%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX155^1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:35 AM UTC 2026
% Result : Theorem 2.11s 0.57s
% Output : Refutation 2.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX155^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n003.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:10:49 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.25 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
% 0.74/0.37 % (2684107)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.37 % (2684112)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1419567298:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.37 % (2684118)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.37 % (2684118)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
% 0.74/0.37 % (2684113)lrs+10_16_si=on:nwc=1.5:random_seed=2474262879:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.37 % (2684114)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2011909487:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.37 % (2684115)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=3950475795: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)
% 0.74/0.37 % (2684116)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4194483636:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.37 % (2684117)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3261388820:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.37 % (2684118)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=2537572840:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.37 % (2684114)Instruction limit reached!
% 0.74/0.37 % (2684114)------------------------------
% 0.74/0.37 % (2684114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2684114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2684114)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2684114)Termination reason: Instruction limit
% 0.74/0.37 % (2684114)Termination phase: shuffling
% 0.74/0.37 % (2684114)Time elapsed: 0.002 s
% 0.74/0.37 % (2684114)Peak memory usage: 9 MB
% 0.74/0.37 % (2684114)Instructions burned: 4 (million)
% 0.74/0.37 % (2684113)Instruction limit reached!
% 0.74/0.37 % (2684113)------------------------------
% 0.74/0.37 % (2684113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2684113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2684113)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2684113)Termination reason: Instruction limit
% 0.74/0.37 % (2684113)Termination phase: shuffling
% 0.74/0.37 % (2684113)Time elapsed: 0.008 s
% 0.74/0.37 % (2684113)Peak memory usage: 10 MB
% 0.74/0.37 % (2684113)Instructions burned: 19 (million)
% 0.74/0.37 % (2684116)Instruction limit reached!
% 0.74/0.37 % (2684116)------------------------------
% 0.74/0.37 % (2684116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2684116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2684116)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2684116)Termination reason: Instruction limit
% 0.74/0.37 % (2684116)Termination phase: Property scanning
% 0.74/0.37 % (2684116)Time elapsed: 0.011 s
% 0.74/0.37 % (2684116)Peak memory usage: 10 MB
% 0.74/0.37 % (2684116)Instructions burned: 24 (million)
% 0.74/0.37 % (2684112)Instruction limit reached!
% 0.74/0.37 % (2684112)------------------------------
% 0.74/0.37 % (2684112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2684112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2684112)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2684112)Termination reason: Instruction limit
% 0.74/0.37 % (2684112)Termination phase: Preprocessing 3
% 0.74/0.37 % (2684112)Time elapsed: 0.021 s
% 0.74/0.37 % (2684112)Peak memory usage: 13 MB
% 0.74/0.37 % (2684112)Instructions burned: 88 (million)
% 0.74/0.37 % (2684126)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4086819839:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.37 % (2684129)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=114173480:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.40 % (2684126)Instruction limit reached!
% 0.74/0.40 % (2684126)------------------------------
% 0.74/0.40 % (2684126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (2684126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (2684126)CaDiCaL version: 2.1.3
% 0.74/0.40 % (2684126)Termination reason: Instruction limit
% 0.74/0.40 % (2684126)Termination phase: shuffling
% 0.74/0.40 % (2684126)Time elapsed: 0.002 s
% 0.74/0.40 % (2684126)Peak memory usage: 9 MB
% 0.74/0.40 % (2684126)Instructions burned: 4 (million)
% 0.74/0.40 % (2684128)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.40 % (2684129)Instruction limit reached!
% 0.74/0.40 % (2684129)------------------------------
% 0.74/0.40 % (2684129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (2684129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (2684129)CaDiCaL version: 2.1.3
% 0.74/0.40 % (2684129)Termination reason: Instruction limit
% 0.74/0.40 % (2684129)Termination phase: shuffling
% 0.74/0.40 % (2684129)Time elapsed: 0.003 s
% 0.74/0.40 % (2684129)Peak memory usage: 10 MB
% 0.74/0.40 % (2684129)Instructions burned: 14 (million)
% 0.74/0.40 % (2684127)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=551322642:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.40 % (2684128)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1129247875:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.40 % (2684127)Instruction limit reached!
% 0.74/0.40 % (2684127)------------------------------
% 0.74/0.40 % (2684127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (2684127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (2684127)CaDiCaL version: 2.1.3
% 0.74/0.40 % (2684127)Termination reason: Instruction limit
% 0.74/0.40 % (2684127)Termination phase: shuffling
% 0.74/0.40 % (2684127)Time elapsed: 0.003 s
% 0.74/0.40 % (2684127)Peak memory usage: 10 MB
% 0.74/0.40 % (2684127)Instructions burned: 6 (million)
% 0.74/0.40 % (2684117)Instruction limit reached!
% 0.74/0.40 % (2684117)------------------------------
% 0.74/0.40 % (2684117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (2684117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (2684117)CaDiCaL version: 2.1.3
% 0.74/0.40 % (2684117)Termination reason: Instruction limit
% 0.74/0.40 % (2684117)Termination phase: Preprocessing 3
% 0.74/0.40 % (2684117)Time elapsed: 0.033 s
% 0.74/0.40 % (2684117)Peak memory usage: 12 MB
% 0.74/0.40 % (2684117)Instructions burned: 75 (million)
% 0.74/0.40 % (2684128)Instruction limit reached!
% 0.74/0.40 % (2684128)------------------------------
% 0.74/0.40 % (2684128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.40 % (2684128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.40 % (2684128)CaDiCaL version: 2.1.3
% 0.74/0.40 % (2684128)Termination reason: Instruction limit
% 0.74/0.40 % (2684128)Termination phase: shuffling
% 0.74/0.40 % (2684128)Time elapsed: 0.004 s
% 0.74/0.41 % (2684128)Peak memory usage: 9 MB
% 0.74/0.41 % (2684128)Instructions burned: 9 (million)
% 0.74/0.41 % (2684133)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=3416887222:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.41 % (2684132)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
% 0.74/0.41 % (2684132)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.41 % (2684132)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3332766203:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.41 % (2684137)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.44 % (2684136)lrs+10_1_si=on:cs=on:random_seed=137330129:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.44 % (2684137)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=2593504859:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.44 % (2684136)Instruction limit reached!
% 0.74/0.44 % (2684136)------------------------------
% 0.74/0.44 % (2684136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684136)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684136)Termination reason: Instruction limit
% 0.74/0.44 % (2684136)Termination phase: shuffling
% 0.74/0.44 % (2684136)Time elapsed: 0.004 s
% 0.74/0.44 % (2684136)Peak memory usage: 10 MB
% 0.74/0.44 % (2684136)Instructions burned: 8 (million)
% 0.74/0.44 % (2684138)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2662187174:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.44 % (2684137)Instruction limit reached!
% 0.74/0.44 % (2684137)------------------------------
% 0.74/0.44 % (2684137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684137)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684137)Termination reason: Instruction limit
% 0.74/0.44 % (2684137)Termination phase: shuffling
% 0.74/0.44 % (2684137)Time elapsed: 0.001 s
% 0.74/0.44 % (2684137)Peak memory usage: 9 MB
% 0.74/0.44 % (2684137)Instructions burned: 3 (million)
% 0.74/0.44 % (2684133)Instruction limit reached!
% 0.74/0.44 % (2684133)------------------------------
% 0.74/0.44 % (2684133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684133)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684133)Termination reason: Instruction limit
% 0.74/0.44 % (2684133)Termination phase: Saturation
% 0.74/0.44 % (2684133)Time elapsed: 0.019 s
% 0.74/0.44 % (2684133)Peak memory usage: 12 MB
% 0.74/0.44 % (2684133)Instructions burned: 86 (million)
% 0.74/0.44 % (2684132)Instruction limit reached!
% 0.74/0.44 % (2684132)------------------------------
% 0.74/0.44 % (2684132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684132)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684132)Termination reason: Instruction limit
% 0.74/0.44 % (2684132)Termination phase: shuffling
% 0.74/0.44 % (2684132)Time elapsed: 0.013 s
% 0.74/0.44 % (2684132)Peak memory usage: 10 MB
% 0.74/0.44 % (2684132)Instructions burned: 29 (million)
% 0.74/0.44 % (2684146)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3407468230:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.74/0.44 % (2684118)Instruction limit reached!
% 0.74/0.44 % (2684118)------------------------------
% 0.74/0.44 % (2684118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684118)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684118)Termination reason: Instruction limit
% 0.74/0.44 % (2684118)Termination phase: Property scanning
% 0.74/0.44 % (2684118)Time elapsed: 0.068 s
% 0.74/0.44 % (2684118)Peak memory usage: 13 MB
% 0.74/0.44 % (2684118)Instructions burned: 157 (million)
% 0.74/0.44 % (2684146)Instruction limit reached!
% 0.74/0.44 % (2684146)------------------------------
% 0.74/0.44 % (2684146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.44 % (2684146)CaDiCaL version: 2.1.3
% 0.74/0.44 % (2684146)Termination reason: Instruction limit
% 0.74/0.44 % (2684146)Termination phase: shuffling
% 0.74/0.44 % (2684146)Time elapsed: 0.004 s
% 0.74/0.44 % (2684146)Peak memory usage: 10 MB
% 0.74/0.44 % (2684146)Instructions burned: 19 (million)
% 0.74/0.44 % (2684138)Refutation not found, incomplete strategy
% 0.74/0.44 % (2684138)------------------------------
% 0.74/0.44 % (2684138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.44 % (2684138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (2684138)CaDiCaL version: 2.1.3
% 1.41/0.50 % (2684138)Termination reason: Refutation not found, incomplete strategy
% 1.41/0.50 % (2684138)Time elapsed: 0.017 s
% 1.41/0.50 % (2684138)Peak memory usage: 12 MB
% 1.41/0.50 % (2684138)Instructions burned: 36 (million)
% 1.41/0.50 % (2684138)------------------------------
% 1.41/0.50 % (2684138)------------------------------
% 1.41/0.50 % (2684144)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3035722583:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.41/0.50 % (2684145)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2142984001:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.41/0.50 % (2684147)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1508556581:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.41/0.50 % (2684150)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3157966026:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.41/0.50 % (2684150)Instruction limit reached!
% 1.41/0.50 % (2684150)------------------------------
% 1.41/0.50 % (2684150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (2684150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (2684150)CaDiCaL version: 2.1.3
% 1.41/0.50 % (2684150)Termination reason: Instruction limit
% 1.41/0.50 % (2684150)Termination phase: shuffling
% 1.41/0.50 % (2684150)Time elapsed: 0.001 s
% 1.41/0.50 % (2684150)Peak memory usage: 9 MB
% 1.41/0.50 % (2684150)Instructions burned: 4 (million)
% 1.41/0.50 % (2684145)Instruction limit reached!
% 1.41/0.50 % (2684145)------------------------------
% 1.41/0.50 % (2684145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (2684145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (2684145)CaDiCaL version: 2.1.3
% 1.41/0.50 % (2684145)Termination reason: Instruction limit
% 1.41/0.50 % (2684145)Termination phase: Property scanning
% 1.41/0.50 % (2684145)Time elapsed: 0.011 s
% 1.41/0.50 % (2684145)Peak memory usage: 10 MB
% 1.41/0.50 % (2684145)Instructions burned: 27 (million)
% 1.41/0.50 % (2684149)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=817414537:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.41/0.50 % (2684151)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2394694133:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.41/0.50 % (2684149)Instruction limit reached!
% 1.41/0.50 % (2684149)------------------------------
% 1.41/0.50 % (2684149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (2684149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (2684149)CaDiCaL version: 2.1.3
% 1.41/0.50 % (2684149)Termination reason: Instruction limit
% 1.41/0.50 % (2684149)Termination phase: shuffling
% 1.41/0.50 % (2684149)Time elapsed: 0.007 s
% 1.41/0.50 % (2684149)Peak memory usage: 10 MB
% 1.41/0.50 % (2684149)Instructions burned: 16 (million)
% 1.41/0.50 % (2684156)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=78994961:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.41/0.50 % (2684151)Instruction limit reached!
% 1.41/0.50 % (2684151)------------------------------
% 1.41/0.50 % (2684151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.41/0.50 % (2684151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.41/0.50 % (2684151)CaDiCaL version: 2.1.3
% 1.41/0.50 % (2684151)Termination reason: Instruction limit
% 1.41/0.50 % (2684151)Termination phase: shuffling
% 1.41/0.50 % (2684151)Time elapsed: 0.011 s
% 1.41/0.50 % (2684151)Peak memory usage: 10 MB
% 1.41/0.50 % (2684151)Instructions burned: 27 (million)
% 1.41/0.50 % (2684157)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2015664356:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.41/0.50 % (2684160)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.41/0.50 % (2684160)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.11/0.56 % (2684156)Instruction limit reached!
% 2.11/0.56 % (2684156)------------------------------
% 2.11/0.56 % (2684156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684156)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684156)Termination reason: Instruction limit
% 2.11/0.56 % (2684156)Termination phase: Property scanning
% 2.11/0.56 % (2684156)Time elapsed: 0.010 s
% 2.11/0.56 % (2684156)Peak memory usage: 10 MB
% 2.11/0.56 % (2684156)Instructions burned: 25 (million)
% 2.11/0.56 % (2684160)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=1994323353:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.11/0.56 % (2684163)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.11/0.56 % (2684160)Instruction limit reached!
% 2.11/0.56 % (2684160)------------------------------
% 2.11/0.56 % (2684160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684160)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684160)Termination reason: Instruction limit
% 2.11/0.56 % (2684160)Termination phase: shuffling
% 2.11/0.56 % (2684160)Time elapsed: 0.006 s
% 2.11/0.56 % (2684160)Peak memory usage: 10 MB
% 2.11/0.56 % (2684160)Instructions burned: 14 (million)
% 2.11/0.56 % (2684163)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=1705951716:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.11/0.56 % (2684163)Instruction limit reached!
% 2.11/0.56 % (2684163)------------------------------
% 2.11/0.56 % (2684163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684163)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684163)Termination reason: Instruction limit
% 2.11/0.56 % (2684163)Termination phase: shuffling
% 2.11/0.56 % (2684163)Time elapsed: 0.004 s
% 2.11/0.56 % (2684163)Peak memory usage: 10 MB
% 2.11/0.56 % (2684163)Instructions burned: 9 (million)
% 2.11/0.56 % (2684164)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=83855963:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.11/0.56 % (2684157)Instruction limit reached!
% 2.11/0.56 % (2684157)------------------------------
% 2.11/0.56 % (2684157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684157)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684157)Termination reason: Instruction limit
% 2.11/0.56 % (2684157)Termination phase: Preprocessing 3
% 2.11/0.56 % (2684157)Time elapsed: 0.027 s
% 2.11/0.56 % (2684157)Peak memory usage: 11 MB
% 2.11/0.56 % (2684157)Instructions burned: 61 (million)
% 2.11/0.56 % (2684164)Instruction limit reached!
% 2.11/0.56 % (2684164)------------------------------
% 2.11/0.56 % (2684164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684164)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684164)Termination reason: Instruction limit
% 2.11/0.56 % (2684164)Termination phase: Property scanning
% 2.11/0.56 % (2684164)Time elapsed: 0.009 s
% 2.11/0.56 % (2684164)Peak memory usage: 10 MB
% 2.11/0.56 % (2684164)Instructions burned: 33 (million)
% 2.11/0.56 % (2684166)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1603093234:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.11/0.56 % (2684166)Instruction limit reached!
% 2.11/0.56 % (2684166)------------------------------
% 2.11/0.56 % (2684166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.56 % (2684166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.56 % (2684166)CaDiCaL version: 2.1.3
% 2.11/0.56 % (2684166)Termination reason: Instruction limit
% 2.11/0.56 % (2684166)Termination phase: shuffling
% 2.11/0.57 % (2684166)Time elapsed: 0.003 s
% 2.11/0.57 % (2684166)Peak memory usage: 10 MB
% 2.11/0.57 % (2684166)Instructions burned: 7 (million)
% 2.11/0.57 % (2684168)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3457278087:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.11/0.57 % (2684170)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1180051590:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.11/0.57 % (2684172)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1713205563:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.11/0.57 % (2684168)Instruction limit reached!
% 2.11/0.57 % (2684168)------------------------------
% 2.11/0.57 % (2684168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684168)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684168)Termination reason: Instruction limit
% 2.11/0.57 % (2684168)Termination phase: shuffling
% 2.11/0.57 % (2684168)Time elapsed: 0.010 s
% 2.11/0.57 % (2684168)Peak memory usage: 10 MB
% 2.11/0.57 % (2684168)Instructions burned: 23 (million)
% 2.11/0.57 % (2684170)Instruction limit reached!
% 2.11/0.57 % (2684170)------------------------------
% 2.11/0.57 % (2684170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684170)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684170)Termination reason: Instruction limit
% 2.11/0.57 % (2684170)Termination phase: shuffling
% 2.11/0.57 % (2684170)Time elapsed: 0.009 s
% 2.11/0.57 % (2684170)Peak memory usage: 10 MB
% 2.11/0.57 % (2684170)Instructions burned: 22 (million)
% 2.11/0.57 % (2684173)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1016973423:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.11/0.57 % (2684177)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2449170383:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.11/0.57 % (2684178)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=545228617:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.11/0.57 % (2684144)Instruction limit reached!
% 2.11/0.57 % (2684144)------------------------------
% 2.11/0.57 % (2684144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684144)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684144)Termination reason: Instruction limit
% 2.11/0.57 % (2684144)Termination phase: Saturation
% 2.11/0.57 % (2684144)Time elapsed: 0.110 s
% 2.11/0.57 % (2684144)Peak memory usage: 15 MB
% 2.11/0.57 % (2684144)Instructions burned: 250 (million)
% 2.11/0.57 % (2684178)Instruction limit reached!
% 2.11/0.57 % (2684178)------------------------------
% 2.11/0.57 % (2684178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684178)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684178)Termination reason: Instruction limit
% 2.11/0.57 % (2684178)Termination phase: Naming
% 2.11/0.57 % (2684178)Time elapsed: 0.019 s
% 2.11/0.57 % (2684178)Peak memory usage: 11 MB
% 2.11/0.57 % (2684178)Instructions burned: 44 (million)
% 2.11/0.57 % (2684182)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.11/0.57 % (2684182)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=36599970:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.11/0.57 % (2684182)Instruction limit reached!
% 2.11/0.57 % (2684182)------------------------------
% 2.11/0.57 % (2684182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684182)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684182)Termination reason: Instruction limit
% 2.11/0.57 % (2684182)Termination phase: shuffling
% 2.11/0.57 % (2684182)Time elapsed: 0.004 s
% 2.11/0.57 % (2684182)Peak memory usage: 10 MB
% 2.11/0.57 % (2684182)Instructions burned: 9 (million)
% 2.11/0.57 % (2684115) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2684107-2684115"...
% 2.11/0.57 % (2684183)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=615140939:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.11/0.57 % (2684147) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2684107-2684147"...
% 2.11/0.57 % (2684173)Instruction limit reached!
% 2.11/0.57 % (2684173)------------------------------
% 2.11/0.57 % (2684173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684173)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684173)Termination reason: Instruction limit
% 2.11/0.57 % (2684173)Termination phase: Property scanning
% 2.11/0.57 % (2684173)Time elapsed: 0.062 s
% 2.11/0.57 % (2684173)Peak memory usage: 13 MB
% 2.11/0.57 % (2684173)Instructions burned: 145 (million)
% 2.11/0.57 % (2684185)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=2864598549:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.11/0.57 % (2684183)Refutation not found, incomplete strategy
% 2.11/0.57 % (2684183)------------------------------
% 2.11/0.57 % (2684183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684183)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684183)Termination reason: Refutation not found, incomplete strategy
% 2.11/0.57 % (2684183)Time elapsed: 0.016 s
% 2.11/0.57 % (2684183)Peak memory usage: 13 MB
% 2.11/0.57 % (2684183)Instructions burned: 37 (million)
% 2.11/0.57 % (2684183)------------------------------
% 2.11/0.57 % (2684183)------------------------------
% 2.11/0.57 % (2684187)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.11/0.57 % (2684187)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1480629616:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.11/0.57 % (2684187)Instruction limit reached!
% 2.11/0.57 % (2684187)------------------------------
% 2.11/0.57 % (2684187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684187)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684187)Termination reason: Instruction limit
% 2.11/0.57 % (2684187)Termination phase: shuffling
% 2.11/0.57 % (2684187)Time elapsed: 0.003 s
% 2.11/0.57 % (2684187)Peak memory usage: 9 MB
% 2.11/0.57 % (2684187)Instructions burned: 6 (million)
% 2.11/0.57 % (2684189)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1583858659:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.11/0.57 % (2684177)Instruction limit reached!
% 2.11/0.57 % (2684177)------------------------------
% 2.11/0.57 % (2684177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684177)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684177)Termination reason: Instruction limit
% 2.11/0.57 % (2684177)Termination phase: Property scanning
% 2.11/0.57 % (2684177)Time elapsed: 0.081 s
% 2.11/0.57 % (2684177)Peak memory usage: 13 MB
% 2.11/0.57 % (2684177)Instructions burned: 194 (million)
% 2.11/0.57 % (2684189)Instruction limit reached!
% 2.11/0.57 % (2684189)------------------------------
% 2.11/0.57 % (2684189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684189)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684189)Termination reason: Instruction limit
% 2.11/0.57 % (2684189)Termination phase: shuffling
% 2.11/0.57 % (2684189)Time elapsed: 0.011 s
% 2.11/0.57 % (2684189)Peak memory usage: 10 MB
% 2.11/0.57 % (2684189)Instructions burned: 23 (million)
% 2.11/0.57 % (2684147)...printing done.
% 2.11/0.57 % (2684147)Refutation found. Thanks to Tanya!
% 2.11/0.57 % SZS status Theorem for theBenchmark
% 2.11/0.57 % SZS output start Proof for theBenchmark
% 2.11/0.57 thf(type_def_5, type, term: $tType).
% 2.11/0.57 thf(type_def_6, type, subst: $tType).
% 2.11/0.57 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 2.11/0.57 thf(type_def_8, type, d_term: $tType).
% 2.11/0.57 thf(type_def_9, type, d_subst: $tType).
% 2.11/0.57 thf(func_def_0, type, one: term).
% 2.11/0.57 thf(func_def_1, type, ap: (term > term > term)).
% 2.11/0.57 thf(func_def_2, type, lam: (term > term)).
% 2.11/0.57 thf(func_def_3, type, sub: (term > subst > term)).
% 2.11/0.57 thf(func_def_4, type, id: subst).
% 2.11/0.57 thf(func_def_5, type, sh: subst).
% 2.11/0.57 thf(func_def_6, type, push: (term > subst > subst)).
% 2.11/0.57 thf(func_def_7, type, comp: (subst > subst > subst)).
% 2.11/0.57 thf(func_def_8, type, var: (term > $o)).
% 2.11/0.57 thf(func_def_9, type, pushprop_lem1v2: $o).
% 2.11/0.57 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 2.11/0.57 thf(func_def_11, type, axmap: $o).
% 2.11/0.57 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 2.11/0.57 thf(func_def_13, type, shinj: $o).
% 2.11/0.57 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 2.11/0.57 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 2.11/0.57 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 2.11/0.57 thf(func_def_17, type, induction2lem: $o).
% 2.11/0.57 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 2.11/0.57 thf(func_def_19, type, axvarshift: $o).
% 2.11/0.57 thf(func_def_20, type, hoasapinj2: $o).
% 2.11/0.57 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 2.11/0.57 thf(func_def_22, type, hoasapinj1: $o).
% 2.11/0.57 thf(func_def_23, type, ulamvar1: $o).
% 2.11/0.57 thf(func_def_24, type, induction2lem_lthm: $o).
% 2.11/0.57 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 2.11/0.57 thf(func_def_26, type, apnotvar: $o).
% 2.11/0.57 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 2.11/0.57 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 2.11/0.57 thf(func_def_29, type, hoasinduction_lthm: $o).
% 2.11/0.57 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 2.11/0.57 thf(func_def_31, type, hoaslaminj: $o).
% 2.11/0.57 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 2.11/0.57 thf(func_def_33, type, induction2lem_gthm: $o).
% 2.11/0.57 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 2.11/0.57 thf(func_def_35, type, hoasinduction_lem3: $o).
% 2.11/0.57 thf(func_def_36, type, hoasinduction_lem2: $o).
% 2.11/0.57 thf(func_def_37, type, termmset_lthm: $o).
% 2.11/0.57 thf(func_def_38, type, hoasinduction_lem1: $o).
% 2.11/0.57 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 2.11/0.57 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 2.11/0.57 thf(func_def_41, type, hoasapnotvar: $o).
% 2.11/0.57 thf(func_def_42, type, hoasinduction_lem0: $o).
% 2.11/0.57 thf(func_def_43, type, hoasinduction: $o).
% 2.11/0.57 thf(func_def_44, type, hoasinduction_gthm: $o).
% 2.11/0.57 thf(func_def_45, type, axapp: $o).
% 2.11/0.57 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 2.11/0.57 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 2.11/0.57 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 2.11/0.57 thf(func_def_49, type, ulamvarind: $o).
% 2.11/0.57 thf(func_def_50, type, induction: $o).
% 2.11/0.57 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 2.11/0.57 thf(func_def_52, type, termmset_gthm: $o).
% 2.11/0.57 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 2.11/0.57 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 2.11/0.57 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 2.11/0.57 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 2.11/0.57 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 2.11/0.57 thf(func_def_58, type, pushprop_lem2v2: $o).
% 2.11/0.57 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 2.11/0.57 thf(func_def_60, type, axclos: $o).
% 2.11/0.57 thf(func_def_61, type, axassoc: $o).
% 2.11/0.57 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 2.11/0.57 thf(func_def_63, type, pushprop_lthm: $o).
% 2.11/0.57 thf(func_def_64, type, apinj2: $o).
% 2.11/0.57 thf(func_def_65, type, apinj1: $o).
% 2.11/0.57 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 2.11/0.57 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 2.11/0.57 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 2.11/0.57 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 2.11/0.57 thf(func_def_70, type, axvarcons: $o).
% 2.11/0.57 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 2.11/0.57 thf(func_def_72, type, axscons: $o).
% 2.11/0.57 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 2.11/0.57 thf(func_def_74, type, axidr: $o).
% 2.11/0.57 thf(func_def_75, type, pushprop_lem1: $o).
% 2.11/0.57 thf(func_def_76, type, laminj: $o).
% 2.11/0.57 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 2.11/0.57 thf(func_def_78, type, pushprop_lem0: $o).
% 2.11/0.57 thf(func_def_79, type, pushprop_gthm: $o).
% 2.11/0.57 thf(func_def_80, type, axabs: $o).
% 2.11/0.57 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 2.11/0.57 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 2.11/0.57 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 2.11/0.57 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 2.11/0.57 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 2.11/0.57 thf(func_def_86, type, lamnotap: $o).
% 2.11/0.57 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 2.11/0.57 thf(func_def_88, type, hoaslamnotvar: $o).
% 2.11/0.57 thf(func_def_89, type, axidl: $o).
% 2.11/0.57 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 2.11/0.57 thf(func_def_91, type, induction2_lthm: $o).
% 2.11/0.57 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 2.11/0.57 thf(func_def_93, type, substmonoid_lthm: $o).
% 2.11/0.57 thf(func_def_94, type, pushprop: $o).
% 2.11/0.57 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 2.11/0.57 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 2.11/0.57 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 2.11/0.57 thf(func_def_98, type, substmonoid: $o).
% 2.11/0.57 thf(func_def_99, type, lamnotvar: $o).
% 2.11/0.57 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 2.11/0.57 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 2.11/0.57 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 2.11/0.57 thf(func_def_103, type, induction2_gthm: $o).
% 2.11/0.57 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 2.11/0.57 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_106, type, hoaslamnotap: $o).
% 2.11/0.57 thf(func_def_107, type, substmonoid_gthm: $o).
% 2.11/0.57 thf(func_def_108, type, ulamvarsh: $o).
% 2.11/0.57 thf(func_def_109, type, induction2: $o).
% 2.11/0.57 thf(func_def_110, type, pushprop_lem3v2: $o).
% 2.11/0.57 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 2.11/0.57 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 2.11/0.57 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 2.11/0.57 thf(func_def_114, type, axshiftcons: $o).
% 2.11/0.57 thf(func_def_115, type, termmset: $o).
% 2.11/0.57 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 2.11/0.57 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 2.11/0.57 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 2.11/0.57 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 2.11/0.57 thf(func_def_120, type, axvarid: $o).
% 2.11/0.57 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 2.11/0.57 thf(func_def_122, type, d2term: (d_term > term)).
% 2.11/0.57 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 2.11/0.57 thf(func_def_124, type, d_one: d_term).
% 2.11/0.57 thf(func_def_125, type, d_id: d_subst).
% 2.11/0.57 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.11/0.57 thf(func_def_128, type, vNOT: ($o > $o)).
% 2.11/0.57 thf(func_def_129, type, db0: !>[X0: $tType]:(X0)).
% 2.11/0.57 thf(func_def_130, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.11/0.57 thf(func_def_133, type, db2: !>[X0: $tType]:(X0)).
% 2.11/0.57 thf(func_def_134, type, db4: !>[X0: $tType]:(X0)).
% 2.11/0.57 thf(func_def_135, type, db3: !>[X0: $tType]:(X0)).
% 2.11/0.57 thf(func_def_136, type, db1: !>[X0: $tType]:(X0)).
% 2.11/0.57 thf(func_def_137, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.11/0.57 thf(func_def_138, type, sP0: $o).
% 2.11/0.57 thf(func_def_139, type, sP1: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_140, type, sP2: $o).
% 2.11/0.57 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_142, type, sP4: $o).
% 2.11/0.57 thf(func_def_143, type, sP5: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_145, type, sP7: $o).
% 2.11/0.57 thf(func_def_146, type, sP8: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_147, type, sP9: $o).
% 2.11/0.57 thf(func_def_148, type, sP10: $o).
% 2.11/0.57 thf(func_def_149, type, sP11: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_150, type, sP12: $o).
% 2.11/0.57 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_152, type, sP14: $o).
% 2.11/0.57 thf(func_def_153, type, sP15: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_154, type, sP16: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_155, type, sP17: $o).
% 2.11/0.57 thf(func_def_156, type, sP18: $o).
% 2.11/0.57 thf(func_def_157, type, sP19: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_158, type, sP20: $o).
% 2.11/0.57 thf(func_def_159, type, sP21: $o).
% 2.11/0.57 thf(func_def_160, type, sP22: $o).
% 2.11/0.57 thf(func_def_161, type, sP23: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_162, type, sP24: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_163, type, sP25: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_164, type, sP26: $o).
% 2.11/0.57 thf(func_def_165, type, sP27: $o).
% 2.11/0.57 thf(func_def_166, type, sP28: $o).
% 2.11/0.57 thf(func_def_167, type, sP29: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_168, type, sP30: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_169, type, sP31: $o).
% 2.11/0.57 thf(func_def_170, type, sP32: $o).
% 2.11/0.57 thf(func_def_171, type, sP33: $o).
% 2.11/0.57 thf(func_def_172, type, sP34: $o).
% 2.11/0.57 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_174, type, sP36: $o).
% 2.11/0.57 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_176, type, sP38: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_177, type, sP39: $o).
% 2.11/0.57 thf(func_def_178, type, sP40: $o).
% 2.11/0.57 thf(func_def_179, type, sP41: $o).
% 2.11/0.57 thf(func_def_180, type, sP42: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_181, type, sP43: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_182, type, sP44: ((term > $o) > $o)).
% 2.11/0.57 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_184, type, sP46: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_185, type, sP47: $o).
% 2.11/0.57 thf(func_def_186, type, sP48: $o).
% 2.11/0.57 thf(func_def_187, type, sP49: $o).
% 2.11/0.57 thf(func_def_188, type, sP50: $o).
% 2.11/0.57 thf(func_def_189, type, sP51: $o).
% 2.11/0.57 thf(func_def_190, type, sP52: $o).
% 2.11/0.57 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_192, type, sP54: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_193, type, sP55: $o).
% 2.11/0.57 thf(func_def_194, type, sP56: ((subst > term > subst > $o) > $o)).
% 2.11/0.57 thf(func_def_195, type, sP57: $o).
% 2.11/0.57 thf(func_def_196, type, sP58: $o).
% 2.11/0.57 thf(func_def_197, type, sK59: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_198, type, sK60: term).
% 2.11/0.57 thf(func_def_199, type, sK61: term).
% 2.11/0.57 thf(func_def_200, type, sK62: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_201, type, sK63: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_202, type, sK64: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_203, type, sK65: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_206, type, sK68: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_208, type, sK70: (term > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_209, type, sK71: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_210, type, sK72: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_211, type, sK73: term).
% 2.11/0.57 thf(func_def_212, type, sK74: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_213, type, sK75: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_214, type, sK76: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_215, type, sK77: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_216, type, sK78: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_217, type, sK79: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_218, type, sK80: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_219, type, sK81: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_220, type, sK82: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_221, type, sK83: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_222, type, sK84: term).
% 2.11/0.57 thf(func_def_223, type, sK85: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_225, type, sK87: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_226, type, sK88: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_227, type, sK89: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_228, type, sK90: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_229, type, sK91: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_230, type, sK92: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_231, type, sK93: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_232, type, sK94: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_233, type, sK95: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_234, type, sK96: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_235, type, sK97: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_236, type, sK98: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_237, type, sK99: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_238, type, sK100: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_240, type, sK102: term).
% 2.11/0.57 thf(func_def_241, type, sK103: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_242, type, sK104: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_243, type, sK105: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_244, type, sK106: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_245, type, sK107: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_246, type, sK108: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_247, type, sK109: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_248, type, sK110: term).
% 2.11/0.57 thf(func_def_249, type, sK111: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_250, type, sK112: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_251, type, sK113: term).
% 2.11/0.57 thf(func_def_252, type, sK114: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_253, type, sK115: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_254, type, sK116: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_255, type, sK117: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_256, type, sK118: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_257, type, sK119: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_258, type, sK120: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_259, type, sK121: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_260, type, sK122: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_261, type, sK123: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_263, type, sK125: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_265, type, sK127: term).
% 2.11/0.57 thf(func_def_266, type, sK128: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_267, type, sK129: term).
% 2.11/0.57 thf(func_def_268, type, sK130: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_269, type, sK131: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_270, type, sK132: (term > $o)).
% 2.11/0.57 thf(func_def_271, type, sK133: term).
% 2.11/0.57 thf(func_def_272, type, sK134: (term > term)).
% 2.11/0.57 thf(func_def_273, type, sK135: term).
% 2.11/0.57 thf(func_def_274, type, sK136: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_275, type, sK137: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_276, type, sK138: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_277, type, sK139: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_278, type, sK140: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_282, type, sK144: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_284, type, sK146: (term > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_288, type, sK150: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_289, type, sK151: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_290, type, sK152: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_291, type, sK153: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_293, type, sK155: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_294, type, sK156: term).
% 2.11/0.57 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_296, type, sK158: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_297, type, sK159: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_298, type, sK160: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_299, type, sK161: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_300, type, sK162: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_302, type, sK164: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_303, type, sK165: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_304, type, sK166: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_305, type, sK167: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_306, type, sK168: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_307, type, sK169: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_309, type, sK171: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_310, type, sK172: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > term > $o)).
% 2.11/0.57 thf(func_def_312, type, sK174: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_313, type, sK175: term).
% 2.11/0.57 thf(func_def_314, type, sK176: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_315, type, sK177: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_316, type, sK178: term).
% 2.11/0.57 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_319, type, sK181: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_320, type, sK182: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_321, type, sK183: term).
% 2.11/0.57 thf(func_def_322, type, sK184: (term > $o)).
% 2.11/0.57 thf(func_def_323, type, sK185: (term > term)).
% 2.11/0.57 thf(func_def_324, type, sK186: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_325, type, sK187: ((term > $o) > term > term)).
% 2.11/0.57 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_327, type, sK189: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_328, type, sK190: term).
% 2.11/0.57 thf(func_def_329, type, sK191: (term > $o)).
% 2.11/0.57 thf(func_def_330, type, sK192: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_331, type, sK193: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_332, type, sK194: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_333, type, sK195: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_334, type, sK196: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_335, type, sK197: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_336, type, sK198: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_337, type, sK199: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_338, type, sK200: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_339, type, sK201: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_341, type, sK203: term).
% 2.11/0.57 thf(func_def_342, type, sK204: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_343, type, sK205: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_348, type, sK210: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_349, type, sK211: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_350, type, sK212: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_351, type, sK213: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_352, type, sK214: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_353, type, sK215: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_354, type, sK216: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_355, type, sK217: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_356, type, sK218: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_357, type, sK219: (term > $o)).
% 2.11/0.57 thf(func_def_358, type, sK220: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_359, type, sK221: term).
% 2.11/0.57 thf(func_def_360, type, sK222: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_361, type, sK223: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_362, type, sK224: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_363, type, sK225: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_364, type, sK226: (term > subst > term > term)).
% 2.11/0.57 thf(func_def_365, type, sK227: term).
% 2.11/0.57 thf(func_def_366, type, sK228: (term > (term > $o) > term)).
% 2.11/0.57 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.11/0.57 thf(func_def_369, type, sK231: term).
% 2.11/0.57 thf(func_def_370, type, sK232: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_371, type, sK233: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_372, type, sK234: term).
% 2.11/0.57 thf(func_def_373, type, sK235: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_374, type, sK236: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_375, type, sK237: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_376, type, sK238: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_377, type, sK239: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_380, type, sK242: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_381, type, sK243: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_382, type, sK244: term).
% 2.11/0.57 thf(func_def_383, type, sK245: subst).
% 2.11/0.57 thf(func_def_384, type, sK246: term).
% 2.11/0.57 thf(func_def_385, type, sK247: (term > $o)).
% 2.11/0.57 thf(func_def_386, type, sK248: subst).
% 2.11/0.57 thf(func_def_387, type, sK249: term).
% 2.11/0.57 thf(func_def_388, type, sK250: subst).
% 2.11/0.57 thf(func_def_389, type, sK251: term).
% 2.11/0.57 thf(func_def_390, type, sK252: subst).
% 2.11/0.57 thf(func_def_391, type, sK253: (term > $o)).
% 2.11/0.57 thf(func_def_392, type, sK254: (term > term)).
% 2.11/0.57 thf(func_def_393, type, sK255: ((term > $o) > subst > term)).
% 2.11/0.57 thf(func_def_394, type, sK256: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_395, type, sK257: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_396, type, sK258: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_397, type, sK259: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_398, type, sK260: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_399, type, sK261: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_400, type, sK262: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > term > $o)).
% 2.11/0.57 thf(func_def_402, type, sK264: term).
% 2.11/0.57 thf(func_def_403, type, sK265: (term > $o)).
% 2.11/0.57 thf(func_def_404, type, sK266: (term > term)).
% 2.11/0.57 thf(func_def_405, type, sK267: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_406, type, sK268: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_407, type, sK269: term).
% 2.11/0.57 thf(func_def_408, type, sK270: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_409, type, sK271: ((term > $o) > term > term)).
% 2.11/0.57 thf(func_def_410, type, sK272: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_411, type, sK273: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_412, type, sK274: term).
% 2.11/0.57 thf(func_def_413, type, sK275: (term > $o)).
% 2.11/0.57 thf(func_def_414, type, sK276: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_415, type, sK277: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_416, type, sK278: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_417, type, sK279: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_418, type, sK280: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_419, type, sK281: term).
% 2.11/0.57 thf(func_def_420, type, sK282: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_422, type, sK284: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_423, type, sK285: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_424, type, sK286: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_425, type, sK287: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_426, type, sK288: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_427, type, sK289: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_428, type, sK290: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_429, type, sK291: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_430, type, sK292: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_431, type, sK293: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_432, type, sK294: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_433, type, sK295: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_434, type, sK296: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_435, type, sK297: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_438, type, sK300: term).
% 2.11/0.57 thf(func_def_439, type, sK301: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_440, type, sK302: ((subst > term > term) > term > term)).
% 2.11/0.57 thf(func_def_441, type, sK303: ((subst > term > term) > term > subst)).
% 2.11/0.57 thf(func_def_442, type, sK304: ((subst > term > term) > term > subst)).
% 2.11/0.57 thf(func_def_443, type, sK305: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_444, type, sK306: ((subst > term > term) > term > subst)).
% 2.11/0.57 thf(func_def_445, type, sK307: ((subst > term > term) > term > subst)).
% 2.11/0.57 thf(func_def_446, type, sK308: ((subst > term > term) > term > term)).
% 2.11/0.57 thf(func_def_447, type, sK309: ((subst > term > subst > $o) > term > term)).
% 2.11/0.57 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_449, type, sK311: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_450, type, sK312: (subst > term > term)).
% 2.11/0.57 thf(func_def_451, type, sK313: term).
% 2.11/0.57 thf(func_def_452, type, sK314: (subst > term > term)).
% 2.11/0.57 thf(func_def_453, type, sK315: subst).
% 2.11/0.57 thf(func_def_454, type, sK316: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_455, type, sK317: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_456, type, sK318: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_457, type, sK319: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_458, type, sK320: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_459, type, sK321: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_460, type, sK322: term).
% 2.11/0.57 thf(func_def_461, type, sK323: term).
% 2.11/0.57 thf(func_def_462, type, sK324: subst).
% 2.11/0.57 thf(func_def_463, type, sK325: term).
% 2.11/0.57 thf(func_def_464, type, sK326: term).
% 2.11/0.57 thf(func_def_465, type, sK327: subst).
% 2.11/0.57 thf(func_def_466, type, sK328: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_467, type, sK329: (term > $o)).
% 2.11/0.57 thf(func_def_468, type, sK330: term).
% 2.11/0.57 thf(func_def_469, type, sK331: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_471, type, sK333: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_473, type, sK335: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_474, type, sK336: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_475, type, sK337: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_477, type, sK339: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_478, type, sK340: (term > (term > $o) > term)).
% 2.11/0.57 thf(func_def_479, type, sK341: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_480, type, sK342: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_481, type, sK343: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_482, type, sK344: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_483, type, sK345: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_484, type, sK346: (subst > (term > $o) > term)).
% 2.11/0.57 thf(func_def_485, type, sK347: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_486, type, sK348: (term > $o)).
% 2.11/0.57 thf(func_def_487, type, sK349: term).
% 2.11/0.57 thf(func_def_488, type, sK350: subst).
% 2.11/0.57 thf(func_def_489, type, sK351: (term > term)).
% 2.11/0.57 thf(func_def_490, type, sK352: term).
% 2.11/0.57 thf(func_def_491, type, sK353: (term > $o)).
% 2.11/0.57 thf(func_def_492, type, sK354: term).
% 2.11/0.57 thf(func_def_493, type, sK355: (term > term)).
% 2.11/0.57 thf(func_def_494, type, sK356: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_495, type, sK357: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_496, type, sK358: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_497, type, sK359: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_498, type, sK360: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_499, type, sK361: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_500, type, sK362: term).
% 2.11/0.57 thf(func_def_501, type, sK363: (term > $o)).
% 2.11/0.57 thf(func_def_502, type, sK364: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_503, type, sK365: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_505, type, sK367: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_506, type, sK368: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.11/0.57 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_509, type, sK371: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_510, type, sK372: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_511, type, sK373: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_512, type, sK374: ((term > $o) > term > term)).
% 2.11/0.57 thf(func_def_513, type, sK375: term).
% 2.11/0.57 thf(func_def_514, type, sK376: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_515, type, sK377: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_516, type, sK378: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_517, type, sK379: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_519, type, sK381: term).
% 2.11/0.57 thf(func_def_520, type, sK382: (term > $o)).
% 2.11/0.57 thf(func_def_521, type, sK383: term).
% 2.11/0.57 thf(func_def_522, type, sK384: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_523, type, sK385: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.11/0.57 thf(func_def_524, type, sK386: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_526, type, sK388: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_527, type, sK389: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_532, type, sK394: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_534, type, sK396: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_535, type, sK397: term).
% 2.11/0.57 thf(func_def_536, type, sK398: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_537, type, sK399: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_538, type, sK400: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_539, type, sK401: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_540, type, sK402: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_541, type, sK403: (term > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_542, type, sK404: term).
% 2.11/0.57 thf(func_def_543, type, sK405: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_544, type, sK406: term).
% 2.11/0.57 thf(func_def_545, type, sK407: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_547, type, sK409: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_548, type, sK410: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_549, type, sK411: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_552, type, sK414: ((subst > term > subst > $o) > subst)).
% 2.11/0.57 thf(func_def_553, type, sK415: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_554, type, sK416: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_555, type, sK417: term).
% 2.11/0.57 thf(func_def_556, type, sK418: (term > $o)).
% 2.11/0.57 thf(func_def_557, type, sK419: (term > term)).
% 2.11/0.57 thf(func_def_558, type, sK420: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_559, type, sK421: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_560, type, sK422: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_561, type, sK423: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_563, type, sK425: ((subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_564, type, sK426: term).
% 2.11/0.57 thf(func_def_565, type, sK427: subst).
% 2.11/0.57 thf(func_def_566, type, sK428: (term > $o)).
% 2.11/0.57 thf(func_def_567, type, sK429: (term > term)).
% 2.11/0.57 thf(func_def_568, type, sK430: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_569, type, sK431: ((term > $o) > subst > term)).
% 2.11/0.57 thf(func_def_570, type, sK432: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_571, type, sK433: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_572, type, sK434: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_573, type, sK435: term).
% 2.11/0.57 thf(func_def_574, type, sK436: (term > $o)).
% 2.11/0.57 thf(func_def_575, type, sK437: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_576, type, sK438: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_577, type, sK439: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_578, type, sK440: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_579, type, sK441: ((term > $o) > term > term)).
% 2.11/0.57 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_581, type, sK443: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_582, type, sK444: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_583, type, sK445: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_584, type, sK446: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_585, type, sK447: term).
% 2.11/0.57 thf(func_def_586, type, sK448: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_587, type, sK449: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_588, type, sK450: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_589, type, sK451: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_590, type, sK452: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_591, type, sK453: (term > (subst > term > subst > $o) > term)).
% 2.11/0.57 thf(func_def_592, type, sK454: subst).
% 2.11/0.57 thf(func_def_593, type, sK455: subst).
% 2.11/0.57 thf(func_def_594, type, sK456: subst).
% 2.11/0.57 thf(func_def_595, type, sK457: subst).
% 2.11/0.57 thf(func_def_596, type, sK458: term).
% 2.11/0.57 thf(func_def_597, type, sK459: subst).
% 2.11/0.57 thf(func_def_598, type, sK460: (term > $o)).
% 2.11/0.57 thf(func_def_599, type, sK461: subst).
% 2.11/0.57 thf(func_def_600, type, sK462: term).
% 2.11/0.57 thf(func_def_601, type, sK463: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_602, type, sK464: (term > subst > (term > $o) > term > $o)).
% 2.11/0.57 thf(func_def_603, type, sK465: subst).
% 2.11/0.57 thf(func_def_604, type, sK466: term).
% 2.11/0.57 thf(func_def_605, type, sK467: (term > $o)).
% 2.11/0.57 thf(func_def_606, type, sK468: (term > $o)).
% 2.11/0.57 thf(func_def_607, type, sK469: subst).
% 2.11/0.57 thf(func_def_608, type, sK470: term).
% 2.11/0.57 thf(func_def_609, type, sK471: ((term > $o) > (term > $o) > term > subst > term)).
% 2.11/0.57 thf(func_def_610, type, sK472: term).
% 2.11/0.57 thf(func_def_611, type, sK473: term).
% 2.11/0.57 thf(func_def_612, type, sK474: term).
% 2.11/0.57 thf(func_def_613, type, sK475: term).
% 2.11/0.57 thf(func_def_614, type, sK476: term).
% 2.11/0.57 thf(func_def_615, type, sK477: term).
% 2.11/0.57 thf(func_def_616, type, sK478: term).
% 2.11/0.57 thf(func_def_617, type, sK479: subst).
% 2.11/0.57 thf(func_def_618, type, sK480: (term > $o)).
% 2.11/0.57 thf(func_def_619, type, sK481: (term > $o)).
% 2.11/0.57 thf(func_def_620, type, sK482: term).
% 2.11/0.57 thf(func_def_621, type, sK483: term).
% 2.11/0.57 thf(func_def_622, type, sK484: subst).
% 2.11/0.57 thf(func_def_623, type, sK485: subst).
% 2.11/0.57 thf(func_def_624, type, sK486: term).
% 2.11/0.57 thf(func_def_625, type, sK487: term).
% 2.11/0.57 thf(func_def_626, type, sK488: term).
% 2.11/0.57 thf(func_def_627, type, sK489: term).
% 2.11/0.57 thf(func_def_628, type, sK490: term).
% 2.11/0.57 thf(func_def_629, type, sK491: ((subst > term > subst > $o) > term > $o)).
% 2.11/0.57 thf(func_def_630, type, sK492: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_631, type, sK493: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_632, type, sK494: ((term > $o) > (term > $o) > term > subst > term)).
% 2.11/0.57 thf(func_def_633, type, sK495: subst).
% 2.11/0.57 thf(func_def_634, type, sK496: term).
% 2.11/0.57 thf(func_def_635, type, sK497: (term > $o)).
% 2.11/0.57 thf(func_def_636, type, sK498: (term > $o)).
% 2.11/0.57 thf(func_def_637, type, sK499: term).
% 2.11/0.57 thf(func_def_638, type, sK500: term).
% 2.11/0.57 thf(func_def_639, type, sK501: term).
% 2.11/0.57 thf(func_def_640, type, sK502: term).
% 2.11/0.57 thf(func_def_641, type, sK503: term).
% 2.11/0.57 thf(func_def_642, type, sK504: term).
% 2.11/0.57 thf(func_def_643, type, sK505: term).
% 2.11/0.57 thf(func_def_644, type, sK506: term).
% 2.11/0.57 thf(func_def_645, type, sK507: term).
% 2.11/0.57 thf(func_def_646, type, sK508: term).
% 2.11/0.57 thf(func_def_647, type, sK509: term).
% 2.11/0.57 thf(func_def_648, type, sK510: subst).
% 2.11/0.57 thf(func_def_649, type, sK511: (term > $o)).
% 2.11/0.57 thf(func_def_650, type, sK512: term).
% 2.11/0.57 thf(func_def_651, type, sK513: term).
% 2.11/0.57 thf(func_def_652, type, sK514: (term > $o)).
% 2.11/0.57 thf(func_def_653, type, sK515: term).
% 2.11/0.57 thf(func_def_654, type, sK516: term).
% 2.11/0.57 thf(func_def_655, type, sK517: term).
% 2.11/0.57 thf(func_def_656, type, sK518: term).
% 2.11/0.57 thf(func_def_657, type, sK519: term).
% 2.11/0.57 thf(func_def_658, type, sK520: term).
% 2.11/0.57 thf(func_def_659, type, sK521: term).
% 2.11/0.57 thf(func_def_660, type, sK522: term).
