%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX160^1 : 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:36 AM UTC 2026
% Result : Theorem 1.42s 0.51s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX160^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 % Computer : n013.cluster.edu
% 0.06/0.20 % Model : x86_64 x86_64
% 0.06/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.20 % Memory : 8046.5625MB
% 0.06/0.20 % OS : Linux 6.8.0-71-generic
% 0.06/0.20 % CPULimit : 300
% 0.06/0.20 % WCLimit : 300
% 0.06/0.20 % DateTime : Tue Sep 29 16:08:36 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.21/0.27 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
% 0.60/0.41 % (2300672)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.60/0.41 % (2300678)lrs+10_16_si=on:nwc=1.5:random_seed=1104173204:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.60/0.41 % (2300683)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.60/0.41 % (2300683)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
% 0.60/0.41 % (2300678)Instruction limit reached!
% 0.60/0.41 % (2300678)------------------------------
% 0.60/0.41 % (2300678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (2300678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (2300678)CaDiCaL version: 2.1.3
% 0.60/0.41 % (2300678)Termination reason: Instruction limit
% 0.60/0.41 % (2300678)Termination phase: shuffling
% 0.60/0.41 % (2300678)Time elapsed: 0.004 s
% 0.60/0.41 % (2300678)Peak memory usage: 10 MB
% 0.60/0.41 % (2300678)Instructions burned: 19 (million)
% 0.60/0.41 % (2300677)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1339328454:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.60/0.41 % (2300680)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=2909692069: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)
% 0.60/0.41 % (2300679)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1398254488:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.60/0.41 % (2300681)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=388336548:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.60/0.41 % (2300682)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=846894913:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.60/0.41 % (2300683)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=1571187606:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.60/0.41 % (2300679)Instruction limit reached!
% 0.60/0.41 % (2300679)------------------------------
% 0.60/0.41 % (2300679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (2300679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (2300679)CaDiCaL version: 2.1.3
% 0.60/0.41 % (2300679)Termination reason: Instruction limit
% 0.60/0.41 % (2300679)Termination phase: shuffling
% 0.60/0.41 % (2300679)Time elapsed: 0.002 s
% 0.60/0.41 % (2300679)Peak memory usage: 9 MB
% 0.60/0.41 % (2300679)Instructions burned: 3 (million)
% 0.60/0.41 % (2300685)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2878799678:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.41 % (2300681)Instruction limit reached!
% 0.60/0.41 % (2300681)------------------------------
% 0.60/0.41 % (2300681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (2300681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (2300681)CaDiCaL version: 2.1.3
% 0.60/0.41 % (2300681)Termination reason: Instruction limit
% 0.60/0.41 % (2300681)Termination phase: Property scanning
% 0.60/0.41 % (2300681)Time elapsed: 0.011 s
% 0.60/0.41 % (2300681)Peak memory usage: 10 MB
% 0.60/0.41 % (2300681)Instructions burned: 25 (million)
% 0.60/0.41 % (2300685)Instruction limit reached!
% 0.60/0.41 % (2300685)------------------------------
% 0.60/0.41 % (2300685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.41 % (2300685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.41 % (2300685)CaDiCaL version: 2.1.3
% 0.60/0.41 % (2300685)Termination reason: Instruction limit
% 0.60/0.41 % (2300685)Termination phase: shuffling
% 0.60/0.41 % (2300685)Time elapsed: 0.001 s
% 0.60/0.41 % (2300685)Peak memory usage: 9 MB
% 0.60/0.41 % (2300685)Instructions burned: 4 (million)
% 0.60/0.41 % (2300694)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.45 % (2300692)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2875790559:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.60/0.45 % (2300694)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2872101692:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.60/0.45 % (2300692)Instruction limit reached!
% 0.60/0.45 % (2300692)------------------------------
% 0.60/0.45 % (2300692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.45 % (2300692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.45 % (2300692)CaDiCaL version: 2.1.3
% 0.60/0.45 % (2300692)Termination reason: Instruction limit
% 0.60/0.45 % (2300692)Termination phase: shuffling
% 0.60/0.45 % (2300692)Time elapsed: 0.003 s
% 0.60/0.45 % (2300692)Peak memory usage: 9 MB
% 0.60/0.45 % (2300692)Instructions burned: 5 (million)
% 0.60/0.45 % (2300694)Instruction limit reached!
% 0.60/0.45 % (2300694)------------------------------
% 0.60/0.45 % (2300694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.45 % (2300694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.45 % (2300694)CaDiCaL version: 2.1.3
% 0.60/0.45 % (2300694)Termination reason: Instruction limit
% 0.60/0.45 % (2300694)Termination phase: shuffling
% 0.60/0.45 % (2300694)Time elapsed: 0.002 s
% 0.60/0.45 % (2300694)Peak memory usage: 9 MB
% 0.60/0.45 % (2300694)Instructions burned: 8 (million)
% 0.60/0.45 % (2300682)Instruction limit reached!
% 0.60/0.45 % (2300682)------------------------------
% 0.60/0.45 % (2300682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.45 % (2300682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.45 % (2300682)CaDiCaL version: 2.1.3
% 0.60/0.45 % (2300682)Termination reason: Instruction limit
% 0.60/0.45 % (2300682)Termination phase: Preprocessing 3
% 0.60/0.45 % (2300682)Time elapsed: 0.034 s
% 0.60/0.45 % (2300682)Peak memory usage: 12 MB
% 0.60/0.45 % (2300682)Instructions burned: 77 (million)
% 0.60/0.45 % (2300695)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4115128981:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.60/0.45 % (2300698)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
% 0.60/0.45 % (2300698)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.60/0.45 % (2300677)Instruction limit reached!
% 0.60/0.45 % (2300677)------------------------------
% 0.60/0.45 % (2300677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.45 % (2300677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.45 % (2300677)CaDiCaL version: 2.1.3
% 0.60/0.45 % (2300677)Termination reason: Instruction limit
% 0.60/0.45 % (2300677)Termination phase: Preprocessing 3
% 0.60/0.45 % (2300677)Time elapsed: 0.042 s
% 0.60/0.45 % (2300677)Peak memory usage: 12 MB
% 0.60/0.45 % (2300677)Instructions burned: 89 (million)
% 0.60/0.45 % (2300698)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1781670945:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.60/0.45 % (2300695)Instruction limit reached!
% 0.60/0.45 % (2300695)------------------------------
% 0.60/0.45 % (2300695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.45 % (2300695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.45 % (2300695)CaDiCaL version: 2.1.3
% 0.60/0.45 % (2300695)Termination reason: Instruction limit
% 0.60/0.45 % (2300695)Termination phase: shuffling
% 0.60/0.45 % (2300695)Time elapsed: 0.005 s
% 0.60/0.45 % (2300695)Peak memory usage: 10 MB
% 0.60/0.45 % (2300695)Instructions burned: 12 (million)
% 0.60/0.45 % (2300699)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=833405656:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.60/0.45 % (2300698)Instruction limit reached!
% 0.60/0.45 % (2300698)------------------------------
% 0.60/0.45 % (2300698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.50 % (2300698)CaDiCaL version: 2.1.3
% 0.60/0.50 % (2300698)Termination reason: Instruction limit
% 0.60/0.50 % (2300698)Termination phase: shuffling
% 0.60/0.50 % (2300698)Time elapsed: 0.012 s
% 0.60/0.50 % (2300698)Peak memory usage: 10 MB
% 0.60/0.50 % (2300698)Instructions burned: 28 (million)
% 0.60/0.50 % (2300703)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.60/0.50 % (2300700)lrs+10_1_si=on:cs=on:random_seed=1701140926:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.60/0.50 % (2300703)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=1875201597:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.60/0.50 % (2300703)Instruction limit reached!
% 0.60/0.50 % (2300703)------------------------------
% 0.60/0.50 % (2300703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.50 % (2300703)CaDiCaL version: 2.1.3
% 0.60/0.50 % (2300703)Termination reason: Instruction limit
% 0.60/0.50 % (2300703)Termination phase: shuffling
% 0.60/0.50 % (2300703)Time elapsed: 0.002 s
% 0.60/0.50 % (2300703)Peak memory usage: 10 MB
% 0.60/0.50 % (2300703)Instructions burned: 3 (million)
% 0.60/0.50 % (2300700)Instruction limit reached!
% 0.60/0.50 % (2300700)------------------------------
% 0.60/0.50 % (2300700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.50 % (2300700)CaDiCaL version: 2.1.3
% 0.60/0.50 % (2300700)Termination reason: Instruction limit
% 0.60/0.50 % (2300700)Termination phase: shuffling
% 0.60/0.50 % (2300700)Time elapsed: 0.004 s
% 0.60/0.50 % (2300700)Peak memory usage: 9 MB
% 0.60/0.50 % (2300700)Instructions burned: 10 (million)
% 0.60/0.50 % (2300699)Instruction limit reached!
% 0.60/0.50 % (2300699)------------------------------
% 0.60/0.50 % (2300699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.50 % (2300699)CaDiCaL version: 2.1.3
% 0.60/0.50 % (2300699)Termination reason: Instruction limit
% 0.60/0.50 % (2300699)Termination phase: Saturation
% 0.60/0.50 % (2300699)Time elapsed: 0.019 s
% 0.60/0.50 % (2300699)Peak memory usage: 12 MB
% 0.60/0.50 % (2300699)Instructions burned: 87 (million)
% 0.60/0.50 % (2300683)Instruction limit reached!
% 0.60/0.50 % (2300683)------------------------------
% 0.60/0.50 % (2300683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.60/0.50 % (2300683)CaDiCaL version: 2.1.3
% 0.60/0.50 % (2300683)Termination reason: Instruction limit
% 0.60/0.50 % (2300683)Termination phase: Property scanning
% 0.60/0.50 % (2300683)Time elapsed: 0.069 s
% 0.60/0.50 % (2300683)Peak memory usage: 13 MB
% 0.60/0.50 % (2300683)Instructions burned: 158 (million)
% 0.60/0.50 % (2300704)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2131988113:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.60/0.50 % (2300706)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=768577905:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.60/0.50 % (2300711)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3930637340:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.60/0.50 % (2300709)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4084430809:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.60/0.50 % (2300710)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4028398908:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.60/0.50 % (2300704)Instruction limit reached!
% 0.60/0.50 % (2300704)------------------------------
% 0.60/0.50 % (2300704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.60/0.50 % (2300704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300704)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300704)Termination reason: Instruction limit
% 1.42/0.51 % (2300704)Termination phase: Saturation
% 1.42/0.51 % (2300704)Time elapsed: 0.017 s
% 1.42/0.51 % (2300704)Peak memory usage: 12 MB
% 1.42/0.51 % (2300704)Instructions burned: 38 (million)
% 1.42/0.51 % (2300713)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4077180188:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.51 % (2300710)Instruction limit reached!
% 1.42/0.51 % (2300710)------------------------------
% 1.42/0.51 % (2300710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300710)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300710)Termination reason: Instruction limit
% 1.42/0.51 % (2300710)Termination phase: shuffling
% 1.42/0.51 % (2300710)Time elapsed: 0.006 s
% 1.42/0.51 % (2300710)Peak memory usage: 10 MB
% 1.42/0.51 % (2300710)Instructions burned: 14 (million)
% 1.42/0.51 % (2300713)Instruction limit reached!
% 1.42/0.51 % (2300713)------------------------------
% 1.42/0.51 % (2300713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300713)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300713)Termination reason: Instruction limit
% 1.42/0.51 % (2300713)Termination phase: shuffling
% 1.42/0.51 % (2300713)Time elapsed: 0.006 s
% 1.42/0.51 % (2300713)Peak memory usage: 10 MB
% 1.42/0.51 % (2300713)Instructions burned: 15 (million)
% 1.42/0.51 % (2300709)Instruction limit reached!
% 1.42/0.51 % (2300709)------------------------------
% 1.42/0.51 % (2300709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300709)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300709)Termination reason: Instruction limit
% 1.42/0.51 % (2300709)Termination phase: Property scanning
% 1.42/0.51 % (2300709)Time elapsed: 0.011 s
% 1.42/0.51 % (2300709)Peak memory usage: 10 MB
% 1.42/0.51 % (2300709)Instructions burned: 27 (million)
% 1.42/0.51 % (2300718)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3344754391: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)
% 1.42/0.51 % (2300718)Instruction limit reached!
% 1.42/0.51 % (2300718)------------------------------
% 1.42/0.51 % (2300718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300718)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300718)Termination reason: Instruction limit
% 1.42/0.51 % (2300718)Termination phase: shuffling
% 1.42/0.51 % (2300718)Time elapsed: 0.003 s
% 1.42/0.51 % (2300718)Peak memory usage: 10 MB
% 1.42/0.51 % (2300718)Instructions burned: 6 (million)
% 1.42/0.51 % (2300720)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=105093932:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.51 % (2300722)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2236595913:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.42/0.51 % (2300721)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4194946548:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.51 % (2300720)Instruction limit reached!
% 1.42/0.51 % (2300720)------------------------------
% 1.42/0.51 % (2300720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300720)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300720)Termination reason: Instruction limit
% 1.42/0.51 % (2300720)Termination phase: Property scanning
% 1.42/0.51 % (2300720)Time elapsed: 0.015 s
% 1.42/0.51 % (2300720)Peak memory usage: 10 MB
% 1.42/0.51 % (2300720)Instructions burned: 35 (million)
% 1.42/0.51 % (2300721)Instruction limit reached!
% 1.42/0.51 % (2300721)------------------------------
% 1.42/0.51 % (2300721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300721)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300721)Termination reason: Instruction limit
% 1.42/0.51 % (2300721)Termination phase: Property scanning
% 1.42/0.51 % (2300721)Time elapsed: 0.012 s
% 1.42/0.51 % (2300721)Peak memory usage: 10 MB
% 1.42/0.51 % (2300721)Instructions burned: 29 (million)
% 1.42/0.51 % (2300724)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
% 1.42/0.51 % (2300724)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.51 % (2300722)Instruction limit reached!
% 1.42/0.51 % (2300722)------------------------------
% 1.42/0.51 % (2300722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300722)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300722)Termination reason: Instruction limit
% 1.42/0.51 % (2300722)Termination phase: Preprocessing 3
% 1.42/0.51 % (2300722)Time elapsed: 0.026 s
% 1.42/0.51 % (2300722)Peak memory usage: 11 MB
% 1.42/0.51 % (2300722)Instructions burned: 60 (million)
% 1.42/0.51 % (2300728)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.51 % (2300724)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=2281662216:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.51 % (2300728)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=2080242387:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.51 % (2300729)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=1165134578:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.42/0.51 % (2300711) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2300672-2300711"...
% 1.42/0.51 % (2300728)Instruction limit reached!
% 1.42/0.51 % (2300728)------------------------------
% 1.42/0.51 % (2300728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300728)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300728)Termination reason: Instruction limit
% 1.42/0.51 % (2300728)Termination phase: shuffling
% 1.42/0.51 % (2300728)Time elapsed: 0.004 s
% 1.42/0.51 % (2300728)Peak memory usage: 10 MB
% 1.42/0.51 % (2300728)Instructions burned: 8 (million)
% 1.42/0.51 % (2300724)Instruction limit reached!
% 1.42/0.51 % (2300724)------------------------------
% 1.42/0.51 % (2300724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300724)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300724)Termination reason: Instruction limit
% 1.42/0.51 % (2300724)Termination phase: shuffling
% 1.42/0.51 % (2300724)Time elapsed: 0.012 s
% 1.42/0.51 % (2300724)Peak memory usage: 10 MB
% 1.42/0.51 % (2300724)Instructions burned: 14 (million)
% 1.42/0.51 % (2300730)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2957510862:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.51 % (2300729)Instruction limit reached!
% 1.42/0.51 % (2300729)------------------------------
% 1.42/0.51 % (2300729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300729)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300729)Termination reason: Instruction limit
% 1.42/0.51 % (2300729)Termination phase: Property scanning
% 1.42/0.51 % (2300729)Time elapsed: 0.018 s
% 1.42/0.51 % (2300729)Peak memory usage: 10 MB
% 1.42/0.51 % (2300729)Instructions burned: 32 (million)
% 1.42/0.51 % (2300730)Instruction limit reached!
% 1.42/0.51 % (2300730)------------------------------
% 1.42/0.51 % (2300730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (2300730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (2300730)CaDiCaL version: 2.1.3
% 1.42/0.51 % (2300730)Termination reason: Instruction limit
% 1.42/0.51 % (2300730)Termination phase: shuffling
% 1.42/0.51 % (2300730)Time elapsed: 0.004 s
% 1.42/0.51 % (2300730)Peak memory usage: 10 MB
% 1.42/0.51 % (2300730)Instructions burned: 8 (million)
% 1.42/0.51 % (2300734)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3821828561:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.42/0.51 % (2300711)...printing done.
% 1.42/0.51 % (2300711)Refutation found. Thanks to Tanya!
% 1.42/0.51 % SZS status Theorem for theBenchmark
% 1.42/0.51 % SZS output start Proof for theBenchmark
% 1.42/0.51 thf(type_def_5, type, term: $tType).
% 1.42/0.51 thf(type_def_6, type, subst: $tType).
% 1.42/0.51 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 1.42/0.51 thf(type_def_8, type, d_term: $tType).
% 1.42/0.51 thf(type_def_9, type, d_subst: $tType).
% 1.42/0.51 thf(func_def_0, type, one: term).
% 1.42/0.51 thf(func_def_1, type, ap: (term > term > term)).
% 1.42/0.51 thf(func_def_2, type, lam: (term > term)).
% 1.42/0.51 thf(func_def_3, type, sub: (term > subst > term)).
% 1.42/0.51 thf(func_def_4, type, id: subst).
% 1.42/0.51 thf(func_def_5, type, sh: subst).
% 1.42/0.51 thf(func_def_6, type, push: (term > subst > subst)).
% 1.42/0.51 thf(func_def_7, type, comp: (subst > subst > subst)).
% 1.42/0.51 thf(func_def_8, type, var: (term > $o)).
% 1.42/0.51 thf(func_def_9, type, pushprop_lem1v2: $o).
% 1.42/0.51 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 1.42/0.51 thf(func_def_11, type, axmap: $o).
% 1.42/0.51 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 1.42/0.51 thf(func_def_13, type, shinj: $o).
% 1.42/0.51 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 1.42/0.51 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 1.42/0.51 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 1.42/0.51 thf(func_def_17, type, induction2lem: $o).
% 1.42/0.51 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 1.42/0.51 thf(func_def_19, type, axvarshift: $o).
% 1.42/0.51 thf(func_def_20, type, hoasapinj2: $o).
% 1.42/0.51 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 1.42/0.51 thf(func_def_22, type, hoasapinj1: $o).
% 1.42/0.51 thf(func_def_23, type, ulamvar1: $o).
% 1.42/0.51 thf(func_def_24, type, induction2lem_lthm: $o).
% 1.42/0.51 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 1.42/0.51 thf(func_def_26, type, apnotvar: $o).
% 1.42/0.51 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 1.42/0.51 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 1.42/0.51 thf(func_def_29, type, hoasinduction_lthm: $o).
% 1.42/0.51 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 1.42/0.51 thf(func_def_31, type, hoaslaminj: $o).
% 1.42/0.51 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 1.42/0.51 thf(func_def_33, type, induction2lem_gthm: $o).
% 1.42/0.51 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 1.42/0.51 thf(func_def_35, type, hoasinduction_lem3: $o).
% 1.42/0.51 thf(func_def_36, type, hoasinduction_lem2: $o).
% 1.42/0.51 thf(func_def_37, type, termmset_lthm: $o).
% 1.42/0.51 thf(func_def_38, type, hoasinduction_lem1: $o).
% 1.42/0.51 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 1.42/0.51 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 1.42/0.51 thf(func_def_41, type, hoasapnotvar: $o).
% 1.42/0.51 thf(func_def_42, type, hoasinduction_lem0: $o).
% 1.42/0.51 thf(func_def_43, type, hoasinduction: $o).
% 1.42/0.51 thf(func_def_44, type, hoasinduction_gthm: $o).
% 1.42/0.51 thf(func_def_45, type, axapp: $o).
% 1.42/0.51 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 1.42/0.51 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 1.42/0.51 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 1.42/0.51 thf(func_def_49, type, ulamvarind: $o).
% 1.42/0.51 thf(func_def_50, type, induction: $o).
% 1.42/0.51 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 1.42/0.51 thf(func_def_52, type, termmset_gthm: $o).
% 1.42/0.51 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 1.42/0.51 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 1.42/0.51 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 1.42/0.51 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 1.42/0.51 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 1.42/0.51 thf(func_def_58, type, pushprop_lem2v2: $o).
% 1.42/0.51 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 1.42/0.51 thf(func_def_60, type, axclos: $o).
% 1.42/0.51 thf(func_def_61, type, axassoc: $o).
% 1.42/0.51 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 1.42/0.51 thf(func_def_63, type, pushprop_lthm: $o).
% 1.42/0.51 thf(func_def_64, type, apinj2: $o).
% 1.42/0.51 thf(func_def_65, type, apinj1: $o).
% 1.42/0.51 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 1.42/0.51 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 1.42/0.51 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 1.42/0.51 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 1.42/0.51 thf(func_def_70, type, axvarcons: $o).
% 1.42/0.51 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 1.42/0.51 thf(func_def_72, type, axscons: $o).
% 1.42/0.51 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 1.42/0.51 thf(func_def_74, type, axidr: $o).
% 1.42/0.51 thf(func_def_75, type, pushprop_lem1: $o).
% 1.42/0.51 thf(func_def_76, type, laminj: $o).
% 1.42/0.51 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 1.42/0.51 thf(func_def_78, type, pushprop_lem0: $o).
% 1.42/0.51 thf(func_def_79, type, pushprop_gthm: $o).
% 1.42/0.51 thf(func_def_80, type, axabs: $o).
% 1.42/0.51 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 1.42/0.51 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 1.42/0.51 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 1.42/0.51 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 1.42/0.51 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 1.42/0.51 thf(func_def_86, type, lamnotap: $o).
% 1.42/0.51 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 1.42/0.51 thf(func_def_88, type, hoaslamnotvar: $o).
% 1.42/0.51 thf(func_def_89, type, axidl: $o).
% 1.42/0.51 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 1.42/0.51 thf(func_def_91, type, induction2_lthm: $o).
% 1.42/0.51 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 1.42/0.51 thf(func_def_93, type, substmonoid_lthm: $o).
% 1.42/0.51 thf(func_def_94, type, pushprop: $o).
% 1.42/0.51 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 1.42/0.51 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 1.42/0.51 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 1.42/0.51 thf(func_def_98, type, substmonoid: $o).
% 1.42/0.51 thf(func_def_99, type, lamnotvar: $o).
% 1.42/0.51 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 1.42/0.51 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 1.42/0.51 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 1.42/0.51 thf(func_def_103, type, induction2_gthm: $o).
% 1.42/0.51 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 1.42/0.51 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_106, type, hoaslamnotap: $o).
% 1.42/0.51 thf(func_def_107, type, substmonoid_gthm: $o).
% 1.42/0.51 thf(func_def_108, type, ulamvarsh: $o).
% 1.42/0.51 thf(func_def_109, type, induction2: $o).
% 1.42/0.51 thf(func_def_110, type, pushprop_lem3v2: $o).
% 1.42/0.51 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 1.42/0.51 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 1.42/0.51 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 1.42/0.51 thf(func_def_114, type, axshiftcons: $o).
% 1.42/0.51 thf(func_def_115, type, termmset: $o).
% 1.42/0.51 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 1.42/0.51 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 1.42/0.51 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 1.42/0.51 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 1.42/0.51 thf(func_def_120, type, axvarid: $o).
% 1.42/0.51 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 1.42/0.51 thf(func_def_122, type, d2term: (d_term > term)).
% 1.42/0.51 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 1.42/0.51 thf(func_def_124, type, d_one: d_term).
% 1.42/0.51 thf(func_def_125, type, d_id: d_subst).
% 1.42/0.51 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.51 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 1.42/0.51 thf(func_def_129, type, db3: !>[X0: $tType]:(X0)).
% 1.42/0.51 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 1.42/0.51 thf(func_def_131, type, db2: !>[X0: $tType]:(X0)).
% 1.42/0.51 thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
% 1.42/0.51 thf(func_def_133, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.51 thf(func_def_134, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.42/0.51 thf(func_def_137, type, db4: !>[X0: $tType]:(X0)).
% 1.42/0.51 thf(func_def_138, type, sP0: $o).
% 1.42/0.51 thf(func_def_139, type, sP1: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_140, type, sP2: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_141, type, sP3: $o).
% 1.42/0.51 thf(func_def_142, type, sP4: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_143, type, sP5: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_144, type, sP6: $o).
% 1.42/0.51 thf(func_def_145, type, sP7: $o).
% 1.42/0.51 thf(func_def_146, type, sP8: $o).
% 1.42/0.51 thf(func_def_147, type, sP9: $o).
% 1.42/0.51 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_149, type, sP11: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_150, type, sP12: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_152, type, sP14: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_153, type, sP15: $o).
% 1.42/0.51 thf(func_def_154, type, sP16: $o).
% 1.42/0.51 thf(func_def_155, type, sP17: $o).
% 1.42/0.51 thf(func_def_156, type, sP18: $o).
% 1.42/0.51 thf(func_def_157, type, sP19: $o).
% 1.42/0.51 thf(func_def_158, type, sP20: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_159, type, sP21: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_160, type, sP22: $o).
% 1.42/0.51 thf(func_def_161, type, sP23: $o).
% 1.42/0.51 thf(func_def_162, type, sP24: $o).
% 1.42/0.51 thf(func_def_163, type, sP25: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_164, type, sP26: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_165, type, sP27: $o).
% 1.42/0.51 thf(func_def_166, type, sP28: $o).
% 1.42/0.51 thf(func_def_167, type, sP29: $o).
% 1.42/0.51 thf(func_def_168, type, sP30: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_169, type, sP31: $o).
% 1.42/0.51 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_171, type, sP33: $o).
% 1.42/0.51 thf(func_def_172, type, sP34: $o).
% 1.42/0.51 thf(func_def_173, type, sP35: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_174, type, sP36: $o).
% 1.42/0.51 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_176, type, sP38: $o).
% 1.42/0.51 thf(func_def_177, type, sP39: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_178, type, sP40: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_179, type, sP41: $o).
% 1.42/0.51 thf(func_def_180, type, sP42: $o).
% 1.42/0.51 thf(func_def_181, type, sP43: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_182, type, sP44: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_183, type, sP45: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_184, type, sP46: $o).
% 1.42/0.51 thf(func_def_185, type, sP47: $o).
% 1.42/0.51 thf(func_def_186, type, sP48: $o).
% 1.42/0.51 thf(func_def_187, type, sP49: $o).
% 1.42/0.51 thf(func_def_188, type, sP50: $o).
% 1.42/0.51 thf(func_def_189, type, sP51: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_190, type, sP52: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_191, type, sP53: $o).
% 1.42/0.51 thf(func_def_192, type, sP54: $o).
% 1.42/0.51 thf(func_def_193, type, sP55: ((term > $o) > $o)).
% 1.42/0.51 thf(func_def_194, type, sP56: $o).
% 1.42/0.51 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 1.42/0.51 thf(func_def_196, type, sP58: $o).
% 1.42/0.51 thf(func_def_197, type, sK59: term).
% 1.42/0.51 thf(func_def_198, type, sK60: term).
% 1.42/0.51 thf(func_def_199, type, sK61: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_200, type, sK62: (term > $o)).
% 1.42/0.51 thf(func_def_201, type, sK63: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_202, type, sK64: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_203, type, sK65: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_205, type, sK67: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_206, type, sK68: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_207, type, sK69: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_208, type, sK70: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_209, type, sK71: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_210, type, sK72: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_211, type, sK73: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_212, type, sK74: (term > $o)).
% 1.42/0.51 thf(func_def_213, type, sK75: term).
% 1.42/0.51 thf(func_def_214, type, sK76: (term > term)).
% 1.42/0.51 thf(func_def_215, type, sK77: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_216, type, sK78: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_217, type, sK79: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_218, type, sK80: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_219, type, sK81: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_220, type, sK82: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_221, type, sK83: subst).
% 1.42/0.51 thf(func_def_222, type, sK84: term).
% 1.42/0.51 thf(func_def_223, type, sK85: subst).
% 1.42/0.51 thf(func_def_224, type, sK86: subst).
% 1.42/0.51 thf(func_def_225, type, sK87: term).
% 1.42/0.51 thf(func_def_226, type, sK88: (term > $o)).
% 1.42/0.51 thf(func_def_227, type, sK89: term).
% 1.42/0.51 thf(func_def_228, type, sK90: term).
% 1.42/0.51 thf(func_def_229, type, sK91: subst).
% 1.42/0.51 thf(func_def_230, type, sK92: (term > $o)).
% 1.42/0.51 thf(func_def_231, type, sK93: (term > term)).
% 1.42/0.51 thf(func_def_232, type, sK94: ((term > $o) > subst > term)).
% 1.42/0.51 thf(func_def_233, type, sK95: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_234, type, sK96: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_235, type, sK97: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_236, type, sK98: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_237, type, sK99: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_238, type, sK100: (subst > term > term)).
% 1.42/0.51 thf(func_def_239, type, sK101: term).
% 1.42/0.51 thf(func_def_240, type, sK102: (subst > term > term)).
% 1.42/0.51 thf(func_def_241, type, sK103: subst).
% 1.42/0.51 thf(func_def_242, type, sK104: subst).
% 1.42/0.51 thf(func_def_243, type, sK105: term).
% 1.42/0.51 thf(func_def_244, type, sK106: term).
% 1.42/0.51 thf(func_def_245, type, sK107: term).
% 1.42/0.51 thf(func_def_246, type, sK108: term).
% 1.42/0.51 thf(func_def_247, type, sK109: subst).
% 1.42/0.51 thf(func_def_248, type, sK110: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_249, type, sK111: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_250, type, sK112: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_251, type, sK113: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_252, type, sK114: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_253, type, sK115: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_254, type, sK116: term).
% 1.42/0.51 thf(func_def_255, type, sK117: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_256, type, sK118: (term > $o)).
% 1.42/0.51 thf(func_def_257, type, sK119: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_258, type, sK120: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_259, type, sK121: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_260, type, sK122: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_261, type, sK123: (term > subst > term > term)).
% 1.42/0.51 thf(func_def_262, type, sK124: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_263, type, sK125: ((term > $o) > term > term)).
% 1.42/0.51 thf(func_def_264, type, sK126: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_265, type, sK127: term).
% 1.42/0.51 thf(func_def_266, type, sK128: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_267, type, sK129: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_268, type, sK130: term).
% 1.42/0.51 thf(func_def_269, type, sK131: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_270, type, sK132: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > term > $o)).
% 1.42/0.51 thf(func_def_272, type, sK134: term).
% 1.42/0.51 thf(func_def_273, type, sK135: term).
% 1.42/0.51 thf(func_def_274, type, sK136: (term > $o)).
% 1.42/0.51 thf(func_def_275, type, sK137: (term > term)).
% 1.42/0.51 thf(func_def_276, type, sK138: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_277, type, sK139: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_278, type, sK140: term).
% 1.42/0.51 thf(func_def_279, type, sK141: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_281, type, sK143: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_282, type, sK144: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_283, type, sK145: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_284, type, sK146: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_285, type, sK147: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_288, type, sK150: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_289, type, sK151: (term > (term > $o) > term)).
% 1.42/0.51 thf(func_def_290, type, sK152: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_291, type, sK153: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.42/0.51 thf(func_def_292, type, sK154: (term > $o)).
% 1.42/0.51 thf(func_def_293, type, sK155: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_294, type, sK156: term).
% 1.42/0.51 thf(func_def_295, type, sK157: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_296, type, sK158: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_297, type, sK159: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_298, type, sK160: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_299, type, sK161: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_300, type, sK162: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_301, type, sK163: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_302, type, sK164: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_303, type, sK165: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_305, type, sK167: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_306, type, sK168: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_307, type, sK169: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_308, type, sK170: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_309, type, sK171: term).
% 1.42/0.51 thf(func_def_310, type, sK172: term).
% 1.42/0.51 thf(func_def_311, type, sK173: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_312, type, sK174: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_315, type, sK177: (term > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_317, type, sK179: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_318, type, sK180: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_319, type, sK181: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_320, type, sK182: (term > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_322, type, sK184: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_323, type, sK185: term).
% 1.42/0.51 thf(func_def_324, type, sK186: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_325, type, sK187: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_326, type, sK188: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_327, type, sK189: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_328, type, sK190: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_329, type, sK191: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_330, type, sK192: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_331, type, sK193: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_332, type, sK194: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_333, type, sK195: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_334, type, sK196: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_335, type, sK197: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_336, type, sK198: (term > $o)).
% 1.42/0.51 thf(func_def_337, type, sK199: term).
% 1.42/0.51 thf(func_def_338, type, sK200: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_342, type, sK204: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_343, type, sK205: (term > (term > $o) > term)).
% 1.42/0.51 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_348, type, sK210: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_349, type, sK211: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_350, type, sK212: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_351, type, sK213: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_352, type, sK214: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_353, type, sK215: term).
% 1.42/0.51 thf(func_def_354, type, sK216: (term > $o)).
% 1.42/0.51 thf(func_def_355, type, sK217: subst).
% 1.42/0.51 thf(func_def_356, type, sK218: (term > term)).
% 1.42/0.51 thf(func_def_357, type, sK219: (subst > (term > $o) > term)).
% 1.42/0.51 thf(func_def_358, type, sK220: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_359, type, sK221: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_360, type, sK222: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_361, type, sK223: term).
% 1.42/0.51 thf(func_def_362, type, sK224: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_363, type, sK225: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_364, type, sK226: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_365, type, sK227: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_366, type, sK228: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > term > term)).
% 1.42/0.51 thf(func_def_369, type, sK231: term).
% 1.42/0.51 thf(func_def_370, type, sK232: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_371, type, sK233: (term > $o)).
% 1.42/0.51 thf(func_def_372, type, sK234: ((term > $o) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_374, type, sK236: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_375, type, sK237: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_376, type, sK238: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_377, type, sK239: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_378, type, sK240: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_379, type, sK241: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_380, type, sK242: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_381, type, sK243: ((term > $o) > term > term)).
% 1.42/0.51 thf(func_def_382, type, sK244: term).
% 1.42/0.51 thf(func_def_383, type, sK245: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_384, type, sK246: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_385, type, sK247: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_386, type, sK248: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_387, type, sK249: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_388, type, sK250: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_389, type, sK251: term).
% 1.42/0.51 thf(func_def_390, type, sK252: term).
% 1.42/0.51 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_392, type, sK254: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_393, type, sK255: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_394, type, sK256: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_397, type, sK259: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_398, type, sK260: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_399, type, sK261: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_400, type, sK262: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_401, type, sK263: term).
% 1.42/0.51 thf(func_def_402, type, sK264: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_403, type, sK265: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_404, type, sK266: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_405, type, sK267: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_406, type, sK268: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_407, type, sK269: ((subst > term > subst > $o) > term > term)).
% 1.42/0.51 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_409, type, sK271: ((term > $o) > subst > term)).
% 1.42/0.51 thf(func_def_410, type, sK272: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_411, type, sK273: term).
% 1.42/0.51 thf(func_def_412, type, sK274: subst).
% 1.42/0.51 thf(func_def_413, type, sK275: (term > $o)).
% 1.42/0.51 thf(func_def_414, type, sK276: (term > term)).
% 1.42/0.51 thf(func_def_415, type, sK277: term).
% 1.42/0.51 thf(func_def_416, type, sK278: (term > $o)).
% 1.42/0.51 thf(func_def_417, type, sK279: term).
% 1.42/0.51 thf(func_def_418, type, sK280: (term > term)).
% 1.42/0.51 thf(func_def_419, type, sK281: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_420, type, sK282: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_421, type, sK283: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_422, type, sK284: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_423, type, sK285: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_424, type, sK286: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_425, type, sK287: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_426, type, sK288: term).
% 1.42/0.51 thf(func_def_427, type, sK289: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_428, type, sK290: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_429, type, sK291: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_430, type, sK292: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_431, type, sK293: ((subst > term > subst > $o) > term > $o)).
% 1.42/0.51 thf(func_def_432, type, sK294: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_433, type, sK295: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_434, type, sK296: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_435, type, sK297: term).
% 1.42/0.51 thf(func_def_436, type, sK298: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_437, type, sK299: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_438, type, sK300: term).
% 1.42/0.51 thf(func_def_439, type, sK301: (term > $o)).
% 1.42/0.51 thf(func_def_440, type, sK302: (term > term)).
% 1.42/0.51 thf(func_def_441, type, sK303: (term > (term > $o) > term)).
% 1.42/0.51 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_443, type, sK305: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.42/0.51 thf(func_def_444, type, sK306: (term > $o)).
% 1.42/0.51 thf(func_def_445, type, sK307: term).
% 1.42/0.51 thf(func_def_446, type, sK308: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_447, type, sK309: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_448, type, sK310: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_449, type, sK311: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_450, type, sK312: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_451, type, sK313: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_452, type, sK314: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_453, type, sK315: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_454, type, sK316: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_455, type, sK317: term).
% 1.42/0.51 thf(func_def_456, type, sK318: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_457, type, sK319: (term > (subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_458, type, sK320: (term > (subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_459, type, sK321: (term > (subst > term > term) > term)).
% 1.42/0.51 thf(func_def_460, type, sK322: (term > (subst > term > term) > term)).
% 1.42/0.51 thf(func_def_461, type, sK323: (term > (subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_462, type, sK324: (term > (subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_463, type, sK325: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_464, type, sK326: ((subst > term > subst > $o) > term > term)).
% 1.42/0.51 thf(func_def_465, type, sK327: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_466, type, sK328: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_467, type, sK329: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_468, type, sK330: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_469, type, sK331: term).
% 1.42/0.51 thf(func_def_470, type, sK332: (term > $o)).
% 1.42/0.51 thf(func_def_471, type, sK333: (term > term)).
% 1.42/0.51 thf(func_def_472, type, sK334: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_473, type, sK335: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_474, type, sK336: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_475, type, sK337: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_476, type, sK338: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_477, type, sK339: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_478, type, sK340: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_479, type, sK341: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_480, type, sK342: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_481, type, sK343: term).
% 1.42/0.51 thf(func_def_482, type, sK344: term).
% 1.42/0.51 thf(func_def_483, type, sK345: term).
% 1.42/0.51 thf(func_def_484, type, sK346: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_485, type, sK347: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_486, type, sK348: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_487, type, sK349: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_488, type, sK350: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_489, type, sK351: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_490, type, sK352: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_491, type, sK353: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_492, type, sK354: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_493, type, sK355: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_494, type, sK356: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_495, type, sK357: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_496, type, sK358: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_497, type, sK359: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_498, type, sK360: (term > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_499, type, sK361: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_503, type, sK365: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_504, type, sK366: term).
% 1.42/0.51 thf(func_def_505, type, sK367: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_506, type, sK368: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_508, type, sK370: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_509, type, sK371: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_510, type, sK372: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_511, type, sK373: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_512, type, sK374: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_513, type, sK375: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_516, type, sK378: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_517, type, sK379: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_518, type, sK380: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_519, type, sK381: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_520, type, sK382: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_521, type, sK383: term).
% 1.42/0.51 thf(func_def_522, type, sK384: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_523, type, sK385: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_524, type, sK386: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_525, type, sK387: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_526, type, sK388: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_527, type, sK389: term).
% 1.42/0.51 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > term > term)).
% 1.42/0.51 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_531, type, sK393: (term > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_532, type, sK394: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_533, type, sK395: term).
% 1.42/0.51 thf(func_def_534, type, sK396: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_535, type, sK397: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_536, type, sK398: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_537, type, sK399: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_538, type, sK400: (term > $o)).
% 1.42/0.51 thf(func_def_539, type, sK401: term).
% 1.42/0.51 thf(func_def_540, type, sK402: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_541, type, sK403: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_542, type, sK404: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_543, type, sK405: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_544, type, sK406: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_545, type, sK407: (term > (term > $o) > term)).
% 1.42/0.51 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_547, type, sK409: ((subst > term > subst > $o) > (term > $o) > term)).
% 1.42/0.51 thf(func_def_548, type, sK410: term).
% 1.42/0.51 thf(func_def_549, type, sK411: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_552, type, sK414: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_553, type, sK415: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_554, type, sK416: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_555, type, sK417: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_556, type, sK418: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_557, type, sK419: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_558, type, sK420: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_559, type, sK421: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_560, type, sK422: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_561, type, sK423: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_562, type, sK424: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_563, type, sK425: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_564, type, sK426: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_566, type, sK428: term).
% 1.42/0.51 thf(func_def_567, type, sK429: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > term > term)).
% 1.42/0.51 thf(func_def_569, type, sK431: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_570, type, sK432: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_571, type, sK433: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_572, type, sK434: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_573, type, sK435: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_574, type, sK436: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_575, type, sK437: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_576, type, sK438: ((subst > term > subst > $o) > subst)).
% 1.42/0.51 thf(func_def_577, type, sK439: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_578, type, sK440: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_579, type, sK441: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_580, type, sK442: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_582, type, sK444: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_583, type, sK445: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_584, type, sK446: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_585, type, sK447: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_587, type, sK449: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_588, type, sK450: term).
% 1.42/0.51 thf(func_def_589, type, sK451: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_590, type, sK452: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_591, type, sK453: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_592, type, sK454: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_593, type, sK455: (term > (subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > subst > term > term)).
% 1.42/0.51 thf(func_def_595, type, sK457: term).
% 1.42/0.51 thf(func_def_596, type, sK458: term).
% 1.42/0.51 thf(func_def_597, type, sK459: (term > $o)).
% 1.42/0.51 thf(func_def_598, type, sK460: (term > $o)).
% 1.42/0.51 thf(func_def_599, type, sK461: subst).
% 1.42/0.51 thf(func_def_600, type, sK462: term).
% 1.42/0.51 thf(func_def_601, type, sK463: subst).
% 1.42/0.51 thf(func_def_602, type, sK464: (subst > (term > $o) > (term > $o) > term > term)).
% 1.42/0.51 thf(func_def_603, type, sK465: term).
% 1.42/0.51 thf(func_def_604, type, sK466: term).
% 1.42/0.51 thf(func_def_605, type, sK467: term).
% 1.42/0.51 thf(func_def_606, type, sK468: term).
% 1.42/0.51 thf(func_def_607, type, sK469: term).
% 1.42/0.51 thf(func_def_608, type, sK470: term).
% 1.42/0.51 thf(func_def_609, type, sK471: term).
% 1.42/0.51 thf(func_def_610, type, sK472: term).
% 1.42/0.51 thf(func_def_611, type, sK473: term).
% 1.42/0.51 thf(func_def_612, type, sK474: term).
% 1.42/0.51 thf(func_def_613, type, sK475: (term > subst > (term > $o) > term > $o)).
% 1.42/0.51 thf(func_def_614, type, sK476: (term > $o)).
% 1.42/0.51 thf(func_def_615, type, sK477: subst).
% 1.42/0.51 thf(func_def_616, type, sK478: term).
% 1.42/0.51 thf(func_def_617, type, sK479: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_618, type, sK480: term).
% 1.42/0.51 thf(func_def_619, type, sK481: (term > $o)).
% 1.42/0.51 thf(func_def_620, type, sK482: (term > $o)).
% 1.42/0.51 thf(func_def_621, type, sK483: subst).
% 1.42/0.51 thf(func_def_622, type, sK484: term).
% 1.42/0.51 thf(func_def_623, type, sK485: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_624, type, sK486: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_625, type, sK487: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_626, type, sK488: term).
% 1.42/0.51 thf(func_def_627, type, sK489: term).
% 1.42/0.51 thf(func_def_628, type, sK490: (subst > term > term)).
% 1.42/0.51 thf(func_def_629, type, sK491: subst).
% 1.42/0.51 thf(func_def_630, type, sK492: subst).
% 1.42/0.51 thf(func_def_631, type, sK493: subst).
% 1.42/0.51 thf(func_def_632, type, sK494: subst).
% 1.42/0.51 thf(func_def_633, type, sK495: ((subst > term > subst > $o) > term > $o)).
