : (((X51 @ (sub @ X53 @ (push @ X52 @ X50)))) != ((X49 @ X53))) | ($true != ((X51 @ X52)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X54 : (term > $o),X55 : subst,X56 : (term > $o),X57 : term] : (($true != ((X54 @ one))) & ! [X58 : term] : (((X54 @ X58)) = ((X56 @ (sub @ X58 @ (push @ X57 @ X55))))) & ($true = ((X56 @ X57))))) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & (! [X59 : term,X60 : (term > $o),X61 : (subst > term > subst > $o)] : (($true = ((X60 @ (lam @ X59)))) | ? [X62 : term] : (($true != ((X60 @ (sub @ X59 @ (push @ X62 @ id))))) & ($true = ((X60 @ X62)))) | ? [X63 : term] : (((X61 @ id @ X63 @ id)) != ((X60 @ X63))) | ? [X64 : subst,X65 : subst,X66 : term,X67 : subst] : (($true != ((X61 @ (comp @ X64 @ X65) @ (sub @ X66 @ X65) @ X67))) & (((X61 @ X64 @ X66 @ (comp @ X65 @ X67))) = $true)) | ? [X68 : (subst > term > term)] : (($true != ((X61 @ id @ (lam @ (X68 @ sh @ one)) @ id))) & ! [X69 : term,X70 : subst,X71 : subst] : (((X68 @ (comp @ X70 @ X71) @ (sub @ X69 @ X71))) = ((sub @ (X68 @ X70 @ X69) @ X71))) & ! [X72 : term] : (($true != ((X61 @ id @ X72 @ id))) | (((X61 @ id @ (X68 @ id @ X72) @ id)) = $true))) | ? [X73 : subst,X74 : subst,X75 : term,X76 : subst] : ((((X61 @ X74 @ X75 @ (comp @ X76 @ X73))) != $true) & (((X61 @ (comp @ X74 @ X76) @ (sub @ X75 @ X76) @ X73)) = $true))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | ? [X77 : term,X78 : (term > $o),X79 : (subst > term > subst > $o)] : (($true != ((X78 @ (lam @ X77)))) & ! [X80 : term] : (($true = ((X78 @ (sub @ X77 @ (push @ X80 @ id))))) | (((X78 @ X80)) != $true)) & ! [X81 : term] : (((X78 @ X81)) = ((X79 @ id @ X81 @ id))) & ! [X82 : subst,X83 : subst,X84 : term,X85 : subst] : (($true = ((X79 @ (comp @ X82 @ X83) @ (sub @ X84 @ X83) @ X85))) | ($true != ((X79 @ X82 @ X84 @ (comp @ X83 @ X85))))) & ! [X86 : (subst > term > term)] : ((((X79 @ id @ (lam @ (X86 @ sh @ one)) @ id)) = $true) | ? [X87 : term,X88 : subst,X89 : subst] : (((sub @ (X86 @ X88 @ X87) @ X89)) != ((X86 @ (comp @ X88 @ X89) @ (sub @ X87 @ X89)))) | ? [X90 : term] : ((((X79 @ id @ X90 @ id)) = $true) & ($true != ((X79 @ id @ (X86 @ id @ X90) @ id))))) & ! [X91 : subst,X92 : subst,X93 : term,X94 : subst] : ((((X79 @ X92 @ X93 @ (comp @ X94 @ X91))) = $true) | ($true != ((X79 @ (comp @ X92 @ X94) @ (sub @ X93 @ X94) @ X91)))))) & ((pushprop_lem0 = $true) | ? [X95 : subst,X96 : (term > $o),X97 : term] : ! [X98 : (term > $o)] : ? [X99 : term] : (((X98 @ X99)) != ((X96 @ (sub @ X99 @ (push @ X97 @ X95)))))) & (! [X100 : subst,X101 : (term > $o),X102 : term] : ? [X103 : (term > $o)] : ! [X104 : term] : (((X103 @ X104)) = ((X101 @ (sub @ X104 @ (push @ X102 @ X100))))) | (pushprop_lem0 != $true)) & ((axvarcons = $true) | ? [X105 : term,X106 : subst] : (((sub @ one @ (push @ X105 @ X106))) != X105)) & (! [X107 : term,X108 : subst] : (((sub @ one @ (push @ X107 @ X108))) = X107) | (axvarcons != $true)) & (! [X109 : subst] : (((push @ (sub @ one @ X109) @ (comp @ sh @ X109))) = X109) | (axscons != $true)) & ((axscons = $true) | ? [X110 : subst] : (((push @ (sub @ one @ X110) @ (comp @ sh @ X110))) != X110)) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1_lthm = $true) | (! [X111 : term,X112 : term,X113 : term,X114 : term] : ((X111 = X113) | (((ap @ X111 @ X114)) != ((ap @ X113 @ X112)))) & ? [X115 : term,X116 : term,X117 : term,X118 : term] : ((((ap @ (sub @ X116 @ id) @ X115)) = ((ap @ (sub @ X117 @ id) @ X118))) & (X116 != X117)) & ! [X119 : term] : (((sub @ X119 @ id)) = X119))) & (? [X120 : term,X121 : term,X122 : term,X123 : term] : ((X120 != X122) & (((ap @ X120 @ X123)) = ((ap @ X122 @ X121)))) | ! [X124 : term,X125 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X126 @ id) @ X127)) != ((ap @ (sub @ X125 @ id) @ X124))) | (X125 = X126)) | ? [X128 : term] : (((sub @ X128 @ id)) != X128) | (hoasapinj1_lthm != $true)) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((laminj = $true) | ? [X129 : term,X130 : term] : ((X129 != X130) & (((lam @ X130)) = ((lam @ X129))))) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X132)) != ((lam @ X131)))) | (laminj != $true)) & ((induction2lem = $true) | ? [X133 : (term > $o),X134 : subst,X135 : term] : (! [X136 : term] : ((((X133 @ (lam @ X136))) = $true) | ? [X137 : term] : (($true = ((X133 @ X137))) & ($true != ((X133 @ (sub @ X136 @ (push @ X137 @ id))))))) & ! [X138 : term,X139 : term] : (($true != ((X133 @ X138))) | (((X133 @ (ap @ X138 @ X139))) = $true) | ($true != ((X133 @ X139)))) & ! [X140 : term] : ((((X133 @ (sub @ X140 @ X134))) = $true) | ($true != ((var @ X140)))) & (((X133 @ (sub @ X135 @ X134))) != $true))) & (! [X141 : (term > $o),X142 : subst,X143 : term] : (? [X144 : term] : ((((X141 @ (lam @ X144))) != $true) & ! [X145 : term] : ((((X141 @ X145)) != $true) | ($true = ((X141 @ (sub @ X144 @ (push @ X145 @ id))))))) | ? [X146 : term,X147 : term] : (($true = ((X141 @ X146))) & (((X141 @ (ap @ X146 @ X147))) != $true) & ($true = ((X141 @ X147)))) | ? [X148 : term] : ((((X141 @ (sub @ X148 @ X142))) != $true) & ($true = ((var @ X148)))) | ($true = ((X141 @ (sub @ X143 @ X142))))) | (induction2lem != $true)) & (! [X149 : term,X150 : term,X151 : term,X152 : term] : ((X151 = X152) | (((ap @ (sub @ X152 @ id) @ X149)) != ((ap @ (sub @ X151 @ id) @ X150)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X153 : term,X154 : term,X155 : term,X156 : term] : ((X155 != X156) & (((ap @ (sub @ X156 @ id) @ X153)) = ((ap @ (sub @ X155 @ id) @ X154))))) & (pushprop_lem3v2_lthm = $true) & (! [X157 : (term > $o),X158 : term] : (? [X159 : term] : (($true != ((X157 @ X159))) & ($true = ((var @ X159)))) | ($true = ((X157 @ X158))) | ? [X160 : term,X161 : term] : ((((X157 @ (ap @ X160 @ X161))) != $true) & (((X157 @ X160)) = $true) & (((X157 @ X161)) = $true)) | ? [X162 : term] : ((((X157 @ (lam @ X162))) != $true) & ($true = ((X157 @ X162))))) | (induction != $true)) & ((induction = $true) | ? [X163 : (term > $o),X164 : term] : (! [X165 : term] : ((((X163 @ X165)) = $true) | ($true != ((var @ X165)))) & ($true != ((X163 @ X164))) & ! [X166 : term,X167 : term] : ((((X163 @ (ap @ X166 @ X167))) = $true) | ($true != ((X163 @ X166))) | ($true != ((X163 @ X167)))) & ! [X168 : term] : (($true = ((X163 @ (lam @ X168)))) | ($true != ((X163 @ X168)))))) & (hoaslamnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X169 : term,X170 : term,X171 : term,X172 : term] : ((X169 = X170) | (((ap @ X171 @ X170)) != ((ap @ X172 @ X169)))) & ? [X173 : term,X174 : term,X175 : term,X176 : term] : ((((ap @ (sub @ X175 @ id) @ X173)) = ((ap @ (sub @ X176 @ id) @ X174))) & (X173 != X174)))) & (? [X177 : term,X178 : term,X179 : term,X180 : term] : ((X177 != X178) & (((ap @ X179 @ X178)) = ((ap @ X180 @ X177)))) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((((ap @ (sub @ X183 @ id) @ X181)) != ((ap @ (sub @ X184 @ id) @ X182))) | (X181 = X182)) | (hoasapinj2_lthm != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) | ? [X185 : (subst > term > subst > $o),X186 : term] : (! [X187 : term] : (($true != ((X185 @ id @ X187 @ id))) | ($true = ((X185 @ id @ (sub @ X186 @ (push @ X187 @ id)) @ id)))) & (((X185 @ id @ (lam @ X186) @ id)) != $true) & ! [X188 : subst,X189 : subst,X190 : subst,X191 : term] : (($true != ((X185 @ (comp @ X188 @ X190) @ (sub @ X191 @ X190) @ X189))) | (((X185 @ X188 @ X191 @ (comp @ X190 @ X189))) = $true)) & ! [X192 : (subst > term > term)] : (? [X193 : term] : (($true = ((X185 @ id @ X193 @ id))) & (((X185 @ id @ (X192 @ id @ X193) @ id)) != $true)) | ($true = ((X185 @ id @ (lam @ (X192 @ sh @ one)) @ id))) | ? [X194 : subst,X195 : term,X196 : subst] : (((sub @ (X192 @ X194 @ X195) @ X196)) != ((X192 @ (comp @ X194 @ X196) @ (sub @ X195 @ X196))))) & ! [X197 : subst,X198 : term,X199 : subst,X200 : subst] : (($true != ((X185 @ X197 @ X198 @ (comp @ X200 @ X199)))) | ($true = ((X185 @ (comp @ X197 @ X200) @ (sub @ X198 @ X200) @ X199)))))) & (! [X201 : (subst > term > subst > $o),X202 : term] : (? [X203 : term] : (($true = ((X201 @ id @ X203 @ id))) & (((X201 @ id @ (sub @ X202 @ (push @ X203 @ id)) @ id)) != $true)) | (((X201 @ id @ (lam @ X202) @ id)) = $true) | ? [X204 : subst,X205 : subst,X206 : subst,X207 : term] : ((((X201 @ (comp @ X204 @ X206) @ (sub @ X207 @ X206) @ X205)) = $true) & ($true != ((X201 @ X204 @ X207 @ (comp @ X206 @ X205))))) | ? [X208 : (subst > term > term)] : (! [X209 : term] : (($true != ((X201 @ id @ X209 @ id))) | (((X201 @ id @ (X208 @ id @ X209) @ id)) = $true)) & (((X201 @ id @ (lam @ (X208 @ sh @ one)) @ id)) != $true) & ! [X210 : subst,X211 : term,X212 : subst] : (((sub @ (X208 @ X210 @ X211) @ X212)) = ((X208 @ (comp @ X210 @ X212) @ (sub @ X211 @ X212))))) | ? [X213 : subst,X214 : term,X215 : subst,X216 : subst] : (($true = ((X201 @ X213 @ X214 @ (comp @ X216 @ X215)))) & ($true != ((X201 @ (comp @ X213 @ X216) @ (sub @ X214 @ X216) @ X215))))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem2_lthm = $true) & ((induction2_lthm = $true) | ($true != sP6)) & (($true = sP6) | (induction2_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3b = $true) | ? [X217 : term] : ! [X218 : (subst > term > term)] : (((sub @ X217 @ (push @ one @ sh))) != ((X218 @ sh @ one)))) & (! [X219 : term] : ? [X220 : (subst > term > term)] : (((X220 @ sh @ one)) = ((sub @ X219 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (pushprop_lthm = $true) & ! [X221 : d_term,X222 : d_term] : ((X221 = X222) | (((d2term @ X222)) != ((d2term @ X221)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3v2_lthm = $true) | (! [X223 : term] : (((sub @ X223 @ id)) = X223) & ? [X224 : term,X225 : (term > $o),X226 : (subst > term > subst > $o)] : (! [X227 : term] : (((X226 @ id @ X227 @ id)) = ((X225 @ X227))) & ! [X228 : (subst > term > term)] : ((((X226 @ id @ (lam @ (X228 @ sh @ one)) @ id)) = $true) | ? [X229 : subst,X230 : term,X231 : subst] : (((X228 @ (comp @ X229 @ X231) @ (sub @ X230 @ X231))) != ((sub @ (X228 @ X229 @ X230) @ X231))) | ? [X232 : term] : (($true = ((X226 @ id @ X232 @ id))) & (((X226 @ id @ (X228 @ id @ X232) @ id)) != $true))) & ($true != ((X225 @ (lam @ X224)))) & ! [X233 : term] : (($true = ((X225 @ (sub @ X224 @ (push @ X233 @ id))))) | (((X225 @ X233)) != $true)) & ! [X234 : term,X235 : subst,X236 : subst,X237 : subst] : ((((X226 @ X236 @ X234 @ (comp @ X237 @ X235))) != $true) | (((X226 @ (comp @ X236 @ X237) @ (sub @ X234 @ X237) @ X235)) = $true)) & ! [X238 : subst,X239 : subst,X240 : term,X241 : subst] : (($true = ((X226 @ X241 @ X240 @ (comp @ X239 @ X238)))) | ($true != ((X226 @ (comp @ X241 @ X239) @ (sub @ X240 @ X239) @ X238))))))) & (? [X242 : term] : (((sub @ X242 @ id)) != X242) | ! [X243 : term,X244 : (term > $o),X245 : (subst > term > subst > $o)] : (? [X246 : term] : (((X245 @ id @ X246 @ id)) != ((X244 @ X246))) | ? [X247 : (subst > term > term)] : ((((X245 @ id @ (lam @ (X247 @ sh @ one)) @ id)) != $true) & ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (X247 @ X248 @ X249) @ X250)) = ((X247 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) & ! [X251 : term] : (($true != ((X245 @ id @ X251 @ id))) | ($true = ((X245 @ id @ (X247 @ id @ X251) @ id))))) | ($true = ((X244 @ (lam @ X243)))) | ? [X252 : term] : (($true != ((X244 @ (sub @ X243 @ (push @ X252 @ id))))) & (((X244 @ X252)) = $true)) | ? [X253 : term,X254 : subst,X255 : subst,X256 : subst] : ((((X245 @ X255 @ X253 @ (comp @ X256 @ X254))) = $true) & ($true != ((X245 @ (comp @ X255 @ X256) @ (sub @ X253 @ X256) @ X254)))) | ? [X257 : subst,X258 : subst,X259 : term,X260 : subst] : ((((X245 @ X260 @ X259 @ (comp @ X258 @ X257))) != $true) & ($true = ((X245 @ (comp @ X260 @ X258) @ (sub @ X259 @ X258) @ X257))))) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((! [X261 : subst] : (((comp @ X261 @ id)) = X261) & ! [X262 : subst] : (((comp @ id @ X262)) = X262)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X263 : subst] : (((comp @ X263 @ id)) != X263) | ? [X264 : subst] : (((comp @ id @ X264)) != X264)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X265 : (term > $o),X266 : term] : (? [X267 : term,X268 : term] : (($true != ((X265 @ (ap @ X268 @ X267)))) & (((X265 @ X267)) = $true) & ($true = ((X265 @ X268)))) | ? [X269 : term] : (($true != ((X265 @ (lam @ X269)))) & ! [X270 : term] : (($true = ((X265 @ (sub @ X269 @ (push @ X270 @ id))))) | ($true != ((X265 @ X270))))) | (((X265 @ X266)) = $true) | ? [X271 : term] : ((((var @ X271)) = $true) & ($true != ((X265 @ X271))))) & ! [X272 : (subst > term > subst > $o)] : ? [X273 : (term > $o)] : ! [X274 : term] : (((X272 @ id @ X274 @ id)) = ((X273 @ X274))) & ! [X275 : term,X276 : (subst > term > subst > $o),X277 : (term > $o)] : (($true = ((X277 @ (lam @ X275)))) | ? [X278 : term] : (($true != ((X277 @ (sub @ X275 @ (push @ X278 @ id))))) & ($true = ((X277 @ X278)))) | ? [X279 : term] : (((X277 @ X279)) != ((X276 @ id @ X279 @ id))) | ? [X280 : (subst > term > term)] : (! [X281 : term] : (($true = ((X276 @ id @ (X280 @ id @ X281) @ id))) | (((X276 @ id @ X281 @ id)) != $true)) & ($true != ((X276 @ id @ (lam @ (X280 @ sh @ one)) @ id))) & ! [X282 : term,X283 : subst,X284 : subst] : (((sub @ (X280 @ X284 @ X282) @ X283)) = ((X280 @ (comp @ X284 @ X283) @ (sub @ X282 @ X283)))))) & ! [X285 : term] : (((sub @ X285 @ id)) = X285) & ($true != sP5))) & (? [X286 : (term > $o),X287 : term] : (! [X288 : term,X289 : term] : ((((X286 @ (ap @ X289 @ X288))) = $true) | (((X286 @ X288)) != $true) | ($true != ((X286 @ X289)))) & ! [X290 : term] : (($true = ((X286 @ (lam @ X290)))) | ? [X291 : term] : (($true != ((X286 @ (sub @ X290 @ (push @ X291 @ id))))) & ($true = ((X286 @ X291))))) & (((X286 @ X287)) != $true) & ! [X292 : term] : ((((var @ X292)) != $true) | ($true = ((X286 @ X292))))) | ? [X293 : (subst > term > subst > $o)] : ! [X294 : (term > $o)] : ? [X295 : term] : (((X293 @ id @ X295 @ id)) != ((X294 @ X295))) | ? [X296 : term,X297 : (subst > term > subst > $o),X298 : (term > $o)] : ((((X298 @ (lam @ X296))) != $true) & ! [X299 : term] : (($true = ((X298 @ (sub @ X296 @ (push @ X299 @ id))))) | (((X298 @ X299)) != $true)) & ! [X300 : term] : (((X297 @ id @ X300 @ id)) = ((X298 @ X300))) & ! [X301 : (subst > term > term)] : (? [X302 : term] : (($true != ((X297 @ id @ (X301 @ id @ X302) @ id))) & (((X297 @ id @ X302 @ id)) = $true)) | (((X297 @ id @ (lam @ (X301 @ sh @ one)) @ id)) = $true) | ? [X303 : term,X304 : subst,X305 : subst] : (((X301 @ (comp @ X305 @ X304) @ (sub @ X303 @ X304))) != ((sub @ (X301 @ X305 @ X303) @ X304))))) | ? [X306 : term] : (((sub @ X306 @ id)) != X306) | ($true = sP5) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X307 : d_subst,X308 : d_subst] : ((X307 = X308) | (((d2subst @ X308)) != ((d2subst @ X307)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2a = $true) | ? [X309 : (term > $o),X310 : (subst > term > subst > $o),X311 : term] : (! [X312 : term] : (((X310 @ id @ X312 @ id)) = ((X309 @ X312))) & ($true != ((X309 @ (lam @ X311)))) & ! [X313 : term] : (($true = ((X309 @ (sub @ X311 @ (push @ X313 @ id))))) | ($true != ((X309 @ X313)))) & ! [X314 : (subst > term > term)] : (? [X315 : term] : (($true != ((X310 @ id @ (X314 @ id @ X315) @ id))) & ($true = ((X310 @ id @ X315 @ id)))) | ($true = ((X310 @ id @ (lam @ (X314 @ sh @ one)) @ id))) | ? [X316 : term,X317 : subst,X318 : subst] : (((sub @ (X314 @ X318 @ X316) @ X317)) != ((X314 @ (comp @ X318 @ X317) @ (sub @ X316 @ X317))))))) & (! [X319 : (term > $o),X320 : (subst > term > subst > $o),X321 : term] : (? [X322 : term] : (((X320 @ id @ X322 @ id)) != ((X319 @ X322))) | (((X319 @ (lam @ X321))) = $true) | ? [X323 : term] : ((((X319 @ (sub @ X321 @ (push @ X323 @ id)))) != $true) & ($true = ((X319 @ X323)))) | ? [X324 : (subst > term > term)] : (! [X325 : term] : (($true = ((X320 @ id @ (X324 @ id @ X325) @ id))) | ($true != ((X320 @ id @ X325 @ id)))) & (((X320 @ id @ (lam @ (X324 @ sh @ one)) @ id)) != $true) & ! [X326 : term,X327 : subst,X328 : subst] : (((X324 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327))) = ((sub @ (X324 @ X328 @ X326) @ X327))))) | (hoasinduction_lem3v2a != $true)) & (? [X329 : term,X330 : term] : ((((lam @ X329)) = ((lam @ X330))) & (X329 != X330)) | ! [X331 : (subst > term > term),X332 : (subst > term > term),X333 : subst,X334 : term] : (? [X335 : subst,X336 : subst,X337 : term] : (((X332 @ (comp @ X335 @ X336) @ (sub @ X337 @ X336))) != ((sub @ (X332 @ X335 @ X337) @ X336))) | (((lam @ (X331 @ sh @ one))) != ((lam @ (X332 @ sh @ one)))) | (((X332 @ X333 @ X334)) = ((X331 @ X333 @ X334))) | ? [X338 : subst,X339 : subst,X340 : term] : (((sub @ (X331 @ X338 @ X340) @ X339)) != ((X331 @ (comp @ X338 @ X339) @ (sub @ X340 @ X339))))) | ? [X341 : subst,X342 : term] : (((comp @ sh @ (push @ X342 @ X341))) != X341) | ? [X343 : term,X344 : subst] : (((sub @ one @ (push @ X343 @ X344))) != X343) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (! [X345 : term,X346 : term] : ((((lam @ X345)) != ((lam @ X346))) | (X345 = X346)) & ? [X347 : (subst > term > term),X348 : (subst > term > term),X349 : subst,X350 : term] : (! [X351 : subst,X352 : subst,X353 : term] : (((sub @ (X348 @ X351 @ X353) @ X352)) = ((X348 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352)))) & (((lam @ (X348 @ sh @ one))) = ((lam @ (X347 @ sh @ one)))) & (((X347 @ X349 @ X350)) != ((X348 @ X349 @ X350))) & ! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (X347 @ X354 @ X356) @ X355)) = ((X347 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355))))) & ! [X357 : subst,X358 : term] : (((comp @ sh @ (push @ X358 @ X357))) = X357) & ! [X359 : term,X360 : subst] : (((sub @ one @ (push @ X359 @ X360))) = X359))) & ((apinj1 = $true) | ? [X361 : term,X362 : term,X363 : term,X364 : term] : ((X361 != X363) & (((ap @ X363 @ X364)) = ((ap @ X361 @ X362))))) & (! [X365 : term,X366 : term,X367 : term,X368 : term] : ((X365 = X367) | (((ap @ X365 @ X366)) != ((ap @ X367 @ X368)))) | (apinj1 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X369 : (subst > term > subst > $o)] : ? [X370 : (term > $o)] : ! [X371 : term] : (((X369 @ id @ X371 @ id)) = ((X370 @ X371))) & ($true != sP4) & ! [X372 : term] : (((sub @ X372 @ id)) = X372) & ! [X373 : term,X374 : (term > $o)] : (? [X375 : term] : (($true != ((X374 @ (lam @ X375)))) & ! [X376 : term] : ((((X374 @ X376)) != $true) | (((X374 @ (sub @ X375 @ (push @ X376 @ id)))) = $true))) | (((X374 @ X373)) = $true) | ? [X377 : term] : (($true = ((var @ X377))) & (((X374 @ X377)) != $true)) | ? [X378 : term,X379 : term] : ((((X374 @ (ap @ X379 @ X378))) != $true) & ($true = ((X374 @ X378))) & ($true = ((X374 @ X379))))) & ! [X380 : term,X381 : (subst > term > subst > $o),X382 : (term > $o)] : (? [X383 : (subst > term > term)] : (($true != ((X381 @ id @ (lam @ (X383 @ sh @ one)) @ id))) & ! [X384 : term] : (($true = ((X381 @ id @ (X383 @ id @ X384) @ id))) | (((X381 @ id @ X384 @ id)) != $true)) & ! [X385 : subst,X386 : subst,X387 : term] : (((X383 @ (comp @ X385 @ X386) @ (sub @ X387 @ X386))) = ((sub @ (X383 @ X385 @ X387) @ X386)))) | ($true = ((X382 @ (lam @ X380)))) | ? [X388 : term] : (((X381 @ id @ X388 @ id)) != ((X382 @ X388))) | ? [X389 : term] : ((((X382 @ X389)) = $true) & (((X382 @ (sub @ X380 @ (push @ X389 @ id)))) != $true))))) & (? [X390 : (subst > term > subst > $o)] : ! [X391 : (term > $o)] : ? [X392 : term] : (((X390 @ id @ X392 @ id)) != ((X391 @ X392))) | ($true = sP4) | ? [X393 : term] : (((sub @ X393 @ id)) != X393) | ? [X394 : term,X395 : (term > $o)] : (! [X396 : term] : ((((X395 @ (lam @ X396))) = $true) | ? [X397 : term] : ((((X395 @ X397)) = $true) & ($true != ((X395 @ (sub @ X396 @ (push @ X397 @ id))))))) & ($true != ((X395 @ X394))) & ! [X398 : term] : (($true != ((var @ X398))) | (((X395 @ X398)) = $true)) & ! [X399 : term,X400 : term] : ((((X395 @ (ap @ X400 @ X399))) = $true) | (((X395 @ X399)) != $true) | ($true != ((X395 @ X400))))) | ? [X401 : term,X402 : (subst > term > subst > $o),X403 : (term > $o)] : (! [X404 : (subst > term > term)] : (($true = ((X402 @ id @ (lam @ (X404 @ sh @ one)) @ id))) | ? [X405 : term] : (($true != ((X402 @ id @ (X404 @ id @ X405) @ id))) & ($true = ((X402 @ id @ X405 @ id)))) | ? [X406 : subst,X407 : subst,X408 : term] : (((X404 @ (comp @ X406 @ X407) @ (sub @ X408 @ X407))) != ((sub @ (X404 @ X406 @ X408) @ X407)))) & (((X403 @ (lam @ X401))) != $true) & ! [X409 : term] : (((X402 @ id @ X409 @ id)) = ((X403 @ X409))) & ! [X410 : term] : (($true != ((X403 @ X410))) | ($true = ((X403 @ (sub @ X401 @ (push @ X410 @ id))))))) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X411 : term,X412 : (subst > term > subst > $o)] : (? [X413 : (subst > term > term)] : (! [X414 : term] : (($true != ((X412 @ id @ X414 @ id))) | ($true = ((X412 @ id @ (X413 @ id @ X414) @ id)))) & ($true != ((X412 @ id @ (lam @ (X413 @ sh @ one)) @ id))) & ! [X415 : term,X416 : subst,X417 : subst] : (((X413 @ (comp @ X417 @ X416) @ (sub @ X415 @ X416))) = ((sub @ (X413 @ X417 @ X415) @ X416)))) | (((X412 @ id @ (lam @ (sub @ X411 @ (push @ one @ sh))) @ id)) = $true) | ? [X418 : term] : ((((X412 @ id @ (sub @ X411 @ (push @ X418 @ id)) @ id)) != $true) & (((X412 @ id @ X418 @ id)) = $true))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ? [X419 : term,X420 : (subst > term > subst > $o)] : (! [X421 : (subst > term > term)] : (? [X422 : term] : (($true = ((X420 @ id @ X422 @ id))) & ($true != ((X420 @ id @ (X421 @ id @ X422) @ id)))) | (((X420 @ id @ (lam @ (X421 @ sh @ one)) @ id)) = $true) | ? [X423 : term,X424 : subst,X425 : subst] : (((sub @ (X421 @ X425 @ X423) @ X424)) != ((X421 @ (comp @ X425 @ X424) @ (sub @ X423 @ X424))))) & (((X420 @ id @ (lam @ (sub @ X419 @ (push @ one @ sh))) @ id)) != $true) & ! [X426 : term] : ((((X420 @ id @ (sub @ X419 @ (push @ X426 @ id)) @ id)) = $true) | (((X420 @ id @ X426 @ id)) != $true)))) & (? [X427 : (subst > term > subst > $o),X428 : term] : ((((X427 @ id @ (lam @ (sub @ X428 @ (push @ one @ sh))) @ id)) != $true) & ! [X429 : term] : (($true = ((X427 @ id @ (sub @ X428 @ (push @ X429 @ id)) @ id))) | ($true != ((X427 @ id @ X429 @ id)))) & ! [X430 : (subst > term > term)] : (? [X431 : subst,X432 : term,X433 : subst] : (((sub @ (X430 @ X431 @ X432) @ X433)) != ((X430 @ (comp @ X431 @ X433) @ (sub @ X432 @ X433)))) | ? [X434 : term] : (($true != ((X427 @ id @ (X430 @ id @ X434) @ id))) & ($true = ((X427 @ id @ X434 @ id)))) | (((X427 @ id @ (lam @ (X430 @ sh @ one)) @ id)) = $true))) | ? [X435 : term] : (((sub @ X435 @ id)) != X435) | ($true = sP2) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X436 : (subst > term > subst > $o),X437 : term] : ((((X436 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id)) = $true) | ? [X438 : term] : ((((X436 @ id @ (sub @ X437 @ (push @ X438 @ id)) @ id)) != $true) & (((X436 @ id @ X438 @ id)) = $true)) | ? [X439 : (subst > term > term)] : (! [X440 : subst,X441 : term,X442 : subst] : (((sub @ (X439 @ X440 @ X441) @ X442)) = ((X439 @ (comp @ X440 @ X442) @ (sub @ X441 @ X442)))) & ! [X443 : term] : (($true = ((X436 @ id @ (X439 @ id @ X443) @ id))) | (((X436 @ id @ X443 @ id)) != $true)) & ($true != ((X436 @ id @ (lam @ (X439 @ sh @ one)) @ id))))) & ! [X444 : term] : (((sub @ X444 @ id)) = X444) & ($true != sP2))) & (! [X445 : (subst > term > term),X446 : (subst > term > term),X447 : term,X448 : subst] : (? [X449 : subst,X450 : subst,X451 : term] : (((X445 @ (comp @ X450 @ X449) @ (sub @ X451 @ X449))) != ((sub @ (X445 @ X450 @ X451) @ X449))) | (((lam @ (X445 @ sh @ one))) != ((lam @ (X446 @ sh @ one)))) | ? [X452 : subst,X453 : subst,X454 : term] : (((sub @ (X446 @ X453 @ X454) @ X452)) != ((X446 @ (comp @ X453 @ X452) @ (sub @ X454 @ X452)))) | (((X445 @ X448 @ X447)) = ((X446 @ X448 @ X447)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X455 : (subst > term > term),X456 : (subst > term > term),X457 : term,X458 : subst] : (! [X459 : subst,X460 : subst,X461 : term] : (((sub @ (X455 @ X460 @ X461) @ X459)) = ((X455 @ (comp @ X460 @ X459) @ (sub @ X461 @ X459)))) & (((lam @ (X455 @ sh @ one))) = ((lam @ (X456 @ sh @ one)))) & ! [X462 : subst,X463 : subst,X464 : term] : (((sub @ (X456 @ X463 @ X464) @ X462)) = ((X456 @ (comp @ X463 @ X462) @ (sub @ X464 @ X462)))) & (((X455 @ X458 @ X457)) != ((X456 @ X458 @ X457))))) & (! [X465 : term] : ? [X466 : (subst > term > term)] : ! [X467 : term,X468 : subst] : (((X466 @ X468 @ X467)) = ((sub @ X465 @ (push @ X467 @ X468)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X469 : term] : ! [X470 : (subst > term > term)] : ? [X471 : term,X472 : subst] : (((X470 @ X472 @ X471)) != ((sub @ X469 @ (push @ X471 @ X472))))) & (! [X473 : term] : (((sub @ X473 @ id)) = X473) | (axvarid != $true)) & ((axvarid = $true) | ? [X474 : term] : (((sub @ X474 @ id)) != X474)) & ((hoasinduction_lem3b_lthm = $true) | ? [X475 : term] : ! [X476 : (subst > term > term)] : (((X476 @ sh @ one)) != ((sub @ X475 @ (push @ one @ sh))))) & (! [X477 : term] : ? [X478 : (subst > term > term)] : (((sub @ X477 @ (push @ one @ sh))) = ((X478 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (! [X479 : term] : ? [X480 : (subst > term > term)] : ! [X481 : subst,X482 : term] : (((X480 @ X481 @ X482)) = ((sub @ X479 @ (push @ X482 @ X481)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X483 : term] : ! [X484 : (subst > term > term)] : ? [X485 : subst,X486 : term] : (((sub @ X483 @ (push @ X486 @ X485))) != ((X484 @ X485 @ X486)))) & (lamnotvar = $true) & (pushprop = $true) & ((axshiftcons = $true) | ? [X487 : term,X488 : subst] : (((comp @ sh @ (push @ X487 @ X488))) != X488)) & (! [X489 : term,X490 : subst] : (((comp @ sh @ (push @ X489 @ X490))) = X490) | (axshiftcons != $true)) & (substmonoid_gthm = $true) & (! [X491 : (subst > term > subst > $o),X492 : (term > $o),X493 : term,X494 : term] : (($true = ((X492 @ (ap @ X494 @ X493)))) | (((X492 @ X494)) != $true) | ? [X495 : term] : (((X492 @ X495)) != ((X491 @ id @ X495 @ id))) | ? [X496 : subst,X497 : subst,X498 : term,X499 : subst] : (($true != ((X491 @ X496 @ X498 @ (comp @ X499 @ X497)))) & (((X491 @ (comp @ X496 @ X499) @ (sub @ X498 @ X499) @ X497)) = $true)) | ? [X500 : term,X501 : term] : ((((X491 @ id @ X500 @ id)) = $true) & ($true = ((X491 @ id @ X501 @ id))) & (((X491 @ id @ (ap @ (sub @ X501 @ id) @ X500) @ id)) != $true)) | (((X492 @ X493)) != $true) | ? [X502 : subst,X503 : subst,X504 : term,X505 : subst] : (($true = ((X491 @ X503 @ X504 @ (comp @ X505 @ X502)))) & ($true != ((X491 @ (comp @ X503 @ X505) @ (sub @ X504 @ X505) @ X502))))) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ? [X506 : (subst > term > subst > $o),X507 : (term > $o),X508 : term,X509 : term] : (($true != ((X507 @ (ap @ X509 @ X508)))) & ($true = ((X507 @ X509))) & ! [X510 : term] : (((X506 @ id @ X510 @ id)) = ((X507 @ X510))) & ! [X511 : subst,X512 : subst,X513 : term,X514 : subst] : ((((X506 @ X511 @ X513 @ (comp @ X514 @ X512))) = $true) | ($true != ((X506 @ (comp @ X511 @ X514) @ (sub @ X513 @ X514) @ X512)))) & ! [X515 : term,X516 : term] : (($true != ((X506 @ id @ X515 @ id))) | ($true != ((X506 @ id @ X516 @ id))) | ($true = ((X506 @ id @ (ap @ (sub @ X516 @ id) @ X515) @ id)))) & (((X507 @ X508)) = $true) & ! [X517 : subst,X518 : subst,X519 : term,X520 : subst] : (($true != ((X506 @ X518 @ X519 @ (comp @ X520 @ X517)))) | (((X506 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520) @ X517)) = $true)))) & (axvarshift = $true) & ! [X521 : term] : ? [X522 : d_term] : (((d2term @ X522)) = X521) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & ((substmonoid_lthm = $true) | (! [X523 : subst] : (((comp @ X523 @ id)) = X523) & ! [X524 : subst] : (((comp @ id @ X524)) = X524) & (? [X525 : subst] : (((comp @ X525 @ id)) != X525) | ? [X526 : subst] : (((comp @ id @ X526)) != X526)))) & (? [X527 : subst] : (((comp @ X527 @ id)) != X527) | ? [X528 : subst] : (((comp @ id @ X528)) != X528) | (! [X529 : subst] : (((comp @ X529 @ id)) = X529) & ! [X530 : subst] : (((comp @ id @ X530)) = X530)) | (substmonoid_lthm != $true)) & (! [X531 : term] : (((sub @ X531 @ id)) = X531) | ? [X532 : term] : (((sub @ X532 @ id)) != X532) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X533 : term] : (((sub @ X533 @ id)) != X533) & ! [X534 : term] : (((sub @ X534 @ id)) = X534))) & ((hoasinduction_lem0_lthm = $true) | ? [X535 : (subst > term > subst > $o)] : ! [X536 : (term > $o)] : ? [X537 : term] : (((X536 @ X537)) != ((X535 @ id @ X537 @ id)))) & (! [X538 : (subst > term > subst > $o)] : ? [X539 : (term > $o)] : ! [X540 : term] : (((X538 @ id @ X540 @ id)) = ((X539 @ X540))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X541 : term] : ? [X542 : (subst > term > term)] : ! [X543 : term,X544 : subst] : (((X542 @ X544 @ X543)) = ((sub @ X541 @ (push @ X543 @ X544)))) & ? [X545 : (term > $o),X546 : (subst > term > subst > $o),X547 : term] : (! [X548 : (subst > term > term)] : (? [X549 : subst,X550 : term,X551 : subst] : (((sub @ (X548 @ X549 @ X550) @ X551)) != ((X548 @ (comp @ X549 @ X551) @ (sub @ X550 @ X551)))) | (((X546 @ id @ (lam @ (X548 @ sh @ one)) @ id)) = $true) | ? [X552 : term] : ((((X546 @ id @ (X548 @ id @ X552) @ id)) != $true) & ($true = ((X546 @ id @ X552 @ id))))) & (((X545 @ (lam @ X547))) != $true) & ! [X553 : term] : (($true = ((X545 @ (sub @ X547 @ (push @ X553 @ id))))) | (((X545 @ X553)) != $true)) & ! [X554 : term] : (((X546 @ id @ X554 @ id)) = ((X545 @ X554)))) & ! [X555 : term] : (((sub @ X555 @ id)) = X555))) & (? [X556 : term] : ! [X557 : (subst > term > term)] : ? [X558 : term,X559 : subst] : (((X557 @ X559 @ X558)) != ((sub @ X556 @ (push @ X558 @ X559)))) | ! [X560 : (term > $o),X561 : (subst > term > subst > $o),X562 : term] : (? [X563 : (subst > term > term)] : (! [X564 : subst,X565 : term,X566 : subst] : (((X563 @ (comp @ X564 @ X566) @ (sub @ X565 @ X566))) = ((sub @ (X563 @ X564 @ X565) @ X566))) & ($true != ((X561 @ id @ (lam @ (X563 @ sh @ one)) @ id))) & ! [X567 : term] : ((((X561 @ id @ (X563 @ id @ X567) @ id)) = $true) | (((X561 @ id @ X567 @ id)) != $true))) | ($true = ((X560 @ (lam @ X562)))) | ? [X568 : term] : (($true != ((X560 @ (sub @ X562 @ (push @ X568 @ id))))) & (((X560 @ X568)) = $true)) | ? [X569 : term] : (((X560 @ X569)) != ((X561 @ id @ X569 @ id)))) | ? [X570 : term] : (((sub @ X570 @ id)) != X570) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X571 : subst] : ? [X572 : d_subst] : (((d2subst @ X572)) = X571) & (hoasapnotvar_lthm = $true) & (? [X573 : term] : (((sub @ X573 @ id)) != X573) | ! [X574 : term,X575 : (subst > term > subst > $o)] : (? [X576 : (subst > term > term)] : (! [X577 : term] : ((((X575 @ id @ (X576 @ id @ X577) @ id)) = $true) | (((X575 @ id @ X577 @ id)) != $true)) & ($true != ((X575 @ id @ (lam @ (X576 @ sh @ one)) @ id))) & ! [X578 : subst,X579 : subst,X580 : term] : (((X576 @ (comp @ X578 @ X579) @ (sub @ X580 @ X579))) = ((sub @ (X576 @ X578 @ X580) @ X579)))) | ? [X581 : term] : ((((X575 @ id @ (sub @ X574 @ (push @ X581 @ id)) @ id)) != $true) & ($true = ((X575 @ id @ X581 @ id)))) | ($true = ((X575 @ id @ (lam @ X574) @ id)))) | ? [X582 : (subst > term > subst > $o),X583 : term] : (($true != ((X582 @ id @ (lam @ (sub @ X583 @ (push @ one @ sh))) @ id))) & ! [X584 : term] : ((((X582 @ id @ X584 @ id)) != $true) | (((X582 @ id @ (sub @ X583 @ (push @ X584 @ id)) @ id)) = $true)) & ! [X585 : (subst > term > term)] : (? [X586 : subst,X587 : term,X588 : subst] : (((X585 @ (comp @ X586 @ X588) @ (sub @ X587 @ X588))) != ((sub @ (X585 @ X586 @ X587) @ X588))) | ? [X589 : term] : ((((X582 @ id @ (X585 @ id @ X589) @ id)) != $true) & ($true = ((X582 @ id @ X589 @ id)))) | ($true = ((X582 @ id @ (lam @ (X585 @ sh @ one)) @ id))))) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X590 : term] : (((sub @ X590 @ id)) = X590) & ? [X591 : term,X592 : (subst > term > subst > $o)] : (! [X593 : (subst > term > term)] : (? [X594 : term] : (($true != ((X592 @ id @ (X593 @ id @ X594) @ id))) & ($true = ((X592 @ id @ X594 @ id)))) | (((X592 @ id @ (lam @ (X593 @ sh @ one)) @ id)) = $true) | ? [X595 : subst,X596 : subst,X597 : term] : (((sub @ (X593 @ X595 @ X597) @ X596)) != ((X593 @ (comp @ X595 @ X596) @ (sub @ X597 @ X596))))) & ! [X598 : term] : ((((X592 @ id @ (sub @ X591 @ (push @ X598 @ id)) @ id)) = $true) | (((X592 @ id @ X598 @ id)) != $true)) & (((X592 @ id @ (lam @ X591) @ id)) != $true)) & ! [X599 : (subst > term > subst > $o),X600 : term] : (($true = ((X599 @ id @ (lam @ (sub @ X600 @ (push @ one @ sh))) @ id))) | ? [X601 : term] : (($true = ((X599 @ id @ X601 @ id))) & (((X599 @ id @ (sub @ X600 @ (push @ X601 @ id)) @ id)) != $true)) | ? [X602 : (subst > term > term)] : (! [X603 : subst,X604 : term,X605 : subst] : (((sub @ (X602 @ X603 @ X604) @ X605)) = ((X602 @ (comp @ X603 @ X605) @ (sub @ X604 @ X605)))) & ! [X606 : term] : (($true = ((X599 @ id @ (X602 @ id @ X606) @ id))) | ($true != ((X599 @ id @ X606 @ id)))) & ($true != ((X599 @ id @ (lam @ (X602 @ sh @ one)) @ id))))))) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X607 : d_subst] : (d_id = X607) & (! [X608 : term,X609 : (subst > term > term),X610 : term] : ((((lam @ (X609 @ sh @ one))) != ((ap @ (sub @ X610 @ id) @ X608))) | ? [X611 : term,X612 : subst,X613 : subst] : (((X609 @ (comp @ X612 @ X613) @ (sub @ X611 @ X613))) != ((sub @ (X609 @ X612 @ X611) @ X613)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X614 : term,X615 : (subst > term > term),X616 : term] : ((((ap @ (sub @ X616 @ id) @ X614)) = ((lam @ (X615 @ sh @ one)))) & ! [X617 : term,X618 : subst,X619 : subst] : (((sub @ (X615 @ X618 @ X617) @ X619)) = ((X615 @ (comp @ X618 @ X619) @ (sub @ X617 @ X619)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X620 : term,X621 : (subst > term > subst > $o)] : ((((X621 @ id @ (lam @ X620) @ id)) = $true) | ? [X622 : (subst > term > term)] : (! [X623 : term] : (($true != ((X621 @ id @ X623 @ id))) | ($true = ((X621 @ id @ (X622 @ id @ X623) @ id)))) & (((X621 @ id @ (lam @ (X622 @ sh @ one)) @ id)) != $true) & ! [X624 : term,X625 : subst,X626 : subst] : (((X622 @ (comp @ X625 @ X626) @ (sub @ X624 @ X626))) = ((sub @ (X622 @ X625 @ X624) @ X626)))) | ? [X627 : term] : (($true = ((X621 @ id @ X627 @ id))) & (((X621 @ id @ (sub @ X620 @ (push @ X627 @ id)) @ id)) != $true))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ? [X628 : term,X629 : (subst > term > subst > $o)] : (($true != ((X629 @ id @ (lam @ X628) @ id))) & ! [X630 : (subst > term > term)] : (? [X631 : term] : ((((X629 @ id @ X631 @ id)) = $true) & (((X629 @ id @ (X630 @ id @ X631) @ id)) != $true)) | ($true = ((X629 @ id @ (lam @ (X630 @ sh @ one)) @ id))) | ? [X632 : term,X633 : subst,X634 : subst] : (((sub @ (X630 @ X633 @ X632) @ X634)) != ((X630 @ (comp @ X633 @ X634) @ (sub @ X632 @ X634))))) & ! [X635 : term] : ((((X629 @ id @ X635 @ id)) != $true) | (((X629 @ id @ (sub @ X628 @ (push @ X635 @ id)) @ id)) = $true)))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (! [X636 : term,X637 : term,X638 : term,X639 : term] : ((((ap @ X639 @ X636)) != ((ap @ X637 @ X638))) | (X636 = X638)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X640 : term,X641 : term,X642 : term,X643 : term] : ((((ap @ X643 @ X640)) = ((ap @ X641 @ X642))) & (X640 != X642))) & (axassoc = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X644 : (subst > term > subst > $o),X645 : term] : (! [X646 : term,X647 : term] : (($true != ((X644 @ id @ X646 @ id))) | (((X644 @ id @ (ap @ (sub @ X647 @ id) @ X646) @ id)) = $true) | ($true != ((X644 @ id @ X647 @ id)))) & ! [X648 : (subst > term > term)] : (($true = ((X644 @ id @ (lam @ (X648 @ sh @ one)) @ id))) | ? [X649 : term] : (($true != ((X644 @ id @ (X648 @ id @ X649) @ id))) & (((X644 @ id @ X649 @ id)) = $true)) | ? [X650 : subst,X651 : subst,X652 : term] : (((X648 @ (comp @ X650 @ X651) @ (sub @ X652 @ X651))) != ((sub @ (X648 @ X650 @ X652) @ X651)))) & ($true != ((X644 @ id @ X645 @ id))))) & (! [X653 : (subst > term > subst > $o),X654 : term] : (? [X655 : term,X656 : term] : ((((X653 @ id @ X655 @ id)) = $true) & ($true != ((X653 @ id @ (ap @ (sub @ X656 @ id) @ X655) @ id))) & ($true = ((X653 @ id @ X656 @ id)))) | ? [X657 : (subst > term > term)] : (($true != ((X653 @ id @ (lam @ (X657 @ sh @ one)) @ id))) & ! [X658 : term] : ((((X653 @ id @ (X657 @ id @ X658) @ id)) = $true) | (((X653 @ id @ X658 @ id)) != $true)) & ! [X659 : subst,X660 : subst,X661 : term] : (((X657 @ (comp @ X659 @ X660) @ (sub @ X661 @ X660))) = ((sub @ (X657 @ X659 @ X661) @ X660)))) | ($true = ((X653 @ id @ X654 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (! [X662 : subst] : (((comp @ X662 @ id)) = X662) | (axidr != $true)) & ((axidr = $true) | ? [X663 : subst] : (((comp @ X663 @ id)) != X663)) & ((induction2 = $true) | ? [X664 : term,X665 : (term > $o)] : (! [X666 : term] : (($true = ((X665 @ (lam @ X666)))) | ? [X667 : term] : ((((X665 @ X667)) = $true) & ($true != ((X665 @ (sub @ X666 @ (push @ X667 @ id))))))) & ! [X668 : term] : ((((var @ X668)) != $true) | (((X665 @ X668)) = $true)) & ! [X669 : term,X670 : term] : (($true != ((X665 @ X669))) | ($true = ((X665 @ (ap @ X669 @ X670)))) | (((X665 @ X670)) != $true)) & ($true != ((X665 @ X664))))) & (! [X671 : term,X672 : (term > $o)] : (? [X673 : term] : ((((X672 @ (lam @ X673))) != $true) & ! [X674 : term] : (($true != ((X672 @ X674))) | (((X672 @ (sub @ X673 @ (push @ X674 @ id)))) = $true))) | ? [X675 : term] : (($true = ((var @ X675))) & ($true != ((X672 @ X675)))) | ? [X676 : term,X677 : term] : (($true = ((X672 @ X676))) & (((X672 @ (ap @ X676 @ X677))) != $true) & ($true = ((X672 @ X677)))) | (((X672 @ X671)) = $true)) | (induction2 != $true)) & (pushprop_lem3v2 = $true) & (! [X678 : term,X679 : term,X680 : term,X681 : term] : ((((ap @ (sub @ X681 @ id) @ X678)) != ((ap @ (sub @ X679 @ id) @ X680))) | (X678 = X680)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X682 : term,X683 : term,X684 : term,X685 : term] : ((((ap @ (sub @ X685 @ id) @ X682)) = ((ap @ (sub @ X683 @ id) @ X684))) & (X682 != X684))) & (ulamvar1 != $true) & (lamnotap != $true) & (! [X686 : (subst > term > subst > $o)] : ? [X687 : (term > $o)] : ! [X688 : term] : (((X687 @ X688)) = ((X686 @ id @ X688 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X689 : (subst > term > subst > $o)] : ! [X690 : (term > $o)] : ? [X691 : term] : (((X690 @ X691)) != ((X689 @ id @ X691 @ id)))) & (pushprop_lem1v2_gthm = $true) & (($true = sP1) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & ((hoasinduction = $true) | ? [X692 : term,X693 : (subst > term > subst > $o)] : (! [X694 : term,X695 : subst,X696 : subst,X697 : subst] : (($true != ((X693 @ (comp @ X697 @ X695) @ (sub @ X694 @ X695) @ X696))) | (((X693 @ X697 @ X694 @ (comp @ X695 @ X696))) = $true)) & (((X693 @ id @ X692 @ id)) != $true) & ! [X698 : term,X699 : term] : ((((X693 @ id @ (ap @ (sub @ X698 @ id) @ X699) @ id)) = $true) | (((X693 @ id @ X699 @ id)) != $true) | (((X693 @ id @ X698 @ id)) != $true)) & ($true != ((sP0 @ X693))) & ! [X700 : term] : ((((var @ (sub @ X700 @ id))) != $true) | ($true = ((X693 @ id @ X700 @ id)))) & ! [X701 : subst,X702 : term,X703 : subst,X704 : subst] : ((((X693 @ (comp @ X704 @ X701) @ (sub @ X702 @ X701) @ X703)) = $true) | ($true != ((X693 @ X704 @ X702 @ (comp @ X701 @ X703))))))) & (! [X705 : term,X706 : (subst > term > subst > $o)] : (? [X707 : term,X708 : subst,X709 : subst,X710 : subst] : ((((X706 @ (comp @ X710 @ X708) @ (sub @ X707 @ X708) @ X709)) = $true) & (((X706 @ X710 @ X707 @ (comp @ X708 @ X709))) != $true)) | ($true = ((X706 @ id @ X705 @ id))) | ? [X711 : term,X712 : term] : ((((X706 @ id @ (ap @ (sub @ X711 @ id) @ X712) @ id)) != $true) & (((X706 @ id @ X712 @ id)) = $true) & (((X706 @ id @ X711 @ id)) = $true)) | ($true = ((sP0 @ X706))) | ? [X713 : term] : (($true = ((var @ (sub @ X713 @ id)))) & (((X706 @ id @ X713 @ id)) != $true)) | ? [X714 : subst,X715 : term,X716 : subst,X717 : subst] : (($true != ((X706 @ (comp @ X717 @ X714) @ (sub @ X715 @ X714) @ X716))) & (((X706 @ X717 @ X715 @ (comp @ X714 @ X716))) = $true))) | (hoasinduction != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & ((pushprop_lem1 = $true) | ? [X718 : (term > $o),X719 : term,X720 : term,X721 : (term > $o),X722 : subst] : (($true = ((X718 @ X719))) & (((X721 @ (sub @ X719 @ (push @ X720 @ X722)))) != $true))) & (! [X723 : (term > $o),X724 : term,X725 : term,X726 : (term > $o),X727 : subst] : (($true != ((X723 @ X724))) | ($true = ((X726 @ (sub @ X724 @ (push @ X725 @ X727)))))) | (pushprop_lem1 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X728 : subst,X729 : (term > $o),X730 : term] : ? [X731 : (term > $o)] : ! [X732 : term] : (((X731 @ X732)) = ((X729 @ (sub @ X732 @ (push @ X730 @ X728))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X733 : subst,X734 : (term > $o),X735 : term] : ! [X736 : (term > $o)] : ? [X737 : term] : (((X734 @ (sub @ X737 @ (push @ X735 @ X733)))) != ((X736 @ X737)))) & (hoasinduction_lem3b_gthm = $true) & (! [X738 : subst] : (((comp @ id @ X738)) = X738) | (axidl != $true)) & ((axidl = $true) | ? [X739 : subst] : (((comp @ id @ X739)) != X739)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) | ? [X740 : (subst > term > subst > $o),X741 : term] : (! [X742 : (subst > term > term)] : (? [X743 : term,X744 : subst,X745 : subst] : (((X742 @ (comp @ X744 @ X745) @ (sub @ X743 @ X745))) != ((sub @ (X742 @ X744 @ X743) @ X745))) | ($true = ((X740 @ id @ (lam @ (X742 @ sh @ one)) @ id))) | ? [X746 : term] : (($true = ((X740 @ id @ X746 @ id))) & ($true != ((X740 @ id @ (X742 @ id @ X746) @ id))))) & ! [X747 : term] : ((((X740 @ id @ (sub @ X741 @ (push @ X747 @ id)) @ id)) = $true) | ($true != ((X740 @ id @ X747 @ id)))) & (((X740 @ id @ (lam @ (sub @ X741 @ (push @ one @ sh))) @ id)) != $true))) & (! [X748 : (subst > term > subst > $o),X749 : term] : (? [X750 : (subst > term > term)] : (! [X751 : term,X752 : subst,X753 : subst] : (((sub @ (X750 @ X752 @ X751) @ X753)) = ((X750 @ (comp @ X752 @ X753) @ (sub @ X751 @ X753)))) & (((X748 @ id @ (lam @ (X750 @ sh @ one)) @ id)) != $true) & ! [X754 : term] : (($true != ((X748 @ id @ X754 @ id))) | (((X748 @ id @ (X750 @ id @ X754) @ id)) = $true))) | ? [X755 : term] : ((((X748 @ id @ (sub @ X749 @ (push @ X755 @ id)) @ id)) != $true) & ($true = ((X748 @ id @ X755 @ id)))) | (((X748 @ id @ (lam @ (sub @ X749 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X756 : (term > $o),X757 : term,X758 : subst,X759 : (term > $o)] : (($true = ((X756 @ X757))) & ! [X760 : term] : (((X759 @ X760)) = ((X756 @ (sub @ X760 @ (push @ X757 @ X758))))) & ($true != ((X759 @ one)))) & ! [X761 : term,X762 : subst] : (((sub @ one @ (push @ X761 @ X762))) = X761))) & (! [X763 : (term > $o),X764 : term,X765 : subst,X766 : (term > $o)] : ((((X763 @ X764)) != $true) | ? [X767 : term] : (((X766 @ X767)) != ((X763 @ (sub @ X767 @ (push @ X764 @ X765))))) | ($true = ((X766 @ one)))) | ? [X768 : term,X769 : subst] : (((sub @ one @ (push @ X768 @ X769))) != X768) | (pushprop_lem1v2_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X770 : term,X771 : term,X772 : (subst > term > subst > $o)] : (($true = ((X772 @ id @ (ap @ X771 @ X770) @ id))) | ($true != ((X772 @ id @ X770 @ id))) | (((X772 @ id @ X771 @ id)) != $true) | ? [X773 : subst,X774 : subst,X775 : subst,X776 : term] : (($true = ((X772 @ X775 @ X776 @ (comp @ X773 @ X774)))) & ($true != ((X772 @ (comp @ X775 @ X773) @ (sub @ X776 @ X773) @ X774)))) | ? [X777 : term,X778 : term] : (($true = ((X772 @ id @ X777 @ id))) & (((X772 @ id @ (ap @ (sub @ X778 @ id) @ X777) @ id)) != $true) & ($true = ((X772 @ id @ X778 @ id)))) | ? [X779 : subst,X780 : subst,X781 : term,X782 : subst] : ((((X772 @ (comp @ X782 @ X780) @ (sub @ X781 @ X780) @ X779)) = $true) & (((X772 @ X782 @ X781 @ (comp @ X780 @ X779))) != $true))) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ? [X783 : term,X784 : term,X785 : (subst > term > subst > $o)] : (($true != ((X785 @ id @ (ap @ X784 @ X783) @ id))) & (((X785 @ id @ X783 @ id)) = $true) & (((X785 @ id @ X784 @ id)) = $true) & ! [X786 : subst,X787 : subst,X788 : subst,X789 : term] : (($true != ((X785 @ X788 @ X789 @ (comp @ X786 @ X787)))) | ($true = ((X785 @ (comp @ X788 @ X786) @ (sub @ X789 @ X786) @ X787)))) & ! [X790 : term,X791 : term] : (($true != ((X785 @ id @ X790 @ id))) | (((X785 @ id @ (ap @ (sub @ X791 @ id) @ X790) @ id)) = $true) | (((X785 @ id @ X791 @ id)) != $true)) & ! [X792 : subst,X793 : subst,X794 : term,X795 : subst] : ((((X785 @ (comp @ X795 @ X793) @ (sub @ X794 @ X793) @ X792)) != $true) | ($true = ((X785 @ X795 @ X794 @ (comp @ X793 @ X792)))))))),
% 5.43/1.21 inference(rectify,[],[f63])).