% 2.11/0.57 thf(func_def_661, type, sK523: term).
% 2.11/0.57 thf(func_def_662, type, sK524: term).
% 2.11/0.57 thf(func_def_663, type, sK525: term).
% 2.11/0.57 thf(func_def_664, type, sK526: term).
% 2.11/0.57 thf(func_def_665, type, sK527: subst).
% 2.11/0.57 thf(func_def_666, type, sK528: subst).
% 2.11/0.57 thf(func_def_667, type, sK529: subst).
% 2.11/0.57 thf(func_def_668, type, sK530: subst).
% 2.11/0.57 thf(func_def_669, type, sK531: term).
% 2.11/0.57 thf(func_def_670, type, sK532: (subst > term > term)).
% 2.11/0.57 thf(func_def_671, type, sK533: term).
% 2.11/0.57 thf(func_def_672, type, sK534: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_673, type, sK535: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_674, type, sK536: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_675, type, sK537: subst).
% 2.11/0.57 thf(func_def_676, type, sK538: term).
% 2.11/0.57 thf(func_def_677, type, sK539: (subst > d_subst)).
% 2.11/0.57 thf(func_def_678, type, sK540: term).
% 2.11/0.57 thf(func_def_679, type, sK541: term).
% 2.11/0.57 thf(func_def_680, type, sK542: term).
% 2.11/0.57 thf(func_def_681, type, sK543: term).
% 2.11/0.57 thf(func_def_682, type, sK544: term).
% 2.11/0.57 thf(func_def_683, type, sK545: term).
% 2.11/0.57 thf(func_def_684, type, sK546: (term > subst > term > term)).
% 2.11/0.57 thf(func_def_685, type, sK547: term).
% 2.11/0.57 thf(func_def_686, type, sK548: term).
% 2.11/0.57 thf(func_def_687, type, sK549: (term > subst > term > term)).
% 2.11/0.57 thf(func_def_688, type, sK550: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_689, type, sK551: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_690, type, sK552: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_691, type, sK553: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_692, type, sK554: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_693, type, sK555: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_694, type, sK556: subst).
% 2.11/0.57 thf(func_def_695, type, sK557: term).
% 2.11/0.57 thf(func_def_696, type, sK558: (subst > term > term)).
% 2.11/0.57 thf(func_def_697, type, sK559: (subst > term > term)).
% 2.11/0.57 thf(func_def_698, type, sK560: (term > subst > (term > $o) > term > $o)).
% 2.11/0.57 thf(func_def_699, type, sK561: (term > $o)).
% 2.11/0.57 thf(func_def_700, type, sK562: subst).
% 2.11/0.57 thf(func_def_701, type, sK563: term).
% 2.11/0.57 thf(func_def_702, type, sK564: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_703, type, sK565: term).
% 2.11/0.57 thf(func_def_704, type, sK566: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_705, type, sK567: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_706, type, sK568: (term > subst > term > term)).
% 2.11/0.57 thf(func_def_707, type, sK569: ((subst > term > subst > $o) > subst > term > term)).
% 2.11/0.57 thf(func_def_708, type, sK570: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_709, type, sK571: term).
% 2.11/0.57 thf(func_def_710, type, sK572: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_711, type, sK573: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_712, type, sK574: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_713, type, sK575: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_714, type, sK576: subst).
% 2.11/0.57 thf(func_def_715, type, sK577: (term > d_term)).
% 2.11/0.57 thf(func_def_716, type, sK578: term).
% 2.11/0.57 thf(func_def_717, type, sK579: (term > subst > term > term)).
% 2.11/0.57 thf(func_def_718, type, sK580: term).
% 2.11/0.57 thf(func_def_719, type, sK581: ((subst > term > term) > subst)).
% 2.11/0.57 thf(func_def_720, type, sK582: ((subst > term > term) > term)).
% 2.11/0.57 thf(func_def_721, type, sK583: term).
% 2.11/0.57 thf(func_def_722, type, sK584: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_723, type, sK585: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_724, type, sK586: term).
% 2.11/0.57 thf(func_def_725, type, sK587: (term > $o)).
% 2.11/0.57 thf(func_def_726, type, sK588: (subst > term > subst > $o)).
% 2.11/0.57 thf(func_def_727, type, sK589: ((term > $o) > term)).
% 2.11/0.57 thf(func_def_728, type, sK590: ((subst > term > subst > $o) > term > $o)).
% 2.11/0.57 thf(func_def_729, type, sK591: term).
% 2.11/0.57 thf(f1,axiom,(
% 2.11/0.57 ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & hoasinduction_lem2v2_gthm & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & termmset_gthm & axabs & hoasinduction_lem2_gthm & hoasinduction_lem1v2_gthm & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & ~lamnotap & hoasinduction_lem1v2 & hoasinduction_lem3v2_gthm & hoasapinj1_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axclos & (hoasapinj2_lthm <=> (! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) & (one = ((d2term @ d_one))) & hoaslamnotap_gthm & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & induction2_gthm & ((! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ 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))))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))))) <=> hoasinduction_lem3v2a_lthm) & pushprop & (hoasapinj1_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X13 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X20 : term,X19 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15))))) & pushprop_lem2v2_gthm & hoaslamnotap_lthm & (! [X10 : (subst > term > subst > $o),X45 : term,X44 : term,X11 : (term > $o)] : (~(X11 @ X44) | ~(X11 @ X45) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_lem2v2) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & (pushprop_lem0 <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoasinduction_lem2_lthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (sh = ((d2subst @ d_id))) & ! [X5 : d_subst] : (X5 = d_id) & ((^[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) & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ 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)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id))) & hoasinduction_gthm & (apinj2 <=> ! [X15 : term,X19 : term,X20 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20))) & (id = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & axmap & ulamvarind & pushprop_lem1_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0_lthm) & hoaslamnotvar_gthm & axapp & apnotvar & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X18 : (subst > term > term),X33 : term,X32 : subst,X31 : (subst > term > term)] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & (induction2lem_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)))))))) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem3v2a) & (pushprop_lem0_lthm <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & hoaslamnotvar_lthm & hoasapnotvar_lthm & (! [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) | ~ ! [X38 : subst,X36 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [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 @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aaa) & ! [X1 : d_term] : (X1 = d_one) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & (induction <=> ! [X21 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X21))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X16 : term,X10 : (term > $o),X17 : subst] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))))) <=> induction2_lthm) & ~ulamvar1 & (laminj <=> ! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15))) & hoasapnotvar_gthm & (! [X15 : term,X13 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & pushprop_lem1v2_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1 & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3v2) & pushprop_gthm & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (hoasinduction_lem3aa <=> ! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ 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,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & ((! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [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)) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [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) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id)) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) <=> hoasinduction_lthm) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & (hoasinduction_lem3aa_lthm <=> ! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))) <=> hoasinduction_lem3_lthm) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1_lthm & substmonoid_gthm & pushprop_lem2v2_lthm & (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) <=> induction2) & pushprop_lem3v2_lthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : ((X11 @ (lam @ X48)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : ((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)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) <=> hoasinduction_lem3v2_lthm) & hoaslamnotvar & induction2lem_gthm & ((! [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] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X14 : subst,X26 : subst,X25 : 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)) | (X10 @ id @ X28 @ 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)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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))))))) <=> hoasinduction_lthm_3) & hoaslaminj_gthm & hoasinduction_lem3b_gthm & pushprop_lem0_gthm & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))))) & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & lamnotvar & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ X30 @ id))))))) & (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))) <=> hoasapinj1) & hoasinduction_lem3_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X19 : term,X20 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20)) <=> hoasapinj2) & axassoc & (hoasinduction_lem3b <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (pushprop_lem1 <=> ! [X15 : term,X13 : term,X26 : (term > $o),X10 : (term > $o),X14 : subst] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))) & (! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ 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)) | (X10 @ id @ X30 @ id)) <=> hoasinduction_no_psi_cond) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & hoasapnotvar & (induction2lem <=> ! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))))) & hoasapinj2_gthm & axvarshift & (! [X14 : subst,X10 : (term > $o),X13 : term,X11 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)) <=> pushprop_lem1v2) & (apinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15))) & ulamvarsh & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X11 : (term > $o),X10 : (term > $o),X14 : subst,X13 : term] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) <=> pushprop_lem1v2_lthm) & hoasinduction_lem3a_gthm & pushprop_lthm_orig & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X14 : subst,X15 : term,X26 : (term > $o),X13 : term,X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & hoasinduction_lem1_gthm & (hoaslaminj <=> ! [X32 : subst,X18 : (subst > term > term),X33 : term,X31 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> termmset) & pushprop_lem3v2 & (hoaslamnotap <=> ! [X46 : term,X47 : term,X18 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))),
% 2.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 2.11/0.57 thf(f2,conjecture,(
% 2.11/0.57 (! [X0 : term] : ~(var @ (lam @ X0)) = lamnotvar)),
% 2.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar)).
% 2.11/0.57 thf(f3,negated_conjecture,(
% 2.11/0.57 ~ (! [X0 : term] : ~(var @ (lam @ X0)) = lamnotvar)),
% 2.11/0.57 inference(negated_conjecture,[status(cth)],[f2])).
% 2.11/0.57 thf(f4,plain,(
% 2.11/0.57 ~ (! [X0 : term] : ~(var @ (lam @ X0)) = lamnotvar)),
% 2.11/0.57 inference(rectify,[],[f3])).
% 2.11/0.57 thf(f5,plain,(
% 2.11/0.57 ~ (lamnotvar = ((!! @ term @ (^[Y0 : term]: (~ (var @ (lam @ Y0)))))))),
% 2.11/0.57 inference(fool_elimination,[],[f4])).
% 2.11/0.57 thf(f6,plain,(
% 2.11/0.57 ((! [X0 : term] : (((sub @ X0 @ id)) = X0) => ! [X1 : term] : (((sub @ X1 @ id)) = X1)) <=> termmset_lthm) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> axvarcons) & hoasinduction_lem2v2_gthm & (hoasinduction_lem3v2_f <=> ! [X4 : term] : ~ ! [X5 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7))))) & (axscons <=> ! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8)) & termmset_gthm & axabs & hoasinduction_lem2_gthm & hoasinduction_lem1v2_gthm & (! [X9 : (subst > term > subst > $o)] : ~ ! [X10 : (term > $o)] : ~ ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) <=> hoasinduction_lem0) & pushprop_lem2v2 & (hoasinduction_lem3 <=> ! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : subst,X15 : subst,X16 : term,X17 : subst] : (~(X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14) | (X12 @ X17 @ X16 @ (comp @ X15 @ X14))) | (X12 @ id @ (lam @ X13) @ id) | ~ ! [X18 : term] : (~(X12 @ id @ X18 @ id) | (X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id)) | ~ ! [X19 : subst,X20 : term,X21 : subst,X22 : subst] : ((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19) | ~(X12 @ X21 @ X20 @ (comp @ X22 @ X19))) | ~ ! [X23 : (subst > term > term)] : (~ ! [X24 : subst,X25 : term,X26 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) | (X12 @ id @ (lam @ (X23 @ sh @ one)) @ id) | ~ ! [X27 : term] : (~(X12 @ id @ X27 @ id) | (X12 @ id @ (X23 @ id @ X27) @ id))))) & ~lamnotap & hoasinduction_lem1v2 & hoasinduction_lem3v2_gthm & hoasapinj1_gthm & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axclos & (hoasapinj2_lthm <=> (! [X28 : term,X29 : term,X30 : term,X31 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)) => ! [X32 : term,X33 : term,X34 : term,X35 : term] : ((X32 = X35) | (((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32)))))) & (one = ((d2term @ d_one))) & hoaslamnotap_gthm & (hoasinduction_lem2 <=> ! [X36 : (subst > term > subst > $o),X37 : term,X38 : term] : (~ ! [X39 : term,X40 : term] : (~(X36 @ id @ X39 @ id) | (X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id) | ~(X36 @ id @ X40 @ id)) | (X36 @ id @ (ap @ X37 @ X38) @ id) | ~(X36 @ id @ X37 @ id) | ~ ! [X41 : subst,X42 : subst,X43 : subst,X44 : term] : ((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42) | ~(X36 @ X41 @ X44 @ (comp @ X43 @ X42))) | ~(X36 @ id @ X38 @ id) | ~ ! [X45 : term,X46 : subst,X47 : subst,X48 : subst] : (~(X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48) | (X36 @ X46 @ X45 @ (comp @ X47 @ X48))))) & ! [X49 : d_term,X50 : d_term] : ((((d2term @ X50)) = ((d2term @ X49))) => (X49 = X50)) & induction2_gthm & ((! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X53 : term,X54 : subst] : (((X52 @ X54 @ X53)) = ((sub @ X51 @ (push @ X53 @ X54)))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : term,X58 : (subst > term > subst > $o)] : ((X56 @ (lam @ X57)) | ~ ! [X59 : term] : (((X56 @ X59)) = ((X58 @ id @ X59 @ id))) | ~ ! [X60 : (subst > term > term)] : ((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id) | ~ ! [X61 : term] : (~(X58 @ id @ X61 @ id) | (X58 @ id @ (X60 @ id @ X61) @ id)) | ~ ! [X62 : subst,X63 : term,X64 : subst] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64))))) | ~ ! [X65 : term] : (~(X56 @ X65) | (X56 @ (sub @ X57 @ (push @ X65 @ id))))))) <=> hoasinduction_lem3v2a_lthm) & pushprop & (hoasapinj1_lthm <=> (! [X66 : term] : (((sub @ X66 @ id)) = X66) => (! [X67 : term,X68 : term,X69 : term,X70 : term] : ((((ap @ X68 @ X70)) != ((ap @ X69 @ X67))) | (X68 = X69)) => ! [X71 : term,X72 : term,X73 : term,X74 : term] : ((((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72))) | (X73 = X74))))) & pushprop_lem2v2_gthm & hoaslamnotap_lthm & (! [X75 : (subst > term > subst > $o),X76 : term,X77 : term,X78 : (term > $o)] : (~(X78 @ X77) | ~(X78 @ X76) | ~ ! [X79 : subst,X80 : subst,X81 : subst,X82 : term] : ((X75 @ X80 @ X82 @ (comp @ X81 @ X79)) | ~(X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) | (X78 @ (ap @ X77 @ X76)) | ~ ! [X83 : subst,X84 : term,X85 : subst,X86 : subst] : ((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85) | ~(X75 @ X83 @ X84 @ (comp @ X86 @ X85))) | ~ ! [X87 : term] : (((X75 @ id @ X87 @ id)) = ((X78 @ X87))) | ~ ! [X88 : term,X89 : term] : (~(X75 @ id @ X89 @ id) | (X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id) | ~(X75 @ id @ X88 @ id))) <=> hoasinduction_lem2v2) & (hoasinduction_p_and_p_prime = (^[X90 : (subst > term > subst > $o), X91 : (term > $o)] : (! [X92 : term] : (((X90 @ id @ X92 @ id)) = ((X91 @ X92)))))) & (pushprop_lem0 <=> ! [X93 : (term > $o),X94 : term,X95 : subst] : ~ ! [X96 : (term > $o)] : ~ ! [X97 : term] : (((X93 @ (sub @ X97 @ (push @ X94 @ X95)))) = ((X96 @ X97)))) & (axvarid <=> ! [X98 : term] : (((sub @ X98 @ id)) = X98)) & hoasinduction_lem2_lthm & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (sh = ((d2subst @ d_id))) & ! [X99 : d_subst] : (d_id = X99) & ((^[X100 : term, X101 : subst, X102 : (term > $o), X103 : (term > $o)] : (! [X104 : term] : (((X102 @ (sub @ X104 @ (push @ X100 @ X101)))) = ((X103 @ X104))))) = pushprop_p_and_p_prime) & (hoasinduction <=> ! [X105 : (subst > term > subst > $o),X106 : term] : (~ ! [X107 : term] : ((X105 @ id @ X107 @ id) | ~(var @ (sub @ X107 @ id))) | ~ ! [X108 : subst,X109 : subst,X110 : subst,X111 : term] : ((X105 @ X110 @ X111 @ (comp @ X109 @ X108)) | ~(X105 @ (comp @ X110 @ X109) @ (sub @ X111 @ X109) @ X108)) | ~ ! [X112 : (subst > term > term)] : (~ ! [X113 : term] : ((X105 @ id @ (X112 @ id @ X113) @ id) | ~(X105 @ id @ X113 @ id)) | ~ ! [X114 : term,X115 : subst,X116 : subst] : (((X112 @ (comp @ X115 @ X116) @ (sub @ X114 @ X116))) = ((sub @ (X112 @ X115 @ X114) @ X116))) | (X105 @ id @ (lam @ (X112 @ sh @ one)) @ id)) | ~ ! [X117 : term,X118 : term] : (~(X105 @ id @ X118 @ id) | (X105 @ id @ (ap @ (sub @ X117 @ id) @ X118) @ id) | ~(X105 @ id @ X117 @ id)) | ~ ! [X119 : subst,X120 : term,X121 : subst,X122 : subst] : (~(X105 @ X119 @ X120 @ (comp @ X121 @ X122)) | (X105 @ (comp @ X119 @ X121) @ (sub @ X120 @ X121) @ X122)) | (X105 @ id @ X106 @ id))) & hoasinduction_gthm & (apinj2 <=> ! [X123 : term,X124 : term,X125 : term,X126 : term] : ((((ap @ X123 @ X125)) != ((ap @ X126 @ X124))) | (X124 = X125))) & (id = ((d2subst @ d_id))) & (hoasinduction_lem3a <=> ! [X127 : term,X128 : (subst > term > subst > $o)] : (~ ! [X129 : (subst > term > term)] : (~ ! [X130 : term,X131 : subst,X132 : subst] : (((sub @ (X129 @ X131 @ X130) @ X132)) = ((X129 @ (comp @ X131 @ X132) @ (sub @ X130 @ X132)))) | (X128 @ id @ (lam @ (X129 @ sh @ one)) @ id) | ~ ! [X133 : term] : ((X128 @ id @ (X129 @ id @ X133) @ id) | ~(X128 @ id @ X133 @ id))) | (X128 @ id @ (lam @ X127) @ id) | ~ ! [X134 : term] : ((X128 @ id @ (sub @ X127 @ (push @ X134 @ id)) @ id) | ~(X128 @ id @ X134 @ id)))) & axmap & ulamvarind & pushprop_lem1_gthm & (! [X135 : subst] : (((comp @ id @ X135)) = X135) <=> axidl) & (! [X136 : (subst > term > subst > $o)] : ~ ! [X137 : (term > $o)] : ~ ! [X138 : term] : (((X136 @ id @ X138 @ id)) = ((X137 @ X138))) <=> hoasinduction_lem0_lthm) & hoaslamnotvar_gthm & axapp & apnotvar & (hoaslaminj_lthm <=> (! [X139 : term,X140 : subst] : (((sub @ one @ (push @ X139 @ X140))) = X139) => (! [X141 : term,X142 : subst] : (((comp @ sh @ (push @ X141 @ X142))) = X142) => (! [X143 : term,X144 : term] : ((X143 = X144) | (((lam @ X143)) != ((lam @ X144)))) => ! [X145 : (subst > term > term),X146 : term,X147 : subst,X148 : (subst > term > term)] : ((((X148 @ X147 @ X146)) = ((X145 @ X147 @ X146))) | ~ ! [X149 : subst,X150 : subst,X151 : term] : (((X148 @ (comp @ X150 @ X149) @ (sub @ X151 @ X149))) = ((sub @ (X148 @ X150 @ X151) @ X149))) | (((lam @ (X145 @ sh @ one))) != ((lam @ (X148 @ sh @ one)))) | ~ ! [X152 : subst,X153 : subst,X154 : term] : (((sub @ (X145 @ X153 @ X154) @ X152)) = ((X145 @ (comp @ X153 @ X152) @ (sub @ X154 @ X152))))))))) & (induction2lem_lthm <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => (! [X159 : subst] : (((comp @ X159 @ id)) = X159) => (! [X160 : term,X161 : (term > $o)] : ((X161 @ X160) | ~ ! [X162 : term] : ((X161 @ X162) | ~(var @ X162)) | ~ ! [X163 : term] : (~(X161 @ X163) | (X161 @ (lam @ X163))) | ~ ! [X164 : term,X165 : term] : (~(X161 @ X165) | ~(X161 @ X164) | (X161 @ (ap @ X165 @ X164)))) => ! [X166 : (term > $o),X167 : subst,X168 : term] : (~ ! [X169 : term] : (~ ! [X170 : term] : (~(X166 @ X170) | (X166 @ (sub @ X169 @ (push @ X170 @ id)))) | (X166 @ (lam @ X169))) | ~ ! [X171 : term,X172 : term] : (~(X166 @ X172) | ~(X166 @ X171) | (X166 @ (ap @ X172 @ X171))) | ~ ! [X173 : term] : ((X166 @ (sub @ X173 @ X167)) | ~(var @ X173)) | (X166 @ (sub @ X168 @ X167)))))))) & (hoasinduction_lem3b_lthm <=> ! [X174 : term] : ~ ! [X175 : (subst > term > term)] : (((X175 @ sh @ one)) != ((sub @ X174 @ (push @ one @ sh))))) & (! [X176 : (subst > term > subst > $o),X177 : (term > $o),X178 : term] : (~ ! [X179 : term] : ((X177 @ (sub @ X178 @ (push @ X179 @ id))) | ~(X177 @ X179)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term] : (~(X176 @ id @ X181 @ id) | (X176 @ id @ (X180 @ id @ X181) @ id)) | ~ ! [X182 : term,X183 : subst,X184 : subst] : (((sub @ (X180 @ X183 @ X182) @ X184)) = ((X180 @ (comp @ X183 @ X184) @ (sub @ X182 @ X184)))) | (X176 @ id @ (lam @ (X180 @ sh @ one)) @ id)) | (X177 @ (lam @ X178)) | ~ ! [X185 : term] : (((X177 @ X185)) = ((X176 @ id @ X185 @ id)))) <=> hoasinduction_lem3v2a) & (pushprop_lem0_lthm <=> ! [X186 : (term > $o),X187 : term,X188 : subst] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X189 @ X190)) = ((X186 @ (sub @ X190 @ (push @ X187 @ X188)))))) & hoaslamnotvar_lthm & hoasapnotvar_lthm & (! [X191 : term,X192 : (subst > term > subst > $o)] : ((X192 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id) | ~ ! [X193 : (subst > term > term),X194 : term] : ((X192 @ id @ (lam @ (X193 @ sh @ one)) @ id) | ~ ! [X195 : subst,X196 : subst,X197 : term] : (((sub @ (X193 @ X196 @ X197) @ X195)) = ((sub @ (sub @ X194 @ (push @ X197 @ X196)) @ X195))) | ~ ! [X198 : term] : (~(X192 @ id @ X198 @ id) | (X192 @ id @ (X193 @ id @ X198) @ id)) | ~ ! [X199 : subst,X200 : subst,X201 : term] : (((sub @ X194 @ (push @ (sub @ X201 @ X200) @ (comp @ X199 @ X200)))) = ((X193 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200))))) | ~ ! [X202 : term] : (~(X192 @ id @ X202 @ id) | (X192 @ id @ (sub @ X191 @ (push @ X202 @ id)) @ id))) <=> hoasinduction_lem3aaa) & ! [X203 : d_term] : (d_one = X203) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ~(var @ (d2term @ d_one)) & (induction <=> ! [X204 : term,X205 : (term > $o)] : (~ ! [X206 : term] : (~(X205 @ X206) | (X205 @ (lam @ X206))) | ~ ! [X207 : term] : (~(var @ X207) | (X205 @ X207)) | ~ ! [X208 : term,X209 : term] : (~(X205 @ X208) | ~(X205 @ X209) | (X205 @ (ap @ X208 @ X209))) | (X205 @ X204))) & ((! [X210 : term] : (((sub @ X210 @ id)) = X210) => (! [X211 : term,X212 : (term > $o),X213 : subst] : (~ ! [X214 : term] : ((X212 @ (lam @ X214)) | ~ ! [X215 : term] : (~(X212 @ X215) | (X212 @ (sub @ X214 @ (push @ X215 @ id))))) | ~ ! [X216 : term] : ((X212 @ (sub @ X216 @ X213)) | ~(var @ X216)) | ~ ! [X217 : term,X218 : term] : (~(X212 @ X217) | (X212 @ (ap @ X217 @ X218)) | ~(X212 @ X218)) | (X212 @ (sub @ X211 @ X213))) => ! [X219 : (term > $o),X220 : term] : (~ ! [X221 : term] : (~ ! [X222 : term] : (~(X219 @ X222) | (X219 @ (sub @ X221 @ (push @ X222 @ id)))) | (X219 @ (lam @ X221))) | ~ ! [X223 : term] : ((X219 @ X223) | ~(var @ X223)) | (X219 @ X220) | ~ ! [X224 : term,X225 : term] : (~(X219 @ X225) | ~(X219 @ X224) | (X219 @ (ap @ X225 @ X224)))))) <=> induction2_lthm) & ~ulamvar1 & (laminj <=> ! [X226 : term,X227 : term] : ((((lam @ X226)) != ((lam @ X227))) | (X226 = X227))) & hoasapnotvar_gthm & (! [X228 : term,X229 : term] : ((((sub @ X229 @ sh)) != ((sub @ X228 @ sh))) | (X228 = X229)) <=> shinj) & pushprop_lem1v2_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem1 & (! [X230 : (term > $o),X231 : (subst > term > subst > $o),X232 : term] : (~ ! [X233 : term] : (~(X230 @ X233) | (X230 @ (sub @ X232 @ (push @ X233 @ id)))) | ~ ! [X234 : subst,X235 : term,X236 : subst,X237 : subst] : ((X231 @ (comp @ X236 @ X234) @ (sub @ X235 @ X234) @ X237) | ~(X231 @ X236 @ X235 @ (comp @ X234 @ X237))) | ~ ! [X238 : term] : (((X230 @ X238)) = ((X231 @ id @ X238 @ id))) | (X230 @ (lam @ X232)) | ~ ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : ((X231 @ X242 @ X240 @ (comp @ X239 @ X241)) | ~(X231 @ (comp @ X242 @ X239) @ (sub @ X240 @ X239) @ X241)) | ~ ! [X243 : (subst > term > term)] : (~ ! [X244 : term,X245 : subst,X246 : subst] : (((X243 @ (comp @ X245 @ X246) @ (sub @ X244 @ X246))) = ((sub @ (X243 @ X245 @ X244) @ X246))) | ~ ! [X247 : term] : ((X231 @ id @ (X243 @ id @ X247) @ id) | ~(X231 @ id @ X247 @ id)) | (X231 @ id @ (lam @ (X243 @ sh @ one)) @ id))) <=> hoasinduction_lem3v2) & pushprop_gthm & (axshiftcons <=> ! [X248 : term,X249 : subst] : (((comp @ sh @ (push @ X248 @ X249))) = X249)) & (hoasinduction_lem3aa <=> ! [X250 : (subst > term > subst > $o),X251 : term] : (~ ! [X252 : term] : ((X250 @ id @ (sub @ X251 @ (push @ X252 @ id)) @ id) | ~(X250 @ id @ X252 @ id)) | (X250 @ id @ (lam @ (sub @ X251 @ (push @ one @ sh))) @ id) | ~ ! [X253 : (subst > term > term)] : (~ ! [X254 : term] : ((X250 @ id @ (X253 @ id @ X254) @ id) | ~(X250 @ id @ X254 @ id)) | (X250 @ id @ (lam @ (X253 @ sh @ one)) @ id) | ~ ! [X255 : subst,X256 : term,X257 : subst] : (((X253 @ (comp @ X257 @ X255) @ (sub @ X256 @ X255))) = ((sub @ (X253 @ X257 @ X256) @ X255)))))) & ((! [X258 : (term > $o),X259 : term] : (~ ! [X260 : term] : ((X258 @ X260) | ~(var @ X260)) | (X258 @ X259) | ~ ! [X261 : term] : (~ ! [X262 : term] : (~(X258 @ X262) | (X258 @ (sub @ X261 @ (push @ X262 @ id)))) | (X258 @ (lam @ X261))) | ~ ! [X263 : term,X264 : term] : (~(X258 @ X264) | (X258 @ (ap @ X263 @ X264)) | ~(X258 @ X263))) => (! [X265 : term,X266 : (subst > term > subst > $o),X267 : term] : ((X266 @ id @ (ap @ X267 @ X265) @ id) | ~ ! [X268 : term,X269 : term] : ((X266 @ id @ (ap @ (sub @ X268 @ id) @ X269) @ id) | ~(X266 @ id @ X269 @ id) | ~(X266 @ id @ X268 @ id)) | ~ ! [X270 : term,X271 : subst,X272 : subst,X273 : subst] : ((X266 @ (comp @ X272 @ X271) @ (sub @ X270 @ X271) @ X273) | ~(X266 @ X272 @ X270 @ (comp @ X271 @ X273))) | ~ ! [X274 : subst,X275 : subst,X276 : subst,X277 : term] : (~(X266 @ (comp @ X276 @ X274) @ (sub @ X277 @ X274) @ X275) | (X266 @ X276 @ X277 @ (comp @ X274 @ X275))) | ~(X266 @ id @ X265 @ id) | ~(X266 @ id @ X267 @ id)) => (! [X278 : (subst > term > subst > $o),X279 : term] : (~ ! [X280 : subst,X281 : term,X282 : subst,X283 : subst] : ((X278 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282) @ X280) | ~(X278 @ X283 @ X281 @ (comp @ X282 @ X280))) | ~ ! [X284 : subst,X285 : subst,X286 : subst,X287 : term] : ((X278 @ X286 @ X287 @ (comp @ X285 @ X284)) | ~(X278 @ (comp @ X286 @ X285) @ (sub @ X287 @ X285) @ X284)) | ~ ! [X288 : (subst > term > term)] : ((X278 @ id @ (lam @ (X288 @ sh @ one)) @ id) | ~ ! [X289 : term,X290 : subst,X291 : subst] : (((sub @ (X288 @ X291 @ X289) @ X290)) = ((X288 @ (comp @ X291 @ X290) @ (sub @ X289 @ X290)))) | ~ ! [X292 : term] : (~(X278 @ id @ X292 @ id) | (X278 @ id @ (X288 @ id @ X292) @ id))) | ~ ! [X293 : term] : (~(X278 @ id @ X293 @ id) | (X278 @ id @ (sub @ X279 @ (push @ X293 @ id)) @ id)) | (X278 @ id @ (lam @ X279) @ id)) => ! [X294 : term,X295 : (subst > term > subst > $o)] : (~ ! [X296 : subst,X297 : subst,X298 : term,X299 : subst] : (~(X295 @ X296 @ X298 @ (comp @ X299 @ X297)) | (X295 @ (comp @ X296 @ X299) @ (sub @ X298 @ X299) @ X297)) | ~ ! [X300 : term,X301 : term] : ((X295 @ id @ (ap @ (sub @ X300 @ id) @ X301) @ id) | ~(X295 @ id @ X300 @ id) | ~(X295 @ id @ X301 @ id)) | ~ ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~(X295 @ (comp @ X302 @ X305) @ (sub @ X303 @ X305) @ X304) | (X295 @ X302 @ X303 @ (comp @ X305 @ X304))) | (X295 @ id @ X294 @ id) | ~ ! [X306 : term] : ((X295 @ id @ X306 @ id) | ~(var @ (sub @ X306 @ id))) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : term] : (~(X295 @ id @ X308 @ id) | (X295 @ id @ (X307 @ id @ X308) @ id)) | (X295 @ id @ (lam @ (X307 @ sh @ one)) @ id) | ~ ! [X309 : subst,X310 : term,X311 : subst] : (((X307 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311))) = ((sub @ (X307 @ X309 @ X310) @ X311)))))))) <=> hoasinduction_lthm) & ! [X312 : term] : ? [X313 : d_term] : (((d2term @ X313)) = X312) & (hoasinduction_lem3aa_lthm <=> ! [X314 : (subst > term > subst > $o),X315 : term] : ((X314 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id) | ~ ! [X316 : (subst > term > term)] : ((X314 @ id @ (lam @ (X316 @ sh @ one)) @ id) | ~ ! [X317 : term] : (~(X314 @ id @ X317 @ id) | (X314 @ id @ (X316 @ id @ X317) @ id)) | ~ ! [X318 : subst,X319 : term,X320 : subst] : (((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))) = ((sub @ (X316 @ X318 @ X319) @ X320)))) | ~ ! [X321 : term] : (~(X314 @ id @ X321 @ id) | (X314 @ id @ (sub @ X315 @ (push @ X321 @ id)) @ id)))) & ((! [X322 : term] : (((sub @ X322 @ id)) = X322) => (! [X323 : term,X324 : (subst > term > subst > $o)] : (~ ! [X325 : (subst > term > term)] : ((X324 @ id @ (lam @ (X325 @ sh @ one)) @ id) | ~ ! [X326 : term] : (~(X324 @ id @ X326 @ id) | (X324 @ id @ (X325 @ id @ X326) @ id)) | ~ ! [X327 : subst,X328 : subst,X329 : term] : (((X325 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327))) = ((sub @ (X325 @ X328 @ X329) @ X327)))) | ~ ! [X330 : term] : ((X324 @ id @ (sub @ X323 @ (push @ X330 @ id)) @ id) | ~(X324 @ id @ X330 @ id)) | (X324 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id)) => ! [X331 : term,X332 : (subst > term > subst > $o)] : ((X332 @ id @ (lam @ X331) @ id) | ~ ! [X333 : subst,X334 : subst,X335 : subst,X336 : term] : ((X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334) @ X333) | ~(X332 @ X335 @ X336 @ (comp @ X334 @ X333))) | ~ ! [X337 : term] : ((X332 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id) | ~(X332 @ id @ X337 @ id)) | ~ ! [X338 : subst,X339 : subst,X340 : subst,X341 : term] : (~(X332 @ (comp @ X339 @ X338) @ (sub @ X341 @ X338) @ X340) | (X332 @ X339 @ X341 @ (comp @ X338 @ X340))) | ~ ! [X342 : (subst > term > term)] : ((X332 @ id @ (lam @ (X342 @ sh @ one)) @ id) | ~ ! [X343 : term,X344 : subst,X345 : subst] : (((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345))) = ((sub @ (X342 @ X344 @ X343) @ X345))) | ~ ! [X346 : term] : ((X332 @ id @ (X342 @ id @ X346) @ id) | ~(X332 @ id @ X346 @ id)))))) <=> hoasinduction_lem3_lthm) & (hoaslam = (^[X347 : subst, X348 : (subst > term > term)] : ((d2term @ d_one)))) & pushprop_lthm & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & hoasinduction_lem1_lthm & substmonoid_gthm & pushprop_lem2v2_lthm & (! [X349 : term,X350 : (term > $o)] : (~ ! [X351 : term] : (~(var @ X351) | (X350 @ X351)) | ~ ! [X352 : term] : (~ ! [X353 : term] : ((X350 @ (sub @ X352 @ (push @ X353 @ id))) | ~(X350 @ X353)) | (X350 @ (lam @ X352))) | (X350 @ X349) | ~ ! [X354 : term,X355 : term] : ((X350 @ (ap @ X354 @ X355)) | ~(X350 @ X354) | ~(X350 @ X355))) <=> induction2) & pushprop_lem3v2_lthm & ((! [X356 : term] : (((sub @ X356 @ id)) = X356) => ! [X357 : (term > $o),X358 : (subst > term > subst > $o),X359 : term] : ((X357 @ (lam @ X359)) | ~ ! [X360 : term] : (~(X357 @ X360) | (X357 @ (sub @ X359 @ (push @ X360 @ id)))) | ~ ! [X361 : (subst > term > term)] : ((X358 @ id @ (lam @ (X361 @ sh @ one)) @ id) | ~ ! [X362 : term,X363 : subst,X364 : subst] : (((X361 @ (comp @ X364 @ X363) @ (sub @ X362 @ X363))) = ((sub @ (X361 @ X364 @ X362) @ X363))) | ~ ! [X365 : term] : (~(X358 @ id @ X365 @ id) | (X358 @ id @ (X361 @ id @ X365) @ id))) | ~ ! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : ((X358 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367) | ~(X358 @ X366 @ X368 @ (comp @ X369 @ X367))) | ~ ! [X370 : subst,X371 : subst,X372 : term,X373 : subst] : (~(X358 @ (comp @ X371 @ X370) @ (sub @ X372 @ X370) @ X373) | (X358 @ X371 @ X372 @ (comp @ X370 @ X373))) | ~ ! [X374 : term] : (((X358 @ id @ X374 @ id)) = ((X357 @ X374))))) <=> hoasinduction_lem3v2_lthm) & hoaslamnotvar & induction2lem_gthm & ((! [X375 : (subst > term > subst > $o)] : ~ ! [X376 : (term > $o)] : ~ ! [X377 : term] : (((X375 @ id @ X377 @ id)) = ((X376 @ X377))) => (! [X378 : (term > $o),X379 : term] : ((X378 @ X379) | ~ ! [X380 : term] : (~(var @ X380) | (X378 @ X380)) | ~ ! [X381 : term,X382 : term] : (~(X378 @ X382) | ~(X378 @ X381) | (X378 @ (ap @ X381 @ X382))) | ~ ! [X383 : term] : ((X378 @ (lam @ X383)) | ~ ! [X384 : term] : (~(X378 @ X384) | (X378 @ (sub @ X383 @ (push @ X384 @ id)))))) => (! [X385 : term] : (((sub @ X385 @ id)) = X385) => (! [X386 : term,X387 : (subst > term > subst > $o),X388 : (term > $o)] : ((X388 @ (lam @ X386)) | ~ ! [X389 : (subst > term > term)] : (~ ! [X390 : subst,X391 : subst,X392 : term] : (((sub @ (X389 @ X391 @ X392) @ X390)) = ((X389 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) | (X387 @ id @ (lam @ (X389 @ sh @ one)) @ id) | ~ ! [X393 : term] : (~(X387 @ id @ X393 @ id) | (X387 @ id @ (X389 @ id @ X393) @ id))) | ~ ! [X394 : term] : (((X388 @ X394)) = ((X387 @ id @ X394 @ id))) | ~ ! [X395 : term] : (~(X388 @ X395) | (X388 @ (sub @ X386 @ (push @ X395 @ id))))) => ! [X396 : term,X397 : (subst > term > subst > $o)] : (~ ! [X398 : term,X399 : subst,X400 : subst,X401 : subst] : ((X397 @ (comp @ X399 @ X400) @ (sub @ X398 @ X400) @ X401) | ~(X397 @ X399 @ X398 @ (comp @ X400 @ X401))) | ~ ! [X402 : term,X403 : term] : (~(X397 @ id @ X402 @ id) | ~(X397 @ id @ X403 @ id) | (X397 @ id @ (ap @ (sub @ X403 @ id) @ X402) @ id)) | (X397 @ id @ X396 @ id) | ~ ! [X404 : term] : ((X397 @ id @ X404 @ id) | ~(var @ (sub @ X404 @ id))) | ~ ! [X405 : subst,X406 : subst,X407 : subst,X408 : term] : ((X397 @ X405 @ X408 @ (comp @ X406 @ X407)) | ~(X397 @ (comp @ X405 @ X406) @ (sub @ X408 @ X406) @ X407)) | ~ ! [X409 : (subst > term > term)] : (~ ! [X410 : term] : ((X397 @ id @ (X409 @ id @ X410) @ id) | ~(X397 @ id @ X410 @ id)) | ~ ! [X411 : subst,X412 : subst,X413 : term] : (((sub @ (X409 @ X412 @ X413) @ X411)) = ((X409 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)))) | (X397 @ id @ (lam @ (X409 @ sh @ one)) @ id))))))) <=> hoasinduction_lthm_3) & hoaslaminj_gthm & hoasinduction_lem3b_gthm & pushprop_lem0_gthm & (substmonoid_lthm <=> (! [X414 : subst] : (((comp @ id @ X414)) = X414) => (! [X415 : subst] : (((comp @ X415 @ id)) = X415) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) & ! [X417 : subst] : (((comp @ id @ X417)) = X417))))) & ! [X418 : d_subst,X419 : d_subst] : ((((d2subst @ X418)) = ((d2subst @ X419))) => (X418 = X419)) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & lamnotvar & (hoasinduction_no_psi_cond_lthm <=> (! [X420 : (subst > term > subst > $o)] : ~ ! [X421 : (term > $o)] : ~ ! [X422 : term] : (((X420 @ id @ X422 @ id)) = ((X421 @ X422))) => (! [X423 : term,X424 : (term > $o)] : (~ ! [X425 : term] : (~ ! [X426 : term] : (~(X424 @ X426) | (X424 @ (sub @ X425 @ (push @ X426 @ id)))) | (X424 @ (lam @ X425))) | ~ ! [X427 : term] : (~(var @ X427) | (X424 @ X427)) | (X424 @ X423) | ~ ! [X428 : term,X429 : term] : (~(X424 @ X428) | ~(X424 @ X429) | (X424 @ (ap @ X428 @ X429)))) => (! [X430 : term] : (((sub @ X430 @ id)) = X430) => (! [X431 : term,X432 : (term > $o),X433 : (subst > term > subst > $o)] : ((X432 @ (lam @ X431)) | ~ ! [X434 : (subst > term > term)] : (~ ! [X435 : term,X436 : subst,X437 : subst] : (((sub @ (X434 @ X436 @ X435) @ X437)) = ((X434 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | ~ ! [X438 : term] : (~(X433 @ id @ X438 @ id) | (X433 @ id @ (X434 @ id @ X438) @ id)) | (X433 @ id @ (lam @ (X434 @ sh @ one)) @ id)) | ~ ! [X439 : term] : ((X432 @ (sub @ X431 @ (push @ X439 @ id))) | ~(X432 @ X439)) | ~ ! [X440 : term] : (((X432 @ X440)) = ((X433 @ id @ X440 @ id)))) => ! [X441 : (subst > term > subst > $o),X442 : term] : (~ ! [X443 : term,X444 : term] : (~(X441 @ id @ X444 @ id) | (X441 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id) | ~(X441 @ id @ X443 @ id)) | ~ ! [X445 : (subst > term > term)] : (~ ! [X446 : term] : ((X441 @ id @ (X445 @ id @ X446) @ id) | ~(X441 @ id @ X446 @ id)) | ~ ! [X447 : subst,X448 : term,X449 : subst] : (((X445 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) = ((sub @ (X445 @ X447 @ X448) @ X449))) | (X441 @ id @ (lam @ (X445 @ sh @ one)) @ id)) | (X441 @ id @ X442 @ id))))))) & (! [X450 : term,X451 : term,X452 : term,X453 : term] : ((X450 = X451) | (((ap @ (sub @ X451 @ id) @ X452)) != ((ap @ (sub @ X450 @ id) @ X453)))) <=> hoasapinj1) & hoasinduction_lem3_gthm & ((! [X454 : term] : (((sub @ X454 @ id)) = X454) => (! [X455 : term,X456 : (subst > term > subst > $o)] : (~ ! [X457 : term] : ((X456 @ id @ (sub @ X455 @ (push @ X457 @ id)) @ id) | ~(X456 @ id @ X457 @ id)) | ~ ! [X458 : (subst > term > term)] : (~ ! [X459 : term] : ((X456 @ id @ (X458 @ id @ X459) @ id) | ~(X456 @ id @ X459 @ id)) | ~ ! [X460 : subst,X461 : term,X462 : subst] : (((sub @ (X458 @ X460 @ X461) @ X462)) = ((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462)))) | (X456 @ id @ (lam @ (X458 @ sh @ one)) @ id)) | (X456 @ id @ (lam @ (sub @ X455 @ (push @ one @ sh))) @ id)) => ! [X463 : term,X464 : (subst > term > subst > $o)] : (~ ! [X465 : (subst > term > term)] : (~ ! [X466 : subst,X467 : subst,X468 : term] : (((sub @ (X465 @ X466 @ X468) @ X467)) = ((X465 @ (comp @ X466 @ X467) @ (sub @ X468 @ X467)))) | ~ ! [X469 : term] : (~(X464 @ id @ X469 @ id) | (X464 @ id @ (X465 @ id @ X469) @ id)) | (X464 @ id @ (lam @ (X465 @ sh @ one)) @ id)) | ~ ! [X470 : term] : ((X464 @ id @ (sub @ X463 @ (push @ X470 @ id)) @ id) | ~(X464 @ id @ X470 @ id)) | (X464 @ id @ (lam @ X463) @ id)))) <=> hoasinduction_lem3a_lthm) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_f_lthm <=> ! [X471 : term] : ~ ! [X472 : (subst > term > term)] : ~ ! [X473 : term,X474 : subst] : (((sub @ X471 @ (push @ X473 @ X474))) = ((X472 @ X474 @ X473)))) & (! [X475 : term,X476 : term,X477 : term,X478 : term] : ((((ap @ (sub @ X478 @ id) @ X476)) != ((ap @ (sub @ X477 @ id) @ X475))) | (X475 = X476)) <=> hoasapinj2) & axassoc & (hoasinduction_lem3b <=> ! [X479 : term] : ~ ! [X480 : (subst > term > term)] : (((X480 @ sh @ one)) != ((sub @ X479 @ (push @ one @ sh))))) & (pushprop_lem1 <=> ! [X481 : term,X482 : term,X483 : (term > $o),X484 : (term > $o),X485 : subst] : (~(X484 @ X482) | (X483 @ (sub @ X482 @ (push @ X481 @ X485))))) & (! [X486 : term,X487 : (subst > term > subst > $o)] : (~ ! [X488 : term,X489 : term] : ((X487 @ id @ (ap @ (sub @ X489 @ id) @ X488) @ id) | ~(X487 @ id @ X489 @ id) | ~(X487 @ id @ X488 @ id)) | ~ ! [X490 : (subst > term > term)] : (~ ! [X491 : term] : ((X487 @ id @ (X490 @ id @ X491) @ id) | ~(X487 @ id @ X491 @ id)) | ~ ! [X492 : subst,X493 : subst,X494 : term] : (((sub @ (X490 @ X493 @ X494) @ X492)) = ((X490 @ (comp @ X493 @ X492) @ (sub @ X494 @ X492)))) | (X487 @ id @ (lam @ (X490 @ sh @ one)) @ id)) | (X487 @ id @ X486 @ id)) <=> hoasinduction_no_psi_cond) & (substmonoid <=> (! [X495 : subst] : (((comp @ X495 @ id)) = X495) & ! [X496 : subst] : (((comp @ id @ X496)) = X496))) & hoasapnotvar & (induction2lem <=> ! [X497 : (term > $o),X498 : term,X499 : subst] : (~ ! [X500 : term,X501 : term] : (~(X497 @ X501) | (X497 @ (ap @ X501 @ X500)) | ~(X497 @ X500)) | ~ ! [X502 : term] : ((X497 @ (lam @ X502)) | ~ ! [X503 : term] : (~(X497 @ X503) | (X497 @ (sub @ X502 @ (push @ X503 @ id))))) | (X497 @ (sub @ X498 @ X499)) | ~ ! [X504 : term] : (~(var @ X504) | (X497 @ (sub @ X504 @ X499))))) & hoasapinj2_gthm & axvarshift & (! [X505 : subst,X506 : (term > $o),X507 : term,X508 : (term > $o)] : ((X508 @ one) | ~ ! [X509 : term] : (((X508 @ X509)) = ((X506 @ (sub @ X509 @ (push @ X507 @ X505))))) | ~(X506 @ X507)) <=> pushprop_lem1v2) & (apinj1 <=> ! [X510 : term,X511 : term,X512 : term,X513 : term] : ((((ap @ X512 @ X511)) != ((ap @ X510 @ X513))) | (X510 = X512))) & ulamvarsh & ! [X514 : subst] : ? [X515 : d_subst] : (((d2subst @ X515)) = X514) & ((! [X516 : subst,X517 : term] : (((sub @ one @ (push @ X517 @ X516))) = X517) => ! [X518 : (term > $o),X519 : (term > $o),X520 : subst,X521 : term] : ((X518 @ one) | ~(X519 @ X521) | ~ ! [X522 : term] : (((X518 @ X522)) = ((X519 @ (sub @ X522 @ (push @ X521 @ X520))))))) <=> pushprop_lem1v2_lthm) & hoasinduction_lem3a_gthm & pushprop_lthm_orig & (pushprop_lem1_lthm <=> (! [X523 : subst,X524 : term] : (((sub @ one @ (push @ X524 @ X523))) = X524) => (! [X525 : subst,X526 : term] : (((comp @ sh @ (push @ X526 @ X525))) = X525) => ! [X527 : subst,X528 : term,X529 : (term > $o),X530 : term,X531 : (term > $o)] : ((X529 @ (sub @ X530 @ (push @ X528 @ X527))) | ~(X531 @ X530))))) & hoasinduction_lem1_gthm & (hoaslaminj <=> ! [X532 : subst,X533 : (subst > term > term),X534 : term,X535 : (subst > term > term)] : ((((lam @ (X533 @ sh @ one))) != ((lam @ (X535 @ sh @ one)))) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((sub @ (X535 @ X536 @ X538) @ X537)) = ((X535 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537)))) | (((X535 @ X532 @ X534)) = ((X533 @ X532 @ X534))) | ~ ! [X539 : subst,X540 : term,X541 : subst] : (((X533 @ (comp @ X541 @ X539) @ (sub @ X540 @ X539))) = ((sub @ (X533 @ X541 @ X540) @ X539))))) & (! [X542 : subst] : (((comp @ X542 @ id)) = X542) <=> axidr) & (! [X543 : term] : (((sub @ X543 @ id)) = X543) <=> termmset) & pushprop_lem3v2 & (hoaslamnotap <=> ! [X544 : term,X545 : term,X546 : (subst > term > term)] : ((((lam @ (X546 @ sh @ one))) != ((ap @ (sub @ X544 @ id) @ X545))) | ~ ! [X547 : subst,X548 : subst,X549 : term] : (((X546 @ (comp @ X548 @ X547) @ (sub @ X549 @ X547))) = ((sub @ (X546 @ X548 @ X549) @ X547)))))),
% 2.11/0.57 inference(rectify,[],[f1])).