% 1.42/0.51 thf(func_def_634, type, sK496: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_635, type, sK497: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_636, type, sK498: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_637, type, sK499: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_638, type, sK500: term).
% 1.42/0.51 thf(func_def_639, type, sK501: (term > $o)).
% 1.42/0.51 thf(func_def_640, type, sK502: term).
% 1.42/0.51 thf(func_def_641, type, sK503: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_642, type, sK504: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_643, type, sK505: (term > subst > term > term)).
% 1.42/0.51 thf(func_def_644, type, sK506: term).
% 1.42/0.51 thf(func_def_645, type, sK507: term).
% 1.42/0.51 thf(func_def_646, type, sK508: term).
% 1.42/0.51 thf(func_def_647, type, sK509: term).
% 1.42/0.51 thf(func_def_648, type, sK510: subst).
% 1.42/0.51 thf(func_def_649, type, sK511: term).
% 1.42/0.51 thf(func_def_650, type, sK512: (term > subst > term > term)).
% 1.42/0.51 thf(func_def_651, type, sK513: term).
% 1.42/0.51 thf(func_def_652, type, sK514: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_653, type, sK515: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_654, type, sK516: term).
% 1.42/0.51 thf(func_def_655, type, sK517: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_656, type, sK518: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_657, type, sK519: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_658, type, sK520: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_659, type, sK521: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_660, type, sK522: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_661, type, sK523: term).
% 1.42/0.51 thf(func_def_662, type, sK524: (subst > term > term)).
% 1.42/0.51 thf(func_def_663, type, sK525: (subst > term > term)).
% 1.42/0.51 thf(func_def_664, type, sK526: subst).
% 1.42/0.51 thf(func_def_665, type, sK527: subst).
% 1.42/0.51 thf(func_def_666, type, sK528: subst).
% 1.42/0.51 thf(func_def_667, type, sK529: term).
% 1.42/0.51 thf(func_def_668, type, sK530: (term > subst > term > term)).
% 1.42/0.51 thf(func_def_669, type, sK531: term).
% 1.42/0.51 thf(func_def_670, type, sK532: term).
% 1.42/0.51 thf(func_def_671, type, sK533: (term > d_term)).
% 1.42/0.51 thf(func_def_672, type, sK534: subst).
% 1.42/0.51 thf(func_def_673, type, sK535: subst).
% 1.42/0.51 thf(func_def_674, type, sK536: term).
% 1.42/0.51 thf(func_def_675, type, sK537: term).
% 1.42/0.51 thf(func_def_676, type, sK538: term).
% 1.42/0.51 thf(func_def_677, type, sK539: term).
% 1.42/0.51 thf(func_def_678, type, sK540: term).
% 1.42/0.51 thf(func_def_679, type, sK541: subst).
% 1.42/0.51 thf(func_def_680, type, sK542: term).
% 1.42/0.51 thf(func_def_681, type, sK543: term).
% 1.42/0.51 thf(func_def_682, type, sK544: term).
% 1.42/0.51 thf(func_def_683, type, sK545: term).
% 1.42/0.51 thf(func_def_684, type, sK546: term).
% 1.42/0.51 thf(func_def_685, type, sK547: term).
% 1.42/0.51 thf(func_def_686, type, sK548: term).
% 1.42/0.51 thf(func_def_687, type, sK549: term).
% 1.42/0.51 thf(func_def_688, type, sK550: subst).
% 1.42/0.51 thf(func_def_689, type, sK551: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_690, type, sK552: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_691, type, sK553: ((subst > term > subst > $o) > term > $o)).
% 1.42/0.51 thf(func_def_692, type, sK554: (subst > d_subst)).
% 1.42/0.51 thf(func_def_693, type, sK555: (subst > (term > $o) > term > (term > $o) > term)).
% 1.42/0.51 thf(func_def_694, type, sK556: (term > $o)).
% 1.42/0.51 thf(func_def_695, type, sK557: term).
% 1.42/0.51 thf(func_def_696, type, sK558: (term > $o)).
% 1.42/0.51 thf(func_def_697, type, sK559: subst).
% 1.42/0.51 thf(func_def_698, type, sK560: term).
% 1.42/0.51 thf(func_def_699, type, sK561: (term > subst > term > term)).
% 1.42/0.51 thf(func_def_700, type, sK562: term).
% 1.42/0.51 thf(func_def_701, type, sK563: term).
% 1.42/0.51 thf(func_def_702, type, sK564: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_703, type, sK565: ((subst > term > subst > $o) > term)).
% 1.42/0.51 thf(func_def_704, type, sK566: term).
% 1.42/0.51 thf(func_def_705, type, sK567: (subst > term > subst > $o)).
% 1.42/0.51 thf(func_def_706, type, sK568: term).
% 1.42/0.51 thf(func_def_707, type, sK569: term).
% 1.42/0.51 thf(func_def_708, type, sK570: term).
% 1.42/0.51 thf(func_def_709, type, sK571: term).
% 1.42/0.51 thf(func_def_710, type, sK572: term).
% 1.42/0.51 thf(func_def_711, type, sK573: term).
% 1.42/0.51 thf(func_def_712, type, sK574: term).
% 1.42/0.51 thf(func_def_713, type, sK575: term).
% 1.42/0.51 thf(func_def_714, type, sK576: term).
% 1.42/0.51 thf(func_def_715, type, sK577: subst).
% 1.42/0.51 thf(func_def_716, type, sK578: term).
% 1.42/0.51 thf(func_def_717, type, sK579: subst).
% 1.42/0.51 thf(func_def_718, type, sK580: term).
% 1.42/0.51 thf(func_def_719, type, sK581: term).
% 1.42/0.51 thf(func_def_720, type, sK582: (term > $o)).
% 1.42/0.51 thf(func_def_721, type, sK583: (term > $o)).
% 1.42/0.51 thf(func_def_722, type, sK584: term).
% 1.42/0.51 thf(func_def_723, type, sK585: subst).
% 1.42/0.51 thf(func_def_724, type, sK586: (subst > (term > $o) > term > term > $o)).
% 1.42/0.51 thf(func_def_725, type, sK587: term).
% 1.42/0.51 thf(func_def_726, type, sK588: (term > $o)).
% 1.42/0.51 thf(func_def_727, type, sK589: subst).
% 1.42/0.51 thf(func_def_728, type, sK590: ((term > $o) > term)).
% 1.42/0.51 thf(func_def_729, type, vNOT: ($o > $o)).
% 1.42/0.51 thf(func_def_730, type, sK591: (subst > term > term)).
% 1.42/0.51 thf(func_def_731, type, sK592: (subst > term > term)).
% 1.42/0.51 thf(func_def_732, type, sK593: subst).
% 1.42/0.51 thf(func_def_733, type, sK594: term).
% 1.42/0.51 thf(func_def_734, type, sK595: ((subst > term > term) > term)).
% 1.42/0.51 thf(func_def_735, type, sK596: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_736, type, sK597: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_737, type, sK598: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_738, type, sK599: ((subst > term > term) > subst)).
% 1.42/0.51 thf(func_def_739, type, sK600: ((subst > term > term) > term)).
% 1.42/0.51 thf(f1,axiom,(
% 1.42/0.51 (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & hoaslamnotvar_lthm & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))))) <=> substmonoid_lthm) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)))))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)))))) & hoasapnotvar_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X13 : term,X15 : term,X20 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) <=> hoasapinj1_lthm) & pushprop & (hoasinduction_lem2v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X45 : term,X44 : term] : (~(X11 @ X44) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45) | (X11 @ (ap @ X44 @ X45)) | ~ ! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (! [X15 : term,X13 : term,X19 : term,X20 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj1) & (shinj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((sub @ X13 @ sh)) != ((sub @ X15 @ sh))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & hoasinduction_gthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X14 : subst,X11 : (term > $o),X10 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | (X11 @ one) | ~(X10 @ X13))) <=> pushprop_lem1v2_lthm) & (pushprop_lem1_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X26 : (term > $o),X14 : subst,X13 : term,X15 : term,X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & ~(var @ (d2term @ d_one)) & pushprop_lthm & ((! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14)))) <=> substmonoid) & pushprop_lem2v2 & axmap & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & apnotvar & pushprop_gthm & pushprop_lem0_gthm & ((! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => (! [X23 : term,X24 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X10 @ id @ X24 @ id)) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [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)) | (X10 @ id @ (lam @ X27) @ id)) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) <=> hoasinduction_lthm) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))) => ! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X29))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & induction2_gthm & (! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13))) <=> induction) & hoasinduction_lem1_lthm & (hoasinduction_lem2 <=> ! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : (~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X24 @ id))) & (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & induction2lem_gthm & lamnotvar & hoasinduction_lem3v2_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X14 : subst,X13 : term] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f) & hoasinduction_lem1v2_gthm & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & ulamvarind & ! [X2 : d_term,X3 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & pushprop_lem2v2_lthm & (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) <=> laminj) & (! [X16 : term,X17 : subst,X10 : (term > $o)] : (~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) <=> induction2lem) & (id = ((d2subst @ d_id))) & termmset_gthm & hoasinduction_lem3_gthm & hoaslamnotap_lthm & (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) <=> induction2) & (! [X10 : (subst > term > subst > $o),X48 : term,X11 : (term > $o)] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X48))) <=> hoasinduction_lem3v2) & (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [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)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem3v2a) & hoasapinj2_gthm & (pushprop_lem1v2 <=> ! [X13 : term,X10 : (term > $o),X11 : (term > $o),X14 : subst] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) & (! [X13 : term,X10 : (term > $o),X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0) & ulamvarsh & hoaslamnotvar & hoasinduction_lem3b_gthm & ! [X5 : d_subst] : (X5 = d_id) & hoasapnotvar & (! [X30 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) <=> hoasinduction_no_psi_cond) & (apinj2 <=> ! [X13 : term,X20 : term,X19 : term,X15 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20))))) & hoasinduction_lem1v2 & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & hoasinduction_lem3a_gthm & ~ulamvar1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ~lamnotap & hoasapinj1_gthm & (axscons <=> ! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14))))) & axassoc & (! [X15 : term,X14 : subst,X13 : term,X10 : (term > $o),X26 : (term > $o)] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & (pushprop_p_and_p_prime = (^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))))) & (! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & hoaslaminj_gthm & hoasapnotvar_lthm & pushprop_lem3v2 & hoasinduction_lem2_gthm & (hoaslaminj <=> ! [X33 : term,X31 : (subst > term > term),X32 : subst,X18 : (subst > term > term)] : ((((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))) & axclos & hoaslamnotvar_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (induction2lem_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : (~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X21)) => ! [X10 : (term > $o),X16 : term,X17 : subst] : (~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)))))))) & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & (axshiftcons <=> ! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem2v2_gthm & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & axabs & hoasinduction_lem1_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))))))) <=> hoasinduction_lthm_3) & (! [X13 : term,X15 : term,X20 : term,X19 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)) <=> hoasapinj1) & (hoasinduction_lem3aa_lthm <=> ! [X42 : term,X10 : (subst > term > subst > $o)] : (~ ! [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 @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X35 : term,X18 : (subst > term > term)] : (~ ! [X36 : subst,X38 : subst,X37 : term] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | ~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id))) & ((! [X15 : term,X13 : term,X19 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) <=> hoasapinj2_lthm) & (hoasinduction_lem3 <=> ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & pushprop_lthm_orig & hoasinduction_lem1 & pushprop_lem3v2_lthm & pushprop_lem1_gthm & pushprop_lem1v2_gthm & (sh = ((d2subst @ d_id))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & hoaslamnotap_gthm & hoasinduction_lem2_lthm & (hoaslamnotap <=> ! [X46 : term,X18 : (subst > term > term),X47 : 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)))))) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) <=> axidr) & (one = ((d2term @ d_one))) & axvarshift & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) => ! [X32 : subst,X18 : (subst > term > term),X33 : term,X31 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))))))) <=> hoaslaminj_lthm) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X48 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X11 @ (lam @ X48)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))))) & axapp & (hoasapinj2 <=> ! [X19 : term,X15 : term,X20 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) & substmonoid_gthm & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ 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))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (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))))) | (X10 @ id @ (lam @ X43) @ id))))) & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ! [X1 : d_term] : (X1 = d_one) & pushprop_lem2v2_gthm & (hoasinduction <=> ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [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))))) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X14 : subst,X26 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id))))),
% 1.42/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 1.42/0.51 thf(f2,conjecture,(
% 1.42/0.51 (! [X0 : (subst > term > term)] : (! [X3 : subst,X1 : subst,X2 : term] : (((sub @ (X0 @ X1 @ X2) @ X3)) = ((X0 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => ! [X4 : (subst > term > term)] : (! [X2 : term,X3 : subst,X1 : subst] : (((sub @ (X4 @ X1 @ X2) @ X3)) = ((X4 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => ((((hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X4 @ X1 @ X2))))) = ((hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X0 @ X1 @ X2)))))) => ! [X2 : term,X1 : subst] : (((X0 @ X1 @ X2)) = ((X4 @ X1 @ X2)))))) = hoaslaminj)),
% 1.42/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj)).
% 1.42/0.51 thf(f3,negated_conjecture,(
% 1.42/0.51 ~ (! [X0 : (subst > term > term)] : (! [X3 : subst,X1 : subst,X2 : term] : (((sub @ (X0 @ X1 @ X2) @ X3)) = ((X0 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => ! [X4 : (subst > term > term)] : (! [X2 : term,X3 : subst,X1 : subst] : (((sub @ (X4 @ X1 @ X2) @ X3)) = ((X4 @ (comp @ X1 @ X3) @ (sub @ X2 @ X3)))) => ((((hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X4 @ X1 @ X2))))) = ((hoaslam @ id @ (^[X1 : subst, X2 : term] : ((X0 @ X1 @ X2)))))) => ! [X2 : term,X1 : subst] : (((X0 @ X1 @ X2)) = ((X4 @ X1 @ X2)))))) = hoaslaminj)),
% 1.42/0.51 inference(negated_conjecture,[status(cth)],[f2])).
% 1.42/0.51 thf(f4,plain,(
% 1.42/0.51 ~ (! [X0 : (subst > term > term)] : (! [X1 : subst,X2 : subst,X3 : term] : (((sub @ (X0 @ X2 @ X3) @ X1)) = ((X0 @ (comp @ X2 @ X1) @ (sub @ X3 @ X1)))) => ! [X4 : (subst > term > term)] : (! [X5 : term,X6 : subst,X7 : subst] : (((X4 @ (comp @ X7 @ X6) @ (sub @ X5 @ X6))) = ((sub @ (X4 @ X7 @ X5) @ X6))) => ((((hoaslam @ id @ (^[X8 : subst, X9 : term] : ((X4 @ X8 @ X9))))) = ((hoaslam @ id @ (^[X10 : subst, X11 : term] : ((X0 @ X10 @ X11)))))) => ! [X12 : term,X13 : subst] : (((X0 @ X13 @ X12)) = ((X4 @ X13 @ X12)))))) = hoaslaminj)),
% 1.42/0.51 inference(rectify,[],[f3])).
% 1.42/0.51 thf(f5,plain,(
% 1.42/0.51 ~ (hoaslaminj = ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))))))),
% 1.42/0.51 inference(fool_elimination,[],[f4])).
% 1.42/0.51 thf(f6,plain,(
% 1.42/0.51 (termmset <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & hoaslamnotvar_lthm & ((! [X1 : subst] : (((comp @ id @ X1)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) => (! [X3 : subst] : (((comp @ X3 @ id)) = X3) & ! [X4 : subst] : (((comp @ id @ X4)) = X4)))) <=> substmonoid_lthm) & (hoasinduction_lem3v2a_lthm <=> (! [X5 : term] : ~ ! [X6 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) = ((X6 @ X8 @ X7))) => (! [X9 : term] : (((sub @ X9 @ id)) = X9) => ! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (~ ! [X13 : term] : (((X11 @ id @ X13 @ id)) = ((X12 @ X13))) | ~ ! [X14 : term] : ((X12 @ (sub @ X10 @ (push @ X14 @ id))) | ~(X12 @ X14)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : ((X11 @ id @ (X15 @ id @ X16) @ id) | ~(X11 @ id @ X16 @ id)) | ~ ! [X17 : term,X18 : subst,X19 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) | (X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | (X12 @ (lam @ X10)))))) & (hoasinduction_lem3_lthm <=> (! [X20 : term] : (((sub @ X20 @ id)) = X20) => (! [X21 : term,X22 : (subst > term > subst > $o)] : ((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id) | ~ ! [X23 : term] : (~(X22 @ id @ X23 @ id) | (X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)) | ~ ! [X24 : (subst > term > term)] : ((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id) | ~ ! [X25 : term,X26 : subst,X27 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) = ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X28 : term] : (~(X22 @ id @ X28 @ id) | (X22 @ id @ (X24 @ id @ X28) @ id)))) => ! [X29 : term,X30 : (subst > term > subst > $o)] : ((X30 @ id @ (lam @ X29) @ id) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~(X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34) | (X30 @ X32 @ X31 @ (comp @ X33 @ X34))) | ~ ! [X35 : (subst > term > term)] : ((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id) | ~ ! [X36 : term] : ((X30 @ id @ (X35 @ id @ X36) @ id) | ~(X30 @ id @ X36 @ id)) | ~ ! [X37 : term,X38 : subst,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38))))) | ~ ! [X40 : term] : ((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id) | ~(X30 @ id @ X40 @ id)) | ~ ! [X41 : subst,X42 : subst,X43 : term,X44 : subst] : (~(X30 @ X42 @ X43 @ (comp @ X44 @ X41)) | (X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41)))))) & hoasapnotvar_gthm & ((! [X45 : term] : (((sub @ X45 @ id)) = X45) => (! [X46 : term,X47 : term,X48 : term,X49 : term] : ((X46 = X47) | (((ap @ X47 @ X48)) != ((ap @ X46 @ X49)))) => ! [X50 : term,X51 : term,X52 : term,X53 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53)))))) <=> hoasapinj1_lthm) & pushprop & (hoasinduction_lem2v2 <=> ! [X54 : (subst > term > subst > $o),X55 : (term > $o),X56 : term,X57 : term] : (~(X55 @ X57) | ~ ! [X58 : term] : (((X55 @ X58)) = ((X54 @ id @ X58 @ id))) | ~ ! [X59 : term,X60 : term] : (~(X54 @ id @ X59 @ id) | ~(X54 @ id @ X60 @ id) | (X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)) | ~ ! [X61 : subst,X62 : subst,X63 : subst,X64 : term] : ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62) | ~(X54 @ X63 @ X64 @ (comp @ X61 @ X62))) | ~(X55 @ X56) | (X55 @ (ap @ X57 @ X56)) | ~ ! [X65 : term,X66 : subst,X67 : subst,X68 : subst] : (~(X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66) | (X54 @ X67 @ X65 @ (comp @ X68 @ X66))))) & (! [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 = X70) | (((ap @ X70 @ X71)) != ((ap @ X69 @ X72)))) <=> apinj1) & (shinj <=> ! [X73 : term,X74 : term] : ((X73 = X74) | (((sub @ X73 @ sh)) != ((sub @ X74 @ sh))))) & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasinduction_lem3a <=> ! [X75 : (subst > term > subst > $o),X76 : term] : ((X75 @ id @ (lam @ X76) @ id) | ~ ! [X77 : term] : ((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id) | ~(X75 @ id @ X77 @ id)) | ~ ! [X78 : (subst > term > term)] : ((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id) | ~ ! [X79 : term] : (~(X75 @ id @ X79 @ id) | (X75 @ id @ (X78 @ id @ X79) @ id)) | ~ ! [X80 : subst,X81 : subst,X82 : term] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80)))))) & hoasinduction_gthm & ((! [X83 : subst,X84 : term] : (((sub @ one @ (push @ X84 @ X83))) = X84) => ! [X85 : term,X86 : subst,X87 : (term > $o),X88 : (term > $o)] : (~ ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | (X87 @ one) | ~(X88 @ X85))) <=> pushprop_lem1v2_lthm) & (pushprop_lem1_lthm <=> (! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : (term > $o),X95 : subst,X96 : term,X97 : term,X98 : (term > $o)] : ((X94 @ (sub @ X96 @ (push @ X97 @ X95))) | ~(X98 @ X96))))) & ~(var @ (d2term @ d_one)) & pushprop_lthm & ((! [X99 : subst] : (((comp @ X99 @ id)) = X99) & ! [X100 : subst] : (((comp @ id @ X100)) = X100)) <=> substmonoid) & pushprop_lem2v2 & axmap & (hoasinduction_lem3b_lthm <=> ! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & apnotvar & pushprop_gthm & pushprop_lem0_gthm & ((! [X103 : (term > $o),X104 : term] : (~ ! [X105 : term,X106 : term] : (~(X103 @ X106) | (X103 @ (ap @ X105 @ X106)) | ~(X103 @ X105)) | (X103 @ X104) | ~ ! [X107 : term] : (~(var @ X107) | (X103 @ X107)) | ~ ! [X108 : term] : (~ ! [X109 : term] : (~(X103 @ X109) | (X103 @ (sub @ X108 @ (push @ X109 @ id)))) | (X103 @ (lam @ X108)))) => (! [X110 : term,X111 : term,X112 : (subst > term > subst > $o)] : (~ ! [X113 : term,X114 : term] : ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id) | ~(X112 @ id @ X113 @ id) | ~(X112 @ id @ X114 @ id)) | ~ ! [X115 : subst,X116 : term,X117 : subst,X118 : subst] : ((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115) | ~(X112 @ X117 @ X116 @ (comp @ X118 @ X115))) | (X112 @ id @ (ap @ X110 @ X111) @ id) | ~(X112 @ id @ X110 @ id) | ~ ! [X119 : term,X120 : subst,X121 : subst,X122 : subst] : (~(X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121) | (X112 @ X122 @ X119 @ (comp @ X120 @ X121))) | ~(X112 @ id @ X111 @ id)) => (! [X123 : (subst > term > subst > $o),X124 : term] : (~ ! [X125 : (subst > term > term)] : (~ ! [X126 : subst,X127 : subst,X128 : term] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) = ((sub @ (X125 @ X126 @ X128) @ X127))) | (X123 @ id @ (lam @ (X125 @ sh @ one)) @ id) | ~ ! [X129 : term] : (~(X123 @ id @ X129 @ id) | (X123 @ id @ (X125 @ id @ X129) @ id))) | ~ ! [X130 : subst,X131 : term,X132 : subst,X133 : subst] : (~(X123 @ X130 @ X131 @ (comp @ X132 @ X133)) | (X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133)) | ~ ! [X134 : subst,X135 : subst,X136 : subst,X137 : term] : (~(X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134) | (X123 @ X136 @ X137 @ (comp @ X135 @ X134))) | ~ ! [X138 : term] : ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id) | ~(X123 @ id @ X138 @ id)) | (X123 @ id @ (lam @ X124) @ id)) => ! [X139 : term,X140 : (subst > term > subst > $o)] : (~ ! [X141 : term,X142 : term] : ((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id) | ~(X140 @ id @ X141 @ id) | ~(X140 @ id @ X142 @ id)) | (X140 @ id @ X139 @ id) | ~ ! [X143 : term] : (~(var @ (sub @ X143 @ id)) | (X140 @ id @ X143 @ id)) | ~ ! [X144 : (subst > term > term)] : (~ ! [X145 : term,X146 : subst,X147 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) | (X140 @ id @ (lam @ (X144 @ sh @ one)) @ id) | ~ ! [X148 : term] : (~(X140 @ id @ X148 @ id) | (X140 @ id @ (X144 @ id @ X148) @ id))) | ~ ! [X149 : subst,X150 : subst,X151 : subst,X152 : term] : ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151) | ~(X140 @ X150 @ X152 @ (comp @ X149 @ X151))) | ~ ! [X153 : subst,X154 : term,X155 : subst,X156 : subst] : (~(X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156) | (X140 @ X155 @ X154 @ (comp @ X153 @ X156))))))) <=> hoasinduction_lthm) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ((^[X157 : (subst > term > subst > $o), X158 : (term > $o)] : (! [X159 : term] : (((X158 @ X159)) = ((X157 @ id @ X159 @ id))))) = hoasinduction_p_and_p_prime) & (induction2_lthm <=> (! [X160 : term] : (((sub @ X160 @ id)) = X160) => (! [X161 : (term > $o),X162 : subst,X163 : term] : (~ ! [X164 : term] : ((X161 @ (lam @ X164)) | ~ ! [X165 : term] : ((X161 @ (sub @ X164 @ (push @ X165 @ id))) | ~(X161 @ X165))) | (X161 @ (sub @ X163 @ X162)) | ~ ! [X166 : term,X167 : term] : (~(X161 @ X167) | ~(X161 @ X166) | (X161 @ (ap @ X167 @ X166))) | ~ ! [X168 : term] : ((X161 @ (sub @ X168 @ X162)) | ~(var @ X168))) => ! [X169 : (term > $o),X170 : term] : (~ ! [X171 : term] : ((X169 @ (lam @ X171)) | ~ ! [X172 : term] : (~(X169 @ X172) | (X169 @ (sub @ X171 @ (push @ X172 @ id))))) | (X169 @ X170) | ~ ! [X173 : term,X174 : term] : ((X169 @ (ap @ X174 @ X173)) | ~(X169 @ X173) | ~(X169 @ X174)) | ~ ! [X175 : term] : (~(var @ X175) | (X169 @ X175)))))) & ((! [X176 : (subst > term > subst > $o)] : ~ ! [X177 : (term > $o)] : ~ ! [X178 : term] : (((X177 @ X178)) = ((X176 @ id @ X178 @ id))) => (! [X179 : (term > $o),X180 : term] : (~ ! [X181 : term] : (~ ! [X182 : term] : (~(X179 @ X182) | (X179 @ (sub @ X181 @ (push @ X182 @ id)))) | (X179 @ (lam @ X181))) | ~ ! [X183 : term,X184 : term] : ((X179 @ (ap @ X183 @ X184)) | ~(X179 @ X183) | ~(X179 @ X184)) | ~ ! [X185 : term] : ((X179 @ X185) | ~(var @ X185)) | (X179 @ X180)) => (! [X186 : term] : (((sub @ X186 @ id)) = X186) => (! [X187 : (term > $o),X188 : term,X189 : (subst > term > subst > $o)] : (~ ! [X190 : term] : (((X189 @ id @ X190 @ id)) = ((X187 @ X190))) | ~ ! [X191 : term] : (~(X187 @ X191) | (X187 @ (sub @ X188 @ (push @ X191 @ id)))) | ~ ! [X192 : (subst > term > term)] : (~ ! [X193 : subst,X194 : subst,X195 : term] : (((X192 @ (comp @ X193 @ X194) @ (sub @ X195 @ X194))) = ((sub @ (X192 @ X193 @ X195) @ X194))) | (X189 @ id @ (lam @ (X192 @ sh @ one)) @ id) | ~ ! [X196 : term] : (~(X189 @ id @ X196 @ id) | (X189 @ id @ (X192 @ id @ X196) @ id))) | (X187 @ (lam @ X188))) => ! [X197 : term,X198 : (subst > term > subst > $o)] : (~ ! [X199 : term,X200 : term] : (~(X198 @ id @ X200 @ id) | ~(X198 @ id @ X199 @ id) | (X198 @ id @ (ap @ (sub @ X200 @ id) @ X199) @ id)) | (X198 @ id @ X197 @ id) | ~ ! [X201 : (subst > term > term)] : ((X198 @ id @ (lam @ (X201 @ sh @ one)) @ id) | ~ ! [X202 : term] : ((X198 @ id @ (X201 @ id @ X202) @ id) | ~(X198 @ id @ X202 @ id)) | ~ ! [X203 : subst,X204 : subst,X205 : term] : (((X201 @ (comp @ X203 @ X204) @ (sub @ X205 @ X204))) = ((sub @ (X201 @ X203 @ X205) @ X204))))))))) <=> hoasinduction_no_psi_cond_lthm) & (! [X206 : term] : ~ ! [X207 : (subst > term > term)] : (((X207 @ sh @ one)) != ((sub @ X206 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & induction2_gthm & (! [X208 : (term > $o),X209 : term] : ((X208 @ X209) | ~ ! [X210 : term] : ((X208 @ X210) | ~(var @ X210)) | ~ ! [X211 : term,X212 : term] : ((X208 @ (ap @ X212 @ X211)) | ~(X208 @ X211) | ~(X208 @ X212)) | ~ ! [X213 : term] : ((X208 @ (lam @ X213)) | ~(X208 @ X213))) <=> induction) & hoasinduction_lem1_lthm & (hoasinduction_lem2 <=> ! [X214 : term,X215 : (subst > term > subst > $o),X216 : term] : (~ ! [X217 : subst,X218 : subst,X219 : term,X220 : subst] : ((X215 @ X218 @ X219 @ (comp @ X217 @ X220)) | ~(X215 @ (comp @ X218 @ X217) @ (sub @ X219 @ X217) @ X220)) | ~(X215 @ id @ X216 @ id) | ~ ! [X221 : subst,X222 : subst,X223 : subst,X224 : term] : ((X215 @ (comp @ X223 @ X222) @ (sub @ X224 @ X222) @ X221) | ~(X215 @ X223 @ X224 @ (comp @ X222 @ X221))) | (X215 @ id @ (ap @ X216 @ X214) @ id) | ~ ! [X225 : term,X226 : term] : (~(X215 @ id @ X225 @ id) | (X215 @ id @ (ap @ (sub @ X226 @ id) @ X225) @ id) | ~(X215 @ id @ X226 @ id)) | ~(X215 @ id @ X214 @ id))) & (! [X227 : term,X228 : subst] : (((sub @ one @ (push @ X227 @ X228))) = X227) <=> axvarcons) & induction2lem_gthm & lamnotvar & hoasinduction_lem3v2_gthm & (! [X229 : term] : ~ ! [X230 : (subst > term > term)] : ~ ! [X231 : subst,X232 : term] : (((X230 @ X231 @ X232)) = ((sub @ X229 @ (push @ X232 @ X231)))) <=> hoasinduction_lem3v2_f) & hoasinduction_lem1v2_gthm & (hoasinduction_lem0_lthm <=> ! [X233 : (subst > term > subst > $o)] : ~ ! [X234 : (term > $o)] : ~ ! [X235 : term] : (((X234 @ X235)) = ((X233 @ id @ X235 @ id)))) & ! [X236 : subst] : ? [X237 : d_subst] : (((d2subst @ X237)) = X236) & ulamvarind & ! [X238 : d_term,X239 : d_term] : ((((d2term @ X238)) = ((d2term @ X239))) => (X238 = X239)) & pushprop_lem2v2_lthm & (! [X240 : term,X241 : term] : ((X240 = X241) | (((lam @ X241)) != ((lam @ X240)))) <=> laminj) & (! [X242 : term,X243 : subst,X244 : (term > $o)] : (~ ! [X245 : term] : ((X244 @ (sub @ X245 @ X243)) | ~(var @ X245)) | ~ ! [X246 : term] : (~ ! [X247 : term] : (~(X244 @ X247) | (X244 @ (sub @ X246 @ (push @ X247 @ id)))) | (X244 @ (lam @ X246))) | (X244 @ (sub @ X242 @ X243)) | ~ ! [X248 : term,X249 : term] : (~(X244 @ X249) | (X244 @ (ap @ X248 @ X249)) | ~(X244 @ X248))) <=> induction2lem) & (id = ((d2subst @ d_id))) & termmset_gthm & hoasinduction_lem3_gthm & hoaslamnotap_lthm & (! [X250 : (term > $o),X251 : term] : (~ ! [X252 : term] : (~(var @ X252) | (X250 @ X252)) | ~ ! [X253 : term] : (~ ! [X254 : term] : (~(X250 @ X254) | (X250 @ (sub @ X253 @ (push @ X254 @ id)))) | (X250 @ (lam @ X253))) | (X250 @ X251) | ~ ! [X255 : term,X256 : term] : (~(X250 @ X256) | ~(X250 @ X255) | (X250 @ (ap @ X255 @ X256)))) <=> induction2) & (! [X257 : (subst > term > subst > $o),X258 : term,X259 : (term > $o)] : (~ ! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : ((X257 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262) @ X263) | ~(X257 @ X260 @ X261 @ (comp @ X262 @ X263))) | ~ ! [X264 : term] : (((X257 @ id @ X264 @ id)) = ((X259 @ X264))) | ~ ! [X265 : subst,X266 : subst,X267 : term,X268 : subst] : ((X257 @ X268 @ X267 @ (comp @ X265 @ X266)) | ~(X257 @ (comp @ X268 @ X265) @ (sub @ X267 @ X265) @ X266)) | ~ ! [X269 : term] : ((X259 @ (sub @ X258 @ (push @ X269 @ id))) | ~(X259 @ X269)) | ~ ! [X270 : (subst > term > term)] : ((X257 @ id @ (lam @ (X270 @ sh @ one)) @ id) | ~ ! [X271 : term] : (~(X257 @ id @ X271 @ id) | (X257 @ id @ (X270 @ id @ X271) @ id)) | ~ ! [X272 : term,X273 : subst,X274 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273))))) | (X259 @ (lam @ X258))) <=> hoasinduction_lem3v2) & (! [X275 : (subst > term > subst > $o),X276 : term,X277 : (term > $o)] : (~ ! [X278 : term] : ((X277 @ (sub @ X276 @ (push @ X278 @ id))) | ~(X277 @ X278)) | (X277 @ (lam @ X276)) | ~ ! [X279 : (subst > term > term)] : (~ ! [X280 : term] : ((X275 @ id @ (X279 @ id @ X280) @ id) | ~(X275 @ id @ X280 @ id)) | ~ ! [X281 : subst,X282 : term,X283 : subst] : (((X279 @ (comp @ X281 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X279 @ X281 @ X282) @ X283))) | (X275 @ id @ (lam @ (X279 @ sh @ one)) @ id)) | ~ ! [X284 : term] : (((X277 @ X284)) = ((X275 @ id @ X284 @ id)))) <=> hoasinduction_lem3v2a) & hoasapinj2_gthm & (pushprop_lem1v2 <=> ! [X285 : term,X286 : (term > $o),X287 : (term > $o),X288 : subst] : (~ ! [X289 : term] : (((X287 @ X289)) = ((X286 @ (sub @ X289 @ (push @ X285 @ X288))))) | ~(X286 @ X285) | (X287 @ one))) & (! [X290 : term,X291 : (term > $o),X292 : subst] : ~ ! [X293 : (term > $o)] : ~ ! [X294 : term] : (((X293 @ X294)) = ((X291 @ (sub @ X294 @ (push @ X290 @ X292))))) <=> pushprop_lem0) & ulamvarsh & hoaslamnotvar & hoasinduction_lem3b_gthm & ! [X295 : d_subst] : (d_id = X295) & hoasapnotvar & (! [X296 : term,X297 : (subst > term > subst > $o)] : ((X297 @ id @ X296 @ id) | ~ ! [X298 : term,X299 : term] : ((X297 @ id @ (ap @ (sub @ X298 @ id) @ X299) @ id) | ~(X297 @ id @ X299 @ id) | ~(X297 @ id @ X298 @ id)) | ~ ! [X300 : (subst > term > term)] : ((X297 @ id @ (lam @ (X300 @ sh @ one)) @ id) | ~ ! [X301 : term] : (~(X297 @ id @ X301 @ id) | (X297 @ id @ (X300 @ id @ X301) @ id)) | ~ ! [X302 : subst,X303 : term,X304 : subst] : (((sub @ (X300 @ X304 @ X303) @ X302)) = ((X300 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302)))))) <=> hoasinduction_no_psi_cond) & (apinj2 <=> ! [X305 : term,X306 : term,X307 : term,X308 : term] : ((X306 = X307) | (((ap @ X305 @ X307)) != ((ap @ X308 @ X306))))) & hoasinduction_lem1v2 & ((^[X309 : subst, X310 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & hoasinduction_lem3a_gthm & ~ulamvar1 & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ~lamnotap & hoasapinj1_gthm & (axscons <=> ! [X311 : subst] : (((push @ (sub @ one @ X311) @ (comp @ sh @ X311))) = X311)) & axassoc & (! [X312 : term,X313 : subst,X314 : term,X315 : (term > $o),X316 : (term > $o)] : (~(X315 @ X314) | (X316 @ (sub @ X314 @ (push @ X312 @ X313)))) <=> pushprop_lem1) & (pushprop_p_and_p_prime = (^[X317 : term, X318 : subst, X319 : (term > $o), X320 : (term > $o)] : (! [X321 : term] : (((X319 @ (sub @ X321 @ (push @ X317 @ X318)))) = ((X320 @ X321)))))) & (! [X322 : subst,X323 : (term > $o),X324 : term] : ~ ! [X325 : (term > $o)] : ~ ! [X326 : term] : (((X325 @ X326)) = ((X323 @ (sub @ X326 @ (push @ X324 @ X322))))) <=> pushprop_lem0_lthm) & hoaslaminj_gthm & hoasapnotvar_lthm & pushprop_lem3v2 & hoasinduction_lem2_gthm & (hoaslaminj <=> ! [X327 : term,X328 : (subst > term > term),X329 : subst,X330 : (subst > term > term)] : ((((lam @ (X330 @ sh @ one))) != ((lam @ (X328 @ sh @ one)))) | ~ ! [X331 : term,X332 : subst,X333 : subst] : (((X330 @ (comp @ X333 @ X332) @ (sub @ X331 @ X332))) = ((sub @ (X330 @ X333 @ X331) @ X332))) | ~ ! [X334 : term,X335 : subst,X336 : subst] : (((X328 @ (comp @ X336 @ X335) @ (sub @ X334 @ X335))) = ((sub @ (X328 @ X336 @ X334) @ X335))) | (((X328 @ X329 @ X327)) = ((X330 @ X329 @ X327))))) & axclos & hoaslamnotvar_gthm & (! [X337 : subst] : (((comp @ id @ X337)) = X337) <=> axidl) & (hoasinduction_lem3v2_f_lthm <=> ! [X338 : term] : ~ ! [X339 : (subst > term > term)] : ~ ! [X340 : term,X341 : subst] : (((sub @ X338 @ (push @ X340 @ X341))) = ((X339 @ X341 @ X340)))) & (induction2lem_lthm <=> (! [X342 : term,X343 : subst] : (((sub @ one @ (push @ X342 @ X343))) = X342) => (! [X344 : term,X345 : subst] : (((comp @ sh @ (push @ X344 @ X345))) = X345) => (! [X346 : subst] : (((comp @ X346 @ id)) = X346) => (! [X347 : term,X348 : (term > $o)] : (~ ! [X349 : term,X350 : term] : (~(X348 @ X350) | (X348 @ (ap @ X350 @ X349)) | ~(X348 @ X349)) | ~ ! [X351 : term] : (~(X348 @ X351) | (X348 @ (lam @ X351))) | ~ ! [X352 : term] : ((X348 @ X352) | ~(var @ X352)) | (X348 @ X347)) => ! [X353 : (term > $o),X354 : term,X355 : subst] : (~ ! [X356 : term,X357 : term] : ((X353 @ (ap @ X357 @ X356)) | ~(X353 @ X356) | ~(X353 @ X357)) | ~ ! [X358 : term] : (~ ! [X359 : term] : ((X353 @ (sub @ X358 @ (push @ X359 @ id))) | ~(X353 @ X359)) | (X353 @ (lam @ X358))) | (X353 @ (sub @ X354 @ X355)) | ~ ! [X360 : term] : ((X353 @ (sub @ X360 @ X355)) | ~(var @ X360)))))))) & (! [X361 : (subst > term > subst > $o)] : ~ ! [X362 : (term > $o)] : ~ ! [X363 : term] : (((X362 @ X363)) = ((X361 @ id @ X363 @ id))) <=> hoasinduction_lem0) & (axshiftcons <=> ! [X364 : term,X365 : subst] : (((comp @ sh @ (push @ X364 @ X365))) = X365)) & (! [X366 : term,X367 : (subst > term > subst > $o)] : (~ ! [X368 : (subst > term > term)] : ((X367 @ id @ (lam @ (X368 @ sh @ one)) @ id) | ~ ! [X369 : subst,X370 : term,X371 : subst] : (((sub @ (X368 @ X371 @ X370) @ X369)) = ((X368 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | ~ ! [X372 : term] : ((X367 @ id @ (X368 @ id @ X372) @ id) | ~(X367 @ id @ X372 @ id))) | (X367 @ id @ (lam @ (sub @ X366 @ (push @ one @ sh))) @ id) | ~ ! [X373 : term] : (~(X367 @ id @ X373 @ id) | (X367 @ id @ (sub @ X366 @ (push @ X373 @ id)) @ id))) <=> hoasinduction_lem3aa) & hoasinduction_lem2v2_gthm & ! [X374 : term] : ? [X375 : d_term] : (((d2term @ X375)) = X374) & axabs & hoasinduction_lem1_gthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X376 : (subst > term > subst > $o)] : ~ ! [X377 : (term > $o)] : ~ ! [X378 : term] : (((X376 @ id @ X378 @ id)) = ((X377 @ X378))) => (! [X379 : (term > $o),X380 : term] : (~ ! [X381 : term] : ((X379 @ (lam @ X381)) | ~ ! [X382 : term] : (~(X379 @ X382) | (X379 @ (sub @ X381 @ (push @ X382 @ id))))) | ~ ! [X383 : term] : ((X379 @ X383) | ~(var @ X383)) | (X379 @ X380) | ~ ! [X384 : term,X385 : term] : (~(X379 @ X384) | (X379 @ (ap @ X385 @ X384)) | ~(X379 @ X385))) => (! [X386 : term] : (((sub @ X386 @ id)) = X386) => (! [X387 : (subst > term > subst > $o),X388 : term,X389 : (term > $o)] : (~ ! [X390 : term] : (((X387 @ id @ X390 @ id)) = ((X389 @ X390))) | (X389 @ (lam @ X388)) | ~ ! [X391 : term] : (~(X389 @ X391) | (X389 @ (sub @ X388 @ (push @ X391 @ id)))) | ~ ! [X392 : (subst > term > term)] : ((X387 @ id @ (lam @ (X392 @ sh @ one)) @ id) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X392 @ X395 @ X394) @ X393)) = ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)))) | ~ ! [X396 : term] : (~(X387 @ id @ X396 @ id) | (X387 @ id @ (X392 @ id @ X396) @ id)))) => ! [X397 : (subst > term > subst > $o),X398 : term] : (~ ! [X399 : term] : ((X397 @ id @ X399 @ id) | ~(var @ (sub @ X399 @ id))) | ~ ! [X400 : term,X401 : term] : ((X397 @ id @ (ap @ (sub @ X401 @ id) @ X400) @ id) | ~(X397 @ id @ X401 @ id) | ~(X397 @ id @ X400 @ id)) | ~ ! [X402 : subst,X403 : subst,X404 : subst,X405 : term] : ((X397 @ (comp @ X403 @ X404) @ (sub @ X405 @ X404) @ X402) | ~(X397 @ X403 @ X405 @ (comp @ X404 @ X402))) | ~ ! [X406 : subst,X407 : subst,X408 : subst,X409 : term] : ((X397 @ X406 @ X409 @ (comp @ X408 @ X407)) | ~(X397 @ (comp @ X406 @ X408) @ (sub @ X409 @ X408) @ X407)) | (X397 @ id @ X398 @ id) | ~ ! [X410 : (subst > term > term)] : ((X397 @ id @ (lam @ (X410 @ sh @ one)) @ id) | ~ ! [X411 : subst,X412 : term,X413 : subst] : (((X410 @ (comp @ X411 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X411 @ X412) @ X413))) | ~ ! [X414 : term] : ((X397 @ id @ (X410 @ id @ X414) @ id) | ~(X397 @ id @ X414 @ id)))))))) <=> hoasinduction_lthm_3) & (! [X415 : term,X416 : term,X417 : term,X418 : term] : ((((ap @ (sub @ X416 @ id) @ X417)) != ((ap @ (sub @ X415 @ id) @ X418))) | (X415 = X416)) <=> hoasapinj1) & (hoasinduction_lem3aa_lthm <=> ! [X419 : term,X420 : (subst > term > subst > $o)] : (~ ! [X421 : term] : ((X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id) | ~(X420 @ id @ X421 @ id)) | (X420 @ id @ (lam @ (sub @ X419 @ (push @ one @ sh))) @ id) | ~ ! [X422 : (subst > term > term)] : (~ ! [X423 : term] : (~(X420 @ id @ X423 @ id) | (X420 @ id @ (X422 @ id @ X423) @ id)) | (X420 @ id @ (lam @ (X422 @ sh @ one)) @ id) | ~ ! [X424 : term,X425 : subst,X426 : subst] : (((sub @ (X422 @ X426 @ X424) @ X425)) = ((X422 @ (comp @ X426 @ X425) @ (sub @ X424 @ X425))))))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3aaa <=> ! [X427 : term,X428 : (subst > term > subst > $o)] : (~ ! [X429 : term,X430 : (subst > term > term)] : (~ ! [X431 : subst,X432 : subst,X433 : term] : (((sub @ (sub @ X429 @ (push @ X433 @ X431)) @ X432)) = ((sub @ (X430 @ X431 @ X433) @ X432))) | ~ ! [X434 : term,X435 : subst,X436 : subst] : (((X430 @ (comp @ X435 @ X436) @ (sub @ X434 @ X436))) = ((sub @ X429 @ (push @ (sub @ X434 @ X436) @ (comp @ X435 @ X436))))) | (X428 @ id @ (lam @ (X430 @ sh @ one)) @ id) | ~ ! [X437 : term] : (~(X428 @ id @ X437 @ id) | (X428 @ id @ (X430 @ id @ X437) @ id))) | ~ ! [X438 : term] : (~(X428 @ id @ X438 @ id) | (X428 @ id @ (sub @ X427 @ (push @ X438 @ id)) @ id)) | (X428 @ id @ (lam @ (sub @ X427 @ (push @ one @ sh))) @ id))) & ((! [X439 : term,X440 : term,X441 : term,X442 : term] : ((((ap @ X440 @ X441)) != ((ap @ X439 @ X442))) | (X441 = X442)) => ! [X443 : term,X444 : term,X445 : term,X446 : term] : ((((ap @ (sub @ X445 @ id) @ X443)) != ((ap @ (sub @ X446 @ id) @ X444))) | (X443 = X444))) <=> hoasapinj2_lthm) & (hoasinduction_lem3 <=> ! [X447 : (subst > term > subst > $o),X448 : term] : (~ ! [X449 : subst,X450 : subst,X451 : subst,X452 : term] : (~(X447 @ X451 @ X452 @ (comp @ X450 @ X449)) | (X447 @ (comp @ X451 @ X450) @ (sub @ X452 @ X450) @ X449)) | ~ ! [X453 : term] : (~(X447 @ id @ X453 @ id) | (X447 @ id @ (sub @ X448 @ (push @ X453 @ id)) @ id)) | ~ ! [X454 : term,X455 : subst,X456 : subst,X457 : subst] : (~(X447 @ (comp @ X457 @ X455) @ (sub @ X454 @ X455) @ X456) | (X447 @ X457 @ X454 @ (comp @ X455 @ X456))) | (X447 @ id @ (lam @ X448) @ id) | ~ ! [X458 : (subst > term > term)] : ((X447 @ id @ (lam @ (X458 @ sh @ one)) @ id) | ~ ! [X459 : subst,X460 : subst,X461 : term] : (((sub @ (X458 @ X459 @ X461) @ X460)) = ((X458 @ (comp @ X459 @ X460) @ (sub @ X461 @ X460)))) | ~ ! [X462 : term] : ((X447 @ id @ (X458 @ id @ X462) @ id) | ~(X447 @ id @ X462 @ id))))) & pushprop_lthm_orig & hoasinduction_lem1 & pushprop_lem3v2_lthm & pushprop_lem1_gthm & pushprop_lem1v2_gthm & (sh = ((d2subst @ d_id))) & (termmset_lthm <=> (! [X463 : term] : (((sub @ X463 @ id)) = X463) => ! [X464 : term] : (((sub @ X464 @ id)) = X464))) & hoaslamnotap_gthm & hoasinduction_lem2_lthm & (hoaslamnotap <=> ! [X465 : term,X466 : (subst > term > term),X467 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((lam @ (X466 @ sh @ one)))) | ~ ! [X468 : subst,X469 : subst,X470 : term] : (((sub @ (X466 @ X469 @ X470) @ X468)) = ((X466 @ (comp @ X469 @ X468) @ (sub @ X470 @ X468)))))) & (! [X471 : term] : (((sub @ X471 @ id)) = X471) <=> axvarid) & (! [X472 : subst] : (((comp @ X472 @ id)) = X472) <=> axidr) & (one = ((d2term @ d_one))) & axvarshift & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X473 : subst,X474 : term] : (((sub @ one @ (push @ X474 @ X473))) = X474) => (! [X475 : subst,X476 : term] : (((comp @ sh @ (push @ X476 @ X475))) = X475) => (! [X477 : term,X478 : term] : ((X477 = X478) | (((lam @ X477)) != ((lam @ X478)))) => ! [X479 : subst,X480 : (subst > term > term),X481 : term,X482 : (subst > term > term)] : (~ ! [X483 : subst,X484 : subst,X485 : term] : (((sub @ (X480 @ X483 @ X485) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484)))) | ~ ! [X486 : term,X487 : subst,X488 : subst] : (((X482 @ (comp @ X487 @ X488) @ (sub @ X486 @ X488))) = ((sub @ (X482 @ X487 @ X486) @ X488))) | (((lam @ (X480 @ sh @ one))) != ((lam @ (X482 @ sh @ one)))) | (((X482 @ X479 @ X481)) = ((X480 @ X479 @ X481))))))) <=> hoaslaminj_lthm) & (hoasinduction_lem3v2_lthm <=> (! [X489 : term] : (((sub @ X489 @ id)) = X489) => ! [X490 : term,X491 : (term > $o),X492 : (subst > term > subst > $o)] : (~ ! [X493 : term] : ((X491 @ (sub @ X490 @ (push @ X493 @ id))) | ~(X491 @ X493)) | ~ ! [X494 : subst,X495 : subst,X496 : subst,X497 : term] : (~(X492 @ X494 @ X497 @ (comp @ X495 @ X496)) | (X492 @ (comp @ X494 @ X495) @ (sub @ X497 @ X495) @ X496)) | ~ ! [X498 : term] : (((X492 @ id @ X498 @ id)) = ((X491 @ X498))) | ~ ! [X499 : subst,X500 : subst,X501 : term,X502 : subst] : ((X492 @ X499 @ X501 @ (comp @ X502 @ X500)) | ~(X492 @ (comp @ X499 @ X502) @ (sub @ X501 @ X502) @ X500)) | (X491 @ (lam @ X490)) | ~ ! [X503 : (subst > term > term)] : (~ ! [X504 : subst,X505 : subst,X506 : term] : (((X503 @ (comp @ X504 @ X505) @ (sub @ X506 @ X505))) = ((sub @ (X503 @ X504 @ X506) @ X505))) | (X492 @ id @ (lam @ (X503 @ sh @ one)) @ id) | ~ ! [X507 : term] : (~(X492 @ id @ X507 @ id) | (X492 @ id @ (X503 @ id @ X507) @ id)))))) & axapp & (hoasapinj2 <=> ! [X508 : term,X509 : term,X510 : term,X511 : term] : ((((ap @ (sub @ X511 @ id) @ X508)) != ((ap @ (sub @ X509 @ id) @ X510))) | (X508 = X510))) & substmonoid_gthm & (hoasinduction_lem3a_lthm <=> (! [X512 : term] : (((sub @ X512 @ id)) = X512) => (! [X513 : term,X514 : (subst > term > subst > $o)] : ((X514 @ id @ (lam @ (sub @ X513 @ (push @ one @ sh))) @ id) | ~ ! [X515 : (subst > term > term)] : ((X514 @ id @ (lam @ (X515 @ sh @ one)) @ id) | ~ ! [X516 : term] : (~(X514 @ id @ X516 @ id) | (X514 @ id @ (X515 @ id @ X516) @ id)) | ~ ! [X517 : term,X518 : subst,X519 : subst] : (((X515 @ (comp @ X518 @ X519) @ (sub @ X517 @ X519))) = ((sub @ (X515 @ X518 @ X517) @ X519)))) | ~ ! [X520 : term] : (~(X514 @ id @ X520 @ id) | (X514 @ id @ (sub @ X513 @ (push @ X520 @ id)) @ id))) => ! [X521 : term,X522 : (subst > term > subst > $o)] : (~ ! [X523 : term] : (~(X522 @ id @ X523 @ id) | (X522 @ id @ (sub @ X521 @ (push @ X523 @ id)) @ id)) | ~ ! [X524 : (subst > term > term)] : (~ ! [X525 : term] : (~(X522 @ id @ X525 @ id) | (X522 @ id @ (X524 @ id @ X525) @ id)) | (X522 @ id @ (lam @ (X524 @ sh @ one)) @ id) | ~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X524 @ X527 @ X526) @ X528)) = ((X524 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528))))) | (X522 @ id @ (lam @ X521) @ id))))) & ! [X529 : d_subst,X530 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X529))) => (X529 = X530)) & ! [X531 : d_term] : (d_one = X531) & pushprop_lem2v2_gthm & (hoasinduction <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (~ ! [X534 : (subst > term > term)] : ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id) | ~ ! [X535 : term] : (~(X532 @ id @ X535 @ id) | (X532 @ id @ (X534 @ id @ X535) @ id)) | ~ ! [X536 : subst,X537 : term,X538 : subst] : (((X534 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538))) = ((sub @ (X534 @ X536 @ X537) @ X538)))) | ~ ! [X539 : subst,X540 : subst,X541 : term,X542 : subst] : (~(X532 @ (comp @ X542 @ X539) @ (sub @ X541 @ X539) @ X540) | (X532 @ X542 @ X541 @ (comp @ X539 @ X540))) | ~ ! [X543 : term] : ((X532 @ id @ X543 @ id) | ~(var @ (sub @ X543 @ id))) | (X532 @ id @ X533 @ id) | ~ ! [X544 : term,X545 : subst,X546 : subst,X547 : subst] : (~(X532 @ X545 @ X544 @ (comp @ X546 @ X547)) | (X532 @ (comp @ X545 @ X546) @ (sub @ X544 @ X546) @ X547)) | ~ ! [X548 : term,X549 : term] : ((X532 @ id @ (ap @ (sub @ X549 @ id) @ X548) @ id) | ~(X532 @ id @ X549 @ id) | ~(X532 @ id @ X548 @ id))))),
% 1.42/0.51 inference(rectify,[],[f1])).