% 5.43/1.21 thf(f65,plain,(
% 5.43/1.21 (hoasinduction_lem1_lthm = $true) & (! [X0 : term] : (((sub @ X0 @ id)) = X0) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK148 @ id)) != sK148)) & ((pushprop_lem1_lthm = $true) | ((($true = ((sK151 @ sK149))) & ($true != ((sK152 @ (sub @ sK149 @ (push @ sK153 @ sK150)))))) & ! [X7 : term,X8 : subst] : (((comp @ sh @ (push @ X7 @ X8))) = X8) & ! [X9 : subst,X10 : term] : (((sub @ one @ (push @ X10 @ X9))) = X10))) & (! [X11 : term,X12 : subst,X13 : (term > $o),X14 : (term > $o),X15 : term] : (($true != ((X13 @ X11))) | (((X14 @ (sub @ X11 @ (push @ X15 @ X12)))) = $true)) | (sK155 != ((comp @ sh @ (push @ sK154 @ sK155)))) | (((sub @ one @ (push @ sK157 @ sK156))) != sK157) | (pushprop_lem1_lthm != $true)) & ! [X20 : d_term] : (d_one = X20) & (! [X21 : term,X22 : (subst > term > subst > $o)] : (((((X22 @ id @ (sK158 @ X22 @ X21) @ id)) = $true) & ($true != ((X22 @ id @ (sub @ X21 @ (push @ (sK158 @ X22 @ X21) @ id)) @ id)))) | (! [X26 : term] : ((((X22 @ id @ X26 @ id)) != $true) | ($true = ((X22 @ id @ (sK159 @ X22 @ id @ X26) @ id)))) & ! [X27 : subst,X28 : term,X29 : subst] : (((sK159 @ X22 @ (comp @ X27 @ X29) @ (sub @ X28 @ X29))) = ((sub @ (sK160 @ X22) @ (push @ (sub @ X28 @ X29) @ (comp @ X27 @ X29))))) & ($true != ((X22 @ id @ (lam @ (sK159 @ X22 @ sh @ one)) @ id))) & ! [X30 : term,X31 : subst,X32 : subst] : (((sub @ (sK159 @ X22 @ X32 @ X30) @ X31)) = ((sub @ (sub @ (sK160 @ X22) @ (push @ X30 @ X32)) @ X31)))) | (((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (! [X35 : term] : (($true != ((sK162 @ id @ X35 @ id))) | (((sK162 @ id @ (sub @ sK161 @ (push @ X35 @ id)) @ id)) = $true)) & ! [X36 : (subst > term > term),X37 : term] : ((($true = ((sK162 @ id @ (sK163 @ X36) @ id))) & (((sK162 @ id @ (X36 @ id @ (sK163 @ X36)) @ id)) != $true)) | (((sub @ X37 @ (push @ (sub @ (sK165 @ X37 @ X36) @ (sK166 @ X37 @ X36)) @ (comp @ (sK164 @ X37 @ X36) @ (sK166 @ X37 @ X36))))) != ((X36 @ (comp @ (sK164 @ X37 @ X36) @ (sK166 @ X37 @ X36)) @ (sub @ (sK165 @ X37 @ X36) @ (sK166 @ X37 @ X36))))) | ($true = ((sK162 @ id @ (lam @ (X36 @ sh @ one)) @ id))) | (((sub @ (sub @ X37 @ (push @ (sK167 @ X37 @ X36) @ (sK169 @ X37 @ X36))) @ (sK168 @ X37 @ X36))) != ((sub @ (X36 @ (sK169 @ X37 @ X36) @ (sK167 @ X37 @ X36)) @ (sK168 @ X37 @ X36))))) & ($true != ((sK162 @ id @ (lam @ (sub @ sK161 @ (push @ one @ sh))) @ id))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasapinj2_gthm = $true) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lthm = $true) | ($true != sP10)) & (($true = sP10) | (hoasinduction_lthm != $true)) & (! [X45 : term,X46 : term] : ((((sub @ X45 @ sh)) != ((sub @ X46 @ sh))) | (X45 = X46)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK170 @ sh)) = ((sub @ sK171 @ sh))) & (sK170 != sK171))) & (! [X49 : (term > $o),X50 : subst,X51 : (term > $o),X52 : term] : ((((X49 @ one)) = $true) | (((X49 @ (sK172 @ X52 @ X51 @ X50 @ X49))) != ((X51 @ (sub @ (sK172 @ X52 @ X51 @ X50 @ X49) @ (push @ X52 @ X50))))) | ($true != ((X51 @ X52)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true != ((sK173 @ one))) & ! [X58 : term] : (((sK175 @ (sub @ X58 @ (push @ sK176 @ sK174)))) = ((sK173 @ X58))) & (((sK175 @ sK176)) = $true))) & (pushprop_gthm = $true) & (axclos = $true) & (induction2_gthm = $true) & (! [X59 : term,X60 : (term > $o),X61 : (subst > term > subst > $o)] : (($true = ((X60 @ (lam @ X59)))) | (($true != ((X60 @ (sub @ X59 @ (push @ (sK177 @ X60 @ X59) @ id))))) & ($true = ((X60 @ (sK177 @ X60 @ X59))))) | (((X61 @ id @ (sK178 @ X61 @ X60) @ id)) != ((X60 @ (sK178 @ X61 @ X60)))) | (($true != ((X61 @ (comp @ (sK179 @ X61) @ (sK180 @ X61)) @ (sub @ (sK181 @ X61) @ (sK180 @ X61)) @ (sK182 @ X61)))) & ($true = ((X61 @ (sK179 @ X61) @ (sK181 @ X61) @ (comp @ (sK180 @ X61) @ (sK182 @ X61)))))) | ((((X61 @ id @ (lam @ (sK183 @ X61 @ sh @ one)) @ id)) != $true) & ! [X69 : term,X70 : subst,X71 : subst] : (((sub @ (sK183 @ X61 @ X70 @ X69) @ X71)) = ((sK183 @ X61 @ (comp @ X70 @ X71) @ (sub @ X69 @ X71)))) & ! [X72 : term] : (($true != ((X61 @ id @ X72 @ id))) | (((X61 @ id @ (sK183 @ X61 @ id @ X72) @ id)) = $true))) | ((((X61 @ (sK185 @ X61) @ (sK186 @ X61) @ (comp @ (sK187 @ X61) @ (sK184 @ X61)))) != $true) & ($true = ((X61 @ (comp @ (sK185 @ X61) @ (sK187 @ X61)) @ (sub @ (sK186 @ X61) @ (sK187 @ X61)) @ (sK184 @ X61)))))) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (($true != ((sK189 @ (lam @ sK188)))) & ! [X80 : term] : (($true = ((sK189 @ (sub @ sK188 @ (push @ X80 @ id))))) | (((sK189 @ X80)) != $true)) & ! [X81 : term] : (((sK190 @ id @ X81 @ id)) = ((sK189 @ X81))) & ! [X82 : subst,X83 : subst,X84 : term,X85 : subst] : (($true = ((sK190 @ (comp @ X82 @ X83) @ (sub @ X84 @ X83) @ X85))) | ($true != ((sK190 @ X82 @ X84 @ (comp @ X83 @ X85))))) & ! [X86 : (subst > term > term)] : (($true = ((sK190 @ id @ (lam @ (X86 @ sh @ one)) @ id))) | (((X86 @ (comp @ (sK192 @ X86) @ (sK193 @ X86)) @ (sub @ (sK191 @ X86) @ (sK193 @ X86)))) != ((sub @ (X86 @ (sK192 @ X86) @ (sK191 @ X86)) @ (sK193 @ X86)))) | (($true = ((sK190 @ id @ (sK194 @ X86) @ id))) & (((sK190 @ id @ (X86 @ id @ (sK194 @ X86)) @ id)) != $true))) & ! [X91 : subst,X92 : subst,X93 : term,X94 : subst] : (($true = ((sK190 @ X92 @ X93 @ (comp @ X94 @ X91)))) | ($true != ((sK190 @ (comp @ X92 @ X94) @ (sub @ X93 @ X94) @ X91)))))) & ((pushprop_lem0 = $true) | ! [X98 : (term > $o)] : (((sK196 @ (sub @ (sK198 @ X98) @ (push @ sK197 @ sK195)))) != ((X98 @ (sK198 @ X98))))) & (! [X100 : subst,X101 : (term > $o),X102 : term] : ! [X104 : term] : (((sK199 @ X102 @ X101 @ X100 @ X104)) = ((X101 @ (sub @ X104 @ (push @ X102 @ X100))))) | (pushprop_lem0 != $true)) & ((axvarcons = $true) | (sK200 != ((sub @ one @ (push @ sK200 @ sK201))))) & (! [X107 : term,X108 : subst] : (((sub @ one @ (push @ X107 @ X108))) = X107) | (axvarcons != $true)) & (! [X109 : subst] : (((push @ (sub @ one @ X109) @ (comp @ sh @ X109))) = X109) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK202) @ (comp @ sh @ sK202))) != sK202)) & (ulamvarsh = $true) & (ulamvarind = $true) & (((d2subst @ d_id)) = sh) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1_lthm = $true) | (! [X111 : term,X112 : term,X113 : term,X114 : term] : ((X111 = X113) | (((ap @ X111 @ X114)) != ((ap @ X113 @ X112)))) & ((((ap @ (sub @ sK205 @ id) @ sK206)) = ((ap @ (sub @ sK204 @ id) @ sK203))) & (sK205 != sK204)) & ! [X119 : term] : (((sub @ X119 @ id)) = X119))) & (((sK209 != sK207) & (((ap @ sK207 @ sK210)) = ((ap @ sK209 @ sK208)))) | ! [X124 : term,X125 : term,X126 : term,X127 : term] : ((((ap @ (sub @ X126 @ id) @ X127)) != ((ap @ (sub @ X125 @ id) @ X124))) | (X125 = X126)) | (sK211 != ((sub @ sK211 @ id))) | (hoasapinj1_lthm != $true)) & (axabs = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((laminj = $true) | ((sK213 != sK212) & (((lam @ sK212)) = ((lam @ sK213))))) & (! [X131 : term,X132 : term] : ((X131 = X132) | (((lam @ X132)) != ((lam @ X131)))) | (laminj != $true)) & ((induction2lem = $true) | (! [X136 : term] : (($true = ((sK214 @ (lam @ X136)))) | ((((sK214 @ (sK217 @ X136))) = $true) & ($true != ((sK214 @ (sub @ X136 @ (push @ (sK217 @ X136) @ id))))))) & ! [X138 : term,X139 : term] : (($true != ((sK214 @ X138))) | ($true = ((sK214 @ (ap @ X138 @ X139)))) | (((sK214 @ X139)) != $true)) & ! [X140 : term] : ((((sK214 @ (sub @ X140 @ sK215))) = $true) | ($true != ((var @ X140)))) & (((sK214 @ (sub @ sK216 @ sK215))) != $true))) & (! [X141 : (term > $o),X142 : subst,X143 : term] : ((($true != ((X141 @ (lam @ (sK218 @ X141))))) & ! [X145 : term] : ((((X141 @ X145)) != $true) | ($true = ((X141 @ (sub @ (sK218 @ X141) @ (push @ X145 @ id))))))) | ((((X141 @ (sK219 @ X141))) = $true) & ($true != ((X141 @ (ap @ (sK219 @ X141) @ (sK220 @ X141))))) & (((X141 @ (sK220 @ X141))) = $true)) | ((((X141 @ (sub @ (sK221 @ X142 @ X141) @ X142))) != $true) & ($true = ((var @ (sK221 @ X142 @ X141))))) | ($true = ((X141 @ (sub @ X143 @ X142))))) | (induction2lem != $true)) & (! [X149 : term,X150 : term,X151 : term,X152 : term] : ((X151 = X152) | (((ap @ (sub @ X152 @ id) @ X149)) != ((ap @ (sub @ X151 @ id) @ X150)))) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((sK224 != sK225) & (((ap @ (sub @ sK224 @ id) @ sK223)) = ((ap @ (sub @ sK225 @ id) @ sK222))))) & (pushprop_lem3v2_lthm = $true) & (! [X157 : (term > $o),X158 : term] : ((($true != ((X157 @ (sK226 @ X157)))) & (((var @ (sK226 @ X157))) = $true)) | ($true = ((X157 @ X158))) | (($true != ((X157 @ (ap @ (sK227 @ X157) @ (sK228 @ X157))))) & ($true = ((X157 @ (sK227 @ X157)))) & (((X157 @ (sK228 @ X157))) = $true)) | (($true != ((X157 @ (lam @ (sK229 @ X157))))) & ($true = ((X157 @ (sK229 @ X157)))))) | (induction != $true)) & ((induction = $true) | (! [X165 : term] : ((((sK230 @ X165)) = $true) | ($true != ((var @ X165)))) & ($true != ((sK230 @ sK231))) & ! [X166 : term,X167 : term] : (($true = ((sK230 @ (ap @ X166 @ X167)))) | (((sK230 @ X166)) != $true) | ($true != ((sK230 @ X167)))) & ! [X168 : term] : (($true = ((sK230 @ (lam @ X168)))) | ($true != ((sK230 @ X168)))))) & (hoaslamnotvar_gthm = $true) & ((hoasapinj2_lthm = $true) | (! [X169 : term,X170 : term,X171 : term,X172 : term] : ((X169 = X170) | (((ap @ X171 @ X170)) != ((ap @ X172 @ X169)))) & ((((ap @ (sub @ sK234 @ id) @ sK232)) = ((ap @ (sub @ sK235 @ id) @ sK233))) & (sK233 != sK232)))) & (((sK236 != sK237) & (((ap @ sK239 @ sK236)) = ((ap @ sK238 @ sK237)))) | ! [X181 : term,X182 : term,X183 : term,X184 : term] : ((((ap @ (sub @ X183 @ id) @ X181)) != ((ap @ (sub @ X184 @ id) @ X182))) | (X181 = X182)) | (hoasapinj2_lthm != $true)) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3 = $true) | (! [X187 : term] : ((((sK240 @ id @ X187 @ id)) != $true) | (((sK240 @ id @ (sub @ sK241 @ (push @ X187 @ id)) @ id)) = $true)) & ($true != ((sK240 @ id @ (lam @ sK241) @ id))) & ! [X188 : subst,X189 : subst,X190 : subst,X191 : term] : (($true != ((sK240 @ (comp @ X188 @ X190) @ (sub @ X191 @ X190) @ X189))) | (((sK240 @ X188 @ X191 @ (comp @ X190 @ X189))) = $true)) & ! [X192 : (subst > term > term)] : ((($true = ((sK240 @ id @ (sK242 @ X192) @ id))) & ($true != ((sK240 @ id @ (X192 @ id @ (sK242 @ X192)) @ id)))) | ($true = ((sK240 @ id @ (lam @ (X192 @ sh @ one)) @ id))) | (((sub @ (X192 @ (sK243 @ X192) @ (sK244 @ X192)) @ (sK245 @ X192))) != ((X192 @ (comp @ (sK243 @ X192) @ (sK245 @ X192)) @ (sub @ (sK244 @ X192) @ (sK245 @ X192)))))) & ! [X197 : subst,X198 : term,X199 : subst,X200 : subst] : (($true != ((sK240 @ X197 @ X198 @ (comp @ X200 @ X199)))) | ($true = ((sK240 @ (comp @ X197 @ X200) @ (sub @ X198 @ X200) @ X199)))))) & (! [X201 : (subst > term > subst > $o),X202 : term] : (((((X201 @ id @ (sK246 @ X202 @ X201) @ id)) = $true) & ($true != ((X201 @ id @ (sub @ X202 @ (push @ (sK246 @ X202 @ X201) @ id)) @ id)))) | (((X201 @ id @ (lam @ X202) @ id)) = $true) | (($true = ((X201 @ (comp @ (sK247 @ X201) @ (sK249 @ X201)) @ (sub @ (sK250 @ X201) @ (sK249 @ X201)) @ (sK248 @ X201)))) & (((X201 @ (sK247 @ X201) @ (sK250 @ X201) @ (comp @ (sK249 @ X201) @ (sK248 @ X201)))) != $true)) | (! [X209 : term] : (($true != ((X201 @ id @ X209 @ id))) | ($true = ((X201 @ id @ (sK251 @ X201 @ id @ X209) @ id)))) & ($true != ((X201 @ id @ (lam @ (sK251 @ X201 @ sh @ one)) @ id))) & ! [X210 : subst,X211 : term,X212 : subst] : (((sK251 @ X201 @ (comp @ X210 @ X212) @ (sub @ X211 @ X212))) = ((sub @ (sK251 @ X201 @ X210 @ X211) @ X212)))) | (($true = ((X201 @ (sK252 @ X201) @ (sK253 @ X201) @ (comp @ (sK255 @ X201) @ (sK254 @ X201))))) & ($true != ((X201 @ (comp @ (sK252 @ X201) @ (sK255 @ X201)) @ (sub @ (sK253 @ X201) @ (sK255 @ X201)) @ (sK254 @ X201)))))) | (hoasinduction_lem3 != $true)) & (hoasinduction_lem2_lthm = $true) & ((induction2_lthm = $true) | ($true != sP6)) & (($true = sP6) | (induction2_lthm != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem3b = $true) | ! [X218 : (subst > term > term)] : (((X218 @ sh @ one)) != ((sub @ sK256 @ (push @ one @ sh))))) & (! [X219 : term] : (((sK257 @ X219 @ sh @ one)) = ((sub @ X219 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (pushprop_lthm = $true) & ! [X221 : d_term,X222 : d_term] : ((X221 = X222) | (((d2term @ X222)) != ((d2term @ X221)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ((hoasinduction_lem3v2_lthm = $true) | (! [X223 : term] : (((sub @ X223 @ id)) = X223) & (! [X227 : term] : (((sK260 @ id @ X227 @ id)) = ((sK259 @ X227))) & ! [X228 : (subst > term > term)] : ((((sK260 @ id @ (lam @ (X228 @ sh @ one)) @ id)) = $true) | (((X228 @ (comp @ (sK261 @ X228) @ (sK263 @ X228)) @ (sub @ (sK262 @ X228) @ (sK263 @ X228)))) != ((sub @ (X228 @ (sK261 @ X228) @ (sK262 @ X228)) @ (sK263 @ X228)))) | ((((sK260 @ id @ (sK264 @ X228) @ id)) = $true) & (((sK260 @ id @ (X228 @ id @ (sK264 @ X228)) @ id)) != $true))) & ($true != ((sK259 @ (lam @ sK258)))) & ! [X233 : term] : ((((sK259 @ (sub @ sK258 @ (push @ X233 @ id)))) = $true) | (((sK259 @ X233)) != $true)) & ! [X234 : term,X235 : subst,X236 : subst,X237 : subst] : (($true != ((sK260 @ X236 @ X234 @ (comp @ X237 @ X235)))) | (((sK260 @ (comp @ X236 @ X237) @ (sub @ X234 @ X237) @ X235)) = $true)) & ! [X238 : subst,X239 : subst,X240 : term,X241 : subst] : (($true = ((sK260 @ X241 @ X240 @ (comp @ X239 @ X238)))) | ($true != ((sK260 @ (comp @ X241 @ X239) @ (sub @ X240 @ X239) @ X238))))))) & ((((sub @ sK265 @ id)) != sK265) | ! [X243 : term,X244 : (term > $o),X245 : (subst > term > subst > $o)] : ((((X244 @ (sK266 @ X245 @ X244))) != ((X245 @ id @ (sK266 @ X245 @ X244) @ id))) | (($true != ((X245 @ id @ (lam @ (sK267 @ X245 @ sh @ one)) @ id))) & ! [X248 : subst,X249 : term,X250 : subst] : (((sub @ (sK267 @ X245 @ X248 @ X249) @ X250)) = ((sK267 @ X245 @ (comp @ X248 @ X250) @ (sub @ X249 @ X250)))) & ! [X251 : term] : (($true != ((X245 @ id @ X251 @ id))) | ($true = ((X245 @ id @ (sK267 @ X245 @ id @ X251) @ id))))) | ($true = ((X244 @ (lam @ X243)))) | (($true != ((X244 @ (sub @ X243 @ (push @ (sK268 @ X244 @ X243) @ id))))) & ($true = ((X244 @ (sK268 @ X244 @ X243))))) | (($true = ((X245 @ (sK271 @ X245) @ (sK269 @ X245) @ (comp @ (sK272 @ X245) @ (sK270 @ X245))))) & (((X245 @ (comp @ (sK271 @ X245) @ (sK272 @ X245)) @ (sub @ (sK269 @ X245) @ (sK272 @ X245)) @ (sK270 @ X245))) != $true)) | ((((X245 @ (sK276 @ X245) @ (sK275 @ X245) @ (comp @ (sK274 @ X245) @ (sK273 @ X245)))) != $true) & ($true = ((X245 @ (comp @ (sK276 @ X245) @ (sK274 @ X245)) @ (sub @ (sK275 @ X245) @ (sK274 @ X245)) @ (sK273 @ X245)))))) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & ((! [X261 : subst] : (((comp @ X261 @ id)) = X261) & ! [X262 : subst] : (((comp @ id @ X262)) = X262)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ sK277 @ id)) != sK277) | (((comp @ id @ sK278)) != sK278)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X265 : (term > $o),X266 : term] : (((((X265 @ (ap @ (sK280 @ X265) @ (sK279 @ X265)))) != $true) & (((X265 @ (sK279 @ X265))) = $true) & ($true = ((X265 @ (sK280 @ X265))))) | (($true != ((X265 @ (lam @ (sK281 @ X265))))) & ! [X270 : term] : ((((X265 @ (sub @ (sK281 @ X265) @ (push @ X270 @ id)))) = $true) | ($true != ((X265 @ X270))))) | (((X265 @ X266)) = $true) | ((((var @ (sK282 @ X265))) = $true) & (((X265 @ (sK282 @ X265))) != $true))) & ! [X272 : (subst > term > subst > $o)] : ! [X274 : term] : (((X272 @ id @ X274 @ id)) = ((sK283 @ X272 @ X274))) & ! [X275 : term,X276 : (subst > term > subst > $o),X277 : (term > $o)] : (($true = ((X277 @ (lam @ X275)))) | ((((X277 @ (sub @ X275 @ (push @ (sK284 @ X277 @ X275) @ id)))) != $true) & ($true = ((X277 @ (sK284 @ X277 @ X275))))) | (((X276 @ id @ (sK285 @ X277 @ X276) @ id)) != ((X277 @ (sK285 @ X277 @ X276)))) | (! [X281 : term] : (($true = ((X276 @ id @ (sK286 @ X276 @ id @ X281) @ id))) | (((X276 @ id @ X281 @ id)) != $true)) & (((X276 @ id @ (lam @ (sK286 @ X276 @ sh @ one)) @ id)) != $true) & ! [X282 : term,X283 : subst,X284 : subst] : (((sK286 @ X276 @ (comp @ X284 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (sK286 @ X276 @ X284 @ X282) @ X283))))) & ! [X285 : term] : (((sub @ X285 @ id)) = X285) & ($true != sP5))) & ((! [X288 : term,X289 : term] : (($true = ((sK287 @ (ap @ X289 @ X288)))) | (((sK287 @ X288)) != $true) | (((sK287 @ X289)) != $true)) & ! [X290 : term] : (($true = ((sK287 @ (lam @ X290)))) | ((((sK287 @ (sub @ X290 @ (push @ (sK289 @ X290) @ id)))) != $true) & ($true = ((sK287 @ (sK289 @ X290)))))) & (((sK287 @ sK288)) != $true) & ! [X292 : term] : ((((var @ X292)) != $true) | (((sK287 @ X292)) = $true))) | ! [X294 : (term > $o)] : (((X294 @ (sK291 @ X294))) != ((sK290 @ id @ (sK291 @ X294) @ id))) | ((((sK294 @ (lam @ sK292))) != $true) & ! [X299 : term] : (($true = ((sK294 @ (sub @ sK292 @ (push @ X299 @ id))))) | ($true != ((sK294 @ X299)))) & ! [X300 : term] : (((sK294 @ X300)) = ((sK293 @ id @ X300 @ id))) & ! [X301 : (subst > term > term)] : (((((sK293 @ id @ (X301 @ id @ (sK295 @ X301)) @ id)) != $true) & ($true = ((sK293 @ id @ (sK295 @ X301) @ id)))) | ($true = ((sK293 @ id @ (lam @ (X301 @ sh @ one)) @ id))) | (((sub @ (X301 @ (sK298 @ X301) @ (sK296 @ X301)) @ (sK297 @ X301))) != ((X301 @ (comp @ (sK298 @ X301) @ (sK297 @ X301)) @ (sub @ (sK296 @ X301) @ (sK297 @ X301))))))) | (sK299 != ((sub @ sK299 @ id))) | ($true = sP5) | (hoasinduction_no_psi_cond_lthm != $true)) & ! [X307 : d_subst,X308 : d_subst] : ((X307 = X308) | (((d2subst @ X308)) != ((d2subst @ X307)))) & (hoaslaminj_gthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2a = $true) | (! [X312 : term] : (((sK301 @ id @ X312 @ id)) = ((sK300 @ X312))) & (((sK300 @ (lam @ sK302))) != $true) & ! [X313 : term] : ((((sK300 @ (sub @ sK302 @ (push @ X313 @ id)))) = $true) | (((sK300 @ X313)) != $true)) & ! [X314 : (subst > term > term)] : ((($true != ((sK301 @ id @ (X314 @ id @ (sK303 @ X314)) @ id))) & (((sK301 @ id @ (sK303 @ X314) @ id)) = $true)) | (((sK301 @ id @ (lam @ (X314 @ sh @ one)) @ id)) = $true) | (((X314 @ (comp @ (sK306 @ X314) @ (sK305 @ X314)) @ (sub @ (sK304 @ X314) @ (sK305 @ X314)))) != ((sub @ (X314 @ (sK306 @ X314) @ (sK304 @ X314)) @ (sK305 @ X314))))))) & (! [X319 : (term > $o),X320 : (subst > term > subst > $o),X321 : term] : ((((X320 @ id @ (sK307 @ X320 @ X319) @ id)) != ((X319 @ (sK307 @ X320 @ X319)))) | (((X319 @ (lam @ X321))) = $true) | (($true != ((X319 @ (sub @ X321 @ (push @ (sK308 @ X321 @ X319) @ id))))) & ($true = ((X319 @ (sK308 @ X321 @ X319))))) | (! [X325 : term] : (($true = ((X320 @ id @ (sK309 @ X320 @ id @ X325) @ id))) | ($true != ((X320 @ id @ X325 @ id)))) & ($true != ((X320 @ id @ (lam @ (sK309 @ X320 @ sh @ one)) @ id))) & ! [X326 : term,X327 : subst,X328 : subst] : (((sub @ (sK309 @ X320 @ X328 @ X326) @ X327)) = ((sK309 @ X320 @ (comp @ X328 @ X327) @ (sub @ X326 @ X327)))))) | (hoasinduction_lem3v2a != $true)) & (((((lam @ sK310)) = ((lam @ sK311))) & (sK310 != sK311)) | ! [X331 : (subst > term > term),X332 : (subst > term > term),X333 : subst,X334 : term] : ((((X332 @ (comp @ (sK312 @ X332) @ (sK313 @ X332)) @ (sub @ (sK314 @ X332) @ (sK313 @ X332)))) != ((sub @ (X332 @ (sK312 @ X332) @ (sK314 @ X332)) @ (sK313 @ X332)))) | (((lam @ (X331 @ sh @ one))) != ((lam @ (X332 @ sh @ one)))) | (((X332 @ X333 @ X334)) = ((X331 @ X333 @ X334))) | (((X331 @ (comp @ (sK315 @ X331) @ (sK316 @ X331)) @ (sub @ (sK317 @ X331) @ (sK316 @ X331)))) != ((sub @ (X331 @ (sK315 @ X331) @ (sK317 @ X331)) @ (sK316 @ X331))))) | (((comp @ sh @ (push @ sK319 @ sK318))) != sK318) | (((sub @ one @ (push @ sK320 @ sK321))) != sK320) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (! [X345 : term,X346 : term] : ((((lam @ X345)) != ((lam @ X346))) | (X345 = X346)) & (! [X351 : subst,X352 : subst,X353 : term] : (((sK323 @ (comp @ X351 @ X352) @ (sub @ X353 @ X352))) = ((sub @ (sK323 @ X351 @ X353) @ X352))) & (((lam @ (sK322 @ sh @ one))) = ((lam @ (sK323 @ sh @ one)))) & (((sK323 @ sK324 @ sK325)) != ((sK322 @ sK324 @ sK325))) & ! [X354 : subst,X355 : subst,X356 : term] : (((sub @ (sK322 @ X354 @ X356) @ X355)) = ((sK322 @ (comp @ X354 @ X355) @ (sub @ X356 @ X355))))) & ! [X357 : subst,X358 : term] : (((comp @ sh @ (push @ X358 @ X357))) = X357) & ! [X359 : term,X360 : subst] : (((sub @ one @ (push @ X359 @ X360))) = X359))) & ((apinj1 = $true) | ((sK328 != sK326) & (((ap @ sK326 @ sK327)) = ((ap @ sK328 @ sK329))))) & (! [X365 : term,X366 : term,X367 : term,X368 : term] : ((X365 = X367) | (((ap @ X365 @ X366)) != ((ap @ X367 @ X368)))) | (apinj1 != $true)) & ((hoasinduction_lthm_3 = $true) | (! [X369 : (subst > term > subst > $o)] : ! [X371 : term] : (((X369 @ id @ X371 @ id)) = ((sK330 @ X369 @ X371))) & ($true != sP4) & ! [X372 : term] : (((sub @ X372 @ id)) = X372) & ! [X373 : term,X374 : (term > $o)] : (((((X374 @ (lam @ (sK331 @ X374)))) != $true) & ! [X376 : term] : ((((X374 @ X376)) != $true) | ($true = ((X374 @ (sub @ (sK331 @ X374) @ (push @ X376 @ id))))))) | (((X374 @ X373)) = $true) | (($true = ((var @ (sK332 @ X374)))) & ($true != ((X374 @ (sK332 @ X374))))) | (($true != ((X374 @ (ap @ (sK334 @ X374) @ (sK333 @ X374))))) & ($true = ((X374 @ (sK333 @ X374)))) & ($true = ((X374 @ (sK334 @ X374)))))) & ! [X380 : term,X381 : (subst > term > subst > $o),X382 : (term > $o)] : ((($true != ((X381 @ id @ (lam @ (sK335 @ X381 @ sh @ one)) @ id))) & ! [X384 : term] : (($true = ((X381 @ id @ (sK335 @ X381 @ id @ X384) @ id))) | (((X381 @ id @ X384 @ id)) != $true)) & ! [X385 : subst,X386 : subst,X387 : term] : (((sub @ (sK335 @ X381 @ X385 @ X387) @ X386)) = ((sK335 @ X381 @ (comp @ X385 @ X386) @ (sub @ X387 @ X386))))) | ($true = ((X382 @ (lam @ X380)))) | (((X381 @ id @ (sK336 @ X382 @ X381) @ id)) != ((X382 @ (sK336 @ X382 @ X381)))) | ((((X382 @ (sK337 @ X382 @ X380))) = $true) & (((X382 @ (sub @ X380 @ (push @ (sK337 @ X382 @ X380) @ id)))) != $true))))) & (! [X391 : (term > $o)] : (((X391 @ (sK339 @ X391))) != ((sK338 @ id @ (sK339 @ X391) @ id))) | ($true = sP4) | (((sub @ sK340 @ id)) != sK340) | (! [X396 : term] : ((((sK342 @ (lam @ X396))) = $true) | ((((sK342 @ (sK343 @ X396))) = $true) & ($true != ((sK342 @ (sub @ X396 @ (push @ (sK343 @ X396) @ id))))))) & (((sK342 @ sK341)) != $true) & ! [X398 : term] : (($true != ((var @ X398))) | ($true = ((sK342 @ X398)))) & ! [X399 : term,X400 : term] : (($true = ((sK342 @ (ap @ X400 @ X399)))) | ($true != ((sK342 @ X399))) | ($true != ((sK342 @ X400))))) | (! [X404 : (subst > term > term)] : ((((sK345 @ id @ (lam @ (X404 @ sh @ one)) @ id)) = $true) | ((((sK345 @ id @ (X404 @ id @ (sK347 @ X404)) @ id)) != $true) & (((sK345 @ id @ (sK347 @ X404) @ id)) = $true)) | (((sub @ (X404 @ (sK348 @ X404) @ (sK350 @ X404)) @ (sK349 @ X404))) != ((X404 @ (comp @ (sK348 @ X404) @ (sK349 @ X404)) @ (sub @ (sK350 @ X404) @ (sK349 @ X404)))))) & (((sK346 @ (lam @ sK344))) != $true) & ! [X409 : term] : (((sK346 @ X409)) = ((sK345 @ id @ X409 @ id))) & ! [X410 : term] : (($true != ((sK346 @ X410))) | (((sK346 @ (sub @ sK344 @ (push @ X410 @ id)))) = $true))) | (hoasinduction_lthm_3 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X411 : term,X412 : (subst > term > subst > $o)] : ((! [X414 : term] : (($true != ((X412 @ id @ X414 @ id))) | (((X412 @ id @ (sK351 @ X412 @ id @ X414) @ id)) = $true)) & (((X412 @ id @ (lam @ (sK351 @ X412 @ sh @ one)) @ id)) != $true) & ! [X415 : term,X416 : subst,X417 : subst] : (((sub @ (sK351 @ X412 @ X417 @ X415) @ X416)) = ((sK351 @ X412 @ (comp @ X417 @ X416) @ (sub @ X415 @ X416))))) | (((X412 @ id @ (lam @ (sub @ X411 @ (push @ one @ sh))) @ id)) = $true) | ((((X412 @ id @ (sub @ X411 @ (push @ (sK352 @ X412 @ X411) @ id)) @ id)) != $true) & ($true = ((X412 @ id @ (sK352 @ X412 @ X411) @ id))))) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (! [X421 : (subst > term > term)] : (((((sK354 @ id @ (sK355 @ X421) @ id)) = $true) & ($true != ((sK354 @ id @ (X421 @ id @ (sK355 @ X421)) @ id)))) | ($true = ((sK354 @ id @ (lam @ (X421 @ sh @ one)) @ id))) | (((sub @ (X421 @ (sK358 @ X421) @ (sK356 @ X421)) @ (sK357 @ X421))) != ((X421 @ (comp @ (sK358 @ X421) @ (sK357 @ X421)) @ (sub @ (sK356 @ X421) @ (sK357 @ X421)))))) & (((sK354 @ id @ (lam @ (sub @ sK353 @ (push @ one @ sh))) @ id)) != $true) & ! [X426 : term] : (($true = ((sK354 @ id @ (sub @ sK353 @ (push @ X426 @ id)) @ id))) | ($true != ((sK354 @ id @ X426 @ id)))))) & (((((sK359 @ id @ (lam @ (sub @ sK360 @ (push @ one @ sh))) @ id)) != $true) & ! [X429 : term] : (($true = ((sK359 @ id @ (sub @ sK360 @ (push @ X429 @ id)) @ id))) | (((sK359 @ id @ X429 @ id)) != $true)) & ! [X430 : (subst > term > term)] : ((((sub @ (X430 @ (sK361 @ X430) @ (sK362 @ X430)) @ (sK363 @ X430))) != ((X430 @ (comp @ (sK361 @ X430) @ (sK363 @ X430)) @ (sub @ (sK362 @ X430) @ (sK363 @ X430))))) | ((((sK359 @ id @ (X430 @ id @ (sK364 @ X430)) @ id)) != $true) & ($true = ((sK359 @ id @ (sK364 @ X430) @ id)))) | ($true = ((sK359 @ id @ (lam @ (X430 @ sh @ one)) @ id))))) | (sK365 != ((sub @ sK365 @ id))) | ($true = sP2) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction_lem3_lthm = $true) | (! [X436 : (subst > term > subst > $o),X437 : term] : ((((X436 @ id @ (lam @ (sub @ X437 @ (push @ one @ sh))) @ id)) = $true) | (($true != ((X436 @ id @ (sub @ X437 @ (push @ (sK366 @ X437 @ X436) @ id)) @ id))) & ($true = ((X436 @ id @ (sK366 @ X437 @ X436) @ id)))) | (! [X440 : subst,X441 : term,X442 : subst] : (((sK367 @ X436 @ (comp @ X440 @ X442) @ (sub @ X441 @ X442))) = ((sub @ (sK367 @ X436 @ X440 @ X441) @ X442))) & ! [X443 : term] : (($true = ((X436 @ id @ (sK367 @ X436 @ id @ X443) @ id))) | (((X436 @ id @ X443 @ id)) != $true)) & (((X436 @ id @ (lam @ (sK367 @ X436 @ sh @ one)) @ id)) != $true))) & ! [X444 : term] : (((sub @ X444 @ id)) = X444) & ($true != sP2))) & (! [X445 : (subst > term > term),X446 : (subst > term > term),X447 : term,X448 : subst] : ((((sub @ (X445 @ (sK369 @ X445) @ (sK370 @ X445)) @ (sK368 @ X445))) != ((X445 @ (comp @ (sK369 @ X445) @ (sK368 @ X445)) @ (sub @ (sK370 @ X445) @ (sK368 @ X445))))) | (((lam @ (X445 @ sh @ one))) != ((lam @ (X446 @ sh @ one)))) | (((X446 @ (comp @ (sK372 @ X446) @ (sK371 @ X446)) @ (sub @ (sK373 @ X446) @ (sK371 @ X446)))) != ((sub @ (X446 @ (sK372 @ X446) @ (sK373 @ X446)) @ (sK371 @ X446)))) | (((X445 @ X448 @ X447)) = ((X446 @ X448 @ X447)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X459 : subst,X460 : subst,X461 : term] : (((sub @ (sK374 @ X460 @ X461) @ X459)) = ((sK374 @ (comp @ X460 @ X459) @ (sub @ X461 @ X459)))) & (((lam @ (sK375 @ sh @ one))) = ((lam @ (sK374 @ sh @ one)))) & ! [X462 : subst,X463 : subst,X464 : term] : (((sK375 @ (comp @ X463 @ X462) @ (sub @ X464 @ X462))) = ((sub @ (sK375 @ X463 @ X464) @ X462))) & (((sK375 @ sK377 @ sK376)) != ((sK374 @ sK377 @ sK376))))) & (! [X465 : term] : ! [X467 : term,X468 : subst] : (((sK378 @ X465 @ X468 @ X467)) = ((sub @ X465 @ (push @ X467 @ X468)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X470 : (subst > term > term)] : (((sub @ sK379 @ (push @ (sK380 @ X470) @ (sK381 @ X470)))) != ((X470 @ (sK381 @ X470) @ (sK380 @ X470))))) & (! [X473 : term] : (((sub @ X473 @ id)) = X473) | (axvarid != $true)) & ((axvarid = $true) | (((sub @ sK382 @ id)) != sK382)) & ((hoasinduction_lem3b_lthm = $true) | ! [X476 : (subst > term > term)] : (((X476 @ sh @ one)) != ((sub @ sK383 @ (push @ one @ sh))))) & (! [X477 : term] : (((sK384 @ X477 @ sh @ one)) = ((sub @ X477 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (! [X479 : term] : ! [X481 : subst,X482 : term] : (((sK385 @ X479 @ X481 @ X482)) = ((sub @ X479 @ (push @ X482 @ X481)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X484 : (subst > term > term)] : (((X484 @ (sK387 @ X484) @ (sK388 @ X484))) != ((sub @ sK386 @ (push @ (sK388 @ X484) @ (sK387 @ X484)))))) & (lamnotvar = $true) & (pushprop = $true) & ((axshiftcons = $true) | (sK390 != ((comp @ sh @ (push @ sK389 @ sK390))))) & (! [X489 : term,X490 : subst] : (((comp @ sh @ (push @ X489 @ X490))) = X490) | (axshiftcons != $true)) & (substmonoid_gthm = $true) & (! [X491 : (subst > term > subst > $o),X492 : (term > $o),X493 : term,X494 : term] : (($true = ((X492 @ (ap @ X494 @ X493)))) | (((X492 @ X494)) != $true) | (((X492 @ (sK391 @ X492 @ X491))) != ((X491 @ id @ (sK391 @ X492 @ X491) @ id))) | ((((X491 @ (sK392 @ X491) @ (sK394 @ X491) @ (comp @ (sK395 @ X491) @ (sK393 @ X491)))) != $true) & (((X491 @ (comp @ (sK392 @ X491) @ (sK395 @ X491)) @ (sub @ (sK394 @ X491) @ (sK395 @ X491)) @ (sK393 @ X491))) = $true)) | ((((X491 @ id @ (sK396 @ X491) @ id)) = $true) & ($true = ((X491 @ id @ (sK397 @ X491) @ id))) & ($true != ((X491 @ id @ (ap @ (sub @ (sK397 @ X491) @ id) @ (sK396 @ X491)) @ id)))) | (((X492 @ X493)) != $true) | (($true = ((X491 @ (sK399 @ X491) @ (sK400 @ X491) @ (comp @ (sK401 @ X491) @ (sK398 @ X491))))) & ($true != ((X491 @ (comp @ (sK399 @ X491) @ (sK401 @ X491)) @ (sub @ (sK400 @ X491) @ (sK401 @ X491)) @ (sK398 @ X491)))))) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (($true != ((sK403 @ (ap @ sK405 @ sK404)))) & ($true = ((sK403 @ sK405))) & ! [X510 : term] : (((sK403 @ X510)) = ((sK402 @ id @ X510 @ id))) & ! [X511 : subst,X512 : subst,X513 : term,X514 : subst] : (($true = ((sK402 @ X511 @ X513 @ (comp @ X514 @ X512)))) | ($true != ((sK402 @ (comp @ X511 @ X514) @ (sub @ X513 @ X514) @ X512)))) & ! [X515 : term,X516 : term] : (($true != ((sK402 @ id @ X515 @ id))) | ($true != ((sK402 @ id @ X516 @ id))) | (((sK402 @ id @ (ap @ (sub @ X516 @ id) @ X515) @ id)) = $true)) & ($true = ((sK403 @ sK404))) & ! [X517 : subst,X518 : subst,X519 : term,X520 : subst] : (($true != ((sK402 @ X518 @ X519 @ (comp @ X520 @ X517)))) | ($true = ((sK402 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520) @ X517)))))) & (axvarshift = $true) & ! [X521 : term] : (((d2term @ (sK406 @ X521))) = X521) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1_gthm = $true) & ((substmonoid_lthm = $true) | (! [X523 : subst] : (((comp @ X523 @ id)) = X523) & ! [X524 : subst] : (((comp @ id @ X524)) = X524) & ((sK407 != ((comp @ sK407 @ id))) | (sK408 != ((comp @ id @ sK408)))))) & ((((comp @ sK409 @ id)) != sK409) | (((comp @ id @ sK410)) != sK410) | (! [X529 : subst] : (((comp @ X529 @ id)) = X529) & ! [X530 : subst] : (((comp @ id @ X530)) = X530)) | (substmonoid_lthm != $true)) & (! [X531 : term] : (((sub @ X531 @ id)) = X531) | (((sub @ sK411 @ id)) != sK411) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | ((((sub @ sK412 @ id)) != sK412) & ! [X534 : term] : (((sub @ X534 @ id)) = X534))) & ((hoasinduction_lem0_lthm = $true) | ! [X536 : (term > $o)] : (((sK413 @ id @ (sK414 @ X536) @ id)) != ((X536 @ (sK414 @ X536))))) & (! [X538 : (subst > term > subst > $o)] : ! [X540 : term] : (((X538 @ id @ X540 @ id)) = ((sK415 @ X538 @ X540))) | (hoasinduction_lem0_lthm != $true)) & (hoasinduction_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) | (! [X541 : term] : ! [X543 : term,X544 : subst] : (((sK416 @ X541 @ X544 @ X543)) = ((sub @ X541 @ (push @ X543 @ X544)))) & (! [X548 : (subst > term > term)] : ((((sub @ (X548 @ (sK420 @ X548) @ (sK421 @ X548)) @ (sK422 @ X548))) != ((X548 @ (comp @ (sK420 @ X548) @ (sK422 @ X548)) @ (sub @ (sK421 @ X548) @ (sK422 @ X548))))) | (((sK418 @ id @ (lam @ (X548 @ sh @ one)) @ id)) = $true) | (($true != ((sK418 @ id @ (X548 @ id @ (sK423 @ X548)) @ id))) & (((sK418 @ id @ (sK423 @ X548) @ id)) = $true))) & ($true != ((sK417 @ (lam @ sK419)))) & ! [X553 : term] : (($true = ((sK417 @ (sub @ sK419 @ (push @ X553 @ id))))) | ($true != ((sK417 @ X553)))) & ! [X554 : term] : (((sK418 @ id @ X554 @ id)) = ((sK417 @ X554)))) & ! [X555 : term] : (((sub @ X555 @ id)) = X555))) & (! [X557 : (subst > term > term)] : (((sub @ sK424 @ (push @ (sK425 @ X557) @ (sK426 @ X557)))) != ((X557 @ (sK426 @ X557) @ (sK425 @ X557)))) | ! [X560 : (term > $o),X561 : (subst > term > subst > $o),X562 : term] : ((! [X564 : subst,X565 : term,X566 : subst] : (((sK427 @ X561 @ (comp @ X564 @ X566) @ (sub @ X565 @ X566))) = ((sub @ (sK427 @ X561 @ X564 @ X565) @ X566))) & ($true != ((X561 @ id @ (lam @ (sK427 @ X561 @ sh @ one)) @ id))) & ! [X567 : term] : ((((X561 @ id @ (sK427 @ X561 @ id @ X567) @ id)) = $true) | (((X561 @ id @ X567 @ id)) != $true))) | ($true = ((X560 @ (lam @ X562)))) | (($true != ((X560 @ (sub @ X562 @ (push @ (sK428 @ X562 @ X560) @ id))))) & ($true = ((X560 @ (sK428 @ X562 @ X560))))) | (((X561 @ id @ (sK429 @ X561 @ X560) @ id)) != ((X560 @ (sK429 @ X561 @ X560))))) | (sK430 != ((sub @ sK430 @ id))) | (hoasinduction_lem3v2a_lthm != $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (hoasapnotvar = $true) & (pushprop_lem0_gthm = $true) & (pushprop_lem2v2_gthm = $true) & ! [X571 : subst] : (((d2subst @ (sK431 @ X571))) = X571) & (hoasapnotvar_lthm = $true) & ((((sub @ sK432 @ id)) != sK432) | ! [X574 : term,X575 : (subst > term > subst > $o)] : ((! [X577 : term] : (($true = ((X575 @ id @ (sK433 @ X575 @ id @ X577) @ id))) | (((X575 @ id @ X577 @ id)) != $true)) & ($true != ((X575 @ id @ (lam @ (sK433 @ X575 @ sh @ one)) @ id))) & ! [X578 : subst,X579 : subst,X580 : term] : (((sub @ (sK433 @ X575 @ X578 @ X580) @ X579)) = ((sK433 @ X575 @ (comp @ X578 @ X579) @ (sub @ X580 @ X579))))) | ((((X575 @ id @ (sub @ X574 @ (push @ (sK434 @ X575 @ X574) @ id)) @ id)) != $true) & ($true = ((X575 @ id @ (sK434 @ X575 @ X574) @ id)))) | ($true = ((X575 @ id @ (lam @ X574) @ id)))) | (($true != ((sK435 @ id @ (lam @ (sub @ sK436 @ (push @ one @ sh))) @ id))) & ! [X584 : term] : (($true != ((sK435 @ id @ X584 @ id))) | (((sK435 @ id @ (sub @ sK436 @ (push @ X584 @ id)) @ id)) = $true)) & ! [X585 : (subst > term > term)] : ((((X585 @ (comp @ (sK437 @ X585) @ (sK439 @ X585)) @ (sub @ (sK438 @ X585) @ (sK439 @ X585)))) != ((sub @ (X585 @ (sK437 @ X585) @ (sK438 @ X585)) @ (sK439 @ X585)))) | ((((sK435 @ id @ (X585 @ id @ (sK440 @ X585)) @ id)) != $true) & ($true = ((sK435 @ id @ (sK440 @ X585) @ id)))) | ($true = ((sK435 @ id @ (lam @ (X585 @ sh @ one)) @ id))))) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (! [X590 : term] : (((sub @ X590 @ id)) = X590) & (! [X593 : (subst > term > term)] : (((((sK442 @ id @ (X593 @ id @ (sK443 @ X593)) @ id)) != $true) & (((sK442 @ id @ (sK443 @ X593) @ id)) = $true)) | (((sK442 @ id @ (lam @ (X593 @ sh @ one)) @ id)) = $true) | (((sub @ (X593 @ (sK444 @ X593) @ (sK446 @ X593)) @ (sK445 @ X593))) != ((X593 @ (comp @ (sK444 @ X593) @ (sK445 @ X593)) @ (sub @ (sK446 @ X593) @ (sK445 @ X593)))))) & ! [X598 : term] : (($true = ((sK442 @ id @ (sub @ sK441 @ (push @ X598 @ id)) @ id))) | ($true != ((sK442 @ id @ X598 @ id)))) & ($true != ((sK442 @ id @ (lam @ sK441) @ id)))) & ! [X599 : (subst > term > subst > $o),X600 : term] : (($true = ((X599 @ id @ (lam @ (sub @ X600 @ (push @ one @ sh))) @ id))) | ((((X599 @ id @ (sK447 @ X600 @ X599) @ id)) = $true) & (((X599 @ id @ (sub @ X600 @ (push @ (sK447 @ X600 @ X599) @ id)) @ id)) != $true)) | (! [X603 : subst,X604 : term,X605 : subst] : (((sK448 @ X599 @ (comp @ X603 @ X605) @ (sub @ X604 @ X605))) = ((sub @ (sK448 @ X599 @ X603 @ X604) @ X605))) & ! [X606 : term] : ((((X599 @ id @ (sK448 @ X599 @ id @ X606) @ id)) = $true) | ($true != ((X599 @ id @ X606 @ id)))) & (((X599 @ id @ (lam @ (sK448 @ X599 @ sh @ one)) @ id)) != $true))))) & (axapp = $true) & (hoasapnotvar_gthm = $true) & ! [X607 : d_subst] : (d_id = X607) & (! [X608 : term,X609 : (subst > term > term),X610 : term] : ((((lam @ (X609 @ sh @ one))) != ((ap @ (sub @ X610 @ id) @ X608))) | (((sub @ (X609 @ (sK450 @ X609) @ (sK449 @ X609)) @ (sK451 @ X609))) != ((X609 @ (comp @ (sK450 @ X609) @ (sK451 @ X609)) @ (sub @ (sK449 @ X609) @ (sK451 @ X609)))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ((((lam @ (sK453 @ sh @ one))) = ((ap @ (sub @ sK454 @ id) @ sK452))) & ! [X617 : term,X618 : subst,X619 : subst] : (((sub @ (sK453 @ X618 @ X617) @ X619)) = ((sK453 @ (comp @ X618 @ X619) @ (sub @ X617 @ X619)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X620 : term,X621 : (subst > term > subst > $o)] : ((((X621 @ id @ (lam @ X620) @ id)) = $true) | (! [X623 : term] : (($true != ((X621 @ id @ X623 @ id))) | (((X621 @ id @ (sK455 @ X621 @ id @ X623) @ id)) = $true)) & (((X621 @ id @ (lam @ (sK455 @ X621 @ sh @ one)) @ id)) != $true) & ! [X624 : term,X625 : subst,X626 : subst] : (((sK455 @ X621 @ (comp @ X625 @ X626) @ (sub @ X624 @ X626))) = ((sub @ (sK455 @ X621 @ X625 @ X624) @ X626)))) | (($true = ((X621 @ id @ (sK456 @ X621 @ X620) @ id))) & ($true != ((X621 @ id @ (sub @ X620 @ (push @ (sK456 @ X621 @ X620) @ id)) @ id))))) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | (($true != ((sK458 @ id @ (lam @ sK457) @ id))) & ! [X630 : (subst > term > term)] : (((((sK458 @ id @ (sK459 @ X630) @ id)) = $true) & (((sK458 @ id @ (X630 @ id @ (sK459 @ X630)) @ id)) != $true)) | (((sK458 @ id @ (lam @ (X630 @ sh @ one)) @ id)) = $true) | (((X630 @ (comp @ (sK461 @ X630) @ (sK462 @ X630)) @ (sub @ (sK460 @ X630) @ (sK462 @ X630)))) != ((sub @ (X630 @ (sK461 @ X630) @ (sK460 @ X630)) @ (sK462 @ X630))))) & ! [X635 : term] : (($true != ((sK458 @ id @ X635 @ id))) | ($true = ((sK458 @ id @ (sub @ sK457 @ (push @ X635 @ id)) @ id)))))) & (apnotvar = $true) & (induction2lem_gthm = $true) & (! [X636 : term,X637 : term,X638 : term,X639 : term] : ((((ap @ X639 @ X636)) != ((ap @ X637 @ X638))) | (X636 = X638)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK464 @ sK465)) = ((ap @ sK466 @ sK463))) & (sK465 != sK463))) & (axassoc = $true) & ((hoasinduction_no_psi_cond = $true) | (! [X646 : term,X647 : term] : ((((sK467 @ id @ X646 @ id)) != $true) | ($true = ((sK467 @ id @ (ap @ (sub @ X647 @ id) @ X646) @ id))) | ($true != ((sK467 @ id @ X647 @ id)))) & ! [X648 : (subst > term > term)] : (($true = ((sK467 @ id @ (lam @ (X648 @ sh @ one)) @ id))) | ((((sK467 @ id @ (X648 @ id @ (sK469 @ X648)) @ id)) != $true) & ($true = ((sK467 @ id @ (sK469 @ X648) @ id)))) | (((X648 @ (comp @ (sK470 @ X648) @ (sK471 @ X648)) @ (sub @ (sK472 @ X648) @ (sK471 @ X648)))) != ((sub @ (X648 @ (sK470 @ X648) @ (sK472 @ X648)) @ (sK471 @ X648))))) & (((sK467 @ id @ sK468 @ id)) != $true))) & (! [X653 : (subst > term > subst > $o),X654 : term] : (((((X653 @ id @ (sK473 @ X653) @ id)) = $true) & (((X653 @ id @ (ap @ (sub @ (sK474 @ X653) @ id) @ (sK473 @ X653)) @ id)) != $true) & ($true = ((X653 @ id @ (sK474 @ X653) @ id)))) | (($true != ((X653 @ id @ (lam @ (sK475 @ X653 @ sh @ one)) @ id))) & ! [X658 : term] : ((((X653 @ id @ (sK475 @ X653 @ id @ X658) @ id)) = $true) | (((X653 @ id @ X658 @ id)) != $true)) & ! [X659 : subst,X660 : subst,X661 : term] : (((sub @ (sK475 @ X653 @ X659 @ X661) @ X660)) = ((sK475 @ X653 @ (comp @ X659 @ X660) @ (sub @ X661 @ X660))))) | ($true = ((X653 @ id @ X654 @ id)))) | (hoasinduction_no_psi_cond != $true)) & (! [X662 : subst] : (((comp @ X662 @ id)) = X662) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK476 @ id)) != sK476)) & ((induction2 = $true) | (! [X666 : term] : (($true = ((sK478 @ (lam @ X666)))) | ((((sK478 @ (sK479 @ X666))) = $true) & (((sK478 @ (sub @ X666 @ (push @ (sK479 @ X666) @ id)))) != $true))) & ! [X668 : term] : ((((var @ X668)) != $true) | (((sK478 @ X668)) = $true)) & ! [X669 : term,X670 : term] : (($true != ((sK478 @ X669))) | ($true = ((sK478 @ (ap @ X669 @ X670)))) | (((sK478 @ X670)) != $true)) & (((sK478 @ sK477)) != $true))) & (! [X671 : term,X672 : (term > $o)] : (((((X672 @ (lam @ (sK480 @ X672)))) != $true) & ! [X674 : term] : (($true != ((X672 @ X674))) | (((X672 @ (sub @ (sK480 @ X672) @ (push @ X674 @ id)))) = $true))) | (($true = ((var @ (sK481 @ X672)))) & ($true != ((X672 @ (sK481 @ X672))))) | ((((X672 @ (sK482 @ X672))) = $true) & ($true != ((X672 @ (ap @ (sK482 @ X672) @ (sK483 @ X672))))) & ($true = ((X672 @ (sK483 @ X672))))) | (((X672 @ X671)) = $true)) | (induction2 != $true)) & (pushprop_lem3v2 = $true) & (! [X678 : term,X679 : term,X680 : term,X681 : term] : ((((ap @ (sub @ X681 @ id) @ X678)) != ((ap @ (sub @ X679 @ id) @ X680))) | (X678 = X680)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((((ap @ (sub @ sK487 @ id) @ sK484)) = ((ap @ (sub @ sK485 @ id) @ sK486))) & (sK484 != sK486))) & (ulamvar1 != $true) & (lamnotap != $true) & (! [X686 : (subst > term > subst > $o)] : ! [X688 : term] : (((sK488 @ X686 @ X688)) = ((X686 @ id @ X688 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X690 : (term > $o)] : (((sK489 @ id @ (sK490 @ X690) @ id)) != ((X690 @ (sK490 @ X690))))) & (pushprop_lem1v2_gthm = $true) & (($true = sP1) | (induction2lem_lthm != $true)) & ((induction2lem_lthm = $true) | ($true != sP1)) & ((hoasinduction = $true) | (! [X694 : term,X695 : subst,X696 : subst,X697 : subst] : ((((sK492 @ (comp @ X697 @ X695) @ (sub @ X694 @ X695) @ X696)) != $true) | (((sK492 @ X697 @ X694 @ (comp @ X695 @ X696))) = $true)) & (((sK492 @ id @ sK491 @ id)) != $true) & ! [X698 : term,X699 : term] : (($true = ((sK492 @ id @ (ap @ (sub @ X698 @ id) @ X699) @ id))) | (((sK492 @ id @ X699 @ id)) != $true) | ($true != ((sK492 @ id @ X698 @ id)))) & (((sP0 @ sK492)) != $true) & ! [X700 : term] : ((((var @ (sub @ X700 @ id))) != $true) | ($true = ((sK492 @ id @ X700 @ id)))) & ! [X701 : subst,X702 : term,X703 : subst,X704 : subst] : ((((sK492 @ (comp @ X704 @ X701) @ (sub @ X702 @ X701) @ X703)) = $true) | (((sK492 @ X704 @ X702 @ (comp @ X701 @ X703))) != $true)))) & (! [X705 : term,X706 : (subst > term > subst > $o)] : (((((X706 @ (comp @ (sK496 @ X706) @ (sK494 @ X706)) @ (sub @ (sK493 @ X706) @ (sK494 @ X706)) @ (sK495 @ X706))) = $true) & (((X706 @ (sK496 @ X706) @ (sK493 @ X706) @ (comp @ (sK494 @ X706) @ (sK495 @ X706)))) != $true)) | ($true = ((X706 @ id @ X705 @ id))) | ((((X706 @ id @ (ap @ (sub @ (sK497 @ X706) @ id) @ (sK498 @ X706)) @ id)) != $true) & (((X706 @ id @ (sK498 @ X706) @ id)) = $true) & ($true = ((X706 @ id @ (sK497 @ X706) @ id)))) | ($true = ((sP0 @ X706))) | ((((var @ (sub @ (sK499 @ X706) @ id))) = $true) & (((X706 @ id @ (sK499 @ X706) @ id)) != $true)) | ((((X706 @ (comp @ (sK503 @ X706) @ (sK500 @ X706)) @ (sub @ (sK501 @ X706) @ (sK500 @ X706)) @ (sK502 @ X706))) != $true) & (((X706 @ (sK503 @ X706) @ (sK501 @ X706) @ (comp @ (sK500 @ X706) @ (sK502 @ X706)))) = $true))) | (hoasinduction != $true)) & (hoasinduction_lem1v2_gthm = $true) & (pushprop_lem2v2 = $true) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (axmap = $true) & (hoasinduction_lem1 = $true) & ((pushprop_lem1 = $true) | (($true = ((sK504 @ sK505))) & ($true != ((sK507 @ (sub @ sK505 @ (push @ sK506 @ sK508))))))) & (! [X723 : (term > $o),X724 : term,X725 : term,X726 : (term > $o),X727 : subst] : (($true != ((X723 @ X724))) | ($true = ((X726 @ (sub @ X724 @ (push @ X725 @ X727)))))) | (pushprop_lem1 != $true)) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar = $true) & (! [X728 : subst,X729 : (term > $o),X730 : term] : ! [X732 : term] : (((sK509 @ X730 @ X729 @ X728 @ X732)) = ((X729 @ (sub @ X732 @ (push @ X730 @ X728))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X736 : (term > $o)] : (((X736 @ (sK513 @ X736))) != ((sK511 @ (sub @ (sK513 @ X736) @ (push @ sK512 @ sK510)))))) & (hoasinduction_lem3b_gthm = $true) & (! [X738 : subst] : (((comp @ id @ X738)) = X738) | (axidl != $true)) & ((axidl = $true) | (sK514 != ((comp @ id @ sK514)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) | (! [X742 : (subst > term > term)] : ((((X742 @ (comp @ (sK518 @ X742) @ (sK519 @ X742)) @ (sub @ (sK517 @ X742) @ (sK519 @ X742)))) != ((sub @ (X742 @ (sK518 @ X742) @ (sK517 @ X742)) @ (sK519 @ X742)))) | (((sK515 @ id @ (lam @ (X742 @ sh @ one)) @ id)) = $true) | (($true = ((sK515 @ id @ (sK520 @ X742) @ id))) & (((sK515 @ id @ (X742 @ id @ (sK520 @ X742)) @ id)) != $true))) & ! [X747 : term] : (($true = ((sK515 @ id @ (sub @ sK516 @ (push @ X747 @ id)) @ id))) | ($true != ((sK515 @ id @ X747 @ id)))) & ($true != ((sK515 @ id @ (lam @ (sub @ sK516 @ (push @ one @ sh))) @ id))))) & (! [X748 : (subst > term > subst > $o),X749 : term] : ((! [X751 : term,X752 : subst,X753 : subst] : (((sK521 @ X748 @ (comp @ X752 @ X753) @ (sub @ X751 @ X753))) = ((sub @ (sK521 @ X748 @ X752 @ X751) @ X753))) & ($true != ((X748 @ id @ (lam @ (sK521 @ X748 @ sh @ one)) @ id))) & ! [X754 : term] : (($true != ((X748 @ id @ X754 @ id))) | ($true = ((X748 @ id @ (sK521 @ X748 @ id @ X754) @ id))))) | (($true != ((X748 @ id @ (sub @ X749 @ (push @ (sK522 @ X749 @ X748) @ id)) @ id))) & (((X748 @ id @ (sK522 @ X749 @ X748) @ id)) = $true)) | (((X748 @ id @ (lam @ (sub @ X749 @ (push @ one @ sh))) @ id)) = $true)) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1v2_lthm = $true) | (((((sK523 @ sK524)) = $true) & ! [X760 : term] : (((sK523 @ (sub @ X760 @ (push @ sK524 @ sK525)))) = ((sK526 @ X760))) & (((sK526 @ one)) != $true)) & ! [X761 : term,X762 : subst] : (((sub @ one @ (push @ X761 @ X762))) = X761))) & (! [X763 : (term > $o),X764 : term,X765 : subst,X766 : (term > $o)] : ((((X763 @ X764)) != $true) | (((X766 @ (sK527 @ X766 @ X765 @ X764 @ X763))) != ((X763 @ (sub @ (sK527 @ X766 @ X765 @ X764 @ X763) @ (push @ X764 @ X765))))) | ($true = ((X766 @ one)))) | (((sub @ one @ (push @ sK528 @ sK529))) != sK528) | (pushprop_lem1v2_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (! [X770 : term,X771 : term,X772 : (subst > term > subst > $o)] : (($true = ((X772 @ id @ (ap @ X771 @ X770) @ id))) | ($true != ((X772 @ id @ X770 @ id))) | (((X772 @ id @ X771 @ id)) != $true) | ((((X772 @ (sK532 @ X772) @ (sK533 @ X772) @ (comp @ (sK530 @ X772) @ (sK531 @ X772)))) = $true) & ($true != ((X772 @ (comp @ (sK532 @ X772) @ (sK530 @ X772)) @ (sub @ (sK533 @ X772) @ (sK530 @ X772)) @ (sK531 @ X772))))) | ((((X772 @ id @ (sK534 @ X772) @ id)) = $true) & ($true != ((X772 @ id @ (ap @ (sub @ (sK535 @ X772) @ id) @ (sK534 @ X772)) @ id))) & ($true = ((X772 @ id @ (sK535 @ X772) @ id)))) | ((((X772 @ (comp @ (sK539 @ X772) @ (sK537 @ X772)) @ (sub @ (sK538 @ X772) @ (sK537 @ X772)) @ (sK536 @ X772))) = $true) & (((X772 @ (sK539 @ X772) @ (sK538 @ X772) @ (comp @ (sK537 @ X772) @ (sK536 @ X772)))) != $true))) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | (($true != ((sK542 @ id @ (ap @ sK541 @ sK540) @ id))) & (((sK542 @ id @ sK540 @ id)) = $true) & (((sK542 @ id @ sK541 @ id)) = $true) & ! [X786 : subst,X787 : subst,X788 : subst,X789 : term] : (($true != ((sK542 @ X788 @ X789 @ (comp @ X786 @ X787)))) | ($true = ((sK542 @ (comp @ X788 @ X786) @ (sub @ X789 @ X786) @ X787)))) & ! [X790 : term,X791 : term] : ((((sK542 @ id @ X790 @ id)) != $true) | ($true = ((sK542 @ id @ (ap @ (sub @ X791 @ id) @ X790) @ id))) | ($true != ((sK542 @ id @ X791 @ id)))) & ! [X792 : subst,X793 : subst,X794 : term,X795 : subst] : (($true != ((sK542 @ (comp @ X795 @ X793) @ (sub @ X794 @ X793) @ X792))) | ($true = ((sK542 @ X795 @ X794 @ (comp @ X793 @ X792)))))))),
% 5.43/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK148,sK149,sK150,sK151,sK152,sK153,sK154,sK155,sK156,sK157,vAPP,vAPP,vAPP,sK161,sK162,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK170,sK171,vAPP,sK173,sK174,sK175,sK176,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK188,sK189,sK190,vAPP,vAPP,vAPP,vAPP,sK195,sK196,sK197,vAPP,vAPP,sK200,sK201,sK202,sK203,sK204,sK205,sK206,sK207,sK208,sK209,sK210,sK211,sK212,sK213,sK214,sK215,sK216,vAPP,vAPP,vAPP,vAPP,vAPP,sK222,sK223,sK224,sK225,vAPP,vAPP,vAPP,vAPP,sK230,sK231,sK232,sK233,sK234,sK235,sK236,sK237,sK238,sK239,sK240,sK241,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK256,vAPP,sK258,sK259,sK260,vAPP,vAPP,vAPP,vAPP,sK265,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK277,sK278,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK287,sK288,vAPP,sK290,vAPP,sK292,sK293,sK294,vAPP,vAPP,vAPP,vAPP,sK299,sK300,sK301,sK302,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK310,sK311,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK318,sK319,sK320,sK321,sK322,sK323,sK324,sK325,sK326,sK327,sK328,sK329,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK338,vAPP,sK340,sK341,sK342,vAPP,sK344,sK345,sK346,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK353,sK354,vAPP,vAPP,vAPP,vAPP,sK359,sK360,vAPP,vAPP,vAPP,vAPP,sK365,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK374,sK375,sK376,sK377,vAPP,sK379,vAPP,vAPP,sK382,sK383,vAPP,vAPP,sK386,vAPP,vAPP,sK389,sK390,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK402,sK403,sK404,sK405,vAPP,sK407,sK408,sK409,sK410,sK411,sK412,sK413,vAPP,vAPP,vAPP,sK417,sK418,sK419,vAPP,vAPP,vAPP,vAPP,sK424,vAPP,vAPP,vAPP,vAPP,vAPP,sK430,vAPP,sK432,vAPP,vAPP,sK435,sK436,vAPP,vAPP,vAPP,vAPP,sK441,sK442,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK452,sK453,sK454,vAPP,vAPP,sK457,sK458,vAPP,vAPP,vAPP,vAPP,sK463,sK464,sK465,sK466,sK467,sK468,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK476,sK477,sK478,vAPP,vAPP,vAPP,vAPP,vAPP,sK484,sK485,sK486,sK487,vAPP,sK489,vAPP,sK491,sK492,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK504,sK505,sK506,sK507,sK508,vAPP,sK510,sK511,sK512,vAPP,sK514,sK515,sK516,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK523,sK524,sK525,sK526,vAPP,sK528,sK529,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK540,sK541,sK542]),skolemize(X1,sK148),skolemize(X2,sK149),skolemize(X3,sK150),skolemize(X4,sK151),skolemize(X5,sK152),skolemize(X6,sK153),skolemize(X16,sK154),skolemize(X17,sK155),skolemize(X18,sK156),skolemize(X19,sK157),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X33,sK161),skolemize(X34,sK162),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X47,sK170),skolemize(X48,sK171),skolemize(X45,sK33 @ X44),skolemize(X54,sK173),skolemize(X55,sK174),skolemize(X56,sK175),skolemize(X57,sK176),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X77,sK188),skolemize(X78,sK189),skolemize(X79,sK190),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X95,sK195),skolemize(X96,sK196),skolemize(X97,sK197),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X105,sK200),skolemize(X106,sK201),skolemize(X110,sK202),skolemize(X115,sK203),skolemize(X116,sK204),skolemize(X117,sK205),skolemize(X118,sK206),skolemize(X120,sK207),skolemize(X121,sK208),skolemize(X122,sK209),skolemize(X123,sK210),skolemize(X128,sK211),skolemize(X129,sK212),skolemize(X130,sK213),skolemize(X133,sK214),skolemize(X134,sK215),skolemize(X135,sK216),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X153,sK222),skolemize(X154,sK223),skolemize(X155,sK224),skolemize(X156,sK225),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X163,sK230),skolemize(X164,sK231),skolemize(X173,sK232),skolemize(X174,sK233),skolemize(X175,sK234),skolemize(X176,sK235),skolemize(X177,sK236),skolemize(X178,sK237),skolemize(X179,sK238),skolemize(X180,sK239),skolemize(X185,sK240),skolemize(X186,sK241),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X217,sK256),skolemize(X45,sK33 @ X44),skolemize(X224,sK258),skolemize(X225,sK259),skolemize(X226,sK260),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X242,sK265),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X263,sK277),skolemize(X264,sK278),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X286,sK287),skolemize(X287,sK288),skolemize(X45,sK33 @ X44),skolemize(X293,sK290),skolemize(X45,sK33 @ X44),skolemize(X296,sK292),skolemize(X297,sK293),skolemize(X298,sK294),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X306,sK299),skolemize(X309,sK300),skolemize(X310,sK301),skolemize(X311,sK302),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X329,sK310),skolemize(X330,sK311),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X341,sK318),skolemize(X342,sK319),skolemize(X343,sK320),skolemize(X344,sK321),skolemize(X347,sK322),skolemize(X348,sK323),skolemize(X349,sK324),skolemize(X350,sK325),skolemize(X361,sK326),skolemize(X362,sK327),skolemize(X363,sK328),skolemize(X364,sK329),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X390,sK338),skolemize(X45,sK33 @ X44),skolemize(X393,sK340),skolemize(X394,sK341),skolemize(X395,sK342),skolemize(X45,sK33 @ X44),skolemize(X401,sK344),skolemize(X402,sK345),skolemize(X403,sK346),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X419,sK353),skolemize(X420,sK354),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X427,sK359),skolemize(X428,sK360),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X435,sK365),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X455,sK374),skolemize(X456,sK375),skolemize(X457,sK376),skolemize(X458,sK377),skolemize(X45,sK33 @ X44),skolemize(X469,sK379),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X474,sK382),skolemize(X475,sK383),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X483,sK386),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X487,sK389),skolemize(X488,sK390),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X506,sK402),skolemize(X507,sK403),skolemize(X508,sK404),skolemize(X509,sK405),skolemize(X45,sK33 @ X44),skolemize(X525,sK407),skolemize(X526,sK408),skolemize(X527,sK409),skolemize(X528,sK410),skolemize(X532,sK411),skolemize(X533,sK412),skolemize(X535,sK413),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X545,sK417),skolemize(X546,sK418),skolemize(X547,sK419),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X556,sK424),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X570,sK430),skolemize(X45,sK33 @ X44),skolemize(X573,sK432),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X582,sK435),skolemize(X583,sK436),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X591,sK441),skolemize(X592,sK442),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X614,sK452),skolemize(X615,sK453),skolemize(X616,sK454),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X628,sK457),skolemize(X629,sK458),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X640,sK463),skolemize(X641,sK464),skolemize(X642,sK465),skolemize(X643,sK466),skolemize(X644,sK467),skolemize(X645,sK468),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X663,sK476),skolemize(X664,sK477),skolemize(X665,sK478),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X682,sK484),skolemize(X683,sK485),skolemize(X684,sK486),skolemize(X685,sK487),skolemize(X45,sK33 @ X44),skolemize(X689,sK489),skolemize(X45,sK33 @ X44),skolemize(X692,sK491),skolemize(X693,sK492),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X718,sK504),skolemize(X719,sK505),skolemize(X720,sK506),skolemize(X721,sK507),skolemize(X722,sK508),skolemize(X45,sK33 @ X44),skolemize(X733,sK510),skolemize(X734,sK511),skolemize(X735,sK512),skolemize(X45,sK33 @ X44),skolemize(X739,sK514),skolemize(X740,sK515),skolemize(X741,sK516),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X756,sK523),skolemize(X757,sK524),skolemize(X758,sK525),skolemize(X759,sK526),skolemize(X45,sK33 @ X44),skolemize(X768,sK528),skolemize(X769,sK529),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X783,sK540),skolemize(X784,sK541),skolemize(X785,sK542)],[f64])).
% 5.43/1.21 thf(f66,plain,(
% 5.43/1.21 (? [X1 : (term > $o),X0 : (subst > term > subst > $o)] : ((((hoasinduction_p_and_p_prime @ X0 @ X1)) = $true) & ! [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8)) != $true) | ($true = ((X0 @ X7 @ X9 @ (comp @ X6 @ X8))))) & ! [X10 : term,X11 : term] : (($true != ((X0 @ id @ X11 @ id))) | (((X0 @ id @ X10 @ id)) != $true) | ($true = ((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)))) & ! [X2 : subst,X5 : subst,X4 : term,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X5 @ X2))) != $true) | ($true = ((X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)))) & ? [X12 : term,X13 : term] : (($true != ((X1 @ (ap @ X13 @ X12)))) & (((X1 @ X13)) = $true) & (((X1 @ X12)) = $true))) | (hoasinduction_lem2v2 != $true)) & (! [X1 : (term > $o),X0 : (subst > term > subst > $o)] : ((((hoasinduction_p_and_p_prime @ X0 @ X1)) != $true) | ? [X6 : subst,X7 : subst,X8 : subst,X9 : term] : ((((X0 @ (comp @ X7 @ X6) @ (sub @ X9 @ X6) @ X8)) = $true) & ($true != ((X0 @ X7 @ X9 @ (comp @ X6 @ X8))))) | ? [X10 : term,X11 : term] : (($true = ((X0 @ id @ X11 @ id))) & (((X0 @ id @ X10 @ id)) = $true) & ($true != ((X0 @ id @ (hoasap @ id @ X11 @ id @ X10) @ id)))) | ? [X2 : subst,X5 : subst,X4 : term,X3 : subst] : ((((X0 @ X3 @ X4 @ (comp @ X5 @ X2))) = $true) & ($true != ((X0 @ (comp @ X3 @ X5) @ (sub @ X4 @ X5) @ X2)))) | ! [X12 : term,X13 : term] : (($true = ((X1 @ (ap @ X13 @ X12)))) | (((X1 @ X13)) != $true) | (((X1 @ X12)) != $true))) | (hoasinduction_lem2v2 = $true))),
% 5.43/1.21 inference(nnf_transformation,[],[f13])).
% 5.43/1.21 thf(f67,plain,(
% 5.43/1.21 (? [X0 : (term > $o),X1 : (subst > term > subst > $o)] : (($true = ((hoasinduction_p_and_p_prime @ X1 @ X0))) & ! [X2 : subst,X3 : subst,X4 : subst,X5 : term] : (($true != ((X1 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4))) | (((X1 @ X3 @ X5 @ (comp @ X2 @ X4))) = $true)) & ! [X6 : term,X7 : term] : (($true != ((X1 @ id @ X7 @ id))) | (((X1 @ id @ X6 @ id)) != $true) | (((X1 @ id @ (hoasap @ id @ X7 @ id @ X6) @ id)) = $true)) & ! [X8 : subst,X9 : subst,X10 : term,X11 : subst] : (($true != ((X1 @ X11 @ X10 @ (comp @ X9 @ X8)))) | (((X1 @ (comp @ X11 @ X9) @ (sub @ X10 @ X9) @ X8)) = $true)) & ? [X12 : term,X13 : term] : (($true != ((X0 @ (ap @ X13 @ X12)))) & ($true = ((X0 @ X13))) & ($true = ((X0 @ X12))))) | (hoasinduction_lem2v2 != $true)) & (! [X14 : (term > $o),X15 : (subst > term > subst > $o)] : (($true != ((hoasinduction_p_and_p_prime @ X15 @ X14))) | ? [X16 : subst,X17 : subst,X18 : subst,X19 : term] : (($true = ((X15 @ (comp @ X17 @ X16) @ (sub @ X19 @ X16) @ X18))) & (((X15 @ X17 @ X19 @ (comp @ X16 @ X18))) != $true)) | ? [X20 : term,X21 : term] : (($true = ((X15 @ id @ X21 @ id))) & ($true = ((X15 @ id @ X20 @ id))) & ($true != ((X15 @ id @ (hoasap @ id @ X21 @ id @ X20) @ id)))) | ? [X22 : subst,X23 : subst,X24 : term,X25 : subst] : (($true = ((X15 @ X25 @ X24 @ (comp @ X23 @ X22)))) & ($true != ((X15 @ (comp @ X25 @ X23) @ (sub @ X24 @ X23) @ X22)))) | ! [X26 : term,X27 : term] : ((((X14 @ (ap @ X27 @ X26))) = $true) | ($true != ((X14 @ X27))) | ($true != ((X14 @ X26))))) | (hoasinduction_lem2v2 = $true))),
% 5.43/1.21 inference(rectify,[],[f66])).