% 2.11/0.57 thf(f7,plain,(
% 2.11/0.57 ((termmset_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => ! [X1 : term] : (((sub @ X1 @ id)) = X1))) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X4 : term] : ~ ! [X5 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & (termmset_gthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X9 : (subst > term > subst > $o)] : ~ ! [X10 : (term > $o)] : ~ ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11)))) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : subst,X15 : subst,X16 : term,X17 : subst] : (~ ($true = ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14))) | (((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) = $true)) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | ~ ! [X18 : term] : (~ (((X12 @ id @ X18 @ id)) = $true) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id)))) | ~ ! [X19 : subst,X20 : term,X21 : subst,X22 : subst] : ((((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) = $true) | ~ ($true = ((X12 @ X21 @ X20 @ (comp @ X22 @ X19))))) | ~ ! [X23 : (subst > term > term)] : (~ ! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) | (((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X27 : term] : (~ (((X12 @ id @ X27 @ id)) = $true) | ($true = ((X12 @ id @ (X23 @ id @ X27) @ id))))))) & ~ (lamnotap = $true) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasapinj1_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axclos = $true) & ((! [X30 : term,X31 : term,X28 : term,X29 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)) => ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35))) <=> (hoasapinj2_lthm = $true)) & (one = ((d2term @ d_one))) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X36 : (subst > term > subst > $o),X37 : term,X38 : term] : (~ ! [X39 : term,X40 : term] : (~ (((X36 @ id @ X39 @ id)) = $true) | (((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) = $true) | ~ ($true = ((X36 @ id @ X40 @ id)))) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))) | ~ ($true = ((X36 @ id @ X37 @ id))) | ~ ! [X41 : subst,X42 : subst,X43 : subst,X44 : term] : ((((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) = $true) | ~ ($true = ((X36 @ X41 @ X44 @ (comp @ X43 @ X42))))) | ~ ($true = ((X36 @ id @ X38 @ id))) | ~ ! [X45 : term,X46 : subst,X47 : subst,X48 : subst] : (~ ($true = ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48))) | ($true = ((X36 @ X46 @ X45 @ (comp @ X47 @ X48))))))) & ! [X50 : d_term,X49 : d_term] : ((((d2term @ X50)) = ((d2term @ X49))) => (X49 = X50)) & (induction2_gthm = $true) & ((! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) = ((sub @ X51 @ (push @ X53 @ X54)))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : term,X58 : (subst > term > subst > $o)] : ((((X56 @ (lam @ X57))) = $true) | ~ ! [X59 : term] : (((X56 @ X59)) = ((X58 @ id @ X59 @ id))) | ~ ! [X60 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) = $true) | ~ ! [X61 : term] : (~ ($true = ((X58 @ id @ X61 @ id))) | (((X58 @ id @ (X60 @ id @ X61) @ id)) = $true)) | ~ ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64))))) | ~ ! [X65 : term] : (~ ($true = ((X56 @ X65))) | (((X56 @ (sub @ X57 @ (push @ X65 @ id)))) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop = $true) & ((hoasapinj1_lthm = $true) <=> (! [X66 : term] : (((sub @ X66 @ id)) = X66) => (! [X67 : term,X69 : term,X68 : term,X70 : term] : ((X68 = X69) | (((ap @ X68 @ X70)) != ((ap @ X69 @ X67)))) => ! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72))))))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X75 : (subst > term > subst > $o),X76 : term,X77 : term,X78 : (term > $o)] : (~ ($true = ((X78 @ X77))) | ~ ($true = ((X78 @ X76))) | ~ ! [X79 : subst,X80 : subst,X81 : subst,X82 : term] : ((((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) = $true) | ~ (((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) = $true)) | (((X78 @ (ap @ X77 @ X76))) = $true) | ~ ! [X83 : subst,X84 : term,X85 : subst,X86 : subst] : ((((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) = $true) | ~ (((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) = $true)) | ~ ! [X87 : term] : (((X75 @ id @ X87 @ id)) = ((X78 @ X87))) | ~ ! [X88 : term,X89 : term] : (~ (((X75 @ id @ X89 @ id)) = $true) | (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) = $true) | ~ (((X75 @ id @ X88 @ id)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((pushprop_lem0 = $true) <=> ! [X93 : (term > $o),X94 : term,X95 : subst] : ~ ! [X96 : (term > $o)] : ~ ! [X97 : term] : (((X93 @ (sub @ X97 @ (push @ X94 @ X95)))) = ((X96 @ X97)))) & ((axvarid = $true) <=> ! [X98 : term] : (((sub @ X98 @ id)) = X98)) & (hoasinduction_lem2_lthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = sh) & ! [X99 : d_subst] : (d_id = X99) & (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 = $true) <=> ! [X105 : (subst > term > subst > $o),X106 : term] : (~ ! [X107 : term] : ((((X105 @ id @ X107 @ id)) = $true) | ~ (((var @ (sub @ X107 @ id))) = $true)) | ~ ! [X108 : subst,X109 : subst,X110 : subst,X111 : term] : ((((X105 @ X110 @ X111 @ (comp @ X109 @ X108))) = $true) | ~ (((X105 @ (comp @ X110 @ X109) @ (sub @ X111 @ X109) @ X108)) = $true)) | ~ ! [X112 : (subst > term > term)] : (~ ! [X113 : term] : ((((X105 @ id @ (X112 @ id @ X113) @ id)) = $true) | ~ (((X105 @ id @ X113 @ id)) = $true)) | ~ ! [X114 : term,X115 : subst,X116 : subst] : (((X112 @ (comp @ X115 @ X116) @ (sub @ X114 @ X116))) = ((sub @ (X112 @ X115 @ X114) @ X116))) | ($true = ((X105 @ id @ (lam @ (X112 @ sh @ one)) @ id)))) | ~ ! [X117 : term,X118 : term] : (~ ($true = ((X105 @ id @ X118 @ id))) | (((X105 @ id @ (ap @ (sub @ X117 @ id) @ X118) @ id)) = $true) | ~ ($true = ((X105 @ id @ X117 @ id)))) | ~ ! [X119 : subst,X120 : term,X121 : subst,X122 : subst] : (~ (((X105 @ X119 @ X120 @ (comp @ X121 @ X122))) = $true) | (((X105 @ (comp @ X119 @ X121) @ (sub @ X120 @ X121) @ X122)) = $true)) | (((X105 @ id @ X106 @ id)) = $true))) & (hoasinduction_gthm = $true) & ((apinj2 = $true) <=> ! [X123 : term,X124 : term,X125 : term,X126 : term] : ((((ap @ X123 @ X125)) != ((ap @ X126 @ X124))) | (X124 = X125))) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3a = $true) <=> ! [X127 : term,X128 : (subst > term > subst > $o)] : (~ ! [X129 : (subst > term > term)] : (~ ! [X130 : term,X131 : subst,X132 : subst] : (((sub @ (X129 @ X131 @ X130) @ X132)) = ((X129 @ (comp @ X131 @ X132) @ (sub @ X130 @ X132)))) | ($true = ((X128 @ id @ (lam @ (X129 @ sh @ one)) @ id))) | ~ ! [X133 : term] : (($true = ((X128 @ id @ (X129 @ id @ X133) @ id))) | ~ (((X128 @ id @ X133 @ id)) = $true))) | ($true = ((X128 @ id @ (lam @ X127) @ id))) | ~ ! [X134 : term] : (($true = ((X128 @ id @ (sub @ X127 @ (push @ X134 @ id)) @ id))) | ~ (((X128 @ id @ X134 @ id)) = $true)))) & (axmap = $true) & (ulamvarind = $true) & (pushprop_lem1_gthm = $true) & (! [X135 : subst] : (((comp @ id @ X135)) = X135) <=> (axidl = $true)) & (! [X136 : (subst > term > subst > $o)] : ~ ! [X137 : (term > $o)] : ~ ! [X138 : term] : (((X136 @ id @ X138 @ id)) = ((X137 @ X138))) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotvar_gthm = $true) & (axapp = $true) & (apnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X139 : term,X140 : subst] : (((sub @ one @ (push @ X139 @ X140))) = X139) => (! [X141 : term,X142 : subst] : (((comp @ sh @ (push @ X141 @ X142))) = X142) => (! [X143 : term,X144 : term] : ((X143 = X144) | (((lam @ X143)) != ((lam @ X144)))) => ! [X145 : (subst > term > term),X146 : term,X147 : subst,X148 : (subst > term > term)] : ((((X148 @ X147 @ X146)) = ((X145 @ X147 @ X146))) | ~ ! [X149 : subst,X150 : subst,X151 : term] : (((X148 @ (comp @ X150 @ X149) @ (sub @ X151 @ X149))) = ((sub @ (X148 @ X150 @ X151) @ X149))) | (((lam @ (X145 @ sh @ one))) != ((lam @ (X148 @ sh @ one)))) | ~ ! [X152 : subst,X153 : subst,X154 : term] : (((sub @ (X145 @ X153 @ X154) @ X152)) = ((X145 @ (comp @ X153 @ X152) @ (sub @ X154 @ X152))))))))) & ((induction2lem_lthm = $true) <=> (! [X155 : term,X156 : subst] : (((sub @ one @ (push @ X155 @ X156))) = X155) => (! [X157 : subst,X158 : term] : (((comp @ sh @ (push @ X158 @ X157))) = X157) => (! [X159 : subst] : (((comp @ X159 @ id)) = X159) => (! [X160 : term,X161 : (term > $o)] : ((((X161 @ X160)) = $true) | ~ ! [X162 : term] : (($true = ((X161 @ X162))) | ~ (((var @ X162)) = $true)) | ~ ! [X163 : term] : (~ (((X161 @ X163)) = $true) | (((X161 @ (lam @ X163))) = $true)) | ~ ! [X164 : term,X165 : term] : (~ (((X161 @ X165)) = $true) | ~ (((X161 @ X164)) = $true) | ($true = ((X161 @ (ap @ X165 @ X164)))))) => ! [X166 : (term > $o),X167 : subst,X168 : term] : (~ ! [X169 : term] : (~ ! [X170 : term] : (~ (((X166 @ X170)) = $true) | ($true = ((X166 @ (sub @ X169 @ (push @ X170 @ id)))))) | ($true = ((X166 @ (lam @ X169))))) | ~ ! [X171 : term,X172 : term] : (~ (((X166 @ X172)) = $true) | ~ (((X166 @ X171)) = $true) | (((X166 @ (ap @ X172 @ X171))) = $true)) | ~ ! [X173 : term] : ((((X166 @ (sub @ X173 @ X167))) = $true) | ~ (((var @ X173)) = $true)) | (((X166 @ (sub @ X168 @ X167))) = $true))))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X174 : term] : ~ ! [X175 : (subst > term > term)] : (((X175 @ sh @ one)) != ((sub @ X174 @ (push @ one @ sh))))) & (! [X176 : (subst > term > subst > $o),X177 : (term > $o),X178 : term] : (~ ! [X179 : term] : ((((X177 @ (sub @ X178 @ (push @ X179 @ id)))) = $true) | ~ (((X177 @ X179)) = $true)) | ~ ! [X180 : (subst > term > term)] : (~ ! [X181 : term] : (~ ($true = ((X176 @ id @ X181 @ id))) | (((X176 @ id @ (X180 @ id @ X181) @ id)) = $true)) | ~ ! [X182 : term,X183 : subst,X184 : subst] : (((sub @ (X180 @ X183 @ X182) @ X184)) = ((X180 @ (comp @ X183 @ X184) @ (sub @ X182 @ X184)))) | (((X176 @ id @ (lam @ (X180 @ sh @ one)) @ id)) = $true)) | (((X177 @ (lam @ X178))) = $true) | ~ ! [X185 : term] : (((X177 @ X185)) = ((X176 @ id @ X185 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X186 : (term > $o),X187 : term,X188 : subst] : ~ ! [X189 : (term > $o)] : ~ ! [X190 : term] : (((X189 @ X190)) = ((X186 @ (sub @ X190 @ (push @ X187 @ X188)))))) & (hoaslamnotvar_lthm = $true) & (hoasapnotvar_lthm = $true) & (! [X191 : term,X192 : (subst > term > subst > $o)] : ((((X192 @ id @ (lam @ (sub @ X191 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X193 : (subst > term > term),X194 : term] : ((((X192 @ id @ (lam @ (X193 @ sh @ one)) @ id)) = $true) | ~ ! [X195 : subst,X196 : subst,X197 : term] : (((sub @ (X193 @ X196 @ X197) @ X195)) = ((sub @ (sub @ X194 @ (push @ X197 @ X196)) @ X195))) | ~ ! [X198 : term] : (~ (((X192 @ id @ X198 @ id)) = $true) | ($true = ((X192 @ id @ (X193 @ id @ X198) @ id)))) | ~ ! [X199 : subst,X200 : subst,X201 : term] : (((sub @ X194 @ (push @ (sub @ X201 @ X200) @ (comp @ X199 @ X200)))) = ((X193 @ (comp @ X199 @ X200) @ (sub @ X201 @ X200))))) | ~ ! [X202 : term] : (~ ($true = ((X192 @ id @ X202 @ id))) | (((X192 @ id @ (sub @ X191 @ (push @ X202 @ id)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ! [X203 : d_term] : (d_one = X203) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (((var @ (d2term @ d_one))) = $true) & ((induction = $true) <=> ! [X204 : term,X205 : (term > $o)] : (~ ! [X206 : term] : (~ ($true = ((X205 @ X206))) | ($true = ((X205 @ (lam @ X206))))) | ~ ! [X207 : term] : (~ (((var @ X207)) = $true) | (((X205 @ X207)) = $true)) | ~ ! [X208 : term,X209 : term] : (~ ($true = ((X205 @ X208))) | ~ (((X205 @ X209)) = $true) | (((X205 @ (ap @ X208 @ X209))) = $true)) | (((X205 @ X204)) = $true))) & ((! [X210 : term] : (((sub @ X210 @ id)) = X210) => (! [X211 : term,X212 : (term > $o),X213 : subst] : (~ ! [X214 : term] : (($true = ((X212 @ (lam @ X214)))) | ~ ! [X215 : term] : (~ (((X212 @ X215)) = $true) | (((X212 @ (sub @ X214 @ (push @ X215 @ id)))) = $true))) | ~ ! [X216 : term] : ((((X212 @ (sub @ X216 @ X213))) = $true) | ~ (((var @ X216)) = $true)) | ~ ! [X217 : term,X218 : term] : (~ (((X212 @ X217)) = $true) | ($true = ((X212 @ (ap @ X217 @ X218)))) | ~ (((X212 @ X218)) = $true)) | (((X212 @ (sub @ X211 @ X213))) = $true)) => ! [X219 : (term > $o),X220 : term] : (~ ! [X221 : term] : (~ ! [X222 : term] : (~ (((X219 @ X222)) = $true) | (((X219 @ (sub @ X221 @ (push @ X222 @ id)))) = $true)) | (((X219 @ (lam @ X221))) = $true)) | ~ ! [X223 : term] : ((((X219 @ X223)) = $true) | ~ (((var @ X223)) = $true)) | ($true = ((X219 @ X220))) | ~ ! [X224 : term,X225 : term] : (~ ($true = ((X219 @ X225))) | ~ ($true = ((X219 @ X224))) | (((X219 @ (ap @ X225 @ X224))) = $true))))) <=> (induction2_lthm = $true)) & ~ (ulamvar1 = $true) & ((laminj = $true) <=> ! [X226 : term,X227 : term] : ((((lam @ X226)) != ((lam @ X227))) | (X226 = X227))) & (hoasapnotvar_gthm = $true) & (! [X228 : term,X229 : term] : ((((sub @ X229 @ sh)) != ((sub @ X228 @ sh))) | (X228 = X229)) <=> (shinj = $true)) & (pushprop_lem1v2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1 = $true) & (! [X230 : (term > $o),X231 : (subst > term > subst > $o),X232 : term] : (~ ! [X233 : term] : (~ (((X230 @ X233)) = $true) | ($true = ((X230 @ (sub @ X232 @ (push @ X233 @ id)))))) | ~ ! [X234 : subst,X235 : term,X236 : subst,X237 : subst] : (($true = ((X231 @ (comp @ X236 @ X234) @ (sub @ X235 @ X234) @ X237))) | ~ (((X231 @ X236 @ X235 @ (comp @ X234 @ X237))) = $true)) | ~ ! [X238 : term] : (((X230 @ X238)) = ((X231 @ id @ X238 @ id))) | (((X230 @ (lam @ X232))) = $true) | ~ ! [X239 : subst,X240 : term,X241 : subst,X242 : subst] : ((((X231 @ X242 @ X240 @ (comp @ X239 @ X241))) = $true) | ~ (((X231 @ (comp @ X242 @ X239) @ (sub @ X240 @ X239) @ X241)) = $true)) | ~ ! [X243 : (subst > term > term)] : (~ ! [X244 : term,X245 : subst,X246 : subst] : (((X243 @ (comp @ X245 @ X246) @ (sub @ X244 @ X246))) = ((sub @ (X243 @ X245 @ X244) @ X246))) | ~ ! [X247 : term] : ((((X231 @ id @ (X243 @ id @ X247) @ id)) = $true) | ~ (((X231 @ id @ X247 @ id)) = $true)) | (((X231 @ id @ (lam @ (X243 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_gthm = $true) & ((axshiftcons = $true) <=> ! [X248 : term,X249 : subst] : (((comp @ sh @ (push @ X248 @ X249))) = X249)) & ((hoasinduction_lem3aa = $true) <=> ! [X250 : (subst > term > subst > $o),X251 : term] : (~ ! [X252 : term] : ((((X250 @ id @ (sub @ X251 @ (push @ X252 @ id)) @ id)) = $true) | ~ ($true = ((X250 @ id @ X252 @ id)))) | (((X250 @ id @ (lam @ (sub @ X251 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X253 : (subst > term > term)] : (~ ! [X254 : term] : ((((X250 @ id @ (X253 @ id @ X254) @ id)) = $true) | ~ (((X250 @ id @ X254 @ id)) = $true)) | (((X250 @ id @ (lam @ (X253 @ sh @ one)) @ id)) = $true) | ~ ! [X255 : subst,X256 : term,X257 : subst] : (((X253 @ (comp @ X257 @ X255) @ (sub @ X256 @ X255))) = ((sub @ (X253 @ X257 @ X256) @ X255)))))) & ((! [X258 : (term > $o),X259 : term] : (~ ! [X260 : term] : ((((X258 @ X260)) = $true) | ~ ($true = ((var @ X260)))) | (((X258 @ X259)) = $true) | ~ ! [X261 : term] : (~ ! [X262 : term] : (~ (((X258 @ X262)) = $true) | ($true = ((X258 @ (sub @ X261 @ (push @ X262 @ id)))))) | (((X258 @ (lam @ X261))) = $true)) | ~ ! [X263 : term,X264 : term] : (~ ($true = ((X258 @ X264))) | (((X258 @ (ap @ X263 @ X264))) = $true) | ~ (((X258 @ X263)) = $true))) => (! [X265 : term,X266 : (subst > term > subst > $o),X267 : term] : (($true = ((X266 @ id @ (ap @ X267 @ X265) @ id))) | ~ ! [X268 : term,X269 : term] : (($true = ((X266 @ id @ (ap @ (sub @ X268 @ id) @ X269) @ id))) | ~ (((X266 @ id @ X269 @ id)) = $true) | ~ (((X266 @ id @ X268 @ id)) = $true)) | ~ ! [X270 : term,X271 : subst,X272 : subst,X273 : subst] : ((((X266 @ (comp @ X272 @ X271) @ (sub @ X270 @ X271) @ X273)) = $true) | ~ (((X266 @ X272 @ X270 @ (comp @ X271 @ X273))) = $true)) | ~ ! [X274 : subst,X275 : subst,X276 : subst,X277 : term] : (~ (((X266 @ (comp @ X276 @ X274) @ (sub @ X277 @ X274) @ X275)) = $true) | ($true = ((X266 @ X276 @ X277 @ (comp @ X274 @ X275))))) | ~ (((X266 @ id @ X265 @ id)) = $true) | ~ (((X266 @ id @ X267 @ id)) = $true)) => (! [X278 : (subst > term > subst > $o),X279 : term] : (~ ! [X280 : subst,X281 : term,X282 : subst,X283 : subst] : (($true = ((X278 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282) @ X280))) | ~ (((X278 @ X283 @ X281 @ (comp @ X282 @ X280))) = $true)) | ~ ! [X284 : subst,X285 : subst,X286 : subst,X287 : term] : ((((X278 @ X286 @ X287 @ (comp @ X285 @ X284))) = $true) | ~ ($true = ((X278 @ (comp @ X286 @ X285) @ (sub @ X287 @ X285) @ X284)))) | ~ ! [X288 : (subst > term > term)] : ((((X278 @ id @ (lam @ (X288 @ sh @ one)) @ id)) = $true) | ~ ! [X289 : term,X290 : subst,X291 : subst] : (((sub @ (X288 @ X291 @ X289) @ X290)) = ((X288 @ (comp @ X291 @ X290) @ (sub @ X289 @ X290)))) | ~ ! [X292 : term] : (~ (((X278 @ id @ X292 @ id)) = $true) | ($true = ((X278 @ id @ (X288 @ id @ X292) @ id))))) | ~ ! [X293 : term] : (~ (((X278 @ id @ X293 @ id)) = $true) | (((X278 @ id @ (sub @ X279 @ (push @ X293 @ id)) @ id)) = $true)) | (((X278 @ id @ (lam @ X279) @ id)) = $true)) => ! [X294 : term,X295 : (subst > term > subst > $o)] : (~ ! [X296 : subst,X297 : subst,X298 : term,X299 : subst] : (~ ($true = ((X295 @ X296 @ X298 @ (comp @ X299 @ X297)))) | (((X295 @ (comp @ X296 @ X299) @ (sub @ X298 @ X299) @ X297)) = $true)) | ~ ! [X300 : term,X301 : term] : (($true = ((X295 @ id @ (ap @ (sub @ X300 @ id) @ X301) @ id))) | ~ ($true = ((X295 @ id @ X300 @ id))) | ~ (((X295 @ id @ X301 @ id)) = $true)) | ~ ! [X302 : subst,X303 : term,X304 : subst,X305 : subst] : (~ (((X295 @ (comp @ X302 @ X305) @ (sub @ X303 @ X305) @ X304)) = $true) | (((X295 @ X302 @ X303 @ (comp @ X305 @ X304))) = $true)) | ($true = ((X295 @ id @ X294 @ id))) | ~ ! [X306 : term] : (($true = ((X295 @ id @ X306 @ id))) | ~ (((var @ (sub @ X306 @ id))) = $true)) | ~ ! [X307 : (subst > term > term)] : (~ ! [X308 : term] : (~ (((X295 @ id @ X308 @ id)) = $true) | (((X295 @ id @ (X307 @ id @ X308) @ id)) = $true)) | (((X295 @ id @ (lam @ (X307 @ sh @ one)) @ id)) = $true) | ~ ! [X309 : subst,X310 : term,X311 : subst] : (((X307 @ (comp @ X309 @ X311) @ (sub @ X310 @ X311))) = ((sub @ (X307 @ X309 @ X310) @ X311)))))))) <=> (hoasinduction_lthm = $true)) & ! [X312 : term] : ? [X313 : d_term] : (((d2term @ X313)) = X312) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X314 : (subst > term > subst > $o),X315 : term] : ((((X314 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X316 : (subst > term > term)] : ((((X314 @ id @ (lam @ (X316 @ sh @ one)) @ id)) = $true) | ~ ! [X317 : term] : (~ (((X314 @ id @ X317 @ id)) = $true) | (((X314 @ id @ (X316 @ id @ X317) @ id)) = $true)) | ~ ! [X318 : subst,X319 : term,X320 : subst] : (((X316 @ (comp @ X318 @ X320) @ (sub @ X319 @ X320))) = ((sub @ (X316 @ X318 @ X319) @ X320)))) | ~ ! [X321 : term] : (~ ($true = ((X314 @ id @ X321 @ id))) | ($true = ((X314 @ id @ (sub @ X315 @ (push @ X321 @ id)) @ id)))))) & ((! [X322 : term] : (((sub @ X322 @ id)) = X322) => (! [X323 : term,X324 : (subst > term > subst > $o)] : (~ ! [X325 : (subst > term > term)] : ((((X324 @ id @ (lam @ (X325 @ sh @ one)) @ id)) = $true) | ~ ! [X326 : term] : (~ ($true = ((X324 @ id @ X326 @ id))) | (((X324 @ id @ (X325 @ id @ X326) @ id)) = $true)) | ~ ! [X327 : subst,X328 : subst,X329 : term] : (((X325 @ (comp @ X328 @ X327) @ (sub @ X329 @ X327))) = ((sub @ (X325 @ X328 @ X329) @ X327)))) | ~ ! [X330 : term] : (($true = ((X324 @ id @ (sub @ X323 @ (push @ X330 @ id)) @ id))) | ~ ($true = ((X324 @ id @ X330 @ id)))) | (((X324 @ id @ (lam @ (sub @ X323 @ (push @ one @ sh))) @ id)) = $true)) => ! [X331 : term,X332 : (subst > term > subst > $o)] : ((((X332 @ id @ (lam @ X331) @ id)) = $true) | ~ ! [X333 : subst,X334 : subst,X335 : subst,X336 : term] : ((((X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334) @ X333)) = $true) | ~ (((X332 @ X335 @ X336 @ (comp @ X334 @ X333))) = $true)) | ~ ! [X337 : term] : (($true = ((X332 @ id @ (sub @ X331 @ (push @ X337 @ id)) @ id))) | ~ (((X332 @ id @ X337 @ id)) = $true)) | ~ ! [X338 : subst,X339 : subst,X340 : subst,X341 : term] : (~ (((X332 @ (comp @ X339 @ X338) @ (sub @ X341 @ X338) @ X340)) = $true) | (((X332 @ X339 @ X341 @ (comp @ X338 @ X340))) = $true)) | ~ ! [X342 : (subst > term > term)] : ((((X332 @ id @ (lam @ (X342 @ sh @ one)) @ id)) = $true) | ~ ! [X343 : term,X344 : subst,X345 : subst] : (((X342 @ (comp @ X344 @ X345) @ (sub @ X343 @ X345))) = ((sub @ (X342 @ X344 @ X343) @ X345))) | ~ ! [X346 : term] : ((((X332 @ id @ (X342 @ id @ X346) @ id)) = $true) | ~ (((X332 @ id @ X346 @ id)) = $true)))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X349 : term,X350 : (term > $o)] : (~ ! [X351 : term] : (~ ($true = ((var @ X351))) | ($true = ((X350 @ X351)))) | ~ ! [X352 : term] : (~ ! [X353 : term] : (($true = ((X350 @ (sub @ X352 @ (push @ X353 @ id))))) | ~ (((X350 @ X353)) = $true)) | ($true = ((X350 @ (lam @ X352))))) | (((X350 @ X349)) = $true) | ~ ! [X354 : term,X355 : term] : (($true = ((X350 @ (ap @ X354 @ X355)))) | ~ (((X350 @ X354)) = $true) | ~ (((X350 @ X355)) = $true))) <=> (induction2 = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X356 : term] : (((sub @ X356 @ id)) = X356) => ! [X357 : (term > $o),X358 : (subst > term > subst > $o),X359 : term] : ((((X357 @ (lam @ X359))) = $true) | ~ ! [X360 : term] : (~ ($true = ((X357 @ X360))) | (((X357 @ (sub @ X359 @ (push @ X360 @ id)))) = $true)) | ~ ! [X361 : (subst > term > term)] : (($true = ((X358 @ id @ (lam @ (X361 @ sh @ one)) @ id))) | ~ ! [X362 : term,X363 : subst,X364 : subst] : (((X361 @ (comp @ X364 @ X363) @ (sub @ X362 @ X363))) = ((sub @ (X361 @ X364 @ X362) @ X363))) | ~ ! [X365 : term] : (~ (((X358 @ id @ X365 @ id)) = $true) | (((X358 @ id @ (X361 @ id @ X365) @ id)) = $true))) | ~ ! [X366 : subst,X367 : subst,X368 : term,X369 : subst] : ((((X358 @ (comp @ X366 @ X369) @ (sub @ X368 @ X369) @ X367)) = $true) | ~ (((X358 @ X366 @ X368 @ (comp @ X369 @ X367))) = $true)) | ~ ! [X370 : subst,X371 : subst,X372 : term,X373 : subst] : (~ (((X358 @ (comp @ X371 @ X370) @ (sub @ X372 @ X370) @ X373)) = $true) | (((X358 @ X371 @ X372 @ (comp @ X370 @ X373))) = $true)) | ~ ! [X374 : term] : (((X358 @ id @ X374 @ id)) = ((X357 @ X374))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslamnotvar = $true) & (induction2lem_gthm = $true) & ((! [X375 : (subst > term > subst > $o)] : ~ ! [X376 : (term > $o)] : ~ ! [X377 : term] : (((X375 @ id @ X377 @ id)) = ((X376 @ X377))) => (! [X378 : (term > $o),X379 : term] : (($true = ((X378 @ X379))) | ~ ! [X380 : term] : (~ (((var @ X380)) = $true) | (((X378 @ X380)) = $true)) | ~ ! [X381 : term,X382 : term] : (~ (((X378 @ X382)) = $true) | ~ (((X378 @ X381)) = $true) | (((X378 @ (ap @ X381 @ X382))) = $true)) | ~ ! [X383 : term] : ((((X378 @ (lam @ X383))) = $true) | ~ ! [X384 : term] : (~ (((X378 @ X384)) = $true) | (((X378 @ (sub @ X383 @ (push @ X384 @ id)))) = $true)))) => (! [X385 : term] : (((sub @ X385 @ id)) = X385) => (! [X386 : term,X387 : (subst > term > subst > $o),X388 : (term > $o)] : (($true = ((X388 @ (lam @ X386)))) | ~ ! [X389 : (subst > term > term)] : (~ ! [X390 : subst,X391 : subst,X392 : term] : (((sub @ (X389 @ X391 @ X392) @ X390)) = ((X389 @ (comp @ X391 @ X390) @ (sub @ X392 @ X390)))) | (((X387 @ id @ (lam @ (X389 @ sh @ one)) @ id)) = $true) | ~ ! [X393 : term] : (~ (((X387 @ id @ X393 @ id)) = $true) | (((X387 @ id @ (X389 @ id @ X393) @ id)) = $true))) | ~ ! [X394 : term] : (((X388 @ X394)) = ((X387 @ id @ X394 @ id))) | ~ ! [X395 : term] : (~ ($true = ((X388 @ X395))) | (((X388 @ (sub @ X386 @ (push @ X395 @ id)))) = $true))) => ! [X396 : term,X397 : (subst > term > subst > $o)] : (~ ! [X398 : term,X399 : subst,X400 : subst,X401 : subst] : (($true = ((X397 @ (comp @ X399 @ X400) @ (sub @ X398 @ X400) @ X401))) | ~ (((X397 @ X399 @ X398 @ (comp @ X400 @ X401))) = $true)) | ~ ! [X402 : term,X403 : term] : (~ (((X397 @ id @ X402 @ id)) = $true) | ~ ($true = ((X397 @ id @ X403 @ id))) | ($true = ((X397 @ id @ (ap @ (sub @ X403 @ id) @ X402) @ id)))) | ($true = ((X397 @ id @ X396 @ id))) | ~ ! [X404 : term] : ((((X397 @ id @ X404 @ id)) = $true) | ~ ($true = ((var @ (sub @ X404 @ id))))) | ~ ! [X405 : subst,X406 : subst,X407 : subst,X408 : term] : (($true = ((X397 @ X405 @ X408 @ (comp @ X406 @ X407)))) | ~ ($true = ((X397 @ (comp @ X405 @ X406) @ (sub @ X408 @ X406) @ X407)))) | ~ ! [X409 : (subst > term > term)] : (~ ! [X410 : term] : (($true = ((X397 @ id @ (X409 @ id @ X410) @ id))) | ~ (((X397 @ id @ X410 @ id)) = $true)) | ~ ! [X411 : subst,X412 : subst,X413 : term] : (((sub @ (X409 @ X412 @ X413) @ X411)) = ((X409 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)))) | (((X397 @ id @ (lam @ (X409 @ sh @ one)) @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem0_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X414 : subst] : (((comp @ id @ X414)) = X414) => (! [X415 : subst] : (((comp @ X415 @ id)) = X415) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) & ! [X417 : subst] : (((comp @ id @ X417)) = X417))))) & ! [X418 : d_subst,X419 : d_subst] : ((((d2subst @ X418)) = ((d2subst @ X419))) => (X418 = X419)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotvar = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X420 : (subst > term > subst > $o)] : ~ ! [X421 : (term > $o)] : ~ ! [X422 : term] : (((X420 @ id @ X422 @ id)) = ((X421 @ X422))) => (! [X423 : term,X424 : (term > $o)] : (~ ! [X425 : term] : (~ ! [X426 : term] : (~ (((X424 @ X426)) = $true) | (((X424 @ (sub @ X425 @ (push @ X426 @ id)))) = $true)) | (((X424 @ (lam @ X425))) = $true)) | ~ ! [X427 : term] : (~ ($true = ((var @ X427))) | (((X424 @ X427)) = $true)) | ($true = ((X424 @ X423))) | ~ ! [X428 : term,X429 : term] : (~ ($true = ((X424 @ X428))) | ~ (((X424 @ X429)) = $true) | ($true = ((X424 @ (ap @ X428 @ X429)))))) => (! [X430 : term] : (((sub @ X430 @ id)) = X430) => (! [X431 : term,X432 : (term > $o),X433 : (subst > term > subst > $o)] : (($true = ((X432 @ (lam @ X431)))) | ~ ! [X434 : (subst > term > term)] : (~ ! [X435 : term,X436 : subst,X437 : subst] : (((sub @ (X434 @ X436 @ X435) @ X437)) = ((X434 @ (comp @ X436 @ X437) @ (sub @ X435 @ X437)))) | ~ ! [X438 : term] : (~ ($true = ((X433 @ id @ X438 @ id))) | ($true = ((X433 @ id @ (X434 @ id @ X438) @ id)))) | (((X433 @ id @ (lam @ (X434 @ sh @ one)) @ id)) = $true)) | ~ ! [X439 : term] : ((((X432 @ (sub @ X431 @ (push @ X439 @ id)))) = $true) | ~ ($true = ((X432 @ X439)))) | ~ ! [X440 : term] : (((X432 @ X440)) = ((X433 @ id @ X440 @ id)))) => ! [X441 : (subst > term > subst > $o),X442 : term] : (~ ! [X443 : term,X444 : term] : (~ (((X441 @ id @ X444 @ id)) = $true) | ($true = ((X441 @ id @ (ap @ (sub @ X443 @ id) @ X444) @ id))) | ~ (((X441 @ id @ X443 @ id)) = $true)) | ~ ! [X445 : (subst > term > term)] : (~ ! [X446 : term] : (($true = ((X441 @ id @ (X445 @ id @ X446) @ id))) | ~ (((X441 @ id @ X446 @ id)) = $true)) | ~ ! [X447 : subst,X448 : term,X449 : subst] : (((X445 @ (comp @ X447 @ X449) @ (sub @ X448 @ X449))) = ((sub @ (X445 @ X447 @ X448) @ X449))) | (((X441 @ id @ (lam @ (X445 @ sh @ one)) @ id)) = $true)) | ($true = ((X441 @ id @ X442 @ id))))))))) & (! [X450 : term,X451 : term,X452 : term,X453 : term] : ((X450 = X451) | (((ap @ (sub @ X451 @ id) @ X452)) != ((ap @ (sub @ X450 @ id) @ X453)))) <=> (hoasapinj1 = $true)) & (hoasinduction_lem3_gthm = $true) & ((! [X454 : term] : (((sub @ X454 @ id)) = X454) => (! [X455 : term,X456 : (subst > term > subst > $o)] : (~ ! [X457 : term] : (($true = ((X456 @ id @ (sub @ X455 @ (push @ X457 @ id)) @ id))) | ~ ($true = ((X456 @ id @ X457 @ id)))) | ~ ! [X458 : (subst > term > term)] : (~ ! [X459 : term] : ((((X456 @ id @ (X458 @ id @ X459) @ id)) = $true) | ~ ($true = ((X456 @ id @ X459 @ id)))) | ~ ! [X460 : subst,X461 : term,X462 : subst] : (((sub @ (X458 @ X460 @ X461) @ X462)) = ((X458 @ (comp @ X460 @ X462) @ (sub @ X461 @ X462)))) | (((X456 @ id @ (lam @ (X458 @ sh @ one)) @ id)) = $true)) | (((X456 @ id @ (lam @ (sub @ X455 @ (push @ one @ sh))) @ id)) = $true)) => ! [X463 : term,X464 : (subst > term > subst > $o)] : (~ ! [X465 : (subst > term > term)] : (~ ! [X466 : subst,X467 : subst,X468 : term] : (((sub @ (X465 @ X466 @ X468) @ X467)) = ((X465 @ (comp @ X466 @ X467) @ (sub @ X468 @ X467)))) | ~ ! [X469 : term] : (~ ($true = ((X464 @ id @ X469 @ id))) | (((X464 @ id @ (X465 @ id @ X469) @ id)) = $true)) | (((X464 @ id @ (lam @ (X465 @ sh @ one)) @ id)) = $true)) | ~ ! [X470 : term] : ((((X464 @ id @ (sub @ X463 @ (push @ X470 @ id)) @ id)) = $true) | ~ (((X464 @ id @ X470 @ id)) = $true)) | (((X464 @ id @ (lam @ X463) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X471 : term] : ~ ! [X472 : (subst > term > term)] : ~ ! [X473 : term,X474 : subst] : (((sub @ X471 @ (push @ X473 @ X474))) = ((X472 @ X474 @ X473)))) & (! [X475 : term,X476 : term,X477 : term,X478 : term] : ((((ap @ (sub @ X478 @ id) @ X476)) != ((ap @ (sub @ X477 @ id) @ X475))) | (X475 = X476)) <=> (hoasapinj2 = $true)) & (axassoc = $true) & ((hoasinduction_lem3b = $true) <=> ! [X479 : term] : ~ ! [X480 : (subst > term > term)] : (((X480 @ sh @ one)) != ((sub @ X479 @ (push @ one @ sh))))) & ((pushprop_lem1 = $true) <=> ! [X481 : term,X482 : term,X483 : (term > $o),X484 : (term > $o),X485 : subst] : (~ ($true = ((X484 @ X482))) | ($true = ((X483 @ (sub @ X482 @ (push @ X481 @ X485))))))) & (! [X486 : term,X487 : (subst > term > subst > $o)] : (~ ! [X488 : term,X489 : term] : ((((X487 @ id @ (ap @ (sub @ X489 @ id) @ X488) @ id)) = $true) | ~ (((X487 @ id @ X489 @ id)) = $true) | ~ (((X487 @ id @ X488 @ id)) = $true)) | ~ ! [X490 : (subst > term > term)] : (~ ! [X491 : term] : (($true = ((X487 @ id @ (X490 @ id @ X491) @ id))) | ~ (((X487 @ id @ X491 @ id)) = $true)) | ~ ! [X492 : subst,X493 : subst,X494 : term] : (((sub @ (X490 @ X493 @ X494) @ X492)) = ((X490 @ (comp @ X493 @ X492) @ (sub @ X494 @ X492)))) | (((X487 @ id @ (lam @ (X490 @ sh @ one)) @ id)) = $true)) | ($true = ((X487 @ id @ X486 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((substmonoid = $true) <=> (! [X495 : subst] : (((comp @ X495 @ id)) = X495) & ! [X496 : subst] : (((comp @ id @ X496)) = X496))) & (hoasapnotvar = $true) & ((induction2lem = $true) <=> ! [X497 : (term > $o),X498 : term,X499 : subst] : (~ ! [X500 : term,X501 : term] : (~ (((X497 @ X501)) = $true) | (((X497 @ (ap @ X501 @ X500))) = $true) | ~ ($true = ((X497 @ X500)))) | ~ ! [X502 : term] : (($true = ((X497 @ (lam @ X502)))) | ~ ! [X503 : term] : (~ (((X497 @ X503)) = $true) | ($true = ((X497 @ (sub @ X502 @ (push @ X503 @ id))))))) | (((X497 @ (sub @ X498 @ X499))) = $true) | ~ ! [X504 : term] : (~ ($true = ((var @ X504))) | ($true = ((X497 @ (sub @ X504 @ X499))))))) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (! [X505 : subst,X506 : (term > $o),X507 : term,X508 : (term > $o)] : ((((X508 @ one)) = $true) | ~ ! [X509 : term] : (((X508 @ X509)) = ((X506 @ (sub @ X509 @ (push @ X507 @ X505))))) | ~ ($true = ((X506 @ X507)))) <=> (pushprop_lem1v2 = $true)) & ((apinj1 = $true) <=> ! [X510 : term,X511 : term,X512 : term,X513 : term] : ((((ap @ X512 @ X511)) != ((ap @ X510 @ X513))) | (X510 = X512))) & (ulamvarsh = $true) & ! [X514 : subst] : ? [X515 : d_subst] : (((d2subst @ X515)) = X514) & ((! [X516 : subst,X517 : term] : (((sub @ one @ (push @ X517 @ X516))) = X517) => ! [X518 : (term > $o),X519 : (term > $o),X520 : subst,X521 : term] : ((((X518 @ one)) = $true) | ~ (((X519 @ X521)) = $true) | ~ ! [X522 : term] : (((X518 @ X522)) = ((X519 @ (sub @ X522 @ (push @ X521 @ X520))))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X523 : subst,X524 : term] : (((sub @ one @ (push @ X524 @ X523))) = X524) => (! [X525 : subst,X526 : term] : (((comp @ sh @ (push @ X526 @ X525))) = X525) => ! [X527 : subst,X528 : term,X529 : (term > $o),X530 : term,X531 : (term > $o)] : ((((X529 @ (sub @ X530 @ (push @ X528 @ X527)))) = $true) | ~ (((X531 @ X530)) = $true))))) & (hoasinduction_lem1_gthm = $true) & ((hoaslaminj = $true) <=> ! [X532 : subst,X533 : (subst > term > term),X534 : term,X535 : (subst > term > term)] : ((((lam @ (X533 @ sh @ one))) != ((lam @ (X535 @ sh @ one)))) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((sub @ (X535 @ X536 @ X538) @ X537)) = ((X535 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537)))) | (((X535 @ X532 @ X534)) = ((X533 @ X532 @ X534))) | ~ ! [X539 : subst,X540 : term,X541 : subst] : (((X533 @ (comp @ X541 @ X539) @ (sub @ X540 @ X539))) = ((sub @ (X533 @ X541 @ X540) @ X539))))) & (! [X542 : subst] : (((comp @ X542 @ id)) = X542) <=> (axidr = $true)) & (! [X543 : term] : (((sub @ X543 @ id)) = X543) <=> (termmset = $true)) & (pushprop_lem3v2 = $true) & ((hoaslamnotap = $true) <=> ! [X544 : term,X545 : term,X546 : (subst > term > term)] : ((((lam @ (X546 @ sh @ one))) != ((ap @ (sub @ X544 @ id) @ X545))) | ~ ! [X547 : subst,X548 : subst,X549 : term] : (((X546 @ (comp @ X548 @ X547) @ (sub @ X549 @ X547))) = ((sub @ (X546 @ X548 @ X549) @ X547)))))),
% 2.11/0.57 inference(fool_elimination,[],[f6])).
% 2.11/0.57 thf(f8,plain,(
% 2.11/0.57 (lamnotvar != ((!! @ term @ (^[Y0 : term]: (~ (var @ (lam @ Y0)))))))),
% 2.11/0.57 inference(flattening,[],[f5])).