% 1.42/0.51 thf(f7,plain,(
% 1.42/0.51 ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & (hoaslamnotvar_lthm = $true) & ((! [X1 : subst] : (((comp @ id @ X1)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) => (! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X5 : term] : ~ ! [X6 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) = ((X6 @ X8 @ X7))) => (! [X9 : term] : (((sub @ X9 @ id)) = X9) => ! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (~ ! [X13 : term] : (((X11 @ id @ X13 @ id)) = ((X12 @ X13))) | ~ ! [X14 : term] : ((((X12 @ (sub @ X10 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | ~ (((X11 @ id @ X16 @ id)) = $true)) | ~ ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) | ($true = ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) | ($true = ((X12 @ (lam @ X10)))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X20 : term] : (((sub @ X20 @ id)) = X20) => (! [X21 : term,X22 : (subst > term > subst > $o)] : ((((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X23 : term] : (~ ($true = ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) | ~ ! [X24 : (subst > term > term)] : ((((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true) | ~ ! [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) = ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X28 : term] : (~ ($true = ((X22 @ id @ X28 @ id))) | (((X22 @ id @ (X24 @ id @ X28) @ id)) = $true)))) => ! [X29 : term,X30 : (subst > term > subst > $o)] : ((((X30 @ id @ (lam @ X29) @ id)) = $true) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~ ($true = ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))) | (((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) = $true)) | ~ ! [X35 : (subst > term > term)] : ((((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) = $true) | ~ ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ~ ($true = ((X30 @ id @ X36 @ id)))) | ~ ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38))))) | ~ ! [X40 : term] : ((((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) = $true) | ~ ($true = ((X30 @ id @ X40 @ id)))) | ~ ! [X41 : subst,X42 : subst,X43 : term,X44 : subst] : (~ ($true = ((X30 @ X42 @ X43 @ (comp @ X44 @ X41)))) | ($true = ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41)))))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X45 : term] : (((sub @ X45 @ id)) = X45) => (! [X49 : term,X47 : term,X48 : term,X46 : term] : ((((ap @ X47 @ X48)) != ((ap @ X46 @ X49))) | (X46 = X47)) => ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))))) & (pushprop = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X54 : (subst > term > subst > $o),X55 : (term > $o),X56 : term,X57 : term] : (~ (((X55 @ X57)) = $true) | ~ ! [X58 : term] : (((X55 @ X58)) = ((X54 @ id @ X58 @ id))) | ~ ! [X59 : term,X60 : term] : (~ (((X54 @ id @ X59 @ id)) = $true) | ~ ($true = ((X54 @ id @ X60 @ id))) | ($true = ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)))) | ~ ! [X61 : subst,X62 : subst,X63 : subst,X64 : term] : (($true = ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) | ~ (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) = $true)) | ~ ($true = ((X55 @ X56))) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ~ ! [X65 : term,X66 : subst,X67 : subst,X68 : subst] : (~ ($true = ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66))) | ($true = ((X54 @ X67 @ X65 @ (comp @ X68 @ X66))))))) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3a = $true) <=> ! [X75 : (subst > term > subst > $o),X76 : term] : (($true = ((X75 @ id @ (lam @ X76) @ id))) | ~ ! [X77 : term] : ((((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) = $true) | ~ ($true = ((X75 @ id @ X77 @ id)))) | ~ ! [X78 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) = $true) | ~ ! [X79 : term] : (~ ($true = ((X75 @ id @ X79 @ id))) | ($true = ((X75 @ id @ (X78 @ id @ X79) @ id)))) | ~ ! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80)))))) & (hoasinduction_gthm = $true) & ((! [X83 : subst,X84 : term] : (((sub @ one @ (push @ X84 @ X83))) = X84) => ! [X85 : term,X86 : subst,X87 : (term > $o),X88 : (term > $o)] : (~ ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true = ((X87 @ one))) | ~ ($true = ((X88 @ X85))))) <=> (pushprop_lem1v2_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X91 : term,X90 : subst] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : (term > $o),X95 : subst,X96 : term,X97 : term,X98 : (term > $o)] : (($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95))))) | ~ (((X98 @ X96)) = $true))))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_lthm = $true) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (pushprop_lem2v2 = $true) & (axmap = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & (apnotvar = $true) & (pushprop_gthm = $true) & (pushprop_lem0_gthm = $true) & ((! [X103 : (term > $o),X104 : term] : (~ ! [X105 : term,X106 : term] : (~ ($true = ((X103 @ X106))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ~ ($true = ((X103 @ X105)))) | (((X103 @ X104)) = $true) | ~ ! [X107 : term] : (~ ($true = ((var @ X107))) | ($true = ((X103 @ X107)))) | ~ ! [X108 : term] : (~ ! [X109 : term] : (~ ($true = ((X103 @ X109))) | ($true = ((X103 @ (sub @ X108 @ (push @ X109 @ id)))))) | ($true = ((X103 @ (lam @ X108)))))) => (! [X110 : term,X111 : term,X112 : (subst > term > subst > $o)] : (~ ! [X113 : term,X114 : term] : (($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id))) | ~ ($true = ((X112 @ id @ X113 @ id))) | ~ (((X112 @ id @ X114 @ id)) = $true)) | ~ ! [X115 : subst,X116 : term,X117 : subst,X118 : subst] : ((((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true) | ~ (((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) = $true)) | ($true = ((X112 @ id @ (ap @ X110 @ X111) @ id))) | ~ ($true = ((X112 @ id @ X110 @ id))) | ~ ! [X119 : term,X120 : subst,X121 : subst,X122 : subst] : (~ ($true = ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) | ~ (((X112 @ id @ X111 @ id)) = $true)) => (! [X123 : (subst > term > subst > $o),X124 : term] : (~ ! [X125 : (subst > term > term)] : (~ ! [X126 : subst,X128 : term,X127 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) = ((sub @ (X125 @ X126 @ X128) @ X127))) | (((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true) | ~ ! [X129 : term] : (~ ($true = ((X123 @ id @ X129 @ id))) | ($true = ((X123 @ id @ (X125 @ id @ X129) @ id))))) | ~ ! [X130 : subst,X131 : term,X132 : subst,X133 : subst] : (~ ($true = ((X123 @ X130 @ X131 @ (comp @ X132 @ X133)))) | ($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133)))) | ~ ! [X134 : subst,X135 : subst,X136 : subst,X137 : term] : (~ ($true = ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134))))) | ~ ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | ~ (((X123 @ id @ X138 @ id)) = $true)) | (((X123 @ id @ (lam @ X124) @ id)) = $true)) => ! [X139 : term,X140 : (subst > term > subst > $o)] : (~ ! [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) = $true) | ~ ($true = ((X140 @ id @ X141 @ id))) | ~ ($true = ((X140 @ id @ X142 @ id)))) | (((X140 @ id @ X139 @ id)) = $true) | ~ ! [X143 : term] : (~ (((var @ (sub @ X143 @ id))) = $true) | ($true = ((X140 @ id @ X143 @ id)))) | ~ ! [X144 : (subst > term > term)] : (~ ! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) | ($true = ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id))) | ~ ! [X148 : term] : (~ (((X140 @ id @ X148 @ id)) = $true) | ($true = ((X140 @ id @ (X144 @ id @ X148) @ id))))) | ~ ! [X149 : subst,X150 : subst,X151 : subst,X152 : term] : (($true = ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) | ~ (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) = $true)) | ~ ! [X153 : subst,X154 : term,X155 : subst,X156 : subst] : (~ ($true = ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) | (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) = $true)))))) <=> (hoasinduction_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((induction2_lthm = $true) <=> (! [X160 : term] : (((sub @ X160 @ id)) = X160) => (! [X161 : (term > $o),X162 : subst,X163 : term] : (~ ! [X164 : term] : ((((X161 @ (lam @ X164))) = $true) | ~ ! [X165 : term] : (($true = ((X161 @ (sub @ X164 @ (push @ X165 @ id))))) | ~ ($true = ((X161 @ X165))))) | ($true = ((X161 @ (sub @ X163 @ X162)))) | ~ ! [X166 : term,X167 : term] : (~ (((X161 @ X167)) = $true) | ~ ($true = ((X161 @ X166))) | (((X161 @ (ap @ X167 @ X166))) = $true)) | ~ ! [X168 : term] : (($true = ((X161 @ (sub @ X168 @ X162)))) | ~ ($true = ((var @ X168))))) => ! [X169 : (term > $o),X170 : term] : (~ ! [X171 : term] : ((((X169 @ (lam @ X171))) = $true) | ~ ! [X172 : term] : (~ ($true = ((X169 @ X172))) | ($true = ((X169 @ (sub @ X171 @ (push @ X172 @ id))))))) | ($true = ((X169 @ X170))) | ~ ! [X173 : term,X174 : term] : ((((X169 @ (ap @ X174 @ X173))) = $true) | ~ ($true = ((X169 @ X173))) | ~ ($true = ((X169 @ X174)))) | ~ ! [X175 : term] : (~ ($true = ((var @ X175))) | ($true = ((X169 @ X175)))))))) & ((! [X176 : (subst > term > subst > $o)] : ~ ! [X177 : (term > $o)] : ~ ! [X178 : term] : (((X177 @ X178)) = ((X176 @ id @ X178 @ id))) => (! [X179 : (term > $o),X180 : term] : (~ ! [X181 : term] : (~ ! [X182 : term] : (~ ($true = ((X179 @ X182))) | ($true = ((X179 @ (sub @ X181 @ (push @ X182 @ id)))))) | ($true = ((X179 @ (lam @ X181))))) | ~ ! [X183 : term,X184 : term] : (($true = ((X179 @ (ap @ X183 @ X184)))) | ~ ($true = ((X179 @ X183))) | ~ ($true = ((X179 @ X184)))) | ~ ! [X185 : term] : ((((X179 @ X185)) = $true) | ~ ($true = ((var @ X185)))) | ($true = ((X179 @ X180)))) => (! [X186 : term] : (((sub @ X186 @ id)) = X186) => (! [X187 : (term > $o),X188 : term,X189 : (subst > term > subst > $o)] : (~ ! [X190 : term] : (((X189 @ id @ X190 @ id)) = ((X187 @ X190))) | ~ ! [X191 : term] : (~ (((X187 @ X191)) = $true) | ($true = ((X187 @ (sub @ X188 @ (push @ X191 @ id)))))) | ~ ! [X192 : (subst > term > term)] : (~ ! [X193 : subst,X194 : subst,X195 : term] : (((X192 @ (comp @ X193 @ X194) @ (sub @ X195 @ X194))) = ((sub @ (X192 @ X193 @ X195) @ X194))) | (((X189 @ id @ (lam @ (X192 @ sh @ one)) @ id)) = $true) | ~ ! [X196 : term] : (~ (((X189 @ id @ X196 @ id)) = $true) | (((X189 @ id @ (X192 @ id @ X196) @ id)) = $true))) | ($true = ((X187 @ (lam @ X188))))) => ! [X197 : term,X198 : (subst > term > subst > $o)] : (~ ! [X199 : term,X200 : term] : (~ ($true = ((X198 @ id @ X200 @ id))) | ~ ($true = ((X198 @ id @ X199 @ id))) | (((X198 @ id @ (ap @ (sub @ X200 @ id) @ X199) @ id)) = $true)) | ($true = ((X198 @ id @ X197 @ id))) | ~ ! [X201 : (subst > term > term)] : (($true = ((X198 @ id @ (lam @ (X201 @ sh @ one)) @ id))) | ~ ! [X202 : term] : ((((X198 @ id @ (X201 @ id @ X202) @ id)) = $true) | ~ ($true = ((X198 @ id @ X202 @ id)))) | ~ ! [X203 : subst,X204 : subst,X205 : term] : (((X201 @ (comp @ X203 @ X204) @ (sub @ X205 @ X204))) = ((sub @ (X201 @ X203 @ X205) @ X204))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X206 : term] : ~ ! [X207 : (subst > term > term)] : (((X207 @ sh @ one)) != ((sub @ X206 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (induction2_gthm = $true) & (! [X208 : (term > $o),X209 : term] : (($true = ((X208 @ X209))) | ~ ! [X210 : term] : ((((X208 @ X210)) = $true) | ~ ($true = ((var @ X210)))) | ~ ! [X211 : term,X212 : term] : ((((X208 @ (ap @ X212 @ X211))) = $true) | ~ ($true = ((X208 @ X211))) | ~ ($true = ((X208 @ X212)))) | ~ ! [X213 : term] : (($true = ((X208 @ (lam @ X213)))) | ~ ($true = ((X208 @ X213))))) <=> (induction = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X214 : term,X215 : (subst > term > subst > $o),X216 : term] : (~ ! [X217 : subst,X218 : subst,X219 : term,X220 : subst] : (($true = ((X215 @ X218 @ X219 @ (comp @ X217 @ X220)))) | ~ ($true = ((X215 @ (comp @ X218 @ X217) @ (sub @ X219 @ X217) @ X220)))) | ~ ($true = ((X215 @ id @ X216 @ id))) | ~ ! [X221 : subst,X222 : subst,X223 : subst,X224 : term] : ((((X215 @ (comp @ X223 @ X222) @ (sub @ X224 @ X222) @ X221)) = $true) | ~ ($true = ((X215 @ X223 @ X224 @ (comp @ X222 @ X221))))) | ($true = ((X215 @ id @ (ap @ X216 @ X214) @ id))) | ~ ! [X225 : term,X226 : term] : (~ (((X215 @ id @ X225 @ id)) = $true) | (((X215 @ id @ (ap @ (sub @ X226 @ id) @ X225) @ id)) = $true) | ~ ($true = ((X215 @ id @ X226 @ id)))) | ~ (((X215 @ id @ X214 @ id)) = $true))) & (! [X227 : term,X228 : subst] : (((sub @ one @ (push @ X227 @ X228))) = X227) <=> (axvarcons = $true)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X229 : term] : ~ ! [X230 : (subst > term > term)] : ~ ! [X231 : subst,X232 : term] : (((X230 @ X231 @ X232)) = ((sub @ X229 @ (push @ X232 @ X231)))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X233 : (subst > term > subst > $o)] : ~ ! [X234 : (term > $o)] : ~ ! [X235 : term] : (((X234 @ X235)) = ((X233 @ id @ X235 @ id)))) & ! [X236 : subst] : ? [X237 : d_subst] : (((d2subst @ X237)) = X236) & (ulamvarind = $true) & ! [X238 : d_term,X239 : d_term] : ((((d2term @ X238)) = ((d2term @ X239))) => (X238 = X239)) & (pushprop_lem2v2_lthm = $true) & (! [X240 : term,X241 : term] : ((X240 = X241) | (((lam @ X241)) != ((lam @ X240)))) <=> (laminj = $true)) & (! [X242 : term,X243 : subst,X244 : (term > $o)] : (~ ! [X245 : term] : (($true = ((X244 @ (sub @ X245 @ X243)))) | ~ (((var @ X245)) = $true)) | ~ ! [X246 : term] : (~ ! [X247 : term] : (~ (((X244 @ X247)) = $true) | ($true = ((X244 @ (sub @ X246 @ (push @ X247 @ id)))))) | ($true = ((X244 @ (lam @ X246))))) | ($true = ((X244 @ (sub @ X242 @ X243)))) | ~ ! [X248 : term,X249 : term] : (~ ($true = ((X244 @ X249))) | ($true = ((X244 @ (ap @ X248 @ X249)))) | ~ ($true = ((X244 @ X248))))) <=> (induction2lem = $true)) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X250 : (term > $o),X251 : term] : (~ ! [X252 : term] : (~ (((var @ X252)) = $true) | (((X250 @ X252)) = $true)) | ~ ! [X253 : term] : (~ ! [X254 : term] : (~ (((X250 @ X254)) = $true) | (((X250 @ (sub @ X253 @ (push @ X254 @ id)))) = $true)) | ($true = ((X250 @ (lam @ X253))))) | ($true = ((X250 @ X251))) | ~ ! [X255 : term,X256 : term] : (~ ($true = ((X250 @ X256))) | ~ (((X250 @ X255)) = $true) | (((X250 @ (ap @ X255 @ X256))) = $true))) <=> (induction2 = $true)) & (! [X257 : (subst > term > subst > $o),X258 : term,X259 : (term > $o)] : (~ ! [X260 : subst,X261 : term,X262 : subst,X263 : subst] : (($true = ((X257 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262) @ X263))) | ~ ($true = ((X257 @ X260 @ X261 @ (comp @ X262 @ X263))))) | ~ ! [X264 : term] : (((X257 @ id @ X264 @ id)) = ((X259 @ X264))) | ~ ! [X265 : subst,X266 : subst,X267 : term,X268 : subst] : ((((X257 @ X268 @ X267 @ (comp @ X265 @ X266))) = $true) | ~ ($true = ((X257 @ (comp @ X268 @ X265) @ (sub @ X267 @ X265) @ X266)))) | ~ ! [X269 : term] : ((((X259 @ (sub @ X258 @ (push @ X269 @ id)))) = $true) | ~ ($true = ((X259 @ X269)))) | ~ ! [X270 : (subst > term > term)] : ((((X257 @ id @ (lam @ (X270 @ sh @ one)) @ id)) = $true) | ~ ! [X271 : term] : (~ ($true = ((X257 @ id @ X271 @ id))) | ($true = ((X257 @ id @ (X270 @ id @ X271) @ id)))) | ~ ! [X272 : term,X273 : subst,X274 : subst] : (((sub @ (X270 @ X274 @ X272) @ X273)) = ((X270 @ (comp @ X274 @ X273) @ (sub @ X272 @ X273))))) | ($true = ((X259 @ (lam @ X258))))) <=> (hoasinduction_lem3v2 = $true)) & (! [X275 : (subst > term > subst > $o),X276 : term,X277 : (term > $o)] : (~ ! [X278 : term] : (($true = ((X277 @ (sub @ X276 @ (push @ X278 @ id))))) | ~ ($true = ((X277 @ X278)))) | ($true = ((X277 @ (lam @ X276)))) | ~ ! [X279 : (subst > term > term)] : (~ ! [X280 : term] : (($true = ((X275 @ id @ (X279 @ id @ X280) @ id))) | ~ ($true = ((X275 @ id @ X280 @ id)))) | ~ ! [X281 : subst,X282 : term,X283 : subst] : (((X279 @ (comp @ X281 @ X283) @ (sub @ X282 @ X283))) = ((sub @ (X279 @ X281 @ X282) @ X283))) | ($true = ((X275 @ id @ (lam @ (X279 @ sh @ one)) @ id)))) | ~ ! [X284 : term] : (((X277 @ X284)) = ((X275 @ id @ X284 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasapinj2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X285 : term,X286 : (term > $o),X287 : (term > $o),X288 : subst] : (~ ! [X289 : term] : (((X287 @ X289)) = ((X286 @ (sub @ X289 @ (push @ X285 @ X288))))) | ~ ($true = ((X286 @ X285))) | (((X287 @ one)) = $true))) & (! [X290 : term,X291 : (term > $o),X292 : subst] : ~ ! [X293 : (term > $o)] : ~ ! [X294 : term] : (((X293 @ X294)) = ((X291 @ (sub @ X294 @ (push @ X290 @ X292))))) <=> (pushprop_lem0 = $true)) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & ! [X295 : d_subst] : (d_id = X295) & (hoasapnotvar = $true) & (! [X296 : term,X297 : (subst > term > subst > $o)] : (($true = ((X297 @ id @ X296 @ id))) | ~ ! [X298 : term,X299 : term] : ((((X297 @ id @ (ap @ (sub @ X298 @ id) @ X299) @ id)) = $true) | ~ (((X297 @ id @ X299 @ id)) = $true) | ~ ($true = ((X297 @ id @ X298 @ id)))) | ~ ! [X300 : (subst > term > term)] : (($true = ((X297 @ id @ (lam @ (X300 @ sh @ one)) @ id))) | ~ ! [X301 : term] : (~ ($true = ((X297 @ id @ X301 @ id))) | ($true = ((X297 @ id @ (X300 @ id @ X301) @ id)))) | ~ ! [X302 : subst,X303 : term,X304 : subst] : (((sub @ (X300 @ X304 @ X303) @ X302)) = ((X300 @ (comp @ X304 @ X302) @ (sub @ X303 @ X302)))))) <=> (hoasinduction_no_psi_cond = $true)) & ((apinj2 = $true) <=> ! [X305 : term,X306 : term,X307 : term,X308 : term] : ((X306 = X307) | (((ap @ X305 @ X307)) != ((ap @ X308 @ X306))))) & (hoasinduction_lem1v2 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem3a_gthm = $true) & ~ (ulamvar1 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ~ (lamnotap = $true) & (hoasapinj1_gthm = $true) & ((axscons = $true) <=> ! [X311 : subst] : (((push @ (sub @ one @ X311) @ (comp @ sh @ X311))) = X311)) & (axassoc = $true) & (! [X312 : term,X313 : subst,X314 : term,X315 : (term > $o),X316 : (term > $o)] : (~ ($true = ((X315 @ X314))) | ($true = ((X316 @ (sub @ X314 @ (push @ X312 @ X313)))))) <=> (pushprop_lem1 = $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)))))))))))) & (! [X322 : subst,X323 : (term > $o),X324 : term] : ~ ! [X325 : (term > $o)] : ~ ! [X326 : term] : (((X325 @ X326)) = ((X323 @ (sub @ X326 @ (push @ X324 @ X322))))) <=> (pushprop_lem0_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X327 : term,X328 : (subst > term > term),X329 : subst,X330 : (subst > term > term)] : ((((lam @ (X330 @ sh @ one))) != ((lam @ (X328 @ sh @ one)))) | ~ ! [X331 : term,X332 : subst,X333 : subst] : (((X330 @ (comp @ X333 @ X332) @ (sub @ X331 @ X332))) = ((sub @ (X330 @ X333 @ X331) @ X332))) | ~ ! [X334 : term,X335 : subst,X336 : subst] : (((X328 @ (comp @ X336 @ X335) @ (sub @ X334 @ X335))) = ((sub @ (X328 @ X336 @ X334) @ X335))) | (((X328 @ X329 @ X327)) = ((X330 @ X329 @ X327))))) & (axclos = $true) & (hoaslamnotvar_gthm = $true) & (! [X337 : subst] : (((comp @ id @ X337)) = X337) <=> (axidl = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X338 : term] : ~ ! [X339 : (subst > term > term)] : ~ ! [X340 : term,X341 : subst] : (((sub @ X338 @ (push @ X340 @ X341))) = ((X339 @ X341 @ X340)))) & ((induction2lem_lthm = $true) <=> (! [X342 : term,X343 : subst] : (((sub @ one @ (push @ X342 @ X343))) = X342) => (! [X344 : term,X345 : subst] : (((comp @ sh @ (push @ X344 @ X345))) = X345) => (! [X346 : subst] : (((comp @ X346 @ id)) = X346) => (! [X347 : term,X348 : (term > $o)] : (~ ! [X349 : term,X350 : term] : (~ ($true = ((X348 @ X350))) | ($true = ((X348 @ (ap @ X350 @ X349)))) | ~ (((X348 @ X349)) = $true)) | ~ ! [X351 : term] : (~ ($true = ((X348 @ X351))) | ($true = ((X348 @ (lam @ X351))))) | ~ ! [X352 : term] : ((((X348 @ X352)) = $true) | ~ (((var @ X352)) = $true)) | (((X348 @ X347)) = $true)) => ! [X353 : (term > $o),X354 : term,X355 : subst] : (~ ! [X356 : term,X357 : term] : (($true = ((X353 @ (ap @ X357 @ X356)))) | ~ ($true = ((X353 @ X356))) | ~ ($true = ((X353 @ X357)))) | ~ ! [X358 : term] : (~ ! [X359 : term] : (($true = ((X353 @ (sub @ X358 @ (push @ X359 @ id))))) | ~ ($true = ((X353 @ X359)))) | (((X353 @ (lam @ X358))) = $true)) | ($true = ((X353 @ (sub @ X354 @ X355)))) | ~ ! [X360 : term] : (($true = ((X353 @ (sub @ X360 @ X355)))) | ~ ($true = ((var @ X360)))))))))) & (! [X361 : (subst > term > subst > $o)] : ~ ! [X362 : (term > $o)] : ~ ! [X363 : term] : (((X362 @ X363)) = ((X361 @ id @ X363 @ id))) <=> (hoasinduction_lem0 = $true)) & ((axshiftcons = $true) <=> ! [X364 : term,X365 : subst] : (((comp @ sh @ (push @ X364 @ X365))) = X365)) & (! [X366 : term,X367 : (subst > term > subst > $o)] : (~ ! [X368 : (subst > term > term)] : (($true = ((X367 @ id @ (lam @ (X368 @ sh @ one)) @ id))) | ~ ! [X369 : subst,X370 : term,X371 : subst] : (((sub @ (X368 @ X371 @ X370) @ X369)) = ((X368 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | ~ ! [X372 : term] : ((((X367 @ id @ (X368 @ id @ X372) @ id)) = $true) | ~ (((X367 @ id @ X372 @ id)) = $true))) | ($true = ((X367 @ id @ (lam @ (sub @ X366 @ (push @ one @ sh))) @ id))) | ~ ! [X373 : term] : (~ ($true = ((X367 @ id @ X373 @ id))) | ($true = ((X367 @ id @ (sub @ X366 @ (push @ X373 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X374 : term] : ? [X375 : d_term] : (((d2term @ X375)) = X374) & (axabs = $true) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X376 : (subst > term > subst > $o)] : ~ ! [X377 : (term > $o)] : ~ ! [X378 : term] : (((X376 @ id @ X378 @ id)) = ((X377 @ X378))) => (! [X379 : (term > $o),X380 : term] : (~ ! [X381 : term] : (($true = ((X379 @ (lam @ X381)))) | ~ ! [X382 : term] : (~ (((X379 @ X382)) = $true) | ($true = ((X379 @ (sub @ X381 @ (push @ X382 @ id))))))) | ~ ! [X383 : term] : (($true = ((X379 @ X383))) | ~ ($true = ((var @ X383)))) | ($true = ((X379 @ X380))) | ~ ! [X384 : term,X385 : term] : (~ ($true = ((X379 @ X384))) | ($true = ((X379 @ (ap @ X385 @ X384)))) | ~ ($true = ((X379 @ X385))))) => (! [X386 : term] : (((sub @ X386 @ id)) = X386) => (! [X387 : (subst > term > subst > $o),X388 : term,X389 : (term > $o)] : (~ ! [X390 : term] : (((X387 @ id @ X390 @ id)) = ((X389 @ X390))) | ($true = ((X389 @ (lam @ X388)))) | ~ ! [X391 : term] : (~ ($true = ((X389 @ X391))) | ($true = ((X389 @ (sub @ X388 @ (push @ X391 @ id)))))) | ~ ! [X392 : (subst > term > term)] : (($true = ((X387 @ id @ (lam @ (X392 @ sh @ one)) @ id))) | ~ ! [X393 : subst,X394 : term,X395 : subst] : (((sub @ (X392 @ X395 @ X394) @ X393)) = ((X392 @ (comp @ X395 @ X393) @ (sub @ X394 @ X393)))) | ~ ! [X396 : term] : (~ ($true = ((X387 @ id @ X396 @ id))) | ($true = ((X387 @ id @ (X392 @ id @ X396) @ id)))))) => ! [X397 : (subst > term > subst > $o),X398 : term] : (~ ! [X399 : term] : (($true = ((X397 @ id @ X399 @ id))) | ~ ($true = ((var @ (sub @ X399 @ id))))) | ~ ! [X400 : term,X401 : term] : (($true = ((X397 @ id @ (ap @ (sub @ X401 @ id) @ X400) @ id))) | ~ (((X397 @ id @ X401 @ id)) = $true) | ~ ($true = ((X397 @ id @ X400 @ id)))) | ~ ! [X402 : subst,X403 : subst,X404 : subst,X405 : term] : (($true = ((X397 @ (comp @ X403 @ X404) @ (sub @ X405 @ X404) @ X402))) | ~ (((X397 @ X403 @ X405 @ (comp @ X404 @ X402))) = $true)) | ~ ! [X406 : subst,X407 : subst,X408 : subst,X409 : term] : (($true = ((X397 @ X406 @ X409 @ (comp @ X408 @ X407)))) | ~ ($true = ((X397 @ (comp @ X406 @ X408) @ (sub @ X409 @ X408) @ X407)))) | ($true = ((X397 @ id @ X398 @ id))) | ~ ! [X410 : (subst > term > term)] : (($true = ((X397 @ id @ (lam @ (X410 @ sh @ one)) @ id))) | ~ ! [X411 : subst,X412 : term,X413 : subst] : (((X410 @ (comp @ X411 @ X413) @ (sub @ X412 @ X413))) = ((sub @ (X410 @ X411 @ X412) @ X413))) | ~ ! [X414 : term] : (($true = ((X397 @ id @ (X410 @ id @ X414) @ id))) | ~ ($true = ((X397 @ id @ X414 @ id)))))))))) <=> (hoasinduction_lthm_3 = $true)) & (! [X415 : term,X416 : term,X417 : term,X418 : term] : ((((ap @ (sub @ X416 @ id) @ X417)) != ((ap @ (sub @ X415 @ id) @ X418))) | (X415 = X416)) <=> (hoasapinj1 = $true)) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X419 : term,X420 : (subst > term > subst > $o)] : (~ ! [X421 : term] : (($true = ((X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id))) | ~ ($true = ((X420 @ id @ X421 @ id)))) | (((X420 @ id @ (lam @ (sub @ X419 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X422 : (subst > term > term)] : (~ ! [X423 : term] : (~ (((X420 @ id @ X423 @ id)) = $true) | ($true = ((X420 @ id @ (X422 @ id @ X423) @ id)))) | ($true = ((X420 @ id @ (lam @ (X422 @ sh @ one)) @ id))) | ~ ! [X424 : term,X425 : subst,X426 : subst] : (((sub @ (X422 @ X426 @ X424) @ X425)) = ((X422 @ (comp @ X426 @ X425) @ (sub @ X424 @ X425))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X427 : term,X428 : (subst > term > subst > $o)] : (~ ! [X429 : term,X430 : (subst > term > term)] : (~ ! [X431 : subst,X432 : subst,X433 : term] : (((sub @ (sub @ X429 @ (push @ X433 @ X431)) @ X432)) = ((sub @ (X430 @ X431 @ X433) @ X432))) | ~ ! [X434 : term,X435 : subst,X436 : subst] : (((X430 @ (comp @ X435 @ X436) @ (sub @ X434 @ X436))) = ((sub @ X429 @ (push @ (sub @ X434 @ X436) @ (comp @ X435 @ X436))))) | (((X428 @ id @ (lam @ (X430 @ sh @ one)) @ id)) = $true) | ~ ! [X437 : term] : (~ ($true = ((X428 @ id @ X437 @ id))) | ($true = ((X428 @ id @ (X430 @ id @ X437) @ id))))) | ~ ! [X438 : term] : (~ ($true = ((X428 @ id @ X438 @ id))) | ($true = ((X428 @ id @ (sub @ X427 @ (push @ X438 @ id)) @ id)))) | (((X428 @ id @ (lam @ (sub @ X427 @ (push @ one @ sh))) @ id)) = $true))) & ((! [X439 : term,X440 : term,X441 : term,X442 : term] : ((((ap @ X440 @ X441)) != ((ap @ X439 @ X442))) | (X441 = X442)) => ! [X443 : term,X444 : term,X445 : term,X446 : term] : ((((ap @ (sub @ X445 @ id) @ X443)) != ((ap @ (sub @ X446 @ id) @ X444))) | (X443 = X444))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X447 : (subst > term > subst > $o),X448 : term] : (~ ! [X449 : subst,X450 : subst,X451 : subst,X452 : term] : (~ (((X447 @ X451 @ X452 @ (comp @ X450 @ X449))) = $true) | (((X447 @ (comp @ X451 @ X450) @ (sub @ X452 @ X450) @ X449)) = $true)) | ~ ! [X453 : term] : (~ ($true = ((X447 @ id @ X453 @ id))) | ($true = ((X447 @ id @ (sub @ X448 @ (push @ X453 @ id)) @ id)))) | ~ ! [X454 : term,X455 : subst,X456 : subst,X457 : subst] : (~ ($true = ((X447 @ (comp @ X457 @ X455) @ (sub @ X454 @ X455) @ X456))) | ($true = ((X447 @ X457 @ X454 @ (comp @ X455 @ X456))))) | ($true = ((X447 @ id @ (lam @ X448) @ id))) | ~ ! [X458 : (subst > term > term)] : (($true = ((X447 @ id @ (lam @ (X458 @ sh @ one)) @ id))) | ~ ! [X459 : subst,X460 : subst,X461 : term] : (((sub @ (X458 @ X459 @ X461) @ X460)) = ((X458 @ (comp @ X459 @ X460) @ (sub @ X461 @ X460)))) | ~ ! [X462 : term] : (($true = ((X447 @ id @ (X458 @ id @ X462) @ id))) | ~ ($true = ((X447 @ id @ X462 @ id))))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2subst @ d_id)) = sh) & ((termmset_lthm = $true) <=> (! [X463 : term] : (((sub @ X463 @ id)) = X463) => ! [X464 : term] : (((sub @ X464 @ id)) = X464))) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X465 : term,X466 : (subst > term > term),X467 : term] : ((((ap @ (sub @ X465 @ id) @ X467)) != ((lam @ (X466 @ sh @ one)))) | ~ ! [X468 : subst,X469 : subst,X470 : term] : (((sub @ (X466 @ X469 @ X470) @ X468)) = ((X466 @ (comp @ X469 @ X468) @ (sub @ X470 @ X468)))))) & (! [X471 : term] : (((sub @ X471 @ id)) = X471) <=> (axvarid = $true)) & (! [X472 : subst] : (((comp @ X472 @ id)) = X472) <=> (axidr = $true)) & (one = ((d2term @ d_one))) & (axvarshift = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X473 : subst,X474 : term] : (((sub @ one @ (push @ X474 @ X473))) = X474) => (! [X475 : subst,X476 : term] : (((comp @ sh @ (push @ X476 @ X475))) = X475) => (! [X477 : term,X478 : term] : ((X477 = X478) | (((lam @ X477)) != ((lam @ X478)))) => ! [X479 : subst,X480 : (subst > term > term),X481 : term,X482 : (subst > term > term)] : (~ ! [X483 : subst,X484 : subst,X485 : term] : (((sub @ (X480 @ X483 @ X485) @ X484)) = ((X480 @ (comp @ X483 @ X484) @ (sub @ X485 @ X484)))) | ~ ! [X486 : term,X487 : subst,X488 : subst] : (((X482 @ (comp @ X487 @ X488) @ (sub @ X486 @ X488))) = ((sub @ (X482 @ X487 @ X486) @ X488))) | (((lam @ (X480 @ sh @ one))) != ((lam @ (X482 @ sh @ one)))) | (((X482 @ X479 @ X481)) = ((X480 @ X479 @ X481))))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X489 : term] : (((sub @ X489 @ id)) = X489) => ! [X490 : term,X491 : (term > $o),X492 : (subst > term > subst > $o)] : (~ ! [X493 : term] : (($true = ((X491 @ (sub @ X490 @ (push @ X493 @ id))))) | ~ ($true = ((X491 @ X493)))) | ~ ! [X494 : subst,X495 : subst,X496 : subst,X497 : term] : (~ (((X492 @ X494 @ X497 @ (comp @ X495 @ X496))) = $true) | (((X492 @ (comp @ X494 @ X495) @ (sub @ X497 @ X495) @ X496)) = $true)) | ~ ! [X498 : term] : (((X492 @ id @ X498 @ id)) = ((X491 @ X498))) | ~ ! [X499 : subst,X500 : subst,X501 : term,X502 : subst] : (($true = ((X492 @ X499 @ X501 @ (comp @ X502 @ X500)))) | ~ ($true = ((X492 @ (comp @ X499 @ X502) @ (sub @ X501 @ X502) @ X500)))) | (((X491 @ (lam @ X490))) = $true) | ~ ! [X503 : (subst > term > term)] : (~ ! [X504 : subst,X505 : subst,X506 : term] : (((X503 @ (comp @ X504 @ X505) @ (sub @ X506 @ X505))) = ((sub @ (X503 @ X504 @ X506) @ X505))) | ($true = ((X492 @ id @ (lam @ (X503 @ sh @ one)) @ id))) | ~ ! [X507 : term] : (~ (((X492 @ id @ X507 @ id)) = $true) | ($true = ((X492 @ id @ (X503 @ id @ X507) @ id)))))))) & (axapp = $true) & ((hoasapinj2 = $true) <=> ! [X508 : term,X509 : term,X510 : term,X511 : term] : ((((ap @ (sub @ X511 @ id) @ X508)) != ((ap @ (sub @ X509 @ id) @ X510))) | (X508 = X510))) & (substmonoid_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X512 : term] : (((sub @ X512 @ id)) = X512) => (! [X513 : term,X514 : (subst > term > subst > $o)] : (($true = ((X514 @ id @ (lam @ (sub @ X513 @ (push @ one @ sh))) @ id))) | ~ ! [X515 : (subst > term > term)] : (($true = ((X514 @ id @ (lam @ (X515 @ sh @ one)) @ id))) | ~ ! [X516 : term] : (~ ($true = ((X514 @ id @ X516 @ id))) | ($true = ((X514 @ id @ (X515 @ id @ X516) @ id)))) | ~ ! [X517 : term,X518 : subst,X519 : subst] : (((X515 @ (comp @ X518 @ X519) @ (sub @ X517 @ X519))) = ((sub @ (X515 @ X518 @ X517) @ X519)))) | ~ ! [X520 : term] : (~ (((X514 @ id @ X520 @ id)) = $true) | (((X514 @ id @ (sub @ X513 @ (push @ X520 @ id)) @ id)) = $true))) => ! [X521 : term,X522 : (subst > term > subst > $o)] : (~ ! [X523 : term] : (~ ($true = ((X522 @ id @ X523 @ id))) | (((X522 @ id @ (sub @ X521 @ (push @ X523 @ id)) @ id)) = $true)) | ~ ! [X524 : (subst > term > term)] : (~ ! [X525 : term] : (~ ($true = ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) | ($true = ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) | ~ ! [X526 : term,X527 : subst,X528 : subst] : (((sub @ (X524 @ X527 @ X526) @ X528)) = ((X524 @ (comp @ X527 @ X528) @ (sub @ X526 @ X528))))) | ($true = ((X522 @ id @ (lam @ X521) @ id))))))) & ! [X529 : d_subst,X530 : d_subst] : ((((d2subst @ X530)) = ((d2subst @ X529))) => (X529 = X530)) & ! [X531 : d_term] : (d_one = X531) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (~ ! [X534 : (subst > term > term)] : ((((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id)) = $true) | ~ ! [X535 : term] : (~ ($true = ((X532 @ id @ X535 @ id))) | ($true = ((X532 @ id @ (X534 @ id @ X535) @ id)))) | ~ ! [X536 : subst,X537 : term,X538 : subst] : (((X534 @ (comp @ X536 @ X538) @ (sub @ X537 @ X538))) = ((sub @ (X534 @ X536 @ X537) @ X538)))) | ~ ! [X539 : subst,X540 : subst,X541 : term,X542 : subst] : (~ ($true = ((X532 @ (comp @ X542 @ X539) @ (sub @ X541 @ X539) @ X540))) | ($true = ((X532 @ X542 @ X541 @ (comp @ X539 @ X540))))) | ~ ! [X543 : term] : ((((X532 @ id @ X543 @ id)) = $true) | ~ ($true = ((var @ (sub @ X543 @ id))))) | ($true = ((X532 @ id @ X533 @ id))) | ~ ! [X544 : term,X545 : subst,X546 : subst,X547 : subst] : (~ ($true = ((X532 @ X545 @ X544 @ (comp @ X546 @ X547)))) | ($true = ((X532 @ (comp @ X545 @ X546) @ (sub @ X544 @ X546) @ X547)))) | ~ ! [X548 : term,X549 : term] : ((((X532 @ id @ (ap @ (sub @ X549 @ id) @ X548) @ id)) = $true) | ~ (((X532 @ id @ X549 @ id)) = $true) | ~ ($true = ((X532 @ id @ X548 @ id))))))),
% 1.42/0.51 inference(fool_elimination,[],[f6])).