% 5.43/1.21 thf(f68,plain,(
% 5.43/1.21 ((($true = ((hoasinduction_p_and_p_prime @ sK544 @ sK543))) & ! [X2 : subst,X3 : subst,X4 : subst,X5 : term] : (($true != ((sK544 @ (comp @ X3 @ X2) @ (sub @ X5 @ X2) @ X4))) | ($true = ((sK544 @ X3 @ X5 @ (comp @ X2 @ X4))))) & ! [X6 : term,X7 : term] : ((((sK544 @ id @ X7 @ id)) != $true) | (((sK544 @ id @ X6 @ id)) != $true) | (((sK544 @ id @ (hoasap @ id @ X7 @ id @ X6) @ id)) = $true)) & ! [X8 : subst,X9 : subst,X10 : term,X11 : subst] : (($true != ((sK544 @ X11 @ X10 @ (comp @ X9 @ X8)))) | (((sK544 @ (comp @ X11 @ X9) @ (sub @ X10 @ X9) @ X8)) = $true)) & ((((sK543 @ (ap @ sK546 @ sK545))) != $true) & (((sK543 @ sK546)) = $true) & ($true = ((sK543 @ sK545))))) | (hoasinduction_lem2v2 != $true)) & (! [X14 : (term > $o),X15 : (subst > term > subst > $o)] : (($true != ((hoasinduction_p_and_p_prime @ X15 @ X14))) | ((((X15 @ (comp @ (sK548 @ X15) @ (sK547 @ X15)) @ (sub @ (sK550 @ X15) @ (sK547 @ X15)) @ (sK549 @ X15))) = $true) & (((X15 @ (sK548 @ X15) @ (sK550 @ X15) @ (comp @ (sK547 @ X15) @ (sK549 @ X15)))) != $true)) | (($true = ((X15 @ id @ (sK552 @ X15) @ id))) & (((X15 @ id @ (sK551 @ X15) @ id)) = $true) & (((X15 @ id @ (hoasap @ id @ (sK552 @ X15) @ id @ (sK551 @ X15)) @ id)) != $true)) | ((((X15 @ (sK556 @ X15) @ (sK555 @ X15) @ (comp @ (sK554 @ X15) @ (sK553 @ X15)))) = $true) & ($true != ((X15 @ (comp @ (sK556 @ X15) @ (sK554 @ X15)) @ (sub @ (sK555 @ X15) @ (sK554 @ X15)) @ (sK553 @ X15))))) | ! [X26 : term,X27 : term] : ((((X14 @ (ap @ X27 @ X26))) = $true) | ($true != ((X14 @ X27))) | ($true != ((X14 @ X26))))) | (hoasinduction_lem2v2 = $true))),
% 5.43/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK543,sK544,sK545,sK546,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK543),skolemize(X1,sK544),skolemize(X12,sK545),skolemize(X13,sK546),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44),skolemize(X45,sK33 @ X44)],[f67])).
% 5.43/1.21 thf(f470,plain,(
% 5.43/1.21 (((d2subst @ d_id)) = id)),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f639,plain,(
% 5.43/1.21 ( ! [X521 : term] : ((((d2term @ (sK406 @ X521))) = X521)) )),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f642,plain,(
% 5.43/1.21 (hoasinduction_lem2v2 = $true) | ($true = ((sK403 @ sK404)))),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f647,plain,(
% 5.43/1.21 ($true != ((sK403 @ (ap @ sK405 @ sK404)))) | (hoasinduction_lem2v2 = $true)),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f897,plain,(
% 5.43/1.21 (one = ((d2term @ d_one)))),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f922,plain,(
% 5.43/1.21 (hoasapinj1 = $true) | (sK224 != sK225)),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f923,plain,(
% 5.43/1.21 ( ! [X152 : term,X150 : term,X151 : term,X149 : term] : ((hoasapinj1 != $true) | (X151 = X152) | (((ap @ (sub @ X152 @ id) @ X149)) != ((ap @ (sub @ X151 @ id) @ X150)))) )),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f953,plain,(
% 5.43/1.21 (((d2subst @ d_id)) = sh)),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f1020,plain,(
% 5.43/1.21 ( ! [X20 : d_term] : ((d_one = X20)) )),
% 5.43/1.21 inference(cnf_transformation,[],[f65])).
% 5.43/1.21 thf(f1042,plain,(
% 5.43/1.21 (((sK543 @ sK546)) = $true) | (hoasinduction_lem2v2 != $true)),
% 5.43/1.21 inference(cnf_transformation,[],[f68])).
% 5.43/1.21 thf(f1043,plain,(
% 5.43/1.21 (hoasinduction_lem2v2 != $true) | (((sK543 @ (ap @ sK546 @ sK545))) != $true)),
% 5.43/1.21 inference(cnf_transformation,[],[f68])).
% 5.43/1.21 thf(f1597,definition,(
% 5.43/1.21 spl557_51 <=> (hoasinduction_lem2v2 = $true)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_51])],[avatar_definition])).
% 5.43/1.21 thf(f1649,definition,(
% 5.43/1.21 spl557_64 <=> (hoasapinj1 = $true)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_64])],[avatar_definition])).
% 5.43/1.21 thf(f2671,definition,(
% 5.43/1.21 spl557_309 <=> (((d2subst @ d_id)) = sh)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_309])],[avatar_definition])).
% 5.43/1.21 thf(f2673,plain,(
% 5.43/1.21 (((d2subst @ d_id)) = sh) | ~spl557_309),
% 5.43/1.21 inference(avatar_component_clause,[],[f2671])).
% 5.43/1.21 thf(f2674,plain,(
% 5.43/1.21 spl557_309),
% 5.43/1.21 inference(avatar_split_clause,[],[f953,f2671])).
% 5.43/1.21 thf(f2707,definition,(
% 5.43/1.21 spl557_317 <=> ! [X150 : term,X152 : term,X149 : term,X151 : term] : ((X151 = X152) | (((ap @ (sub @ X152 @ id) @ X149)) != ((ap @ (sub @ X151 @ id) @ X150))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_317])],[avatar_definition])).
% 5.43/1.21 thf(f2708,plain,(
% 5.43/1.21 ( ! [X152 : term,X150 : term,X151 : term,X149 : term] : ((((ap @ (sub @ X152 @ id) @ X149)) != ((ap @ (sub @ X151 @ id) @ X150))) | (X151 = X152)) ) | ~spl557_317),
% 5.43/1.21 inference(avatar_component_clause,[],[f2707])).
% 5.43/1.21 thf(f2709,plain,(
% 5.43/1.21 ~spl557_64 | spl557_317),
% 5.43/1.21 inference(avatar_split_clause,[],[f923,f2707,f1649])).
% 5.43/1.21 thf(f3090,definition,(
% 5.43/1.21 spl557_406 <=> (((sK543 @ sK546)) = $true)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_406])],[avatar_definition])).
% 5.43/1.21 thf(f3092,plain,(
% 5.43/1.21 (((sK543 @ sK546)) = $true) | ~spl557_406),
% 5.43/1.21 inference(avatar_component_clause,[],[f3090])).
% 5.43/1.21 thf(f3093,plain,(
% 5.43/1.21 spl557_406 | ~spl557_51),
% 5.43/1.21 inference(avatar_split_clause,[],[f1042,f1597,f3090])).
% 5.43/1.21 thf(f3311,definition,(
% 5.43/1.21 spl557_457 <=> (((sK543 @ (ap @ sK546 @ sK545))) = $true)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_457])],[avatar_definition])).
% 5.43/1.21 thf(f3313,plain,(
% 5.43/1.21 (((sK543 @ (ap @ sK546 @ sK545))) != $true) | spl557_457),
% 5.43/1.21 inference(avatar_component_clause,[],[f3311])).
% 5.43/1.21 thf(f3314,plain,(
% 5.43/1.21 ~spl557_51 | ~spl557_457),
% 5.43/1.21 inference(avatar_split_clause,[],[f1043,f3311,f1597])).
% 5.43/1.21 thf(f4032,definition,(
% 5.43/1.21 spl557_620 <=> ($true = ((sK403 @ sK404)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_620])],[avatar_definition])).
% 5.43/1.21 thf(f4034,plain,(
% 5.43/1.21 ($true = ((sK403 @ sK404))) | ~spl557_620),
% 5.43/1.21 inference(avatar_component_clause,[],[f4032])).
% 5.43/1.21 thf(f4035,plain,(
% 5.43/1.21 spl557_620 | spl557_51),
% 5.43/1.21 inference(avatar_split_clause,[],[f642,f1597,f4032])).
% 5.43/1.21 thf(f4348,definition,(
% 5.43/1.21 spl557_687 <=> ($true = ((sK403 @ (ap @ sK405 @ sK404))))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_687])],[avatar_definition])).
% 5.43/1.21 thf(f4350,plain,(
% 5.43/1.21 ($true != ((sK403 @ (ap @ sK405 @ sK404)))) | spl557_687),
% 5.43/1.21 inference(avatar_component_clause,[],[f4348])).
% 5.43/1.21 thf(f4351,plain,(
% 5.43/1.21 spl557_51 | ~spl557_687),
% 5.43/1.21 inference(avatar_split_clause,[],[f647,f4348,f1597])).
% 5.43/1.21 thf(f4551,definition,(
% 5.43/1.21 spl557_729 <=> (one = ((d2term @ d_one)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_729])],[avatar_definition])).
% 5.43/1.21 thf(f4553,plain,(
% 5.43/1.21 (one = ((d2term @ d_one))) | ~spl557_729),
% 5.43/1.21 inference(avatar_component_clause,[],[f4551])).
% 5.43/1.21 thf(f4554,plain,(
% 5.43/1.21 spl557_729),
% 5.43/1.21 inference(avatar_split_clause,[],[f897,f4551])).
% 5.43/1.21 thf(f4682,definition,(
% 5.43/1.21 spl557_760 <=> (sK224 = sK225)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_760])],[avatar_definition])).
% 5.43/1.21 thf(f4684,plain,(
% 5.43/1.21 (sK224 != sK225) | spl557_760),
% 5.43/1.21 inference(avatar_component_clause,[],[f4682])).
% 5.43/1.21 thf(f4685,plain,(
% 5.43/1.21 ~spl557_760 | spl557_64),
% 5.43/1.21 inference(avatar_split_clause,[],[f922,f1649,f4682])).
% 5.43/1.21 thf(f5028,definition,(
% 5.43/1.21 spl557_837 <=> (((d2subst @ d_id)) = id)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_837])],[avatar_definition])).
% 5.43/1.21 thf(f5030,plain,(
% 5.43/1.21 (((d2subst @ d_id)) = id) | ~spl557_837),
% 5.43/1.21 inference(avatar_component_clause,[],[f5028])).
% 5.43/1.21 thf(f5031,plain,(
% 5.43/1.21 spl557_837),
% 5.43/1.21 inference(avatar_split_clause,[],[f470,f5028])).
% 5.43/1.21 thf(f5441,plain,(
% 5.43/1.21 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) ) | ~spl557_729),
% 5.43/1.21 inference(superposition,[],[f4553,f1020])).
% 5.43/1.21 thf(f5442,plain,(
% 5.43/1.21 (id = sh) | (~spl557_309 | ~spl557_837)),
% 5.43/1.21 inference(forward_demodulation,[],[f5030,f2673])).
% 5.43/1.21 thf(f5444,definition,(
% 5.43/1.21 spl557_925 <=> (id = sh)),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_925])],[avatar_definition])).
% 5.43/1.21 thf(f5446,plain,(
% 5.43/1.21 (id = sh) | ~spl557_925),
% 5.43/1.21 inference(avatar_component_clause,[],[f5444])).
% 5.43/1.21 thf(f5447,plain,(
% 5.43/1.21 spl557_925 | ~spl557_309 | ~spl557_837),
% 5.43/1.21 inference(avatar_split_clause,[],[f5442,f5028,f2671,f5444])).
% 5.43/1.21 thf(f5717,plain,(
% 5.43/1.21 ( ! [X152 : term,X150 : term,X151 : term,X149 : term] : ((((ap @ (sub @ X151 @ sh) @ X150)) != ((ap @ (sub @ X152 @ sh) @ X149))) | (X151 = X152)) ) | (~spl557_317 | ~spl557_925)),
% 5.43/1.21 inference(forward_demodulation,[],[f2708,f5446])).
% 5.43/1.21 thf(f6194,plain,(
% 5.43/1.21 ( ! [X521 : term] : ((one = X521)) ) | ~spl557_729),
% 5.43/1.21 inference(backward_demodulation,[],[f639,f5441])).
% 5.43/1.21 thf(f6213,plain,(
% 5.43/1.21 ( ! [X152 : term,X151 : term,X149 : term] : ((one != ((ap @ (sub @ X152 @ sh) @ X149))) | (X151 = X152)) ) | (~spl557_317 | ~spl557_729 | ~spl557_925)),
% 5.43/1.21 inference(backward_demodulation,[],[f5717,f6194])).
% 5.43/1.21 thf(f6215,plain,(
% 5.43/1.21 ($true != ((sK543 @ one))) | (spl557_457 | ~spl557_729)),
% 5.43/1.21 inference(backward_demodulation,[],[f3313,f6194])).
% 5.43/1.21 thf(f6235,plain,(
% 5.43/1.21 ($true = ((sK543 @ one))) | (~spl557_406 | ~spl557_729)),
% 5.43/1.21 inference(backward_demodulation,[],[f3092,f6194])).
% 5.43/1.21 thf(f6236,plain,(
% 5.43/1.21 ( ! [X0 : term,X1 : term] : ((X0 = X1)) ) | ~spl557_729),
% 5.43/1.21 inference(superposition,[],[f6194,f6194])).
% 5.43/1.21 thf(f6251,definition,(
% 5.43/1.21 spl557_982 <=> ($true = ((sK543 @ one)))),
% 5.43/1.21 introduced(definition,[new_symbols(definition,[spl557_982])],[avatar_definition])).
% 5.43/1.21 thf(f6265,plain,(
% 5.43/1.21 spl557_982 | ~spl557_406 | ~spl557_729),
% 5.43/1.21 inference(avatar_split_clause,[],[f6235,f4551,f3090,f6251])).
% 5.43/1.21 thf(f6298,plain,(
% 5.43/1.21 ( ! [X152 : term,X151 : term] : ((X151 = X152)) ) | (~spl557_317 | ~spl557_729 | ~spl557_925)),
% 5.43/1.21 inference(forward_subsumption_resolution,[],[f6213,f6194])).
% 5.43/1.21 thf(f6322,plain,(
% 5.43/1.21 ~spl557_982 | spl557_457 | ~spl557_729),
% 5.43/1.21 inference(avatar_split_clause,[],[f6215,f4551,f3311,f6251])).
% 5.43/1.21 thf(f6383,plain,(
% 5.43/1.21 ( ! [X0 : term] : (($true = ((sK403 @ X0)))) ) | (~spl557_317 | ~spl557_620 | ~spl557_729 | ~spl557_925)),
% 5.43/1.21 inference(superposition,[],[f4034,f6298])).
% 5.43/1.21 thf(f6680,plain,(
% 5.43/1.21 ( ! [X0 : term] : ((sK224 != X0)) ) | (~spl557_729 | spl557_760)),
% 5.43/1.21 inference(superposition,[],[f4684,f6236])).
% 5.43/1.21 thf(f6713,plain,(
% 5.43/1.21 $false | (~spl557_729 | spl557_760)),
% 5.43/1.21 inference(forward_subsumption_resolution,[],[f6680,f6236])).
% 5.43/1.21 thf(f6714,plain,(
% 5.43/1.21 ~spl557_729 | spl557_760),
% 5.43/1.21 inference(avatar_contradiction_clause,[],[f6713])).
% 5.43/1.21 thf(f6935,plain,(
% 5.43/1.21 $false | (~spl557_317 | ~spl557_620 | spl557_687 | ~spl557_729 | ~spl557_925)),
% 5.43/1.21 inference(forward_subsumption_resolution,[],[f4350,f6383])).
% 5.43/1.21 thf(f6936,plain,(
% 5.43/1.21 ~spl557_317 | ~spl557_620 | spl557_687 | ~spl557_729 | ~spl557_925),
% 5.43/1.21 inference(avatar_contradiction_clause,[],[f6935])).
% 5.43/1.21 cnf(s269, plain, spl557_309, inference(sat_conversion,[],[f2674])).
% 5.43/1.21 cnf(s280, plain, ~spl557_64 | spl557_317, inference(sat_conversion,[],[f2709])).
% 5.43/1.21 cnf(s375, plain, ~spl557_51 | spl557_406, inference(sat_conversion,[],[f3093])).
% 5.43/1.21 cnf(s434, plain, ~spl557_51 | ~spl557_457, inference(sat_conversion,[],[f3314])).
% 5.43/1.21 cnf(s646, plain, spl557_51 | spl557_620, inference(sat_conversion,[],[f4035])).
% 5.43/1.21 cnf(s740, plain, spl557_51 | ~spl557_687, inference(sat_conversion,[],[f4351])).
% 5.43/1.21 cnf(s808, plain, spl557_729, inference(sat_conversion,[],[f4554])).
% 5.43/1.21 cnf(s842, plain, spl557_64 | ~spl557_760, inference(sat_conversion,[],[f4685])).
% 5.43/1.21 cnf(s948, plain, spl557_837, inference(sat_conversion,[],[f5031])).
% 5.43/1.21 cnf(s1080, plain, ~spl557_309 | ~spl557_837 | spl557_925, inference(sat_conversion,[],[f5447])).
% 5.43/1.21 cnf(s1131, plain, ~spl557_406 | ~spl557_729 | spl557_982, inference(sat_conversion,[],[f6265])).
% 5.43/1.21 cnf(s1147, plain, spl557_457 | ~spl557_729 | ~spl557_982, inference(sat_conversion,[],[f6322])).
% 5.43/1.21 cnf(s1218, plain, ~spl557_729 | spl557_760, inference(sat_conversion,[],[f6714])).
% 5.43/1.21 cnf(s1274, plain, ~spl557_317 | ~spl557_620 | spl557_687 | ~spl557_729 | ~spl557_925, inference(sat_conversion,[],[f6936])).
% 5.43/1.21 cnf(s1284, plain, spl557_760, inference(rat,[],[s1218,s808])).
% 5.43/1.21 cnf(s1288, plain, spl557_64, inference(rat,[],[s842,s1284])).
% 5.43/1.21 cnf(s1303, plain, spl557_317, inference(rat,[],[s280,s1288])).
% 5.43/1.21 cnf(s1313, plain, spl557_925, inference(rat,[],[s1080,s948,s269])).
% 5.43/1.21 cnf(s1334, plain, ~spl557_51, inference(rat,[],[s1131,s1147,s375,s434,s808])).
% 5.43/1.21 cnf(s1342, plain, ~spl557_687, inference(rat,[],[s740,s1334])).
% 5.43/1.21 cnf(s1343, plain, spl557_620, inference(rat,[],[s646,s1334])).
% 5.43/1.21 cnf(s1355, plain, $false, inference(rat,[],[s1274,s1313,s808,s1303,s1342,s1343])).
% 5.43/1.21 thf(f6937,plain,(
% 5.43/1.21 $false),
% 5.43/1.21 inference(avatar_sat_refutation,[],[s1355])).
% 5.43/1.21 % SZS output end Proof for theBenchmark
% 5.43/1.21 % (1435751)------------------------------
% 5.43/1.21 % (1435751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.43/1.21 % (1435751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.21 % (1435751)CaDiCaL version: 2.1.3
% 5.43/1.21 % (1435751)Termination reason: Refutation
% 5.43/1.21 % (1435751)Time elapsed: 0.406 s
% 5.43/1.21 % (1435751)Peak memory usage: 20 MB
% 5.43/1.21 % (1435751)Instructions burned: 944 (million)
% 5.43/1.21 % (1435636)Success in time 0.889 s
% 5.43/1.21 % Vampire exiting
%------------------------------------------------------------------------------