% 2.11/0.57 thf(f9,plain,(
% 2.11/0.57 ((termmset_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => ! [X1 : term] : (((sub @ X1 @ id)) = X1))) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X4 : term] : ~ ! [X5 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & (termmset_gthm = $true) & (axabs = $true) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X9 : (subst > term > subst > $o)] : ~ ! [X10 : (term > $o)] : ~ ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11)))) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X14 : subst,X15 : subst,X16 : term,X17 : subst] : (~ ($true = ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14))) | (((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) = $true)) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | ~ ! [X18 : term] : (~ (((X12 @ id @ X18 @ id)) = $true) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id)))) | ~ ! [X19 : subst,X20 : term,X21 : subst,X22 : subst] : ((((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) = $true) | ~ ($true = ((X12 @ X21 @ X20 @ (comp @ X22 @ X19))))) | ~ ! [X23 : (subst > term > term)] : (~ ! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) | (((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X27 : term] : (~ (((X12 @ id @ X27 @ id)) = $true) | ($true = ((X12 @ id @ (X23 @ id @ X27) @ id))))))) & ~ (lamnotap = $true) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasapinj1_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axclos = $true) & ((! [X30 : term,X31 : term,X28 : term,X29 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)) => ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35))) <=> (hoasapinj2_lthm = $true)) & (one = ((d2term @ d_one))) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X36 : (subst > term > subst > $o),X37 : term,X38 : term] : (~ ! [X39 : term,X40 : term] : (~ (((X36 @ id @ X39 @ id)) = $true) | (((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) = $true) | ~ ($true = ((X36 @ id @ X40 @ id)))) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))) | ~ ($true = ((X36 @ id @ X37 @ id))) | ~ ! [X41 : subst,X42 : subst,X43 : subst,X44 : term] : ((((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) = $true) | ~ ($true = ((X36 @ X41 @ X44 @ (comp @ X43 @ X42))))) | ~ ($true = ((X36 @ id @ X38 @ id))) | ~ ! [X45 : term,X46 : subst,X47 : subst,X48 : subst] : (~ ($true = ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48))) | ($true = ((X36 @ X46 @ X45 @ (comp @ X47 @ X48))))))) & ! [X50 : d_term,X49 : d_term] : ((((d2term @ X50)) = ((d2term @ X49))) => (X49 = X50)) & (induction2_gthm = $true) & ((! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) = ((sub @ X51 @ (push @ X53 @ X54)))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : term,X58 : (subst > term > subst > $o)] : ((((X56 @ (lam @ X57))) = $true) | ~ ! [X59 : term] : (((X56 @ X59)) = ((X58 @ id @ X59 @ id))) | ~ ! [X60 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) = $true) | ~ ! [X61 : term] : (~ ($true = ((X58 @ id @ X61 @ id))) | (((X58 @ id @ (X60 @ id @ X61) @ id)) = $true)) | ~ ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64))))) | ~ ! [X65 : term] : (~ ($true = ((X56 @ X65))) | (((X56 @ (sub @ X57 @ (push @ X65 @ id)))) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (pushprop = $true) & ((hoasapinj1_lthm = $true) <=> (! [X66 : term] : (((sub @ X66 @ id)) = X66) => (! [X67 : term,X69 : term,X68 : term,X70 : term] : ((X68 = X69) | (((ap @ X68 @ X70)) != ((ap @ X69 @ X67)))) => ! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72))))))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X75 : (subst > term > subst > $o),X76 : term,X77 : term,X78 : (term > $o)] : (~ ($true = ((X78 @ X77))) | ~ ($true = ((X78 @ X76))) | ~ ! [X79 : subst,X80 : subst,X81 : subst,X82 : term] : ((((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) = $true) | ~ (((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) = $true)) | (((X78 @ (ap @ X77 @ X76))) = $true) | ~ ! [X83 : subst,X84 : term,X85 : subst,X86 : subst] : ((((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) = $true) | ~ (((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) = $true)) | ~ ! [X87 : term] : (((X75 @ id @ X87 @ id)) = ((X78 @ X87))) | ~ ! [X88 : term,X89 : term] : (~ (((X75 @ id @ X89 @ id)) = $true) | (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) = $true) | ~ (((X75 @ id @ X88 @ id)) = $true))) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X90 : (term > $o),X92 : subst,X91 : term] : ~ ! [X93 : (term > $o)] : ~ ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94))) <=> (pushprop_lem0 = $true)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) <=> (axvarid = $true)) & (hoasinduction_lem2_lthm = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = sh) & ! [X96 : d_subst] : (d_id = X96) & (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 = $true) <=> ! [X97 : (subst > term > subst > $o),X98 : term] : (~ ! [X99 : term] : (($true = ((X97 @ id @ X99 @ id))) | ~ (((var @ (sub @ X99 @ id))) = $true)) | ~ ! [X100 : subst,X101 : subst,X102 : subst,X103 : term] : ((((X97 @ X102 @ X103 @ (comp @ X101 @ X100))) = $true) | ~ (((X97 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101) @ X100)) = $true)) | ~ ! [X104 : (subst > term > term)] : (~ ! [X105 : term] : ((((X97 @ id @ (X104 @ id @ X105) @ id)) = $true) | ~ (((X97 @ id @ X105 @ id)) = $true)) | ~ ! [X107 : subst,X106 : term,X108 : subst] : (((X104 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X104 @ X107 @ X106) @ X108))) | ($true = ((X97 @ id @ (lam @ (X104 @ sh @ one)) @ id)))) | ~ ! [X109 : term,X110 : term] : (~ (((X97 @ id @ X110 @ id)) = $true) | (((X97 @ id @ (ap @ (sub @ X109 @ id) @ X110) @ id)) = $true) | ~ ($true = ((X97 @ id @ X109 @ id)))) | ~ ! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (~ ($true = ((X97 @ X111 @ X112 @ (comp @ X113 @ X114)))) | (((X97 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114)) = $true)) | (((X97 @ id @ X98 @ id)) = $true))) & (hoasinduction_gthm = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) <=> (apinj2 = $true)) & (((d2subst @ d_id)) = id) & ((hoasinduction_lem3a = $true) <=> ! [X119 : term,X120 : (subst > term > subst > $o)] : (~ ! [X121 : (subst > term > term)] : (~ ! [X123 : subst,X124 : subst,X122 : term] : (((sub @ (X121 @ X123 @ X122) @ X124)) = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124)))) | (((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ~ ! [X125 : term] : ((((X120 @ id @ (X121 @ id @ X125) @ id)) = $true) | ~ (((X120 @ id @ X125 @ id)) = $true))) | (((X120 @ id @ (lam @ X119) @ id)) = $true) | ~ ! [X126 : term] : (($true = ((X120 @ id @ (sub @ X119 @ (push @ X126 @ id)) @ id))) | ~ (((X120 @ id @ X126 @ id)) = $true)))) & (axmap = $true) & (ulamvarind = $true) & (pushprop_lem1_gthm = $true) & ((axidl = $true) <=> ! [X127 : subst] : (((comp @ id @ X127)) = X127)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X128 : (subst > term > subst > $o)] : ~ ! [X129 : (term > $o)] : ~ ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130)))) & (hoaslamnotvar_gthm = $true) & (axapp = $true) & (apnotvar = $true) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X134 : subst,X133 : term] : (((comp @ sh @ (push @ X133 @ X134))) = X134) => (! [X136 : term,X135 : term] : ((((lam @ X136)) != ((lam @ X135))) | (X135 = X136)) => ! [X137 : (subst > term > term),X139 : subst,X138 : term,X140 : (subst > term > term)] : ((((lam @ (X137 @ sh @ one))) != ((lam @ (X140 @ sh @ one)))) | ~ ! [X141 : subst,X143 : term,X142 : subst] : (((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141))) = ((sub @ (X140 @ X142 @ X143) @ X141))) | ~ ! [X144 : subst,X146 : term,X145 : subst] : (((sub @ (X137 @ X145 @ X146) @ X144)) = ((X137 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144)))) | (((X137 @ X139 @ X138)) = ((X140 @ X139 @ X138))))))) <=> (hoaslaminj_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X148 : subst,X147 : term] : (((sub @ one @ (push @ X147 @ X148))) = X147) => (! [X149 : subst,X150 : term] : (((comp @ sh @ (push @ X150 @ X149))) = X149) => (! [X151 : subst] : (((comp @ X151 @ id)) = X151) => (! [X152 : term,X153 : (term > $o)] : (($true = ((X153 @ X152))) | ~ ! [X154 : term] : ((((X153 @ X154)) = $true) | ~ (((var @ X154)) = $true)) | ~ ! [X155 : term] : (~ ($true = ((X153 @ X155))) | ($true = ((X153 @ (lam @ X155))))) | ~ ! [X156 : term,X157 : term] : (~ ($true = ((X153 @ X157))) | ~ ($true = ((X153 @ X156))) | (((X153 @ (ap @ X157 @ X156))) = $true))) => ! [X158 : (term > $o),X159 : subst,X160 : term] : (~ ! [X161 : term] : (~ ! [X162 : term] : (~ (((X158 @ X162)) = $true) | ($true = ((X158 @ (sub @ X161 @ (push @ X162 @ id)))))) | (((X158 @ (lam @ X161))) = $true)) | ~ ! [X163 : term,X164 : term] : (~ (((X158 @ X164)) = $true) | ~ ($true = ((X158 @ X163))) | (((X158 @ (ap @ X164 @ X163))) = $true)) | ~ ! [X165 : term] : (($true = ((X158 @ (sub @ X165 @ X159)))) | ~ (((var @ X165)) = $true)) | (((X158 @ (sub @ X160 @ X159))) = $true))))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X166 : term] : ~ ! [X167 : (subst > term > term)] : (((X167 @ sh @ one)) != ((sub @ X166 @ (push @ one @ sh))))) & (! [X168 : (subst > term > subst > $o),X169 : (term > $o),X170 : term] : (~ ! [X171 : term] : ((((X169 @ (sub @ X170 @ (push @ X171 @ id)))) = $true) | ~ (((X169 @ X171)) = $true)) | ~ ! [X172 : (subst > term > term)] : (~ ! [X173 : term] : (~ ($true = ((X168 @ id @ X173 @ id))) | ($true = ((X168 @ id @ (X172 @ id @ X173) @ id)))) | ~ ! [X174 : term,X176 : subst,X175 : subst] : (((X172 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) = ((sub @ (X172 @ X175 @ X174) @ X176))) | (((X168 @ id @ (lam @ (X172 @ sh @ one)) @ id)) = $true)) | (((X169 @ (lam @ X170))) = $true) | ~ ! [X177 : term] : (((X169 @ X177)) = ((X168 @ id @ X177 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & ((pushprop_lem0_lthm = $true) <=> ! [X178 : (term > $o),X179 : term,X180 : subst] : ~ ! [X181 : (term > $o)] : ~ ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180)))))) & (hoaslamnotvar_lthm = $true) & (hoasapnotvar_lthm = $true) & (! [X183 : term,X184 : (subst > term > subst > $o)] : (($true = ((X184 @ id @ (lam @ (sub @ X183 @ (push @ one @ sh))) @ id))) | ~ ! [X185 : (subst > term > term),X186 : term] : ((((X184 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true) | ~ ! [X187 : subst,X188 : subst,X189 : term] : (((sub @ (X185 @ X188 @ X189) @ X187)) = ((sub @ (sub @ X186 @ (push @ X189 @ X188)) @ X187))) | ~ ! [X190 : term] : (~ ($true = ((X184 @ id @ X190 @ id))) | (((X184 @ id @ (X185 @ id @ X190) @ id)) = $true)) | ~ ! [X193 : term,X191 : subst,X192 : subst] : (((sub @ X186 @ (push @ (sub @ X193 @ X192) @ (comp @ X191 @ X192)))) = ((X185 @ (comp @ X191 @ X192) @ (sub @ X193 @ X192))))) | ~ ! [X194 : term] : (~ (((X184 @ id @ X194 @ id)) = $true) | ($true = ((X184 @ id @ (sub @ X183 @ (push @ X194 @ id)) @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ! [X195 : d_term] : (d_one = X195) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ~ (((var @ (d2term @ d_one))) = $true) & ((induction = $true) <=> ! [X196 : term,X197 : (term > $o)] : (~ ! [X198 : term] : (~ ($true = ((X197 @ X198))) | (((X197 @ (lam @ X198))) = $true)) | ~ ! [X199 : term] : (~ (((var @ X199)) = $true) | (((X197 @ X199)) = $true)) | ~ ! [X200 : term,X201 : term] : (~ (((X197 @ X200)) = $true) | ~ (((X197 @ X201)) = $true) | ($true = ((X197 @ (ap @ X200 @ X201))))) | ($true = ((X197 @ X196))))) & ((! [X202 : term] : (((sub @ X202 @ id)) = X202) => (! [X203 : term,X204 : (term > $o),X205 : subst] : (~ ! [X206 : term] : ((((X204 @ (lam @ X206))) = $true) | ~ ! [X207 : term] : (~ ($true = ((X204 @ X207))) | (((X204 @ (sub @ X206 @ (push @ X207 @ id)))) = $true))) | ~ ! [X208 : term] : ((((X204 @ (sub @ X208 @ X205))) = $true) | ~ (((var @ X208)) = $true)) | ~ ! [X209 : term,X210 : term] : (~ ($true = ((X204 @ X209))) | (((X204 @ (ap @ X209 @ X210))) = $true) | ~ ($true = ((X204 @ X210)))) | (((X204 @ (sub @ X203 @ X205))) = $true)) => ! [X211 : (term > $o),X212 : term] : (~ ! [X213 : term] : (~ ! [X214 : term] : (~ ($true = ((X211 @ X214))) | (((X211 @ (sub @ X213 @ (push @ X214 @ id)))) = $true)) | (((X211 @ (lam @ X213))) = $true)) | ~ ! [X215 : term] : (($true = ((X211 @ X215))) | ~ ($true = ((var @ X215)))) | (((X211 @ X212)) = $true) | ~ ! [X216 : term,X217 : term] : (~ (((X211 @ X217)) = $true) | ~ (((X211 @ X216)) = $true) | (((X211 @ (ap @ X217 @ X216))) = $true))))) <=> (induction2_lthm = $true)) & ~ (ulamvar1 = $true) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) <=> (laminj = $true)) & (hoasapnotvar_gthm = $true) & ((shinj = $true) <=> ! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh))))) & (pushprop_lem1v2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem1 = $true) & (! [X222 : (term > $o),X223 : (subst > term > subst > $o),X224 : term] : (~ ! [X225 : term] : (~ (((X222 @ X225)) = $true) | (((X222 @ (sub @ X224 @ (push @ X225 @ id)))) = $true)) | ~ ! [X226 : subst,X227 : term,X228 : subst,X229 : subst] : ((((X223 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226) @ X229)) = $true) | ~ (((X223 @ X228 @ X227 @ (comp @ X226 @ X229))) = $true)) | ~ ! [X230 : term] : (((X223 @ id @ X230 @ id)) = ((X222 @ X230))) | ($true = ((X222 @ (lam @ X224)))) | ~ ! [X231 : subst,X232 : term,X233 : subst,X234 : subst] : ((((X223 @ X234 @ X232 @ (comp @ X231 @ X233))) = $true) | ~ (((X223 @ (comp @ X234 @ X231) @ (sub @ X232 @ X231) @ X233)) = $true)) | ~ ! [X235 : (subst > term > term)] : (~ ! [X238 : subst,X236 : term,X237 : subst] : (((X235 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X235 @ X237 @ X236) @ X238))) | ~ ! [X239 : term] : ((((X223 @ id @ (X235 @ id @ X239) @ id)) = $true) | ~ (((X223 @ id @ X239 @ id)) = $true)) | (((X223 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3v2 = $true)) & (pushprop_gthm = $true) & ((axshiftcons = $true) <=> ! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241)) & ((hoasinduction_lem3aa = $true) <=> ! [X242 : (subst > term > subst > $o),X243 : term] : (~ ! [X244 : term] : ((((X242 @ id @ (sub @ X243 @ (push @ X244 @ id)) @ id)) = $true) | ~ (((X242 @ id @ X244 @ id)) = $true)) | (((X242 @ id @ (lam @ (sub @ X243 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X245 : (subst > term > term)] : (~ ! [X246 : term] : ((((X242 @ id @ (X245 @ id @ X246) @ id)) = $true) | ~ (((X242 @ id @ X246 @ id)) = $true)) | (((X242 @ id @ (lam @ (X245 @ sh @ one)) @ id)) = $true) | ~ ! [X247 : subst,X249 : subst,X248 : term] : (((sub @ (X245 @ X249 @ X248) @ X247)) = ((X245 @ (comp @ X249 @ X247) @ (sub @ X248 @ X247))))))) & ((! [X250 : (term > $o),X251 : term] : (~ ! [X252 : term] : ((((X250 @ X252)) = $true) | ~ ($true = ((var @ X252)))) | (((X250 @ X251)) = $true) | ~ ! [X253 : term] : (~ ! [X254 : term] : (~ (((X250 @ X254)) = $true) | (((X250 @ (sub @ X253 @ (push @ X254 @ id)))) = $true)) | (((X250 @ (lam @ X253))) = $true)) | ~ ! [X255 : term,X256 : term] : (~ (((X250 @ X256)) = $true) | (((X250 @ (ap @ X255 @ X256))) = $true) | ~ (((X250 @ X255)) = $true))) => (! [X257 : term,X258 : (subst > term > subst > $o),X259 : term] : ((((X258 @ id @ (ap @ X259 @ X257) @ id)) = $true) | ~ ! [X260 : term,X261 : term] : (($true = ((X258 @ id @ (ap @ (sub @ X260 @ id) @ X261) @ id))) | ~ ($true = ((X258 @ id @ X261 @ id))) | ~ (((X258 @ id @ X260 @ id)) = $true)) | ~ ! [X262 : term,X263 : subst,X264 : subst,X265 : subst] : ((((X258 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263) @ X265)) = $true) | ~ (((X258 @ X264 @ X262 @ (comp @ X263 @ X265))) = $true)) | ~ ! [X266 : subst,X267 : subst,X268 : subst,X269 : term] : (~ ($true = ((X258 @ (comp @ X268 @ X266) @ (sub @ X269 @ X266) @ X267))) | (((X258 @ X268 @ X269 @ (comp @ X266 @ X267))) = $true)) | ~ (((X258 @ id @ X257 @ id)) = $true) | ~ (((X258 @ id @ X259 @ id)) = $true)) => (! [X270 : (subst > term > subst > $o),X271 : term] : (~ ! [X272 : subst,X273 : term,X274 : subst,X275 : subst] : (($true = ((X270 @ (comp @ X275 @ X274) @ (sub @ X273 @ X274) @ X272))) | ~ (((X270 @ X275 @ X273 @ (comp @ X274 @ X272))) = $true)) | ~ ! [X276 : subst,X277 : subst,X278 : subst,X279 : term] : ((((X270 @ X278 @ X279 @ (comp @ X277 @ X276))) = $true) | ~ (((X270 @ (comp @ X278 @ X277) @ (sub @ X279 @ X277) @ X276)) = $true)) | ~ ! [X280 : (subst > term > term)] : (($true = ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id))) | ~ ! [X281 : term,X282 : subst,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) | ~ ! [X284 : term] : (~ (((X270 @ id @ X284 @ id)) = $true) | (((X270 @ id @ (X280 @ id @ X284) @ id)) = $true))) | ~ ! [X285 : term] : (~ (((X270 @ id @ X285 @ id)) = $true) | ($true = ((X270 @ id @ (sub @ X271 @ (push @ X285 @ id)) @ id)))) | (((X270 @ id @ (lam @ X271) @ id)) = $true)) => ! [X286 : term,X287 : (subst > term > subst > $o)] : (~ ! [X288 : subst,X289 : subst,X290 : term,X291 : subst] : (~ (((X287 @ X288 @ X290 @ (comp @ X291 @ X289))) = $true) | (((X287 @ (comp @ X288 @ X291) @ (sub @ X290 @ X291) @ X289)) = $true)) | ~ ! [X292 : term,X293 : term] : (($true = ((X287 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id))) | ~ ($true = ((X287 @ id @ X292 @ id))) | ~ (((X287 @ id @ X293 @ id)) = $true)) | ~ ! [X294 : subst,X295 : term,X296 : subst,X297 : subst] : (~ (((X287 @ (comp @ X294 @ X297) @ (sub @ X295 @ X297) @ X296)) = $true) | ($true = ((X287 @ X294 @ X295 @ (comp @ X297 @ X296))))) | (((X287 @ id @ X286 @ id)) = $true) | ~ ! [X298 : term] : ((((X287 @ id @ X298 @ id)) = $true) | ~ (((var @ (sub @ X298 @ id))) = $true)) | ~ ! [X299 : (subst > term > term)] : (~ ! [X300 : term] : (~ (((X287 @ id @ X300 @ id)) = $true) | ($true = ((X287 @ id @ (X299 @ id @ X300) @ id)))) | (((X287 @ id @ (lam @ (X299 @ sh @ one)) @ id)) = $true) | ~ ! [X302 : term,X303 : subst,X301 : subst] : (((sub @ (X299 @ X301 @ X302) @ X303)) = ((X299 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303))))))))) <=> (hoasinduction_lthm = $true)) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X306 : (subst > term > subst > $o),X307 : term] : ((((X306 @ id @ (lam @ (sub @ X307 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X308 : (subst > term > term)] : ((((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)) = $true) | ~ ! [X309 : term] : (~ (((X306 @ id @ X309 @ id)) = $true) | ($true = ((X306 @ id @ (X308 @ id @ X309) @ id)))) | ~ ! [X310 : subst,X311 : term,X312 : subst] : (((sub @ (X308 @ X310 @ X311) @ X312)) = ((X308 @ (comp @ X310 @ X312) @ (sub @ X311 @ X312))))) | ~ ! [X313 : term] : (~ (((X306 @ id @ X313 @ id)) = $true) | (((X306 @ id @ (sub @ X307 @ (push @ X313 @ id)) @ id)) = $true)))) & ((! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X315 : term,X316 : (subst > term > subst > $o)] : (~ ! [X317 : (subst > term > term)] : ((((X316 @ id @ (lam @ (X317 @ sh @ one)) @ id)) = $true) | ~ ! [X318 : term] : (~ ($true = ((X316 @ id @ X318 @ id))) | (((X316 @ id @ (X317 @ id @ X318) @ id)) = $true)) | ~ ! [X321 : term,X319 : subst,X320 : subst] : (((X317 @ (comp @ X320 @ X319) @ (sub @ X321 @ X319))) = ((sub @ (X317 @ X320 @ X321) @ X319)))) | ~ ! [X322 : term] : (($true = ((X316 @ id @ (sub @ X315 @ (push @ X322 @ id)) @ id))) | ~ (((X316 @ id @ X322 @ id)) = $true)) | (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) = $true)) => ! [X323 : term,X324 : (subst > term > subst > $o)] : ((((X324 @ id @ (lam @ X323) @ id)) = $true) | ~ ! [X325 : subst,X326 : subst,X327 : subst,X328 : term] : (($true = ((X324 @ (comp @ X327 @ X326) @ (sub @ X328 @ X326) @ X325))) | ~ (((X324 @ X327 @ X328 @ (comp @ X326 @ X325))) = $true)) | ~ ! [X329 : term] : ((((X324 @ id @ (sub @ X323 @ (push @ X329 @ id)) @ id)) = $true) | ~ (((X324 @ id @ X329 @ id)) = $true)) | ~ ! [X330 : subst,X331 : subst,X332 : subst,X333 : term] : (~ ($true = ((X324 @ (comp @ X331 @ X330) @ (sub @ X333 @ X330) @ X332))) | ($true = ((X324 @ X331 @ X333 @ (comp @ X330 @ X332))))) | ~ ! [X334 : (subst > term > term)] : (($true = ((X324 @ id @ (lam @ (X334 @ sh @ one)) @ id))) | ~ ! [X337 : subst,X335 : term,X336 : subst] : (((sub @ (X334 @ X336 @ X335) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X335 @ X337)))) | ~ ! [X338 : term] : (($true = ((X324 @ id @ (X334 @ id @ X338) @ id))) | ~ ($true = ((X324 @ id @ X338 @ id)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem1_lthm = $true) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X339 : term,X340 : (term > $o)] : (~ ! [X341 : term] : (~ (((var @ X341)) = $true) | (((X340 @ X341)) = $true)) | ~ ! [X342 : term] : (~ ! [X343 : term] : ((((X340 @ (sub @ X342 @ (push @ X343 @ id)))) = $true) | ~ ($true = ((X340 @ X343)))) | ($true = ((X340 @ (lam @ X342))))) | (((X340 @ X339)) = $true) | ~ ! [X344 : term,X345 : term] : ((((X340 @ (ap @ X344 @ X345))) = $true) | ~ (((X340 @ X344)) = $true) | ~ ($true = ((X340 @ X345))))) <=> (induction2 = $true)) & (pushprop_lem3v2_lthm = $true) & ((! [X346 : term] : (((sub @ X346 @ id)) = X346) => ! [X347 : (term > $o),X348 : (subst > term > subst > $o),X349 : term] : (($true = ((X347 @ (lam @ X349)))) | ~ ! [X350 : term] : (~ ($true = ((X347 @ X350))) | (((X347 @ (sub @ X349 @ (push @ X350 @ id)))) = $true)) | ~ ! [X351 : (subst > term > term)] : ((((X348 @ id @ (lam @ (X351 @ sh @ one)) @ id)) = $true) | ~ ! [X352 : term,X354 : subst,X353 : subst] : (((sub @ (X351 @ X354 @ X352) @ X353)) = ((X351 @ (comp @ X354 @ X353) @ (sub @ X352 @ X353)))) | ~ ! [X355 : term] : (~ ($true = ((X348 @ id @ X355 @ id))) | ($true = ((X348 @ id @ (X351 @ id @ X355) @ id))))) | ~ ! [X356 : subst,X357 : subst,X358 : term,X359 : subst] : (($true = ((X348 @ (comp @ X356 @ X359) @ (sub @ X358 @ X359) @ X357))) | ~ (((X348 @ X356 @ X358 @ (comp @ X359 @ X357))) = $true)) | ~ ! [X360 : subst,X361 : subst,X362 : term,X363 : subst] : (~ ($true = ((X348 @ (comp @ X361 @ X360) @ (sub @ X362 @ X360) @ X363))) | (((X348 @ X361 @ X362 @ (comp @ X360 @ X363))) = $true)) | ~ ! [X364 : term] : (((X348 @ id @ X364 @ id)) = ((X347 @ X364))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslamnotvar = $true) & (induction2lem_gthm = $true) & ((! [X365 : (subst > term > subst > $o)] : ~ ! [X366 : (term > $o)] : ~ ! [X367 : term] : (((X366 @ X367)) = ((X365 @ id @ X367 @ id))) => (! [X368 : (term > $o),X369 : term] : ((((X368 @ X369)) = $true) | ~ ! [X370 : term] : (~ (((var @ X370)) = $true) | ($true = ((X368 @ X370)))) | ~ ! [X371 : term,X372 : term] : (~ (((X368 @ X372)) = $true) | ~ ($true = ((X368 @ X371))) | (((X368 @ (ap @ X371 @ X372))) = $true)) | ~ ! [X373 : term] : (($true = ((X368 @ (lam @ X373)))) | ~ ! [X374 : term] : (~ (((X368 @ X374)) = $true) | ($true = ((X368 @ (sub @ X373 @ (push @ X374 @ id)))))))) => (! [X375 : term] : (((sub @ X375 @ id)) = X375) => (! [X376 : term,X377 : (subst > term > subst > $o),X378 : (term > $o)] : ((((X378 @ (lam @ X376))) = $true) | ~ ! [X379 : (subst > term > term)] : (~ ! [X380 : subst,X381 : subst,X382 : term] : (((X379 @ (comp @ X381 @ X380) @ (sub @ X382 @ X380))) = ((sub @ (X379 @ X381 @ X382) @ X380))) | (((X377 @ id @ (lam @ (X379 @ sh @ one)) @ id)) = $true) | ~ ! [X383 : term] : (~ (((X377 @ id @ X383 @ id)) = $true) | (((X377 @ id @ (X379 @ id @ X383) @ id)) = $true))) | ~ ! [X384 : term] : (((X378 @ X384)) = ((X377 @ id @ X384 @ id))) | ~ ! [X385 : term] : (~ ($true = ((X378 @ X385))) | ($true = ((X378 @ (sub @ X376 @ (push @ X385 @ id))))))) => ! [X386 : term,X387 : (subst > term > subst > $o)] : (~ ! [X388 : term,X389 : subst,X390 : subst,X391 : subst] : (($true = ((X387 @ (comp @ X389 @ X390) @ (sub @ X388 @ X390) @ X391))) | ~ (((X387 @ X389 @ X388 @ (comp @ X390 @ X391))) = $true)) | ~ ! [X392 : term,X393 : term] : (~ ($true = ((X387 @ id @ X392 @ id))) | ~ (((X387 @ id @ X393 @ id)) = $true) | ($true = ((X387 @ id @ (ap @ (sub @ X393 @ id) @ X392) @ id)))) | (((X387 @ id @ X386 @ id)) = $true) | ~ ! [X394 : term] : ((((X387 @ id @ X394 @ id)) = $true) | ~ ($true = ((var @ (sub @ X394 @ id))))) | ~ ! [X395 : subst,X396 : subst,X397 : subst,X398 : term] : (($true = ((X387 @ X395 @ X398 @ (comp @ X396 @ X397)))) | ~ (((X387 @ (comp @ X395 @ X396) @ (sub @ X398 @ X396) @ X397)) = $true)) | ~ ! [X399 : (subst > term > term)] : (~ ! [X400 : term] : (($true = ((X387 @ id @ (X399 @ id @ X400) @ id))) | ~ (((X387 @ id @ X400 @ id)) = $true)) | ~ ! [X401 : subst,X402 : subst,X403 : term] : (((sub @ (X399 @ X402 @ X403) @ X401)) = ((X399 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401)))) | (((X387 @ id @ (lam @ (X399 @ sh @ one)) @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslaminj_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem0_gthm = $true) & ((substmonoid_lthm = $true) <=> (! [X404 : subst] : (((comp @ id @ X404)) = X404) => (! [X405 : subst] : (((comp @ X405 @ id)) = X405) => (! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407))))) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) = ((d2subst @ X409))) => (X408 = X409)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotvar = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X410 : (subst > term > subst > $o)] : ~ ! [X411 : (term > $o)] : ~ ! [X412 : term] : (((X411 @ X412)) = ((X410 @ id @ X412 @ id))) => (! [X413 : term,X414 : (term > $o)] : (~ ! [X415 : term] : (~ ! [X416 : term] : (~ ($true = ((X414 @ X416))) | (((X414 @ (sub @ X415 @ (push @ X416 @ id)))) = $true)) | (((X414 @ (lam @ X415))) = $true)) | ~ ! [X417 : term] : (~ ($true = ((var @ X417))) | (((X414 @ X417)) = $true)) | (((X414 @ X413)) = $true) | ~ ! [X418 : term,X419 : term] : (~ ($true = ((X414 @ X418))) | ~ (((X414 @ X419)) = $true) | (((X414 @ (ap @ X418 @ X419))) = $true))) => (! [X420 : term] : (((sub @ X420 @ id)) = X420) => (! [X421 : term,X422 : (term > $o),X423 : (subst > term > subst > $o)] : ((((X422 @ (lam @ X421))) = $true) | ~ ! [X424 : (subst > term > term)] : (~ ! [X427 : subst,X426 : subst,X425 : term] : (((sub @ (X424 @ X426 @ X425) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427)))) | ~ ! [X428 : term] : (~ (((X423 @ id @ X428 @ id)) = $true) | (((X423 @ id @ (X424 @ id @ X428) @ id)) = $true)) | (((X423 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true)) | ~ ! [X429 : term] : ((((X422 @ (sub @ X421 @ (push @ X429 @ id)))) = $true) | ~ (((X422 @ X429)) = $true)) | ~ ! [X430 : term] : (((X422 @ X430)) = ((X423 @ id @ X430 @ id)))) => ! [X431 : (subst > term > subst > $o),X432 : term] : (~ ! [X433 : term,X434 : term] : (~ (((X431 @ id @ X434 @ id)) = $true) | ($true = ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id))) | ~ (((X431 @ id @ X433 @ id)) = $true)) | ~ ! [X435 : (subst > term > term)] : (~ ! [X436 : term] : (($true = ((X431 @ id @ (X435 @ id @ X436) @ id))) | ~ (((X431 @ id @ X436 @ id)) = $true)) | ~ ! [X437 : subst,X439 : subst,X438 : term] : (((sub @ (X435 @ X437 @ X438) @ X439)) = ((X435 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439)))) | (((X431 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true)) | (((X431 @ id @ X432 @ id)) = $true))))))) & ((hoasapinj1 = $true) <=> ! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441))) & (hoasinduction_lem3_gthm = $true) & ((! [X444 : term] : (((sub @ X444 @ id)) = X444) => (! [X445 : term,X446 : (subst > term > subst > $o)] : (~ ! [X447 : term] : (($true = ((X446 @ id @ (sub @ X445 @ (push @ X447 @ id)) @ id))) | ~ ($true = ((X446 @ id @ X447 @ id)))) | ~ ! [X448 : (subst > term > term)] : (~ ! [X449 : term] : (($true = ((X446 @ id @ (X448 @ id @ X449) @ id))) | ~ (((X446 @ id @ X449 @ id)) = $true)) | ~ ! [X452 : subst,X451 : term,X450 : subst] : (((X448 @ (comp @ X450 @ X452) @ (sub @ X451 @ X452))) = ((sub @ (X448 @ X450 @ X451) @ X452))) | (((X446 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true)) | (((X446 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) = $true)) => ! [X453 : term,X454 : (subst > term > subst > $o)] : (~ ! [X455 : (subst > term > term)] : (~ ! [X457 : subst,X458 : term,X456 : subst] : (((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))) = ((sub @ (X455 @ X456 @ X458) @ X457))) | ~ ! [X459 : term] : (~ (((X454 @ id @ X459 @ id)) = $true) | (((X454 @ id @ (X455 @ id @ X459) @ id)) = $true)) | (((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true)) | ~ ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | ~ (((X454 @ id @ X460 @ id)) = $true)) | (((X454 @ id @ (lam @ X453) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X461 : term] : ~ ! [X462 : (subst > term > term)] : ~ ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464))))) & ((hoasapinj2 = $true) <=> ! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466))))) & (axassoc = $true) & ((hoasinduction_lem3b = $true) <=> ! [X469 : term] : ~ ! [X470 : (subst > term > term)] : (((X470 @ sh @ one)) != ((sub @ X469 @ (push @ one @ sh))))) & ((pushprop_lem1 = $true) <=> ! [X471 : term,X472 : term,X473 : (term > $o),X474 : (term > $o),X475 : subst] : (~ (((X474 @ X472)) = $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true))) & (! [X476 : term,X477 : (subst > term > subst > $o)] : (~ ! [X478 : term,X479 : term] : (($true = ((X477 @ id @ (ap @ (sub @ X479 @ id) @ X478) @ id))) | ~ (((X477 @ id @ X479 @ id)) = $true) | ~ ($true = ((X477 @ id @ X478 @ id)))) | ~ ! [X480 : (subst > term > term)] : (~ ! [X481 : term] : (($true = ((X477 @ id @ (X480 @ id @ X481) @ id))) | ~ (((X477 @ id @ X481 @ id)) = $true)) | ~ ! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id)))) | ($true = ((X477 @ id @ X476 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((substmonoid = $true) <=> (! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485))) & (hoasapnotvar = $true) & ((induction2lem = $true) <=> ! [X487 : (term > $o),X488 : term,X489 : subst] : (~ ! [X490 : term,X491 : term] : (~ (((X487 @ X491)) = $true) | (((X487 @ (ap @ X491 @ X490))) = $true) | ~ ($true = ((X487 @ X490)))) | ~ ! [X492 : term] : (($true = ((X487 @ (lam @ X492)))) | ~ ! [X493 : term] : (~ (((X487 @ X493)) = $true) | (((X487 @ (sub @ X492 @ (push @ X493 @ id)))) = $true))) | (((X487 @ (sub @ X488 @ X489))) = $true) | ~ ! [X494 : term] : (~ ($true = ((var @ X494))) | (((X487 @ (sub @ X494 @ X489))) = $true)))) & (hoasapinj2_gthm = $true) & (axvarshift = $true) & (! [X495 : subst,X496 : (term > $o),X497 : term,X498 : (term > $o)] : ((((X498 @ one)) = $true) | ~ ! [X499 : term] : (((X498 @ X499)) = ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | ~ (((X496 @ X497)) = $true)) <=> (pushprop_lem1v2 = $true)) & ((apinj1 = $true) <=> ! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503))))) & (ulamvarsh = $true) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & ((! [X507 : term,X506 : subst] : (((sub @ one @ (push @ X507 @ X506))) = X507) => ! [X508 : (term > $o),X509 : (term > $o),X510 : subst,X511 : term] : ((((X508 @ one)) = $true) | ~ ($true = ((X509 @ X511))) | ~ ! [X512 : term] : (((X508 @ X512)) = ((X509 @ (sub @ X512 @ (push @ X511 @ X510))))))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lthm_orig = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) = X514) => (! [X516 : term,X515 : subst] : (((comp @ sh @ (push @ X516 @ X515))) = X515) => ! [X517 : subst,X518 : term,X519 : (term > $o),X520 : term,X521 : (term > $o)] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | ~ (((X521 @ X520)) = $true))))) & (hoasinduction_lem1_gthm = $true) & (! [X523 : (subst > term > term),X522 : subst,X525 : (subst > term > term),X524 : term] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) = ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ~ ! [X529 : subst,X531 : subst,X530 : term] : (((sub @ (X523 @ X531 @ X530) @ X529)) = ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) <=> (hoaslaminj = $true)) & ((axidr = $true) <=> ! [X532 : subst] : (((comp @ X532 @ id)) = X532)) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) <=> (termmset = $true)) & (pushprop_lem3v2 = $true) & ((hoaslamnotap = $true) <=> ! [X535 : term,X536 : (subst > term > term),X534 : term] : ((((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535))) | ~ ! [X537 : subst,X538 : subst,X539 : term] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) = ((sub @ (X536 @ X538 @ X539) @ X537)))))),
% 2.11/0.57 inference(rectify,[],[f7])).
% 2.11/0.57 thf(f10,plain,(
% 2.11/0.57 ((! [X30 : term,X31 : term,X28 : term,X29 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)) => ! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X307 : term,X306 : (subst > term > subst > $o)] : (~ ! [X308 : (subst > term > term)] : (~ ! [X310 : subst,X311 : term,X312 : subst] : (((sub @ (X308 @ X310 @ X311) @ X312)) = ((X308 @ (comp @ X310 @ X312) @ (sub @ X311 @ X312)))) | ~ ! [X309 : term] : (($true = ((X306 @ id @ (X308 @ id @ X309) @ id))) | (((X306 @ id @ X309 @ id)) != $true)) | (((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)) = $true)) | ~ ! [X313 : term] : ((((X306 @ id @ X313 @ id)) != $true) | (((X306 @ id @ (sub @ X307 @ (push @ X313 @ id)) @ id)) = $true)) | (((X306 @ id @ (lam @ (sub @ X307 @ (push @ one @ sh))) @ id)) = $true))) & ! [X50 : d_term,X49 : d_term] : ((((d2term @ X50)) = ((d2term @ X49))) => (X49 = X50)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X477 : (subst > term > subst > $o),X476 : term] : (~ ! [X479 : term,X478 : term] : (($true != ((X477 @ id @ X478 @ id))) | ($true = ((X477 @ id @ (ap @ (sub @ X479 @ id) @ X478) @ id))) | (((X477 @ id @ X479 @ id)) != $true)) | ($true = ((X477 @ id @ X476 @ id))) | ~ ! [X480 : (subst > term > term)] : (~ ! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ~ ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axassoc = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) <=> (apinj2 = $true)) & (! [X38 : term,X36 : (subst > term > subst > $o),X37 : term] : (~ ! [X42 : subst,X43 : subst,X44 : term,X41 : subst] : ((((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) = $true) | ($true != ((X36 @ X41 @ X44 @ (comp @ X43 @ X42))))) | ~ ! [X47 : subst,X46 : subst,X45 : term,X48 : subst] : (($true = ((X36 @ X46 @ X45 @ (comp @ X47 @ X48)))) | ($true != ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48)))) | ($true != ((X36 @ id @ X38 @ id))) | ~ ! [X39 : term,X40 : term] : ((((X36 @ id @ X39 @ id)) != $true) | ($true != ((X36 @ id @ X40 @ id))) | (((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) = $true)) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))) | ($true != ((X36 @ id @ X37 @ id)))) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X184 : (subst > term > subst > $o),X183 : term] : (~ ! [X186 : term,X185 : (subst > term > term)] : (~ ! [X187 : subst,X188 : subst,X189 : term] : (((sub @ (X185 @ X188 @ X189) @ X187)) = ((sub @ (sub @ X186 @ (push @ X189 @ X188)) @ X187))) | (((X184 @ id @ (lam @ (X185 @ sh @ one)) @ id)) = $true) | ~ ! [X190 : term] : (($true != ((X184 @ id @ X190 @ id))) | (((X184 @ id @ (X185 @ id @ X190) @ id)) = $true)) | ~ ! [X193 : term,X191 : subst,X192 : subst] : (((sub @ X186 @ (push @ (sub @ X193 @ X192) @ (comp @ X191 @ X192)))) = ((X185 @ (comp @ X191 @ X192) @ (sub @ X193 @ X192))))) | ~ ! [X194 : term] : ((((X184 @ id @ X194 @ id)) != $true) | ($true = ((X184 @ id @ (sub @ X183 @ (push @ X194 @ id)) @ id)))) | ($true = ((X184 @ id @ (lam @ (sub @ X183 @ (push @ one @ sh))) @ id))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) = ((sub @ X51 @ (push @ X53 @ X54)))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X58 : (subst > term > subst > $o),X57 : term,X56 : (term > $o)] : (~ ! [X65 : term] : ((((X56 @ (sub @ X57 @ (push @ X65 @ id)))) = $true) | ($true != ((X56 @ X65)))) | ~ ! [X59 : term] : (((X56 @ X59)) = ((X58 @ id @ X59 @ id))) | (((X56 @ (lam @ X57))) = $true) | ~ ! [X60 : (subst > term > term)] : (~ ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64)))) | (((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) = $true) | ~ ! [X61 : term] : ((((X58 @ id @ (X60 @ id @ X61) @ id)) = $true) | ($true != ((X58 @ id @ X61 @ id))))))))) & ((! [X365 : (subst > term > subst > $o)] : ~ ! [X366 : (term > $o)] : ~ ! [X367 : term] : (((X366 @ X367)) = ((X365 @ id @ X367 @ id))) => (! [X368 : (term > $o),X369 : term] : (~ ! [X373 : term] : (~ ! [X374 : term] : (($true = ((X368 @ (sub @ X373 @ (push @ X374 @ id))))) | (((X368 @ X374)) != $true)) | ($true = ((X368 @ (lam @ X373))))) | ~ ! [X370 : term] : ((((var @ X370)) != $true) | ($true = ((X368 @ X370)))) | ~ ! [X372 : term,X371 : term] : ((((X368 @ X372)) != $true) | (((X368 @ (ap @ X371 @ X372))) = $true) | ($true != ((X368 @ X371)))) | (((X368 @ X369)) = $true)) => (! [X375 : term] : (((sub @ X375 @ id)) = X375) => (! [X377 : (subst > term > subst > $o),X376 : term,X378 : (term > $o)] : (~ ! [X385 : term] : (($true = ((X378 @ (sub @ X376 @ (push @ X385 @ id))))) | ($true != ((X378 @ X385)))) | ~ ! [X384 : term] : (((X378 @ X384)) = ((X377 @ id @ X384 @ id))) | ~ ! [X379 : (subst > term > term)] : (~ ! [X383 : term] : ((((X377 @ id @ X383 @ id)) != $true) | (((X377 @ id @ (X379 @ id @ X383) @ id)) = $true)) | ~ ! [X380 : subst,X381 : subst,X382 : term] : (((X379 @ (comp @ X381 @ X380) @ (sub @ X382 @ X380))) = ((sub @ (X379 @ X381 @ X382) @ X380))) | (((X377 @ id @ (lam @ (X379 @ sh @ one)) @ id)) = $true)) | (((X378 @ (lam @ X376))) = $true)) => ! [X386 : term,X387 : (subst > term > subst > $o)] : (~ ! [X390 : subst,X388 : term,X389 : subst,X391 : subst] : ((((X387 @ X389 @ X388 @ (comp @ X390 @ X391))) != $true) | ($true = ((X387 @ (comp @ X389 @ X390) @ (sub @ X388 @ X390) @ X391)))) | ~ ! [X398 : term,X397 : subst,X396 : subst,X395 : subst] : ((((X387 @ (comp @ X395 @ X396) @ (sub @ X398 @ X396) @ X397)) != $true) | ($true = ((X387 @ X395 @ X398 @ (comp @ X396 @ X397))))) | ~ ! [X394 : term] : ((((X387 @ id @ X394 @ id)) = $true) | ($true != ((var @ (sub @ X394 @ id))))) | ~ ! [X392 : term,X393 : term] : (($true != ((X387 @ id @ X392 @ id))) | (((X387 @ id @ X393 @ id)) != $true) | ($true = ((X387 @ id @ (ap @ (sub @ X393 @ id) @ X392) @ id)))) | ~ ! [X399 : (subst > term > term)] : (~ ! [X401 : subst,X402 : subst,X403 : term] : (((sub @ (X399 @ X402 @ X403) @ X401)) = ((X399 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401)))) | (((X387 @ id @ (lam @ (X399 @ sh @ one)) @ id)) = $true) | ~ ! [X400 : term] : (($true = ((X387 @ id @ (X399 @ id @ X400) @ id))) | (((X387 @ id @ X400 @ id)) != $true))) | (((X387 @ id @ X386 @ id)) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & (hoasapinj1_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X461 : term] : ~ ! [X462 : (subst > term > term)] : ~ ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464))))) & ((axshiftcons = $true) <=> ! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241)) & (! [X90 : (term > $o),X92 : subst,X91 : term] : ~ ! [X93 : (term > $o)] : ~ ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94))) <=> (pushprop_lem0 = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X316 : (subst > term > subst > $o),X315 : term] : (~ ! [X317 : (subst > term > term)] : (~ ! [X321 : term,X319 : subst,X320 : subst] : (((X317 @ (comp @ X320 @ X319) @ (sub @ X321 @ X319))) = ((sub @ (X317 @ X320 @ X321) @ X319))) | ~ ! [X318 : term] : (($true != ((X316 @ id @ X318 @ id))) | (((X316 @ id @ (X317 @ id @ X318) @ id)) = $true)) | (((X316 @ id @ (lam @ (X317 @ sh @ one)) @ id)) = $true)) | ~ ! [X322 : term] : ((((X316 @ id @ X322 @ id)) != $true) | ($true = ((X316 @ id @ (sub @ X315 @ (push @ X322 @ id)) @ id)))) | (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) = $true)) => ! [X324 : (subst > term > subst > $o),X323 : term] : (~ ! [X327 : subst,X325 : subst,X328 : term,X326 : subst] : ((((X324 @ X327 @ X328 @ (comp @ X326 @ X325))) != $true) | ($true = ((X324 @ (comp @ X327 @ X326) @ (sub @ X328 @ X326) @ X325)))) | ~ ! [X332 : subst,X333 : term,X331 : subst,X330 : subst] : (($true != ((X324 @ (comp @ X331 @ X330) @ (sub @ X333 @ X330) @ X332))) | ($true = ((X324 @ X331 @ X333 @ (comp @ X330 @ X332))))) | ~ ! [X329 : term] : ((((X324 @ id @ (sub @ X323 @ (push @ X329 @ id)) @ id)) = $true) | (((X324 @ id @ X329 @ id)) != $true)) | ~ ! [X334 : (subst > term > term)] : (~ ! [X337 : subst,X335 : term,X336 : subst] : (((sub @ (X334 @ X336 @ X335) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X335 @ X337)))) | ($true = ((X324 @ id @ (lam @ (X334 @ sh @ one)) @ id))) | ~ ! [X338 : term] : (($true = ((X324 @ id @ (X334 @ id @ X338) @ id))) | ($true != ((X324 @ id @ X338 @ id))))) | (((X324 @ id @ (lam @ X323) @ id)) = $true))))) & (! [X119 : term,X120 : (subst > term > subst > $o)] : (~ ! [X121 : (subst > term > term)] : (~ ! [X125 : term] : ((((X120 @ id @ (X121 @ id @ X125) @ id)) = $true) | (((X120 @ id @ X125 @ id)) != $true)) | (((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)) = $true) | ~ ! [X123 : subst,X124 : subst,X122 : term] : (((sub @ (X121 @ X123 @ X122) @ X124)) = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124))))) | (((X120 @ id @ (lam @ X119) @ id)) = $true) | ~ ! [X126 : term] : (($true = ((X120 @ id @ (sub @ X119 @ (push @ X126 @ id)) @ id))) | (((X120 @ id @ X126 @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X170 : term,X169 : (term > $o),X168 : (subst > term > subst > $o)] : (~ ! [X177 : term] : (((X169 @ X177)) = ((X168 @ id @ X177 @ id))) | ~ ! [X172 : (subst > term > term)] : ((((X168 @ id @ (lam @ (X172 @ sh @ one)) @ id)) = $true) | ~ ! [X174 : term,X176 : subst,X175 : subst] : (((X172 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) = ((sub @ (X172 @ X175 @ X174) @ X176))) | ~ ! [X173 : term] : (($true != ((X168 @ id @ X173 @ id))) | ($true = ((X168 @ id @ (X172 @ id @ X173) @ id))))) | ~ ! [X171 : term] : ((((X169 @ (sub @ X170 @ (push @ X171 @ id)))) = $true) | (((X169 @ X171)) != $true)) | (((X169 @ (lam @ X170))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotap_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar = $true) & ((hoasapinj1_lthm = $true) <=> (! [X66 : term] : (((sub @ X66 @ id)) = X66) => (! [X67 : term,X69 : term,X68 : term,X70 : term] : ((X68 = X69) | (((ap @ X68 @ X70)) != ((ap @ X69 @ X67)))) => ! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72))))))) & ((induction2 = $true) <=> ! [X339 : term,X340 : (term > $o)] : ((((X340 @ X339)) = $true) | ~ ! [X345 : term,X344 : term] : ((((X340 @ (ap @ X344 @ X345))) = $true) | (((X340 @ X344)) != $true) | ($true != ((X340 @ X345)))) | ~ ! [X342 : term] : (($true = ((X340 @ (lam @ X342)))) | ~ ! [X343 : term] : (($true != ((X340 @ X343))) | (((X340 @ (sub @ X342 @ (push @ X343 @ id)))) = $true))) | ~ ! [X341 : term] : ((((X340 @ X341)) = $true) | (((var @ X341)) != $true)))) & (hoasinduction_gthm = $true) & (apnotvar = $true) & (pushprop = $true) & ((induction2_lthm = $true) <=> (! [X202 : term] : (((sub @ X202 @ id)) = X202) => (! [X203 : term,X205 : subst,X204 : (term > $o)] : (~ ! [X208 : term] : ((((var @ X208)) != $true) | (((X204 @ (sub @ X208 @ X205))) = $true)) | ~ ! [X210 : term,X209 : term] : ((((X204 @ (ap @ X209 @ X210))) = $true) | ($true != ((X204 @ X210))) | ($true != ((X204 @ X209)))) | ~ ! [X206 : term] : ((((X204 @ (lam @ X206))) = $true) | ~ ! [X207 : term] : (($true != ((X204 @ X207))) | (((X204 @ (sub @ X206 @ (push @ X207 @ id)))) = $true))) | (((X204 @ (sub @ X203 @ X205))) = $true)) => ! [X212 : term,X211 : (term > $o)] : (~ ! [X215 : term] : (($true != ((var @ X215))) | ($true = ((X211 @ X215)))) | ~ ! [X213 : term] : (~ ! [X214 : term] : ((((X211 @ (sub @ X213 @ (push @ X214 @ id)))) = $true) | ($true != ((X211 @ X214)))) | (((X211 @ (lam @ X213))) = $true)) | (((X211 @ X212)) = $true) | ~ ! [X216 : term,X217 : term] : ((((X211 @ X217)) != $true) | (((X211 @ X216)) != $true) | (((X211 @ (ap @ X217 @ X216))) = $true)))))) & (induction2lem_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction = $true) <=> ! [X197 : (term > $o),X196 : term] : (~ ! [X199 : term] : ((((X197 @ X199)) = $true) | (((var @ X199)) != $true)) | ($true = ((X197 @ X196))) | ~ ! [X200 : term,X201 : term] : (($true = ((X197 @ (ap @ X200 @ X201)))) | (((X197 @ X201)) != $true) | (((X197 @ X200)) != $true)) | ~ ! [X198 : term] : (($true != ((X197 @ X198))) | (((X197 @ (lam @ X198))) = $true)))) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((substmonoid_lthm = $true) <=> (! [X404 : subst] : (((comp @ id @ X404)) = X404) => (! [X405 : subst] : (((comp @ X405 @ id)) = X405) => (! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407))))) & (! [X523 : (subst > term > term),X522 : subst,X525 : (subst > term > term),X524 : term] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) = ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ~ ! [X529 : subst,X531 : subst,X530 : term] : (((sub @ (X523 @ X531 @ X530) @ X529)) = ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) <=> (hoaslaminj = $true)) & (hoasapinj2_gthm = $true) & ((shinj = $true) <=> ! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X128 : (subst > term > subst > $o)] : ~ ! [X129 : (term > $o)] : ~ ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130)))) & (pushprop_lem1v2_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) = ((d2subst @ X409))) => (X408 = X409)) & ((hoasapinj2 = $true) <=> ! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466))))) & (pushprop_gthm = $true) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) <=> (termmset = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X243 : term,X242 : (subst > term > subst > $o)] : (~ ! [X244 : term] : ((((X242 @ id @ X244 @ id)) != $true) | (((X242 @ id @ (sub @ X243 @ (push @ X244 @ id)) @ id)) = $true)) | ~ ! [X245 : (subst > term > term)] : (~ ! [X246 : term] : ((((X242 @ id @ (X245 @ id @ X246) @ id)) = $true) | (((X242 @ id @ X246 @ id)) != $true)) | ~ ! [X247 : subst,X249 : subst,X248 : term] : (((sub @ (X245 @ X249 @ X248) @ X247)) = ((X245 @ (comp @ X249 @ X247) @ (sub @ X248 @ X247)))) | (((X242 @ id @ (lam @ (X245 @ sh @ one)) @ id)) = $true)) | (((X242 @ id @ (lam @ (sub @ X243 @ (push @ one @ sh))) @ id)) = $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvarind = $true) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axabs = $true) & ((apinj1 = $true) <=> ! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503))))) & (axclos = $true) & ((pushprop_lem1v2 = $true) <=> ! [X498 : (term > $o),X495 : subst,X496 : (term > $o),X497 : term] : ((((X496 @ X497)) != $true) | ~ ! [X499 : term] : (((X498 @ X499)) = ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X498 @ one)) = $true))) & (axvarshift = $true) & (ulamvar1 != $true) & ((pushprop_lem1_lthm = $true) <=> (! [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) = X514) => (! [X516 : term,X515 : subst] : (((comp @ sh @ (push @ X516 @ X515))) = X515) => ! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true))))) & ((hoasinduction_lem3b = $true) <=> ! [X469 : term] : ~ ! [X470 : (subst > term > term)] : (((X470 @ sh @ one)) != ((sub @ X469 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & ((pushprop_lem1v2_lthm = $true) <=> (! [X507 : term,X506 : subst] : (((sub @ one @ (push @ X507 @ X506))) = X507) => ! [X508 : (term > $o),X511 : term,X510 : subst,X509 : (term > $o)] : (~ ! [X512 : term] : (((X508 @ X512)) = ((X509 @ (sub @ X512 @ (push @ X511 @ X510))))) | ($true != ((X509 @ X511))) | (((X508 @ one)) = $true)))) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & ((pushprop_lem1 = $true) <=> ! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true))) & (! [X4 : term] : ~ ! [X5 : (subst > term > term)] : ~ ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7)))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem1v2 = $true) & ((! [X131 : term,X132 : subst] : (((sub @ one @ (push @ X131 @ X132))) = X131) => (! [X134 : subst,X133 : term] : (((comp @ sh @ (push @ X133 @ X134))) = X134) => (! [X136 : term,X135 : term] : ((((lam @ X136)) != ((lam @ X135))) | (X135 = X136)) => ! [X137 : (subst > term > term),X139 : subst,X138 : term,X140 : (subst > term > term)] : ((((lam @ (X137 @ sh @ one))) != ((lam @ (X140 @ sh @ one)))) | ~ ! [X141 : subst,X143 : term,X142 : subst] : (((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141))) = ((sub @ (X140 @ X142 @ X143) @ X141))) | ~ ! [X144 : subst,X146 : term,X145 : subst] : (((sub @ (X137 @ X145 @ X146) @ X144)) = ((X137 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144)))) | (((X137 @ X139 @ X138)) = ((X140 @ X139 @ X138))))))) <=> (hoaslaminj_lthm = $true)) & ((termmset_lthm = $true) <=> (! [X0 : term] : (((sub @ X0 @ id)) = X0) => ! [X1 : term] : (((sub @ X1 @ id)) = X1))) & ((axidr = $true) <=> ! [X532 : subst] : (((comp @ X532 @ id)) = X532)) & (hoaslamnotap_gthm = $true) & ! [X96 : d_subst] : (d_id = X96) & (hoasinduction_lem1v2_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)))))))))))) & ((pushprop_lem0_lthm = $true) <=> ! [X178 : (term > $o),X179 : term,X180 : subst] : ~ ! [X181 : (term > $o)] : ~ ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180)))))) & (one = ((d2term @ d_one))) & (pushprop_lem0_gthm = $true) & ((induction2lem_lthm = $true) <=> (! [X148 : subst,X147 : term] : (((sub @ one @ (push @ X147 @ X148))) = X147) => (! [X149 : subst,X150 : term] : (((comp @ sh @ (push @ X150 @ X149))) = X149) => (! [X151 : subst] : (((comp @ X151 @ id)) = X151) => (! [X153 : (term > $o),X152 : term] : (~ ! [X154 : term] : ((((var @ X154)) != $true) | (((X153 @ X154)) = $true)) | ~ ! [X155 : term] : (($true != ((X153 @ X155))) | ($true = ((X153 @ (lam @ X155))))) | ($true = ((X153 @ X152))) | ~ ! [X157 : term,X156 : term] : ((((X153 @ (ap @ X157 @ X156))) = $true) | ($true != ((X153 @ X156))) | ($true != ((X153 @ X157))))) => ! [X160 : term,X158 : (term > $o),X159 : subst] : (~ ! [X164 : term,X163 : term] : (($true != ((X158 @ X163))) | (((X158 @ X164)) != $true) | (((X158 @ (ap @ X164 @ X163))) = $true)) | ~ ! [X161 : term] : ((((X158 @ (lam @ X161))) = $true) | ~ ! [X162 : term] : ((((X158 @ X162)) != $true) | ($true = ((X158 @ (sub @ X161 @ (push @ X162 @ id))))))) | (((X158 @ (sub @ X160 @ X159))) = $true) | ~ ! [X165 : term] : (($true = ((X158 @ (sub @ X165 @ X159)))) | (((var @ X165)) != $true)))))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X346 : term] : (((sub @ X346 @ id)) = X346) => ! [X348 : (subst > term > subst > $o),X347 : (term > $o),X349 : term] : (~ ! [X364 : term] : (((X348 @ id @ X364 @ id)) = ((X347 @ X364))) | ~ ! [X363 : subst,X361 : subst,X360 : subst,X362 : term] : ((((X348 @ X361 @ X362 @ (comp @ X360 @ X363))) = $true) | ($true != ((X348 @ (comp @ X361 @ X360) @ (sub @ X362 @ X360) @ X363)))) | ~ ! [X358 : term,X357 : subst,X356 : subst,X359 : subst] : (($true = ((X348 @ (comp @ X356 @ X359) @ (sub @ X358 @ X359) @ X357))) | (((X348 @ X356 @ X358 @ (comp @ X359 @ X357))) != $true)) | ~ ! [X350 : term] : ((((X347 @ (sub @ X349 @ (push @ X350 @ id)))) = $true) | ($true != ((X347 @ X350)))) | ($true = ((X347 @ (lam @ X349)))) | ~ ! [X351 : (subst > term > term)] : (~ ! [X352 : term,X354 : subst,X353 : subst] : (((sub @ (X351 @ X354 @ X352) @ X353)) = ((X351 @ (comp @ X354 @ X353) @ (sub @ X352 @ X353)))) | ~ ! [X355 : term] : (($true != ((X348 @ id @ X355 @ id))) | ($true = ((X348 @ id @ (X351 @ id @ X355) @ id)))) | (((X348 @ id @ (lam @ (X351 @ sh @ one)) @ id)) = $true))))) & (lamnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) <=> ! [X97 : (subst > term > subst > $o),X98 : term] : (~ ! [X102 : subst,X100 : subst,X101 : subst,X103 : term] : ((((X97 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101) @ X100)) != $true) | (((X97 @ X102 @ X103 @ (comp @ X101 @ X100))) = $true)) | ~ ! [X104 : (subst > term > term)] : (($true = ((X97 @ id @ (lam @ (X104 @ sh @ one)) @ id))) | ~ ! [X105 : term] : ((((X97 @ id @ X105 @ id)) != $true) | (((X97 @ id @ (X104 @ id @ X105) @ id)) = $true)) | ~ ! [X107 : subst,X106 : term,X108 : subst] : (((X104 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X104 @ X107 @ X106) @ X108)))) | ~ ! [X112 : term,X114 : subst,X113 : subst,X111 : subst] : (($true != ((X97 @ X111 @ X112 @ (comp @ X113 @ X114)))) | (((X97 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114)) = $true)) | (((X97 @ id @ X98 @ id)) = $true) | ~ ! [X109 : term,X110 : term] : ((((X97 @ id @ X110 @ id)) != $true) | (((X97 @ id @ (ap @ (sub @ X109 @ id) @ X110) @ id)) = $true) | ($true != ((X97 @ id @ X109 @ id)))) | ~ ! [X99 : term] : (($true = ((X97 @ id @ X99 @ id))) | (((var @ (sub @ X99 @ id))) != $true)))) & ((! [X410 : (subst > term > subst > $o)] : ~ ! [X411 : (term > $o)] : ~ ! [X412 : term] : (((X411 @ X412)) = ((X410 @ id @ X412 @ id))) => (! [X414 : (term > $o),X413 : term] : (~ ! [X419 : term,X418 : term] : ((((X414 @ (ap @ X418 @ X419))) = $true) | (((X414 @ X419)) != $true) | ($true != ((X414 @ X418)))) | ~ ! [X415 : term] : (~ ! [X416 : term] : ((((X414 @ (sub @ X415 @ (push @ X416 @ id)))) = $true) | ($true != ((X414 @ X416)))) | (((X414 @ (lam @ X415))) = $true)) | ~ ! [X417 : term] : (($true != ((var @ X417))) | (((X414 @ X417)) = $true)) | (((X414 @ X413)) = $true)) => (! [X420 : term] : (((sub @ X420 @ id)) = X420) => (! [X421 : term,X422 : (term > $o),X423 : (subst > term > subst > $o)] : (~ ! [X424 : (subst > term > term)] : (~ ! [X428 : term] : ((((X423 @ id @ (X424 @ id @ X428) @ id)) = $true) | (((X423 @ id @ X428 @ id)) != $true)) | (((X423 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ~ ! [X427 : subst,X426 : subst,X425 : term] : (((sub @ (X424 @ X426 @ X425) @ X427)) = ((X424 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427))))) | (((X422 @ (lam @ X421))) = $true) | ~ ! [X429 : term] : ((((X422 @ (sub @ X421 @ (push @ X429 @ id)))) = $true) | (((X422 @ X429)) != $true)) | ~ ! [X430 : term] : (((X422 @ X430)) = ((X423 @ id @ X430 @ id)))) => ! [X432 : term,X431 : (subst > term > subst > $o)] : ((((X431 @ id @ X432 @ id)) = $true) | ~ ! [X434 : term,X433 : term] : (($true = ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id))) | (((X431 @ id @ X433 @ id)) != $true) | (((X431 @ id @ X434 @ id)) != $true)) | ~ ! [X435 : (subst > term > term)] : (~ ! [X437 : subst,X439 : subst,X438 : term] : (((sub @ (X435 @ X437 @ X438) @ X439)) = ((X435 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439)))) | ~ ! [X436 : term] : (($true = ((X431 @ id @ (X435 @ id @ X436) @ id))) | (((X431 @ id @ X436 @ id)) != $true)) | (((X431 @ id @ (lam @ (X435 @ sh @ one)) @ id)) = $true))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axapp = $true) & (lamnotap != $true) & (((d2subst @ d_id)) = sh) & (substmonoid_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X75 : (subst > term > subst > $o),X78 : (term > $o),X77 : term,X76 : term] : (~ ! [X88 : term,X89 : term] : ((((X75 @ id @ X89 @ id)) != $true) | (((X75 @ id @ X88 @ id)) != $true) | (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) = $true)) | ~ ! [X87 : term] : (((X75 @ id @ X87 @ id)) = ((X78 @ X87))) | ($true != ((X78 @ X77))) | ~ ! [X83 : subst,X86 : subst,X85 : subst,X84 : term] : ((((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) != $true) | (((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) = $true)) | (((X78 @ (ap @ X77 @ X76))) = $true) | ~ ! [X81 : subst,X82 : term,X79 : subst,X80 : subst] : ((((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) = $true) | (((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) != $true)) | ($true != ((X78 @ X76))))) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X166 : term] : ~ ! [X167 : (subst > term > term)] : (((X167 @ sh @ one)) != ((sub @ X166 @ (push @ one @ sh))))) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) <=> (axvarid = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem2v2_gthm = $true) & (! [X222 : (term > $o),X223 : (subst > term > subst > $o),X224 : term] : (~ ! [X235 : (subst > term > term)] : ((((X223 @ id @ (lam @ (X235 @ sh @ one)) @ id)) = $true) | ~ ! [X238 : subst,X236 : term,X237 : subst] : (((X235 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X235 @ X237 @ X236) @ X238))) | ~ ! [X239 : term] : ((((X223 @ id @ (X235 @ id @ X239) @ id)) = $true) | (((X223 @ id @ X239 @ id)) != $true))) | ~ ! [X225 : term] : ((((X222 @ (sub @ X224 @ (push @ X225 @ id)))) = $true) | (((X222 @ X225)) != $true)) | ~ ! [X230 : term] : (((X223 @ id @ X230 @ id)) = ((X222 @ X230))) | ~ ! [X233 : subst,X231 : subst,X232 : term,X234 : subst] : ((((X223 @ X234 @ X232 @ (comp @ X231 @ X233))) = $true) | (((X223 @ (comp @ X234 @ X231) @ (sub @ X232 @ X231) @ X233)) != $true)) | ($true = ((X222 @ (lam @ X224)))) | ~ ! [X228 : subst,X226 : subst,X227 : term,X229 : subst] : ((((X223 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226) @ X229)) = $true) | (((X223 @ X228 @ X227 @ (comp @ X226 @ X229))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X12 : (subst > term > subst > $o),X13 : term] : (~ ! [X23 : (subst > term > term)] : ((((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) = $true) | ~ ! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) | ~ ! [X27 : term] : (($true = ((X12 @ id @ (X23 @ id @ X27) @ id))) | (((X12 @ id @ X27 @ id)) != $true))) | ~ ! [X18 : term] : ((((X12 @ id @ X18 @ id)) != $true) | ($true = ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id)))) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | ~ ! [X21 : subst,X20 : term,X19 : subst,X22 : subst] : ((((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) = $true) | ($true != ((X12 @ X21 @ X20 @ (comp @ X22 @ X19))))) | ~ ! [X17 : subst,X15 : subst,X14 : subst,X16 : term] : (($true != ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14))) | (((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) = $true)))) & ((axidl = $true) <=> ! [X127 : subst] : (((comp @ id @ X127)) = X127)) & ((hoaslamnotap = $true) <=> ! [X535 : term,X536 : (subst > term > term),X534 : term] : ((((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535))) | ~ ! [X537 : subst,X538 : subst,X539 : term] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) = ((sub @ (X536 @ X538 @ X539) @ X537))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (! [X250 : (term > $o),X251 : term] : ((((X250 @ X251)) = $true) | ~ ! [X253 : term] : ((((X250 @ (lam @ X253))) = $true) | ~ ! [X254 : term] : ((((X250 @ (sub @ X253 @ (push @ X254 @ id)))) = $true) | (((X250 @ X254)) != $true))) | ~ ! [X256 : term,X255 : term] : ((((X250 @ X256)) != $true) | (((X250 @ (ap @ X255 @ X256))) = $true) | (((X250 @ X255)) != $true)) | ~ ! [X252 : term] : ((((X250 @ X252)) = $true) | ($true != ((var @ X252))))) => (! [X257 : term,X258 : (subst > term > subst > $o),X259 : term] : ((((X258 @ id @ X259 @ id)) != $true) | (((X258 @ id @ (ap @ X259 @ X257) @ id)) = $true) | (((X258 @ id @ X257 @ id)) != $true) | ~ ! [X264 : subst,X262 : term,X265 : subst,X263 : subst] : ((((X258 @ X264 @ X262 @ (comp @ X263 @ X265))) != $true) | (((X258 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263) @ X265)) = $true)) | ~ ! [X268 : subst,X266 : subst,X267 : subst,X269 : term] : (($true != ((X258 @ (comp @ X268 @ X266) @ (sub @ X269 @ X266) @ X267))) | (((X258 @ X268 @ X269 @ (comp @ X266 @ X267))) = $true)) | ~ ! [X260 : term,X261 : term] : ((((X258 @ id @ X260 @ id)) != $true) | ($true = ((X258 @ id @ (ap @ (sub @ X260 @ id) @ X261) @ id))) | ($true != ((X258 @ id @ X261 @ id))))) => (! [X271 : term,X270 : (subst > term > subst > $o)] : (~ ! [X280 : (subst > term > term)] : (~ ! [X281 : term,X282 : subst,X283 : subst] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) = ((sub @ (X280 @ X283 @ X281) @ X282))) | ($true = ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id))) | ~ ! [X284 : term] : ((((X270 @ id @ X284 @ id)) != $true) | (((X270 @ id @ (X280 @ id @ X284) @ id)) = $true))) | ~ ! [X276 : subst,X277 : subst,X279 : term,X278 : subst] : ((((X270 @ X278 @ X279 @ (comp @ X277 @ X276))) = $true) | (((X270 @ (comp @ X278 @ X277) @ (sub @ X279 @ X277) @ X276)) != $true)) | ~ ! [X285 : term] : (($true = ((X270 @ id @ (sub @ X271 @ (push @ X285 @ id)) @ id))) | (((X270 @ id @ X285 @ id)) != $true)) | ~ ! [X273 : term,X274 : subst,X272 : subst,X275 : subst] : ((((X270 @ X275 @ X273 @ (comp @ X274 @ X272))) != $true) | ($true = ((X270 @ (comp @ X275 @ X274) @ (sub @ X273 @ X274) @ X272)))) | (((X270 @ id @ (lam @ X271) @ id)) = $true)) => ! [X287 : (subst > term > subst > $o),X286 : term] : (~ ! [X294 : subst,X296 : subst,X297 : subst,X295 : term] : ((((X287 @ (comp @ X294 @ X297) @ (sub @ X295 @ X297) @ X296)) != $true) | ($true = ((X287 @ X294 @ X295 @ (comp @ X297 @ X296))))) | ~ ! [X298 : term] : ((((X287 @ id @ X298 @ id)) = $true) | (((var @ (sub @ X298 @ id))) != $true)) | ~ ! [X299 : (subst > term > term)] : ((((X287 @ id @ (lam @ (X299 @ sh @ one)) @ id)) = $true) | ~ ! [X302 : term,X303 : subst,X301 : subst] : (((sub @ (X299 @ X301 @ X302) @ X303)) = ((X299 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303)))) | ~ ! [X300 : term] : ((((X287 @ id @ X300 @ id)) != $true) | ($true = ((X287 @ id @ (X299 @ id @ X300) @ id))))) | ~ ! [X291 : subst,X289 : subst,X288 : subst,X290 : term] : ((((X287 @ (comp @ X288 @ X291) @ (sub @ X290 @ X291) @ X289)) = $true) | (((X287 @ X288 @ X290 @ (comp @ X291 @ X289))) != $true)) | ~ ! [X292 : term,X293 : term] : ((((X287 @ id @ X293 @ id)) != $true) | ($true = ((X287 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id))) | ($true != ((X287 @ id @ X292 @ id)))) | (((X287 @ id @ X286 @ id)) = $true)))))) & (hoaslamnotvar_gthm = $true) & (termmset_gthm = $true) & ((induction2lem = $true) <=> ! [X488 : term,X489 : subst,X487 : (term > $o)] : (~ ! [X492 : term] : (~ ! [X493 : term] : ((((X487 @ X493)) != $true) | (((X487 @ (sub @ X492 @ (push @ X493 @ id)))) = $true)) | ($true = ((X487 @ (lam @ X492))))) | ~ ! [X491 : term,X490 : term] : ((((X487 @ X491)) != $true) | (((X487 @ (ap @ X491 @ X490))) = $true) | ($true != ((X487 @ X490)))) | (((X487 @ (sub @ X488 @ X489))) = $true) | ~ ! [X494 : term] : ((((X487 @ (sub @ X494 @ X489))) = $true) | ($true != ((var @ X494)))))) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) <=> (laminj = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X9 : (subst > term > subst > $o)] : ~ ! [X10 : (term > $o)] : ~ ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X195 : d_term] : (d_one = X195) & ((substmonoid = $true) <=> (! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X444 : term] : (((sub @ X444 @ id)) = X444) => (! [X445 : term,X446 : (subst > term > subst > $o)] : ((((X446 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X447 : term] : (($true != ((X446 @ id @ X447 @ id))) | ($true = ((X446 @ id @ (sub @ X445 @ (push @ X447 @ id)) @ id)))) | ~ ! [X448 : (subst > term > term)] : (~ ! [X452 : subst,X451 : term,X450 : subst] : (((X448 @ (comp @ X450 @ X452) @ (sub @ X451 @ X452))) = ((sub @ (X448 @ X450 @ X451) @ X452))) | (((X446 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ~ ! [X449 : term] : (($true = ((X446 @ id @ (X448 @ id @ X449) @ id))) | (((X446 @ id @ X449 @ id)) != $true)))) => ! [X454 : (subst > term > subst > $o),X453 : term] : (~ ! [X455 : (subst > term > term)] : ((((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)) = $true) | ~ ! [X459 : term] : ((((X454 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X454 @ id @ X459 @ id)) != $true)) | ~ ! [X457 : subst,X458 : term,X456 : subst] : (((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))) = ((sub @ (X455 @ X456 @ X458) @ X457)))) | ~ ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | (((X454 @ id @ X460 @ id)) != $true)) | (((X454 @ id @ (lam @ X453) @ id)) = $true)))))),
% 2.11/0.57 inference(flattening,[],[f9])).
% 2.11/0.57 thf(f11,plain,(
% 2.11/0.57 ((hoasapinj2_lthm = $true) <=> (! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35)) | ? [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) = ((ap @ X30 @ X29))) & (X28 != X29)))) & (! [X306 : (subst > term > subst > $o),X307 : term] : (? [X308 : (subst > term > term)] : ((((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)) != $true) & ! [X310 : subst,X311 : term,X312 : subst] : (((sub @ (X308 @ X310 @ X311) @ X312)) = ((X308 @ (comp @ X310 @ X312) @ (sub @ X311 @ X312)))) & ! [X309 : term] : (($true = ((X306 @ id @ (X308 @ id @ X309) @ id))) | (((X306 @ id @ X309 @ id)) != $true))) | ? [X313 : term] : ((((X306 @ id @ (sub @ X307 @ (push @ X313 @ id)) @ id)) != $true) & (((X306 @ id @ X313 @ id)) = $true)) | (((X306 @ id @ (lam @ (sub @ X307 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X50 : d_term,X49 : d_term] : ((X49 = X50) | (((d2term @ X50)) != ((d2term @ X49)))) & (! [X477 : (subst > term > subst > $o),X476 : term] : (($true = ((X477 @ id @ X476 @ id))) | ? [X480 : (subst > term > term)] : (! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))) | ? [X479 : term,X478 : term] : (($true = ((X477 @ id @ X478 @ id))) & ($true != ((X477 @ id @ (ap @ (sub @ X479 @ id) @ X478) @ id))) & (((X477 @ id @ X479 @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axassoc = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) <=> (apinj2 = $true)) & ((hoasinduction_lem2 = $true) <=> ! [X38 : term,X36 : (subst > term > subst > $o),X37 : term] : (($true != ((X36 @ id @ X37 @ id))) | ($true != ((X36 @ id @ X38 @ id))) | ? [X39 : term,X40 : term] : ((((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) != $true) & ($true = ((X36 @ id @ X40 @ id))) & (((X36 @ id @ X39 @ id)) = $true)) | ? [X46 : subst,X47 : subst,X45 : term,X48 : subst] : (($true != ((X36 @ X46 @ X45 @ (comp @ X47 @ X48)))) & ($true = ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48)))) | ? [X41 : subst,X42 : subst,X44 : term,X43 : subst] : (($true = ((X36 @ X41 @ X44 @ (comp @ X43 @ X42)))) & (((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) != $true)) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))))) & (! [X183 : term,X184 : (subst > term > subst > $o)] : (($true = ((X184 @ id @ (lam @ (sub @ X183 @ (push @ one @ sh))) @ id))) | ? [X194 : term] : ((((X184 @ id @ X194 @ id)) = $true) & ($true != ((X184 @ id @ (sub @ X183 @ (push @ X194 @ id)) @ id)))) | ? [X186 : term,X185 : (subst > term > term)] : ((((X184 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X193 : term,X191 : subst,X192 : subst] : (((sub @ X186 @ (push @ (sub @ X193 @ X192) @ (comp @ X191 @ X192)))) = ((X185 @ (comp @ X191 @ X192) @ (sub @ X193 @ X192)))) & ! [X190 : term] : (($true != ((X184 @ id @ X190 @ id))) | (((X184 @ id @ (X185 @ id @ X190) @ id)) = $true)) & ! [X187 : subst,X188 : subst,X189 : term] : (((sub @ (X185 @ X188 @ X189) @ X187)) = ((sub @ (sub @ X186 @ (push @ X189 @ X188)) @ X187))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X56 : (term > $o),X58 : (subst > term > subst > $o),X57 : term] : (? [X65 : term] : (($true = ((X56 @ X65))) & (((X56 @ (sub @ X57 @ (push @ X65 @ id)))) != $true)) | (((X56 @ (lam @ X57))) = $true) | ? [X60 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) != $true) & ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64)))) & ! [X61 : term] : ((((X58 @ id @ (X60 @ id @ X61) @ id)) = $true) | ($true != ((X58 @ id @ X61 @ id))))) | ? [X59 : term] : (((X56 @ X59)) != ((X58 @ id @ X59 @ id)))) | ? [X55 : term] : (((sub @ X55 @ id)) != X55)) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) != ((sub @ X51 @ (push @ X53 @ X54)))))) & (((((! [X387 : (subst > term > subst > $o),X386 : term] : (? [X389 : subst,X388 : term,X391 : subst,X390 : subst] : ((((X387 @ X389 @ X388 @ (comp @ X390 @ X391))) = $true) & ($true != ((X387 @ (comp @ X389 @ X390) @ (sub @ X388 @ X390) @ X391)))) | ? [X399 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X399 @ sh @ one)) @ id)) != $true) & ! [X400 : term] : (($true = ((X387 @ id @ (X399 @ id @ X400) @ id))) | (((X387 @ id @ X400 @ id)) != $true)) & ! [X401 : subst,X402 : subst,X403 : term] : (((sub @ (X399 @ X402 @ X403) @ X401)) = ((X399 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401))))) | ? [X393 : term,X392 : term] : (($true = ((X387 @ id @ X392 @ id))) & (((X387 @ id @ X393 @ id)) = $true) & ($true != ((X387 @ id @ (ap @ (sub @ X393 @ id) @ X392) @ id)))) | ? [X394 : term] : (($true = ((var @ (sub @ X394 @ id)))) & (((X387 @ id @ X394 @ id)) != $true)) | ? [X398 : term,X396 : subst,X395 : subst,X397 : subst] : ((((X387 @ (comp @ X395 @ X396) @ (sub @ X398 @ X396) @ X397)) = $true) & ($true != ((X387 @ X395 @ X398 @ (comp @ X396 @ X397))))) | (((X387 @ id @ X386 @ id)) = $true)) | ? [X377 : (subst > term > subst > $o),X376 : term,X378 : (term > $o)] : ((((X378 @ (lam @ X376))) != $true) & ! [X384 : term] : (((X378 @ X384)) = ((X377 @ id @ X384 @ id))) & ! [X385 : term] : (($true = ((X378 @ (sub @ X376 @ (push @ X385 @ id))))) | ($true != ((X378 @ X385)))) & ! [X379 : (subst > term > term)] : (? [X381 : subst,X380 : subst,X382 : term] : (((X379 @ (comp @ X381 @ X380) @ (sub @ X382 @ X380))) != ((sub @ (X379 @ X381 @ X382) @ X380))) | (((X377 @ id @ (lam @ (X379 @ sh @ one)) @ id)) = $true) | ? [X383 : term] : ((((X377 @ id @ X383 @ id)) = $true) & (((X377 @ id @ (X379 @ id @ X383) @ id)) != $true))))) | ? [X375 : term] : (((sub @ X375 @ id)) != X375)) | ? [X369 : term,X368 : (term > $o)] : (! [X373 : term] : (? [X374 : term] : ((((X368 @ X374)) = $true) & ($true != ((X368 @ (sub @ X373 @ (push @ X374 @ id)))))) | ($true = ((X368 @ (lam @ X373))))) & ! [X370 : term] : ((((var @ X370)) != $true) | ($true = ((X368 @ X370)))) & (((X368 @ X369)) != $true) & ! [X372 : term,X371 : term] : ((((X368 @ X372)) != $true) | (((X368 @ (ap @ X371 @ X372))) = $true) | ($true != ((X368 @ X371)))))) | ? [X365 : (subst > term > subst > $o)] : ! [X366 : (term > $o)] : ? [X367 : term] : (((X366 @ X367)) != ((X365 @ id @ X367 @ id)))) <=> (hoasinduction_lthm_3 = $true)) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & (hoasapinj1_gthm = $true) & (! [X461 : term] : ? [X462 : (subst > term > term)] : ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((axshiftcons = $true) <=> ! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241)) & ((pushprop_lem0 = $true) <=> ! [X90 : (term > $o),X92 : subst,X91 : term] : ? [X93 : (term > $o)] : ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94)))) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X324 : (subst > term > subst > $o),X323 : term] : (? [X333 : term,X330 : subst,X331 : subst,X332 : subst] : (($true != ((X324 @ X331 @ X333 @ (comp @ X330 @ X332)))) & ($true = ((X324 @ (comp @ X331 @ X330) @ (sub @ X333 @ X330) @ X332)))) | (((X324 @ id @ (lam @ X323) @ id)) = $true) | ? [X334 : (subst > term > term)] : (! [X337 : subst,X335 : term,X336 : subst] : (((sub @ (X334 @ X336 @ X335) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X335 @ X337)))) & ($true != ((X324 @ id @ (lam @ (X334 @ sh @ one)) @ id))) & ! [X338 : term] : (($true = ((X324 @ id @ (X334 @ id @ X338) @ id))) | ($true != ((X324 @ id @ X338 @ id))))) | ? [X327 : subst,X326 : subst,X328 : term,X325 : subst] : ((((X324 @ X327 @ X328 @ (comp @ X326 @ X325))) = $true) & ($true != ((X324 @ (comp @ X327 @ X326) @ (sub @ X328 @ X326) @ X325)))) | ? [X329 : term] : ((((X324 @ id @ (sub @ X323 @ (push @ X329 @ id)) @ id)) != $true) & (((X324 @ id @ X329 @ id)) = $true))) | ? [X315 : term,X316 : (subst > term > subst > $o)] : (! [X322 : term] : ((((X316 @ id @ X322 @ id)) != $true) | ($true = ((X316 @ id @ (sub @ X315 @ (push @ X322 @ id)) @ id)))) & ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true = ((X316 @ id @ X318 @ id))) & (((X316 @ id @ (X317 @ id @ X318) @ id)) != $true)) | (((X316 @ id @ (lam @ (X317 @ sh @ one)) @ id)) = $true) | ? [X320 : subst,X321 : term,X319 : subst] : (((X317 @ (comp @ X320 @ X319) @ (sub @ X321 @ X319))) != ((sub @ (X317 @ X320 @ X321) @ X319)))) & (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) != $true))) | ? [X314 : term] : (((sub @ X314 @ id)) != X314))) & (! [X119 : term,X120 : (subst > term > subst > $o)] : ((((X120 @ id @ (lam @ X119) @ id)) = $true) | ? [X126 : term] : (($true != ((X120 @ id @ (sub @ X119 @ (push @ X126 @ id)) @ id))) & (((X120 @ id @ X126 @ id)) = $true)) | ? [X121 : (subst > term > term)] : (! [X125 : term] : ((((X120 @ id @ (X121 @ id @ X125) @ id)) = $true) | (((X120 @ id @ X125 @ id)) != $true)) & ! [X123 : subst,X124 : subst,X122 : term] : (((sub @ (X121 @ X123 @ X122) @ X124)) = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124)))) & (((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X168 : (subst > term > subst > $o),X170 : term,X169 : (term > $o)] : ((((X169 @ (lam @ X170))) = $true) | ? [X171 : term] : ((((X169 @ (sub @ X170 @ (push @ X171 @ id)))) != $true) & (((X169 @ X171)) = $true)) | ? [X172 : (subst > term > term)] : (! [X174 : term,X176 : subst,X175 : subst] : (((X172 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) = ((sub @ (X172 @ X175 @ X174) @ X176))) & ! [X173 : term] : (($true != ((X168 @ id @ X173 @ id))) | ($true = ((X168 @ id @ (X172 @ id @ X173) @ id)))) & (((X168 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)) | ? [X177 : term] : (((X169 @ X177)) != ((X168 @ id @ X177 @ id))))) & (hoaslamnotap_lthm = $true) & (hoasapnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar = $true) & ((hoasapinj1_lthm = $true) <=> ((! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72)))) | ? [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 != X69) & (((ap @ X68 @ X70)) = ((ap @ X69 @ X67))))) | ? [X66 : term] : (((sub @ X66 @ id)) != X66))) & ((induction2 = $true) <=> ! [X339 : term,X340 : (term > $o)] : (? [X341 : term] : ((((var @ X341)) = $true) & (((X340 @ X341)) != $true)) | (((X340 @ X339)) = $true) | ? [X342 : term] : (($true != ((X340 @ (lam @ X342)))) & ! [X343 : term] : (($true != ((X340 @ X343))) | (((X340 @ (sub @ X342 @ (push @ X343 @ id)))) = $true))) | ? [X344 : term,X345 : term] : ((((X340 @ X344)) = $true) & ($true = ((X340 @ X345))) & (((X340 @ (ap @ X344 @ X345))) != $true)))) & (hoasinduction_gthm = $true) & (apnotvar = $true) & (pushprop = $true) & ((induction2_lthm = $true) <=> ((! [X211 : (term > $o),X212 : term] : (? [X217 : term,X216 : term] : ((((X211 @ (ap @ X217 @ X216))) != $true) & (((X211 @ X217)) = $true) & (((X211 @ X216)) = $true)) | ? [X213 : term] : (! [X214 : term] : ((((X211 @ (sub @ X213 @ (push @ X214 @ id)))) = $true) | ($true != ((X211 @ X214)))) & (((X211 @ (lam @ X213))) != $true)) | (((X211 @ X212)) = $true) | ? [X215 : term] : (($true = ((var @ X215))) & ($true != ((X211 @ X215))))) | ? [X204 : (term > $o),X203 : term,X205 : subst] : (! [X210 : term,X209 : term] : ((((X204 @ (ap @ X209 @ X210))) = $true) | ($true != ((X204 @ X210))) | ($true != ((X204 @ X209)))) & ! [X208 : term] : ((((var @ X208)) != $true) | (((X204 @ (sub @ X208 @ X205))) = $true)) & ! [X206 : term] : (? [X207 : term] : ((((X204 @ (sub @ X206 @ (push @ X207 @ id)))) != $true) & ($true = ((X204 @ X207)))) | (((X204 @ (lam @ X206))) = $true)) & (((X204 @ (sub @ X203 @ X205))) != $true))) | ? [X202 : term] : (((sub @ X202 @ id)) != X202))) & (induction2lem_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X196 : term,X197 : (term > $o)] : (? [X199 : term] : ((((var @ X199)) = $true) & (((X197 @ X199)) != $true)) | ($true = ((X197 @ X196))) | ? [X198 : term] : ((((X197 @ (lam @ X198))) != $true) & ($true = ((X197 @ X198)))) | ? [X200 : term,X201 : term] : (($true != ((X197 @ (ap @ X200 @ X201)))) & (((X197 @ X201)) = $true) & (((X197 @ X200)) = $true))) <=> (induction = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((substmonoid_lthm = $true) <=> (((! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407)) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405)) | ? [X404 : subst] : (((comp @ id @ X404)) != X404))) & (! [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ? [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) != ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | ? [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) != ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) <=> (hoaslaminj = $true)) & (hoasapinj2_gthm = $true) & ((shinj = $true) <=> ! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh))))) & (((var @ (d2term @ d_one))) != $true) & (pushprop_lem3v2 = $true) & (induction2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X128 : (subst > term > subst > $o)] : ? [X129 : (term > $o)] : ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130)))) & (pushprop_lem1v2_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) != ((d2subst @ X409))) | (X408 = X409)) & ((hoasapinj2 = $true) <=> ! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466))))) & (pushprop_gthm = $true) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) <=> (termmset = $true)) & (! [X242 : (subst > term > subst > $o),X243 : term] : ((((X242 @ id @ (lam @ (sub @ X243 @ (push @ one @ sh))) @ id)) = $true) | ? [X245 : (subst > term > term)] : (! [X246 : term] : ((((X242 @ id @ (X245 @ id @ X246) @ id)) = $true) | (((X242 @ id @ X246 @ id)) != $true)) & (((X242 @ id @ (lam @ (X245 @ sh @ one)) @ id)) != $true) & ! [X247 : subst,X249 : subst,X248 : term] : (((sub @ (X245 @ X249 @ X248) @ X247)) = ((X245 @ (comp @ X249 @ X247) @ (sub @ X248 @ X247))))) | ? [X244 : term] : ((((X242 @ id @ X244 @ id)) = $true) & (((X242 @ id @ (sub @ X243 @ (push @ X244 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (ulamvarind = $true) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axabs = $true) & ((apinj1 = $true) <=> ! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503))))) & (axclos = $true) & (! [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (? [X499 : term] : (((X498 @ X499)) != ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X496 @ X497)) != $true) | (((X498 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (axvarshift = $true) & (ulamvar1 != $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true)) | ? [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) != X515)) | ? [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) != X514))) & ((hoasinduction_lem3b = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((X470 @ sh @ one)) = ((sub @ X469 @ (push @ one @ sh))))) & (((d2subst @ d_id)) = id) & ((pushprop_lem1v2_lthm = $true) <=> (? [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) != X507) | ! [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) = $true) | ($true != ((X509 @ X511))) | ? [X512 : term] : (((X508 @ X512)) != ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))))) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & ((pushprop_lem1 = $true) <=> ! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X4 : term] : ? [X5 : (subst > term > term)] : ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7))))) & (hoasinduction_lem1v2 = $true) & ((((! [X137 : (subst > term > term),X138 : term,X140 : (subst > term > term),X139 : subst] : (? [X142 : subst,X143 : term,X141 : subst] : (((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141))) != ((sub @ (X140 @ X142 @ X143) @ X141))) | (((lam @ (X137 @ sh @ one))) != ((lam @ (X140 @ sh @ one)))) | (((X137 @ X139 @ X138)) = ((X140 @ X139 @ X138))) | ? [X146 : term,X145 : subst,X144 : subst] : (((sub @ (X137 @ X145 @ X146) @ X144)) != ((X137 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))))) | ? [X135 : term,X136 : term] : ((((lam @ X136)) = ((lam @ X135))) & (X135 != X136))) | ? [X133 : term,X134 : subst] : (((comp @ sh @ (push @ X133 @ X134))) != X134)) | ? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131)) <=> (hoaslaminj_lthm = $true)) & ((? [X0 : term] : (((sub @ X0 @ id)) != X0) | ! [X1 : term] : (((sub @ X1 @ id)) = X1)) <=> (termmset_lthm = $true)) & ((axidr = $true) <=> ! [X532 : subst] : (((comp @ X532 @ id)) = X532)) & (hoaslamnotap_gthm = $true) & ! [X96 : d_subst] : (d_id = X96) & (hoasinduction_lem1v2_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)))))))))))) & (! [X178 : (term > $o),X180 : subst,X179 : term] : ? [X181 : (term > $o)] : ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))) <=> (pushprop_lem0_lthm = $true)) & (one = ((d2term @ d_one))) & (pushprop_lem0_gthm = $true) & ((induction2lem_lthm = $true) <=> ((((! [X160 : term,X159 : subst,X158 : (term > $o)] : (? [X165 : term] : ((((var @ X165)) = $true) & ($true != ((X158 @ (sub @ X165 @ X159))))) | (((X158 @ (sub @ X160 @ X159))) = $true) | ? [X163 : term,X164 : term] : ((((X158 @ X164)) = $true) & ($true = ((X158 @ X163))) & (((X158 @ (ap @ X164 @ X163))) != $true)) | ? [X161 : term] : (! [X162 : term] : ((((X158 @ X162)) != $true) | ($true = ((X158 @ (sub @ X161 @ (push @ X162 @ id)))))) & (((X158 @ (lam @ X161))) != $true))) | ? [X152 : term,X153 : (term > $o)] : (! [X155 : term] : (($true != ((X153 @ X155))) | ($true = ((X153 @ (lam @ X155))))) & ! [X157 : term,X156 : term] : ((((X153 @ (ap @ X157 @ X156))) = $true) | ($true != ((X153 @ X156))) | ($true != ((X153 @ X157)))) & ! [X154 : term] : ((((var @ X154)) != $true) | (((X153 @ X154)) = $true)) & ($true != ((X153 @ X152))))) | ? [X151 : subst] : (((comp @ X151 @ id)) != X151)) | ? [X150 : term,X149 : subst] : (((comp @ sh @ (push @ X150 @ X149))) != X149)) | ? [X148 : subst,X147 : term] : (((sub @ one @ (push @ X147 @ X148))) != X147))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X349 : term,X347 : (term > $o),X348 : (subst > term > subst > $o)] : (? [X362 : term,X361 : subst,X360 : subst,X363 : subst] : (($true = ((X348 @ (comp @ X361 @ X360) @ (sub @ X362 @ X360) @ X363))) & (((X348 @ X361 @ X362 @ (comp @ X360 @ X363))) != $true)) | ? [X364 : term] : (((X348 @ id @ X364 @ id)) != ((X347 @ X364))) | ? [X351 : (subst > term > term)] : ((((X348 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : term] : (($true != ((X348 @ id @ X355 @ id))) | ($true = ((X348 @ id @ (X351 @ id @ X355) @ id)))) & ! [X352 : term,X354 : subst,X353 : subst] : (((sub @ (X351 @ X354 @ X352) @ X353)) = ((X351 @ (comp @ X354 @ X353) @ (sub @ X352 @ X353))))) | ($true = ((X347 @ (lam @ X349)))) | ? [X359 : subst,X357 : subst,X358 : term,X356 : subst] : (($true != ((X348 @ (comp @ X356 @ X359) @ (sub @ X358 @ X359) @ X357))) & (((X348 @ X356 @ X358 @ (comp @ X359 @ X357))) = $true)) | ? [X350 : term] : (($true = ((X347 @ X350))) & (((X347 @ (sub @ X349 @ (push @ X350 @ id)))) != $true))) | ? [X346 : term] : (((sub @ X346 @ id)) != X346))) & (lamnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & (axmap = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction = $true) <=> ! [X98 : term,X97 : (subst > term > subst > $o)] : (? [X104 : (subst > term > term)] : (! [X105 : term] : ((((X97 @ id @ X105 @ id)) != $true) | (((X97 @ id @ (X104 @ id @ X105) @ id)) = $true)) & ! [X107 : subst,X106 : term,X108 : subst] : (((X104 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X104 @ X107 @ X106) @ X108))) & ($true != ((X97 @ id @ (lam @ (X104 @ sh @ one)) @ id)))) | (((X97 @ id @ X98 @ id)) = $true) | ? [X110 : term,X109 : term] : ((((X97 @ id @ X110 @ id)) = $true) & (((X97 @ id @ (ap @ (sub @ X109 @ id) @ X110) @ id)) != $true) & ($true = ((X97 @ id @ X109 @ id)))) | ? [X112 : term,X114 : subst,X111 : subst,X113 : subst] : ((((X97 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114)) != $true) & ($true = ((X97 @ X111 @ X112 @ (comp @ X113 @ X114))))) | ? [X102 : subst,X101 : subst,X103 : term,X100 : subst] : ((((X97 @ X102 @ X103 @ (comp @ X101 @ X100))) != $true) & (((X97 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101) @ X100)) = $true)) | ? [X99 : term] : (($true != ((X97 @ id @ X99 @ id))) & (((var @ (sub @ X99 @ id))) = $true)))) & (((((! [X431 : (subst > term > subst > $o),X432 : term] : (? [X433 : term,X434 : term] : ((((X431 @ id @ X433 @ id)) = $true) & (((X431 @ id @ X434 @ id)) = $true) & ($true != ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id)))) | ? [X435 : (subst > term > term)] : (! [X436 : term] : (($true = ((X431 @ id @ (X435 @ id @ X436) @ id))) | (((X431 @ id @ X436 @ id)) != $true)) & ! [X437 : subst,X439 : subst,X438 : term] : (((sub @ (X435 @ X437 @ X438) @ X439)) = ((X435 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439)))) & (((X431 @ id @ (lam @ (X435 @ sh @ one)) @ id)) != $true)) | (((X431 @ id @ X432 @ id)) = $true)) | ? [X423 : (subst > term > subst > $o),X421 : term,X422 : (term > $o)] : (! [X430 : term] : (((X422 @ X430)) = ((X423 @ id @ X430 @ id))) & ! [X429 : term] : ((((X422 @ (sub @ X421 @ (push @ X429 @ id)))) = $true) | (((X422 @ X429)) != $true)) & (((X422 @ (lam @ X421))) != $true) & ! [X424 : (subst > term > term)] : ((((X423 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X425 : term,X426 : subst,X427 : subst] : (((sub @ (X424 @ X426 @ X425) @ X427)) != ((X424 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427)))) | ? [X428 : term] : ((((X423 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X423 @ id @ X428 @ id)) = $true))))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420)) | ? [X413 : term,X414 : (term > $o)] : (! [X419 : term,X418 : term] : ((((X414 @ (ap @ X418 @ X419))) = $true) | (((X414 @ X419)) != $true) | ($true != ((X414 @ X418)))) & ! [X417 : term] : (($true != ((var @ X417))) | (((X414 @ X417)) = $true)) & ! [X415 : term] : (? [X416 : term] : ((((X414 @ (sub @ X415 @ (push @ X416 @ id)))) != $true) & ($true = ((X414 @ X416)))) | (((X414 @ (lam @ X415))) = $true)) & (((X414 @ X413)) != $true))) | ? [X410 : (subst > term > subst > $o)] : ! [X411 : (term > $o)] : ? [X412 : term] : (((X411 @ X412)) != ((X410 @ id @ X412 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axapp = $true) & (lamnotap != $true) & (((d2subst @ d_id)) = sh) & (substmonoid_gthm = $true) & (! [X77 : term,X78 : (term > $o),X76 : term,X75 : (subst > term > subst > $o)] : (? [X88 : term,X89 : term] : ((((X75 @ id @ X88 @ id)) = $true) & (((X75 @ id @ X89 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) != $true)) | ? [X87 : term] : (((X75 @ id @ X87 @ id)) != ((X78 @ X87))) | ($true != ((X78 @ X76))) | (((X78 @ (ap @ X77 @ X76))) = $true) | ? [X85 : subst,X83 : subst,X84 : term,X86 : subst] : ((((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) = $true) & (((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) != $true)) | ($true != ((X78 @ X77))) | ? [X80 : subst,X79 : subst,X81 : subst,X82 : term] : ((((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) = $true) & (((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) != $true))) <=> (hoasinduction_lem2v2 = $true)) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & (! [X166 : term] : ? [X167 : (subst > term > term)] : (((X167 @ sh @ one)) = ((sub @ X166 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) <=> (axvarid = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoaslaminj_gthm = $true) & (hoasapnotvar_gthm = $true) & (ulamvarsh = $true) & (pushprop_lem2v2_gthm = $true) & (! [X223 : (subst > term > subst > $o),X222 : (term > $o),X224 : term] : (? [X230 : term] : (((X223 @ id @ X230 @ id)) != ((X222 @ X230))) | ? [X227 : term,X229 : subst,X226 : subst,X228 : subst] : ((((X223 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226) @ X229)) != $true) & (((X223 @ X228 @ X227 @ (comp @ X226 @ X229))) = $true)) | ? [X235 : (subst > term > term)] : (! [X239 : term] : ((((X223 @ id @ (X235 @ id @ X239) @ id)) = $true) | (((X223 @ id @ X239 @ id)) != $true)) & (((X223 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true) & ! [X238 : subst,X236 : term,X237 : subst] : (((X235 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X235 @ X237 @ X236) @ X238)))) | ? [X231 : subst,X232 : term,X234 : subst,X233 : subst] : ((((X223 @ X234 @ X232 @ (comp @ X231 @ X233))) != $true) & (((X223 @ (comp @ X234 @ X231) @ (sub @ X232 @ X231) @ X233)) = $true)) | ? [X225 : term] : ((((X222 @ (sub @ X224 @ (push @ X225 @ id)))) != $true) & (((X222 @ X225)) = $true)) | ($true = ((X222 @ (lam @ X224))))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X13 : term,X12 : (subst > term > subst > $o)] : (? [X18 : term] : (($true != ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) & ! [X27 : term] : (($true = ((X12 @ id @ (X23 @ id @ X27) @ id))) | (((X12 @ id @ X27 @ id)) != $true)) & (((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X15 : subst,X16 : term,X17 : subst,X14 : subst] : ((((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) != $true) & ($true = ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14)))) | ? [X19 : subst,X21 : subst,X22 : subst,X20 : term] : (($true = ((X12 @ X21 @ X20 @ (comp @ X22 @ X19)))) & (((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) != $true)))) & ((axidl = $true) <=> ! [X127 : subst] : (((comp @ id @ X127)) = X127)) & ((hoaslamnotap = $true) <=> ! [X534 : term,X536 : (subst > term > term),X535 : term] : (? [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) != ((sub @ (X536 @ X538 @ X539) @ X537))) | (((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lthm = $true) <=> (((! [X286 : term,X287 : (subst > term > subst > $o)] : (? [X297 : subst,X296 : subst,X294 : subst,X295 : term] : ((((X287 @ (comp @ X294 @ X297) @ (sub @ X295 @ X297) @ X296)) = $true) & ($true != ((X287 @ X294 @ X295 @ (comp @ X297 @ X296))))) | ? [X298 : term] : ((((X287 @ id @ X298 @ id)) != $true) & (((var @ (sub @ X298 @ id))) = $true)) | ? [X291 : subst,X288 : subst,X289 : subst,X290 : term] : ((((X287 @ (comp @ X288 @ X291) @ (sub @ X290 @ X291) @ X289)) != $true) & (((X287 @ X288 @ X290 @ (comp @ X291 @ X289))) = $true)) | ? [X299 : (subst > term > term)] : (! [X300 : term] : ((((X287 @ id @ X300 @ id)) != $true) | ($true = ((X287 @ id @ (X299 @ id @ X300) @ id)))) & ! [X302 : term,X303 : subst,X301 : subst] : (((sub @ (X299 @ X301 @ X302) @ X303)) = ((X299 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303)))) & (((X287 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true)) | (((X287 @ id @ X286 @ id)) = $true) | ? [X292 : term,X293 : term] : ((((X287 @ id @ X293 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id))) & ($true = ((X287 @ id @ X292 @ id))))) | ? [X270 : (subst > term > subst > $o),X271 : term] : ((((X270 @ id @ (lam @ X271) @ id)) != $true) & ! [X285 : term] : (($true = ((X270 @ id @ (sub @ X271 @ (push @ X285 @ id)) @ id))) | (((X270 @ id @ X285 @ id)) != $true)) & ! [X273 : term,X274 : subst,X272 : subst,X275 : subst] : ((((X270 @ X275 @ X273 @ (comp @ X274 @ X272))) != $true) | ($true = ((X270 @ (comp @ X275 @ X274) @ (sub @ X273 @ X274) @ X272)))) & ! [X276 : subst,X277 : subst,X279 : term,X278 : subst] : ((((X270 @ X278 @ X279 @ (comp @ X277 @ X276))) = $true) | (((X270 @ (comp @ X278 @ X277) @ (sub @ X279 @ X277) @ X276)) != $true)) & ! [X280 : (subst > term > term)] : (? [X284 : term] : ((((X270 @ id @ X284 @ id)) = $true) & (((X270 @ id @ (X280 @ id @ X284) @ id)) != $true)) | ? [X283 : subst,X282 : subst,X281 : term] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) != ((sub @ (X280 @ X283 @ X281) @ X282))) | ($true = ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id)))))) | ? [X259 : term,X258 : (subst > term > subst > $o),X257 : term] : ((((X258 @ id @ X259 @ id)) = $true) & (((X258 @ id @ X257 @ id)) = $true) & (((X258 @ id @ (ap @ X259 @ X257) @ id)) != $true) & ! [X268 : subst,X266 : subst,X267 : subst,X269 : term] : (($true != ((X258 @ (comp @ X268 @ X266) @ (sub @ X269 @ X266) @ X267))) | (((X258 @ X268 @ X269 @ (comp @ X266 @ X267))) = $true)) & ! [X264 : subst,X262 : term,X265 : subst,X263 : subst] : ((((X258 @ X264 @ X262 @ (comp @ X263 @ X265))) != $true) | (((X258 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263) @ X265)) = $true)) & ! [X260 : term,X261 : term] : ((((X258 @ id @ X260 @ id)) != $true) | ($true = ((X258 @ id @ (ap @ (sub @ X260 @ id) @ X261) @ id))) | ($true != ((X258 @ id @ X261 @ id)))))) | ? [X250 : (term > $o),X251 : term] : (! [X252 : term] : ((((X250 @ X252)) = $true) | ($true != ((var @ X252)))) & (((X250 @ X251)) != $true) & ! [X253 : term] : ((((X250 @ (lam @ X253))) = $true) | ? [X254 : term] : ((((X250 @ X254)) = $true) & (((X250 @ (sub @ X253 @ (push @ X254 @ id)))) != $true))) & ! [X256 : term,X255 : term] : ((((X250 @ X256)) != $true) | (((X250 @ (ap @ X255 @ X256))) = $true) | (((X250 @ X255)) != $true))))) & (hoaslamnotvar_gthm = $true) & (termmset_gthm = $true) & (! [X488 : term,X489 : subst,X487 : (term > $o)] : (? [X492 : term] : (! [X493 : term] : ((((X487 @ X493)) != $true) | (((X487 @ (sub @ X492 @ (push @ X493 @ id)))) = $true)) & ($true != ((X487 @ (lam @ X492))))) | (((X487 @ (sub @ X488 @ X489))) = $true) | ? [X494 : term] : ((((X487 @ (sub @ X494 @ X489))) != $true) & ($true = ((var @ X494)))) | ? [X490 : term,X491 : term] : ((((X487 @ X491)) = $true) & ($true = ((X487 @ X490))) & (((X487 @ (ap @ X491 @ X490))) != $true))) <=> (induction2lem = $true)) & (pushprop_lem2v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoaslamnotvar_lthm = $true) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) <=> (laminj = $true)) & (! [X9 : (subst > term > subst > $o)] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) <=> (hoasinduction_lem0 = $true)) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem2_gthm = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ! [X195 : d_term] : (d_one = X195) & ((substmonoid = $true) <=> (! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lthm_orig = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X453 : term,X454 : (subst > term > subst > $o)] : (? [X460 : term] : (($true != ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) & (((X454 @ id @ X460 @ id)) = $true)) | (((X454 @ id @ (lam @ X453) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X457 : subst,X458 : term,X456 : subst] : (((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))) = ((sub @ (X455 @ X456 @ X458) @ X457))) & ! [X459 : term] : ((((X454 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X454 @ id @ X459 @ id)) != $true)) & (((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true))) | ? [X445 : term,X446 : (subst > term > subst > $o)] : (! [X447 : term] : (($true != ((X446 @ id @ X447 @ id))) | ($true = ((X446 @ id @ (sub @ X445 @ (push @ X447 @ id)) @ id)))) & (((X446 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) != $true) & ! [X448 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ? [X449 : term] : (($true != ((X446 @ id @ (X448 @ id @ X449) @ id))) & (((X446 @ id @ X449 @ id)) = $true)) | ? [X451 : term,X452 : subst,X450 : subst] : (((X448 @ (comp @ X450 @ X452) @ (sub @ X451 @ X452))) != ((sub @ (X448 @ X450 @ X451) @ X452)))))) | ? [X444 : term] : (((sub @ X444 @ id)) != X444)))),
% 2.11/0.57 inference(ennf_transformation,[],[f10])).