% 1.42/0.51 thf(f8,plain,(
% 1.42/0.51 (hoaslaminj != ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))))))),
% 1.42/0.51 inference(flattening,[],[f5])).
% 1.42/0.51 thf(f9,plain,(
% 1.42/0.51 ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & (hoaslamnotvar_lthm = $true) & ((! [X1 : subst] : (((comp @ id @ X1)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) => (! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)))) <=> (substmonoid_lthm = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X5 : term] : ~ ! [X6 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) = ((X6 @ X8 @ X7))) => (! [X9 : term] : (((sub @ X9 @ id)) = X9) => ! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (~ ! [X13 : term] : (((X11 @ id @ X13 @ id)) = ((X12 @ X13))) | ~ ! [X14 : term] : ((((X12 @ (sub @ X10 @ (push @ X14 @ id)))) = $true) | ~ (((X12 @ X14)) = $true)) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | ~ (((X11 @ id @ X16 @ id)) = $true)) | ~ ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) | ($true = ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) | ($true = ((X12 @ (lam @ X10)))))))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X20 : term] : (((sub @ X20 @ id)) = X20) => (! [X21 : term,X22 : (subst > term > subst > $o)] : ((((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X23 : term] : (~ ($true = ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) | ~ ! [X24 : (subst > term > term)] : ((((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true) | ~ ! [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) = ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X28 : term] : (~ ($true = ((X22 @ id @ X28 @ id))) | (((X22 @ id @ (X24 @ id @ X28) @ id)) = $true)))) => ! [X29 : term,X30 : (subst > term > subst > $o)] : ((((X30 @ id @ (lam @ X29) @ id)) = $true) | ~ ! [X31 : term,X32 : subst,X33 : subst,X34 : subst] : (~ ($true = ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))) | (((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) = $true)) | ~ ! [X35 : (subst > term > term)] : ((((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) = $true) | ~ ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ~ ($true = ((X30 @ id @ X36 @ id)))) | ~ ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38))))) | ~ ! [X40 : term] : ((((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) = $true) | ~ ($true = ((X30 @ id @ X40 @ id)))) | ~ ! [X41 : subst,X42 : subst,X43 : term,X44 : subst] : (~ ($true = ((X30 @ X42 @ X43 @ (comp @ X44 @ X41)))) | ($true = ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41)))))))) & (hoasapnotvar_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X45 : term] : (((sub @ X45 @ id)) = X45) => (! [X49 : term,X47 : term,X48 : term,X46 : term] : ((((ap @ X47 @ X48)) != ((ap @ X46 @ X49))) | (X46 = X47)) => ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))))) & (pushprop = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X54 : (subst > term > subst > $o),X55 : (term > $o),X56 : term,X57 : term] : (~ (((X55 @ X57)) = $true) | ~ ! [X58 : term] : (((X55 @ X58)) = ((X54 @ id @ X58 @ id))) | ~ ! [X59 : term,X60 : term] : (~ (((X54 @ id @ X59 @ id)) = $true) | ~ ($true = ((X54 @ id @ X60 @ id))) | ($true = ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id)))) | ~ ! [X61 : subst,X62 : subst,X63 : subst,X64 : term] : (($true = ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) | ~ (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) = $true)) | ~ ($true = ((X55 @ X56))) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ~ ! [X65 : term,X66 : subst,X67 : subst,X68 : subst] : (~ ($true = ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66))) | ($true = ((X54 @ X67 @ X65 @ (comp @ X68 @ X66))))))) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3a = $true) <=> ! [X75 : (subst > term > subst > $o),X76 : term] : (($true = ((X75 @ id @ (lam @ X76) @ id))) | ~ ! [X77 : term] : ((((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) = $true) | ~ ($true = ((X75 @ id @ X77 @ id)))) | ~ ! [X78 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) = $true) | ~ ! [X79 : term] : (~ ($true = ((X75 @ id @ X79 @ id))) | ($true = ((X75 @ id @ (X78 @ id @ X79) @ id)))) | ~ ! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80)))))) & (hoasinduction_gthm = $true) & ((! [X83 : subst,X84 : term] : (((sub @ one @ (push @ X84 @ X83))) = X84) => ! [X85 : term,X86 : subst,X87 : (term > $o),X88 : (term > $o)] : (~ ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true = ((X87 @ one))) | ~ ($true = ((X88 @ X85))))) <=> (pushprop_lem1v2_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X91 : term,X90 : subst] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X94 : (term > $o),X95 : subst,X96 : term,X97 : term,X98 : (term > $o)] : (($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95))))) | ~ (((X98 @ X96)) = $true))))) & ~ (((var @ (d2term @ d_one))) = $true) & (pushprop_lthm = $true) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (pushprop_lem2v2 = $true) & (axmap = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & (apnotvar = $true) & (pushprop_gthm = $true) & (pushprop_lem0_gthm = $true) & ((! [X103 : (term > $o),X104 : term] : (~ ! [X105 : term,X106 : term] : (~ ($true = ((X103 @ X106))) | ($true = ((X103 @ (ap @ X105 @ X106)))) | ~ ($true = ((X103 @ X105)))) | (((X103 @ X104)) = $true) | ~ ! [X107 : term] : (~ ($true = ((var @ X107))) | ($true = ((X103 @ X107)))) | ~ ! [X108 : term] : (~ ! [X109 : term] : (~ ($true = ((X103 @ X109))) | ($true = ((X103 @ (sub @ X108 @ (push @ X109 @ id)))))) | ($true = ((X103 @ (lam @ X108)))))) => (! [X110 : term,X111 : term,X112 : (subst > term > subst > $o)] : (~ ! [X113 : term,X114 : term] : (($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id))) | ~ ($true = ((X112 @ id @ X113 @ id))) | ~ (((X112 @ id @ X114 @ id)) = $true)) | ~ ! [X115 : subst,X116 : term,X117 : subst,X118 : subst] : ((((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true) | ~ (((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) = $true)) | ($true = ((X112 @ id @ (ap @ X110 @ X111) @ id))) | ~ ($true = ((X112 @ id @ X110 @ id))) | ~ ! [X119 : term,X120 : subst,X121 : subst,X122 : subst] : (~ ($true = ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) | ~ (((X112 @ id @ X111 @ id)) = $true)) => (! [X123 : (subst > term > subst > $o),X124 : term] : (~ ! [X125 : (subst > term > term)] : (~ ! [X126 : subst,X128 : term,X127 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) = ((sub @ (X125 @ X126 @ X128) @ X127))) | (((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true) | ~ ! [X129 : term] : (~ ($true = ((X123 @ id @ X129 @ id))) | ($true = ((X123 @ id @ (X125 @ id @ X129) @ id))))) | ~ ! [X130 : subst,X131 : term,X132 : subst,X133 : subst] : (~ ($true = ((X123 @ X130 @ X131 @ (comp @ X132 @ X133)))) | ($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133)))) | ~ ! [X134 : subst,X135 : subst,X136 : subst,X137 : term] : (~ ($true = ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134))))) | ~ ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | ~ (((X123 @ id @ X138 @ id)) = $true)) | (((X123 @ id @ (lam @ X124) @ id)) = $true)) => ! [X139 : term,X140 : (subst > term > subst > $o)] : (~ ! [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) = $true) | ~ ($true = ((X140 @ id @ X141 @ id))) | ~ ($true = ((X140 @ id @ X142 @ id)))) | (((X140 @ id @ X139 @ id)) = $true) | ~ ! [X143 : term] : (~ (((var @ (sub @ X143 @ id))) = $true) | ($true = ((X140 @ id @ X143 @ id)))) | ~ ! [X144 : (subst > term > term)] : (~ ! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) | ($true = ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id))) | ~ ! [X148 : term] : (~ (((X140 @ id @ X148 @ id)) = $true) | ($true = ((X140 @ id @ (X144 @ id @ X148) @ id))))) | ~ ! [X149 : subst,X150 : subst,X151 : subst,X152 : term] : (($true = ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) | ~ (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) = $true)) | ~ ! [X153 : subst,X154 : term,X155 : subst,X156 : subst] : (~ ($true = ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) | (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) = $true)))))) <=> (hoasinduction_lthm = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((induction2_lthm = $true) <=> (! [X157 : term] : (((sub @ X157 @ id)) = X157) => (! [X158 : (term > $o),X159 : subst,X160 : term] : (~ ! [X161 : term] : (($true = ((X158 @ (lam @ X161)))) | ~ ! [X162 : term] : ((((X158 @ (sub @ X161 @ (push @ X162 @ id)))) = $true) | ~ ($true = ((X158 @ X162))))) | ($true = ((X158 @ (sub @ X160 @ X159)))) | ~ ! [X163 : term,X164 : term] : (~ ($true = ((X158 @ X164))) | ~ ($true = ((X158 @ X163))) | (((X158 @ (ap @ X164 @ X163))) = $true)) | ~ ! [X165 : term] : (($true = ((X158 @ (sub @ X165 @ X159)))) | ~ ($true = ((var @ X165))))) => ! [X166 : (term > $o),X167 : term] : (~ ! [X168 : term] : (($true = ((X166 @ (lam @ X168)))) | ~ ! [X169 : term] : (~ ($true = ((X166 @ X169))) | (((X166 @ (sub @ X168 @ (push @ X169 @ id)))) = $true))) | ($true = ((X166 @ X167))) | ~ ! [X170 : term,X171 : term] : ((((X166 @ (ap @ X171 @ X170))) = $true) | ~ ($true = ((X166 @ X170))) | ~ ($true = ((X166 @ X171)))) | ~ ! [X172 : term] : (~ (((var @ X172)) = $true) | (((X166 @ X172)) = $true)))))) & ((! [X173 : (subst > term > subst > $o)] : ~ ! [X174 : (term > $o)] : ~ ! [X175 : term] : (((X174 @ X175)) = ((X173 @ id @ X175 @ id))) => (! [X176 : (term > $o),X177 : term] : (~ ! [X178 : term] : (~ ! [X179 : term] : (~ ($true = ((X176 @ X179))) | ($true = ((X176 @ (sub @ X178 @ (push @ X179 @ id)))))) | (((X176 @ (lam @ X178))) = $true)) | ~ ! [X180 : term,X181 : term] : (($true = ((X176 @ (ap @ X180 @ X181)))) | ~ ($true = ((X176 @ X180))) | ~ ($true = ((X176 @ X181)))) | ~ ! [X182 : term] : (($true = ((X176 @ X182))) | ~ ($true = ((var @ X182)))) | ($true = ((X176 @ X177)))) => (! [X183 : term] : (((sub @ X183 @ id)) = X183) => (! [X184 : (term > $o),X185 : term,X186 : (subst > term > subst > $o)] : (~ ! [X187 : term] : (((X186 @ id @ X187 @ id)) = ((X184 @ X187))) | ~ ! [X188 : term] : (~ (((X184 @ X188)) = $true) | ($true = ((X184 @ (sub @ X185 @ (push @ X188 @ id)))))) | ~ ! [X189 : (subst > term > term)] : (~ ! [X190 : subst,X192 : term,X191 : subst] : (((X189 @ (comp @ X190 @ X191) @ (sub @ X192 @ X191))) = ((sub @ (X189 @ X190 @ X192) @ X191))) | (((X186 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true) | ~ ! [X193 : term] : (~ ($true = ((X186 @ id @ X193 @ id))) | (((X186 @ id @ (X189 @ id @ X193) @ id)) = $true))) | (((X184 @ (lam @ X185))) = $true)) => ! [X194 : term,X195 : (subst > term > subst > $o)] : (~ ! [X196 : term,X197 : term] : (~ (((X195 @ id @ X197 @ id)) = $true) | ~ (((X195 @ id @ X196 @ id)) = $true) | (((X195 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) = $true)) | ($true = ((X195 @ id @ X194 @ id))) | ~ ! [X198 : (subst > term > term)] : ((((X195 @ id @ (lam @ (X198 @ sh @ one)) @ id)) = $true) | ~ ! [X199 : term] : ((((X195 @ id @ (X198 @ id @ X199) @ id)) = $true) | ~ (((X195 @ id @ X199 @ id)) = $true)) | ~ ! [X202 : term,X201 : subst,X200 : subst] : (((sub @ (X198 @ X200 @ X202) @ X201)) = ((X198 @ (comp @ X200 @ X201) @ (sub @ X202 @ X201)))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X203 : term] : ~ ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ X203 @ (push @ one @ sh))))) & (induction2_gthm = $true) & (! [X205 : (term > $o),X206 : term] : ((((X205 @ X206)) = $true) | ~ ! [X207 : term] : (($true = ((X205 @ X207))) | ~ (((var @ X207)) = $true)) | ~ ! [X208 : term,X209 : term] : (($true = ((X205 @ (ap @ X209 @ X208)))) | ~ ($true = ((X205 @ X208))) | ~ ($true = ((X205 @ X209)))) | ~ ! [X210 : term] : ((((X205 @ (lam @ X210))) = $true) | ~ ($true = ((X205 @ X210))))) <=> (induction = $true)) & (hoasinduction_lem1_lthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X211 : term,X212 : (subst > term > subst > $o),X213 : term] : (~ ! [X214 : subst,X215 : subst,X216 : term,X217 : subst] : (($true = ((X212 @ X215 @ X216 @ (comp @ X214 @ X217)))) | ~ (((X212 @ (comp @ X215 @ X214) @ (sub @ X216 @ X214) @ X217)) = $true)) | ~ ($true = ((X212 @ id @ X213 @ id))) | ~ ! [X218 : subst,X219 : subst,X220 : subst,X221 : term] : (($true = ((X212 @ (comp @ X220 @ X219) @ (sub @ X221 @ X219) @ X218))) | ~ ($true = ((X212 @ X220 @ X221 @ (comp @ X219 @ X218))))) | ($true = ((X212 @ id @ (ap @ X213 @ X211) @ id))) | ~ ! [X222 : term,X223 : term] : (~ ($true = ((X212 @ id @ X222 @ id))) | (((X212 @ id @ (ap @ (sub @ X223 @ id) @ X222) @ id)) = $true) | ~ ($true = ((X212 @ id @ X223 @ id)))) | ~ ($true = ((X212 @ id @ X211 @ id))))) & ((axvarcons = $true) <=> ! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224)) & (induction2lem_gthm = $true) & (lamnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & (! [X226 : term] : ~ ! [X227 : (subst > term > term)] : ~ ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X230 : (subst > term > subst > $o)] : ~ ! [X231 : (term > $o)] : ~ ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232)))) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (ulamvarind = $true) & ! [X236 : d_term,X235 : d_term] : ((((d2term @ X236)) = ((d2term @ X235))) => (X235 = X236)) & (pushprop_lem2v2_lthm = $true) & ((laminj = $true) <=> ! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237))))) & (! [X239 : term,X240 : subst,X241 : (term > $o)] : (~ ! [X242 : term] : (($true = ((X241 @ (sub @ X242 @ X240)))) | ~ ($true = ((var @ X242)))) | ~ ! [X243 : term] : (~ ! [X244 : term] : (~ ($true = ((X241 @ X244))) | ($true = ((X241 @ (sub @ X243 @ (push @ X244 @ id)))))) | ($true = ((X241 @ (lam @ X243))))) | ($true = ((X241 @ (sub @ X239 @ X240)))) | ~ ! [X245 : term,X246 : term] : (~ ($true = ((X241 @ X246))) | (((X241 @ (ap @ X245 @ X246))) = $true) | ~ ($true = ((X241 @ X245))))) <=> (induction2lem = $true)) & (((d2subst @ d_id)) = id) & (termmset_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (hoaslamnotap_lthm = $true) & (! [X247 : (term > $o),X248 : term] : (~ ! [X249 : term] : (~ (((var @ X249)) = $true) | (((X247 @ X249)) = $true)) | ~ ! [X250 : term] : (~ ! [X251 : term] : (~ ($true = ((X247 @ X251))) | ($true = ((X247 @ (sub @ X250 @ (push @ X251 @ id)))))) | ($true = ((X247 @ (lam @ X250))))) | ($true = ((X247 @ X248))) | ~ ! [X252 : term,X253 : term] : (~ ($true = ((X247 @ X253))) | ~ (((X247 @ X252)) = $true) | ($true = ((X247 @ (ap @ X252 @ X253)))))) <=> (induction2 = $true)) & (! [X254 : (subst > term > subst > $o),X255 : term,X256 : (term > $o)] : (~ ! [X257 : subst,X258 : term,X259 : subst,X260 : subst] : (($true = ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259) @ X260))) | ~ ($true = ((X254 @ X257 @ X258 @ (comp @ X259 @ X260))))) | ~ ! [X261 : term] : (((X254 @ id @ X261 @ id)) = ((X256 @ X261))) | ~ ! [X262 : subst,X263 : subst,X264 : term,X265 : subst] : ((((X254 @ X265 @ X264 @ (comp @ X262 @ X263))) = $true) | ~ ($true = ((X254 @ (comp @ X265 @ X262) @ (sub @ X264 @ X262) @ X263)))) | ~ ! [X266 : term] : ((((X256 @ (sub @ X255 @ (push @ X266 @ id)))) = $true) | ~ ($true = ((X256 @ X266)))) | ~ ! [X267 : (subst > term > term)] : ((((X254 @ id @ (lam @ (X267 @ sh @ one)) @ id)) = $true) | ~ ! [X268 : term] : (~ ($true = ((X254 @ id @ X268 @ id))) | ($true = ((X254 @ id @ (X267 @ id @ X268) @ id)))) | ~ ! [X270 : subst,X271 : subst,X269 : term] : (((X267 @ (comp @ X271 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X271 @ X269) @ X270)))) | (((X256 @ (lam @ X255))) = $true)) <=> (hoasinduction_lem3v2 = $true)) & (! [X272 : (subst > term > subst > $o),X273 : term,X274 : (term > $o)] : (~ ! [X275 : term] : (($true = ((X274 @ (sub @ X273 @ (push @ X275 @ id))))) | ~ (((X274 @ X275)) = $true)) | ($true = ((X274 @ (lam @ X273)))) | ~ ! [X276 : (subst > term > term)] : (~ ! [X277 : term] : ((((X272 @ id @ (X276 @ id @ X277) @ id)) = $true) | ~ (((X272 @ id @ X277 @ id)) = $true)) | ~ ! [X279 : term,X280 : subst,X278 : subst] : (((sub @ (X276 @ X278 @ X279) @ X280)) = ((X276 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280)))) | ($true = ((X272 @ id @ (lam @ (X276 @ sh @ one)) @ id)))) | ~ ! [X281 : term] : (((X274 @ X281)) = ((X272 @ id @ X281 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasapinj2_gthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X282 : term,X283 : (term > $o),X284 : (term > $o),X285 : subst] : (~ ! [X286 : term] : (((X284 @ X286)) = ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ~ ($true = ((X283 @ X282))) | (((X284 @ one)) = $true))) & ((pushprop_lem0 = $true) <=> ! [X287 : term,X289 : subst,X288 : (term > $o)] : ~ ! [X290 : (term > $o)] : ~ ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289)))))) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem3b_gthm = $true) & ! [X292 : d_subst] : (d_id = X292) & (hoasapnotvar = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ~ ! [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) = $true) | ~ ($true = ((X294 @ id @ X296 @ id))) | ~ (((X294 @ id @ X295 @ id)) = $true)) | ~ ! [X297 : (subst > term > term)] : (($true = ((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id))) | ~ ! [X298 : term] : (~ ($true = ((X294 @ id @ X298 @ id))) | (((X294 @ id @ (X297 @ id @ X298) @ id)) = $true)) | ~ ! [X300 : term,X301 : subst,X299 : subst] : (((sub @ (X297 @ X301 @ X300) @ X299)) = ((X297 @ (comp @ X301 @ X299) @ (sub @ X300 @ X299)))))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) <=> (apinj2 = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem3a_gthm = $true) & ~ (ulamvar1 = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ~ (lamnotap = $true) & (hoasapinj1_gthm = $true) & ((axscons = $true) <=> ! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306)) & (axassoc = $true) & (! [X307 : term,X308 : subst,X309 : term,X310 : (term > $o),X311 : (term > $o)] : (~ ($true = ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) <=> (pushprop_lem1 = $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)))))))))))) & (! [X313 : (term > $o),X312 : subst,X314 : term] : ~ ! [X315 : (term > $o)] : ~ ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) <=> (pushprop_lem0_lthm = $true)) & (hoaslaminj_gthm = $true) & (hoasapnotvar_lthm = $true) & (pushprop_lem3v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X318 : (subst > term > term),X319 : subst,X320 : (subst > term > term),X317 : term] : (~ ! [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) = ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ~ ! [X322 : subst,X321 : term,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) = ((sub @ (X320 @ X323 @ X321) @ X322))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))))) & (axclos = $true) & (hoaslamnotvar_gthm = $true) & ((axidl = $true) <=> ! [X327 : subst] : (((comp @ id @ X327)) = X327)) & (! [X328 : term] : ~ ! [X329 : (subst > term > term)] : ~ ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((induction2lem_lthm = $true) <=> (! [X332 : term,X333 : subst] : (((sub @ one @ (push @ X332 @ X333))) = X332) => (! [X334 : term,X335 : subst] : (((comp @ sh @ (push @ X334 @ X335))) = X335) => (! [X336 : subst] : (((comp @ X336 @ id)) = X336) => (! [X337 : term,X338 : (term > $o)] : (~ ! [X339 : term,X340 : term] : (~ ($true = ((X338 @ X340))) | ($true = ((X338 @ (ap @ X340 @ X339)))) | ~ (((X338 @ X339)) = $true)) | ~ ! [X341 : term] : (~ (((X338 @ X341)) = $true) | (((X338 @ (lam @ X341))) = $true)) | ~ ! [X342 : term] : (($true = ((X338 @ X342))) | ~ ($true = ((var @ X342)))) | ($true = ((X338 @ X337)))) => ! [X343 : (term > $o),X344 : term,X345 : subst] : (~ ! [X346 : term,X347 : term] : ((((X343 @ (ap @ X347 @ X346))) = $true) | ~ ($true = ((X343 @ X346))) | ~ ($true = ((X343 @ X347)))) | ~ ! [X348 : term] : (~ ! [X349 : term] : (($true = ((X343 @ (sub @ X348 @ (push @ X349 @ id))))) | ~ ($true = ((X343 @ X349)))) | ($true = ((X343 @ (lam @ X348))))) | ($true = ((X343 @ (sub @ X344 @ X345)))) | ~ ! [X350 : term] : (($true = ((X343 @ (sub @ X350 @ X345)))) | ~ ($true = ((var @ X350)))))))))) & ((hoasinduction_lem0 = $true) <=> ! [X351 : (subst > term > subst > $o)] : ~ ! [X352 : (term > $o)] : ~ ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id)))) & ((axshiftcons = $true) <=> ! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355)) & (! [X356 : term,X357 : (subst > term > subst > $o)] : (~ ! [X358 : (subst > term > term)] : ((((X357 @ id @ (lam @ (X358 @ sh @ one)) @ id)) = $true) | ~ ! [X361 : subst,X359 : subst,X360 : term] : (((X358 @ (comp @ X361 @ X359) @ (sub @ X360 @ X359))) = ((sub @ (X358 @ X361 @ X360) @ X359))) | ~ ! [X362 : term] : (($true = ((X357 @ id @ (X358 @ id @ X362) @ id))) | ~ ($true = ((X357 @ id @ X362 @ id))))) | ($true = ((X357 @ id @ (lam @ (sub @ X356 @ (push @ one @ sh))) @ id))) | ~ ! [X363 : term] : (~ (((X357 @ id @ X363 @ id)) = $true) | ($true = ((X357 @ id @ (sub @ X356 @ (push @ X363 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & (hoasinduction_lem2v2_gthm = $true) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & (axabs = $true) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((! [X366 : (subst > term > subst > $o)] : ~ ! [X367 : (term > $o)] : ~ ! [X368 : term] : (((X366 @ id @ X368 @ id)) = ((X367 @ X368))) => (! [X369 : (term > $o),X370 : term] : (~ ! [X371 : term] : ((((X369 @ (lam @ X371))) = $true) | ~ ! [X372 : term] : (~ ($true = ((X369 @ X372))) | ($true = ((X369 @ (sub @ X371 @ (push @ X372 @ id))))))) | ~ ! [X373 : term] : ((((X369 @ X373)) = $true) | ~ ($true = ((var @ X373)))) | (((X369 @ X370)) = $true) | ~ ! [X374 : term,X375 : term] : (~ ($true = ((X369 @ X374))) | ($true = ((X369 @ (ap @ X375 @ X374)))) | ~ ($true = ((X369 @ X375))))) => (! [X376 : term] : (((sub @ X376 @ id)) = X376) => (! [X377 : (subst > term > subst > $o),X378 : term,X379 : (term > $o)] : (~ ! [X380 : term] : (((X377 @ id @ X380 @ id)) = ((X379 @ X380))) | ($true = ((X379 @ (lam @ X378)))) | ~ ! [X381 : term] : (~ ($true = ((X379 @ X381))) | ($true = ((X379 @ (sub @ X378 @ (push @ X381 @ id)))))) | ~ ! [X382 : (subst > term > term)] : ((((X377 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X382 @ X385 @ X384) @ X383)) = ((X382 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383)))) | ~ ! [X386 : term] : (~ ($true = ((X377 @ id @ X386 @ id))) | ($true = ((X377 @ id @ (X382 @ id @ X386) @ id)))))) => ! [X387 : (subst > term > subst > $o),X388 : term] : (~ ! [X389 : term] : (($true = ((X387 @ id @ X389 @ id))) | ~ ($true = ((var @ (sub @ X389 @ id))))) | ~ ! [X390 : term,X391 : term] : (($true = ((X387 @ id @ (ap @ (sub @ X391 @ id) @ X390) @ id))) | ~ ($true = ((X387 @ id @ X391 @ id))) | ~ ($true = ((X387 @ id @ X390 @ id)))) | ~ ! [X392 : subst,X393 : subst,X394 : subst,X395 : term] : (($true = ((X387 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394) @ X392))) | ~ (((X387 @ X393 @ X395 @ (comp @ X394 @ X392))) = $true)) | ~ ! [X396 : subst,X397 : subst,X398 : subst,X399 : term] : ((((X387 @ X396 @ X399 @ (comp @ X398 @ X397))) = $true) | ~ (((X387 @ (comp @ X396 @ X398) @ (sub @ X399 @ X398) @ X397)) = $true)) | (((X387 @ id @ X388 @ id)) = $true) | ~ ! [X400 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X400 @ sh @ one)) @ id)) = $true) | ~ ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X401 @ X403) @ (sub @ X402 @ X403))) = ((sub @ (X400 @ X401 @ X402) @ X403))) | ~ ! [X404 : term] : ((((X387 @ id @ (X400 @ id @ X404) @ id)) = $true) | ~ ($true = ((X387 @ id @ X404 @ id)))))))))) <=> (hoasinduction_lthm_3 = $true)) & ((hoasapinj1 = $true) <=> ! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408))))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X409 : term,X410 : (subst > term > subst > $o)] : (~ ! [X411 : term] : (($true = ((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id))) | ~ (((X410 @ id @ X411 @ id)) = $true)) | ($true = ((X410 @ id @ (lam @ (sub @ X409 @ (push @ one @ sh))) @ id))) | ~ ! [X412 : (subst > term > term)] : (~ ! [X413 : term] : (~ ($true = ((X410 @ id @ X413 @ id))) | ($true = ((X410 @ id @ (X412 @ id @ X413) @ id)))) | ($true = ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) | ~ ! [X414 : term,X416 : subst,X415 : subst] : (((sub @ (X412 @ X416 @ X414) @ X415)) = ((X412 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415))))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X417 : term,X418 : (subst > term > subst > $o)] : (~ ! [X419 : term,X420 : (subst > term > term)] : (~ ! [X423 : term,X422 : subst,X421 : subst] : (((sub @ (sub @ X419 @ (push @ X423 @ X421)) @ X422)) = ((sub @ (X420 @ X421 @ X423) @ X422))) | ~ ! [X426 : subst,X425 : subst,X424 : term] : (((X420 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426))) = ((sub @ X419 @ (push @ (sub @ X424 @ X426) @ (comp @ X425 @ X426))))) | ($true = ((X418 @ id @ (lam @ (X420 @ sh @ one)) @ id))) | ~ ! [X427 : term] : (~ ($true = ((X418 @ id @ X427 @ id))) | (((X418 @ id @ (X420 @ id @ X427) @ id)) = $true))) | ~ ! [X428 : term] : (~ ($true = ((X418 @ id @ X428 @ id))) | ($true = ((X418 @ id @ (sub @ X417 @ (push @ X428 @ id)) @ id)))) | ($true = ((X418 @ id @ (lam @ (sub @ X417 @ (push @ one @ sh))) @ id))))) & ((! [X429 : term,X430 : term,X432 : term,X431 : term] : ((((ap @ X430 @ X431)) != ((ap @ X429 @ X432))) | (X431 = X432)) => ! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434))))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X437 : (subst > term > subst > $o),X438 : term] : (~ ! [X439 : subst,X440 : subst,X441 : subst,X442 : term] : (~ ($true = ((X437 @ X441 @ X442 @ (comp @ X440 @ X439)))) | ($true = ((X437 @ (comp @ X441 @ X440) @ (sub @ X442 @ X440) @ X439)))) | ~ ! [X443 : term] : (~ (((X437 @ id @ X443 @ id)) = $true) | (((X437 @ id @ (sub @ X438 @ (push @ X443 @ id)) @ id)) = $true)) | ~ ! [X444 : term,X445 : subst,X446 : subst,X447 : subst] : (~ ($true = ((X437 @ (comp @ X447 @ X445) @ (sub @ X444 @ X445) @ X446))) | ($true = ((X437 @ X447 @ X444 @ (comp @ X445 @ X446))))) | ($true = ((X437 @ id @ (lam @ X438) @ id))) | ~ ! [X448 : (subst > term > term)] : (($true = ((X437 @ id @ (lam @ (X448 @ sh @ one)) @ id))) | ~ ! [X449 : subst,X451 : term,X450 : subst] : (((sub @ (X448 @ X449 @ X451) @ X450)) = ((X448 @ (comp @ X449 @ X450) @ (sub @ X451 @ X450)))) | ~ ! [X452 : term] : (($true = ((X437 @ id @ (X448 @ id @ X452) @ id))) | ~ ($true = ((X437 @ id @ X452 @ id))))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (pushprop_lem1_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (((d2subst @ d_id)) = sh) & ((termmset_lthm = $true) <=> (! [X453 : term] : (((sub @ X453 @ id)) = X453) => ! [X454 : term] : (((sub @ X454 @ id)) = X454))) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (! [X456 : (subst > term > term),X455 : term,X457 : term] : (~ ! [X458 : subst,X459 : subst,X460 : term] : (((sub @ (X456 @ X459 @ X460) @ X458)) = ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) <=> (hoaslamnotap = $true)) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) <=> (axvarid = $true)) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) <=> (axidr = $true)) & (one = ((d2term @ d_one))) & (axvarshift = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj_lthm = $true) <=> (! [X464 : term,X463 : subst] : (((sub @ one @ (push @ X464 @ X463))) = X464) => (! [X466 : term,X465 : subst] : (((comp @ sh @ (push @ X466 @ X465))) = X465) => (! [X467 : term,X468 : term] : ((((lam @ X468)) != ((lam @ X467))) | (X467 = X468)) => ! [X470 : (subst > term > term),X471 : term,X472 : (subst > term > term),X469 : subst] : ((((X472 @ X469 @ X471)) = ((X470 @ X469 @ X471))) | (((lam @ (X470 @ sh @ one))) != ((lam @ (X472 @ sh @ one)))) | ~ ! [X476 : term,X477 : subst,X478 : subst] : (((X472 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) = ((sub @ (X472 @ X477 @ X476) @ X478))) | ~ ! [X475 : term,X473 : subst,X474 : subst] : (((X470 @ (comp @ X473 @ X474) @ (sub @ X475 @ X474))) = ((sub @ (X470 @ X473 @ X475) @ X474)))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X479 : term] : (((sub @ X479 @ id)) = X479) => ! [X480 : term,X481 : (term > $o),X482 : (subst > term > subst > $o)] : (~ ! [X483 : term] : (($true = ((X481 @ (sub @ X480 @ (push @ X483 @ id))))) | ~ (((X481 @ X483)) = $true)) | ~ ! [X484 : subst,X485 : subst,X486 : subst,X487 : term] : (~ ($true = ((X482 @ X484 @ X487 @ (comp @ X485 @ X486)))) | ($true = ((X482 @ (comp @ X484 @ X485) @ (sub @ X487 @ X485) @ X486)))) | ~ ! [X488 : term] : (((X482 @ id @ X488 @ id)) = ((X481 @ X488))) | ~ ! [X489 : subst,X490 : subst,X491 : term,X492 : subst] : ((((X482 @ X489 @ X491 @ (comp @ X492 @ X490))) = $true) | ~ (((X482 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) = $true)) | ($true = ((X481 @ (lam @ X480)))) | ~ ! [X493 : (subst > term > term)] : (~ ! [X496 : term,X495 : subst,X494 : subst] : (((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495))) = ((sub @ (X493 @ X494 @ X496) @ X495))) | ($true = ((X482 @ id @ (lam @ (X493 @ sh @ one)) @ id))) | ~ ! [X497 : term] : (~ ($true = ((X482 @ id @ X497 @ id))) | ($true = ((X482 @ id @ (X493 @ id @ X497) @ id)))))))) & (axapp = $true) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) <=> (hoasapinj2 = $true)) & (substmonoid_gthm = $true) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X502 : term] : (((sub @ X502 @ id)) = X502) => (! [X503 : term,X504 : (subst > term > subst > $o)] : (($true = ((X504 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) | ~ ! [X505 : (subst > term > term)] : (($true = ((X504 @ id @ (lam @ (X505 @ sh @ one)) @ id))) | ~ ! [X506 : term] : (~ (((X504 @ id @ X506 @ id)) = $true) | ($true = ((X504 @ id @ (X505 @ id @ X506) @ id)))) | ~ ! [X508 : subst,X509 : subst,X507 : term] : (((sub @ (X505 @ X508 @ X507) @ X509)) = ((X505 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509))))) | ~ ! [X510 : term] : (~ (((X504 @ id @ X510 @ id)) = $true) | ($true = ((X504 @ id @ (sub @ X503 @ (push @ X510 @ id)) @ id))))) => ! [X511 : term,X512 : (subst > term > subst > $o)] : (~ ! [X513 : term] : (~ ($true = ((X512 @ id @ X513 @ id))) | (((X512 @ id @ (sub @ X511 @ (push @ X513 @ id)) @ id)) = $true)) | ~ ! [X514 : (subst > term > term)] : (~ ! [X515 : term] : (~ (((X512 @ id @ X515 @ id)) = $true) | ($true = ((X512 @ id @ (X514 @ id @ X515) @ id)))) | ($true = ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X516 : term,X518 : subst,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518)))) | ($true = ((X512 @ id @ (lam @ X511) @ id))))))) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) = ((d2subst @ X520))) => (X519 = X520)) & ! [X521 : d_term] : (d_one = X521) & (pushprop_lem2v2_gthm = $true) & ((hoasinduction = $true) <=> ! [X522 : (subst > term > subst > $o),X523 : term] : (~ ! [X524 : (subst > term > term)] : (($true = ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) | ~ ! [X525 : term] : (~ ($true = ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) | ~ ! [X528 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X528)) = ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528))))) | ~ ! [X529 : subst,X530 : subst,X531 : term,X532 : subst] : (~ ($true = ((X522 @ (comp @ X532 @ X529) @ (sub @ X531 @ X529) @ X530))) | ($true = ((X522 @ X532 @ X531 @ (comp @ X529 @ X530))))) | ~ ! [X533 : term] : ((((X522 @ id @ X533 @ id)) = $true) | ~ ($true = ((var @ (sub @ X533 @ id))))) | ($true = ((X522 @ id @ X523 @ id))) | ~ ! [X534 : term,X535 : subst,X536 : subst,X537 : subst] : (~ ($true = ((X522 @ X535 @ X534 @ (comp @ X536 @ X537)))) | ($true = ((X522 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536) @ X537)))) | ~ ! [X538 : term,X539 : term] : ((((X522 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) = $true) | ~ ($true = ((X522 @ id @ X539 @ id))) | ~ ($true = ((X522 @ id @ X538 @ id))))))),
% 1.42/0.51 inference(rectify,[],[f7])).
% 1.42/0.51 thf(f10,plain,(
% 1.42/0.51 ((induction2_lthm = $true) <=> (! [X157 : term] : (((sub @ X157 @ id)) = X157) => (! [X160 : term,X159 : subst,X158 : (term > $o)] : (~ ! [X161 : term] : (~ ! [X162 : term] : ((((X158 @ (sub @ X161 @ (push @ X162 @ id)))) = $true) | ($true != ((X158 @ X162)))) | ($true = ((X158 @ (lam @ X161))))) | ~ ! [X165 : term] : (($true != ((var @ X165))) | ($true = ((X158 @ (sub @ X165 @ X159))))) | ~ ! [X164 : term,X163 : term] : ((((X158 @ (ap @ X164 @ X163))) = $true) | ($true != ((X158 @ X163))) | ($true != ((X158 @ X164)))) | ($true = ((X158 @ (sub @ X160 @ X159))))) => ! [X166 : (term > $o),X167 : term] : (~ ! [X168 : term] : (($true = ((X166 @ (lam @ X168)))) | ~ ! [X169 : term] : ((((X166 @ (sub @ X168 @ (push @ X169 @ id)))) = $true) | ($true != ((X166 @ X169))))) | ($true = ((X166 @ X167))) | ~ ! [X171 : term,X170 : term] : (($true != ((X166 @ X170))) | ($true != ((X166 @ X171))) | (((X166 @ (ap @ X171 @ X170))) = $true)) | ~ ! [X172 : term] : ((((var @ X172)) != $true) | (((X166 @ X172)) = $true)))))) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj1 = $true) <=> ! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408))))) & (axapp = $true) & (apnotvar = $true) & ((pushprop_lem0 = $true) <=> ! [X287 : term,X289 : subst,X288 : (term > $o)] : ~ ! [X290 : (term > $o)] : ~ ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289)))))) & (hoasapnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ! [X236 : d_term,X235 : d_term] : ((((d2term @ X236)) = ((d2term @ X235))) => (X235 = X236)) & (ulamvar1 != $true) & (hoasapinj2_gthm = $true) & ((hoasinduction_lem2v2 = $true) <=> ! [X55 : (term > $o),X57 : term,X56 : term,X54 : (subst > term > subst > $o)] : ((((X55 @ X57)) != $true) | ~ ! [X58 : term] : (((X55 @ X58)) = ((X54 @ id @ X58 @ id))) | ($true != ((X55 @ X56))) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ~ ! [X62 : subst,X63 : subst,X61 : subst,X64 : term] : (($true = ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) | (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) != $true)) | ~ ! [X60 : term,X59 : term] : (($true != ((X54 @ id @ X60 @ id))) | ($true = ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id))) | (((X54 @ id @ X59 @ id)) != $true)) | ~ ! [X65 : term,X68 : subst,X67 : subst,X66 : subst] : (($true != ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66))) | ($true = ((X54 @ X67 @ X65 @ (comp @ X68 @ X66))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X272 : (subst > term > subst > $o),X274 : (term > $o),X273 : term] : (~ ! [X281 : term] : (((X274 @ X281)) = ((X272 @ id @ X281 @ id))) | ~ ! [X276 : (subst > term > term)] : (~ ! [X279 : term,X280 : subst,X278 : subst] : (((sub @ (X276 @ X278 @ X279) @ X280)) = ((X276 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280)))) | ($true = ((X272 @ id @ (lam @ (X276 @ sh @ one)) @ id))) | ~ ! [X277 : term] : ((((X272 @ id @ X277 @ id)) != $true) | (((X272 @ id @ (X276 @ id @ X277) @ id)) = $true))) | ($true = ((X274 @ (lam @ X273)))) | ~ ! [X275 : term] : ((((X274 @ X275)) != $true) | ($true = ((X274 @ (sub @ X273 @ (push @ X275 @ id)))))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X502 : term] : (((sub @ X502 @ id)) = X502) => (! [X504 : (subst > term > subst > $o),X503 : term] : (($true = ((X504 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) | ~ ! [X505 : (subst > term > term)] : (~ ! [X508 : subst,X509 : subst,X507 : term] : (((sub @ (X505 @ X508 @ X507) @ X509)) = ((X505 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509)))) | ~ ! [X506 : term] : ((((X504 @ id @ X506 @ id)) != $true) | ($true = ((X504 @ id @ (X505 @ id @ X506) @ id)))) | ($true = ((X504 @ id @ (lam @ (X505 @ sh @ one)) @ id)))) | ~ ! [X510 : term] : ((((X504 @ id @ X510 @ id)) != $true) | ($true = ((X504 @ id @ (sub @ X503 @ (push @ X510 @ id)) @ id))))) => ! [X511 : term,X512 : (subst > term > subst > $o)] : (~ ! [X514 : (subst > term > term)] : (($true = ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) | ~ ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | (((X512 @ id @ X515 @ id)) != $true)) | ~ ! [X516 : term,X518 : subst,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518)))) | ~ ! [X513 : term] : (($true != ((X512 @ id @ X513 @ id))) | (((X512 @ id @ (sub @ X511 @ (push @ X513 @ id)) @ id)) = $true)) | ($true = ((X512 @ id @ (lam @ X511) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (axassoc = $true) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & (! [X226 : term] : ~ ! [X227 : (subst > term > term)] : ~ ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) <=> (hoasapinj2 = $true)) & (hoaslaminj_gthm = $true) & (! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X203 : term] : ~ ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ X203 @ (push @ one @ sh))))) & (hoaslamnotap_gthm = $true) & ((induction2 = $true) <=> ! [X247 : (term > $o),X248 : term] : (~ ! [X249 : term] : ((((var @ X249)) != $true) | (((X247 @ X249)) = $true)) | ($true = ((X247 @ X248))) | ~ ! [X252 : term,X253 : term] : (($true != ((X247 @ X253))) | ($true = ((X247 @ (ap @ X252 @ X253)))) | (((X247 @ X252)) != $true)) | ~ ! [X250 : term] : (~ ! [X251 : term] : (($true != ((X247 @ X251))) | ($true = ((X247 @ (sub @ X250 @ (push @ X251 @ id)))))) | ($true = ((X247 @ (lam @ X250))))))) & (! [X328 : term] : ~ ! [X329 : (subst > term > term)] : ~ ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X173 : (subst > term > subst > $o)] : ~ ! [X174 : (term > $o)] : ~ ! [X175 : term] : (((X174 @ X175)) = ((X173 @ id @ X175 @ id))) => (! [X176 : (term > $o),X177 : term] : (~ ! [X178 : term] : ((((X176 @ (lam @ X178))) = $true) | ~ ! [X179 : term] : (($true != ((X176 @ X179))) | ($true = ((X176 @ (sub @ X178 @ (push @ X179 @ id))))))) | ~ ! [X180 : term,X181 : term] : (($true != ((X176 @ X180))) | ($true = ((X176 @ (ap @ X180 @ X181)))) | ($true != ((X176 @ X181)))) | ~ ! [X182 : term] : (($true = ((X176 @ X182))) | ($true != ((var @ X182)))) | ($true = ((X176 @ X177)))) => (! [X183 : term] : (((sub @ X183 @ id)) = X183) => (! [X185 : term,X186 : (subst > term > subst > $o),X184 : (term > $o)] : (~ ! [X188 : term] : (($true = ((X184 @ (sub @ X185 @ (push @ X188 @ id))))) | (((X184 @ X188)) != $true)) | ~ ! [X189 : (subst > term > term)] : (~ ! [X190 : subst,X192 : term,X191 : subst] : (((X189 @ (comp @ X190 @ X191) @ (sub @ X192 @ X191))) = ((sub @ (X189 @ X190 @ X192) @ X191))) | (((X186 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true) | ~ ! [X193 : term] : (($true != ((X186 @ id @ X193 @ id))) | (((X186 @ id @ (X189 @ id @ X193) @ id)) = $true))) | ~ ! [X187 : term] : (((X186 @ id @ X187 @ id)) = ((X184 @ X187))) | (((X184 @ (lam @ X185))) = $true)) => ! [X195 : (subst > term > subst > $o),X194 : term] : (~ ! [X198 : (subst > term > term)] : (~ ! [X202 : term,X201 : subst,X200 : subst] : (((sub @ (X198 @ X200 @ X202) @ X201)) = ((X198 @ (comp @ X200 @ X201) @ (sub @ X202 @ X201)))) | ~ ! [X199 : term] : ((((X195 @ id @ (X198 @ id @ X199) @ id)) = $true) | (((X195 @ id @ X199 @ id)) != $true)) | (((X195 @ id @ (lam @ (X198 @ sh @ one)) @ id)) = $true)) | ($true = ((X195 @ id @ X194 @ id))) | ~ ! [X197 : term,X196 : term] : ((((X195 @ id @ X197 @ id)) != $true) | (((X195 @ id @ X196 @ id)) != $true) | (((X195 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) = $true)))))))) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) <=> (apinj2 = $true)) & ((! [X103 : (term > $o),X104 : term] : (~ ! [X106 : term,X105 : term] : (($true != ((X103 @ X106))) | ($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106))))) | (((X103 @ X104)) = $true) | ~ ! [X108 : term] : (~ ! [X109 : term] : (($true = ((X103 @ (sub @ X108 @ (push @ X109 @ id))))) | ($true != ((X103 @ X109)))) | ($true = ((X103 @ (lam @ X108))))) | ~ ! [X107 : term] : (($true != ((var @ X107))) | ($true = ((X103 @ X107))))) => (! [X112 : (subst > term > subst > $o),X110 : term,X111 : term] : (($true != ((X112 @ id @ X110 @ id))) | (((X112 @ id @ X111 @ id)) != $true) | ($true = ((X112 @ id @ (ap @ X110 @ X111) @ id))) | ~ ! [X119 : term,X120 : subst,X122 : subst,X121 : subst] : (($true != ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) | ~ ! [X117 : subst,X118 : subst,X116 : term,X115 : subst] : ((((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) != $true) | (((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true)) | ~ ! [X114 : term,X113 : term] : (($true != ((X112 @ id @ X113 @ id))) | (((X112 @ id @ X114 @ id)) != $true) | ($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id))))) => (! [X123 : (subst > term > subst > $o),X124 : term] : (~ ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | (((X123 @ id @ X138 @ id)) != $true)) | (((X123 @ id @ (lam @ X124) @ id)) = $true) | ~ ! [X132 : subst,X133 : subst,X131 : term,X130 : subst] : (($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133))) | ($true != ((X123 @ X130 @ X131 @ (comp @ X132 @ X133))))) | ~ ! [X125 : (subst > term > term)] : ((((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true) | ~ ! [X129 : term] : (($true != ((X123 @ id @ X129 @ id))) | ($true = ((X123 @ id @ (X125 @ id @ X129) @ id)))) | ~ ! [X126 : subst,X128 : term,X127 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) = ((sub @ (X125 @ X126 @ X128) @ X127)))) | ~ ! [X136 : subst,X134 : subst,X135 : subst,X137 : term] : (($true != ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134)))))) => ! [X139 : term,X140 : (subst > term > subst > $o)] : ((((X140 @ id @ X139 @ id)) = $true) | ~ ! [X155 : subst,X154 : term,X156 : subst,X153 : subst] : (($true != ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) | (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) = $true)) | ~ ! [X152 : term,X151 : subst,X149 : subst,X150 : subst] : (($true = ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) | (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) != $true)) | ~ ! [X143 : term] : ((((var @ (sub @ X143 @ id))) != $true) | ($true = ((X140 @ id @ X143 @ id)))) | ~ ! [X144 : (subst > term > term)] : (~ ! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) | ~ ! [X148 : term] : (($true = ((X140 @ id @ (X144 @ id @ X148) @ id))) | (((X140 @ id @ X148 @ id)) != $true)) | ($true = ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id)))) | ~ ! [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) = $true) | ($true != ((X140 @ id @ X141 @ id))) | ($true != ((X140 @ id @ X142 @ id)))))))) <=> (hoasinduction_lthm = $true)) & (pushprop_lthm_orig = $true) & ((hoasinduction = $true) <=> ! [X522 : (subst > term > subst > $o),X523 : term] : (($true = ((X522 @ id @ X523 @ id))) | ~ ! [X538 : term,X539 : term] : ((((X522 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) = $true) | ($true != ((X522 @ id @ X538 @ id))) | ($true != ((X522 @ id @ X539 @ id)))) | ~ ! [X533 : term] : ((((X522 @ id @ X533 @ id)) = $true) | ($true != ((var @ (sub @ X533 @ id))))) | ~ ! [X532 : subst,X531 : term,X529 : subst,X530 : subst] : (($true = ((X522 @ X532 @ X531 @ (comp @ X529 @ X530)))) | ($true != ((X522 @ (comp @ X532 @ X529) @ (sub @ X531 @ X529) @ X530)))) | ~ ! [X524 : (subst > term > term)] : (($true = ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) | ~ ! [X525 : term] : (($true != ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) | ~ ! [X528 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X528)) = ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528))))) | ~ ! [X536 : subst,X537 : subst,X534 : term,X535 : subst] : (($true != ((X522 @ X535 @ X534 @ (comp @ X536 @ X537)))) | ($true = ((X522 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536) @ X537)))))) & (lamnotap != $true) & (axvarshift = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ~ ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X417 : term,X418 : (subst > term > subst > $o)] : (~ ! [X420 : (subst > term > term),X419 : term] : (($true = ((X418 @ id @ (lam @ (X420 @ sh @ one)) @ id))) | ~ ! [X426 : subst,X425 : subst,X424 : term] : (((X420 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426))) = ((sub @ X419 @ (push @ (sub @ X424 @ X426) @ (comp @ X425 @ X426))))) | ~ ! [X427 : term] : (($true != ((X418 @ id @ X427 @ id))) | (((X418 @ id @ (X420 @ id @ X427) @ id)) = $true)) | ~ ! [X423 : term,X422 : subst,X421 : subst] : (((sub @ (sub @ X419 @ (push @ X423 @ X421)) @ X422)) = ((sub @ (X420 @ X421 @ X423) @ X422)))) | ~ ! [X428 : term] : (($true != ((X418 @ id @ X428 @ id))) | ($true = ((X418 @ id @ (sub @ X417 @ (push @ X428 @ id)) @ id)))) | ($true = ((X418 @ id @ (lam @ (sub @ X417 @ (push @ one @ sh))) @ id))))) & (hoasinduction_lem1_lthm = $true) & ((! [X429 : term,X430 : term,X432 : term,X431 : term] : ((((ap @ X430 @ X431)) != ((ap @ X429 @ X432))) | (X431 = X432)) => ! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434))))) <=> (hoasapinj2_lthm = $true)) & ((! [X20 : term] : (((sub @ X20 @ id)) = X20) => (! [X21 : term,X22 : (subst > term > subst > $o)] : (~ ! [X23 : term] : (($true != ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) | ~ ! [X24 : (subst > term > term)] : (~ ! [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) = ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ~ ! [X28 : term] : (($true != ((X22 @ id @ X28 @ id))) | (((X22 @ id @ (X24 @ id @ X28) @ id)) = $true)) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)) | (((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) = $true)) => ! [X30 : (subst > term > subst > $o),X29 : term] : (~ ! [X35 : (subst > term > term)] : (~ ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ($true != ((X30 @ id @ X36 @ id)))) | (((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) = $true) | ~ ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38))))) | ~ ! [X43 : term,X41 : subst,X44 : subst,X42 : subst] : (($true != ((X30 @ X42 @ X43 @ (comp @ X44 @ X41)))) | ($true = ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41)))) | ~ ! [X40 : term] : ((((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) = $true) | ($true != ((X30 @ id @ X40 @ id)))) | (((X30 @ id @ (lam @ X29) @ id)) = $true) | ~ ! [X34 : subst,X33 : subst,X31 : term,X32 : subst] : ((((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) = $true) | ($true != ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X256 : (term > $o),X254 : (subst > term > subst > $o),X255 : term] : (~ ! [X262 : subst,X265 : subst,X263 : subst,X264 : term] : ((((X254 @ X265 @ X264 @ (comp @ X262 @ X263))) = $true) | ($true != ((X254 @ (comp @ X265 @ X262) @ (sub @ X264 @ X262) @ X263)))) | ~ ! [X266 : term] : (($true != ((X256 @ X266))) | (((X256 @ (sub @ X255 @ (push @ X266 @ id)))) = $true)) | (((X256 @ (lam @ X255))) = $true) | ~ ! [X267 : (subst > term > term)] : (~ ! [X268 : term] : (($true = ((X254 @ id @ (X267 @ id @ X268) @ id))) | ($true != ((X254 @ id @ X268 @ id)))) | (((X254 @ id @ (lam @ (X267 @ sh @ one)) @ id)) = $true) | ~ ! [X270 : subst,X271 : subst,X269 : term] : (((X267 @ (comp @ X271 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X271 @ X269) @ X270)))) | ~ ! [X257 : subst,X259 : subst,X260 : subst,X258 : term] : (($true != ((X254 @ X257 @ X258 @ (comp @ X259 @ X260)))) | ($true = ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259) @ X260)))) | ~ ! [X261 : term] : (((X254 @ id @ X261 @ id)) = ((X256 @ X261)))) <=> (hoasinduction_lem3v2 = $true)) & (hoasapnotvar_lthm = $true) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X285 : subst,X282 : term,X284 : (term > $o),X283 : (term > $o)] : ((((X284 @ one)) = $true) | ($true != ((X283 @ X282))) | ~ ! [X286 : term] : (((X284 @ X286)) = ((X283 @ (sub @ X286 @ (push @ X282 @ X285)))))) <=> (pushprop_lem1v2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2_gthm = $true) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) = ((d2subst @ X520))) => (X519 = X520)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X351 : (subst > term > subst > $o)] : ~ ! [X352 : (term > $o)] : ~ ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id)))) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & ((induction2lem_lthm = $true) <=> (! [X332 : term,X333 : subst] : (((sub @ one @ (push @ X332 @ X333))) = X332) => (! [X334 : term,X335 : subst] : (((comp @ sh @ (push @ X334 @ X335))) = X335) => (! [X336 : subst] : (((comp @ X336 @ id)) = X336) => (! [X337 : term,X338 : (term > $o)] : (~ ! [X340 : term,X339 : term] : ((((X338 @ X339)) != $true) | ($true = ((X338 @ (ap @ X340 @ X339)))) | ($true != ((X338 @ X340)))) | ($true = ((X338 @ X337))) | ~ ! [X342 : term] : (($true != ((var @ X342))) | ($true = ((X338 @ X342)))) | ~ ! [X341 : term] : ((((X338 @ X341)) != $true) | (((X338 @ (lam @ X341))) = $true))) => ! [X343 : (term > $o),X344 : term,X345 : subst] : (~ ! [X350 : term] : (($true = ((X343 @ (sub @ X350 @ X345)))) | ($true != ((var @ X350)))) | ($true = ((X343 @ (sub @ X344 @ X345)))) | ~ ! [X348 : term] : (($true = ((X343 @ (lam @ X348)))) | ~ ! [X349 : term] : (($true = ((X343 @ (sub @ X348 @ (push @ X349 @ id))))) | ($true != ((X343 @ X349))))) | ~ ! [X346 : term,X347 : term] : (($true != ((X343 @ X346))) | ($true != ((X343 @ X347))) | (((X343 @ (ap @ X347 @ X346))) = $true)))))))) & (! [X241 : (term > $o),X240 : subst,X239 : term] : (~ ! [X243 : term] : (($true = ((X241 @ (lam @ X243)))) | ~ ! [X244 : term] : (($true != ((X241 @ X244))) | ($true = ((X241 @ (sub @ X243 @ (push @ X244 @ id))))))) | ~ ! [X246 : term,X245 : term] : (($true != ((X241 @ X245))) | ($true != ((X241 @ X246))) | (((X241 @ (ap @ X245 @ X246))) = $true)) | ~ ! [X242 : term] : (($true != ((var @ X242))) | ($true = ((X241 @ (sub @ X242 @ X240))))) | ($true = ((X241 @ (sub @ X239 @ X240))))) <=> (induction2lem = $true)) & (! [X357 : (subst > term > subst > $o),X356 : term] : (~ ! [X358 : (subst > term > term)] : (~ ! [X362 : term] : (($true != ((X357 @ id @ X362 @ id))) | ($true = ((X357 @ id @ (X358 @ id @ X362) @ id)))) | ~ ! [X361 : subst,X359 : subst,X360 : term] : (((X358 @ (comp @ X361 @ X359) @ (sub @ X360 @ X359))) = ((sub @ (X358 @ X361 @ X360) @ X359))) | (((X357 @ id @ (lam @ (X358 @ sh @ one)) @ id)) = $true)) | ($true = ((X357 @ id @ (lam @ (sub @ X356 @ (push @ one @ sh))) @ id))) | ~ ! [X363 : term] : ((((X357 @ id @ X363 @ id)) != $true) | ($true = ((X357 @ id @ (sub @ X356 @ (push @ X363 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $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_lem2 = $true) <=> ! [X211 : term,X213 : term,X212 : (subst > term > subst > $o)] : (($true = ((X212 @ id @ (ap @ X213 @ X211) @ id))) | ($true != ((X212 @ id @ X213 @ id))) | ~ ! [X223 : term,X222 : term] : (($true != ((X212 @ id @ X222 @ id))) | (((X212 @ id @ (ap @ (sub @ X223 @ id) @ X222) @ id)) = $true) | ($true != ((X212 @ id @ X223 @ id)))) | ($true != ((X212 @ id @ X211 @ id))) | ~ ! [X221 : term,X220 : subst,X219 : subst,X218 : subst] : (($true = ((X212 @ (comp @ X220 @ X219) @ (sub @ X221 @ X219) @ X218))) | ($true != ((X212 @ X220 @ X221 @ (comp @ X219 @ X218))))) | ~ ! [X215 : subst,X217 : subst,X216 : term,X214 : subst] : (($true = ((X212 @ X215 @ X216 @ (comp @ X214 @ X217)))) | (((X212 @ (comp @ X215 @ X214) @ (sub @ X216 @ X214) @ X217)) != $true)))) & (pushprop_lem2v2_lthm = $true) & (ulamvarind = $true) & ((hoaslaminj = $true) <=> ! [X318 : (subst > term > term),X319 : subst,X320 : (subst > term > term),X317 : term] : (~ ! [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) = ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ~ ! [X322 : subst,X321 : term,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) = ((sub @ (X320 @ X323 @ X321) @ X322))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))))) & ((! [X5 : term] : ~ ! [X6 : (subst > term > term)] : ~ ! [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) = ((X6 @ X8 @ X7))) => (! [X9 : term] : (((sub @ X9 @ id)) = X9) => ! [X10 : term,X12 : (term > $o),X11 : (subst > term > subst > $o)] : (($true = ((X12 @ (lam @ X10)))) | ~ ! [X15 : (subst > term > term)] : (~ ! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | (((X11 @ id @ X16 @ id)) != $true)) | ($true = ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ~ ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18)))) | ~ ! [X13 : term] : (((X11 @ id @ X13 @ id)) = ((X12 @ X13))) | ~ ! [X14 : term] : ((((X12 @ X14)) != $true) | (((X12 @ (sub @ X10 @ (push @ X14 @ id)))) = $true))))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X456 : (subst > term > term),X455 : term,X457 : term] : (~ ! [X458 : subst,X459 : subst,X460 : term] : (((sub @ (X456 @ X459 @ X460) @ X458)) = ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) <=> (hoaslamnotap = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X45 : term] : (((sub @ X45 @ id)) = X45) => (! [X49 : term,X47 : term,X48 : term,X46 : term] : ((((ap @ X47 @ X48)) != ((ap @ X46 @ X49))) | (X46 = X47)) => ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))))) & ((axscons = $true) <=> ! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306)) & (! [X294 : (subst > term > subst > $o),X293 : term] : (~ ! [X297 : (subst > term > term)] : (($true = ((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id))) | ~ ! [X298 : term] : ((((X294 @ id @ (X297 @ id @ X298) @ id)) = $true) | ($true != ((X294 @ id @ X298 @ id)))) | ~ ! [X300 : term,X301 : subst,X299 : subst] : (((sub @ (X297 @ X301 @ X300) @ X299)) = ((X297 @ (comp @ X301 @ X299) @ (sub @ X300 @ X299))))) | ~ ! [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) = $true) | (((X294 @ id @ X295 @ id)) != $true) | ($true != ((X294 @ id @ X296 @ id)))) | ($true = ((X294 @ id @ X293 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X366 : (subst > term > subst > $o)] : ~ ! [X367 : (term > $o)] : ~ ! [X368 : term] : (((X366 @ id @ X368 @ id)) = ((X367 @ X368))) => (! [X369 : (term > $o),X370 : term] : (~ ! [X371 : term] : (~ ! [X372 : term] : (($true != ((X369 @ X372))) | ($true = ((X369 @ (sub @ X371 @ (push @ X372 @ id)))))) | (((X369 @ (lam @ X371))) = $true)) | ~ ! [X375 : term,X374 : term] : (($true = ((X369 @ (ap @ X375 @ X374)))) | ($true != ((X369 @ X374))) | ($true != ((X369 @ X375)))) | ~ ! [X373 : term] : (($true != ((var @ X373))) | (((X369 @ X373)) = $true)) | (((X369 @ X370)) = $true)) => (! [X376 : term] : (((sub @ X376 @ id)) = X376) => (! [X378 : term,X379 : (term > $o),X377 : (subst > term > subst > $o)] : (($true = ((X379 @ (lam @ X378)))) | ~ ! [X382 : (subst > term > term)] : ((((X377 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ~ ! [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X382 @ X385 @ X384) @ X383)) = ((X382 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383)))) | ~ ! [X386 : term] : (($true != ((X377 @ id @ X386 @ id))) | ($true = ((X377 @ id @ (X382 @ id @ X386) @ id))))) | ~ ! [X381 : term] : (($true = ((X379 @ (sub @ X378 @ (push @ X381 @ id))))) | ($true != ((X379 @ X381)))) | ~ ! [X380 : term] : (((X377 @ id @ X380 @ id)) = ((X379 @ X380)))) => ! [X388 : term,X387 : (subst > term > subst > $o)] : (~ ! [X389 : term] : (($true != ((var @ (sub @ X389 @ id)))) | ($true = ((X387 @ id @ X389 @ id)))) | ~ ! [X398 : subst,X396 : subst,X397 : subst,X399 : term] : ((((X387 @ (comp @ X396 @ X398) @ (sub @ X399 @ X398) @ X397)) != $true) | (((X387 @ X396 @ X399 @ (comp @ X398 @ X397))) = $true)) | ~ ! [X395 : term,X392 : subst,X394 : subst,X393 : subst] : ((((X387 @ X393 @ X395 @ (comp @ X394 @ X392))) != $true) | ($true = ((X387 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394) @ X392)))) | ~ ! [X391 : term,X390 : term] : (($true != ((X387 @ id @ X390 @ id))) | ($true != ((X387 @ id @ X391 @ id))) | ($true = ((X387 @ id @ (ap @ (sub @ X391 @ id) @ X390) @ id)))) | ~ ! [X400 : (subst > term > term)] : (~ ! [X404 : term] : ((((X387 @ id @ (X400 @ id @ X404) @ id)) = $true) | ($true != ((X387 @ id @ X404 @ id)))) | (((X387 @ id @ (lam @ (X400 @ sh @ one)) @ id)) = $true) | ~ ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X401 @ X403) @ (sub @ X402 @ X403))) = ((sub @ (X400 @ X401 @ X402) @ X403)))) | (((X387 @ id @ X388 @ id)) = $true)))))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotvar_lthm = $true) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237))))) & (((d2subst @ d_id)) = id) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lthm = $true) & (lamnotvar = $true) & ((axshiftcons = $true) <=> ! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axabs = $true) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) <=> (axvarid = $true)) & ((hoasinduction_lem0_lthm = $true) <=> ! [X230 : (subst > term > subst > $o)] : ~ ! [X231 : (term > $o)] : ~ ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232)))) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X437 : (subst > term > subst > $o),X438 : term] : (~ ! [X448 : (subst > term > term)] : (($true = ((X437 @ id @ (lam @ (X448 @ sh @ one)) @ id))) | ~ ! [X449 : subst,X451 : term,X450 : subst] : (((sub @ (X448 @ X449 @ X451) @ X450)) = ((X448 @ (comp @ X449 @ X450) @ (sub @ X451 @ X450)))) | ~ ! [X452 : term] : (($true = ((X437 @ id @ (X448 @ id @ X452) @ id))) | ($true != ((X437 @ id @ X452 @ id))))) | ~ ! [X447 : subst,X444 : term,X446 : subst,X445 : subst] : (($true != ((X437 @ (comp @ X447 @ X445) @ (sub @ X444 @ X445) @ X446))) | ($true = ((X437 @ X447 @ X444 @ (comp @ X445 @ X446))))) | ($true = ((X437 @ id @ (lam @ X438) @ id))) | ~ ! [X443 : term] : ((((X437 @ id @ X443 @ id)) != $true) | (((X437 @ id @ (sub @ X438 @ (push @ X443 @ id)) @ id)) = $true)) | ~ ! [X441 : subst,X439 : subst,X442 : term,X440 : subst] : (($true != ((X437 @ X441 @ X442 @ (comp @ X440 @ X439)))) | ($true = ((X437 @ (comp @ X441 @ X440) @ (sub @ X442 @ X440) @ X439)))))) & ((pushprop_lem1_lthm = $true) <=> (! [X91 : term,X90 : subst] : (((sub @ one @ (push @ X91 @ X90))) = X91) => (! [X93 : term,X92 : subst] : (((comp @ sh @ (push @ X93 @ X92))) = X92) => ! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95))))))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) <=> (axidr = $true)) & (! [X313 : (term > $o),X312 : subst,X314 : term] : ~ ! [X315 : (term > $o)] : ~ ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem3v2 = $true) & ! [X292 : d_subst] : (d_id = X292) & (axclos = $true) & ((hoaslaminj_lthm = $true) <=> (! [X464 : term,X463 : subst] : (((sub @ one @ (push @ X464 @ X463))) = X464) => (! [X466 : term,X465 : subst] : (((comp @ sh @ (push @ X466 @ X465))) = X465) => (! [X467 : term,X468 : term] : ((((lam @ X468)) != ((lam @ X467))) | (X467 = X468)) => ! [X470 : (subst > term > term),X471 : term,X472 : (subst > term > term),X469 : subst] : ((((X472 @ X469 @ X471)) = ((X470 @ X469 @ X471))) | (((lam @ (X470 @ sh @ one))) != ((lam @ (X472 @ sh @ one)))) | ~ ! [X476 : term,X477 : subst,X478 : subst] : (((X472 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) = ((sub @ (X472 @ X477 @ X476) @ X478))) | ~ ! [X475 : term,X473 : subst,X474 : subst] : (((X470 @ (comp @ X473 @ X474) @ (sub @ X475 @ X474))) = ((sub @ (X470 @ X473 @ X475) @ X474)))))))) & ((axidl = $true) <=> ! [X327 : subst] : (((comp @ id @ X327)) = X327)) & ((! [X1 : subst] : (((comp @ id @ X1)) = X1) => (! [X2 : subst] : (((comp @ X2 @ id)) = X2) => (! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)))) <=> (substmonoid_lthm = $true)) & (hoasapinj1_gthm = $true) & ((termmset_lthm = $true) <=> (! [X453 : term] : (((sub @ X453 @ id)) = X453) => ! [X454 : term] : (((sub @ X454 @ id)) = X454))) & (! [X205 : (term > $o),X206 : term] : (~ ! [X210 : term] : ((((X205 @ (lam @ X210))) = $true) | ($true != ((X205 @ X210)))) | ~ ! [X209 : term,X208 : term] : (($true != ((X205 @ X208))) | ($true = ((X205 @ (ap @ X209 @ X208)))) | ($true != ((X205 @ X209)))) | ~ ! [X207 : term] : (($true = ((X205 @ X207))) | (((var @ X207)) != $true)) | (((X205 @ X206)) = $true)) <=> (induction = $true)) & (pushprop = $true) & ! [X521 : d_term] : (d_one = X521) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (! [X83 : subst,X84 : term] : (((sub @ one @ (push @ X84 @ X83))) = X84) => ! [X87 : (term > $o),X88 : (term > $o),X86 : subst,X85 : term] : (($true != ((X88 @ X85))) | ~ ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true = ((X87 @ one)))))) & (((d2subst @ d_id)) = sh) & (hoaslamnotvar_gthm = $true) & (axmap = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X409 : term,X410 : (subst > term > subst > $o)] : (~ ! [X412 : (subst > term > term)] : (~ ! [X413 : term] : (($true = ((X410 @ id @ (X412 @ id @ X413) @ id))) | ($true != ((X410 @ id @ X413 @ id)))) | ~ ! [X414 : term,X416 : subst,X415 : subst] : (((sub @ (X412 @ X416 @ X414) @ X415)) = ((X412 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415)))) | ($true = ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id)))) | ($true = ((X410 @ id @ (lam @ (sub @ X409 @ (push @ one @ sh))) @ id))) | ~ ! [X411 : term] : ((((X410 @ id @ X411 @ id)) != $true) | ($true = ((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2 = $true) & ((! [X479 : term] : (((sub @ X479 @ id)) = X479) => ! [X480 : term,X482 : (subst > term > subst > $o),X481 : (term > $o)] : (~ ! [X488 : term] : (((X482 @ id @ X488 @ id)) = ((X481 @ X488))) | ~ ! [X483 : term] : (($true = ((X481 @ (sub @ X480 @ (push @ X483 @ id))))) | (((X481 @ X483)) != $true)) | ~ ! [X493 : (subst > term > term)] : (($true = ((X482 @ id @ (lam @ (X493 @ sh @ one)) @ id))) | ~ ! [X496 : term,X495 : subst,X494 : subst] : (((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495))) = ((sub @ (X493 @ X494 @ X496) @ X495))) | ~ ! [X497 : term] : (($true != ((X482 @ id @ X497 @ id))) | ($true = ((X482 @ id @ (X493 @ id @ X497) @ id))))) | ($true = ((X481 @ (lam @ X480)))) | ~ ! [X491 : term,X490 : subst,X492 : subst,X489 : subst] : ((((X482 @ X489 @ X491 @ (comp @ X492 @ X490))) = $true) | (((X482 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) != $true)) | ~ ! [X484 : subst,X486 : subst,X485 : subst,X487 : term] : (($true != ((X482 @ X484 @ X487 @ (comp @ X485 @ X486)))) | ($true = ((X482 @ (comp @ X484 @ X485) @ (sub @ X487 @ X485) @ X486)))))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X75 : (subst > term > subst > $o),X76 : term] : (~ ! [X77 : term] : (($true != ((X75 @ id @ X77 @ id))) | (((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) = $true)) | ~ ! [X78 : (subst > term > term)] : ((((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) = $true) | ~ ! [X79 : term] : (($true = ((X75 @ id @ (X78 @ id @ X79) @ id))) | ($true != ((X75 @ id @ X79 @ id)))) | ~ ! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80)))) | ($true = ((X75 @ id @ (lam @ X76) @ id))))) & ((axvarcons = $true) <=> ! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224))),
% 1.42/0.51 inference(flattening,[],[f9])).