% 2.11/0.57 thf(f12,plain,(
% 2.11/0.57 ((hoasinduction_lem3_lthm = $true) <=> (? [X314 : term] : (((sub @ X314 @ id)) != X314) | ! [X324 : (subst > term > subst > $o),X323 : term] : (? [X333 : term,X330 : subst,X331 : subst,X332 : subst] : (($true != ((X324 @ X331 @ X333 @ (comp @ X330 @ X332)))) & ($true = ((X324 @ (comp @ X331 @ X330) @ (sub @ X333 @ X330) @ X332)))) | (((X324 @ id @ (lam @ X323) @ id)) = $true) | ? [X334 : (subst > term > term)] : (! [X337 : subst,X335 : term,X336 : subst] : (((sub @ (X334 @ X336 @ X335) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X335 @ X337)))) & ($true != ((X324 @ id @ (lam @ (X334 @ sh @ one)) @ id))) & ! [X338 : term] : (($true = ((X324 @ id @ (X334 @ id @ X338) @ id))) | ($true != ((X324 @ id @ X338 @ id))))) | ? [X327 : subst,X326 : subst,X328 : term,X325 : subst] : ((((X324 @ X327 @ X328 @ (comp @ X326 @ X325))) = $true) & ($true != ((X324 @ (comp @ X327 @ X326) @ (sub @ X328 @ X326) @ X325)))) | ? [X329 : term] : ((((X324 @ id @ (sub @ X323 @ (push @ X329 @ id)) @ id)) != $true) & (((X324 @ id @ X329 @ id)) = $true))) | ? [X315 : term,X316 : (subst > term > subst > $o)] : (! [X322 : term] : ((((X316 @ id @ X322 @ id)) != $true) | ($true = ((X316 @ id @ (sub @ X315 @ (push @ X322 @ id)) @ id)))) & ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true = ((X316 @ id @ X318 @ id))) & (((X316 @ id @ (X317 @ id @ X318) @ id)) != $true)) | (((X316 @ id @ (lam @ (X317 @ sh @ one)) @ id)) = $true) | ? [X320 : subst,X321 : term,X319 : subst] : (((X317 @ (comp @ X320 @ X319) @ (sub @ X321 @ X319))) != ((sub @ (X317 @ X320 @ X321) @ X319)))) & (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) != $true)))) & ((hoasinduction = $true) <=> ! [X98 : term,X97 : (subst > term > subst > $o)] : (? [X104 : (subst > term > term)] : (! [X105 : term] : ((((X97 @ id @ X105 @ id)) != $true) | (((X97 @ id @ (X104 @ id @ X105) @ id)) = $true)) & ! [X107 : subst,X106 : term,X108 : subst] : (((X104 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X104 @ X107 @ X106) @ X108))) & ($true != ((X97 @ id @ (lam @ (X104 @ sh @ one)) @ id)))) | (((X97 @ id @ X98 @ id)) = $true) | ? [X110 : term,X109 : term] : ((((X97 @ id @ X110 @ id)) = $true) & (((X97 @ id @ (ap @ (sub @ X109 @ id) @ X110) @ id)) != $true) & ($true = ((X97 @ id @ X109 @ id)))) | ? [X112 : term,X114 : subst,X111 : subst,X113 : subst] : ((((X97 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114)) != $true) & ($true = ((X97 @ X111 @ X112 @ (comp @ X113 @ X114))))) | ? [X102 : subst,X101 : subst,X103 : term,X100 : subst] : ((((X97 @ X102 @ X103 @ (comp @ X101 @ X100))) != $true) & (((X97 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101) @ X100)) = $true)) | ? [X99 : term] : (($true != ((X97 @ id @ X99 @ id))) & (((var @ (sub @ X99 @ id))) = $true)))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X453 : term,X454 : (subst > term > subst > $o)] : (? [X460 : term] : (($true != ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) & (((X454 @ id @ X460 @ id)) = $true)) | (((X454 @ id @ (lam @ X453) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X457 : subst,X458 : term,X456 : subst] : (((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))) = ((sub @ (X455 @ X456 @ X458) @ X457))) & ! [X459 : term] : ((((X454 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X454 @ id @ X459 @ id)) != $true)) & (((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true))) | ? [X444 : term] : (((sub @ X444 @ id)) != X444) | ? [X445 : term,X446 : (subst > term > subst > $o)] : (! [X447 : term] : (($true != ((X446 @ id @ X447 @ id))) | ($true = ((X446 @ id @ (sub @ X445 @ (push @ X447 @ id)) @ id)))) & (((X446 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) != $true) & ! [X448 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ? [X449 : term] : (($true != ((X446 @ id @ (X448 @ id @ X449) @ id))) & (((X446 @ id @ X449 @ id)) = $true)) | ? [X451 : term,X452 : subst,X450 : subst] : (((X448 @ (comp @ X450 @ X452) @ (sub @ X451 @ X452))) != ((sub @ (X448 @ X450 @ X451) @ X452))))))) & ((hoasinduction_lthm = $true) <=> (? [X270 : (subst > term > subst > $o),X271 : term] : ((((X270 @ id @ (lam @ X271) @ id)) != $true) & ! [X285 : term] : (($true = ((X270 @ id @ (sub @ X271 @ (push @ X285 @ id)) @ id))) | (((X270 @ id @ X285 @ id)) != $true)) & ! [X273 : term,X274 : subst,X272 : subst,X275 : subst] : ((((X270 @ X275 @ X273 @ (comp @ X274 @ X272))) != $true) | ($true = ((X270 @ (comp @ X275 @ X274) @ (sub @ X273 @ X274) @ X272)))) & ! [X276 : subst,X277 : subst,X279 : term,X278 : subst] : ((((X270 @ X278 @ X279 @ (comp @ X277 @ X276))) = $true) | (((X270 @ (comp @ X278 @ X277) @ (sub @ X279 @ X277) @ X276)) != $true)) & ! [X280 : (subst > term > term)] : (? [X284 : term] : ((((X270 @ id @ X284 @ id)) = $true) & (((X270 @ id @ (X280 @ id @ X284) @ id)) != $true)) | ? [X283 : subst,X282 : subst,X281 : term] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) != ((sub @ (X280 @ X283 @ X281) @ X282))) | ($true = ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id))))) | ? [X259 : term,X258 : (subst > term > subst > $o),X257 : term] : ((((X258 @ id @ X259 @ id)) = $true) & (((X258 @ id @ X257 @ id)) = $true) & (((X258 @ id @ (ap @ X259 @ X257) @ id)) != $true) & ! [X268 : subst,X266 : subst,X267 : subst,X269 : term] : (($true != ((X258 @ (comp @ X268 @ X266) @ (sub @ X269 @ X266) @ X267))) | (((X258 @ X268 @ X269 @ (comp @ X266 @ X267))) = $true)) & ! [X264 : subst,X262 : term,X265 : subst,X263 : subst] : ((((X258 @ X264 @ X262 @ (comp @ X263 @ X265))) != $true) | (((X258 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263) @ X265)) = $true)) & ! [X260 : term,X261 : term] : ((((X258 @ id @ X260 @ id)) != $true) | ($true = ((X258 @ id @ (ap @ (sub @ X260 @ id) @ X261) @ id))) | ($true != ((X258 @ id @ X261 @ id))))) | ? [X250 : (term > $o),X251 : term] : (! [X252 : term] : ((((X250 @ X252)) = $true) | ($true != ((var @ X252)))) & (((X250 @ X251)) != $true) & ! [X253 : term] : ((((X250 @ (lam @ X253))) = $true) | ? [X254 : term] : ((((X250 @ X254)) = $true) & (((X250 @ (sub @ X253 @ (push @ X254 @ id)))) != $true))) & ! [X256 : term,X255 : term] : ((((X250 @ X256)) != $true) | (((X250 @ (ap @ X255 @ X256))) = $true) | (((X250 @ X255)) != $true))) | ! [X286 : term,X287 : (subst > term > subst > $o)] : (? [X297 : subst,X296 : subst,X294 : subst,X295 : term] : ((((X287 @ (comp @ X294 @ X297) @ (sub @ X295 @ X297) @ X296)) = $true) & ($true != ((X287 @ X294 @ X295 @ (comp @ X297 @ X296))))) | ? [X298 : term] : ((((X287 @ id @ X298 @ id)) != $true) & (((var @ (sub @ X298 @ id))) = $true)) | ? [X291 : subst,X288 : subst,X289 : subst,X290 : term] : ((((X287 @ (comp @ X288 @ X291) @ (sub @ X290 @ X291) @ X289)) != $true) & (((X287 @ X288 @ X290 @ (comp @ X291 @ X289))) = $true)) | ? [X299 : (subst > term > term)] : (! [X300 : term] : ((((X287 @ id @ X300 @ id)) != $true) | ($true = ((X287 @ id @ (X299 @ id @ X300) @ id)))) & ! [X302 : term,X303 : subst,X301 : subst] : (((sub @ (X299 @ X301 @ X302) @ X303)) = ((X299 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303)))) & (((X287 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true)) | (((X287 @ id @ X286 @ id)) = $true) | ? [X292 : term,X293 : term] : ((((X287 @ id @ X293 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id))) & ($true = ((X287 @ id @ X292 @ id))))))) & ((axidl = $true) <=> ! [X127 : subst] : (((comp @ id @ X127)) = X127)) & (hoasinduction_lem1_gthm = $true) & ((substmonoid = $true) <=> (! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485))) & ((axshiftcons = $true) <=> ! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & (termmset_gthm = $true) & ! [X50 : d_term,X49 : d_term] : ((X49 = X50) | (((d2term @ X50)) != ((d2term @ X49)))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X90 : (term > $o),X92 : subst,X91 : term] : ? [X93 : (term > $o)] : ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94)))) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) != X507) | ! [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) = $true) | ($true != ((X509 @ X511))) | ? [X512 : term] : (((X508 @ X512)) != ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))))) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X410 : (subst > term > subst > $o)] : ! [X411 : (term > $o)] : ? [X412 : term] : (((X411 @ X412)) != ((X410 @ id @ X412 @ id))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420) | ? [X413 : term,X414 : (term > $o)] : (! [X419 : term,X418 : term] : ((((X414 @ (ap @ X418 @ X419))) = $true) | (((X414 @ X419)) != $true) | ($true != ((X414 @ X418)))) & ! [X417 : term] : (($true != ((var @ X417))) | (((X414 @ X417)) = $true)) & ! [X415 : term] : (? [X416 : term] : ((((X414 @ (sub @ X415 @ (push @ X416 @ id)))) != $true) & ($true = ((X414 @ X416)))) | (((X414 @ (lam @ X415))) = $true)) & (((X414 @ X413)) != $true)) | ? [X423 : (subst > term > subst > $o),X421 : term,X422 : (term > $o)] : (! [X430 : term] : (((X422 @ X430)) = ((X423 @ id @ X430 @ id))) & ! [X429 : term] : ((((X422 @ (sub @ X421 @ (push @ X429 @ id)))) = $true) | (((X422 @ X429)) != $true)) & (((X422 @ (lam @ X421))) != $true) & ! [X424 : (subst > term > term)] : ((((X423 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X425 : term,X426 : subst,X427 : subst] : (((sub @ (X424 @ X426 @ X425) @ X427)) != ((X424 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427)))) | ? [X428 : term] : ((((X423 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X423 @ id @ X428 @ id)) = $true)))) | ! [X431 : (subst > term > subst > $o),X432 : term] : (? [X433 : term,X434 : term] : ((((X431 @ id @ X433 @ id)) = $true) & (((X431 @ id @ X434 @ id)) = $true) & ($true != ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id)))) | ? [X435 : (subst > term > term)] : (! [X436 : term] : (($true = ((X431 @ id @ (X435 @ id @ X436) @ id))) | (((X431 @ id @ X436 @ id)) != $true)) & ! [X437 : subst,X439 : subst,X438 : term] : (((sub @ (X435 @ X437 @ X438) @ X439)) = ((X435 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439)))) & (((X431 @ id @ (lam @ (X435 @ sh @ one)) @ id)) != $true)) | (((X431 @ id @ X432 @ id)) = $true)))) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X13 : term,X12 : (subst > term > subst > $o)] : (? [X18 : term] : (($true != ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | ? [X23 : (subst > term > term)] : (! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) & ! [X27 : term] : (($true = ((X12 @ id @ (X23 @ id @ X27) @ id))) | (((X12 @ id @ X27 @ id)) != $true)) & (((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)) | ? [X15 : subst,X16 : term,X17 : subst,X14 : subst] : ((((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) != $true) & ($true = ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14)))) | ? [X19 : subst,X21 : subst,X22 : subst,X20 : term] : (($true = ((X12 @ X21 @ X20 @ (comp @ X22 @ X19)))) & (((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) != $true)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((? [X55 : term] : (((sub @ X55 @ id)) != X55) | ! [X56 : (term > $o),X58 : (subst > term > subst > $o),X57 : term] : (? [X65 : term] : (($true = ((X56 @ X65))) & (((X56 @ (sub @ X57 @ (push @ X65 @ id)))) != $true)) | (((X56 @ (lam @ X57))) = $true) | ? [X60 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) != $true) & ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64)))) & ! [X61 : term] : ((((X58 @ id @ (X60 @ id @ X61) @ id)) = $true) | ($true != ((X58 @ id @ X61 @ id))))) | ? [X59 : term] : (((X56 @ X59)) != ((X58 @ id @ X59 @ id)))) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) != ((sub @ X51 @ (push @ X53 @ X54))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (axvarshift = $true) & ((shinj = $true) <=> ! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh))))) & ((hoasapinj2 = $true) <=> ! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466))))) & (! [X119 : term,X120 : (subst > term > subst > $o)] : ((((X120 @ id @ (lam @ X119) @ id)) = $true) | ? [X126 : term] : (($true != ((X120 @ id @ (sub @ X119 @ (push @ X126 @ id)) @ id))) & (((X120 @ id @ X126 @ id)) = $true)) | ? [X121 : (subst > term > term)] : (! [X125 : term] : ((((X120 @ id @ (X121 @ id @ X125) @ id)) = $true) | (((X120 @ id @ X125 @ id)) != $true)) & ! [X123 : subst,X124 : subst,X122 : term] : (((sub @ (X121 @ X123 @ X122) @ X124)) = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124)))) & (((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true))) <=> (hoasinduction_lem3a = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) != X514) | ? [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) != X515) | ! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true)))) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) <=> (? [X150 : term,X149 : subst] : (((comp @ sh @ (push @ X150 @ X149))) != X149) | ! [X160 : term,X159 : subst,X158 : (term > $o)] : (? [X165 : term] : ((((var @ X165)) = $true) & ($true != ((X158 @ (sub @ X165 @ X159))))) | (((X158 @ (sub @ X160 @ X159))) = $true) | ? [X163 : term,X164 : term] : ((((X158 @ X164)) = $true) & ($true = ((X158 @ X163))) & (((X158 @ (ap @ X164 @ X163))) != $true)) | ? [X161 : term] : (! [X162 : term] : ((((X158 @ X162)) != $true) | ($true = ((X158 @ (sub @ X161 @ (push @ X162 @ id)))))) & (((X158 @ (lam @ X161))) != $true))) | ? [X152 : term,X153 : (term > $o)] : (! [X155 : term] : (($true != ((X153 @ X155))) | ($true = ((X153 @ (lam @ X155))))) & ! [X157 : term,X156 : term] : ((((X153 @ (ap @ X157 @ X156))) = $true) | ($true != ((X153 @ X156))) | ($true != ((X153 @ X157)))) & ! [X154 : term] : ((((var @ X154)) != $true) | (((X153 @ X154)) = $true)) & ($true != ((X153 @ X152)))) | ? [X148 : subst,X147 : term] : (((sub @ one @ (push @ X147 @ X148))) != X147) | ? [X151 : subst] : (((comp @ X151 @ id)) != X151))) & ! [X195 : d_term] : (d_one = X195) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((apinj1 = $true) <=> ! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503))))) & (hoaslamnotap_gthm = $true) & ((? [X377 : (subst > term > subst > $o),X376 : term,X378 : (term > $o)] : ((((X378 @ (lam @ X376))) != $true) & ! [X384 : term] : (((X378 @ X384)) = ((X377 @ id @ X384 @ id))) & ! [X385 : term] : (($true = ((X378 @ (sub @ X376 @ (push @ X385 @ id))))) | ($true != ((X378 @ X385)))) & ! [X379 : (subst > term > term)] : (? [X381 : subst,X380 : subst,X382 : term] : (((X379 @ (comp @ X381 @ X380) @ (sub @ X382 @ X380))) != ((sub @ (X379 @ X381 @ X382) @ X380))) | (((X377 @ id @ (lam @ (X379 @ sh @ one)) @ id)) = $true) | ? [X383 : term] : ((((X377 @ id @ X383 @ id)) = $true) & (((X377 @ id @ (X379 @ id @ X383) @ id)) != $true)))) | ? [X369 : term,X368 : (term > $o)] : (! [X373 : term] : (? [X374 : term] : ((((X368 @ X374)) = $true) & ($true != ((X368 @ (sub @ X373 @ (push @ X374 @ id)))))) | ($true = ((X368 @ (lam @ X373))))) & ! [X370 : term] : ((((var @ X370)) != $true) | ($true = ((X368 @ X370)))) & (((X368 @ X369)) != $true) & ! [X372 : term,X371 : term] : ((((X368 @ X372)) != $true) | (((X368 @ (ap @ X371 @ X372))) = $true) | ($true != ((X368 @ X371))))) | ? [X365 : (subst > term > subst > $o)] : ! [X366 : (term > $o)] : ? [X367 : term] : (((X366 @ X367)) != ((X365 @ id @ X367 @ id))) | ! [X387 : (subst > term > subst > $o),X386 : term] : (? [X389 : subst,X388 : term,X391 : subst,X390 : subst] : ((((X387 @ X389 @ X388 @ (comp @ X390 @ X391))) = $true) & ($true != ((X387 @ (comp @ X389 @ X390) @ (sub @ X388 @ X390) @ X391)))) | ? [X399 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X399 @ sh @ one)) @ id)) != $true) & ! [X400 : term] : (($true = ((X387 @ id @ (X399 @ id @ X400) @ id))) | (((X387 @ id @ X400 @ id)) != $true)) & ! [X401 : subst,X402 : subst,X403 : term] : (((sub @ (X399 @ X402 @ X403) @ X401)) = ((X399 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401))))) | ? [X393 : term,X392 : term] : (($true = ((X387 @ id @ X392 @ id))) & (((X387 @ id @ X393 @ id)) = $true) & ($true != ((X387 @ id @ (ap @ (sub @ X393 @ id) @ X392) @ id)))) | ? [X394 : term] : (($true = ((var @ (sub @ X394 @ id)))) & (((X387 @ id @ X394 @ id)) != $true)) | ? [X398 : term,X396 : subst,X395 : subst,X397 : subst] : ((((X387 @ (comp @ X395 @ X396) @ (sub @ X398 @ X396) @ X397)) = $true) & ($true != ((X387 @ X395 @ X398 @ (comp @ X396 @ X397))))) | (((X387 @ id @ X386 @ id)) = $true)) | ? [X375 : term] : (((sub @ X375 @ id)) != X375)) <=> (hoasinduction_lthm_3 = $true)) & (! [X9 : (subst > term > subst > $o)] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & (! [X183 : term,X184 : (subst > term > subst > $o)] : (($true = ((X184 @ id @ (lam @ (sub @ X183 @ (push @ one @ sh))) @ id))) | ? [X194 : term] : ((((X184 @ id @ X194 @ id)) = $true) & ($true != ((X184 @ id @ (sub @ X183 @ (push @ X194 @ id)) @ id)))) | ? [X186 : term,X185 : (subst > term > term)] : ((((X184 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X193 : term,X191 : subst,X192 : subst] : (((sub @ X186 @ (push @ (sub @ X193 @ X192) @ (comp @ X191 @ X192)))) = ((X185 @ (comp @ X191 @ X192) @ (sub @ X193 @ X192)))) & ! [X190 : term] : (($true != ((X184 @ id @ X190 @ id))) | (((X184 @ id @ (X185 @ id @ X190) @ id)) = $true)) & ! [X187 : subst,X188 : subst,X189 : term] : (((sub @ (X185 @ X188 @ X189) @ X187)) = ((sub @ (sub @ X186 @ (push @ X189 @ X188)) @ X187))))) <=> (hoasinduction_lem3aaa = $true)) & ((! [X137 : (subst > term > term),X138 : term,X140 : (subst > term > term),X139 : subst] : (? [X142 : subst,X143 : term,X141 : subst] : (((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141))) != ((sub @ (X140 @ X142 @ X143) @ X141))) | (((lam @ (X137 @ sh @ one))) != ((lam @ (X140 @ sh @ one)))) | (((X137 @ X139 @ X138)) = ((X140 @ X139 @ X138))) | ? [X146 : term,X145 : subst,X144 : subst] : (((sub @ (X137 @ X145 @ X146) @ X144)) != ((X137 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))))) | ? [X135 : term,X136 : term] : ((((lam @ X136)) = ((lam @ X135))) & (X135 != X136)) | ? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131) | ? [X133 : term,X134 : subst] : (((comp @ sh @ (push @ X133 @ X134))) != X134)) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (? [X499 : term] : (((X498 @ X499)) != ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X496 @ X497)) != $true) | (((X498 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) <=> (laminj = $true)) & (! [X223 : (subst > term > subst > $o),X222 : (term > $o),X224 : term] : (? [X230 : term] : (((X223 @ id @ X230 @ id)) != ((X222 @ X230))) | ? [X227 : term,X229 : subst,X226 : subst,X228 : subst] : ((((X223 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226) @ X229)) != $true) & (((X223 @ X228 @ X227 @ (comp @ X226 @ X229))) = $true)) | ? [X235 : (subst > term > term)] : (! [X239 : term] : ((((X223 @ id @ (X235 @ id @ X239) @ id)) = $true) | (((X223 @ id @ X239 @ id)) != $true)) & (((X223 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true) & ! [X238 : subst,X236 : term,X237 : subst] : (((X235 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X235 @ X237 @ X236) @ X238)))) | ? [X231 : subst,X232 : term,X234 : subst,X233 : subst] : ((((X223 @ X234 @ X232 @ (comp @ X231 @ X233))) != $true) & (((X223 @ (comp @ X234 @ X231) @ (sub @ X232 @ X231) @ X233)) = $true)) | ? [X225 : term] : ((((X222 @ (sub @ X224 @ (push @ X225 @ id)))) != $true) & (((X222 @ X225)) = $true)) | ($true = ((X222 @ (lam @ X224))))) <=> (hoasinduction_lem3v2 = $true)) & ((! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72)))) | ? [X66 : term] : (((sub @ X66 @ id)) != X66) | ? [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 != X69) & (((ap @ X68 @ X70)) = ((ap @ X69 @ X67))))) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1 = $true) <=> ! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true))) & (pushprop_lthm = $true) & (lamnotap != $true) & ((hoasapinj2_lthm = $true) <=> (! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35)) | ? [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) = ((ap @ X30 @ X29))) & (X28 != X29)))) & (hoasapinj1_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) != ((d2subst @ X409))) | (X408 = X409)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) <=> (apinj2 = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((substmonoid_lthm = $true) <=> ((! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407)) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404))) & ((? [X204 : (term > $o),X203 : term,X205 : subst] : (! [X210 : term,X209 : term] : ((((X204 @ (ap @ X209 @ X210))) = $true) | ($true != ((X204 @ X210))) | ($true != ((X204 @ X209)))) & ! [X208 : term] : ((((var @ X208)) != $true) | (((X204 @ (sub @ X208 @ X205))) = $true)) & ! [X206 : term] : (? [X207 : term] : ((((X204 @ (sub @ X206 @ (push @ X207 @ id)))) != $true) & ($true = ((X204 @ X207)))) | (((X204 @ (lam @ X206))) = $true)) & (((X204 @ (sub @ X203 @ X205))) != $true)) | ! [X211 : (term > $o),X212 : term] : (? [X217 : term,X216 : term] : ((((X211 @ (ap @ X217 @ X216))) != $true) & (((X211 @ X217)) = $true) & (((X211 @ X216)) = $true)) | ? [X213 : term] : (! [X214 : term] : ((((X211 @ (sub @ X213 @ (push @ X214 @ id)))) = $true) | ($true != ((X211 @ X214)))) & (((X211 @ (lam @ X213))) != $true)) | (((X211 @ X212)) = $true) | ? [X215 : term] : (($true = ((var @ X215))) & ($true != ((X211 @ X215))))) | ? [X202 : term] : (((sub @ X202 @ id)) != X202)) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X349 : term,X347 : (term > $o),X348 : (subst > term > subst > $o)] : (? [X362 : term,X361 : subst,X360 : subst,X363 : subst] : (($true = ((X348 @ (comp @ X361 @ X360) @ (sub @ X362 @ X360) @ X363))) & (((X348 @ X361 @ X362 @ (comp @ X360 @ X363))) != $true)) | ? [X364 : term] : (((X348 @ id @ X364 @ id)) != ((X347 @ X364))) | ? [X351 : (subst > term > term)] : ((((X348 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : term] : (($true != ((X348 @ id @ X355 @ id))) | ($true = ((X348 @ id @ (X351 @ id @ X355) @ id)))) & ! [X352 : term,X354 : subst,X353 : subst] : (((sub @ (X351 @ X354 @ X352) @ X353)) = ((X351 @ (comp @ X354 @ X353) @ (sub @ X352 @ X353))))) | ($true = ((X347 @ (lam @ X349)))) | ? [X359 : subst,X357 : subst,X358 : term,X356 : subst] : (($true != ((X348 @ (comp @ X356 @ X359) @ (sub @ X358 @ X359) @ X357))) & (((X348 @ X356 @ X358 @ (comp @ X359 @ X357))) = $true)) | ? [X350 : term] : (($true = ((X347 @ X350))) & (((X347 @ (sub @ X349 @ (push @ X350 @ id)))) != $true))) | ? [X346 : term] : (((sub @ X346 @ id)) != X346))) & (! [X77 : term,X78 : (term > $o),X76 : term,X75 : (subst > term > subst > $o)] : (? [X88 : term,X89 : term] : ((((X75 @ id @ X88 @ id)) = $true) & (((X75 @ id @ X89 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) != $true)) | ? [X87 : term] : (((X75 @ id @ X87 @ id)) != ((X78 @ X87))) | ($true != ((X78 @ X76))) | (((X78 @ (ap @ X77 @ X76))) = $true) | ? [X85 : subst,X83 : subst,X84 : term,X86 : subst] : ((((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) = $true) & (((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) != $true)) | ($true != ((X78 @ X77))) | ? [X80 : subst,X79 : subst,X81 : subst,X82 : term] : ((((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) = $true) & (((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) != $true))) <=> (hoasinduction_lem2v2 = $true)) & ((hoaslamnotap = $true) <=> ! [X534 : term,X536 : (subst > term > term),X535 : term] : (? [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) != ((sub @ (X536 @ X538 @ X539) @ X537))) | (((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535))))) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & (! [X306 : (subst > term > subst > $o),X307 : term] : (? [X308 : (subst > term > term)] : ((((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)) != $true) & ! [X310 : subst,X311 : term,X312 : subst] : (((sub @ (X308 @ X310 @ X311) @ X312)) = ((X308 @ (comp @ X310 @ X312) @ (sub @ X311 @ X312)))) & ! [X309 : term] : (($true = ((X306 @ id @ (X308 @ id @ X309) @ id))) | (((X306 @ id @ X309 @ id)) != $true))) | ? [X313 : term] : ((((X306 @ id @ (sub @ X307 @ (push @ X313 @ id)) @ id)) != $true) & (((X306 @ id @ X313 @ id)) = $true)) | (((X306 @ id @ (lam @ (sub @ X307 @ (push @ one @ sh))) @ id)) = $true)) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & ((? [X0 : term] : (((sub @ X0 @ id)) != X0) | ! [X1 : term] : (((sub @ X1 @ id)) = X1)) <=> (termmset_lthm = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) <=> ! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441))) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X166 : term] : ? [X167 : (subst > term > term)] : (((X167 @ sh @ one)) = ((sub @ X166 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((X470 @ sh @ one)) = ((sub @ X469 @ (push @ one @ sh))))) & ((hoasinduction_lem2 = $true) <=> ! [X38 : term,X36 : (subst > term > subst > $o),X37 : term] : (($true != ((X36 @ id @ X37 @ id))) | ($true != ((X36 @ id @ X38 @ id))) | ? [X39 : term,X40 : term] : ((((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) != $true) & ($true = ((X36 @ id @ X40 @ id))) & (((X36 @ id @ X39 @ id)) = $true)) | ? [X46 : subst,X47 : subst,X45 : term,X48 : subst] : (($true != ((X36 @ X46 @ X45 @ (comp @ X47 @ X48)))) & ($true = ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48)))) | ? [X41 : subst,X42 : subst,X44 : term,X43 : subst] : (($true = ((X36 @ X41 @ X44 @ (comp @ X43 @ X42)))) & (((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) != $true)) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))))) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & (! [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ? [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) != ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | ? [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) != ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) <=> (hoaslaminj = $true)) & ((induction2 = $true) <=> ! [X339 : term,X340 : (term > $o)] : (? [X341 : term] : ((((var @ X341)) = $true) & (((X340 @ X341)) != $true)) | (((X340 @ X339)) = $true) | ? [X342 : term] : (($true != ((X340 @ (lam @ X342)))) & ! [X343 : term] : (($true != ((X340 @ X343))) | (((X340 @ (sub @ X342 @ (push @ X343 @ id)))) = $true))) | ? [X344 : term,X345 : term] : ((((X340 @ X344)) = $true) & ($true = ((X340 @ X345))) & (((X340 @ (ap @ X344 @ X345))) != $true)))) & (! [X178 : (term > $o),X180 : subst,X179 : term] : ? [X181 : (term > $o)] : ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X4 : term] : ? [X5 : (subst > term > term)] : ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7))))) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (! [X477 : (subst > term > subst > $o),X476 : term] : (($true = ((X477 @ id @ X476 @ id))) | ? [X480 : (subst > term > term)] : (! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))) | ? [X479 : term,X478 : term] : (($true = ((X477 @ id @ X478 @ id))) & ($true != ((X477 @ id @ (ap @ (sub @ X479 @ id) @ X478) @ id))) & (((X477 @ id @ X479 @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X488 : term,X489 : subst,X487 : (term > $o)] : (? [X492 : term] : (! [X493 : term] : ((((X487 @ X493)) != $true) | (((X487 @ (sub @ X492 @ (push @ X493 @ id)))) = $true)) & ($true != ((X487 @ (lam @ X492))))) | (((X487 @ (sub @ X488 @ X489))) = $true) | ? [X494 : term] : ((((X487 @ (sub @ X494 @ X489))) != $true) & ($true = ((var @ X494)))) | ? [X490 : term,X491 : term] : ((((X487 @ X491)) = $true) & ($true = ((X487 @ X490))) & (((X487 @ (ap @ X491 @ X490))) != $true))) <=> (induction2lem = $true)) & (hoaslaminj_gthm = $true) & ((axidr = $true) <=> ! [X532 : subst] : (((comp @ X532 @ id)) = X532)) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axassoc = $true) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) <=> (termmset = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (! [X461 : term] : ? [X462 : (subst > term > term)] : ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) <=> (axvarid = $true)) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X168 : (subst > term > subst > $o),X170 : term,X169 : (term > $o)] : ((((X169 @ (lam @ X170))) = $true) | ? [X171 : term] : ((((X169 @ (sub @ X170 @ (push @ X171 @ id)))) != $true) & (((X169 @ X171)) = $true)) | ? [X172 : (subst > term > term)] : (! [X174 : term,X176 : subst,X175 : subst] : (((X172 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) = ((sub @ (X172 @ X175 @ X174) @ X176))) & ! [X173 : term] : (($true != ((X168 @ id @ X173 @ id))) | ($true = ((X168 @ id @ (X172 @ id @ X173) @ id)))) & (((X168 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)) | ? [X177 : term] : (((X169 @ X177)) != ((X168 @ id @ X177 @ id))))) & ! [X96 : d_subst] : (d_id = X96) & (! [X196 : term,X197 : (term > $o)] : (? [X199 : term] : ((((var @ X199)) = $true) & (((X197 @ X199)) != $true)) | ($true = ((X197 @ X196))) | ? [X198 : term] : ((((X197 @ (lam @ X198))) != $true) & ($true = ((X197 @ X198)))) | ? [X200 : term,X201 : term] : (($true != ((X197 @ (ap @ X200 @ X201)))) & (((X197 @ X201)) = $true) & (((X197 @ X200)) = $true))) <=> (induction = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X128 : (subst > term > subst > $o)] : ? [X129 : (term > $o)] : ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130)))) & (! [X242 : (subst > term > subst > $o),X243 : term] : ((((X242 @ id @ (lam @ (sub @ X243 @ (push @ one @ sh))) @ id)) = $true) | ? [X245 : (subst > term > term)] : (! [X246 : term] : ((((X242 @ id @ (X245 @ id @ X246) @ id)) = $true) | (((X242 @ id @ X246 @ id)) != $true)) & (((X242 @ id @ (lam @ (X245 @ sh @ one)) @ id)) != $true) & ! [X247 : subst,X249 : subst,X248 : term] : (((sub @ (X245 @ X249 @ X248) @ X247)) = ((X245 @ (comp @ X249 @ X247) @ (sub @ X248 @ X247))))) | ? [X244 : term] : ((((X242 @ id @ X244 @ id)) = $true) & (((X242 @ id @ (sub @ X243 @ (push @ X244 @ id)) @ id)) != $true))) <=> (hoasinduction_lem3aa = $true))),
% 2.11/0.57 inference(flattening,[],[f11])).
% 2.11/0.57 thf(f13,definition,(
% 2.11/0.57 (sP0 = $true) <=> ! [X242 : (subst > term > subst > $o),X243 : term] : ((((X242 @ id @ (lam @ (sub @ X243 @ (push @ one @ sh))) @ id)) = $true) | ? [X245 : (subst > term > term)] : (! [X246 : term] : ((((X242 @ id @ (X245 @ id @ X246) @ id)) = $true) | (((X242 @ id @ X246 @ id)) != $true)) & (((X242 @ id @ (lam @ (X245 @ sh @ one)) @ id)) != $true) & ! [X247 : subst,X249 : subst,X248 : term] : (((sub @ (X245 @ X249 @ X248) @ X247)) = ((X245 @ (comp @ X249 @ X247) @ (sub @ X248 @ X247))))) | ? [X244 : term] : ((((X242 @ id @ X244 @ id)) = $true) & (((X242 @ id @ (sub @ X243 @ (push @ X244 @ id)) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f14,definition,(
% 2.11/0.57 ! [X197 : (term > $o)] : ((((sP1 @ X197)) = $true) <=> ? [X200 : term,X201 : term] : (($true != ((X197 @ (ap @ X200 @ X201)))) & (((X197 @ X201)) = $true) & (((X197 @ X200)) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f15,definition,(
% 2.11/0.57 (sP2 = $true) <=> ! [X168 : (subst > term > subst > $o),X170 : term,X169 : (term > $o)] : ((((X169 @ (lam @ X170))) = $true) | ? [X171 : term] : ((((X169 @ (sub @ X170 @ (push @ X171 @ id)))) != $true) & (((X169 @ X171)) = $true)) | ? [X172 : (subst > term > term)] : (! [X174 : term,X176 : subst,X175 : subst] : (((X172 @ (comp @ X175 @ X176) @ (sub @ X174 @ X176))) = ((sub @ (X172 @ X175 @ X174) @ X176))) & ! [X173 : term] : (($true != ((X168 @ id @ X173 @ id))) | ($true = ((X168 @ id @ (X172 @ id @ X173) @ id)))) & (((X168 @ id @ (lam @ (X172 @ sh @ one)) @ id)) != $true)) | ? [X177 : term] : (((X169 @ X177)) != ((X168 @ id @ X177 @ id))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f16,definition,(
% 2.11/0.57 ! [X487 : (term > $o)] : (($true = ((sP3 @ X487))) <=> ? [X490 : term,X491 : term] : ((((X487 @ X491)) = $true) & ($true = ((X487 @ X490))) & (((X487 @ (ap @ X491 @ X490))) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f17,definition,(
% 2.11/0.57 (sP4 = $true) <=> ! [X488 : term,X489 : subst,X487 : (term > $o)] : (? [X492 : term] : (! [X493 : term] : ((((X487 @ X493)) != $true) | (((X487 @ (sub @ X492 @ (push @ X493 @ id)))) = $true)) & ($true != ((X487 @ (lam @ X492))))) | (((X487 @ (sub @ X488 @ X489))) = $true) | ? [X494 : term] : ((((X487 @ (sub @ X494 @ X489))) != $true) & ($true = ((var @ X494)))) | ($true = ((sP3 @ X487))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f18,definition,(
% 2.11/0.57 ! [X477 : (subst > term > subst > $o)] : ((((sP5 @ X477)) = $true) <=> ? [X479 : term,X478 : term] : (($true = ((X477 @ id @ X478 @ id))) & ($true != ((X477 @ id @ (ap @ (sub @ X479 @ id) @ X478) @ id))) & (((X477 @ id @ X479 @ id)) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f19,definition,(
% 2.11/0.57 ! [X340 : (term > $o)] : ((((sP6 @ X340)) = $true) <=> ? [X344 : term,X345 : term] : ((((X340 @ X344)) = $true) & ($true = ((X340 @ X345))) & (((X340 @ (ap @ X344 @ X345))) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f20,definition,(
% 2.11/0.57 ($true = sP7) <=> ! [X339 : term,X340 : (term > $o)] : (? [X341 : term] : ((((var @ X341)) = $true) & (((X340 @ X341)) != $true)) | (((X340 @ X339)) = $true) | ? [X342 : term] : (($true != ((X340 @ (lam @ X342)))) & ! [X343 : term] : (($true != ((X340 @ X343))) | (((X340 @ (sub @ X342 @ (push @ X343 @ id)))) = $true))) | (((sP6 @ X340)) = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f21,definition,(
% 2.11/0.57 ! [X36 : (subst > term > subst > $o)] : ((((sP8 @ X36)) = $true) <=> ? [X39 : term,X40 : term] : ((((X36 @ id @ (ap @ (sub @ X39 @ id) @ X40) @ id)) != $true) & ($true = ((X36 @ id @ X40 @ id))) & (((X36 @ id @ X39 @ id)) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f22,definition,(
% 2.11/0.57 (sP9 = $true) <=> ! [X38 : term,X36 : (subst > term > subst > $o),X37 : term] : (($true != ((X36 @ id @ X37 @ id))) | ($true != ((X36 @ id @ X38 @ id))) | (((sP8 @ X36)) = $true) | ? [X46 : subst,X47 : subst,X45 : term,X48 : subst] : (($true != ((X36 @ X46 @ X45 @ (comp @ X47 @ X48)))) & ($true = ((X36 @ (comp @ X46 @ X47) @ (sub @ X45 @ X47) @ X48)))) | ? [X41 : subst,X42 : subst,X44 : term,X43 : subst] : (($true = ((X36 @ X41 @ X44 @ (comp @ X43 @ X42)))) & (((X36 @ (comp @ X41 @ X43) @ (sub @ X44 @ X43) @ X42)) != $true)) | ($true = ((X36 @ id @ (ap @ X37 @ X38) @ id))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f23,definition,(
% 2.11/0.57 ($true = sP10) <=> ! [X306 : (subst > term > subst > $o),X307 : term] : (? [X308 : (subst > term > term)] : ((((X306 @ id @ (lam @ (X308 @ sh @ one)) @ id)) != $true) & ! [X310 : subst,X311 : term,X312 : subst] : (((sub @ (X308 @ X310 @ X311) @ X312)) = ((X308 @ (comp @ X310 @ X312) @ (sub @ X311 @ X312)))) & ! [X309 : term] : (($true = ((X306 @ id @ (X308 @ id @ X309) @ id))) | (((X306 @ id @ X309 @ id)) != $true))) | ? [X313 : term] : ((((X306 @ id @ (sub @ X307 @ (push @ X313 @ id)) @ id)) != $true) & (((X306 @ id @ X313 @ id)) = $true)) | (((X306 @ id @ (lam @ (sub @ X307 @ (push @ one @ sh))) @ id)) = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f24,definition,(
% 2.11/0.57 ! [X75 : (subst > term > subst > $o)] : ((((sP11 @ X75)) = $true) <=> ? [X88 : term,X89 : term] : ((((X75 @ id @ X88 @ id)) = $true) & (((X75 @ id @ X89 @ id)) = $true) & (((X75 @ id @ (ap @ (sub @ X89 @ id) @ X88) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f25,definition,(
% 2.11/0.57 ($true = sP12) <=> ! [X77 : term,X78 : (term > $o),X76 : term,X75 : (subst > term > subst > $o)] : ((((sP11 @ X75)) = $true) | ? [X87 : term] : (((X75 @ id @ X87 @ id)) != ((X78 @ X87))) | ($true != ((X78 @ X76))) | (((X78 @ (ap @ X77 @ X76))) = $true) | ? [X85 : subst,X83 : subst,X84 : term,X86 : subst] : ((((X75 @ X83 @ X84 @ (comp @ X86 @ X85))) = $true) & (((X75 @ (comp @ X83 @ X86) @ (sub @ X84 @ X86) @ X85)) != $true)) | ($true != ((X78 @ X77))) | ? [X80 : subst,X79 : subst,X81 : subst,X82 : term] : ((((X75 @ (comp @ X80 @ X81) @ (sub @ X82 @ X81) @ X79)) = $true) & (((X75 @ X80 @ X82 @ (comp @ X81 @ X79))) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f26,definition,(
% 2.11/0.57 ! [X348 : (subst > term > subst > $o)] : (($true = ((sP13 @ X348))) <=> ? [X351 : (subst > term > term)] : ((((X348 @ id @ (lam @ (X351 @ sh @ one)) @ id)) != $true) & ! [X355 : term] : (($true != ((X348 @ id @ X355 @ id))) | ($true = ((X348 @ id @ (X351 @ id @ X355) @ id)))) & ! [X352 : term,X354 : subst,X353 : subst] : (((sub @ (X351 @ X354 @ X352) @ X353)) = ((X351 @ (comp @ X354 @ X353) @ (sub @ X352 @ X353))))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f27,definition,(
% 2.11/0.57 (sP14 = $true) <=> (! [X349 : term,X347 : (term > $o),X348 : (subst > term > subst > $o)] : (? [X362 : term,X361 : subst,X360 : subst,X363 : subst] : (($true = ((X348 @ (comp @ X361 @ X360) @ (sub @ X362 @ X360) @ X363))) & (((X348 @ X361 @ X362 @ (comp @ X360 @ X363))) != $true)) | ? [X364 : term] : (((X348 @ id @ X364 @ id)) != ((X347 @ X364))) | ($true = ((sP13 @ X348))) | ($true = ((X347 @ (lam @ X349)))) | ? [X359 : subst,X357 : subst,X358 : term,X356 : subst] : (($true != ((X348 @ (comp @ X356 @ X359) @ (sub @ X358 @ X359) @ X357))) & (((X348 @ X356 @ X358 @ (comp @ X359 @ X357))) = $true)) | ? [X350 : term] : (($true = ((X347 @ X350))) & (((X347 @ (sub @ X349 @ (push @ X350 @ id)))) != $true))) | ? [X346 : term] : (((sub @ X346 @ id)) != X346))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f28,definition,(
% 2.11/0.57 ! [X211 : (term > $o)] : ((((sP15 @ X211)) = $true) <=> ? [X217 : term,X216 : term] : ((((X211 @ (ap @ X217 @ X216))) != $true) & (((X211 @ X217)) = $true) & (((X211 @ X216)) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f29,definition,(
% 2.11/0.57 ! [X204 : (term > $o)] : ((((sP16 @ X204)) = $true) <=> ! [X210 : term,X209 : term] : ((((X204 @ (ap @ X209 @ X210))) = $true) | ($true != ((X204 @ X210))) | ($true != ((X204 @ X209)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f30,definition,(
% 2.11/0.57 (sP17 = $true) <=> ! [X211 : (term > $o),X212 : term] : ((((sP15 @ X211)) = $true) | ? [X213 : term] : (! [X214 : term] : ((((X211 @ (sub @ X213 @ (push @ X214 @ id)))) = $true) | ($true != ((X211 @ X214)))) & (((X211 @ (lam @ X213))) != $true)) | (((X211 @ X212)) = $true) | ? [X215 : term] : (($true = ((var @ X215))) & ($true != ((X211 @ X215)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f31,definition,(
% 2.11/0.57 ($true = sP18) <=> (? [X204 : (term > $o),X203 : term,X205 : subst] : ((((sP16 @ X204)) = $true) & ! [X208 : term] : ((((var @ X208)) != $true) | (((X204 @ (sub @ X208 @ X205))) = $true)) & ! [X206 : term] : (? [X207 : term] : ((((X204 @ (sub @ X206 @ (push @ X207 @ id)))) != $true) & ($true = ((X204 @ X207)))) | (((X204 @ (lam @ X206))) = $true)) & (((X204 @ (sub @ X203 @ X205))) != $true)) | (sP17 = $true) | ? [X202 : term] : (((sub @ X202 @ id)) != X202))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f32,definition,(
% 2.11/0.57 ! [X223 : (subst > term > subst > $o)] : (($true = ((sP19 @ X223))) <=> ? [X235 : (subst > term > term)] : (! [X239 : term] : ((((X223 @ id @ (X235 @ id @ X239) @ id)) = $true) | (((X223 @ id @ X239 @ id)) != $true)) & (((X223 @ id @ (lam @ (X235 @ sh @ one)) @ id)) != $true) & ! [X238 : subst,X236 : term,X237 : subst] : (((X235 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))) = ((sub @ (X235 @ X237 @ X236) @ X238)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f33,definition,(
% 2.11/0.57 (sP20 = $true) <=> ! [X223 : (subst > term > subst > $o),X222 : (term > $o),X224 : term] : (? [X230 : term] : (((X223 @ id @ X230 @ id)) != ((X222 @ X230))) | ? [X227 : term,X229 : subst,X226 : subst,X228 : subst] : ((((X223 @ (comp @ X228 @ X226) @ (sub @ X227 @ X226) @ X229)) != $true) & (((X223 @ X228 @ X227 @ (comp @ X226 @ X229))) = $true)) | ($true = ((sP19 @ X223))) | ? [X231 : subst,X232 : term,X234 : subst,X233 : subst] : ((((X223 @ X234 @ X232 @ (comp @ X231 @ X233))) != $true) & (((X223 @ (comp @ X234 @ X231) @ (sub @ X232 @ X231) @ X233)) = $true)) | ? [X225 : term] : ((((X222 @ (sub @ X224 @ (push @ X225 @ id)))) != $true) & (((X222 @ X225)) = $true)) | ($true = ((X222 @ (lam @ X224)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f34,definition,(
% 2.11/0.57 (sP21 = $true) <=> (! [X137 : (subst > term > term),X138 : term,X140 : (subst > term > term),X139 : subst] : (? [X142 : subst,X143 : term,X141 : subst] : (((X140 @ (comp @ X142 @ X141) @ (sub @ X143 @ X141))) != ((sub @ (X140 @ X142 @ X143) @ X141))) | (((lam @ (X137 @ sh @ one))) != ((lam @ (X140 @ sh @ one)))) | (((X137 @ X139 @ X138)) = ((X140 @ X139 @ X138))) | ? [X146 : term,X145 : subst,X144 : subst] : (((sub @ (X137 @ X145 @ X146) @ X144)) != ((X137 @ (comp @ X145 @ X144) @ (sub @ X146 @ X144))))) | ? [X135 : term,X136 : term] : ((((lam @ X136)) = ((lam @ X135))) & (X135 != X136)) | ? [X132 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X132))) != X131) | ? [X133 : term,X134 : subst] : (((comp @ sh @ (push @ X133 @ X134))) != X134))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f35,definition,(
% 2.11/0.57 (sP22 = $true) <=> ! [X183 : term,X184 : (subst > term > subst > $o)] : (($true = ((X184 @ id @ (lam @ (sub @ X183 @ (push @ one @ sh))) @ id))) | ? [X194 : term] : ((((X184 @ id @ X194 @ id)) = $true) & ($true != ((X184 @ id @ (sub @ X183 @ (push @ X194 @ id)) @ id)))) | ? [X186 : term,X185 : (subst > term > term)] : ((((X184 @ id @ (lam @ (X185 @ sh @ one)) @ id)) != $true) & ! [X193 : term,X191 : subst,X192 : subst] : (((sub @ X186 @ (push @ (sub @ X193 @ X192) @ (comp @ X191 @ X192)))) = ((X185 @ (comp @ X191 @ X192) @ (sub @ X193 @ X192)))) & ! [X190 : term] : (($true != ((X184 @ id @ X190 @ id))) | (((X184 @ id @ (X185 @ id @ X190) @ id)) = $true)) & ! [X187 : subst,X188 : subst,X189 : term] : (((sub @ (X185 @ X188 @ X189) @ X187)) = ((sub @ (sub @ X186 @ (push @ X189 @ X188)) @ X187)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f36,definition,(
% 2.11/0.57 ! [X387 : (subst > term > subst > $o)] : (($true = ((sP23 @ X387))) <=> ? [X393 : term,X392 : term] : (($true = ((X387 @ id @ X392 @ id))) & (((X387 @ id @ X393 @ id)) = $true) & ($true != ((X387 @ id @ (ap @ (sub @ X393 @ id) @ X392) @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f37,definition,(
% 2.11/0.57 ! [X387 : (subst > term > subst > $o)] : ((((sP24 @ X387)) = $true) <=> ? [X399 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X399 @ sh @ one)) @ id)) != $true) & ! [X400 : term] : (($true = ((X387 @ id @ (X399 @ id @ X400) @ id))) | (((X387 @ id @ X400 @ id)) != $true)) & ! [X401 : subst,X402 : subst,X403 : term] : (((sub @ (X399 @ X402 @ X403) @ X401)) = ((X399 @ (comp @ X402 @ X401) @ (sub @ X403 @ X401))))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f38,definition,(
% 2.11/0.57 ! [X368 : (term > $o)] : ((((sP25 @ X368)) = $true) <=> ! [X372 : term,X371 : term] : ((((X368 @ X372)) != $true) | (((X368 @ (ap @ X371 @ X372))) = $true) | ($true != ((X368 @ X371)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f39,definition,(
% 2.11/0.57 (sP26 = $true) <=> ! [X387 : (subst > term > subst > $o),X386 : term] : (? [X389 : subst,X388 : term,X391 : subst,X390 : subst] : ((((X387 @ X389 @ X388 @ (comp @ X390 @ X391))) = $true) & ($true != ((X387 @ (comp @ X389 @ X390) @ (sub @ X388 @ X390) @ X391)))) | (((sP24 @ X387)) = $true) | ($true = ((sP23 @ X387))) | ? [X394 : term] : (($true = ((var @ (sub @ X394 @ id)))) & (((X387 @ id @ X394 @ id)) != $true)) | ? [X398 : term,X396 : subst,X395 : subst,X397 : subst] : ((((X387 @ (comp @ X395 @ X396) @ (sub @ X398 @ X396) @ X397)) = $true) & ($true != ((X387 @ X395 @ X398 @ (comp @ X396 @ X397))))) | (((X387 @ id @ X386 @ id)) = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f40,definition,(
% 2.11/0.57 (sP27 = $true) <=> ? [X377 : (subst > term > subst > $o),X376 : term,X378 : (term > $o)] : ((((X378 @ (lam @ X376))) != $true) & ! [X384 : term] : (((X378 @ X384)) = ((X377 @ id @ X384 @ id))) & ! [X385 : term] : (($true = ((X378 @ (sub @ X376 @ (push @ X385 @ id))))) | ($true != ((X378 @ X385)))) & ! [X379 : (subst > term > term)] : (? [X381 : subst,X380 : subst,X382 : term] : (((X379 @ (comp @ X381 @ X380) @ (sub @ X382 @ X380))) != ((sub @ (X379 @ X381 @ X382) @ X380))) | (((X377 @ id @ (lam @ (X379 @ sh @ one)) @ id)) = $true) | ? [X383 : term] : ((((X377 @ id @ X383 @ id)) = $true) & (((X377 @ id @ (X379 @ id @ X383) @ id)) != $true))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f41,definition,(
% 2.11/0.57 (sP28 = $true) <=> ((sP27 = $true) | ? [X369 : term,X368 : (term > $o)] : (! [X373 : term] : (? [X374 : term] : ((((X368 @ X374)) = $true) & ($true != ((X368 @ (sub @ X373 @ (push @ X374 @ id)))))) | ($true = ((X368 @ (lam @ X373))))) & ! [X370 : term] : ((((var @ X370)) != $true) | ($true = ((X368 @ X370)))) & (((X368 @ X369)) != $true) & (((sP25 @ X368)) = $true)) | ? [X365 : (subst > term > subst > $o)] : ! [X366 : (term > $o)] : ? [X367 : term] : (((X366 @ X367)) != ((X365 @ id @ X367 @ id))) | (sP26 = $true) | ? [X375 : term] : (((sub @ X375 @ id)) != X375))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f42,definition,(
% 2.11/0.57 ! [X153 : (term > $o)] : (($true = ((sP29 @ X153))) <=> ! [X157 : term,X156 : term] : ((((X153 @ (ap @ X157 @ X156))) = $true) | ($true != ((X153 @ X156))) | ($true != ((X153 @ X157)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f43,definition,(
% 2.11/0.57 ! [X158 : (term > $o)] : ((((sP30 @ X158)) = $true) <=> ? [X163 : term,X164 : term] : ((((X158 @ X164)) = $true) & ($true = ((X158 @ X163))) & (((X158 @ (ap @ X164 @ X163))) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f44,definition,(
% 2.11/0.57 (sP31 = $true) <=> ! [X160 : term,X159 : subst,X158 : (term > $o)] : (? [X165 : term] : ((((var @ X165)) = $true) & ($true != ((X158 @ (sub @ X165 @ X159))))) | (((X158 @ (sub @ X160 @ X159))) = $true) | (((sP30 @ X158)) = $true) | ? [X161 : term] : (! [X162 : term] : ((((X158 @ X162)) != $true) | ($true = ((X158 @ (sub @ X161 @ (push @ X162 @ id)))))) & (((X158 @ (lam @ X161))) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f45,definition,(
% 2.11/0.57 (sP32 = $true) <=> (? [X150 : term,X149 : subst] : (((comp @ sh @ (push @ X150 @ X149))) != X149) | (sP31 = $true) | ? [X152 : term,X153 : (term > $o)] : (! [X155 : term] : (($true != ((X153 @ X155))) | ($true = ((X153 @ (lam @ X155))))) & ($true = ((sP29 @ X153))) & ! [X154 : term] : ((((var @ X154)) != $true) | (((X153 @ X154)) = $true)) & ($true != ((X153 @ X152)))) | ? [X148 : subst,X147 : term] : (((sub @ one @ (push @ X147 @ X148))) != X147) | ? [X151 : subst] : (((comp @ X151 @ id)) != X151))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f46,definition,(
% 2.11/0.57 ($true = sP33) <=> ! [X119 : term,X120 : (subst > term > subst > $o)] : ((((X120 @ id @ (lam @ X119) @ id)) = $true) | ? [X126 : term] : (($true != ((X120 @ id @ (sub @ X119 @ (push @ X126 @ id)) @ id))) & (((X120 @ id @ X126 @ id)) = $true)) | ? [X121 : (subst > term > term)] : (! [X125 : term] : ((((X120 @ id @ (X121 @ id @ X125) @ id)) = $true) | (((X120 @ id @ X125 @ id)) != $true)) & ! [X123 : subst,X124 : subst,X122 : term] : (((sub @ (X121 @ X123 @ X122) @ X124)) = ((X121 @ (comp @ X123 @ X124) @ (sub @ X122 @ X124)))) & (((X120 @ id @ (lam @ (X121 @ sh @ one)) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f47,definition,(
% 2.11/0.57 (sP34 = $true) <=> (? [X55 : term] : (((sub @ X55 @ id)) != X55) | ! [X56 : (term > $o),X58 : (subst > term > subst > $o),X57 : term] : (? [X65 : term] : (($true = ((X56 @ X65))) & (((X56 @ (sub @ X57 @ (push @ X65 @ id)))) != $true)) | (((X56 @ (lam @ X57))) = $true) | ? [X60 : (subst > term > term)] : ((((X58 @ id @ (lam @ (X60 @ sh @ one)) @ id)) != $true) & ! [X64 : subst,X62 : subst,X63 : term] : (((sub @ (X60 @ X62 @ X63) @ X64)) = ((X60 @ (comp @ X62 @ X64) @ (sub @ X63 @ X64)))) & ! [X61 : term] : ((((X58 @ id @ (X60 @ id @ X61) @ id)) = $true) | ($true != ((X58 @ id @ X61 @ id))))) | ? [X59 : term] : (((X56 @ X59)) != ((X58 @ id @ X59 @ id)))) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X54 : subst,X53 : term] : (((X52 @ X54 @ X53)) != ((sub @ X51 @ (push @ X53 @ X54)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f48,definition,(
% 2.11/0.57 ! [X12 : (subst > term > subst > $o)] : ((((sP35 @ X12)) = $true) <=> ? [X23 : (subst > term > term)] : (! [X26 : subst,X25 : term,X24 : subst] : (((X23 @ (comp @ X26 @ X24) @ (sub @ X25 @ X24))) = ((sub @ (X23 @ X26 @ X25) @ X24))) & ! [X27 : term] : (($true = ((X12 @ id @ (X23 @ id @ X27) @ id))) | (((X12 @ id @ X27 @ id)) != $true)) & (((X12 @ id @ (lam @ (X23 @ sh @ one)) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f49,definition,(