% 1.42/0.51 thf(f11,plain,(
% 1.42/0.51 ((induction2_lthm = $true) <=> ((! [X166 : (term > $o),X167 : term] : (? [X168 : term] : (! [X169 : term] : ((((X166 @ (sub @ X168 @ (push @ X169 @ id)))) = $true) | ($true != ((X166 @ X169)))) & ($true != ((X166 @ (lam @ X168))))) | ? [X172 : term] : ((((X166 @ X172)) != $true) & (((var @ X172)) = $true)) | ($true = ((X166 @ X167))) | ? [X170 : term,X171 : term] : (($true = ((X166 @ X170))) & (((X166 @ (ap @ X171 @ X170))) != $true) & ($true = ((X166 @ X171))))) | ? [X160 : term,X159 : subst,X158 : (term > $o)] : (($true != ((X158 @ (sub @ X160 @ X159)))) & ! [X164 : term,X163 : term] : ((((X158 @ (ap @ X164 @ X163))) = $true) | ($true != ((X158 @ X163))) | ($true != ((X158 @ X164)))) & ! [X165 : term] : (($true != ((var @ X165))) | ($true = ((X158 @ (sub @ X165 @ X159))))) & ! [X161 : term] : (($true = ((X158 @ (lam @ X161)))) | ? [X162 : term] : (($true = ((X158 @ X162))) & (((X158 @ (sub @ X161 @ (push @ X162 @ id)))) != $true))))) | ? [X157 : term] : (((sub @ X157 @ id)) != X157))) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj1 = $true) <=> ! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408))))) & (axapp = $true) & (apnotvar = $true) & (! [X288 : (term > $o),X289 : subst,X287 : term] : ? [X290 : (term > $o)] : ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))) <=> (pushprop_lem0 = $true)) & (hoasapnotvar = $true) & (hoasinduction_lem3v2_gthm = $true) & ! [X235 : d_term,X236 : d_term] : ((((d2term @ X236)) != ((d2term @ X235))) | (X235 = X236)) & (ulamvar1 != $true) & (hoasapinj2_gthm = $true) & (! [X57 : term,X56 : term,X54 : (subst > term > subst > $o),X55 : (term > $o)] : (($true != ((X55 @ X56))) | ? [X58 : term] : (((X55 @ X58)) != ((X54 @ id @ X58 @ id))) | ? [X63 : subst,X62 : subst,X61 : subst,X64 : term] : (($true != ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) & (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) = $true)) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ? [X68 : subst,X67 : subst,X66 : subst,X65 : term] : (($true != ((X54 @ X67 @ X65 @ (comp @ X68 @ X66)))) & ($true = ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66)))) | ? [X60 : term,X59 : term] : (($true = ((X54 @ id @ X60 @ id))) & ($true != ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id))) & (((X54 @ id @ X59 @ id)) = $true)) | (((X55 @ X57)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X274 : (term > $o),X273 : term,X272 : (subst > term > subst > $o)] : (($true = ((X274 @ (lam @ X273)))) | ? [X275 : term] : (($true != ((X274 @ (sub @ X273 @ (push @ X275 @ id))))) & (((X274 @ X275)) = $true)) | ? [X276 : (subst > term > term)] : (! [X277 : term] : ((((X272 @ id @ X277 @ id)) != $true) | (((X272 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X279 : term,X280 : subst,X278 : subst] : (((sub @ (X276 @ X278 @ X279) @ X280)) = ((X276 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280)))) & ($true != ((X272 @ id @ (lam @ (X276 @ sh @ one)) @ id)))) | ? [X281 : term] : (((X274 @ X281)) != ((X272 @ id @ X281 @ id))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((! [X511 : term,X512 : (subst > term > subst > $o)] : (? [X513 : term] : ((((X512 @ id @ (sub @ X511 @ (push @ X513 @ id)) @ id)) != $true) & ($true = ((X512 @ id @ X513 @ id)))) | ? [X514 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) & ! [X516 : term,X518 : subst,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | (((X512 @ id @ X515 @ id)) != $true))) | ($true = ((X512 @ id @ (lam @ X511) @ id)))) | ? [X504 : (subst > term > subst > $o),X503 : term] : (($true != ((X504 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) & ! [X505 : (subst > term > term)] : (? [X506 : term] : (($true != ((X504 @ id @ (X505 @ id @ X506) @ id))) & (((X504 @ id @ X506 @ id)) = $true)) | ? [X507 : term,X508 : subst,X509 : subst] : (((sub @ (X505 @ X508 @ X507) @ X509)) != ((X505 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509)))) | ($true = ((X504 @ id @ (lam @ (X505 @ sh @ one)) @ id)))) & ! [X510 : term] : ((((X504 @ id @ X510 @ id)) != $true) | ($true = ((X504 @ id @ (sub @ X503 @ (push @ X510 @ id)) @ id)))))) | ? [X502 : term] : (((sub @ X502 @ id)) != X502)) <=> (hoasinduction_lem3a_lthm = $true)) & (axassoc = $true) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X226 : term] : ? [X227 : (subst > term > term)] : ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229)))) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) <=> (hoasapinj2 = $true)) & (hoaslaminj_gthm = $true) & (! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) <=> (pushprop_lem1 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((X204 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh))))) & (hoaslamnotap_gthm = $true) & (! [X247 : (term > $o),X248 : term] : (? [X250 : term] : (! [X251 : term] : (($true != ((X247 @ X251))) | ($true = ((X247 @ (sub @ X250 @ (push @ X251 @ id)))))) & ($true != ((X247 @ (lam @ X250))))) | ? [X249 : term] : ((((X247 @ X249)) != $true) & (((var @ X249)) = $true)) | ? [X253 : term,X252 : term] : ((((X247 @ X252)) = $true) & ($true != ((X247 @ (ap @ X252 @ X253)))) & ($true = ((X247 @ X253)))) | ($true = ((X247 @ X248)))) <=> (induction2 = $true)) & (! [X328 : term] : ? [X329 : (subst > term > term)] : ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (hoasinduction_lem2_lthm = $true) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X195 : (subst > term > subst > $o),X194 : term] : (? [X198 : (subst > term > term)] : (! [X199 : term] : ((((X195 @ id @ (X198 @ id @ X199) @ id)) = $true) | (((X195 @ id @ X199 @ id)) != $true)) & ! [X202 : term,X201 : subst,X200 : subst] : (((sub @ (X198 @ X200 @ X202) @ X201)) = ((X198 @ (comp @ X200 @ X201) @ (sub @ X202 @ X201)))) & (((X195 @ id @ (lam @ (X198 @ sh @ one)) @ id)) != $true)) | ? [X197 : term,X196 : term] : ((((X195 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) != $true) & (((X195 @ id @ X197 @ id)) = $true) & (((X195 @ id @ X196 @ id)) = $true)) | ($true = ((X195 @ id @ X194 @ id)))) | ? [X184 : (term > $o),X185 : term,X186 : (subst > term > subst > $o)] : ((((X184 @ (lam @ X185))) != $true) & ! [X188 : term] : (($true = ((X184 @ (sub @ X185 @ (push @ X188 @ id))))) | (((X184 @ X188)) != $true)) & ! [X189 : (subst > term > term)] : (? [X190 : subst,X192 : term,X191 : subst] : (((X189 @ (comp @ X190 @ X191) @ (sub @ X192 @ X191))) != ((sub @ (X189 @ X190 @ X192) @ X191))) | ? [X193 : term] : ((((X186 @ id @ (X189 @ id @ X193) @ id)) != $true) & ($true = ((X186 @ id @ X193 @ id)))) | (((X186 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true)) & ! [X187 : term] : (((X186 @ id @ X187 @ id)) = ((X184 @ X187))))) | ? [X183 : term] : (((sub @ X183 @ id)) != X183)) | ? [X177 : term,X176 : (term > $o)] : (! [X180 : term,X181 : term] : (($true != ((X176 @ X180))) | ($true = ((X176 @ (ap @ X180 @ X181)))) | ($true != ((X176 @ X181)))) & ! [X178 : term] : ((((X176 @ (lam @ X178))) = $true) | ? [X179 : term] : (($true = ((X176 @ X179))) & ($true != ((X176 @ (sub @ X178 @ (push @ X179 @ id))))))) & ! [X182 : term] : (($true = ((X176 @ X182))) | ($true != ((var @ X182)))) & ($true != ((X176 @ X177))))) | ? [X173 : (subst > term > subst > $o)] : ! [X174 : (term > $o)] : ? [X175 : term] : (((X174 @ X175)) != ((X173 @ id @ X175 @ id))))) & (hoasinduction_lem1 = $true) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) <=> (apinj2 = $true)) & ((((! [X139 : term,X140 : (subst > term > subst > $o)] : (? [X143 : term] : (($true != ((X140 @ id @ X143 @ id))) & (((var @ (sub @ X143 @ id))) = $true)) | ? [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) != $true) & ($true = ((X140 @ id @ X141 @ id))) & ($true = ((X140 @ id @ X142 @ id)))) | (((X140 @ id @ X139 @ id)) = $true) | ? [X144 : (subst > term > term)] : (! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) & ! [X148 : term] : (($true = ((X140 @ id @ (X144 @ id @ X148) @ id))) | (((X140 @ id @ X148 @ id)) != $true)) & ($true != ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id)))) | ? [X150 : subst,X152 : term,X149 : subst,X151 : subst] : (($true != ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) & (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) = $true)) | ? [X154 : term,X156 : subst,X155 : subst,X153 : subst] : (($true = ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) & (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) != $true))) | ? [X123 : (subst > term > subst > $o),X124 : term] : (! [X136 : subst,X134 : subst,X135 : subst,X137 : term] : (($true != ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134))))) & ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | (((X123 @ id @ X138 @ id)) != $true)) & (((X123 @ id @ (lam @ X124) @ id)) != $true) & ! [X125 : (subst > term > term)] : (? [X128 : term,X127 : subst,X126 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) != ((sub @ (X125 @ X126 @ X128) @ X127))) | ? [X129 : term] : (($true = ((X123 @ id @ X129 @ id))) & ($true != ((X123 @ id @ (X125 @ id @ X129) @ id)))) | (((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true)) & ! [X132 : subst,X133 : subst,X131 : term,X130 : subst] : (($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133))) | ($true != ((X123 @ X130 @ X131 @ (comp @ X132 @ X133))))))) | ? [X112 : (subst > term > subst > $o),X111 : term,X110 : term] : (($true = ((X112 @ id @ X110 @ id))) & ! [X119 : term,X120 : subst,X122 : subst,X121 : subst] : (($true != ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) & ($true != ((X112 @ id @ (ap @ X110 @ X111) @ id))) & ! [X114 : term,X113 : term] : (($true != ((X112 @ id @ X113 @ id))) | (((X112 @ id @ X114 @ id)) != $true) | ($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id)))) & ! [X117 : subst,X118 : subst,X116 : term,X115 : subst] : ((((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) != $true) | (((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true)) & (((X112 @ id @ X111 @ id)) = $true))) | ? [X104 : term,X103 : (term > $o)] : (! [X106 : term,X105 : term] : (($true != ((X103 @ X106))) | ($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106))))) & ! [X107 : term] : (($true != ((var @ X107))) | ($true = ((X103 @ X107)))) & ! [X108 : term] : (? [X109 : term] : (($true != ((X103 @ (sub @ X108 @ (push @ X109 @ id))))) & ($true = ((X103 @ X109)))) | ($true = ((X103 @ (lam @ X108))))) & (((X103 @ X104)) != $true))) <=> (hoasinduction_lthm = $true)) & (pushprop_lthm_orig = $true) & (! [X523 : term,X522 : (subst > term > subst > $o)] : (? [X533 : term] : (($true = ((var @ (sub @ X533 @ id)))) & (((X522 @ id @ X533 @ id)) != $true)) | ? [X535 : subst,X537 : subst,X534 : term,X536 : subst] : (($true = ((X522 @ X535 @ X534 @ (comp @ X536 @ X537)))) & ($true != ((X522 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536) @ X537)))) | ? [X539 : term,X538 : term] : ((((X522 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true) & ($true = ((X522 @ id @ X539 @ id))) & ($true = ((X522 @ id @ X538 @ id)))) | ? [X529 : subst,X530 : subst,X532 : subst,X531 : term] : (($true != ((X522 @ X532 @ X531 @ (comp @ X529 @ X530)))) & ($true = ((X522 @ (comp @ X532 @ X529) @ (sub @ X531 @ X529) @ X530)))) | ($true = ((X522 @ id @ X523 @ id))) | ? [X524 : (subst > term > term)] : (($true != ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) & ! [X525 : term] : (($true != ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) & ! [X528 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X528)) = ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)))))) <=> (hoasinduction = $true)) & (lamnotap != $true) & (axvarshift = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ? [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) = ((X102 @ sh @ one)))) & ((hoasinduction_lem3aaa = $true) <=> ! [X417 : term,X418 : (subst > term > subst > $o)] : (($true = ((X418 @ id @ (lam @ (sub @ X417 @ (push @ one @ sh))) @ id))) | ? [X428 : term] : (($true = ((X418 @ id @ X428 @ id))) & ($true != ((X418 @ id @ (sub @ X417 @ (push @ X428 @ id)) @ id)))) | ? [X420 : (subst > term > term),X419 : term] : (! [X426 : subst,X425 : subst,X424 : term] : (((X420 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426))) = ((sub @ X419 @ (push @ (sub @ X424 @ X426) @ (comp @ X425 @ X426))))) & ! [X423 : term,X422 : subst,X421 : subst] : (((sub @ (sub @ X419 @ (push @ X423 @ X421)) @ X422)) = ((sub @ (X420 @ X421 @ X423) @ X422))) & ! [X427 : term] : (($true != ((X418 @ id @ X427 @ id))) | (((X418 @ id @ (X420 @ id @ X427) @ id)) = $true)) & ($true != ((X418 @ id @ (lam @ (X420 @ sh @ one)) @ id)))))) & (hoasinduction_lem1_lthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434)))) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 != X432) & (((ap @ X430 @ X431)) = ((ap @ X429 @ X432)))))) & (((! [X30 : (subst > term > subst > $o),X29 : term] : (? [X32 : subst,X31 : term,X34 : subst,X33 : subst] : (($true = ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))) & (((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) != $true)) | ? [X40 : term] : (($true = ((X30 @ id @ X40 @ id))) & (((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X44 : subst,X43 : term,X41 : subst,X42 : subst] : (($true != ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X30 @ X42 @ X43 @ (comp @ X44 @ X41))))) | ? [X35 : (subst > term > term)] : ((((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) != $true) & ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38)))) & ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ($true != ((X30 @ id @ X36 @ id))))) | (((X30 @ id @ (lam @ X29) @ id)) = $true)) | ? [X22 : (subst > term > subst > $o),X21 : term] : ((((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) != $true) & ! [X23 : term] : (($true != ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) & ! [X24 : (subst > term > term)] : (? [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) != ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ? [X28 : term] : (($true = ((X22 @ id @ X28 @ id))) & (((X22 @ id @ (X24 @ id @ X28) @ id)) != $true)) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)))) | ? [X20 : term] : (((sub @ X20 @ id)) != X20)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X254 : (subst > term > subst > $o),X256 : (term > $o),X255 : term] : (? [X258 : term,X257 : subst,X259 : subst,X260 : subst] : (($true = ((X254 @ X257 @ X258 @ (comp @ X259 @ X260)))) & ($true != ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259) @ X260)))) | ? [X267 : (subst > term > term)] : (! [X270 : subst,X271 : subst,X269 : term] : (((X267 @ (comp @ X271 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X271 @ X269) @ X270))) & ! [X268 : term] : (($true = ((X254 @ id @ (X267 @ id @ X268) @ id))) | ($true != ((X254 @ id @ X268 @ id)))) & (((X254 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true)) | ? [X261 : term] : (((X254 @ id @ X261 @ id)) != ((X256 @ X261))) | ? [X266 : term] : (($true = ((X256 @ X266))) & (((X256 @ (sub @ X255 @ (push @ X266 @ id)))) != $true)) | (((X256 @ (lam @ X255))) = $true) | ? [X265 : subst,X264 : term,X263 : subst,X262 : subst] : (($true = ((X254 @ (comp @ X265 @ X262) @ (sub @ X264 @ X262) @ X263))) & (((X254 @ X265 @ X264 @ (comp @ X262 @ X263))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (hoasapnotvar_lthm = $true) & (substmonoid_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) = $true) | ? [X286 : term] : (((X284 @ X286)) != ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ($true != ((X283 @ X282)))) <=> (pushprop_lem1v2 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (hoasinduction_lem1v2_gthm = $true) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) != ((d2subst @ X520))) | (X519 = X520)) & (hoasinduction_lem1v2 = $true) & ((hoasinduction_lem0 = $true) <=> ! [X351 : (subst > term > subst > $o)] : ? [X352 : (term > $o)] : ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id)))) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & ((induction2lem_lthm = $true) <=> ((((! [X344 : term,X345 : subst,X343 : (term > $o)] : (? [X350 : term] : (($true != ((X343 @ (sub @ X350 @ X345)))) & ($true = ((var @ X350)))) | ($true = ((X343 @ (sub @ X344 @ X345)))) | ? [X348 : term] : (($true != ((X343 @ (lam @ X348)))) & ! [X349 : term] : (($true = ((X343 @ (sub @ X348 @ (push @ X349 @ id))))) | ($true != ((X343 @ X349))))) | ? [X346 : term,X347 : term] : (($true = ((X343 @ X346))) & (((X343 @ (ap @ X347 @ X346))) != $true) & ($true = ((X343 @ X347))))) | ? [X338 : (term > $o),X337 : term] : (! [X342 : term] : (($true != ((var @ X342))) | ($true = ((X338 @ X342)))) & ! [X341 : term] : ((((X338 @ X341)) != $true) | (((X338 @ (lam @ X341))) = $true)) & ! [X340 : term,X339 : term] : ((((X338 @ X339)) != $true) | ($true = ((X338 @ (ap @ X340 @ X339)))) | ($true != ((X338 @ X340)))) & ($true != ((X338 @ X337))))) | ? [X336 : subst] : (((comp @ X336 @ id)) != X336)) | ? [X335 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X335))) != X335)) | ? [X332 : term,X333 : subst] : (((sub @ one @ (push @ X332 @ X333))) != X332))) & ((induction2lem = $true) <=> ! [X239 : term,X241 : (term > $o),X240 : subst] : (($true = ((X241 @ (sub @ X239 @ X240)))) | ? [X245 : term,X246 : term] : (($true = ((X241 @ X245))) & (((X241 @ (ap @ X245 @ X246))) != $true) & ($true = ((X241 @ X246)))) | ? [X242 : term] : (($true != ((X241 @ (sub @ X242 @ X240)))) & ($true = ((var @ X242)))) | ? [X243 : term] : (($true != ((X241 @ (lam @ X243)))) & ! [X244 : term] : (($true != ((X241 @ X244))) | ($true = ((X241 @ (sub @ X243 @ (push @ X244 @ id))))))))) & (! [X356 : term,X357 : (subst > term > subst > $o)] : (? [X358 : (subst > term > term)] : (! [X362 : term] : (($true != ((X357 @ id @ X362 @ id))) | ($true = ((X357 @ id @ (X358 @ id @ X362) @ id)))) & (((X357 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X361 : subst,X359 : subst,X360 : term] : (((X358 @ (comp @ X361 @ X359) @ (sub @ X360 @ X359))) = ((sub @ (X358 @ X361 @ X360) @ X359)))) | ($true = ((X357 @ id @ (lam @ (sub @ X356 @ (push @ one @ sh))) @ id))) | ? [X363 : term] : ((((X357 @ id @ X363 @ id)) = $true) & ($true != ((X357 @ id @ (sub @ X356 @ (push @ X363 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $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_lem2 = $true) <=> ! [X212 : (subst > term > subst > $o),X211 : term,X213 : term] : (($true != ((X212 @ id @ X213 @ id))) | ($true != ((X212 @ id @ X211 @ id))) | ? [X220 : subst,X219 : subst,X221 : term,X218 : subst] : (($true = ((X212 @ X220 @ X221 @ (comp @ X219 @ X218)))) & ($true != ((X212 @ (comp @ X220 @ X219) @ (sub @ X221 @ X219) @ X218)))) | ? [X222 : term,X223 : term] : (($true = ((X212 @ id @ X223 @ id))) & ($true = ((X212 @ id @ X222 @ id))) & (((X212 @ id @ (ap @ (sub @ X223 @ id) @ X222) @ id)) != $true)) | ($true = ((X212 @ id @ (ap @ X213 @ X211) @ id))) | ? [X214 : subst,X217 : subst,X215 : subst,X216 : term] : ((((X212 @ (comp @ X215 @ X214) @ (sub @ X216 @ X214) @ X217)) = $true) & ($true != ((X212 @ X215 @ X216 @ (comp @ X214 @ X217))))))) & (pushprop_lem2v2_lthm = $true) & (ulamvarind = $true) & (! [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (? [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) != ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ? [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) != ((sub @ (X320 @ X323 @ X321) @ X322)))) <=> (hoaslaminj = $true)) & (((! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (? [X15 : (subst > term > term)] : (! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | (((X11 @ id @ X16 @ id)) != $true)) & ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) & ($true != ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) | ? [X14 : term] : ((((X12 @ X14)) = $true) & (((X12 @ (sub @ X10 @ (push @ X14 @ id)))) != $true)) | ($true = ((X12 @ (lam @ X10)))) | ? [X13 : term] : (((X11 @ id @ X13 @ id)) != ((X12 @ X13)))) | ? [X9 : term] : (((sub @ X9 @ id)) != X9)) | ? [X5 : term] : ! [X6 : (subst > term > term)] : ? [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) != ((X6 @ X8 @ X7)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X455 : term,X457 : term,X456 : (subst > term > term)] : (? [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) != ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) <=> (hoaslamnotap = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53)))) | ? [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 != X47) & (((ap @ X47 @ X48)) = ((ap @ X46 @ X49))))) | ? [X45 : term] : (((sub @ X45 @ id)) != X45))) & ((axscons = $true) <=> ! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306)) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ? [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) != $true) & ($true = ((X294 @ id @ X296 @ id))) & (((X294 @ id @ X295 @ id)) = $true)) | ? [X297 : (subst > term > term)] : (! [X300 : term,X301 : subst,X299 : subst] : (((sub @ (X297 @ X301 @ X300) @ X299)) = ((X297 @ (comp @ X301 @ X299) @ (sub @ X300 @ X299)))) & ($true != ((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id))) & ! [X298 : term] : ((((X294 @ id @ (X297 @ id @ X298) @ id)) = $true) | ($true != ((X294 @ id @ X298 @ id)))))) <=> (hoasinduction_no_psi_cond = $true)) & (((((! [X388 : term,X387 : (subst > term > subst > $o)] : (? [X400 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X400 @ sh @ one)) @ id)) != $true) & ! [X404 : term] : ((((X387 @ id @ (X400 @ id @ X404) @ id)) = $true) | ($true != ((X387 @ id @ X404 @ id)))) & ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X401 @ X403) @ (sub @ X402 @ X403))) = ((sub @ (X400 @ X401 @ X402) @ X403)))) | (((X387 @ id @ X388 @ id)) = $true) | ? [X390 : term,X391 : term] : (($true = ((X387 @ id @ X390 @ id))) & ($true = ((X387 @ id @ X391 @ id))) & ($true != ((X387 @ id @ (ap @ (sub @ X391 @ id) @ X390) @ id)))) | ? [X393 : subst,X394 : subst,X395 : term,X392 : subst] : ((((X387 @ X393 @ X395 @ (comp @ X394 @ X392))) = $true) & ($true != ((X387 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394) @ X392)))) | ? [X396 : subst,X397 : subst,X398 : subst,X399 : term] : ((((X387 @ X396 @ X399 @ (comp @ X398 @ X397))) != $true) & (((X387 @ (comp @ X396 @ X398) @ (sub @ X399 @ X398) @ X397)) = $true)) | ? [X389 : term] : (($true != ((X387 @ id @ X389 @ id))) & ($true = ((var @ (sub @ X389 @ id)))))) | ? [X379 : (term > $o),X377 : (subst > term > subst > $o),X378 : term] : (! [X381 : term] : (($true = ((X379 @ (sub @ X378 @ (push @ X381 @ id))))) | ($true != ((X379 @ X381)))) & ! [X382 : (subst > term > term)] : ((((X377 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X382 @ X385 @ X384) @ X383)) != ((X382 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383)))) | ? [X386 : term] : (($true = ((X377 @ id @ X386 @ id))) & ($true != ((X377 @ id @ (X382 @ id @ X386) @ id))))) & ($true != ((X379 @ (lam @ X378)))) & ! [X380 : term] : (((X377 @ id @ X380 @ id)) = ((X379 @ X380))))) | ? [X376 : term] : (((sub @ X376 @ id)) != X376)) | ? [X370 : term,X369 : (term > $o)] : (! [X371 : term] : (? [X372 : term] : (($true = ((X369 @ X372))) & ($true != ((X369 @ (sub @ X371 @ (push @ X372 @ id)))))) | (((X369 @ (lam @ X371))) = $true)) & ! [X375 : term,X374 : term] : (($true = ((X369 @ (ap @ X375 @ X374)))) | ($true != ((X369 @ X374))) | ($true != ((X369 @ X375)))) & ! [X373 : term] : (($true != ((var @ X373))) | (((X369 @ X373)) = $true)) & (((X369 @ X370)) != $true))) | ? [X366 : (subst > term > subst > $o)] : ! [X367 : (term > $o)] : ? [X368 : term] : (((X366 @ id @ X368 @ id)) != ((X367 @ X368)))) <=> (hoasinduction_lthm_3 = $true)) & (hoaslamnotvar_lthm = $true) & (ulamvarsh = $true) & ((laminj = $true) <=> ! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237))))) & (((d2subst @ d_id)) = id) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem0_gthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (pushprop_lthm = $true) & (lamnotvar = $true) & ((axshiftcons = $true) <=> ! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355)) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (axabs = $true) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) <=> (axvarid = $true)) & (! [X230 : (subst > term > subst > $o)] : ? [X231 : (term > $o)] : ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232))) <=> (hoasinduction_lem0_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X438 : term,X437 : (subst > term > subst > $o)] : (? [X448 : (subst > term > term)] : (! [X449 : subst,X451 : term,X450 : subst] : (((sub @ (X448 @ X449 @ X451) @ X450)) = ((X448 @ (comp @ X449 @ X450) @ (sub @ X451 @ X450)))) & ($true != ((X437 @ id @ (lam @ (X448 @ sh @ one)) @ id))) & ! [X452 : term] : (($true = ((X437 @ id @ (X448 @ id @ X452) @ id))) | ($true != ((X437 @ id @ X452 @ id))))) | ? [X443 : term] : ((((X437 @ id @ (sub @ X438 @ (push @ X443 @ id)) @ id)) != $true) & (((X437 @ id @ X443 @ id)) = $true)) | ? [X442 : term,X441 : subst,X439 : subst,X440 : subst] : (($true = ((X437 @ X441 @ X442 @ (comp @ X440 @ X439)))) & ($true != ((X437 @ (comp @ X441 @ X440) @ (sub @ X442 @ X440) @ X439)))) | ? [X447 : subst,X444 : term,X445 : subst,X446 : subst] : (($true = ((X437 @ (comp @ X447 @ X445) @ (sub @ X444 @ X445) @ X446))) & ($true != ((X437 @ X447 @ X444 @ (comp @ X445 @ X446))))) | ($true = ((X437 @ id @ (lam @ X438) @ id))))) & ((pushprop_lem1_lthm = $true) <=> ((! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) | ? [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) != X92)) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3b_gthm = $true) & (hoasapnotvar_gthm = $true) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) <=> (axidr = $true)) & (! [X314 : term,X313 : (term > $o),X312 : subst] : ? [X315 : (term > $o)] : ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) <=> (pushprop_lem0_lthm = $true)) & (pushprop_lem3v2 = $true) & ! [X292 : d_subst] : (d_id = X292) & (axclos = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X472 : (subst > term > term),X471 : term,X470 : (subst > term > term),X469 : subst] : (? [X478 : subst,X477 : subst,X476 : term] : (((X472 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) != ((sub @ (X472 @ X477 @ X476) @ X478))) | (((X472 @ X469 @ X471)) = ((X470 @ X469 @ X471))) | ? [X475 : term,X474 : subst,X473 : subst] : (((X470 @ (comp @ X473 @ X474) @ (sub @ X475 @ X474))) != ((sub @ (X470 @ X473 @ X475) @ X474))) | (((lam @ (X470 @ sh @ one))) != ((lam @ (X472 @ sh @ one))))) | ? [X468 : term,X467 : term] : ((X467 != X468) & (((lam @ X468)) = ((lam @ X467))))) | ? [X465 : subst,X466 : term] : (((comp @ sh @ (push @ X466 @ X465))) != X465)) | ? [X464 : term,X463 : subst] : (((sub @ one @ (push @ X464 @ X463))) != X464))) & ((axidl = $true) <=> ! [X327 : subst] : (((comp @ id @ X327)) = X327)) & ((((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | ? [X2 : subst] : (((comp @ X2 @ id)) != X2)) | ? [X1 : subst] : (((comp @ id @ X1)) != X1)) <=> (substmonoid_lthm = $true)) & (hoasapinj1_gthm = $true) & ((termmset_lthm = $true) <=> (! [X454 : term] : (((sub @ X454 @ id)) = X454) | ? [X453 : term] : (((sub @ X453 @ id)) != X453))) & (! [X206 : term,X205 : (term > $o)] : (? [X210 : term] : ((((X205 @ (lam @ X210))) != $true) & ($true = ((X205 @ X210)))) | ? [X207 : term] : ((((var @ X207)) = $true) & ($true != ((X205 @ X207)))) | ? [X208 : term,X209 : term] : (($true != ((X205 @ (ap @ X209 @ X208)))) & ($true = ((X205 @ X209))) & ($true = ((X205 @ X208)))) | (((X205 @ X206)) = $true)) <=> (induction = $true)) & (pushprop = $true) & ! [X521 : d_term] : (d_one = X521) & (one = ((d2term @ d_one))) & (termmset_gthm = $true) & (induction2lem_gthm = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) != X84) | ! [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true = ((X87 @ one))) | ? [X89 : term] : (((X87 @ X89)) != ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true != ((X88 @ X85)))))) & (((d2subst @ d_id)) = sh) & (hoaslamnotvar_gthm = $true) & (axmap = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true != ((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id))) & (((X410 @ id @ X411 @ id)) = $true)) | ($true = ((X410 @ id @ (lam @ (sub @ X409 @ (push @ one @ sh))) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : term] : (($true = ((X410 @ id @ (X412 @ id @ X413) @ id))) | ($true != ((X410 @ id @ X413 @ id)))) & ! [X414 : term,X416 : subst,X415 : subst] : (((sub @ (X412 @ X416 @ X414) @ X415)) = ((X412 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasinduction_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem2v2 = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X480 : term,X482 : (subst > term > subst > $o),X481 : (term > $o)] : (? [X488 : term] : (((X482 @ id @ X488 @ id)) != ((X481 @ X488))) | ? [X484 : subst,X485 : subst,X486 : subst,X487 : term] : (($true != ((X482 @ (comp @ X484 @ X485) @ (sub @ X487 @ X485) @ X486))) & ($true = ((X482 @ X484 @ X487 @ (comp @ X485 @ X486))))) | ? [X493 : (subst > term > term)] : (($true != ((X482 @ id @ (lam @ (X493 @ sh @ one)) @ id))) & ! [X497 : term] : (($true != ((X482 @ id @ X497 @ id))) | ($true = ((X482 @ id @ (X493 @ id @ X497) @ id)))) & ! [X496 : term,X495 : subst,X494 : subst] : (((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495))) = ((sub @ (X493 @ X494 @ X496) @ X495)))) | ? [X492 : subst,X491 : term,X489 : subst,X490 : subst] : ((((X482 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) = $true) & (((X482 @ X489 @ X491 @ (comp @ X492 @ X490))) != $true)) | ($true = ((X481 @ (lam @ X480)))) | ? [X483 : term] : ((((X481 @ X483)) = $true) & ($true != ((X481 @ (sub @ X480 @ (push @ X483 @ id))))))) | ? [X479 : term] : (((sub @ X479 @ id)) != X479))) & (hoaslamnotvar = $true) & (induction2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X75 : (subst > term > subst > $o),X76 : term] : (? [X77 : term] : (($true = ((X75 @ id @ X77 @ id))) & (((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) != $true)) | ? [X78 : (subst > term > term)] : (! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80))) & ! [X79 : term] : (($true = ((X75 @ id @ (X78 @ id @ X79) @ id))) | ($true != ((X75 @ id @ X79 @ id)))) & (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) != $true)) | ($true = ((X75 @ id @ (lam @ X76) @ id)))) <=> (hoasinduction_lem3a = $true)) & ((axvarcons = $true) <=> ! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224))),
% 1.42/0.51 inference(ennf_transformation,[],[f10])).
% 1.42/0.51 thf(f12,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (! [X57 : term,X56 : term,X54 : (subst > term > subst > $o),X55 : (term > $o)] : (($true != ((X55 @ X56))) | ? [X58 : term] : (((X55 @ X58)) != ((X54 @ id @ X58 @ id))) | ? [X63 : subst,X62 : subst,X61 : subst,X64 : term] : (($true != ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) & (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) = $true)) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ? [X68 : subst,X67 : subst,X66 : subst,X65 : term] : (($true != ((X54 @ X67 @ X65 @ (comp @ X68 @ X66)))) & ($true = ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66)))) | ? [X60 : term,X59 : term] : (($true = ((X54 @ id @ X60 @ id))) & ($true != ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id))) & (((X54 @ id @ X59 @ id)) = $true)) | (((X55 @ X57)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) != X84) | ! [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true = ((X87 @ one))) | ? [X89 : term] : (((X87 @ X89)) != ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true != ((X88 @ X85)))))) & (! [X247 : (term > $o),X248 : term] : (? [X250 : term] : (! [X251 : term] : (($true != ((X247 @ X251))) | ($true = ((X247 @ (sub @ X250 @ (push @ X251 @ id)))))) & ($true != ((X247 @ (lam @ X250))))) | ? [X249 : term] : ((((X247 @ X249)) != $true) & (((var @ X249)) = $true)) | ? [X253 : term,X252 : term] : ((((X247 @ X252)) = $true) & ($true != ((X247 @ (ap @ X252 @ X253)))) & ($true = ((X247 @ X253)))) | ($true = ((X247 @ X248)))) <=> (induction2 = $true)) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & ((induction2lem_lthm = $true) <=> (? [X336 : subst] : (((comp @ X336 @ id)) != X336) | ! [X344 : term,X345 : subst,X343 : (term > $o)] : (? [X350 : term] : (($true != ((X343 @ (sub @ X350 @ X345)))) & ($true = ((var @ X350)))) | ($true = ((X343 @ (sub @ X344 @ X345)))) | ? [X348 : term] : (($true != ((X343 @ (lam @ X348)))) & ! [X349 : term] : (($true = ((X343 @ (sub @ X348 @ (push @ X349 @ id))))) | ($true != ((X343 @ X349))))) | ? [X346 : term,X347 : term] : (($true = ((X343 @ X346))) & (((X343 @ (ap @ X347 @ X346))) != $true) & ($true = ((X343 @ X347))))) | ? [X332 : term,X333 : subst] : (((sub @ one @ (push @ X332 @ X333))) != X332) | ? [X335 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X335))) != X335) | ? [X338 : (term > $o),X337 : term] : (! [X342 : term] : (($true != ((var @ X342))) | ($true = ((X338 @ X342)))) & ! [X341 : term] : ((((X338 @ X341)) != $true) | (((X338 @ (lam @ X341))) = $true)) & ! [X340 : term,X339 : term] : ((((X338 @ X339)) != $true) | ($true = ((X338 @ (ap @ X340 @ X339)))) | ($true != ((X338 @ X340)))) & ($true != ((X338 @ X337)))))) & ((termmset_lthm = $true) <=> (! [X454 : term] : (((sub @ X454 @ id)) = X454) | ? [X453 : term] : (((sub @ X453 @ id)) != X453))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) <=> (? [X465 : subst,X466 : term] : (((comp @ sh @ (push @ X466 @ X465))) != X465) | ? [X468 : term,X467 : term] : ((X467 != X468) & (((lam @ X468)) = ((lam @ X467)))) | ? [X464 : term,X463 : subst] : (((sub @ one @ (push @ X464 @ X463))) != X464) | ! [X472 : (subst > term > term),X471 : term,X470 : (subst > term > term),X469 : subst] : (? [X478 : subst,X477 : subst,X476 : term] : (((X472 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) != ((sub @ (X472 @ X477 @ X476) @ X478))) | (((X472 @ X469 @ X471)) = ((X470 @ X469 @ X471))) | ? [X475 : term,X474 : subst,X473 : subst] : (((X470 @ (comp @ X473 @ X474) @ (sub @ X475 @ X474))) != ((sub @ (X470 @ X473 @ X475) @ X474))) | (((lam @ (X470 @ sh @ one))) != ((lam @ (X472 @ sh @ one))))))) & (hoasinduction_lem3_gthm = $true) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) <=> (apinj2 = $true)) & (! [X288 : (term > $o),X289 : subst,X287 : term] : ? [X290 : (term > $o)] : ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))) <=> (pushprop_lem0 = $true)) & (hoasapnotvar_gthm = $true) & (! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) <=> (pushprop_lem1 = $true)) & ((! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (? [X15 : (subst > term > term)] : (! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | (((X11 @ id @ X16 @ id)) != $true)) & ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) & ($true != ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) | ? [X14 : term] : ((((X12 @ X14)) = $true) & (((X12 @ (sub @ X10 @ (push @ X14 @ id)))) != $true)) | ($true = ((X12 @ (lam @ X10)))) | ? [X13 : term] : (((X11 @ id @ X13 @ id)) != ((X12 @ X13)))) | ? [X5 : term] : ! [X6 : (subst > term > term)] : ? [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) != ((X6 @ X8 @ X7))) | ? [X9 : term] : (((sub @ X9 @ id)) != X9)) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X455 : term,X457 : term,X456 : (subst > term > term)] : (? [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) != ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) <=> (hoaslamnotap = $true)) & (apnotvar = $true) & ((substmonoid_lthm = $true) <=> ((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | ? [X1 : subst] : (((comp @ id @ X1)) != X1) | ? [X2 : subst] : (((comp @ X2 @ id)) != X2))) & (! [X230 : (subst > term > subst > $o)] : ? [X231 : (term > $o)] : ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232))) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lthm_3 = $true) <=> (? [X376 : term] : (((sub @ X376 @ id)) != X376) | ! [X388 : term,X387 : (subst > term > subst > $o)] : (? [X400 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X400 @ sh @ one)) @ id)) != $true) & ! [X404 : term] : ((((X387 @ id @ (X400 @ id @ X404) @ id)) = $true) | ($true != ((X387 @ id @ X404 @ id)))) & ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X401 @ X403) @ (sub @ X402 @ X403))) = ((sub @ (X400 @ X401 @ X402) @ X403)))) | (((X387 @ id @ X388 @ id)) = $true) | ? [X390 : term,X391 : term] : (($true = ((X387 @ id @ X390 @ id))) & ($true = ((X387 @ id @ X391 @ id))) & ($true != ((X387 @ id @ (ap @ (sub @ X391 @ id) @ X390) @ id)))) | ? [X393 : subst,X394 : subst,X395 : term,X392 : subst] : ((((X387 @ X393 @ X395 @ (comp @ X394 @ X392))) = $true) & ($true != ((X387 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394) @ X392)))) | ? [X396 : subst,X397 : subst,X398 : subst,X399 : term] : ((((X387 @ X396 @ X399 @ (comp @ X398 @ X397))) != $true) & (((X387 @ (comp @ X396 @ X398) @ (sub @ X399 @ X398) @ X397)) = $true)) | ? [X389 : term] : (($true != ((X387 @ id @ X389 @ id))) & ($true = ((var @ (sub @ X389 @ id)))))) | ? [X379 : (term > $o),X377 : (subst > term > subst > $o),X378 : term] : (! [X381 : term] : (($true = ((X379 @ (sub @ X378 @ (push @ X381 @ id))))) | ($true != ((X379 @ X381)))) & ! [X382 : (subst > term > term)] : ((((X377 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X382 @ X385 @ X384) @ X383)) != ((X382 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383)))) | ? [X386 : term] : (($true = ((X377 @ id @ X386 @ id))) & ($true != ((X377 @ id @ (X382 @ id @ X386) @ id))))) & ($true != ((X379 @ (lam @ X378)))) & ! [X380 : term] : (((X377 @ id @ X380 @ id)) = ((X379 @ X380)))) | ? [X370 : term,X369 : (term > $o)] : (! [X371 : term] : (? [X372 : term] : (($true = ((X369 @ X372))) & ($true != ((X369 @ (sub @ X371 @ (push @ X372 @ id)))))) | (((X369 @ (lam @ X371))) = $true)) & ! [X375 : term,X374 : term] : (($true = ((X369 @ (ap @ X375 @ X374)))) | ($true != ((X369 @ X374))) | ($true != ((X369 @ X375)))) & ! [X373 : term] : (($true != ((var @ X373))) | (((X369 @ X373)) = $true)) & (((X369 @ X370)) != $true)) | ? [X366 : (subst > term > subst > $o)] : ! [X367 : (term > $o)] : ? [X368 : term] : (((X366 @ id @ X368 @ id)) != ((X367 @ X368))))) & ((hoasinduction_lem3_lthm = $true) <=> (? [X22 : (subst > term > subst > $o),X21 : term] : ((((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) != $true) & ! [X23 : term] : (($true != ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) & ! [X24 : (subst > term > term)] : (? [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) != ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ? [X28 : term] : (($true = ((X22 @ id @ X28 @ id))) & (((X22 @ id @ (X24 @ id @ X28) @ id)) != $true)) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true))) | ? [X20 : term] : (((sub @ X20 @ id)) != X20) | ! [X30 : (subst > term > subst > $o),X29 : term] : (? [X32 : subst,X31 : term,X34 : subst,X33 : subst] : (($true = ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))) & (((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) != $true)) | ? [X40 : term] : (($true = ((X30 @ id @ X40 @ id))) & (((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X44 : subst,X43 : term,X41 : subst,X42 : subst] : (($true != ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X30 @ X42 @ X43 @ (comp @ X44 @ X41))))) | ? [X35 : (subst > term > term)] : ((((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) != $true) & ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38)))) & ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ($true != ((X30 @ id @ X36 @ id))))) | (((X30 @ id @ (lam @ X29) @ id)) = $true)))) & (hoaslaminj_gthm = $true) & (! [X206 : term,X205 : (term > $o)] : (? [X210 : term] : ((((X205 @ (lam @ X210))) != $true) & ($true = ((X205 @ X210)))) | ? [X207 : term] : ((((var @ X207)) = $true) & ($true != ((X205 @ X207)))) | ? [X208 : term,X209 : term] : (($true != ((X205 @ (ap @ X209 @ X208)))) & ($true = ((X205 @ X209))) & ($true = ((X205 @ X208)))) | (((X205 @ X206)) = $true)) <=> (induction = $true)) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (! [X254 : (subst > term > subst > $o),X256 : (term > $o),X255 : term] : (? [X258 : term,X257 : subst,X259 : subst,X260 : subst] : (($true = ((X254 @ X257 @ X258 @ (comp @ X259 @ X260)))) & ($true != ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259) @ X260)))) | ? [X267 : (subst > term > term)] : (! [X270 : subst,X271 : subst,X269 : term] : (((X267 @ (comp @ X271 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X271 @ X269) @ X270))) & ! [X268 : term] : (($true = ((X254 @ id @ (X267 @ id @ X268) @ id))) | ($true != ((X254 @ id @ X268 @ id)))) & (((X254 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true)) | ? [X261 : term] : (((X254 @ id @ X261 @ id)) != ((X256 @ X261))) | ? [X266 : term] : (($true = ((X256 @ X266))) & (((X256 @ (sub @ X255 @ (push @ X266 @ id)))) != $true)) | (((X256 @ (lam @ X255))) = $true) | ? [X265 : subst,X264 : term,X263 : subst,X262 : subst] : (($true = ((X254 @ (comp @ X265 @ X262) @ (sub @ X264 @ X262) @ X263))) & (((X254 @ X265 @ X264 @ (comp @ X262 @ X263))) != $true))) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2lem = $true) <=> ! [X239 : term,X241 : (term > $o),X240 : subst] : (($true = ((X241 @ (sub @ X239 @ X240)))) | ? [X245 : term,X246 : term] : (($true = ((X241 @ X245))) & (((X241 @ (ap @ X245 @ X246))) != $true) & ($true = ((X241 @ X246)))) | ? [X242 : term] : (($true != ((X241 @ (sub @ X242 @ X240)))) & ($true = ((var @ X242)))) | ? [X243 : term] : (($true != ((X241 @ (lam @ X243)))) & ! [X244 : term] : (($true != ((X241 @ X244))) | ($true = ((X241 @ (sub @ X243 @ (push @ X244 @ id))))))))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X226 : term] : ? [X227 : (subst > term > term)] : ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229)))) & ((hoasapinj1 = $true) <=> ! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408))))) & ((axshiftcons = $true) <=> ! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X328 : term] : ? [X329 : (subst > term > term)] : ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) <=> (axvarid = $true)) & (hoasinduction_gthm = $true) & (! [X356 : term,X357 : (subst > term > subst > $o)] : (? [X358 : (subst > term > term)] : (! [X362 : term] : (($true != ((X357 @ id @ X362 @ id))) | ($true = ((X357 @ id @ (X358 @ id @ X362) @ id)))) & (((X357 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X361 : subst,X359 : subst,X360 : term] : (((X358 @ (comp @ X361 @ X359) @ (sub @ X360 @ X359))) = ((sub @ (X358 @ X361 @ X360) @ X359)))) | ($true = ((X357 @ id @ (lam @ (sub @ X356 @ (push @ one @ sh))) @ id))) | ? [X363 : term] : ((((X357 @ id @ X363 @ id)) = $true) & ($true != ((X357 @ id @ (sub @ X356 @ (push @ X363 @ id)) @ id))))) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X480 : term,X482 : (subst > term > subst > $o),X481 : (term > $o)] : (? [X488 : term] : (((X482 @ id @ X488 @ id)) != ((X481 @ X488))) | ? [X484 : subst,X485 : subst,X486 : subst,X487 : term] : (($true != ((X482 @ (comp @ X484 @ X485) @ (sub @ X487 @ X485) @ X486))) & ($true = ((X482 @ X484 @ X487 @ (comp @ X485 @ X486))))) | ? [X493 : (subst > term > term)] : (($true != ((X482 @ id @ (lam @ (X493 @ sh @ one)) @ id))) & ! [X497 : term] : (($true != ((X482 @ id @ X497 @ id))) | ($true = ((X482 @ id @ (X493 @ id @ X497) @ id)))) & ! [X496 : term,X495 : subst,X494 : subst] : (((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495))) = ((sub @ (X493 @ X494 @ X496) @ X495)))) | ? [X492 : subst,X491 : term,X489 : subst,X490 : subst] : ((((X482 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) = $true) & (((X482 @ X489 @ X491 @ (comp @ X492 @ X490))) != $true)) | ($true = ((X481 @ (lam @ X480)))) | ? [X483 : term] : ((((X481 @ X483)) = $true) & ($true != ((X481 @ (sub @ X480 @ (push @ X483 @ id))))))) | ? [X479 : term] : (((sub @ X479 @ id)) != X479))) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (! [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (? [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) != ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ? [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) != ((sub @ (X320 @ X323 @ X321) @ X322)))) <=> (hoaslaminj = $true)) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((X204 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoaslamnotvar = $true) & ! [X292 : d_subst] : (d_id = X292) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((laminj = $true) <=> ! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237))))) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & ((hoasinduction_lem2 = $true) <=> ! [X212 : (subst > term > subst > $o),X211 : term,X213 : term] : (($true != ((X212 @ id @ X213 @ id))) | ($true != ((X212 @ id @ X211 @ id))) | ? [X220 : subst,X219 : subst,X221 : term,X218 : subst] : (($true = ((X212 @ X220 @ X221 @ (comp @ X219 @ X218)))) & ($true != ((X212 @ (comp @ X220 @ X219) @ (sub @ X221 @ X219) @ X218)))) | ? [X222 : term,X223 : term] : (($true = ((X212 @ id @ X223 @ id))) & ($true = ((X212 @ id @ X222 @ id))) & (((X212 @ id @ (ap @ (sub @ X223 @ id) @ X222) @ id)) != $true)) | ($true = ((X212 @ id @ (ap @ X213 @ X211) @ id))) | ? [X214 : subst,X217 : subst,X215 : subst,X216 : term] : ((((X212 @ (comp @ X215 @ X214) @ (sub @ X216 @ X214) @ X217)) = $true) & ($true != ((X212 @ X215 @ X216 @ (comp @ X214 @ X217))))))) & ((axidl = $true) <=> ! [X327 : subst] : (((comp @ id @ X327)) = X327)) & (! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true != ((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id))) & (((X410 @ id @ X411 @ id)) = $true)) | ($true = ((X410 @ id @ (lam @ (sub @ X409 @ (push @ one @ sh))) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : term] : (($true = ((X410 @ id @ (X412 @ id @ X413) @ id))) | ($true != ((X410 @ id @ X413 @ id)))) & ! [X414 : term,X416 : subst,X415 : subst] : (((sub @ (X412 @ X416 @ X414) @ X415)) = ((X412 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415)))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((? [X160 : term,X159 : subst,X158 : (term > $o)] : (($true != ((X158 @ (sub @ X160 @ X159)))) & ! [X164 : term,X163 : term] : ((((X158 @ (ap @ X164 @ X163))) = $true) | ($true != ((X158 @ X163))) | ($true != ((X158 @ X164)))) & ! [X165 : term] : (($true != ((var @ X165))) | ($true = ((X158 @ (sub @ X165 @ X159))))) & ! [X161 : term] : (($true = ((X158 @ (lam @ X161)))) | ? [X162 : term] : (($true = ((X158 @ X162))) & (((X158 @ (sub @ X161 @ (push @ X162 @ id)))) != $true)))) | ? [X157 : term] : (((sub @ X157 @ id)) != X157) | ! [X166 : (term > $o),X167 : term] : (? [X168 : term] : (! [X169 : term] : ((((X166 @ (sub @ X168 @ (push @ X169 @ id)))) = $true) | ($true != ((X166 @ X169)))) & ($true != ((X166 @ (lam @ X168))))) | ? [X172 : term] : ((((X166 @ X172)) != $true) & (((var @ X172)) = $true)) | ($true = ((X166 @ X167))) | ? [X170 : term,X171 : term] : (($true = ((X166 @ X170))) & (((X166 @ (ap @ X171 @ X170))) != $true) & ($true = ((X166 @ X171)))))) <=> (induction2_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (? [X184 : (term > $o),X185 : term,X186 : (subst > term > subst > $o)] : ((((X184 @ (lam @ X185))) != $true) & ! [X188 : term] : (($true = ((X184 @ (sub @ X185 @ (push @ X188 @ id))))) | (((X184 @ X188)) != $true)) & ! [X189 : (subst > term > term)] : (? [X190 : subst,X192 : term,X191 : subst] : (((X189 @ (comp @ X190 @ X191) @ (sub @ X192 @ X191))) != ((sub @ (X189 @ X190 @ X192) @ X191))) | ? [X193 : term] : ((((X186 @ id @ (X189 @ id @ X193) @ id)) != $true) & ($true = ((X186 @ id @ X193 @ id)))) | (((X186 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true)) & ! [X187 : term] : (((X186 @ id @ X187 @ id)) = ((X184 @ X187)))) | ! [X195 : (subst > term > subst > $o),X194 : term] : (? [X198 : (subst > term > term)] : (! [X199 : term] : ((((X195 @ id @ (X198 @ id @ X199) @ id)) = $true) | (((X195 @ id @ X199 @ id)) != $true)) & ! [X202 : term,X201 : subst,X200 : subst] : (((sub @ (X198 @ X200 @ X202) @ X201)) = ((X198 @ (comp @ X200 @ X201) @ (sub @ X202 @ X201)))) & (((X195 @ id @ (lam @ (X198 @ sh @ one)) @ id)) != $true)) | ? [X197 : term,X196 : term] : ((((X195 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) != $true) & (((X195 @ id @ X197 @ id)) = $true) & (((X195 @ id @ X196 @ id)) = $true)) | ($true = ((X195 @ id @ X194 @ id)))) | ? [X173 : (subst > term > subst > $o)] : ! [X174 : (term > $o)] : ? [X175 : term] : (((X174 @ X175)) != ((X173 @ id @ X175 @ id))) | ? [X177 : term,X176 : (term > $o)] : (! [X180 : term,X181 : term] : (($true != ((X176 @ X180))) | ($true = ((X176 @ (ap @ X180 @ X181)))) | ($true != ((X176 @ X181)))) & ! [X178 : term] : ((((X176 @ (lam @ X178))) = $true) | ? [X179 : term] : (($true = ((X176 @ X179))) & ($true != ((X176 @ (sub @ X178 @ (push @ X179 @ id))))))) & ! [X182 : term] : (($true = ((X176 @ X182))) | ($true != ((var @ X182)))) & ($true != ((X176 @ X177)))) | ? [X183 : term] : (((sub @ X183 @ id)) != X183))) & ((hoasinduction_lem3aaa = $true) <=> ! [X417 : term,X418 : (subst > term > subst > $o)] : (($true = ((X418 @ id @ (lam @ (sub @ X417 @ (push @ one @ sh))) @ id))) | ? [X428 : term] : (($true = ((X418 @ id @ X428 @ id))) & ($true != ((X418 @ id @ (sub @ X417 @ (push @ X428 @ id)) @ id)))) | ? [X420 : (subst > term > term),X419 : term] : (! [X426 : subst,X425 : subst,X424 : term] : (((X420 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426))) = ((sub @ X419 @ (push @ (sub @ X424 @ X426) @ (comp @ X425 @ X426))))) & ! [X423 : term,X422 : subst,X421 : subst] : (((sub @ (sub @ X419 @ (push @ X423 @ X421)) @ X422)) = ((sub @ (X420 @ X421 @ X423) @ X422))) & ! [X427 : term] : (($true != ((X418 @ id @ X427 @ id))) | (((X418 @ id @ (X420 @ id @ X427) @ id)) = $true)) & ($true != ((X418 @ id @ (lam @ (X420 @ sh @ one)) @ id)))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) <=> (axidr = $true)) & (pushprop_gthm = $true) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) <=> (hoasapinj2 = $true)) & ! [X521 : d_term] : (d_one = X521) & ((axvarcons = $true) <=> ! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224)) & ((? [X104 : term,X103 : (term > $o)] : (! [X106 : term,X105 : term] : (($true != ((X103 @ X106))) | ($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106))))) & ! [X107 : term] : (($true != ((var @ X107))) | ($true = ((X103 @ X107)))) & ! [X108 : term] : (? [X109 : term] : (($true != ((X103 @ (sub @ X108 @ (push @ X109 @ id))))) & ($true = ((X103 @ X109)))) | ($true = ((X103 @ (lam @ X108))))) & (((X103 @ X104)) != $true)) | ? [X112 : (subst > term > subst > $o),X111 : term,X110 : term] : (($true = ((X112 @ id @ X110 @ id))) & ! [X119 : term,X120 : subst,X122 : subst,X121 : subst] : (($true != ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) & ($true != ((X112 @ id @ (ap @ X110 @ X111) @ id))) & ! [X114 : term,X113 : term] : (($true != ((X112 @ id @ X113 @ id))) | (((X112 @ id @ X114 @ id)) != $true) | ($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id)))) & ! [X117 : subst,X118 : subst,X116 : term,X115 : subst] : ((((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) != $true) | (((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true)) & (((X112 @ id @ X111 @ id)) = $true)) | ? [X123 : (subst > term > subst > $o),X124 : term] : (! [X136 : subst,X134 : subst,X135 : subst,X137 : term] : (($true != ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134))))) & ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | (((X123 @ id @ X138 @ id)) != $true)) & (((X123 @ id @ (lam @ X124) @ id)) != $true) & ! [X125 : (subst > term > term)] : (? [X128 : term,X127 : subst,X126 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) != ((sub @ (X125 @ X126 @ X128) @ X127))) | ? [X129 : term] : (($true = ((X123 @ id @ X129 @ id))) & ($true != ((X123 @ id @ (X125 @ id @ X129) @ id)))) | (((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true)) & ! [X132 : subst,X133 : subst,X131 : term,X130 : subst] : (($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133))) | ($true != ((X123 @ X130 @ X131 @ (comp @ X132 @ X133)))))) | ! [X139 : term,X140 : (subst > term > subst > $o)] : (? [X143 : term] : (($true != ((X140 @ id @ X143 @ id))) & (((var @ (sub @ X143 @ id))) = $true)) | ? [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) != $true) & ($true = ((X140 @ id @ X141 @ id))) & ($true = ((X140 @ id @ X142 @ id)))) | (((X140 @ id @ X139 @ id)) = $true) | ? [X144 : (subst > term > term)] : (! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) & ! [X148 : term] : (($true = ((X140 @ id @ (X144 @ id @ X148) @ id))) | (((X140 @ id @ X148 @ id)) != $true)) & ($true != ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id)))) | ? [X150 : subst,X152 : term,X149 : subst,X151 : subst] : (($true != ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) & (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) = $true)) | ? [X154 : term,X156 : subst,X155 : subst,X153 : subst] : (($true = ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) & (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) != $true)))) <=> (hoasinduction_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434)))) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 != X432) & (((ap @ X430 @ X431)) = ((ap @ X429 @ X432)))))) & ((axscons = $true) <=> ! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306)) & ((hoasinduction_lem3a_lthm = $true) <=> (? [X502 : term] : (((sub @ X502 @ id)) != X502) | ? [X504 : (subst > term > subst > $o),X503 : term] : (($true != ((X504 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) & ! [X505 : (subst > term > term)] : (? [X506 : term] : (($true != ((X504 @ id @ (X505 @ id @ X506) @ id))) & (((X504 @ id @ X506 @ id)) = $true)) | ? [X507 : term,X508 : subst,X509 : subst] : (((sub @ (X505 @ X508 @ X507) @ X509)) != ((X505 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509)))) | ($true = ((X504 @ id @ (lam @ (X505 @ sh @ one)) @ id)))) & ! [X510 : term] : ((((X504 @ id @ X510 @ id)) != $true) | ($true = ((X504 @ id @ (sub @ X503 @ (push @ X510 @ id)) @ id))))) | ! [X511 : term,X512 : (subst > term > subst > $o)] : (? [X513 : term] : ((((X512 @ id @ (sub @ X511 @ (push @ X513 @ id)) @ id)) != $true) & ($true = ((X512 @ id @ X513 @ id)))) | ? [X514 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) & ! [X516 : term,X518 : subst,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | (((X512 @ id @ X515 @ id)) != $true))) | ($true = ((X512 @ id @ (lam @ X511) @ id)))))) & ((hoasinduction_lem0 = $true) <=> ! [X351 : (subst > term > subst > $o)] : ? [X352 : (term > $o)] : ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id)))) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> ! [X274 : (term > $o),X273 : term,X272 : (subst > term > subst > $o)] : (($true = ((X274 @ (lam @ X273)))) | ? [X275 : term] : (($true != ((X274 @ (sub @ X273 @ (push @ X275 @ id))))) & (((X274 @ X275)) = $true)) | ? [X276 : (subst > term > term)] : (! [X277 : term] : ((((X272 @ id @ X277 @ id)) != $true) | (((X272 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X279 : term,X280 : subst,X278 : subst] : (((sub @ (X276 @ X278 @ X279) @ X280)) = ((X276 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280)))) & ($true != ((X272 @ id @ (lam @ (X276 @ sh @ one)) @ id)))) | ? [X281 : term] : (((X274 @ X281)) != ((X272 @ id @ X281 @ id))))) & (axclos = $true) & (! [X523 : term,X522 : (subst > term > subst > $o)] : (? [X533 : term] : (($true = ((var @ (sub @ X533 @ id)))) & (((X522 @ id @ X533 @ id)) != $true)) | ? [X535 : subst,X537 : subst,X534 : term,X536 : subst] : (($true = ((X522 @ X535 @ X534 @ (comp @ X536 @ X537)))) & ($true != ((X522 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536) @ X537)))) | ? [X539 : term,X538 : term] : ((((X522 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true) & ($true = ((X522 @ id @ X539 @ id))) & ($true = ((X522 @ id @ X538 @ id)))) | ? [X529 : subst,X530 : subst,X532 : subst,X531 : term] : (($true != ((X522 @ X532 @ X531 @ (comp @ X529 @ X530)))) & ($true = ((X522 @ (comp @ X532 @ X529) @ (sub @ X531 @ X529) @ X530)))) | ($true = ((X522 @ id @ X523 @ id))) | ? [X524 : (subst > term > term)] : (($true != ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) & ! [X525 : term] : (($true != ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) & ! [X528 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X528)) = ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528)))))) <=> (hoasinduction = $true)) & (! [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) = $true) | ? [X286 : term] : (((X284 @ X286)) != ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ($true != ((X283 @ X282)))) <=> (pushprop_lem1v2 = $true)) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) != ((d2subst @ X520))) | (X519 = X520)) & (termmset_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ? [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) = ((X102 @ sh @ one)))) & (axabs = $true) & ! [X235 : d_term,X236 : d_term] : ((((d2term @ X236)) != ((d2term @ X235))) | (X235 = X236)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) <=> ! [X438 : term,X437 : (subst > term > subst > $o)] : (? [X448 : (subst > term > term)] : (! [X449 : subst,X451 : term,X450 : subst] : (((sub @ (X448 @ X449 @ X451) @ X450)) = ((X448 @ (comp @ X449 @ X450) @ (sub @ X451 @ X450)))) & ($true != ((X437 @ id @ (lam @ (X448 @ sh @ one)) @ id))) & ! [X452 : term] : (($true = ((X437 @ id @ (X448 @ id @ X452) @ id))) | ($true != ((X437 @ id @ X452 @ id))))) | ? [X443 : term] : ((((X437 @ id @ (sub @ X438 @ (push @ X443 @ id)) @ id)) != $true) & (((X437 @ id @ X443 @ id)) = $true)) | ? [X442 : term,X441 : subst,X439 : subst,X440 : subst] : (($true = ((X437 @ X441 @ X442 @ (comp @ X440 @ X439)))) & ($true != ((X437 @ (comp @ X441 @ X440) @ (sub @ X442 @ X440) @ X439)))) | ? [X447 : subst,X444 : term,X445 : subst,X446 : subst] : (($true = ((X437 @ (comp @ X447 @ X445) @ (sub @ X444 @ X445) @ X446))) & ($true != ((X437 @ X447 @ X444 @ (comp @ X445 @ X446))))) | ($true = ((X437 @ id @ (lam @ X438) @ id))))) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & (pushprop = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ? [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) != $true) & ($true = ((X294 @ id @ X296 @ id))) & (((X294 @ id @ X295 @ id)) = $true)) | ? [X297 : (subst > term > term)] : (! [X300 : term,X301 : subst,X299 : subst] : (((sub @ (X297 @ X301 @ X300) @ X299)) = ((X297 @ (comp @ X301 @ X299) @ (sub @ X300 @ X299)))) & ($true != ((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id))) & ! [X298 : term] : ((((X294 @ id @ (X297 @ id @ X298) @ id)) = $true) | ($true != ((X294 @ id @ X298 @ id)))))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasapinj2_gthm = $true) & (! [X75 : (subst > term > subst > $o),X76 : term] : (? [X77 : term] : (($true = ((X75 @ id @ X77 @ id))) & (((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) != $true)) | ? [X78 : (subst > term > term)] : (! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80))) & ! [X79 : term] : (($true = ((X75 @ id @ (X78 @ id @ X79) @ id))) | ($true != ((X75 @ id @ X79 @ id)))) & (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) != $true)) | ($true = ((X75 @ id @ (lam @ X76) @ id)))) <=> (hoasinduction_lem3a = $true)) & ((? [X45 : term] : (((sub @ X45 @ id)) != X45) | ? [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 != X47) & (((ap @ X47 @ X48)) = ((ap @ X46 @ X49)))) | ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lthm = $true) & ((? [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) != X92) | ! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91)) <=> (pushprop_lem1_lthm = $true)) & (axassoc = $true) & (hoasapnotvar = $true) & (! [X314 : term,X313 : (term > $o),X312 : subst] : ? [X315 : (term > $o)] : ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) <=> (pushprop_lem0_lthm = $true))),
% 1.42/0.51 inference(flattening,[],[f11])).