% 2.11/0.57 (sP36 = $true) <=> ! [X13 : term,X12 : (subst > term > subst > $o)] : (? [X18 : term] : (($true != ((X12 @ id @ (sub @ X13 @ (push @ X18 @ id)) @ id))) & (((X12 @ id @ X18 @ id)) = $true)) | (((X12 @ id @ (lam @ X13) @ id)) = $true) | (((sP35 @ X12)) = $true) | ? [X15 : subst,X16 : term,X17 : subst,X14 : subst] : ((((X12 @ X17 @ X16 @ (comp @ X15 @ X14))) != $true) & ($true = ((X12 @ (comp @ X17 @ X15) @ (sub @ X16 @ X15) @ X14)))) | ? [X19 : subst,X21 : subst,X22 : subst,X20 : term] : (($true = ((X12 @ X21 @ X20 @ (comp @ X22 @ X19)))) & (((X12 @ (comp @ X21 @ X22) @ (sub @ X20 @ X22) @ X19)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f50,definition,(
% 2.11/0.57 ! [X431 : (subst > term > subst > $o)] : ((((sP37 @ X431)) = $true) <=> ? [X435 : (subst > term > term)] : (! [X436 : term] : (($true = ((X431 @ id @ (X435 @ id @ X436) @ id))) | (((X431 @ id @ X436 @ id)) != $true)) & ! [X437 : subst,X439 : subst,X438 : term] : (((sub @ (X435 @ X437 @ X438) @ X439)) = ((X435 @ (comp @ X437 @ X439) @ (sub @ X438 @ X439)))) & (((X431 @ id @ (lam @ (X435 @ sh @ one)) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f51,definition,(
% 2.11/0.57 ! [X414 : (term > $o)] : (($true = ((sP38 @ X414))) <=> ! [X419 : term,X418 : term] : ((((X414 @ (ap @ X418 @ X419))) = $true) | (((X414 @ X419)) != $true) | ($true != ((X414 @ X418)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f52,definition,(
% 2.11/0.57 ($true = sP39) <=> ? [X423 : (subst > term > subst > $o),X421 : term,X422 : (term > $o)] : (! [X430 : term] : (((X422 @ X430)) = ((X423 @ id @ X430 @ id))) & ! [X429 : term] : ((((X422 @ (sub @ X421 @ (push @ X429 @ id)))) = $true) | (((X422 @ X429)) != $true)) & (((X422 @ (lam @ X421))) != $true) & ! [X424 : (subst > term > term)] : ((((X423 @ id @ (lam @ (X424 @ sh @ one)) @ id)) = $true) | ? [X425 : term,X426 : subst,X427 : subst] : (((sub @ (X424 @ X426 @ X425) @ X427)) != ((X424 @ (comp @ X426 @ X427) @ (sub @ X425 @ X427)))) | ? [X428 : term] : ((((X423 @ id @ (X424 @ id @ X428) @ id)) != $true) & (((X423 @ id @ X428 @ id)) = $true))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f53,definition,(
% 2.11/0.57 ($true = sP40) <=> ? [X413 : term,X414 : (term > $o)] : (($true = ((sP38 @ X414))) & ! [X417 : term] : (($true != ((var @ X417))) | (((X414 @ X417)) = $true)) & ! [X415 : term] : (? [X416 : term] : ((((X414 @ (sub @ X415 @ (push @ X416 @ id)))) != $true) & ($true = ((X414 @ X416)))) | (((X414 @ (lam @ X415))) = $true)) & (((X414 @ X413)) != $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f54,definition,(
% 2.11/0.57 ($true = sP41) <=> (? [X410 : (subst > term > subst > $o)] : ! [X411 : (term > $o)] : ? [X412 : term] : (((X411 @ X412)) != ((X410 @ id @ X412 @ id))) | ? [X420 : term] : (((sub @ X420 @ id)) != X420) | ($true = sP40) | ($true = sP39) | ! [X431 : (subst > term > subst > $o),X432 : term] : (? [X433 : term,X434 : term] : ((((X431 @ id @ X433 @ id)) = $true) & (((X431 @ id @ X434 @ id)) = $true) & ($true != ((X431 @ id @ (ap @ (sub @ X433 @ id) @ X434) @ id)))) | (((sP37 @ X431)) = $true) | (((X431 @ id @ X432 @ id)) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f55,definition,(
% 2.11/0.57 ! [X287 : (subst > term > subst > $o)] : (($true = ((sP42 @ X287))) <=> ? [X292 : term,X293 : term] : ((((X287 @ id @ X293 @ id)) = $true) & ($true != ((X287 @ id @ (ap @ (sub @ X292 @ id) @ X293) @ id))) & ($true = ((X287 @ id @ X292 @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f56,definition,(
% 2.11/0.57 ! [X287 : (subst > term > subst > $o)] : ((((sP43 @ X287)) = $true) <=> ? [X299 : (subst > term > term)] : (! [X300 : term] : ((((X287 @ id @ X300 @ id)) != $true) | ($true = ((X287 @ id @ (X299 @ id @ X300) @ id)))) & ! [X302 : term,X303 : subst,X301 : subst] : (((sub @ (X299 @ X301 @ X302) @ X303)) = ((X299 @ (comp @ X301 @ X303) @ (sub @ X302 @ X303)))) & (((X287 @ id @ (lam @ (X299 @ sh @ one)) @ id)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f57,definition,(
% 2.11/0.57 ! [X250 : (term > $o)] : ((((sP44 @ X250)) = $true) <=> ! [X256 : term,X255 : term] : ((((X250 @ X256)) != $true) | (((X250 @ (ap @ X255 @ X256))) = $true) | (((X250 @ X255)) != $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f58,definition,(
% 2.11/0.57 ! [X258 : (subst > term > subst > $o)] : (($true = ((sP45 @ X258))) <=> ! [X260 : term,X261 : term] : ((((X258 @ id @ X260 @ id)) != $true) | ($true = ((X258 @ id @ (ap @ (sub @ X260 @ id) @ X261) @ id))) | ($true != ((X258 @ id @ X261 @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f59,definition,(
% 2.11/0.57 ! [X270 : (subst > term > subst > $o)] : ((((sP46 @ X270)) = $true) <=> ! [X280 : (subst > term > term)] : (? [X284 : term] : ((((X270 @ id @ X284 @ id)) = $true) & (((X270 @ id @ (X280 @ id @ X284) @ id)) != $true)) | ? [X283 : subst,X282 : subst,X281 : term] : (((X280 @ (comp @ X283 @ X282) @ (sub @ X281 @ X282))) != ((sub @ (X280 @ X283 @ X281) @ X282))) | ($true = ((X270 @ id @ (lam @ (X280 @ sh @ one)) @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f60,definition,(
% 2.11/0.57 (sP47 = $true) <=> ? [X270 : (subst > term > subst > $o),X271 : term] : ((((X270 @ id @ (lam @ X271) @ id)) != $true) & ! [X285 : term] : (($true = ((X270 @ id @ (sub @ X271 @ (push @ X285 @ id)) @ id))) | (((X270 @ id @ X285 @ id)) != $true)) & ! [X273 : term,X274 : subst,X272 : subst,X275 : subst] : ((((X270 @ X275 @ X273 @ (comp @ X274 @ X272))) != $true) | ($true = ((X270 @ (comp @ X275 @ X274) @ (sub @ X273 @ X274) @ X272)))) & ! [X276 : subst,X277 : subst,X279 : term,X278 : subst] : ((((X270 @ X278 @ X279 @ (comp @ X277 @ X276))) = $true) | (((X270 @ (comp @ X278 @ X277) @ (sub @ X279 @ X277) @ X276)) != $true)) & (((sP46 @ X270)) = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f61,definition,(
% 2.11/0.57 ($true = sP48) <=> ! [X286 : term,X287 : (subst > term > subst > $o)] : (? [X297 : subst,X296 : subst,X294 : subst,X295 : term] : ((((X287 @ (comp @ X294 @ X297) @ (sub @ X295 @ X297) @ X296)) = $true) & ($true != ((X287 @ X294 @ X295 @ (comp @ X297 @ X296))))) | ? [X298 : term] : ((((X287 @ id @ X298 @ id)) != $true) & (((var @ (sub @ X298 @ id))) = $true)) | ? [X291 : subst,X288 : subst,X289 : subst,X290 : term] : ((((X287 @ (comp @ X288 @ X291) @ (sub @ X290 @ X291) @ X289)) != $true) & (((X287 @ X288 @ X290 @ (comp @ X291 @ X289))) = $true)) | (((sP43 @ X287)) = $true) | (((X287 @ id @ X286 @ id)) = $true) | ($true = ((sP42 @ X287))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f62,definition,(
% 2.11/0.57 ($true = sP49) <=> ? [X250 : (term > $o),X251 : term] : (! [X252 : term] : ((((X250 @ X252)) = $true) | ($true != ((var @ X252)))) & (((X250 @ X251)) != $true) & ! [X253 : term] : ((((X250 @ (lam @ X253))) = $true) | ? [X254 : term] : ((((X250 @ X254)) = $true) & (((X250 @ (sub @ X253 @ (push @ X254 @ id)))) != $true))) & (((sP44 @ X250)) = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f63,definition,(
% 2.11/0.57 (sP50 = $true) <=> ((sP47 = $true) | ? [X259 : term,X258 : (subst > term > subst > $o),X257 : term] : ((((X258 @ id @ X259 @ id)) = $true) & (((X258 @ id @ X257 @ id)) = $true) & (((X258 @ id @ (ap @ X259 @ X257) @ id)) != $true) & ! [X268 : subst,X266 : subst,X267 : subst,X269 : term] : (($true != ((X258 @ (comp @ X268 @ X266) @ (sub @ X269 @ X266) @ X267))) | (((X258 @ X268 @ X269 @ (comp @ X266 @ X267))) = $true)) & ! [X264 : subst,X262 : term,X265 : subst,X263 : subst] : ((((X258 @ X264 @ X262 @ (comp @ X263 @ X265))) != $true) | (((X258 @ (comp @ X264 @ X263) @ (sub @ X262 @ X263) @ X265)) = $true)) & ($true = ((sP45 @ X258)))) | ($true = sP49) | ($true = sP48))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f64,definition,(
% 2.11/0.57 (sP51 = $true) <=> ? [X445 : term,X446 : (subst > term > subst > $o)] : (! [X447 : term] : (($true != ((X446 @ id @ X447 @ id))) | ($true = ((X446 @ id @ (sub @ X445 @ (push @ X447 @ id)) @ id)))) & (((X446 @ id @ (lam @ (sub @ X445 @ (push @ one @ sh))) @ id)) != $true) & ! [X448 : (subst > term > term)] : ((((X446 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true) | ? [X449 : term] : (($true != ((X446 @ id @ (X448 @ id @ X449) @ id))) & (((X446 @ id @ X449 @ id)) = $true)) | ? [X451 : term,X452 : subst,X450 : subst] : (((X448 @ (comp @ X450 @ X452) @ (sub @ X451 @ X452))) != ((sub @ (X448 @ X450 @ X451) @ X452)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f65,definition,(
% 2.11/0.57 (sP52 = $true) <=> (! [X453 : term,X454 : (subst > term > subst > $o)] : (? [X460 : term] : (($true != ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) & (((X454 @ id @ X460 @ id)) = $true)) | (((X454 @ id @ (lam @ X453) @ id)) = $true) | ? [X455 : (subst > term > term)] : (! [X457 : subst,X458 : term,X456 : subst] : (((X455 @ (comp @ X456 @ X457) @ (sub @ X458 @ X457))) = ((sub @ (X455 @ X456 @ X458) @ X457))) & ! [X459 : term] : ((((X454 @ id @ (X455 @ id @ X459) @ id)) = $true) | (((X454 @ id @ X459 @ id)) != $true)) & (((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)) != $true))) | ? [X444 : term] : (((sub @ X444 @ id)) != X444) | (sP51 = $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f66,definition,(
% 2.11/0.57 ! [X97 : (subst > term > subst > $o)] : (($true = ((sP53 @ X97))) <=> ? [X110 : term,X109 : term] : ((((X97 @ id @ X110 @ id)) = $true) & (((X97 @ id @ (ap @ (sub @ X109 @ id) @ X110) @ id)) != $true) & ($true = ((X97 @ id @ X109 @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f67,definition,(
% 2.11/0.57 ! [X97 : (subst > term > subst > $o)] : ((((sP54 @ X97)) = $true) <=> ? [X104 : (subst > term > term)] : (! [X105 : term] : ((((X97 @ id @ X105 @ id)) != $true) | (((X97 @ id @ (X104 @ id @ X105) @ id)) = $true)) & ! [X107 : subst,X106 : term,X108 : subst] : (((X104 @ (comp @ X107 @ X108) @ (sub @ X106 @ X108))) = ((sub @ (X104 @ X107 @ X106) @ X108))) & ($true != ((X97 @ id @ (lam @ (X104 @ sh @ one)) @ id)))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f68,definition,(
% 2.11/0.57 (sP55 = $true) <=> ! [X98 : term,X97 : (subst > term > subst > $o)] : ((((sP54 @ X97)) = $true) | (((X97 @ id @ X98 @ id)) = $true) | ($true = ((sP53 @ X97))) | ? [X112 : term,X114 : subst,X111 : subst,X113 : subst] : ((((X97 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114)) != $true) & ($true = ((X97 @ X111 @ X112 @ (comp @ X113 @ X114))))) | ? [X102 : subst,X101 : subst,X103 : term,X100 : subst] : ((((X97 @ X102 @ X103 @ (comp @ X101 @ X100))) != $true) & (((X97 @ (comp @ X102 @ X101) @ (sub @ X103 @ X101) @ X100)) = $true)) | ? [X99 : term] : (($true != ((X97 @ id @ X99 @ id))) & (((var @ (sub @ X99 @ id))) = $true)))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f69,definition,(
% 2.11/0.57 ! [X324 : (subst > term > subst > $o)] : ((((sP56 @ X324)) = $true) <=> ? [X334 : (subst > term > term)] : (! [X337 : subst,X335 : term,X336 : subst] : (((sub @ (X334 @ X336 @ X335) @ X337)) = ((X334 @ (comp @ X336 @ X337) @ (sub @ X335 @ X337)))) & ($true != ((X324 @ id @ (lam @ (X334 @ sh @ one)) @ id))) & ! [X338 : term] : (($true = ((X324 @ id @ (X334 @ id @ X338) @ id))) | ($true != ((X324 @ id @ X338 @ id))))))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f70,definition,(
% 2.11/0.57 ($true = sP57) <=> ? [X315 : term,X316 : (subst > term > subst > $o)] : (! [X322 : term] : ((((X316 @ id @ X322 @ id)) != $true) | ($true = ((X316 @ id @ (sub @ X315 @ (push @ X322 @ id)) @ id)))) & ! [X317 : (subst > term > term)] : (? [X318 : term] : (($true = ((X316 @ id @ X318 @ id))) & (((X316 @ id @ (X317 @ id @ X318) @ id)) != $true)) | (((X316 @ id @ (lam @ (X317 @ sh @ one)) @ id)) = $true) | ? [X320 : subst,X321 : term,X319 : subst] : (((X317 @ (comp @ X320 @ X319) @ (sub @ X321 @ X319))) != ((sub @ (X317 @ X320 @ X321) @ X319)))) & (((X316 @ id @ (lam @ (sub @ X315 @ (push @ one @ sh))) @ id)) != $true))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f71,definition,(
% 2.11/0.57 (sP58 = $true) <=> (? [X314 : term] : (((sub @ X314 @ id)) != X314) | ! [X324 : (subst > term > subst > $o),X323 : term] : (? [X333 : term,X330 : subst,X331 : subst,X332 : subst] : (($true != ((X324 @ X331 @ X333 @ (comp @ X330 @ X332)))) & ($true = ((X324 @ (comp @ X331 @ X330) @ (sub @ X333 @ X330) @ X332)))) | (((X324 @ id @ (lam @ X323) @ id)) = $true) | (((sP56 @ X324)) = $true) | ? [X327 : subst,X326 : subst,X328 : term,X325 : subst] : ((((X324 @ X327 @ X328 @ (comp @ X326 @ X325))) = $true) & ($true != ((X324 @ (comp @ X327 @ X326) @ (sub @ X328 @ X326) @ X325)))) | ? [X329 : term] : ((((X324 @ id @ (sub @ X323 @ (push @ X329 @ id)) @ id)) != $true) & (((X324 @ id @ X329 @ id)) = $true))) | ($true = sP57))),
% 2.11/0.57 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.11/0.57 thf(f72,plain,(
% 2.11/0.57 ((hoasinduction_lem3_lthm = $true) <=> (sP58 = $true)) & ((hoasinduction = $true) <=> (sP55 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP52 = $true)) & ((hoasinduction_lthm = $true) <=> (sP50 = $true)) & ((axidl = $true) <=> ! [X127 : subst] : (((comp @ id @ X127)) = X127)) & (hoasinduction_lem1_gthm = $true) & ((substmonoid = $true) <=> (! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485))) & ((axshiftcons = $true) <=> ! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) <=> (axscons = $true)) & (termmset_gthm = $true) & ! [X50 : d_term,X49 : d_term] : ((X49 = X50) | (((d2term @ X50)) != ((d2term @ X49)))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X90 : (term > $o),X92 : subst,X91 : term] : ? [X93 : (term > $o)] : ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94)))) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) != X507) | ! [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) = $true) | ($true != ((X509 @ X511))) | ? [X512 : term] : (((X508 @ X512)) != ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))))) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP41)) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) <=> (sP36 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP34 = $true) <=> (hoasinduction_lem3v2a_lthm = $true)) & (axvarshift = $true) & ((shinj = $true) <=> ! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh))))) & ((hoasapinj2 = $true) <=> ! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466))))) & (($true = sP33) <=> (hoasinduction_lem3a = $true)) & ((pushprop_lem1_lthm = $true) <=> (? [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) != X514) | ? [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) != X515) | ! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true)))) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) <=> (sP32 = $true)) & ! [X195 : d_term] : (d_one = X195) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((apinj1 = $true) <=> ! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503))))) & (hoaslamnotap_gthm = $true) & ((sP28 = $true) <=> (hoasinduction_lthm_3 = $true)) & (! [X9 : (subst > term > subst > $o)] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1v2_gthm = $true) & ((sP22 = $true) <=> (hoasinduction_lem3aaa = $true)) & ((sP21 = $true) <=> (hoaslaminj_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (? [X499 : term] : (((X498 @ X499)) != ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X496 @ X497)) != $true) | (((X498 @ one)) = $true)) <=> (pushprop_lem1v2 = $true)) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) <=> (laminj = $true)) & ((sP20 = $true) <=> (hoasinduction_lem3v2 = $true)) & ((! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72)))) | ? [X66 : term] : (((sub @ X66 @ id)) != X66) | ? [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 != X69) & (((ap @ X68 @ X70)) = ((ap @ X69 @ X67))))) <=> (hoasapinj1_lthm = $true)) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1 = $true) <=> ! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true))) & (pushprop_lthm = $true) & (lamnotap != $true) & ((hoasapinj2_lthm = $true) <=> (! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35)) | ? [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) = ((ap @ X30 @ X29))) & (X28 != X29)))) & (hoasapinj1_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) != ((d2subst @ X409))) | (X408 = X409)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) <=> (apinj2 = $true)) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((substmonoid_lthm = $true) <=> ((! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407)) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404))) & (($true = sP18) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP14 = $true)) & (($true = sP12) <=> (hoasinduction_lem2v2 = $true)) & ((hoaslamnotap = $true) <=> ! [X534 : term,X536 : (subst > term > term),X535 : term] : (? [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) != ((sub @ (X536 @ X538 @ X539) @ X537))) | (((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535))))) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & (($true = sP10) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem2v2_gthm = $true) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) <=> (axvarcons = $true)) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & ((? [X0 : term] : (((sub @ X0 @ id)) != X0) | ! [X1 : term] : (((sub @ X1 @ id)) = X1)) <=> (termmset_lthm = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoasinduction_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) <=> ! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441))) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X166 : term] : ? [X167 : (subst > term > term)] : (((X167 @ sh @ one)) = ((sub @ X166 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X469 : term] : ? [X470 : (subst > term > term)] : (((X470 @ sh @ one)) = ((sub @ X469 @ (push @ one @ sh))))) & ((hoasinduction_lem2 = $true) <=> (sP9 = $true)) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & (! [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ? [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) != ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | ? [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) != ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) <=> (hoaslaminj = $true)) & ((induction2 = $true) <=> ($true = sP7)) & (! [X178 : (term > $o),X180 : subst,X179 : term] : ? [X181 : (term > $o)] : ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))) <=> (pushprop_lem0_lthm = $true)) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X4 : term] : ? [X5 : (subst > term > term)] : ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7))))) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (! [X477 : (subst > term > subst > $o),X476 : term] : (($true = ((X477 @ id @ X476 @ id))) | ? [X480 : (subst > term > term)] : (! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))) | (((sP5 @ X477)) = $true)) <=> (hoasinduction_no_psi_cond = $true)) & ((sP4 = $true) <=> (induction2lem = $true)) & (hoaslaminj_gthm = $true) & ((axidr = $true) <=> ! [X532 : subst] : (((comp @ X532 @ id)) = X532)) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axassoc = $true) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) <=> (termmset = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (! [X461 : term] : ? [X462 : (subst > term > term)] : ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) <=> (axvarid = $true)) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) <=> (sP2 = $true)) & ! [X96 : d_subst] : (d_id = X96) & (! [X196 : term,X197 : (term > $o)] : (? [X199 : term] : ((((var @ X199)) = $true) & (((X197 @ X199)) != $true)) | ($true = ((X197 @ X196))) | ? [X198 : term] : ((((X197 @ (lam @ X198))) != $true) & ($true = ((X197 @ X198)))) | (((sP1 @ X197)) = $true)) <=> (induction = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X128 : (subst > term > subst > $o)] : ? [X129 : (term > $o)] : ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130)))) & ((sP0 = $true) <=> (hoasinduction_lem3aa = $true))),
% 2.11/0.57 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 2.11/0.57 thf(f260,plain,(
% 2.11/0.57 (((hoasinduction_lem3_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3_lthm != $true))) & (((hoasinduction = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a_lthm != $true))) & (((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true))) & (((axidl = $true) | ? [X127 : subst] : (((comp @ id @ X127)) != X127)) & (! [X127 : subst] : (((comp @ id @ X127)) = X127) | (axidl != $true))) & (hoasinduction_lem1_gthm = $true) & (((substmonoid = $true) | (? [X486 : subst] : (((comp @ id @ X486)) != X486) | ? [X485 : subst] : (((comp @ X485 @ id)) != X485))) & ((! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485)) | (substmonoid != $true))) & (((axshiftcons = $true) | ? [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) != X241)) & (! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241) | (axshiftcons != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) | (axscons != $true)) & ((axscons = $true) | ? [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) != X8))) & (termmset_gthm = $true) & ! [X50 : d_term,X49 : d_term] : ((X49 = X50) | (((d2term @ X50)) != ((d2term @ X49)))) & (hoasinduction_lem2_gthm = $true) & (((pushprop_lem0 = $true) | ? [X90 : (term > $o),X92 : subst,X91 : term] : ! [X93 : (term > $o)] : ? [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) != ((X93 @ X94)))) & (! [X90 : (term > $o),X92 : subst,X91 : term] : ? [X93 : (term > $o)] : ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94))) | (pushprop_lem0 != $true))) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) = X507) & ? [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) != $true) & ($true = ((X509 @ X511))) & ! [X512 : term] : (((X508 @ X512)) = ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))))) & ((? [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) != X507) | ! [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) = $true) | ($true != ((X509 @ X511))) | ? [X512 : term] : (((X508 @ X512)) != ((X509 @ (sub @ X512 @ (push @ X511 @ X510))))))) | (pushprop_lem1v2_lthm != $true))) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_no_psi_cond_lthm != $true))) & (induction2_gthm = $true) & (((hoasinduction_lem3 = $true) | (sP36 != $true)) & ((sP36 = $true) | (hoasinduction_lem3 != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true))) & (axvarshift = $true) & (((shinj = $true) | ? [X221 : term,X220 : term] : ((X220 != X221) & (((sub @ X220 @ sh)) = ((sub @ X221 @ sh))))) & (! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh)))) | (shinj != $true))) & (((hoasapinj2 = $true) | ? [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 != X466) & (((ap @ (sub @ X467 @ id) @ X465)) = ((ap @ (sub @ X468 @ id) @ X466))))) & (! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466)))) | (hoasapinj2 != $true))) & ((($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33))) & (((pushprop_lem1_lthm = $true) | (! [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) = X514) & ! [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) = X515) & ? [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true != ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) & (((X521 @ X520)) = $true)))) & ((? [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) != X514) | ? [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) != X515) | ! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true))) | (pushprop_lem1_lthm != $true))) & (ulamvarsh = $true) & (((induction2lem_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem_lthm != $true))) & ! [X195 : d_term] : (d_one = X195) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((apinj1 = $true) | ? [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 != X502) & (((ap @ X502 @ X501)) = ((ap @ X500 @ X503))))) & (! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503)))) | (apinj1 != $true))) & (hoaslamnotap_gthm = $true) & (((sP28 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP28 != $true))) & ((! [X9 : (subst > term > subst > $o)] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X9 : (subst > term > subst > $o)] : ! [X10 : (term > $o)] : ? [X11 : term] : (((X9 @ id @ X11 @ id)) != ((X10 @ X11))))) & (pushprop_lem1v2_gthm = $true) & (((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true))) & (((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true))) & (hoasinduction_lem3v2_gthm = $true) & ((! [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (? [X499 : term] : (((X498 @ X499)) != ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X496 @ X497)) != $true) | (((X498 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (! [X499 : term] : (((X498 @ X499)) = ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) & (((X496 @ X497)) = $true) & (((X498 @ one)) != $true)))) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ((! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) | (laminj != $true)) & ((laminj = $true) | ? [X219 : term,X218 : term] : ((((lam @ X219)) = ((lam @ X218))) & (X218 != X219)))) & (((sP20 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP20 != $true))) & (((! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72)))) | ? [X66 : term] : (((sub @ X66 @ id)) != X66) | ? [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 != X69) & (((ap @ X68 @ X70)) = ((ap @ X69 @ X67))))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 != X74) & (((ap @ (sub @ X74 @ id) @ X71)) = ((ap @ (sub @ X73 @ id) @ X72)))) & ! [X66 : term] : (((sub @ X66 @ id)) = X66) & ! [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 = X69) | (((ap @ X68 @ X70)) != ((ap @ X69 @ X67))))))) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & (((pushprop_lem1 = $true) | ? [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) = $true) & (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) != $true))) & (! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true)) | (pushprop_lem1 != $true))) & (pushprop_lthm = $true) & (lamnotap != $true) & (((hoasapinj2_lthm = $true) | (? [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) = ((ap @ (sub @ X33 @ id) @ X32))) & (X32 != X35)) & ! [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)))) & ((! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35)) | ? [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) = ((ap @ X30 @ X29))) & (X28 != X29))) | (hoasapinj2_lthm != $true))) & (hoasapinj1_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) != ((d2subst @ X409))) | (X408 = X409)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & ((! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) = ((ap @ X115 @ X117))) & (X116 != X117)))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & (((substmonoid_lthm = $true) | ((? [X406 : subst] : (((comp @ X406 @ id)) != X406) | ? [X407 : subst] : (((comp @ id @ X407)) != X407)) & ! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & (((! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407)) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404)) | (substmonoid_lthm != $true))) & ((($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18))) & (((hoasinduction_lem3v2_lthm = $true) | (sP14 != $true)) & ((sP14 = $true) | (hoasinduction_lem3v2_lthm != $true))) & ((($true = sP12) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP12))) & (((hoaslamnotap = $true) | ? [X534 : term,X536 : (subst > term > term),X535 : term] : (! [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) = ((sub @ (X536 @ X538 @ X539) @ X537))) & (((lam @ (X536 @ sh @ one))) = ((ap @ (sub @ X534 @ id) @ X535))))) & (! [X534 : term,X536 : (subst > term > term),X535 : term] : (? [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) != ((sub @ (X536 @ X538 @ X539) @ X537))) | (((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535)))) | (hoaslamnotap != $true))) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & ((($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10))) & (hoasinduction_lem2v2_gthm = $true) & ((! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) != X3))) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & (((? [X0 : term] : (((sub @ X0 @ id)) != X0) | ! [X1 : term] : (((sub @ X1 @ id)) = X1)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X0 : term] : (((sub @ X0 @ id)) = X0) & ? [X1 : term] : (((sub @ X1 @ id)) != X1)))) & (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_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (((hoasapinj1 = $true) | ? [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) = ((ap @ (sub @ X441 @ id) @ X442))) & (X440 != X441))) & (! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441)) | (hoasapinj1 != $true))) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & ((! [X166 : term] : ? [X167 : (subst > term > term)] : (((X167 @ sh @ one)) = ((sub @ X166 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X166 : term] : ! [X167 : (subst > term > term)] : (((X167 @ sh @ one)) != ((sub @ X166 @ (push @ one @ sh)))))) & (hoasinduction_lem3_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X469 : term] : ! [X470 : (subst > term > term)] : (((X470 @ sh @ one)) != ((sub @ X469 @ (push @ one @ sh))))) & (! [X469 : term] : ? [X470 : (subst > term > term)] : (((X470 @ sh @ one)) = ((sub @ X469 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & (((hoasinduction_lem2 = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem2 != $true))) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & ((! [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ? [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) != ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | ? [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) != ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) != ((X523 @ X522 @ X524))) & (((lam @ (X523 @ sh @ one))) = ((lam @ (X525 @ sh @ one)))) & ! [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) = ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) & ! [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) = ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))))) & (((induction2 = $true) | ($true != sP7)) & (($true = sP7) | (induction2 != $true))) & ((! [X178 : (term > $o),X180 : subst,X179 : term] : ? [X181 : (term > $o)] : ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X178 : (term > $o),X180 : subst,X179 : term] : ! [X181 : (term > $o)] : ? [X182 : term] : (((X181 @ X182)) != ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))))) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X4 : term] : ! [X5 : (subst > term > term)] : ? [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) != ((sub @ X4 @ (push @ X6 @ X7))))) & (! [X4 : term] : ? [X5 : (subst > term > term)] : ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7)))) | (hoasinduction_lem3v2_f != $true))) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & ((! [X477 : (subst > term > subst > $o),X476 : term] : (($true = ((X477 @ id @ X476 @ id))) | ? [X480 : (subst > term > term)] : (! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))) | (((sP5 @ X477)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X477 : (subst > term > subst > $o),X476 : term] : (($true != ((X477 @ id @ X476 @ id))) & ! [X480 : (subst > term > term)] : (? [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) != ((sub @ (X480 @ X483 @ X484) @ X482))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ? [X481 : term] : ((((X477 @ id @ X481 @ id)) = $true) & ($true != ((X477 @ id @ (X480 @ id @ X481) @ id))))) & (((sP5 @ X477)) != $true)))) & (((sP4 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP4 != $true))) & (hoaslaminj_gthm = $true) & (((axidr = $true) | ? [X532 : subst] : (((comp @ X532 @ id)) != X532)) & (! [X532 : subst] : (((comp @ X532 @ id)) = X532) | (axidr != $true))) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axassoc = $true) & ((! [X533 : term] : (((sub @ X533 @ id)) = X533) | (termmset != $true)) & ((termmset = $true) | ? [X533 : term] : (((sub @ X533 @ id)) != X533))) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & ((! [X461 : term] : ? [X462 : (subst > term > term)] : ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X461 : term] : ! [X462 : (subst > term > term)] : ? [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) != ((sub @ X461 @ (push @ X463 @ X464)))))) & ((! [X95 : term] : (((sub @ X95 @ id)) = X95) | (axvarid != $true)) & ((axvarid = $true) | ? [X95 : term] : (((sub @ X95 @ id)) != X95))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & (((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true))) & ! [X96 : d_subst] : (d_id = X96) & ((! [X196 : term,X197 : (term > $o)] : (? [X199 : term] : ((((var @ X199)) = $true) & (((X197 @ X199)) != $true)) | ($true = ((X197 @ X196))) | ? [X198 : term] : ((((X197 @ (lam @ X198))) != $true) & ($true = ((X197 @ X198)))) | (((sP1 @ X197)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X196 : term,X197 : (term > $o)] : (! [X199 : term] : ((((var @ X199)) != $true) | (((X197 @ X199)) = $true)) & ($true != ((X197 @ X196))) & ! [X198 : term] : ((((X197 @ (lam @ X198))) = $true) | ($true != ((X197 @ X198)))) & (((sP1 @ X197)) != $true)))) & (((hoasinduction_lem0_lthm = $true) | ? [X128 : (subst > term > subst > $o)] : ! [X129 : (term > $o)] : ? [X130 : term] : (((X128 @ id @ X130 @ id)) != ((X129 @ X130)))) & (! [X128 : (subst > term > subst > $o)] : ? [X129 : (term > $o)] : ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130))) | (hoasinduction_lem0_lthm != $true))) & (((sP0 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP0 != $true)))),
% 2.11/0.57 inference(nnf_transformation,[],[f72])).
% 2.11/0.57 thf(f261,plain,(
% 2.11/0.57 ((hoasinduction_lem3_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((axidl = $true) | ? [X127 : subst] : (((comp @ id @ X127)) != X127)) & (! [X127 : subst] : (((comp @ id @ X127)) = X127) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & ((substmonoid = $true) | ? [X486 : subst] : (((comp @ id @ X486)) != X486) | ? [X485 : subst] : (((comp @ X485 @ id)) != X485)) & ((! [X486 : subst] : (((comp @ id @ X486)) = X486) & ! [X485 : subst] : (((comp @ X485 @ id)) = X485)) | (substmonoid != $true)) & ((axshiftcons = $true) | ? [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) != X241)) & (! [X241 : subst,X240 : term] : (((comp @ sh @ (push @ X240 @ X241))) = X241) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) = X8) | (axscons != $true)) & ((axscons = $true) | ? [X8 : subst] : (((push @ (sub @ one @ X8) @ (comp @ sh @ X8))) != X8)) & (termmset_gthm = $true) & ! [X50 : d_term,X49 : d_term] : ((X49 = X50) | (((d2term @ X50)) != ((d2term @ X49)))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) | ? [X90 : (term > $o),X92 : subst,X91 : term] : ! [X93 : (term > $o)] : ? [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) != ((X93 @ X94)))) & (! [X90 : (term > $o),X92 : subst,X91 : term] : ? [X93 : (term > $o)] : ! [X94 : term] : (((X90 @ (sub @ X94 @ (push @ X91 @ X92)))) = ((X93 @ X94))) | (pushprop_lem0 != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) = X507) & ? [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) != $true) & ($true = ((X509 @ X511))) & ! [X512 : term] : (((X508 @ X512)) = ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))))) & (? [X506 : subst,X507 : term] : (((sub @ one @ (push @ X507 @ X506))) != X507) | ! [X510 : subst,X511 : term,X508 : (term > $o),X509 : (term > $o)] : ((((X508 @ one)) = $true) | ($true != ((X509 @ X511))) | ? [X512 : term] : (((X508 @ X512)) != ((X509 @ (sub @ X512 @ (push @ X511 @ X510)))))) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP36 != $true)) & ((sP36 = $true) | (hoasinduction_lem3 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (axvarshift = $true) & ((shinj = $true) | ? [X221 : term,X220 : term] : ((X220 != X221) & (((sub @ X220 @ sh)) = ((sub @ X221 @ sh))))) & (! [X221 : term,X220 : term] : ((X220 = X221) | (((sub @ X220 @ sh)) != ((sub @ X221 @ sh)))) | (shinj != $true)) & ((hoasapinj2 = $true) | ? [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 != X466) & (((ap @ (sub @ X467 @ id) @ X465)) = ((ap @ (sub @ X468 @ id) @ X466))))) & (! [X467 : term,X466 : term,X468 : term,X465 : term] : ((X465 = X466) | (((ap @ (sub @ X467 @ id) @ X465)) != ((ap @ (sub @ X468 @ id) @ X466)))) | (hoasapinj2 != $true)) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & ((pushprop_lem1_lthm = $true) | (! [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) = X514) & ! [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) = X515) & ? [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true != ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) & (((X521 @ X520)) = $true)))) & (? [X514 : term,X513 : subst] : (((sub @ one @ (push @ X514 @ X513))) != X514) | ? [X515 : subst,X516 : term] : (((comp @ sh @ (push @ X516 @ X515))) != X515) | ! [X520 : term,X517 : subst,X521 : (term > $o),X519 : (term > $o),X518 : term] : (($true = ((X519 @ (sub @ X520 @ (push @ X518 @ X517))))) | (((X521 @ X520)) != $true)) | (pushprop_lem1_lthm != $true)) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem_lthm != $true)) & ! [X195 : d_term] : (d_one = X195) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((apinj1 = $true) | ? [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 != X502) & (((ap @ X502 @ X501)) = ((ap @ X500 @ X503))))) & (! [X500 : term,X501 : term,X503 : term,X502 : term] : ((X500 = X502) | (((ap @ X502 @ X501)) != ((ap @ X500 @ X503)))) | (apinj1 != $true)) & (hoaslamnotap_gthm = $true) & ((sP28 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP28 != $true)) & (! [X9 : (subst > term > subst > $o)] : ? [X10 : (term > $o)] : ! [X11 : term] : (((X9 @ id @ X11 @ id)) = ((X10 @ X11))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X9 : (subst > term > subst > $o)] : ! [X10 : (term > $o)] : ? [X11 : term] : (((X9 @ id @ X11 @ id)) != ((X10 @ X11)))) & (pushprop_lem1v2_gthm = $true) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (? [X499 : term] : (((X498 @ X499)) != ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) | (((X496 @ X497)) != $true) | (((X498 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X495 : subst,X497 : term,X498 : (term > $o),X496 : (term > $o)] : (! [X499 : term] : (((X498 @ X499)) = ((X496 @ (sub @ X499 @ (push @ X497 @ X495))))) & (((X496 @ X497)) = $true) & (((X498 @ one)) != $true))) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X219 : term,X218 : term] : ((((lam @ X219)) != ((lam @ X218))) | (X218 = X219)) | (laminj != $true)) & ((laminj = $true) | ? [X219 : term,X218 : term] : ((((lam @ X219)) = ((lam @ X218))) & (X218 != X219))) & ((sP20 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP20 != $true)) & (! [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 = X74) | (((ap @ (sub @ X74 @ id) @ X71)) != ((ap @ (sub @ X73 @ id) @ X72)))) | ? [X66 : term] : (((sub @ X66 @ id)) != X66) | ? [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 != X69) & (((ap @ X68 @ X70)) = ((ap @ X69 @ X67)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X72 : term,X71 : term,X74 : term,X73 : term] : ((X73 != X74) & (((ap @ (sub @ X74 @ id) @ X71)) = ((ap @ (sub @ X73 @ id) @ X72)))) & ! [X66 : term] : (((sub @ X66 @ id)) = X66) & ! [X70 : term,X68 : term,X69 : term,X67 : term] : ((X68 = X69) | (((ap @ X68 @ X70)) != ((ap @ X69 @ X67)))))) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1 = $true) | ? [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) = $true) & (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) != $true))) & (! [X475 : subst,X473 : (term > $o),X472 : term,X471 : term,X474 : (term > $o)] : ((((X474 @ X472)) != $true) | (((X473 @ (sub @ X472 @ (push @ X471 @ X475)))) = $true)) | (pushprop_lem1 != $true)) & (pushprop_lthm = $true) & (lamnotap != $true) & ((hoasapinj2_lthm = $true) | (? [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) = ((ap @ (sub @ X33 @ id) @ X32))) & (X32 != X35)) & ! [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) != ((ap @ X30 @ X29))) | (X28 = X29)))) & (! [X35 : term,X32 : term,X33 : term,X34 : term] : ((((ap @ (sub @ X34 @ id) @ X35)) != ((ap @ (sub @ X33 @ id) @ X32))) | (X32 = X35)) | ? [X30 : term,X31 : term,X29 : term,X28 : term] : ((((ap @ X31 @ X28)) = ((ap @ X30 @ X29))) & (X28 != X29)) | (hoasapinj2_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X408 : d_subst,X409 : d_subst] : ((((d2subst @ X408)) != ((d2subst @ X409))) | (X408 = X409)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & (! [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) != ((ap @ X115 @ X117))) | (X116 = X117)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X118 : term,X115 : term,X117 : term,X116 : term] : ((((ap @ X118 @ X116)) = ((ap @ X115 @ X117))) & (X116 != X117))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((substmonoid_lthm = $true) | ((? [X406 : subst] : (((comp @ X406 @ id)) != X406) | ? [X407 : subst] : (((comp @ id @ X407)) != X407)) & ! [X405 : subst] : (((comp @ X405 @ id)) = X405) & ! [X404 : subst] : (((comp @ id @ X404)) = X404))) & ((! [X406 : subst] : (((comp @ X406 @ id)) = X406) & ! [X407 : subst] : (((comp @ id @ X407)) = X407)) | ? [X405 : subst] : (((comp @ X405 @ id)) != X405) | ? [X404 : subst] : (((comp @ id @ X404)) != X404) | (substmonoid_lthm != $true)) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & ((hoasinduction_lem3v2_lthm = $true) | (sP14 != $true)) & ((sP14 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP12) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP12)) & ((hoaslamnotap = $true) | ? [X534 : term,X536 : (subst > term > term),X535 : term] : (! [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) = ((sub @ (X536 @ X538 @ X539) @ X537))) & (((lam @ (X536 @ sh @ one))) = ((ap @ (sub @ X534 @ id) @ X535))))) & (! [X534 : term,X536 : (subst > term > term),X535 : term] : (? [X539 : term,X538 : subst,X537 : subst] : (((X536 @ (comp @ X538 @ X537) @ (sub @ X539 @ X537))) != ((sub @ (X536 @ X538 @ X539) @ X537))) | (((lam @ (X536 @ sh @ one))) != ((ap @ (sub @ X534 @ id) @ X535)))) | (hoaslamnotap != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & (hoasinduction_lem2v2_gthm = $true) & (! [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) = X3) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X2 : subst,X3 : term] : (((sub @ one @ (push @ X3 @ X2))) != X3)) & ! [X504 : subst] : ? [X505 : d_subst] : (((d2subst @ X505)) = X504) & (? [X0 : term] : (((sub @ X0 @ id)) != X0) | ! [X1 : term] : (((sub @ X1 @ id)) = X1) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X0 : term] : (((sub @ X0 @ id)) = X0) & ? [X1 : term] : (((sub @ X1 @ id)) != X1))) & (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_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ? [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) = ((ap @ (sub @ X441 @ id) @ X442))) & (X440 != X441))) & (! [X441 : term,X442 : term,X440 : term,X443 : term] : ((((ap @ (sub @ X440 @ id) @ X443)) != ((ap @ (sub @ X441 @ id) @ X442))) | (X440 = X441)) | (hoasapinj1 != $true)) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X166 : term] : ? [X167 : (subst > term > term)] : (((X167 @ sh @ one)) = ((sub @ X166 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X166 : term] : ! [X167 : (subst > term > term)] : (((X167 @ sh @ one)) != ((sub @ X166 @ (push @ one @ sh))))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X469 : term] : ! [X470 : (subst > term > term)] : (((X470 @ sh @ one)) != ((sub @ X469 @ (push @ one @ sh))))) & (! [X469 : term] : ? [X470 : (subst > term > term)] : (((X470 @ sh @ one)) = ((sub @ X469 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem2 = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem2 != $true)) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & (! [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) = ((X523 @ X522 @ X524))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X525 @ sh @ one)))) | ? [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) != ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) | ? [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) != ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : subst,X524 : term,X523 : (subst > term > term),X525 : (subst > term > term)] : ((((X525 @ X522 @ X524)) != ((X523 @ X522 @ X524))) & (((lam @ (X523 @ sh @ one))) = ((lam @ (X525 @ sh @ one)))) & ! [X528 : term,X526 : subst,X527 : subst] : (((sub @ (X525 @ X526 @ X528) @ X527)) = ((X525 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527)))) & ! [X530 : term,X529 : subst,X531 : subst] : (((sub @ (X523 @ X531 @ X530) @ X529)) = ((X523 @ (comp @ X531 @ X529) @ (sub @ X530 @ X529)))))) & ((induction2 = $true) | ($true != sP7)) & (($true = sP7) | (induction2 != $true)) & (! [X178 : (term > $o),X180 : subst,X179 : term] : ? [X181 : (term > $o)] : ! [X182 : term] : (((X181 @ X182)) = ((X178 @ (sub @ X182 @ (push @ X179 @ X180))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X178 : (term > $o),X180 : subst,X179 : term] : ! [X181 : (term > $o)] : ? [X182 : term] : (((X181 @ X182)) != ((X178 @ (sub @ X182 @ (push @ X179 @ X180)))))) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X4 : term] : ! [X5 : (subst > term > term)] : ? [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) != ((sub @ X4 @ (push @ X6 @ X7))))) & (! [X4 : term] : ? [X5 : (subst > term > term)] : ! [X6 : term,X7 : subst] : (((X5 @ X7 @ X6)) = ((sub @ X4 @ (push @ X6 @ X7)))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (! [X477 : (subst > term > subst > $o),X476 : term] : (($true = ((X477 @ id @ X476 @ id))) | ? [X480 : (subst > term > term)] : (! [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) = ((sub @ (X480 @ X483 @ X484) @ X482))) & ($true != ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) & ! [X481 : term] : ((((X477 @ id @ X481 @ id)) != $true) | ($true = ((X477 @ id @ (X480 @ id @ X481) @ id))))) | (((sP5 @ X477)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X477 : (subst > term > subst > $o),X476 : term] : (($true != ((X477 @ id @ X476 @ id))) & ! [X480 : (subst > term > term)] : (? [X483 : subst,X482 : subst,X484 : term] : (((X480 @ (comp @ X483 @ X482) @ (sub @ X484 @ X482))) != ((sub @ (X480 @ X483 @ X484) @ X482))) | ($true = ((X477 @ id @ (lam @ (X480 @ sh @ one)) @ id))) | ? [X481 : term] : ((((X477 @ id @ X481 @ id)) = $true) & ($true != ((X477 @ id @ (X480 @ id @ X481) @ id))))) & (((sP5 @ X477)) != $true))) & ((sP4 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP4 != $true)) & (hoaslaminj_gthm = $true) & ((axidr = $true) | ? [X532 : subst] : (((comp @ X532 @ id)) != X532)) & (! [X532 : subst] : (((comp @ X532 @ id)) = X532) | (axidr != $true)) & ! [X304 : term] : ? [X305 : d_term] : (((d2term @ X305)) = X304) & (axassoc = $true) & (! [X533 : term] : (((sub @ X533 @ id)) = X533) | (termmset != $true)) & ((termmset = $true) | ? [X533 : term] : (((sub @ X533 @ id)) != X533)) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (! [X461 : term] : ? [X462 : (subst > term > term)] : ! [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) = ((sub @ X461 @ (push @ X463 @ X464)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X461 : term] : ! [X462 : (subst > term > term)] : ? [X464 : subst,X463 : term] : (((X462 @ X464 @ X463)) != ((sub @ X461 @ (push @ X463 @ X464))))) & (! [X95 : term] : (((sub @ X95 @ id)) = X95) | (axvarid != $true)) & ((axvarid = $true) | ? [X95 : term] : (((sub @ X95 @ id)) != X95)) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X96 : d_subst] : (d_id = X96) & (! [X196 : term,X197 : (term > $o)] : (? [X199 : term] : ((((var @ X199)) = $true) & (((X197 @ X199)) != $true)) | ($true = ((X197 @ X196))) | ? [X198 : term] : ((((X197 @ (lam @ X198))) != $true) & ($true = ((X197 @ X198)))) | (((sP1 @ X197)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X196 : term,X197 : (term > $o)] : (! [X199 : term] : ((((var @ X199)) != $true) | (((X197 @ X199)) = $true)) & ($true != ((X197 @ X196))) & ! [X198 : term] : ((((X197 @ (lam @ X198))) = $true) | ($true != ((X197 @ X198)))) & (((sP1 @ X197)) != $true))) & ((hoasinduction_lem0_lthm = $true) | ? [X128 : (subst > term > subst > $o)] : ! [X129 : (term > $o)] : ? [X130 : term] : (((X128 @ id @ X130 @ id)) != ((X129 @ X130)))) & (! [X128 : (subst > term > subst > $o)] : ? [X129 : (term > $o)] : ! [X130 : term] : (((X128 @ id @ X130 @ id)) = ((X129 @ X130))) | (hoasinduction_lem0_lthm != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP0 != $true))),
% 2.11/0.57 inference(flattening,[],[f260])).
% 2.11/0.57 thf(f262,plain,(
% 2.11/0.57 ((hoasinduction_lem3_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((axidl = $true) | ? [X0 : subst] : (((comp @ id @ X0)) != X0)) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & ((substmonoid = $true) | ? [X2 : subst] : (((comp @ id @ X2)) != X2) | ? [X3 : subst] : (((comp @ X3 @ id)) != X3)) & ((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X5 : subst] : (((comp @ X5 @ id)) = X5)) | (substmonoid != $true)) & ((axshiftcons = $true) | ? [X6 : subst,X7 : term] : (((comp @ sh @ (push @ X7 @ X6))) != X6)) & (! [X8 : subst,X9 : term] : (((comp @ sh @ (push @ X9 @ X8))) = X8) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X10 : subst] : (((push @ (sub @ one @ X10) @ (comp @ sh @ X10))) = X10) | (axscons != $true)) & ((axscons = $true) | ? [X11 : subst] : (((push @ (sub @ one @ X11) @ (comp @ sh @ X11))) != X11)) & (termmset_gthm = $true) & ! [X12 : d_term,X13 : d_term] : ((X12 = X13) | (((d2term @ X12)) != ((d2term @ X13)))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) | ? [X14 : (term > $o),X15 : subst,X16 : term] : ! [X17 : (term > $o)] : ? [X18 : term] : (((X17 @ X18)) != ((X14 @ (sub @ X18 @ (push @ X16 @ X15)))))) & (! [X19 : (term > $o),X20 : subst,X21 : term] : ? [X22 : (term > $o)] : ! [X23 : term] : (((X22 @ X23)) = ((X19 @ (sub @ X23 @ (push @ X21 @ X20))))) | (pushprop_lem0 != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X24 : subst,X25 : term] : (((sub @ one @ (push @ X25 @ X24))) = X25) & ? [X26 : subst,X27 : term,X28 : (term > $o),X29 : (term > $o)] : (($true != ((X28 @ one))) & ($true = ((X29 @ X27))) & ! [X30 : term] : (((X28 @ X30)) = ((X29 @ (sub @ X30 @ (push @ X27 @ X26)))))))) & (? [X31 : subst,X32 : term] : (((sub @ one @ (push @ X32 @ X31))) != X32) | ! [X33 : subst,X34 : term,X35 : (term > $o),X36 : (term > $o)] : (($true = ((X35 @ one))) | (((X36 @ X34)) != $true) | ? [X37 : term] : (((X36 @ (sub @ X37 @ (push @ X34 @ X33)))) != ((X35 @ X37)))) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP36 != $true)) & ((sP36 = $true) | (hoasinduction_lem3 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (axvarshift = $true) & ((shinj = $true) | ? [X38 : term,X39 : term] : ((X38 != X39) & (((sub @ X39 @ sh)) = ((sub @ X38 @ sh))))) & (! [X40 : term,X41 : term] : ((X40 = X41) | (((sub @ X41 @ sh)) != ((sub @ X40 @ sh)))) | (shinj != $true)) & ((hoasapinj2 = $true) | ? [X42 : term,X43 : term,X44 : term,X45 : term] : ((X43 != X45) & (((ap @ (sub @ X42 @ id) @ X45)) = ((ap @ (sub @ X44 @ id) @ X43))))) & (! [X46 : term,X47 : term,X48 : term,X49 : term] : ((X47 = X49) | (((ap @ (sub @ X48 @ id) @ X47)) != ((ap @ (sub @ X46 @ id) @ X49)))) | (hoasapinj2 != $true)) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & ((pushprop_lem1_lthm = $true) | (! [X50 : term,X51 : subst] : (((sub @ one @ (push @ X50 @ X51))) = X50) & ! [X52 : subst,X53 : term] : (((comp @ sh @ (push @ X53 @ X52))) = X52) & ? [X54 : term,X55 : subst,X56 : (term > $o),X57 : (term > $o),X58 : term] : (($true != ((X57 @ (sub @ X54 @ (push @ X58 @ X55))))) & ($true = ((X56 @ X54)))))) & (? [X59 : term,X60 : subst] : (((sub @ one @ (push @ X59 @ X60))) != X59) | ? [X61 : subst,X62 : term] : (((comp @ sh @ (push @ X62 @ X61))) != X61) | ! [X63 : term,X64 : subst,X65 : (term > $o),X66 : (term > $o),X67 : term] : ((((X66 @ (sub @ X63 @ (push @ X67 @ X64)))) = $true) | (((X65 @ X63)) != $true)) | (pushprop_lem1_lthm != $true)) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem_lthm != $true)) & ! [X68 : d_term] : (d_one = X68) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((apinj1 = $true) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 != X72) & (((ap @ X69 @ X71)) = ((ap @ X72 @ X70))))) & (! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X76) | (((ap @ X76 @ X74)) != ((ap @ X73 @ X75)))) | (apinj1 != $true)) & (hoaslamnotap_gthm = $true) & ((sP28 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP28 != $true)) & (! [X77 : (subst > term > subst > $o)] : ? [X78 : (term > $o)] : ! [X79 : term] : (((X78 @ X79)) = ((X77 @ id @ X79 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X80 : (subst > term > subst > $o)] : ! [X81 : (term > $o)] : ? [X82 : term] : (((X80 @ id @ X82 @ id)) != ((X81 @ X82)))) & (pushprop_lem1v2_gthm = $true) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X83 : subst,X84 : term,X85 : (term > $o),X86 : (term > $o)] : (? [X87 : term] : (((X85 @ X87)) != ((X86 @ (sub @ X87 @ (push @ X84 @ X83))))) | ($true != ((X86 @ X84))) | (((X85 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X88 : subst,X89 : term,X90 : (term > $o),X91 : (term > $o)] : (! [X92 : term] : (((X91 @ (sub @ X92 @ (push @ X89 @ X88)))) = ((X90 @ X92))) & (((X91 @ X89)) = $true) & (((X90 @ one)) != $true))) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X93 : term,X94 : term] : ((((lam @ X93)) != ((lam @ X94))) | (X93 = X94)) | (laminj != $true)) & ((laminj = $true) | ? [X95 : term,X96 : term] : ((((lam @ X95)) = ((lam @ X96))) & (X95 != X96))) & ((sP20 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP20 != $true)) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X99 = X100) | (((ap @ (sub @ X99 @ id) @ X98)) != ((ap @ (sub @ X100 @ id) @ X97)))) | ? [X101 : term] : (((sub @ X101 @ id)) != X101) | ? [X102 : term,X103 : term,X104 : term,X105 : term] : ((X103 != X104) & (((ap @ X103 @ X102)) = ((ap @ X104 @ X105)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (? [X106 : term,X107 : term,X108 : term,X109 : term] : ((X108 != X109) & (((ap @ (sub @ X108 @ id) @ X107)) = ((ap @ (sub @ X109 @ id) @ X106)))) & ! [X110 : term] : (((sub @ X110 @ id)) = X110) & ! [X111 : term,X112 : term,X113 : term,X114 : term] : ((X112 = X113) | (((ap @ X113 @ X114)) != ((ap @ X112 @ X111)))))) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1 = $true) | ? [X115 : subst,X116 : (term > $o),X117 : term,X118 : term,X119 : (term > $o)] : ((((X119 @ X117)) = $true) & (((X116 @ (sub @ X117 @ (push @ X118 @ X115)))) != $true))) & (! [X120 : subst,X121 : (term > $o),X122 : term,X123 : term,X124 : (term > $o)] : ((((X124 @ X122)) != $true) | (((X121 @ (sub @ X122 @ (push @ X123 @ X120)))) = $true)) | (pushprop_lem1 != $true)) & (pushprop_lthm = $true) & (lamnotap != $true) & ((hoasapinj2_lthm = $true) | (? [X125 : term,X126 : term,X127 : term,X128 : term] : ((((ap @ (sub @ X128 @ id) @ X125)) = ((ap @ (sub @ X127 @ id) @ X126))) & (X125 != X126)) & ! [X129 : term,X130 : term,X131 : term,X132 : term] : ((((ap @ X129 @ X131)) != ((ap @ X130 @ X132))) | (X131 = X132)))) & (! [X133 : term,X134 : term,X135 : term,X136 : term] : ((((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X136 @ id) @ X133))) | (X133 = X134)) | ? [X137 : term,X138 : term,X139 : term,X140 : term] : ((((ap @ X138 @ X140)) = ((ap @ X137 @ X139))) & (X139 != X140)) | (hoasapinj2_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X141 : d_subst,X142 : d_subst] : ((((d2subst @ X141)) != ((d2subst @ X142))) | (X141 = X142)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & (! [X143 : term,X144 : term,X145 : term,X146 : term] : ((((ap @ X143 @ X146)) != ((ap @ X144 @ X145))) | (X145 = X146)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X147 : term,X148 : term,X149 : term,X150 : term] : ((((ap @ X148 @ X149)) = ((ap @ X147 @ X150))) & (X149 != X150))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((substmonoid_lthm = $true) | ((? [X151 : subst] : (((comp @ X151 @ id)) != X151) | ? [X152 : subst] : (((comp @ id @ X152)) != X152)) & ! [X153 : subst] : (((comp @ X153 @ id)) = X153) & ! [X154 : subst] : (((comp @ id @ X154)) = X154))) & ((! [X155 : subst] : (((comp @ X155 @ id)) = X155) & ! [X156 : subst] : (((comp @ id @ X156)) = X156)) | ? [X157 : subst] : (((comp @ X157 @ id)) != X157) | ? [X158 : subst] : (((comp @ id @ X158)) != X158) | (substmonoid_lthm != $true)) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & ((hoasinduction_lem3v2_lthm = $true) | (sP14 != $true)) & ((sP14 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP12) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP12)) & ((hoaslamnotap = $true) | ? [X159 : term,X160 : (subst > term > term),X161 : term] : (! [X162 : term,X163 : subst,X164 : subst] : (((X160 @ (comp @ X163 @ X164) @ (sub @ X162 @ X164))) = ((sub @ (X160 @ X163 @ X162) @ X164))) & (((ap @ (sub @ X159 @ id) @ X161)) = ((lam @ (X160 @ sh @ one)))))) & (! [X165 : term,X166 : (subst > term > term),X167 : term] : (? [X168 : term,X169 : subst,X170 : subst] : (((X166 @ (comp @ X169 @ X170) @ (sub @ X168 @ X170))) != ((sub @ (X166 @ X169 @ X168) @ X170))) | (((ap @ (sub @ X165 @ id) @ X167)) != ((lam @ (X166 @ sh @ one))))) | (hoaslamnotap != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & (hoasinduction_lem2v2_gthm = $true) & (! [X171 : subst,X172 : term] : (((sub @ one @ (push @ X172 @ X171))) = X172) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X173 : subst,X174 : term] : (((sub @ one @ (push @ X174 @ X173))) != X174)) & ! [X175 : subst] : ? [X176 : d_subst] : (((d2subst @ X176)) = X175) & (? [X177 : term] : (((sub @ X177 @ id)) != X177) | ! [X178 : term] : (((sub @ X178 @ id)) = X178) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X179 : term] : (((sub @ X179 @ id)) = X179) & ? [X180 : term] : (((sub @ X180 @ id)) != X180))) & (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_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ? [X181 : term,X182 : term,X183 : term,X184 : term] : ((((ap @ (sub @ X181 @ id) @ X182)) = ((ap @ (sub @ X183 @ id) @ X184))) & (X181 != X183))) & (! [X185 : term,X186 : term,X187 : term,X188 : term] : ((((ap @ (sub @ X187 @ id) @ X188)) != ((ap @ (sub @ X185 @ id) @ X186))) | (X185 = X187)) | (hoasapinj1 != $true)) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X189 : term] : ? [X190 : (subst > term > term)] : (((sub @ X189 @ (push @ one @ sh))) = ((X190 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X191 : term] : ! [X192 : (subst > term > term)] : (((X192 @ sh @ one)) != ((sub @ X191 @ (push @ one @ sh))))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X193 : term] : ! [X194 : (subst > term > term)] : (((sub @ X193 @ (push @ one @ sh))) != ((X194 @ sh @ one)))) & (! [X195 : term] : ? [X196 : (subst > term > term)] : (((X196 @ sh @ one)) = ((sub @ X195 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem2 = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem2 != $true)) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & (! [X197 : subst,X198 : term,X199 : (subst > term > term),X200 : (subst > term > term)] : ((((X200 @ X197 @ X198)) = ((X199 @ X197 @ X198))) | (((lam @ (X199 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | ? [X201 : term,X202 : subst,X203 : subst] : (((X200 @ (comp @ X202 @ X203) @ (sub @ X201 @ X203))) != ((sub @ (X200 @ X202 @ X201) @ X203))) | ? [X204 : term,X205 : subst,X206 : subst] : (((X199 @ (comp @ X206 @ X205) @ (sub @ X204 @ X205))) != ((sub @ (X199 @ X206 @ X204) @ X205)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X207 : subst,X208 : term,X209 : (subst > term > term),X210 : (subst > term > term)] : ((((X209 @ X207 @ X208)) != ((X210 @ X207 @ X208))) & (((lam @ (X210 @ sh @ one))) = ((lam @ (X209 @ sh @ one)))) & ! [X211 : term,X212 : subst,X213 : subst] : (((sub @ (X210 @ X212 @ X211) @ X213)) = ((X210 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213)))) & ! [X214 : term,X215 : subst,X216 : subst] : (((sub @ (X209 @ X216 @ X214) @ X215)) = ((X209 @ (comp @ X216 @ X215) @ (sub @ X214 @ X215)))))) & ((induction2 = $true) | ($true != sP7)) & (($true = sP7) | (induction2 != $true)) & (! [X217 : (term > $o),X218 : subst,X219 : term] : ? [X220 : (term > $o)] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X219 @ X218)))) = ((X220 @ X221))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X222 : (term > $o),X223 : subst,X224 : term] : ! [X225 : (term > $o)] : ? [X226 : term] : (((X225 @ X226)) != ((X222 @ (sub @ X226 @ (push @ X224 @ X223)))))) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X227 : term] : ! [X228 : (subst > term > term)] : ? [X229 : term,X230 : subst] : (((X228 @ X230 @ X229)) != ((sub @ X227 @ (push @ X229 @ X230))))) & (! [X231 : term] : ? [X232 : (subst > term > term)] : ! [X233 : term,X234 : subst] : (((sub @ X231 @ (push @ X233 @ X234))) = ((X232 @ X234 @ X233))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (! [X235 : (subst > term > subst > $o),X236 : term] : (($true = ((X235 @ id @ X236 @ id))) | ? [X237 : (subst > term > term)] : (! [X238 : subst,X239 : subst,X240 : term] : (((X237 @ (comp @ X238 @ X239) @ (sub @ X240 @ X239))) = ((sub @ (X237 @ X238 @ X240) @ X239))) & (((X235 @ id @ (lam @ (X237 @ sh @ one)) @ id)) != $true) & ! [X241 : term] : (($true != ((X235 @ id @ X241 @ id))) | (((X235 @ id @ (X237 @ id @ X241) @ id)) = $true))) | (((sP5 @ X235)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X242 : (subst > term > subst > $o),X243 : term] : ((((X242 @ id @ X243 @ id)) != $true) & ! [X244 : (subst > term > term)] : (? [X245 : subst,X246 : subst,X247 : term] : (((sub @ (X244 @ X245 @ X247) @ X246)) != ((X244 @ (comp @ X245 @ X246) @ (sub @ X247 @ X246)))) | (((X242 @ id @ (lam @ (X244 @ sh @ one)) @ id)) = $true) | ? [X248 : term] : ((((X242 @ id @ X248 @ id)) = $true) & ($true != ((X242 @ id @ (X244 @ id @ X248) @ id))))) & ($true != ((sP5 @ X242))))) & ((sP4 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP4 != $true)) & (hoaslaminj_gthm = $true) & ((axidr = $true) | ? [X249 : subst] : (((comp @ X249 @ id)) != X249)) & (! [X250 : subst] : (((comp @ X250 @ id)) = X250) | (axidr != $true)) & ! [X251 : term] : ? [X252 : d_term] : (((d2term @ X252)) = X251) & (axassoc = $true) & (! [X253 : term] : (((sub @ X253 @ id)) = X253) | (termmset != $true)) & ((termmset = $true) | ? [X254 : term] : (((sub @ X254 @ id)) != X254)) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (! [X255 : term] : ? [X256 : (subst > term > term)] : ! [X257 : subst,X258 : term] : (((sub @ X255 @ (push @ X258 @ X257))) = ((X256 @ X257 @ X258))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X259 : term] : ! [X260 : (subst > term > term)] : ? [X261 : subst,X262 : term] : (((sub @ X259 @ (push @ X262 @ X261))) != ((X260 @ X261 @ X262)))) & (! [X263 : term] : (((sub @ X263 @ id)) = X263) | (axvarid != $true)) & ((axvarid = $true) | ? [X264 : term] : (((sub @ X264 @ id)) != X264)) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X265 : d_subst] : (d_id = X265) & (! [X266 : term,X267 : (term > $o)] : (? [X268 : term] : (($true = ((var @ X268))) & (((X267 @ X268)) != $true)) | (((X267 @ X266)) = $true) | ? [X269 : term] : ((((X267 @ (lam @ X269))) != $true) & ($true = ((X267 @ X269)))) | ($true = ((sP1 @ X267)))) | (induction != $true)) & ((induction = $true) | ? [X270 : term,X271 : (term > $o)] : (! [X272 : term] : ((((var @ X272)) != $true) | ($true = ((X271 @ X272)))) & ($true != ((X271 @ X270))) & ! [X273 : term] : ((((X271 @ (lam @ X273))) = $true) | ($true != ((X271 @ X273)))) & ($true != ((sP1 @ X271))))) & ((hoasinduction_lem0_lthm = $true) | ? [X274 : (subst > term > subst > $o)] : ! [X275 : (term > $o)] : ? [X276 : term] : (((X274 @ id @ X276 @ id)) != ((X275 @ X276)))) & (! [X277 : (subst > term > subst > $o)] : ? [X278 : (term > $o)] : ! [X279 : term] : (((X277 @ id @ X279 @ id)) = ((X278 @ X279))) | (hoasinduction_lem0_lthm != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP0 != $true))),
% 2.11/0.57 inference(rectify,[],[f261])).
% 2.11/0.57 thf(f263,plain,(
% 2.11/0.57 ((hoasinduction_lem3_lthm = $true) | (sP58 != $true)) & ((sP58 = $true) | (hoasinduction_lem3_lthm != $true)) & ((hoasinduction = $true) | (sP55 != $true)) & ((sP55 = $true) | (hoasinduction != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP52 != $true)) & ((sP52 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lthm = $true) | (sP50 != $true)) & ((sP50 = $true) | (hoasinduction_lthm != $true)) & ((axidl = $true) | (sK454 != ((comp @ id @ sK454)))) & (! [X1 : subst] : (((comp @ id @ X1)) = X1) | (axidl != $true)) & (hoasinduction_lem1_gthm = $true) & ((substmonoid = $true) | (((comp @ id @ sK455)) != sK455) | (sK456 != ((comp @ sK456 @ id)))) & ((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X5 : subst] : (((comp @ X5 @ id)) = X5)) | (substmonoid != $true)) & ((axshiftcons = $true) | (sK457 != ((comp @ sh @ (push @ sK458 @ sK457))))) & (! [X8 : subst,X9 : term] : (((comp @ sh @ (push @ X9 @ X8))) = X8) | (axshiftcons != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X10 : subst] : (((push @ (sub @ one @ X10) @ (comp @ sh @ X10))) = X10) | (axscons != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK459) @ (comp @ sh @ sK459))) != sK459)) & (termmset_gthm = $true) & ! [X12 : d_term,X13 : d_term] : ((X12 = X13) | (((d2term @ X12)) != ((d2term @ X13)))) & (hoasinduction_lem2_gthm = $true) & ((pushprop_lem0 = $true) | ! [X17 : (term > $o)] : (((sK460 @ (sub @ (sK463 @ X17) @ (push @ sK462 @ sK461)))) != ((X17 @ (sK463 @ X17))))) & (! [X19 : (term > $o),X20 : subst,X21 : term] : ! [X23 : term] : (((sK464 @ X21 @ X20 @ X19 @ X23)) = ((X19 @ (sub @ X23 @ (push @ X21 @ X20))))) | (pushprop_lem0 != $true)) & (lamnotvar = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoaslamnotvar_lthm = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X24 : subst,X25 : term] : (((sub @ one @ (push @ X25 @ X24))) = X25) & ((((sK467 @ one)) != $true) & ($true = ((sK468 @ sK466))) & ! [X30 : term] : (((sK468 @ (sub @ X30 @ (push @ sK466 @ sK465)))) = ((sK467 @ X30)))))) & ((sK470 != ((sub @ one @ (push @ sK470 @ sK469)))) | ! [X33 : subst,X34 : term,X35 : (term > $o),X36 : (term > $o)] : (($true = ((X35 @ one))) | (((X36 @ X34)) != $true) | (((X36 @ (sub @ (sK471 @ X36 @ X35 @ X34 @ X33) @ (push @ X34 @ X33)))) != ((X35 @ (sK471 @ X36 @ X35 @ X34 @ X33))))) | (pushprop_lem1v2_lthm != $true)) & (pushprop_lem0_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP41)) & (($true = sP41) | (hoasinduction_no_psi_cond_lthm != $true)) & (induction2_gthm = $true) & ((hoasinduction_lem3 = $true) | (sP36 != $true)) & ((sP36 = $true) | (hoasinduction_lem3 != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((sP34 = $true) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (sP34 != $true)) & (axvarshift = $true) & ((shinj = $true) | ((sK472 != sK473) & (((sub @ sK472 @ sh)) = ((sub @ sK473 @ sh))))) & (! [X40 : term,X41 : term] : ((X40 = X41) | (((sub @ X41 @ sh)) != ((sub @ X40 @ sh)))) | (shinj != $true)) & ((hoasapinj2 = $true) | ((sK477 != sK475) & (((ap @ (sub @ sK476 @ id) @ sK475)) = ((ap @ (sub @ sK474 @ id) @ sK477))))) & (! [X46 : term,X47 : term,X48 : term,X49 : term] : ((X47 = X49) | (((ap @ (sub @ X48 @ id) @ X47)) != ((ap @ (sub @ X46 @ id) @ X49)))) | (hoasapinj2 != $true)) & (($true = sP33) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP33)) & ((pushprop_lem1_lthm = $true) | (! [X50 : term,X51 : subst] : (((sub @ one @ (push @ X50 @ X51))) = X50) & ! [X52 : subst,X53 : term] : (((comp @ sh @ (push @ X53 @ X52))) = X52) & ((((sK481 @ (sub @ sK478 @ (push @ sK482 @ sK479)))) != $true) & ($true = ((sK480 @ sK478)))))) & ((sK483 != ((sub @ one @ (push @ sK483 @ sK484)))) | (sK485 != ((comp @ sh @ (push @ sK486 @ sK485)))) | ! [X63 : term,X64 : subst,X65 : (term > $o),X66 : (term > $o),X67 : term] : ((((X66 @ (sub @ X63 @ (push @ X67 @ X64)))) = $true) | (((X65 @ X63)) != $true)) | (pushprop_lem1_lthm != $true)) & (ulamvarsh = $true) & ((induction2lem_lthm = $true) | (sP32 != $true)) & ((sP32 = $true) | (induction2lem_lthm != $true)) & ! [X68 : d_term] : (d_one = X68) & (substmonoid_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((apinj1 = $true) | ((sK487 != sK490) & (((ap @ sK490 @ sK488)) = ((ap @ sK487 @ sK489))))) & (! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X76) | (((ap @ X76 @ X74)) != ((ap @ X73 @ X75)))) | (apinj1 != $true)) & (hoaslamnotap_gthm = $true) & ((sP28 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | (sP28 != $true)) & (! [X77 : (subst > term > subst > $o)] : ! [X79 : term] : (((sK491 @ X77 @ X79)) = ((X77 @ id @ X79 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X81 : (term > $o)] : (((sK492 @ id @ (sK493 @ X81) @ id)) != ((X81 @ (sK493 @ X81))))) & (pushprop_lem1v2_gthm = $true) & ((sP22 = $true) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | (sP22 != $true)) & ((sP21 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP21 != $true)) & (hoasinduction_lem3v2_gthm = $true) & (! [X83 : subst,X84 : term,X85 : (term > $o),X86 : (term > $o)] : ((((X85 @ (sK494 @ X86 @ X85 @ X84 @ X83))) != ((X86 @ (sub @ (sK494 @ X86 @ X85 @ X84 @ X83) @ (push @ X84 @ X83))))) | ($true != ((X86 @ X84))) | (((X85 @ one)) = $true)) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X92 : term] : (((sK497 @ X92)) = ((sK498 @ (sub @ X92 @ (push @ sK496 @ sK495))))) & (((sK498 @ sK496)) = $true) & ($true != ((sK497 @ one))))) & (apnotvar = $true) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (! [X93 : term,X94 : term] : ((((lam @ X93)) != ((lam @ X94))) | (X93 = X94)) | (laminj != $true)) & ((laminj = $true) | ((((lam @ sK499)) = ((lam @ sK500))) & (sK499 != sK500))) & ((sP20 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP20 != $true)) & (! [X97 : term,X98 : term,X99 : term,X100 : term] : ((X99 = X100) | (((ap @ (sub @ X99 @ id) @ X98)) != ((ap @ (sub @ X100 @ id) @ X97)))) | (sK501 != ((sub @ sK501 @ id))) | ((sK504 != sK503) & (((ap @ sK504 @ sK505)) = ((ap @ sK503 @ sK502)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (((sK509 != sK508) & (((ap @ (sub @ sK508 @ id) @ sK507)) = ((ap @ (sub @ sK509 @ id) @ sK506)))) & ! [X110 : term] : (((sub @ X110 @ id)) = X110) & ! [X111 : term,X112 : term,X113 : term,X114 : term] : ((X112 = X113) | (((ap @ X113 @ X114)) != ((ap @ X112 @ X111)))))) & (((d2subst @ d_id)) = sh) & (((var @ (d2term @ d_one))) != $true) & ((pushprop_lem1 = $true) | ((((sK514 @ sK512)) = $true) & (((sK511 @ (sub @ sK512 @ (push @ sK513 @ sK510)))) != $true))) & (! [X120 : subst,X121 : (term > $o),X122 : term,X123 : term,X124 : (term > $o)] : ((((X124 @ X122)) != $true) | (((X121 @ (sub @ X122 @ (push @ X123 @ X120)))) = $true)) | (pushprop_lem1 != $true)) & (pushprop_lthm = $true) & (lamnotap != $true) & ((hoasapinj2_lthm = $true) | (((((ap @ (sub @ sK518 @ id) @ sK515)) = ((ap @ (sub @ sK517 @ id) @ sK516))) & (sK516 != sK515)) & ! [X129 : term,X130 : term,X131 : term,X132 : term] : ((((ap @ X129 @ X131)) != ((ap @ X130 @ X132))) | (X131 = X132)))) & (! [X133 : term,X134 : term,X135 : term,X136 : term] : ((((ap @ (sub @ X135 @ id) @ X134)) != ((ap @ (sub @ X136 @ id) @ X133))) | (X133 = X134)) | ((((ap @ sK520 @ sK522)) = ((ap @ sK519 @ sK521))) & (sK522 != sK521)) | (hoasapinj2_lthm != $true)) & (hoasapinj1_gthm = $true) & ! [X141 : d_subst,X142 : d_subst] : ((((d2subst @ X141)) != ((d2subst @ X142))) | (X141 = X142)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_lem3a_gthm = $true) & (! [X143 : term,X144 : term,X145 : term,X146 : term] : ((((ap @ X143 @ X146)) != ((ap @ X144 @ X145))) | (X145 = X146)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK524 @ sK525)) = ((ap @ sK523 @ sK526))) & (sK526 != sK525))) & (hoasinduction_lem1_lthm = $true) & (pushprop = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (ulamvarind = $true) & ((substmonoid_lthm = $true) | (((sK527 != ((comp @ sK527 @ id))) | (sK528 != ((comp @ id @ sK528)))) & ! [X153 : subst] : (((comp @ X153 @ id)) = X153) & ! [X154 : subst] : (((comp @ id @ X154)) = X154))) & ((! [X155 : subst] : (((comp @ X155 @ id)) = X155) & ! [X156 : subst] : (((comp @ id @ X156)) = X156)) | (sK529 != ((comp @ sK529 @ id))) | (((comp @ id @ sK530)) != sK530) | (substmonoid_lthm != $true)) & (($true = sP18) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP18)) & ((hoasinduction_lem3v2_lthm = $true) | (sP14 != $true)) & ((sP14 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP12) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP12)) & ((hoaslamnotap = $true) | (! [X162 : term,X163 : subst,X164 : subst] : (((sub @ (sK532 @ X163 @ X162) @ X164)) = ((sK532 @ (comp @ X163 @ X164) @ (sub @ X162 @ X164)))) & (((lam @ (sK532 @ sh @ one))) = ((ap @ (sub @ sK531 @ id) @ sK533))))) & (! [X165 : term,X166 : (subst > term > term),X167 : term] : ((((X166 @ (comp @ (sK535 @ X166) @ (sK536 @ X166)) @ (sub @ (sK534 @ X166) @ (sK536 @ X166)))) != ((sub @ (X166 @ (sK535 @ X166) @ (sK534 @ X166)) @ (sK536 @ X166)))) | (((ap @ (sub @ X165 @ id) @ X167)) != ((lam @ (X166 @ sh @ one))))) | (hoaslamnotap != $true)) & (pushprop_lem2v2_gthm = $true) & (hoasapinj2_gthm = $true) & (($true = sP10) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP10)) & (hoasinduction_lem2v2_gthm = $true) & (! [X171 : subst,X172 : term] : (((sub @ one @ (push @ X172 @ X171))) = X172) | (axvarcons != $true)) & ((axvarcons = $true) | (sK538 != ((sub @ one @ (push @ sK538 @ sK537))))) & ! [X175 : subst] : (((d2subst @ (sK539 @ X175))) = X175) & ((((sub @ sK540 @ id)) != sK540) | ! [X178 : term] : (((sub @ X178 @ id)) = X178) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (! [X179 : term] : (((sub @ X179 @ id)) = X179) & (sK541 != ((sub @ sK541 @ 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_lem1v2_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK544 @ id) @ sK545)) = ((ap @ (sub @ sK542 @ id) @ sK543))) & (sK544 != sK542))) & (! [X185 : term,X186 : term,X187 : term,X188 : term] : ((((ap @ (sub @ X187 @ id) @ X188)) != ((ap @ (sub @ X185 @ id) @ X186))) | (X185 = X187)) | (hoasapinj1 != $true)) & (axapp = $true) & (axabs = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (! [X189 : term] : (((sK546 @ X189 @ sh @ one)) = ((sub @ X189 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X192 : (subst > term > term)] : (((sub @ sK547 @ (push @ one @ sh))) != ((X192 @ sh @ one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X194 : (subst > term > term)] : (((sub @ sK548 @ (push @ one @ sh))) != ((X194 @ sh @ one)))) & (! [X195 : term] : (((sK549 @ X195 @ sh @ one)) = ((sub @ X195 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem2 = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem2 != $true)) & (pushprop_lem3v2 = $true) & (hoasapnotvar = $true) & (! [X197 : subst,X198 : term,X199 : (subst > term > term),X200 : (subst > term > term)] : ((((X200 @ X197 @ X198)) = ((X199 @ X197 @ X198))) | (((lam @ (X199 @ sh @ one))) != ((lam @ (X200 @ sh @ one)))) | (((X200 @ (comp @ (sK551 @ X200) @ (sK552 @ X200)) @ (sub @ (sK550 @ X200) @ (sK552 @ X200)))) != ((sub @ (X200 @ (sK551 @ X200) @ (sK550 @ X200)) @ (sK552 @ X200)))) | (((X199 @ (comp @ (sK555 @ X199) @ (sK554 @ X199)) @ (sub @ (sK553 @ X199) @ (sK554 @ X199)))) != ((sub @ (X199 @ (sK555 @ X199) @ (sK553 @ X199)) @ (sK554 @ X199))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ((((sK559 @ sK556 @ sK557)) != ((sK558 @ sK556 @ sK557))) & (((lam @ (sK558 @ sh @ one))) = ((lam @ (sK559 @ sh @ one)))) & ! [X211 : term,X212 : subst,X213 : subst] : (((sK559 @ (comp @ X212 @ X213) @ (sub @ X211 @ X213))) = ((sub @ (sK559 @ X212 @ X211) @ X213))) & ! [X214 : term,X215 : subst,X216 : subst] : (((sub @ (sK558 @ X216 @ X214) @ X215)) = ((sK558 @ (comp @ X216 @ X215) @ (sub @ X214 @ X215)))))) & ((induction2 = $true) | ($true != sP7)) & (($true = sP7) | (induction2 != $true)) & (! [X217 : (term > $o),X218 : subst,X219 : term] : ! [X221 : term] : (((X217 @ (sub @ X221 @ (push @ X219 @ X218)))) = ((sK560 @ X219 @ X218 @ X217 @ X221))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X225 : (term > $o)] : (((X225 @ (sK564 @ X225))) != ((sK561 @ (sub @ (sK564 @ X225) @ (push @ sK563 @ sK562)))))) & (hoaslamnotap_lthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasapnotvar_lthm = $true) & (axmap = $true) & (hoasinduction_lem2_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X228 : (subst > term > term)] : (((sub @ sK565 @ (push @ (sK566 @ X228) @ (sK567 @ X228)))) != ((X228 @ (sK567 @ X228) @ (sK566 @ X228))))) & (! [X231 : term] : ! [X233 : term,X234 : subst] : (((sub @ X231 @ (push @ X233 @ X234))) = ((sK568 @ X231 @ X234 @ X233))) | (hoasinduction_lem3v2_f != $true)) & (((d2subst @ d_id)) = id) & (induction2lem_gthm = $true) & (! [X235 : (subst > term > subst > $o),X236 : term] : (($true = ((X235 @ id @ X236 @ id))) | (! [X238 : subst,X239 : subst,X240 : term] : (((sub @ (sK569 @ X235 @ X238 @ X240) @ X239)) = ((sK569 @ X235 @ (comp @ X238 @ X239) @ (sub @ X240 @ X239)))) & ($true != ((X235 @ id @ (lam @ (sK569 @ X235 @ sh @ one)) @ id))) & ! [X241 : term] : (($true != ((X235 @ id @ X241 @ id))) | (((X235 @ id @ (sK569 @ X235 @ id @ X241) @ id)) = $true))) | (((sP5 @ X235)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK570 @ id @ sK571 @ id)) != $true) & ! [X244 : (subst > term > term)] : ((((X244 @ (comp @ (sK572 @ X244) @ (sK573 @ X244)) @ (sub @ (sK574 @ X244) @ (sK573 @ X244)))) != ((sub @ (X244 @ (sK572 @ X244) @ (sK574 @ X244)) @ (sK573 @ X244)))) | (((sK570 @ id @ (lam @ (X244 @ sh @ one)) @ id)) = $true) | ((((sK570 @ id @ (sK575 @ X244) @ id)) = $true) & (((sK570 @ id @ (X244 @ id @ (sK575 @ X244)) @ id)) != $true))) & ($true != ((sP5 @ sK570))))) & ((sP4 = $true) | (induction2lem != $true)) & ((induction2lem = $true) | (sP4 != $true)) & (hoaslaminj_gthm = $true) & ((axidr = $true) | (((comp @ sK576 @ id)) != sK576)) & (! [X250 : subst] : (((comp @ X250 @ id)) = X250) | (axidr != $true)) & ! [X251 : term] : (((d2term @ (sK577 @ X251))) = X251) & (axassoc = $true) & (! [X253 : term] : (((sub @ X253 @ id)) = X253) | (termmset != $true)) & ((termmset = $true) | (sK578 != ((sub @ sK578 @ id)))) & (pushprop_lem1_gthm = $true) & (hoasinduction_gthm = $true) & (pushprop_gthm = $true) & (axclos = $true) & (pushprop_lthm_orig = $true) & (! [X255 : term] : ! [X257 : subst,X258 : term] : (((sub @ X255 @ (push @ X258 @ X257))) = ((sK579 @ X255 @ X257 @ X258))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X260 : (subst > term > term)] : (((sub @ sK580 @ (push @ (sK582 @ X260) @ (sK581 @ X260)))) != ((X260 @ (sK581 @ X260) @ (sK582 @ X260))))) & (! [X263 : term] : (((sub @ X263 @ id)) = X263) | (axvarid != $true)) & ((axvarid = $true) | (sK583 != ((sub @ sK583 @ id)))) & (one = ((d2term @ d_one))) & (pushprop_lem2v2 = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction_lem3v2a != $true)) & ! [X265 : d_subst] : (d_id = X265) & (! [X266 : term,X267 : (term > $o)] : (((((var @ (sK584 @ X267))) = $true) & (((X267 @ (sK584 @ X267))) != $true)) | (((X267 @ X266)) = $true) | (($true != ((X267 @ (lam @ (sK585 @ X267))))) & ($true = ((X267 @ (sK585 @ X267))))) | ($true = ((sP1 @ X267)))) | (induction != $true)) & ((induction = $true) | (! [X272 : term] : ((((var @ X272)) != $true) | (((sK587 @ X272)) = $true)) & (((sK587 @ sK586)) != $true) & ! [X273 : term] : (($true = ((sK587 @ (lam @ X273)))) | ($true != ((sK587 @ X273)))) & (((sP1 @ sK587)) != $true))) & ((hoasinduction_lem0_lthm = $true) | ! [X275 : (term > $o)] : (((X275 @ (sK589 @ X275))) != ((sK588 @ id @ (sK589 @ X275) @ id)))) & (! [X277 : (subst > term > subst > $o)] : ! [X279 : term] : (((sK590 @ X277 @ X279)) = ((X277 @ id @ X279 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((sP0 = $true) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | (sP0 != $true))),
% 2.11/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK454,sK455,sK456,sK457,sK458,sK459,sK460,sK461,sK462,vAPP,vAPP,sK465,sK466,sK467,sK468,sK469,sK470,vAPP,sK472,sK473,sK474,sK475,sK476,sK477,sK478,sK479,sK480,sK481,sK482,sK483,sK484,sK485,sK486,sK487,sK488,sK489,sK490,vAPP,sK492,vAPP,vAPP,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,sK510,sK511,sK512,sK513,sK514,sK515,sK516,sK517,sK518,sK519,sK520,sK521,sK522,sK523,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,vAPP,vAPP,vAPP,sK537,sK538,vAPP,sK540,sK541,sK542,sK543,sK544,sK545,vAPP,sK547,sK548,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK556,sK557,sK558,sK559,vAPP,sK561,sK562,sK563,vAPP,sK565,vAPP,vAPP,vAPP,vAPP,sK570,sK571,vAPP,vAPP,vAPP,vAPP,sK576,vAPP,sK578,vAPP,sK580,vAPP,vAPP,sK583,vAPP,vAPP,sK586,sK587,sK588,vAPP,vAPP]),skolemize(X0,sK454),skolemize(X2,sK455),skolemize(X3,sK456),skolemize(X6,sK457),skolemize(X7,sK458),skolemize(X11,sK459),skolemize(X14,sK460),skolemize(X15,sK461),skolemize(X16,sK462),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X26,sK465),skolemize(X27,sK466),skolemize(X28,sK467),skolemize(X29,sK468),skolemize(X31,sK469),skolemize(X32,sK470),skolemize(X23,sK70 @ X14 @ X13),skolemize(X38,sK472),skolemize(X39,sK473),skolemize(X42,sK474),skolemize(X43,sK475),skolemize(X44,sK476),skolemize(X45,sK477),skolemize(X54,sK478),skolemize(X55,sK479),skolemize(X56,sK480),skolemize(X57,sK481),skolemize(X58,sK482),skolemize(X59,sK483),skolemize(X60,sK484),skolemize(X61,sK485),skolemize(X62,sK486),skolemize(X69,sK487),skolemize(X70,sK488),skolemize(X71,sK489),skolemize(X72,sK490),skolemize(X23,sK70 @ X14 @ X13),skolemize(X80,sK492),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X88,sK495),skolemize(X89,sK496),skolemize(X90,sK497),skolemize(X91,sK498),skolemize(X95,sK499),skolemize(X96,sK500),skolemize(X101,sK501),skolemize(X102,sK502),skolemize(X103,sK503),skolemize(X104,sK504),skolemize(X105,sK505),skolemize(X106,sK506),skolemize(X107,sK507),skolemize(X108,sK508),skolemize(X109,sK509),skolemize(X115,sK510),skolemize(X116,sK511),skolemize(X117,sK512),skolemize(X118,sK513),skolemize(X119,sK514),skolemize(X125,sK515),skolemize(X126,sK516),skolemize(X127,sK517),skolemize(X128,sK518),skolemize(X137,sK519),skolemize(X138,sK520),skolemize(X139,sK521),skolemize(X140,sK522),skolemize(X147,sK523),skolemize(X148,sK524),skolemize(X149,sK525),skolemize(X150,sK526),skolemize(X151,sK527),skolemize(X152,sK528),skolemize(X157,sK529),skolemize(X158,sK530),skolemize(X159,sK531),skolemize(X160,sK532),skolemize(X161,sK533),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X173,sK537),skolemize(X174,sK538),skolemize(X23,sK70 @ X14 @ X13),skolemize(X177,sK540),skolemize(X180,sK541),skolemize(X181,sK542),skolemize(X182,sK543),skolemize(X183,sK544),skolemize(X184,sK545),skolemize(X23,sK70 @ X14 @ X13),skolemize(X191,sK547),skolemize(X193,sK548),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X207,sK556),skolemize(X208,sK557),skolemize(X209,sK558),skolemize(X210,sK559),skolemize(X23,sK70 @ X14 @ X13),skolemize(X222,sK561),skolemize(X223,sK562),skolemize(X224,sK563),skolemize(X23,sK70 @ X14 @ X13),skolemize(X227,sK565),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X242,sK570),skolemize(X243,sK571),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X249,sK576),skolemize(X23,sK70 @ X14 @ X13),skolemize(X254,sK578),skolemize(X23,sK70 @ X14 @ X13),skolemize(X259,sK580),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X264,sK583),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13),skolemize(X270,sK586),skolemize(X271,sK587),skolemize(X274,sK588),skolemize(X23,sK70 @ X14 @ X13),skolemize(X23,sK70 @ X14 @ X13)],[f262])).
% 2.11/0.57 thf(f770,plain,(
% 2.11/0.57 (one = ((d2term @ d_one)))),
% 2.11/0.57 inference(cnf_transformation,[],[f263])).
% 2.11/0.57 thf(f783,plain,(
% 2.11/0.57 ( ! [X251 : term] : ((((d2term @ (sK577 @ X251))) = X251)) )),
% 2.11/0.57 inference(cnf_transformation,[],[f263])).
% 2.11/0.57 thf(f881,plain,(
% 2.11/0.57 (((var @ (d2term @ d_one))) != $true)),
% 2.11/0.57 inference(cnf_transformation,[],[f263])).
% 2.11/0.57 thf(f918,plain,(
% 2.11/0.57 ( ! [X68 : d_term] : ((d_one = X68)) )),
% 2.11/0.57 inference(cnf_transformation,[],[f263])).
% 2.11/0.57 thf(f953,plain,(
% 2.11/0.57 (lamnotvar = $true)),
% 2.11/0.57 inference(cnf_transformation,[],[f263])).
% 2.11/0.57 thf(f978,plain,(
% 2.11/0.57 (lamnotvar != ((!! @ term @ (^[Y0 : term]: (~ (var @ (lam @ Y0)))))))),
% 2.11/0.57 inference(cnf_transformation,[],[f8])).
% 2.11/0.57 thf(f981,plain,(
% 2.11/0.57 (((!! @ term @ (^[Y0 : term]: (~ (var @ (lam @ Y0)))))) != $true)),
% 2.11/0.57 inference(definition_unfolding,[],[f978,f953])).
% 2.11/0.57 thf(f1044,plain,(
% 2.11/0.57 ($false = (((^[Y0 : term]: (~ (var @ (lam @ Y0)))) @ sK591)))),
% 2.11/0.57 inference(sigma_proxy_clausification,[],[f981])).
% 2.11/0.57 thf(f1045,plain,(
% 2.11/0.57 ($false = ((~ (var @ (lam @ sK591)))))),
% 2.11/0.57 inference(beta-eta_normalization,[],[f1044])).
% 2.11/0.57 thf(f1046,plain,(
% 2.11/0.57 ($true = ((var @ (lam @ sK591))))),
% 2.11/0.57 inference(not_proxy_clausification,[],[f1045])).
% 2.11/0.57 thf(f3928,plain,(
% 2.11/0.57 ( ! [X251 : term] : ((((d2term @ d_one)) = X251)) )),
% 2.11/0.57 inference(forward_demodulation,[],[f783,f918])).
% 2.11/0.57 thf(f3934,plain,(
% 2.11/0.57 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 2.11/0.57 inference(superposition,[],[f3928,f3928])).
% 2.11/0.57 thf(f3956,plain,(
% 2.11/0.57 (((var @ one)) != $true)),
% 2.11/0.57 inference(forward_demodulation,[],[f881,f770])).
% 2.11/0.57 thf(f4186,plain,(
% 2.11/0.57 ( ! [X0 : term] : ((((var @ X0)) = $true)) )),
% 2.11/0.57 inference(superposition,[],[f1046,f3934])).
% 2.11/0.57 thf(f4300,plain,(
% 2.11/0.57 ($true != $true)),
% 2.11/0.57 inference(superposition,[],[f3956,f4186])).
% 2.11/0.57 thf(f4303,plain,(
% 2.11/0.57 $false),
% 2.11/0.57 inference(trivial_inequality_removal,[],[f4300])).
% 2.11/0.57 % SZS output end Proof for theBenchmark
% 2.11/0.57 % (2684147)------------------------------
% 2.11/0.57 % (2684147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.11/0.57 % (2684147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.11/0.57 % (2684147)CaDiCaL version: 2.1.3
% 2.11/0.57 % (2684147)Termination reason: Refutation
% 2.11/0.57 % (2684147)Time elapsed: 0.190 s
% 2.11/0.57 % (2684147)Peak memory usage: 16 MB
% 2.11/0.57 % (2684147)Instructions burned: 428 (million)
% 2.11/0.57 % (2684107)Success in time 0.312 s
% 2.11/0.57 % Vampire exiting
%------------------------------------------------------------------------------