% 1.42/0.51 thf(f13,definition,(
% 1.42/0.51 ($true = sP0) <=> ! [X75 : (subst > term > subst > $o),X76 : term] : (? [X77 : term] : (($true = ((X75 @ id @ X77 @ id))) & (((X75 @ id @ (sub @ X76 @ (push @ X77 @ id)) @ id)) != $true)) | ? [X78 : (subst > term > term)] : (! [X82 : term,X80 : subst,X81 : subst] : (((X78 @ (comp @ X81 @ X80) @ (sub @ X82 @ X80))) = ((sub @ (X78 @ X81 @ X82) @ X80))) & ! [X79 : term] : (($true = ((X75 @ id @ (X78 @ id @ X79) @ id))) | ($true != ((X75 @ id @ X79 @ id)))) & (((X75 @ id @ (lam @ (X78 @ sh @ one)) @ id)) != $true)) | ($true = ((X75 @ id @ (lam @ X76) @ id))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f14,definition,(
% 1.42/0.51 ! [X294 : (subst > term > subst > $o)] : (($true = ((sP1 @ X294))) <=> ? [X297 : (subst > term > term)] : (! [X300 : term,X301 : subst,X299 : subst] : (((sub @ (X297 @ X301 @ X300) @ X299)) = ((X297 @ (comp @ X301 @ X299) @ (sub @ X300 @ X299)))) & ($true != ((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id))) & ! [X298 : term] : ((((X294 @ id @ (X297 @ id @ X298) @ id)) = $true) | ($true != ((X294 @ id @ X298 @ id))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f15,definition,(
% 1.42/0.51 ! [X437 : (subst > term > subst > $o)] : (($true = ((sP2 @ X437))) <=> ? [X448 : (subst > term > term)] : (! [X449 : subst,X451 : term,X450 : subst] : (((sub @ (X448 @ X449 @ X451) @ X450)) = ((X448 @ (comp @ X449 @ X450) @ (sub @ X451 @ X450)))) & ($true != ((X437 @ id @ (lam @ (X448 @ sh @ one)) @ id))) & ! [X452 : term] : (($true = ((X437 @ id @ (X448 @ id @ X452) @ id))) | ($true != ((X437 @ id @ X452 @ id))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f16,definition,(
% 1.42/0.51 ($true = sP3) <=> ! [X438 : term,X437 : (subst > term > subst > $o)] : (($true = ((sP2 @ X437))) | ? [X443 : term] : ((((X437 @ id @ (sub @ X438 @ (push @ X443 @ id)) @ id)) != $true) & (((X437 @ id @ X443 @ id)) = $true)) | ? [X442 : term,X441 : subst,X439 : subst,X440 : subst] : (($true = ((X437 @ X441 @ X442 @ (comp @ X440 @ X439)))) & ($true != ((X437 @ (comp @ X441 @ X440) @ (sub @ X442 @ X440) @ X439)))) | ? [X447 : subst,X444 : term,X445 : subst,X446 : subst] : (($true = ((X437 @ (comp @ X447 @ X445) @ (sub @ X444 @ X445) @ X446))) & ($true != ((X437 @ X447 @ X444 @ (comp @ X445 @ X446))))) | ($true = ((X437 @ id @ (lam @ X438) @ id))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f17,definition,(
% 1.42/0.51 ! [X522 : (subst > term > subst > $o)] : (($true = ((sP4 @ X522))) <=> ? [X524 : (subst > term > term)] : (($true != ((X522 @ id @ (lam @ (X524 @ sh @ one)) @ id))) & ! [X525 : term] : (($true != ((X522 @ id @ X525 @ id))) | ($true = ((X522 @ id @ (X524 @ id @ X525) @ id)))) & ! [X528 : subst,X527 : term,X526 : subst] : (((sub @ (X524 @ X526 @ X527) @ X528)) = ((X524 @ (comp @ X526 @ X528) @ (sub @ X527 @ X528))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f18,definition,(
% 1.42/0.51 ! [X522 : (subst > term > subst > $o)] : (($true = ((sP5 @ X522))) <=> ? [X539 : term,X538 : term] : ((((X522 @ id @ (ap @ (sub @ X539 @ id) @ X538) @ id)) != $true) & ($true = ((X522 @ id @ X539 @ id))) & ($true = ((X522 @ id @ X538 @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f19,definition,(
% 1.42/0.51 (sP6 = $true) <=> ! [X523 : term,X522 : (subst > term > subst > $o)] : (? [X533 : term] : (($true = ((var @ (sub @ X533 @ id)))) & (((X522 @ id @ X533 @ id)) != $true)) | ? [X535 : subst,X537 : subst,X534 : term,X536 : subst] : (($true = ((X522 @ X535 @ X534 @ (comp @ X536 @ X537)))) & ($true != ((X522 @ (comp @ X535 @ X536) @ (sub @ X534 @ X536) @ X537)))) | ($true = ((sP5 @ X522))) | ? [X529 : subst,X530 : subst,X532 : subst,X531 : term] : (($true != ((X522 @ X532 @ X531 @ (comp @ X529 @ X530)))) & ($true = ((X522 @ (comp @ X532 @ X529) @ (sub @ X531 @ X529) @ X530)))) | ($true = ((X522 @ id @ X523 @ id))) | ($true = ((sP4 @ X522))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f20,definition,(
% 1.42/0.51 (sP7 = $true) <=> ! [X274 : (term > $o),X273 : term,X272 : (subst > term > subst > $o)] : (($true = ((X274 @ (lam @ X273)))) | ? [X275 : term] : (($true != ((X274 @ (sub @ X273 @ (push @ X275 @ id))))) & (((X274 @ X275)) = $true)) | ? [X276 : (subst > term > term)] : (! [X277 : term] : ((((X272 @ id @ X277 @ id)) != $true) | (((X272 @ id @ (X276 @ id @ X277) @ id)) = $true)) & ! [X279 : term,X280 : subst,X278 : subst] : (((sub @ (X276 @ X278 @ X279) @ X280)) = ((X276 @ (comp @ X278 @ X280) @ (sub @ X279 @ X280)))) & ($true != ((X272 @ id @ (lam @ (X276 @ sh @ one)) @ id)))) | ? [X281 : term] : (((X274 @ X281)) != ((X272 @ id @ X281 @ id))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f21,definition,(
% 1.42/0.51 (sP8 = $true) <=> ? [X504 : (subst > term > subst > $o),X503 : term] : (($true != ((X504 @ id @ (lam @ (sub @ X503 @ (push @ one @ sh))) @ id))) & ! [X505 : (subst > term > term)] : (? [X506 : term] : (($true != ((X504 @ id @ (X505 @ id @ X506) @ id))) & (((X504 @ id @ X506 @ id)) = $true)) | ? [X507 : term,X508 : subst,X509 : subst] : (((sub @ (X505 @ X508 @ X507) @ X509)) != ((X505 @ (comp @ X508 @ X509) @ (sub @ X507 @ X509)))) | ($true = ((X504 @ id @ (lam @ (X505 @ sh @ one)) @ id)))) & ! [X510 : term] : ((((X504 @ id @ X510 @ id)) != $true) | ($true = ((X504 @ id @ (sub @ X503 @ (push @ X510 @ id)) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f22,definition,(
% 1.42/0.51 (sP9 = $true) <=> (? [X502 : term] : (((sub @ X502 @ id)) != X502) | (sP8 = $true) | ! [X511 : term,X512 : (subst > term > subst > $o)] : (? [X513 : term] : ((((X512 @ id @ (sub @ X511 @ (push @ X513 @ id)) @ id)) != $true) & ($true = ((X512 @ id @ X513 @ id)))) | ? [X514 : (subst > term > term)] : (($true != ((X512 @ id @ (lam @ (X514 @ sh @ one)) @ id))) & ! [X516 : term,X518 : subst,X517 : subst] : (((X514 @ (comp @ X517 @ X518) @ (sub @ X516 @ X518))) = ((sub @ (X514 @ X517 @ X516) @ X518))) & ! [X515 : term] : (($true = ((X512 @ id @ (X514 @ id @ X515) @ id))) | (((X512 @ id @ X515 @ id)) != $true))) | ($true = ((X512 @ id @ (lam @ X511) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f23,definition,(
% 1.42/0.51 ! [X140 : (subst > term > subst > $o)] : (($true = ((sP10 @ X140))) <=> ? [X144 : (subst > term > term)] : (! [X147 : subst,X145 : term,X146 : subst] : (((sub @ (X144 @ X146 @ X145) @ X147)) = ((X144 @ (comp @ X146 @ X147) @ (sub @ X145 @ X147)))) & ! [X148 : term] : (($true = ((X140 @ id @ (X144 @ id @ X148) @ id))) | (((X140 @ id @ X148 @ id)) != $true)) & ($true != ((X140 @ id @ (lam @ (X144 @ sh @ one)) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f24,definition,(
% 1.42/0.51 ! [X140 : (subst > term > subst > $o)] : (($true = ((sP11 @ X140))) <=> ? [X141 : term,X142 : term] : ((((X140 @ id @ (ap @ (sub @ X141 @ id) @ X142) @ id)) != $true) & ($true = ((X140 @ id @ X141 @ id))) & ($true = ((X140 @ id @ X142 @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f25,definition,(
% 1.42/0.51 ! [X123 : (subst > term > subst > $o)] : ((((sP12 @ X123)) = $true) <=> ! [X125 : (subst > term > term)] : (? [X128 : term,X127 : subst,X126 : subst] : (((X125 @ (comp @ X126 @ X127) @ (sub @ X128 @ X127))) != ((sub @ (X125 @ X126 @ X128) @ X127))) | ? [X129 : term] : (($true = ((X123 @ id @ X129 @ id))) & ($true != ((X123 @ id @ (X125 @ id @ X129) @ id)))) | (((X123 @ id @ (lam @ (X125 @ sh @ one)) @ id)) = $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f26,definition,(
% 1.42/0.51 ! [X112 : (subst > term > subst > $o)] : (($true = ((sP13 @ X112))) <=> ! [X114 : term,X113 : term] : (($true != ((X112 @ id @ X113 @ id))) | (((X112 @ id @ X114 @ id)) != $true) | ($true = ((X112 @ id @ (ap @ (sub @ X114 @ id) @ X113) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f27,definition,(
% 1.42/0.51 ! [X103 : (term > $o)] : (($true = ((sP14 @ X103))) <=> ! [X106 : term,X105 : term] : (($true != ((X103 @ X106))) | ($true != ((X103 @ X105))) | ($true = ((X103 @ (ap @ X105 @ X106))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f28,definition,(
% 1.42/0.51 ($true = sP15) <=> ? [X123 : (subst > term > subst > $o),X124 : term] : (! [X136 : subst,X134 : subst,X135 : subst,X137 : term] : (($true != ((X123 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135) @ X134))) | ($true = ((X123 @ X136 @ X137 @ (comp @ X135 @ X134))))) & ! [X138 : term] : (($true = ((X123 @ id @ (sub @ X124 @ (push @ X138 @ id)) @ id))) | (((X123 @ id @ X138 @ id)) != $true)) & (((X123 @ id @ (lam @ X124) @ id)) != $true) & (((sP12 @ X123)) = $true) & ! [X132 : subst,X133 : subst,X131 : term,X130 : subst] : (($true = ((X123 @ (comp @ X130 @ X132) @ (sub @ X131 @ X132) @ X133))) | ($true != ((X123 @ X130 @ X131 @ (comp @ X132 @ X133))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f29,definition,(
% 1.42/0.51 ($true = sP16) <=> ! [X139 : term,X140 : (subst > term > subst > $o)] : (? [X143 : term] : (($true != ((X140 @ id @ X143 @ id))) & (((var @ (sub @ X143 @ id))) = $true)) | ($true = ((sP11 @ X140))) | (((X140 @ id @ X139 @ id)) = $true) | ($true = ((sP10 @ X140))) | ? [X150 : subst,X152 : term,X149 : subst,X151 : subst] : (($true != ((X140 @ (comp @ X150 @ X149) @ (sub @ X152 @ X149) @ X151))) & (((X140 @ X150 @ X152 @ (comp @ X149 @ X151))) = $true)) | ? [X154 : term,X156 : subst,X155 : subst,X153 : subst] : (($true = ((X140 @ (comp @ X155 @ X153) @ (sub @ X154 @ X153) @ X156))) & (((X140 @ X155 @ X154 @ (comp @ X153 @ X156))) != $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f30,definition,(
% 1.42/0.51 (sP17 = $true) <=> ? [X112 : (subst > term > subst > $o),X111 : term,X110 : term] : (($true = ((X112 @ id @ X110 @ id))) & ! [X119 : term,X120 : subst,X122 : subst,X121 : subst] : (($true != ((X112 @ (comp @ X122 @ X120) @ (sub @ X119 @ X120) @ X121))) | ($true = ((X112 @ X122 @ X119 @ (comp @ X120 @ X121))))) & ($true != ((X112 @ id @ (ap @ X110 @ X111) @ id))) & ($true = ((sP13 @ X112))) & ! [X117 : subst,X118 : subst,X116 : term,X115 : subst] : ((((X112 @ X117 @ X116 @ (comp @ X118 @ X115))) != $true) | (((X112 @ (comp @ X117 @ X118) @ (sub @ X116 @ X118) @ X115)) = $true)) & (((X112 @ id @ X111 @ id)) = $true))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f31,definition,(
% 1.42/0.51 ($true = sP18) <=> (? [X104 : term,X103 : (term > $o)] : (($true = ((sP14 @ X103))) & ! [X107 : term] : (($true != ((var @ X107))) | ($true = ((X103 @ X107)))) & ! [X108 : term] : (? [X109 : term] : (($true != ((X103 @ (sub @ X108 @ (push @ X109 @ id))))) & ($true = ((X103 @ X109)))) | ($true = ((X103 @ (lam @ X108))))) & (((X103 @ X104)) != $true)) | (sP17 = $true) | ($true = sP15) | ($true = sP16))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f32,definition,(
% 1.42/0.51 ($true = sP19) <=> ! [X417 : term,X418 : (subst > term > subst > $o)] : (($true = ((X418 @ id @ (lam @ (sub @ X417 @ (push @ one @ sh))) @ id))) | ? [X428 : term] : (($true = ((X418 @ id @ X428 @ id))) & ($true != ((X418 @ id @ (sub @ X417 @ (push @ X428 @ id)) @ id)))) | ? [X420 : (subst > term > term),X419 : term] : (! [X426 : subst,X425 : subst,X424 : term] : (((X420 @ (comp @ X425 @ X426) @ (sub @ X424 @ X426))) = ((sub @ X419 @ (push @ (sub @ X424 @ X426) @ (comp @ X425 @ X426))))) & ! [X423 : term,X422 : subst,X421 : subst] : (((sub @ (sub @ X419 @ (push @ X423 @ X421)) @ X422)) = ((sub @ (X420 @ X421 @ X423) @ X422))) & ! [X427 : term] : (($true != ((X418 @ id @ X427 @ id))) | (((X418 @ id @ (X420 @ id @ X427) @ id)) = $true)) & ($true != ((X418 @ id @ (lam @ (X420 @ sh @ one)) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f33,definition,(
% 1.42/0.51 ! [X176 : (term > $o)] : (($true = ((sP20 @ X176))) <=> ! [X180 : term,X181 : term] : (($true != ((X176 @ X180))) | ($true = ((X176 @ (ap @ X180 @ X181)))) | ($true != ((X176 @ X181)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f34,definition,(
% 1.42/0.51 ! [X195 : (subst > term > subst > $o)] : ((((sP21 @ X195)) = $true) <=> ? [X197 : term,X196 : term] : ((((X195 @ id @ (ap @ (sub @ X197 @ id) @ X196) @ id)) != $true) & (((X195 @ id @ X197 @ id)) = $true) & (((X195 @ id @ X196 @ id)) = $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f35,definition,(
% 1.42/0.51 (sP22 = $true) <=> ? [X184 : (term > $o),X185 : term,X186 : (subst > term > subst > $o)] : ((((X184 @ (lam @ X185))) != $true) & ! [X188 : term] : (($true = ((X184 @ (sub @ X185 @ (push @ X188 @ id))))) | (((X184 @ X188)) != $true)) & ! [X189 : (subst > term > term)] : (? [X190 : subst,X192 : term,X191 : subst] : (((X189 @ (comp @ X190 @ X191) @ (sub @ X192 @ X191))) != ((sub @ (X189 @ X190 @ X192) @ X191))) | ? [X193 : term] : ((((X186 @ id @ (X189 @ id @ X193) @ id)) != $true) & ($true = ((X186 @ id @ X193 @ id)))) | (((X186 @ id @ (lam @ (X189 @ sh @ one)) @ id)) = $true)) & ! [X187 : term] : (((X186 @ id @ X187 @ id)) = ((X184 @ X187))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f36,definition,(
% 1.42/0.51 ($true = sP23) <=> ? [X177 : term,X176 : (term > $o)] : (($true = ((sP20 @ X176))) & ! [X178 : term] : ((((X176 @ (lam @ X178))) = $true) | ? [X179 : term] : (($true = ((X176 @ X179))) & ($true != ((X176 @ (sub @ X178 @ (push @ X179 @ id))))))) & ! [X182 : term] : (($true = ((X176 @ X182))) | ($true != ((var @ X182)))) & ($true != ((X176 @ X177))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f37,definition,(
% 1.42/0.51 ($true = sP24) <=> ((sP22 = $true) | ! [X195 : (subst > term > subst > $o),X194 : term] : (? [X198 : (subst > term > term)] : (! [X199 : term] : ((((X195 @ id @ (X198 @ id @ X199) @ id)) = $true) | (((X195 @ id @ X199 @ id)) != $true)) & ! [X202 : term,X201 : subst,X200 : subst] : (((sub @ (X198 @ X200 @ X202) @ X201)) = ((X198 @ (comp @ X200 @ X201) @ (sub @ X202 @ X201)))) & (((X195 @ id @ (lam @ (X198 @ sh @ one)) @ id)) != $true)) | (((sP21 @ X195)) = $true) | ($true = ((X195 @ id @ X194 @ id)))) | ? [X173 : (subst > term > subst > $o)] : ! [X174 : (term > $o)] : ? [X175 : term] : (((X174 @ X175)) != ((X173 @ id @ X175 @ id))) | ($true = sP23) | ? [X183 : term] : (((sub @ X183 @ id)) != X183))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f38,definition,(
% 1.42/0.51 ! [X166 : (term > $o)] : ((((sP25 @ X166)) = $true) <=> ? [X170 : term,X171 : term] : (($true = ((X166 @ X170))) & (((X166 @ (ap @ X171 @ X170))) != $true) & ($true = ((X166 @ X171)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f39,definition,(
% 1.42/0.51 ! [X158 : (term > $o)] : (($true = ((sP26 @ X158))) <=> ! [X164 : term,X163 : term] : ((((X158 @ (ap @ X164 @ X163))) = $true) | ($true != ((X158 @ X163))) | ($true != ((X158 @ X164)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f40,definition,(
% 1.42/0.51 ($true = sP27) <=> ! [X166 : (term > $o),X167 : term] : (? [X168 : term] : (! [X169 : term] : ((((X166 @ (sub @ X168 @ (push @ X169 @ id)))) = $true) | ($true != ((X166 @ X169)))) & ($true != ((X166 @ (lam @ X168))))) | ? [X172 : term] : ((((X166 @ X172)) != $true) & (((var @ X172)) = $true)) | ($true = ((X166 @ X167))) | (((sP25 @ X166)) = $true))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f41,definition,(
% 1.42/0.51 ($true = sP28) <=> (? [X160 : term,X159 : subst,X158 : (term > $o)] : (($true != ((X158 @ (sub @ X160 @ X159)))) & ($true = ((sP26 @ X158))) & ! [X165 : term] : (($true != ((var @ X165))) | ($true = ((X158 @ (sub @ X165 @ X159))))) & ! [X161 : term] : (($true = ((X158 @ (lam @ X161)))) | ? [X162 : term] : (($true = ((X158 @ X162))) & (((X158 @ (sub @ X161 @ (push @ X162 @ id)))) != $true)))) | ? [X157 : term] : (((sub @ X157 @ id)) != X157) | ($true = sP27))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f42,definition,(
% 1.42/0.51 ($true = sP29) <=> ! [X409 : term,X410 : (subst > term > subst > $o)] : (? [X411 : term] : (($true != ((X410 @ id @ (sub @ X409 @ (push @ X411 @ id)) @ id))) & (((X410 @ id @ X411 @ id)) = $true)) | ($true = ((X410 @ id @ (lam @ (sub @ X409 @ (push @ one @ sh))) @ id))) | ? [X412 : (subst > term > term)] : (($true != ((X410 @ id @ (lam @ (X412 @ sh @ one)) @ id))) & ! [X413 : term] : (($true = ((X410 @ id @ (X412 @ id @ X413) @ id))) | ($true != ((X410 @ id @ X413 @ id)))) & ! [X414 : term,X416 : subst,X415 : subst] : (((sub @ (X412 @ X416 @ X414) @ X415)) = ((X412 @ (comp @ X416 @ X415) @ (sub @ X414 @ X415))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f43,definition,(
% 1.42/0.51 ! [X212 : (subst > term > subst > $o)] : (($true = ((sP30 @ X212))) <=> ? [X222 : term,X223 : term] : (($true = ((X212 @ id @ X223 @ id))) & ($true = ((X212 @ id @ X222 @ id))) & (((X212 @ id @ (ap @ (sub @ X223 @ id) @ X222) @ id)) != $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f44,definition,(
% 1.42/0.51 ($true = sP31) <=> ! [X212 : (subst > term > subst > $o),X211 : term,X213 : term] : (($true != ((X212 @ id @ X213 @ id))) | ($true != ((X212 @ id @ X211 @ id))) | ? [X220 : subst,X219 : subst,X221 : term,X218 : subst] : (($true = ((X212 @ X220 @ X221 @ (comp @ X219 @ X218)))) & ($true != ((X212 @ (comp @ X220 @ X219) @ (sub @ X221 @ X219) @ X218)))) | ($true = ((sP30 @ X212))) | ($true = ((X212 @ id @ (ap @ X213 @ X211) @ id))) | ? [X214 : subst,X217 : subst,X215 : subst,X216 : term] : ((((X212 @ (comp @ X215 @ X214) @ (sub @ X216 @ X214) @ X217)) = $true) & ($true != ((X212 @ X215 @ X216 @ (comp @ X214 @ X217))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f45,definition,(
% 1.42/0.51 ! [X482 : (subst > term > subst > $o)] : ((((sP32 @ X482)) = $true) <=> ? [X493 : (subst > term > term)] : (($true != ((X482 @ id @ (lam @ (X493 @ sh @ one)) @ id))) & ! [X497 : term] : (($true != ((X482 @ id @ X497 @ id))) | ($true = ((X482 @ id @ (X493 @ id @ X497) @ id)))) & ! [X496 : term,X495 : subst,X494 : subst] : (((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495))) = ((sub @ (X493 @ X494 @ X496) @ X495)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f46,definition,(
% 1.42/0.51 (sP33 = $true) <=> (! [X480 : term,X482 : (subst > term > subst > $o),X481 : (term > $o)] : (? [X488 : term] : (((X482 @ id @ X488 @ id)) != ((X481 @ X488))) | ? [X484 : subst,X485 : subst,X486 : subst,X487 : term] : (($true != ((X482 @ (comp @ X484 @ X485) @ (sub @ X487 @ X485) @ X486))) & ($true = ((X482 @ X484 @ X487 @ (comp @ X485 @ X486))))) | (((sP32 @ X482)) = $true) | ? [X492 : subst,X491 : term,X489 : subst,X490 : subst] : ((((X482 @ (comp @ X489 @ X492) @ (sub @ X491 @ X492) @ X490)) = $true) & (((X482 @ X489 @ X491 @ (comp @ X492 @ X490))) != $true)) | ($true = ((X481 @ (lam @ X480)))) | ? [X483 : term] : ((((X481 @ X483)) = $true) & ($true != ((X481 @ (sub @ X480 @ (push @ X483 @ id))))))) | ? [X479 : term] : (((sub @ X479 @ id)) != X479))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f47,definition,(
% 1.42/0.51 ($true = sP34) <=> ! [X356 : term,X357 : (subst > term > subst > $o)] : (? [X358 : (subst > term > term)] : (! [X362 : term] : (($true != ((X357 @ id @ X362 @ id))) | ($true = ((X357 @ id @ (X358 @ id @ X362) @ id)))) & (((X357 @ id @ (lam @ (X358 @ sh @ one)) @ id)) != $true) & ! [X361 : subst,X359 : subst,X360 : term] : (((X358 @ (comp @ X361 @ X359) @ (sub @ X360 @ X359))) = ((sub @ (X358 @ X361 @ X360) @ X359)))) | ($true = ((X357 @ id @ (lam @ (sub @ X356 @ (push @ one @ sh))) @ id))) | ? [X363 : term] : ((((X357 @ id @ X363 @ id)) = $true) & ($true != ((X357 @ id @ (sub @ X356 @ (push @ X363 @ id)) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f48,definition,(
% 1.42/0.51 ! [X241 : (term > $o)] : ((((sP35 @ X241)) = $true) <=> ? [X245 : term,X246 : term] : (($true = ((X241 @ X245))) & (((X241 @ (ap @ X245 @ X246))) != $true) & ($true = ((X241 @ X246)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f49,definition,(
% 1.42/0.51 ($true = sP36) <=> ! [X239 : term,X241 : (term > $o),X240 : subst] : (($true = ((X241 @ (sub @ X239 @ X240)))) | (((sP35 @ X241)) = $true) | ? [X242 : term] : (($true != ((X241 @ (sub @ X242 @ X240)))) & ($true = ((var @ X242)))) | ? [X243 : term] : (($true != ((X241 @ (lam @ X243)))) & ! [X244 : term] : (($true != ((X241 @ X244))) | ($true = ((X241 @ (sub @ X243 @ (push @ X244 @ id))))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f50,definition,(
% 1.42/0.51 ! [X254 : (subst > term > subst > $o)] : (($true = ((sP37 @ X254))) <=> ? [X267 : (subst > term > term)] : (! [X270 : subst,X271 : subst,X269 : term] : (((X267 @ (comp @ X271 @ X270) @ (sub @ X269 @ X270))) = ((sub @ (X267 @ X271 @ X269) @ X270))) & ! [X268 : term] : (($true = ((X254 @ id @ (X267 @ id @ X268) @ id))) | ($true != ((X254 @ id @ X268 @ id)))) & (((X254 @ id @ (lam @ (X267 @ sh @ one)) @ id)) != $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f51,definition,(
% 1.42/0.51 (sP38 = $true) <=> ! [X254 : (subst > term > subst > $o),X256 : (term > $o),X255 : term] : (? [X258 : term,X257 : subst,X259 : subst,X260 : subst] : (($true = ((X254 @ X257 @ X258 @ (comp @ X259 @ X260)))) & ($true != ((X254 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259) @ X260)))) | ($true = ((sP37 @ X254))) | ? [X261 : term] : (((X254 @ id @ X261 @ id)) != ((X256 @ X261))) | ? [X266 : term] : (($true = ((X256 @ X266))) & (((X256 @ (sub @ X255 @ (push @ X266 @ id)))) != $true)) | (((X256 @ (lam @ X255))) = $true) | ? [X265 : subst,X264 : term,X263 : subst,X262 : subst] : (($true = ((X254 @ (comp @ X265 @ X262) @ (sub @ X264 @ X262) @ X263))) & (((X254 @ X265 @ X264 @ (comp @ X262 @ X263))) != $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f52,definition,(
% 1.42/0.51 ! [X205 : (term > $o)] : (($true = ((sP39 @ X205))) <=> ? [X208 : term,X209 : term] : (($true != ((X205 @ (ap @ X209 @ X208)))) & ($true = ((X205 @ X209))) & ($true = ((X205 @ X208)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f53,definition,(
% 1.42/0.51 ! [X30 : (subst > term > subst > $o)] : (($true = ((sP40 @ X30))) <=> ? [X35 : (subst > term > term)] : ((((X30 @ id @ (lam @ (X35 @ sh @ one)) @ id)) != $true) & ! [X38 : subst,X37 : term,X39 : subst] : (((sub @ (X35 @ X39 @ X37) @ X38)) = ((X35 @ (comp @ X39 @ X38) @ (sub @ X37 @ X38)))) & ! [X36 : term] : (($true = ((X30 @ id @ (X35 @ id @ X36) @ id))) | ($true != ((X30 @ id @ X36 @ id))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f54,definition,(
% 1.42/0.51 (sP41 = $true) <=> ? [X22 : (subst > term > subst > $o),X21 : term] : ((((X22 @ id @ (lam @ (sub @ X21 @ (push @ one @ sh))) @ id)) != $true) & ! [X23 : term] : (($true != ((X22 @ id @ X23 @ id))) | ($true = ((X22 @ id @ (sub @ X21 @ (push @ X23 @ id)) @ id)))) & ! [X24 : (subst > term > term)] : (? [X27 : subst,X25 : term,X26 : subst] : (((sub @ (X24 @ X26 @ X25) @ X27)) != ((X24 @ (comp @ X26 @ X27) @ (sub @ X25 @ X27)))) | ? [X28 : term] : (($true = ((X22 @ id @ X28 @ id))) & (((X22 @ id @ (X24 @ id @ X28) @ id)) != $true)) | (((X22 @ id @ (lam @ (X24 @ sh @ one)) @ id)) = $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f55,definition,(
% 1.42/0.51 (sP42 = $true) <=> ((sP41 = $true) | ? [X20 : term] : (((sub @ X20 @ id)) != X20) | ! [X30 : (subst > term > subst > $o),X29 : term] : (? [X32 : subst,X31 : term,X34 : subst,X33 : subst] : (($true = ((X30 @ (comp @ X32 @ X33) @ (sub @ X31 @ X33) @ X34))) & (((X30 @ X32 @ X31 @ (comp @ X33 @ X34))) != $true)) | ? [X40 : term] : (($true = ((X30 @ id @ X40 @ id))) & (((X30 @ id @ (sub @ X29 @ (push @ X40 @ id)) @ id)) != $true)) | ? [X44 : subst,X43 : term,X41 : subst,X42 : subst] : (($true != ((X30 @ (comp @ X42 @ X44) @ (sub @ X43 @ X44) @ X41))) & ($true = ((X30 @ X42 @ X43 @ (comp @ X44 @ X41))))) | ($true = ((sP40 @ X30))) | (((X30 @ id @ (lam @ X29) @ id)) = $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f56,definition,(
% 1.42/0.51 ! [X369 : (term > $o)] : (($true = ((sP43 @ X369))) <=> ! [X375 : term,X374 : term] : (($true = ((X369 @ (ap @ X375 @ X374)))) | ($true != ((X369 @ X374))) | ($true != ((X369 @ X375)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f57,definition,(
% 1.42/0.51 ! [X387 : (subst > term > subst > $o)] : (($true = ((sP44 @ X387))) <=> ? [X390 : term,X391 : term] : (($true = ((X387 @ id @ X390 @ id))) & ($true = ((X387 @ id @ X391 @ id))) & ($true != ((X387 @ id @ (ap @ (sub @ X391 @ id) @ X390) @ id)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f58,definition,(
% 1.42/0.51 ! [X387 : (subst > term > subst > $o)] : ((((sP45 @ X387)) = $true) <=> ? [X400 : (subst > term > term)] : ((((X387 @ id @ (lam @ (X400 @ sh @ one)) @ id)) != $true) & ! [X404 : term] : ((((X387 @ id @ (X400 @ id @ X404) @ id)) = $true) | ($true != ((X387 @ id @ X404 @ id)))) & ! [X401 : subst,X402 : term,X403 : subst] : (((X400 @ (comp @ X401 @ X403) @ (sub @ X402 @ X403))) = ((sub @ (X400 @ X401 @ X402) @ X403)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f59,definition,(
% 1.42/0.51 ($true = sP46) <=> ? [X379 : (term > $o),X377 : (subst > term > subst > $o),X378 : term] : (! [X381 : term] : (($true = ((X379 @ (sub @ X378 @ (push @ X381 @ id))))) | ($true != ((X379 @ X381)))) & ! [X382 : (subst > term > term)] : ((((X377 @ id @ (lam @ (X382 @ sh @ one)) @ id)) = $true) | ? [X385 : subst,X383 : subst,X384 : term] : (((sub @ (X382 @ X385 @ X384) @ X383)) != ((X382 @ (comp @ X385 @ X383) @ (sub @ X384 @ X383)))) | ? [X386 : term] : (($true = ((X377 @ id @ X386 @ id))) & ($true != ((X377 @ id @ (X382 @ id @ X386) @ id))))) & ($true != ((X379 @ (lam @ X378)))) & ! [X380 : term] : (((X377 @ id @ X380 @ id)) = ((X379 @ X380))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f60,definition,(
% 1.42/0.51 (sP47 = $true) <=> ! [X388 : term,X387 : (subst > term > subst > $o)] : ((((sP45 @ X387)) = $true) | (((X387 @ id @ X388 @ id)) = $true) | ($true = ((sP44 @ X387))) | ? [X393 : subst,X394 : subst,X395 : term,X392 : subst] : ((((X387 @ X393 @ X395 @ (comp @ X394 @ X392))) = $true) & ($true != ((X387 @ (comp @ X393 @ X394) @ (sub @ X395 @ X394) @ X392)))) | ? [X396 : subst,X397 : subst,X398 : subst,X399 : term] : ((((X387 @ X396 @ X399 @ (comp @ X398 @ X397))) != $true) & (((X387 @ (comp @ X396 @ X398) @ (sub @ X399 @ X398) @ X397)) = $true)) | ? [X389 : term] : (($true != ((X387 @ id @ X389 @ id))) & ($true = ((var @ (sub @ X389 @ id))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f61,definition,(
% 1.42/0.51 (sP48 = $true) <=> (? [X376 : term] : (((sub @ X376 @ id)) != X376) | (sP47 = $true) | ($true = sP46) | ? [X370 : term,X369 : (term > $o)] : (! [X371 : term] : (? [X372 : term] : (($true = ((X369 @ X372))) & ($true != ((X369 @ (sub @ X371 @ (push @ X372 @ id)))))) | (((X369 @ (lam @ X371))) = $true)) & ($true = ((sP43 @ X369))) & ! [X373 : term] : (($true != ((var @ X373))) | (((X369 @ X373)) = $true)) & (((X369 @ X370)) != $true)) | ? [X366 : (subst > term > subst > $o)] : ! [X367 : (term > $o)] : ? [X368 : term] : (((X366 @ id @ X368 @ id)) != ((X367 @ X368))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f62,definition,(
% 1.42/0.51 ($true = sP49) <=> (! [X10 : term,X11 : (subst > term > subst > $o),X12 : (term > $o)] : (? [X15 : (subst > term > term)] : (! [X16 : term] : (($true = ((X11 @ id @ (X15 @ id @ X16) @ id))) | (((X11 @ id @ X16 @ id)) != $true)) & ! [X17 : term,X19 : subst,X18 : subst] : (((X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) = ((sub @ (X15 @ X19 @ X17) @ X18))) & ($true != ((X11 @ id @ (lam @ (X15 @ sh @ one)) @ id)))) | ? [X14 : term] : ((((X12 @ X14)) = $true) & (((X12 @ (sub @ X10 @ (push @ X14 @ id)))) != $true)) | ($true = ((X12 @ (lam @ X10)))) | ? [X13 : term] : (((X11 @ id @ X13 @ id)) != ((X12 @ X13)))) | ? [X5 : term] : ! [X6 : (subst > term > term)] : ? [X7 : term,X8 : subst] : (((sub @ X5 @ (push @ X7 @ X8))) != ((X6 @ X8 @ X7))) | ? [X9 : term] : (((sub @ X9 @ id)) != X9))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f63,definition,(
% 1.42/0.51 ($true = sP50) <=> (? [X465 : subst,X466 : term] : (((comp @ sh @ (push @ X466 @ X465))) != X465) | ? [X468 : term,X467 : term] : ((X467 != X468) & (((lam @ X468)) = ((lam @ X467)))) | ? [X464 : term,X463 : subst] : (((sub @ one @ (push @ X464 @ X463))) != X464) | ! [X472 : (subst > term > term),X471 : term,X470 : (subst > term > term),X469 : subst] : (? [X478 : subst,X477 : subst,X476 : term] : (((X472 @ (comp @ X477 @ X478) @ (sub @ X476 @ X478))) != ((sub @ (X472 @ X477 @ X476) @ X478))) | (((X472 @ X469 @ X471)) = ((X470 @ X469 @ X471))) | ? [X475 : term,X474 : subst,X473 : subst] : (((X470 @ (comp @ X473 @ X474) @ (sub @ X475 @ X474))) != ((sub @ (X470 @ X473 @ X475) @ X474))) | (((lam @ (X470 @ sh @ one))) != ((lam @ (X472 @ sh @ one))))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f64,definition,(
% 1.42/0.51 ! [X338 : (term > $o)] : (($true = ((sP51 @ X338))) <=> ! [X340 : term,X339 : term] : ((((X338 @ X339)) != $true) | ($true = ((X338 @ (ap @ X340 @ X339)))) | ($true != ((X338 @ X340)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f65,definition,(
% 1.42/0.51 ! [X343 : (term > $o)] : ((((sP52 @ X343)) = $true) <=> ? [X346 : term,X347 : term] : (($true = ((X343 @ X346))) & (((X343 @ (ap @ X347 @ X346))) != $true) & ($true = ((X343 @ X347)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f66,definition,(
% 1.42/0.51 ($true = sP53) <=> ! [X344 : term,X345 : subst,X343 : (term > $o)] : (? [X350 : term] : (($true != ((X343 @ (sub @ X350 @ X345)))) & ($true = ((var @ X350)))) | ($true = ((X343 @ (sub @ X344 @ X345)))) | ? [X348 : term] : (($true != ((X343 @ (lam @ X348)))) & ! [X349 : term] : (($true = ((X343 @ (sub @ X348 @ (push @ X349 @ id))))) | ($true != ((X343 @ X349))))) | (((sP52 @ X343)) = $true))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f67,definition,(
% 1.42/0.51 ($true = sP54) <=> (? [X336 : subst] : (((comp @ X336 @ id)) != X336) | ($true = sP53) | ? [X332 : term,X333 : subst] : (((sub @ one @ (push @ X332 @ X333))) != X332) | ? [X335 : subst,X334 : term] : (((comp @ sh @ (push @ X334 @ X335))) != X335) | ? [X338 : (term > $o),X337 : term] : (! [X342 : term] : (($true != ((var @ X342))) | ($true = ((X338 @ X342)))) & ! [X341 : term] : ((((X338 @ X341)) != $true) | (((X338 @ (lam @ X341))) = $true)) & ($true = ((sP51 @ X338))) & ($true != ((X338 @ X337)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f68,definition,(
% 1.42/0.51 ! [X247 : (term > $o)] : (($true = ((sP55 @ X247))) <=> ? [X253 : term,X252 : term] : ((((X247 @ X252)) = $true) & ($true != ((X247 @ (ap @ X252 @ X253)))) & ($true = ((X247 @ X253)))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f69,definition,(
% 1.42/0.51 ($true = sP56) <=> ! [X247 : (term > $o),X248 : term] : (? [X250 : term] : (! [X251 : term] : (($true != ((X247 @ X251))) | ($true = ((X247 @ (sub @ X250 @ (push @ X251 @ id)))))) & ($true != ((X247 @ (lam @ X250))))) | ? [X249 : term] : ((((X247 @ X249)) != $true) & (((var @ X249)) = $true)) | ($true = ((sP55 @ X247))) | ($true = ((X247 @ X248))))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f70,definition,(
% 1.42/0.51 ! [X54 : (subst > term > subst > $o)] : (($true = ((sP57 @ X54))) <=> ? [X60 : term,X59 : term] : (($true = ((X54 @ id @ X60 @ id))) & ($true != ((X54 @ id @ (ap @ (sub @ X59 @ id) @ X60) @ id))) & (((X54 @ id @ X59 @ id)) = $true)))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f71,definition,(
% 1.42/0.51 (sP58 = $true) <=> ! [X57 : term,X56 : term,X54 : (subst > term > subst > $o),X55 : (term > $o)] : (($true != ((X55 @ X56))) | ? [X58 : term] : (((X55 @ X58)) != ((X54 @ id @ X58 @ id))) | ? [X63 : subst,X62 : subst,X61 : subst,X64 : term] : (($true != ((X54 @ (comp @ X63 @ X61) @ (sub @ X64 @ X61) @ X62))) & (((X54 @ X63 @ X64 @ (comp @ X61 @ X62))) = $true)) | ($true = ((X55 @ (ap @ X57 @ X56)))) | ? [X68 : subst,X67 : subst,X66 : subst,X65 : term] : (($true != ((X54 @ X67 @ X65 @ (comp @ X68 @ X66)))) & ($true = ((X54 @ (comp @ X67 @ X68) @ (sub @ X65 @ X68) @ X66)))) | ($true = ((sP57 @ X54))) | (((X55 @ X57)) != $true))),
% 1.42/0.51 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.42/0.51 thf(f72,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((sP58 = $true) <=> (hoasinduction_lem2v2 = $true)) & ((termmset = $true) <=> ! [X0 : term] : (((sub @ X0 @ id)) = X0)) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2_lthm = $true) <=> (? [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) != X84) | ! [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true = ((X87 @ one))) | ? [X89 : term] : (((X87 @ X89)) != ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true != ((X88 @ X85)))))) & (($true = sP56) <=> (induction2 = $true)) & ((apinj1 = $true) <=> ! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70))) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & ((induction2lem_lthm = $true) <=> ($true = sP54)) & ((termmset_lthm = $true) <=> (! [X454 : term] : (((sub @ X454 @ id)) = X454) | ? [X453 : term] : (((sub @ X453 @ id)) != X453))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) <=> ($true = sP50)) & (hoasinduction_lem3_gthm = $true) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) <=> (apinj2 = $true)) & (! [X288 : (term > $o),X289 : subst,X287 : term] : ? [X290 : (term > $o)] : ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))) <=> (pushprop_lem0 = $true)) & (hoasapnotvar_gthm = $true) & (! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) <=> (pushprop_lem1 = $true)) & (($true = sP49) <=> (hoasinduction_lem3v2a_lthm = $true)) & (! [X455 : term,X457 : term,X456 : (subst > term > term)] : (? [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) != ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) <=> (hoaslamnotap = $true)) & (apnotvar = $true) & ((substmonoid_lthm = $true) <=> ((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | ? [X1 : subst] : (((comp @ id @ X1)) != X1) | ? [X2 : subst] : (((comp @ X2 @ id)) != X2))) & (! [X230 : (subst > term > subst > $o)] : ? [X231 : (term > $o)] : ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232))) <=> (hoasinduction_lem0_lthm = $true)) & ((hoasinduction_lthm_3 = $true) <=> (sP48 = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (sP42 = $true)) & (hoaslaminj_gthm = $true) & (! [X206 : term,X205 : (term > $o)] : (? [X210 : term] : ((((X205 @ (lam @ X210))) != $true) & ($true = ((X205 @ X210)))) | ? [X207 : term] : ((((var @ X207)) = $true) & ($true != ((X205 @ X207)))) | ($true = ((sP39 @ X205))) | (((X205 @ X206)) = $true)) <=> (induction = $true)) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP38 = $true) <=> (hoasinduction_lem3v2 = $true)) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2lem = $true) <=> ($true = sP36)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X226 : term] : ? [X227 : (subst > term > term)] : ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229)))) & ((hoasapinj1 = $true) <=> ! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408))))) & ((axshiftcons = $true) <=> ! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X328 : term] : ? [X329 : (subst > term > term)] : ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) <=> (axvarid = $true)) & (hoasinduction_gthm = $true) & (($true = sP34) <=> (hoasinduction_lem3aa = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP33 = $true)) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (! [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (? [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) != ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ? [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) != ((sub @ (X320 @ X323 @ X321) @ X322)))) <=> (hoaslaminj = $true)) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) <=> (substmonoid = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((X204 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh))))) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (hoaslamnotvar = $true) & ! [X292 : d_subst] : (d_id = X292) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((laminj = $true) <=> ! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237))))) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & ((hoasinduction_lem2 = $true) <=> ($true = sP31)) & ((axidl = $true) <=> ! [X327 : subst] : (((comp @ id @ X327)) = X327)) & (($true = sP29) <=> (hoasinduction_lem3aa_lthm = $true)) & (($true = sP28) <=> (induction2_lthm = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ($true = sP24)) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP19)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) <=> (axidr = $true)) & (pushprop_gthm = $true) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) <=> (hoasapinj2 = $true)) & ! [X521 : d_term] : (d_one = X521) & ((axvarcons = $true) <=> ! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224)) & (($true = sP18) <=> (hoasinduction_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434)))) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 != X432) & (((ap @ X430 @ X431)) = ((ap @ X429 @ X432)))))) & ((axscons = $true) <=> ! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306)) & ((hoasinduction_lem3a_lthm = $true) <=> (sP9 = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X351 : (subst > term > subst > $o)] : ? [X352 : (term > $o)] : ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id)))) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2a = $true) <=> (sP7 = $true)) & (axclos = $true) & ((sP6 = $true) <=> (hoasinduction = $true)) & (! [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) = $true) | ? [X286 : term] : (((X284 @ X286)) != ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ($true != ((X283 @ X282)))) <=> (pushprop_lem1v2 = $true)) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) != ((d2subst @ X520))) | (X519 = X520)) & (termmset_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X101 : term] : ? [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) = ((X102 @ sh @ one)))) & (axabs = $true) & ! [X235 : d_term,X236 : d_term] : ((((d2term @ X236)) != ((d2term @ X235))) | (X235 = X236)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) <=> ($true = sP3)) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) <=> (shinj = $true)) & (pushprop = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ? [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) != $true) & ($true = ((X294 @ id @ X296 @ id))) & (((X294 @ id @ X295 @ id)) = $true)) | ($true = ((sP1 @ X294)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasapinj2_gthm = $true) & (($true = sP0) <=> (hoasinduction_lem3a = $true)) & ((? [X45 : term] : (((sub @ X45 @ id)) != X45) | ? [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 != X47) & (((ap @ X47 @ X48)) = ((ap @ X46 @ X49)))) | ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lthm = $true) & ((? [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) != X92) | ! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91)) <=> (pushprop_lem1_lthm = $true)) & (axassoc = $true) & (hoasapnotvar = $true) & (! [X314 : term,X313 : (term > $o),X312 : subst] : ? [X315 : (term > $o)] : ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) <=> (pushprop_lem0_lthm = $true))),
% 1.42/0.51 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])).
% 1.42/0.51 thf(f260,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((sP58 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP58 != $true))) & (((termmset = $true) | ? [X0 : term] : (((sub @ X0 @ id)) != X0)) & (! [X0 : term] : (((sub @ X0 @ id)) = X0) | (termmset != $true))) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & (((pushprop_lem1v2_lthm = $true) | (! [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) = X84) & ? [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true != ((X87 @ one))) & ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) & ($true = ((X88 @ X85)))))) & ((? [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) != X84) | ! [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true = ((X87 @ one))) | ? [X89 : term] : (((X87 @ X89)) != ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true != ((X88 @ X85))))) | (pushprop_lem1v2_lthm != $true))) & ((($true = sP56) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP56))) & (((apinj1 = $true) | ? [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) = ((ap @ X69 @ X72))) & (X69 != X70))) & (! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70)) | (apinj1 != $true))) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & (((induction2lem_lthm = $true) | ($true != sP54)) & (($true = sP54) | (induction2lem_lthm != $true))) & (((termmset_lthm = $true) | (? [X454 : term] : (((sub @ X454 @ id)) != X454) & ! [X453 : term] : (((sub @ X453 @ id)) = X453))) & ((! [X454 : term] : (((sub @ X454 @ id)) = X454) | ? [X453 : term] : (((sub @ X453 @ id)) != X453)) | (termmset_lthm != $true))) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((hoaslaminj_lthm = $true) | ($true != sP50)) & (($true = sP50) | (hoaslaminj_lthm != $true))) & (hoasinduction_lem3_gthm = $true) & ((! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) = ((ap @ X305 @ X303))) & (X303 != X304)))) & ((! [X288 : (term > $o),X289 : subst,X287 : term] : ? [X290 : (term > $o)] : ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X288 : (term > $o),X289 : subst,X287 : term] : ! [X290 : (term > $o)] : ? [X291 : term] : (((X290 @ X291)) != ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))))) & (hoasapnotvar_gthm = $true) & ((! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true = ((X310 @ X309))) & ($true != ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))))) & ((($true = sP49) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP49))) & ((! [X455 : term,X457 : term,X456 : (subst > term > term)] : (? [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) != ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X455 : term,X457 : term,X456 : (subst > term > term)] : (! [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) = ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) & (((lam @ (X456 @ sh @ one))) = ((ap @ (sub @ X455 @ id) @ X457)))))) & (apnotvar = $true) & (((substmonoid_lthm = $true) | ((? [X4 : subst] : (((comp @ id @ X4)) != X4) | ? [X3 : subst] : (((comp @ X3 @ id)) != X3)) & ! [X1 : subst] : (((comp @ id @ X1)) = X1) & ! [X2 : subst] : (((comp @ X2 @ id)) = X2))) & (((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | ? [X1 : subst] : (((comp @ id @ X1)) != X1) | ? [X2 : subst] : (((comp @ X2 @ id)) != X2)) | (substmonoid_lthm != $true))) & ((! [X230 : (subst > term > subst > $o)] : ? [X231 : (term > $o)] : ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X230 : (subst > term > subst > $o)] : ! [X231 : (term > $o)] : ? [X232 : term] : (((X230 @ id @ X232 @ id)) != ((X231 @ X232))))) & (((hoasinduction_lthm_3 = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lthm_3 != $true))) & (((hoasinduction_lem3_lthm = $true) | (sP42 != $true)) & ((sP42 = $true) | (hoasinduction_lem3_lthm != $true))) & (hoaslaminj_gthm = $true) & ((! [X206 : term,X205 : (term > $o)] : (? [X210 : term] : ((((X205 @ (lam @ X210))) != $true) & ($true = ((X205 @ X210)))) | ? [X207 : term] : ((((var @ X207)) = $true) & ($true != ((X205 @ X207)))) | ($true = ((sP39 @ X205))) | (((X205 @ X206)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X206 : term,X205 : (term > $o)] : (! [X210 : term] : ((((X205 @ (lam @ X210))) = $true) | ($true != ((X205 @ X210)))) & ! [X207 : term] : ((((var @ X207)) != $true) | ($true = ((X205 @ X207)))) & ($true != ((sP39 @ X205))) & (((X205 @ X206)) != $true)))) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & (((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true))) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((induction2lem = $true) | ($true != sP36)) & (($true = sP36) | (induction2lem != $true))) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X226 : term] : ! [X227 : (subst > term > term)] : ? [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) != ((X227 @ X228 @ X229)))) & (! [X226 : term] : ? [X227 : (subst > term > term)] : ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229))) | (hoasinduction_lem3v2_f != $true))) & (((hoasapinj1 = $true) | ? [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 != X406) & (((ap @ (sub @ X406 @ id) @ X407)) = ((ap @ (sub @ X405 @ id) @ X408))))) & (! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408)))) | (hoasapinj1 != $true))) & (((axshiftcons = $true) | ? [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) != X355)) & (! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355) | (axshiftcons != $true))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((! [X328 : term] : ? [X329 : (subst > term > term)] : ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X328 : term] : ! [X329 : (subst > term > term)] : ? [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) != ((sub @ X328 @ (push @ X330 @ X331)))))) & (pushprop_lem3v2_lthm = $true) & ((! [X461 : term] : (((sub @ X461 @ id)) = X461) | (axvarid != $true)) & ((axvarid = $true) | ? [X461 : term] : (((sub @ X461 @ id)) != X461))) & (hoasinduction_gthm = $true) & ((($true = sP34) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP34))) & (((hoasinduction_lem3v2_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2_lthm != $true))) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & ((! [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (? [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) != ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ? [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) != ((sub @ (X320 @ X323 @ X321) @ X322)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (! [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) = ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) & (((lam @ (X320 @ sh @ one))) = ((lam @ (X318 @ sh @ one)))) & (((X318 @ X319 @ X317)) != ((X320 @ X319 @ X317))) & ! [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) = ((sub @ (X320 @ X323 @ X321) @ X322)))))) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X100 : subst] : (((comp @ id @ X100)) != X100) | ? [X99 : subst] : (((comp @ X99 @ id)) != X99)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & (((hoasinduction_lem3b = $true) | ? [X203 : term] : ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ X203 @ (push @ one @ sh))))) & (! [X203 : term] : ? [X204 : (subst > term > term)] : (((X204 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $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)))))))))))) & (hoaslamnotvar = $true) & ! [X292 : d_subst] : (d_id = X292) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((laminj = $true) | ? [X238 : term,X237 : term] : ((X237 != X238) & (((lam @ X238)) = ((lam @ X237))))) & (! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237)))) | (laminj != $true))) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & (((hoasinduction_lem2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2 != $true))) & (((axidl = $true) | ? [X327 : subst] : (((comp @ id @ X327)) != X327)) & (! [X327 : subst] : (((comp @ id @ X327)) = X327) | (axidl != $true))) & ((($true = sP29) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP29))) & ((($true = sP28) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP28))) & (((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true))) & (((hoasinduction_lem3aaa = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lem3aaa != $true))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((! [X462 : subst] : (((comp @ X462 @ id)) = X462) | (axidr != $true)) & ((axidr = $true) | ? [X462 : subst] : (((comp @ X462 @ id)) != X462))) & (pushprop_gthm = $true) & ((! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 != X500) & (((ap @ (sub @ X499 @ id) @ X500)) = ((ap @ (sub @ X501 @ id) @ X498)))))) & ! [X521 : d_term] : (d_one = X521) & (((axvarcons = $true) | ? [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) != X224)) & (! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224) | (axvarcons != $true))) & ((($true = sP18) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP18))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & (((hoasapinj2_lthm = $true) | (? [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 != X434) & (((ap @ (sub @ X435 @ id) @ X433)) = ((ap @ (sub @ X436 @ id) @ X434)))) & ! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 = X432) | (((ap @ X430 @ X431)) != ((ap @ X429 @ X432)))))) & ((! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434)))) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 != X432) & (((ap @ X430 @ X431)) = ((ap @ X429 @ X432))))) | (hoasapinj2_lthm != $true))) & (((axscons = $true) | ? [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) != X306)) & (! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306) | (axscons != $true))) & (((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true))) & (((hoasinduction_lem0 = $true) | ? [X351 : (subst > term > subst > $o)] : ! [X352 : (term > $o)] : ? [X353 : term] : (((X352 @ X353)) != ((X351 @ id @ X353 @ id)))) & (! [X351 : (subst > term > subst > $o)] : ? [X352 : (term > $o)] : ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id))) | (hoasinduction_lem0 != $true))) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & (((hoasinduction_lem3v2a = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3v2a != $true))) & (axclos = $true) & (((sP6 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP6 != $true))) & ((! [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) = $true) | ? [X286 : term] : (((X284 @ X286)) != ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ($true != ((X283 @ X282)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) != $true) & ! [X286 : term] : (((X284 @ X286)) = ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) & ($true = ((X283 @ X282)))))) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) != ((d2subst @ X520))) | (X519 = X520)) & (termmset_gthm = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X101 : term] : ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & (! [X101 : term] : ? [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) = ((X102 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & (axabs = $true) & ! [X235 : d_term,X236 : d_term] : ((((d2term @ X236)) != ((d2term @ X235))) | (X235 = X236)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & (((hoasinduction_lem3 = $true) | ($true != sP3)) & (($true = sP3) | (hoasinduction_lem3 != $true))) & ((! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) | (shinj != $true)) & ((shinj = $true) | ? [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) = ((sub @ X74 @ sh))) & (X73 != X74)))) & (pushprop = $true) & ((! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ? [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) != $true) & ($true = ((X294 @ id @ X296 @ id))) & (((X294 @ id @ X295 @ id)) = $true)) | ($true = ((sP1 @ X294)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X293 : term,X294 : (subst > term > subst > $o)] : (($true != ((X294 @ id @ X293 @ id))) & ! [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) = $true) | ($true != ((X294 @ id @ X296 @ id))) | (((X294 @ id @ X295 @ id)) != $true)) & ($true != ((sP1 @ X294)))))) & (hoasapinj2_gthm = $true) & ((($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0))) & (((? [X45 : term] : (((sub @ X45 @ id)) != X45) | ? [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 != X47) & (((ap @ X47 @ X48)) = ((ap @ X46 @ X49)))) | ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53))))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X45 : term] : (((sub @ X45 @ id)) = X45) & ! [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 = X47) | (((ap @ X47 @ X48)) != ((ap @ X46 @ X49)))) & ? [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 != X51) & (((ap @ (sub @ X51 @ id) @ X52)) = ((ap @ (sub @ X50 @ id) @ X53))))))) & (pushprop_lthm = $true) & (((? [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) != X92) | ! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) & ? [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) = $true) & ($true != ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) & ! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91)))) & (axassoc = $true) & (hoasapnotvar = $true) & ((! [X314 : term,X313 : (term > $o),X312 : subst] : ? [X315 : (term > $o)] : ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X314 : term,X313 : (term > $o),X312 : subst] : ! [X315 : (term > $o)] : ? [X316 : term] : (((X315 @ X316)) != ((X313 @ (sub @ X316 @ (push @ X314 @ X312)))))))),
% 1.42/0.51 inference(nnf_transformation,[],[f72])).
% 1.42/0.51 thf(f261,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((sP58 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP58 != $true)) & ((termmset = $true) | ? [X0 : term] : (((sub @ X0 @ id)) != X0)) & (! [X0 : term] : (((sub @ X0 @ id)) = X0) | (termmset != $true)) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) = X84) & ? [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true != ((X87 @ one))) & ! [X89 : term] : (((X87 @ X89)) = ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) & ($true = ((X88 @ X85)))))) & (? [X84 : term,X83 : subst] : (((sub @ one @ (push @ X84 @ X83))) != X84) | ! [X85 : term,X88 : (term > $o),X87 : (term > $o),X86 : subst] : (($true = ((X87 @ one))) | ? [X89 : term] : (((X87 @ X89)) != ((X88 @ (sub @ X89 @ (push @ X85 @ X86))))) | ($true != ((X88 @ X85)))) | (pushprop_lem1v2_lthm != $true)) & (($true = sP56) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP56)) & ((apinj1 = $true) | ? [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) = ((ap @ X69 @ X72))) & (X69 != X70))) & (! [X69 : term,X71 : term,X70 : term,X72 : term] : ((((ap @ X70 @ X71)) != ((ap @ X69 @ X72))) | (X69 = X70)) | (apinj1 != $true)) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & ((induction2lem_lthm = $true) | ($true != sP54)) & (($true = sP54) | (induction2lem_lthm != $true)) & ((termmset_lthm = $true) | (? [X454 : term] : (((sub @ X454 @ id)) != X454) & ! [X453 : term] : (((sub @ X453 @ id)) = X453))) & (! [X454 : term] : (((sub @ X454 @ id)) = X454) | ? [X453 : term] : (((sub @ X453 @ id)) != X453) | (termmset_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) | ($true != sP50)) & (($true = sP50) | (hoaslaminj_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) != ((ap @ X305 @ X303))) | (X303 = X304)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X302 : term,X305 : term,X303 : term,X304 : term] : ((((ap @ X302 @ X304)) = ((ap @ X305 @ X303))) & (X303 != X304))) & (! [X288 : (term > $o),X289 : subst,X287 : term] : ? [X290 : (term > $o)] : ! [X291 : term] : (((X290 @ X291)) = ((X288 @ (sub @ X291 @ (push @ X287 @ X289))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X288 : (term > $o),X289 : subst,X287 : term] : ! [X290 : (term > $o)] : ? [X291 : term] : (((X290 @ X291)) != ((X288 @ (sub @ X291 @ (push @ X287 @ X289)))))) & (hoasapnotvar_gthm = $true) & (! [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true != ((X310 @ X309))) | ($true = ((X311 @ (sub @ X309 @ (push @ X307 @ X308)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X307 : term,X311 : (term > $o),X310 : (term > $o),X308 : subst,X309 : term] : (($true = ((X310 @ X309))) & ($true != ((X311 @ (sub @ X309 @ (push @ X307 @ X308))))))) & (($true = sP49) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP49)) & (! [X455 : term,X457 : term,X456 : (subst > term > term)] : (? [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) != ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) | (((lam @ (X456 @ sh @ one))) != ((ap @ (sub @ X455 @ id) @ X457)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X455 : term,X457 : term,X456 : (subst > term > term)] : (! [X460 : term,X459 : subst,X458 : subst] : (((sub @ (X456 @ X459 @ X460) @ X458)) = ((X456 @ (comp @ X459 @ X458) @ (sub @ X460 @ X458)))) & (((lam @ (X456 @ sh @ one))) = ((ap @ (sub @ X455 @ id) @ X457))))) & (apnotvar = $true) & ((substmonoid_lthm = $true) | ((? [X4 : subst] : (((comp @ id @ X4)) != X4) | ? [X3 : subst] : (((comp @ X3 @ id)) != X3)) & ! [X1 : subst] : (((comp @ id @ X1)) = X1) & ! [X2 : subst] : (((comp @ X2 @ id)) = X2))) & ((! [X4 : subst] : (((comp @ id @ X4)) = X4) & ! [X3 : subst] : (((comp @ X3 @ id)) = X3)) | ? [X1 : subst] : (((comp @ id @ X1)) != X1) | ? [X2 : subst] : (((comp @ X2 @ id)) != X2) | (substmonoid_lthm != $true)) & (! [X230 : (subst > term > subst > $o)] : ? [X231 : (term > $o)] : ! [X232 : term] : (((X230 @ id @ X232 @ id)) = ((X231 @ X232))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X230 : (subst > term > subst > $o)] : ! [X231 : (term > $o)] : ? [X232 : term] : (((X230 @ id @ X232 @ id)) != ((X231 @ X232)))) & ((hoasinduction_lthm_3 = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP42 != $true)) & ((sP42 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoaslaminj_gthm = $true) & (! [X206 : term,X205 : (term > $o)] : (? [X210 : term] : ((((X205 @ (lam @ X210))) != $true) & ($true = ((X205 @ X210)))) | ? [X207 : term] : ((((var @ X207)) = $true) & ($true != ((X205 @ X207)))) | ($true = ((sP39 @ X205))) | (((X205 @ X206)) = $true)) | (induction != $true)) & ((induction = $true) | ? [X206 : term,X205 : (term > $o)] : (! [X210 : term] : ((((X205 @ (lam @ X210))) = $true) | ($true != ((X205 @ X210)))) & ! [X207 : term] : ((((var @ X207)) != $true) | ($true = ((X205 @ X207)))) & ($true != ((sP39 @ X205))) & (((X205 @ X206)) != $true))) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2lem = $true) | ($true != sP36)) & (($true = sP36) | (induction2lem != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X226 : term] : ! [X227 : (subst > term > term)] : ? [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) != ((X227 @ X228 @ X229)))) & (! [X226 : term] : ? [X227 : (subst > term > term)] : ! [X229 : term,X228 : subst] : (((sub @ X226 @ (push @ X229 @ X228))) = ((X227 @ X228 @ X229))) | (hoasinduction_lem3v2_f != $true)) & ((hoasapinj1 = $true) | ? [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 != X406) & (((ap @ (sub @ X406 @ id) @ X407)) = ((ap @ (sub @ X405 @ id) @ X408))))) & (! [X405 : term,X408 : term,X406 : term,X407 : term] : ((X405 = X406) | (((ap @ (sub @ X406 @ id) @ X407)) != ((ap @ (sub @ X405 @ id) @ X408)))) | (hoasapinj1 != $true)) & ((axshiftcons = $true) | ? [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) != X355)) & (! [X355 : subst,X354 : term] : (((comp @ sh @ (push @ X354 @ X355))) = X355) | (axshiftcons != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X328 : term] : ? [X329 : (subst > term > term)] : ! [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) = ((sub @ X328 @ (push @ X330 @ X331)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X328 : term] : ! [X329 : (subst > term > term)] : ? [X331 : subst,X330 : term] : (((X329 @ X331 @ X330)) != ((sub @ X328 @ (push @ X330 @ X331))))) & (pushprop_lem3v2_lthm = $true) & (! [X461 : term] : (((sub @ X461 @ id)) = X461) | (axvarid != $true)) & ((axvarid = $true) | ? [X461 : term] : (((sub @ X461 @ id)) != X461)) & (hoasinduction_gthm = $true) & (($true = sP34) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP34)) & ((hoasinduction_lem3v2_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (! [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (? [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) != ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) | (((lam @ (X320 @ sh @ one))) != ((lam @ (X318 @ sh @ one)))) | (((X318 @ X319 @ X317)) = ((X320 @ X319 @ X317))) | ? [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) != ((sub @ (X320 @ X323 @ X321) @ X322)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X317 : term,X320 : (subst > term > term),X318 : (subst > term > term),X319 : subst] : (! [X326 : subst,X325 : subst,X324 : term] : (((sub @ (X318 @ X326 @ X324) @ X325)) = ((X318 @ (comp @ X326 @ X325) @ (sub @ X324 @ X325)))) & (((lam @ (X320 @ sh @ one))) = ((lam @ (X318 @ sh @ one)))) & (((X318 @ X319 @ X317)) != ((X320 @ X319 @ X317))) & ! [X321 : term,X322 : subst,X323 : subst] : (((X320 @ (comp @ X323 @ X322) @ (sub @ X321 @ X322))) = ((sub @ (X320 @ X323 @ X321) @ X322))))) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X100 : subst] : (((comp @ id @ X100)) = X100) & ! [X99 : subst] : (((comp @ X99 @ id)) = X99)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X100 : subst] : (((comp @ id @ X100)) != X100) | ? [X99 : subst] : (((comp @ X99 @ id)) != X99)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) | ? [X203 : term] : ! [X204 : (subst > term > term)] : (((X204 @ sh @ one)) != ((sub @ X203 @ (push @ one @ sh))))) & (! [X203 : term] : ? [X204 : (subst > term > term)] : (((X204 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $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)))))))))))) & (hoaslamnotvar = $true) & ! [X292 : d_subst] : (d_id = X292) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((laminj = $true) | ? [X238 : term,X237 : term] : ((X237 != X238) & (((lam @ X238)) = ((lam @ X237))))) & (! [X238 : term,X237 : term] : ((X237 = X238) | (((lam @ X238)) != ((lam @ X237)))) | (laminj != $true)) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X364 : term] : ? [X365 : d_term] : (((d2term @ X365)) = X364) & ((hoasinduction_lem2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2 != $true)) & ((axidl = $true) | ? [X327 : subst] : (((comp @ id @ X327)) != X327)) & (! [X327 : subst] : (((comp @ id @ X327)) = X327) | (axidl != $true)) & (($true = sP29) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP29)) & (($true = sP28) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP28)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X462 : subst] : (((comp @ X462 @ id)) = X462) | (axidr != $true)) & ((axidr = $true) | ? [X462 : subst] : (((comp @ X462 @ id)) != X462)) & (pushprop_gthm = $true) & (! [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 = X500) | (((ap @ (sub @ X499 @ id) @ X500)) != ((ap @ (sub @ X501 @ id) @ X498)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X500 : term,X501 : term,X498 : term,X499 : term] : ((X498 != X500) & (((ap @ (sub @ X499 @ id) @ X500)) = ((ap @ (sub @ X501 @ id) @ X498))))) & ! [X521 : d_term] : (d_one = X521) & ((axvarcons = $true) | ? [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) != X224)) & (! [X224 : term,X225 : subst] : (((sub @ one @ (push @ X224 @ X225))) = X224) | (axvarcons != $true)) & (($true = sP18) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP18)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2_lthm = $true) | (? [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 != X434) & (((ap @ (sub @ X435 @ id) @ X433)) = ((ap @ (sub @ X436 @ id) @ X434)))) & ! [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 = X432) | (((ap @ X430 @ X431)) != ((ap @ X429 @ X432)))))) & (! [X436 : term,X435 : term,X433 : term,X434 : term] : ((X433 = X434) | (((ap @ (sub @ X435 @ id) @ X433)) != ((ap @ (sub @ X436 @ id) @ X434)))) | ? [X429 : term,X432 : term,X431 : term,X430 : term] : ((X431 != X432) & (((ap @ X430 @ X431)) = ((ap @ X429 @ X432)))) | (hoasapinj2_lthm != $true)) & ((axscons = $true) | ? [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) != X306)) & (! [X306 : subst] : (((push @ (sub @ one @ X306) @ (comp @ sh @ X306))) = X306) | (axscons != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem0 = $true) | ? [X351 : (subst > term > subst > $o)] : ! [X352 : (term > $o)] : ? [X353 : term] : (((X352 @ X353)) != ((X351 @ id @ X353 @ id)))) & (! [X351 : (subst > term > subst > $o)] : ? [X352 : (term > $o)] : ! [X353 : term] : (((X352 @ X353)) = ((X351 @ id @ X353 @ id))) | (hoasinduction_lem0 != $true)) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X233 : subst] : ? [X234 : d_subst] : (((d2subst @ X234)) = X233) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3v2a != $true)) & (axclos = $true) & ((sP6 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP6 != $true)) & (! [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) = $true) | ? [X286 : term] : (((X284 @ X286)) != ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) | ($true != ((X283 @ X282)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X283 : (term > $o),X282 : term,X284 : (term > $o),X285 : subst] : ((((X284 @ one)) != $true) & ! [X286 : term] : (((X284 @ X286)) = ((X283 @ (sub @ X286 @ (push @ X282 @ X285))))) & ($true = ((X283 @ X282))))) & ! [X519 : d_subst,X520 : d_subst] : ((((d2subst @ X519)) != ((d2subst @ X520))) | (X519 = X520)) & (termmset_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X101 : term] : ! [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) != ((X102 @ sh @ one)))) & (! [X101 : term] : ? [X102 : (subst > term > term)] : (((sub @ X101 @ (push @ one @ sh))) = ((X102 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X235 : d_term,X236 : d_term] : ((((d2term @ X236)) != ((d2term @ X235))) | (X235 = X236)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) | ($true != sP3)) & (($true = sP3) | (hoasinduction_lem3 != $true)) & (! [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) != ((sub @ X74 @ sh))) | (X73 = X74)) | (shinj != $true)) & ((shinj = $true) | ? [X74 : term,X73 : term] : ((((sub @ X73 @ sh)) = ((sub @ X74 @ sh))) & (X73 != X74))) & (pushprop = $true) & (! [X293 : term,X294 : (subst > term > subst > $o)] : (($true = ((X294 @ id @ X293 @ id))) | ? [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) != $true) & ($true = ((X294 @ id @ X296 @ id))) & (((X294 @ id @ X295 @ id)) = $true)) | ($true = ((sP1 @ X294)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X293 : term,X294 : (subst > term > subst > $o)] : (($true != ((X294 @ id @ X293 @ id))) & ! [X295 : term,X296 : term] : ((((X294 @ id @ (ap @ (sub @ X295 @ id) @ X296) @ id)) = $true) | ($true != ((X294 @ id @ X296 @ id))) | (((X294 @ id @ X295 @ id)) != $true)) & ($true != ((sP1 @ X294))))) & (hoasapinj2_gthm = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & (? [X45 : term] : (((sub @ X45 @ id)) != X45) | ? [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 != X47) & (((ap @ X47 @ X48)) = ((ap @ X46 @ X49)))) | ! [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 = X51) | (((ap @ (sub @ X51 @ id) @ X52)) != ((ap @ (sub @ X50 @ id) @ X53)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X45 : term] : (((sub @ X45 @ id)) = X45) & ! [X47 : term,X46 : term,X49 : term,X48 : term] : ((X46 = X47) | (((ap @ X47 @ X48)) != ((ap @ X46 @ X49)))) & ? [X50 : term,X51 : term,X53 : term,X52 : term] : ((X50 != X51) & (((ap @ (sub @ X51 @ id) @ X52)) = ((ap @ (sub @ X50 @ id) @ X53)))))) & (pushprop_lthm = $true) & (? [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) != X92) | ! [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) != $true) | ($true = ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) | ? [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) != X91) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X92 : subst,X93 : term] : (((comp @ sh @ (push @ X93 @ X92))) = X92) & ? [X96 : term,X98 : (term > $o),X94 : (term > $o),X97 : term,X95 : subst] : ((((X98 @ X96)) = $true) & ($true != ((X94 @ (sub @ X96 @ (push @ X97 @ X95)))))) & ! [X90 : subst,X91 : term] : (((sub @ one @ (push @ X91 @ X90))) = X91))) & (axassoc = $true) & (hoasapnotvar = $true) & (! [X314 : term,X313 : (term > $o),X312 : subst] : ? [X315 : (term > $o)] : ! [X316 : term] : (((X315 @ X316)) = ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X314 : term,X313 : (term > $o),X312 : subst] : ! [X315 : (term > $o)] : ? [X316 : term] : (((X315 @ X316)) != ((X313 @ (sub @ X316 @ (push @ X314 @ X312))))))),
% 1.42/0.51 inference(flattening,[],[f260])).
% 1.42/0.51 thf(f262,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((sP58 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP58 != $true)) & ((termmset = $true) | ? [X0 : term] : (((sub @ X0 @ id)) != X0)) & (! [X1 : term] : (((sub @ X1 @ id)) = X1) | (termmset != $true)) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) & ? [X4 : term,X5 : (term > $o),X6 : (term > $o),X7 : subst] : (($true != ((X6 @ one))) & ! [X8 : term] : (((X6 @ X8)) = ((X5 @ (sub @ X8 @ (push @ X4 @ X7))))) & (((X5 @ X4)) = $true)))) & (? [X9 : term,X10 : subst] : (((sub @ one @ (push @ X9 @ X10))) != X9) | ! [X11 : term,X12 : (term > $o),X13 : (term > $o),X14 : subst] : (($true = ((X13 @ one))) | ? [X15 : term] : (((X12 @ (sub @ X15 @ (push @ X11 @ X14)))) != ((X13 @ X15))) | ($true != ((X12 @ X11)))) | (pushprop_lem1v2_lthm != $true)) & (($true = sP56) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP56)) & ((apinj1 = $true) | ? [X16 : term,X17 : term,X18 : term,X19 : term] : ((((ap @ X18 @ X17)) = ((ap @ X16 @ X19))) & (X16 != X18))) & (! [X20 : term,X21 : term,X22 : term,X23 : term] : ((((ap @ X20 @ X23)) != ((ap @ X22 @ X21))) | (X20 = X22)) | (apinj1 != $true)) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & ((induction2lem_lthm = $true) | ($true != sP54)) & (($true = sP54) | (induction2lem_lthm != $true)) & ((termmset_lthm = $true) | (? [X24 : term] : (((sub @ X24 @ id)) != X24) & ! [X25 : term] : (((sub @ X25 @ id)) = X25))) & (! [X26 : term] : (((sub @ X26 @ id)) = X26) | ? [X27 : term] : (((sub @ X27 @ id)) != X27) | (termmset_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) | ($true != sP50)) & (($true = sP50) | (hoaslaminj_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X28 : term,X29 : term,X30 : term,X31 : term] : ((((ap @ X29 @ X30)) != ((ap @ X28 @ X31))) | (X30 = X31)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X32 : term,X33 : term,X34 : term,X35 : term] : ((((ap @ X32 @ X35)) = ((ap @ X33 @ X34))) & (X34 != X35))) & (! [X36 : (term > $o),X37 : subst,X38 : term] : ? [X39 : (term > $o)] : ! [X40 : term] : (((X39 @ X40)) = ((X36 @ (sub @ X40 @ (push @ X38 @ X37))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X41 : (term > $o),X42 : subst,X43 : term] : ! [X44 : (term > $o)] : ? [X45 : term] : (((X44 @ X45)) != ((X41 @ (sub @ X45 @ (push @ X43 @ X42)))))) & (hoasapnotvar_gthm = $true) & (! [X46 : term,X47 : (term > $o),X48 : (term > $o),X49 : subst,X50 : term] : (($true != ((X48 @ X50))) | ($true = ((X47 @ (sub @ X50 @ (push @ X46 @ X49)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X51 : term,X52 : (term > $o),X53 : (term > $o),X54 : subst,X55 : term] : (($true = ((X53 @ X55))) & ($true != ((X52 @ (sub @ X55 @ (push @ X51 @ X54))))))) & (($true = sP49) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP49)) & (! [X56 : term,X57 : term,X58 : (subst > term > term)] : (? [X59 : term,X60 : subst,X61 : subst] : (((X58 @ (comp @ X60 @ X61) @ (sub @ X59 @ X61))) != ((sub @ (X58 @ X60 @ X59) @ X61))) | (((ap @ (sub @ X56 @ id) @ X57)) != ((lam @ (X58 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X62 : term,X63 : term,X64 : (subst > term > term)] : (! [X65 : term,X66 : subst,X67 : subst] : (((X64 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67))) = ((sub @ (X64 @ X66 @ X65) @ X67))) & (((lam @ (X64 @ sh @ one))) = ((ap @ (sub @ X62 @ id) @ X63))))) & (apnotvar = $true) & ((substmonoid_lthm = $true) | ((? [X68 : subst] : (((comp @ id @ X68)) != X68) | ? [X69 : subst] : (((comp @ X69 @ id)) != X69)) & ! [X70 : subst] : (((comp @ id @ X70)) = X70) & ! [X71 : subst] : (((comp @ X71 @ id)) = X71))) & ((! [X72 : subst] : (((comp @ id @ X72)) = X72) & ! [X73 : subst] : (((comp @ X73 @ id)) = X73)) | ? [X74 : subst] : (((comp @ id @ X74)) != X74) | ? [X75 : subst] : (((comp @ X75 @ id)) != X75) | (substmonoid_lthm != $true)) & (! [X76 : (subst > term > subst > $o)] : ? [X77 : (term > $o)] : ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((X77 @ X78))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X79 : (subst > term > subst > $o)] : ! [X80 : (term > $o)] : ? [X81 : term] : (((X79 @ id @ X81 @ id)) != ((X80 @ X81)))) & ((hoasinduction_lthm_3 = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP42 != $true)) & ((sP42 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoaslaminj_gthm = $true) & (! [X82 : term,X83 : (term > $o)] : (? [X84 : term] : ((((X83 @ (lam @ X84))) != $true) & ($true = ((X83 @ X84)))) | ? [X85 : term] : (($true = ((var @ X85))) & ($true != ((X83 @ X85)))) | ($true = ((sP39 @ X83))) | ($true = ((X83 @ X82)))) | (induction != $true)) & ((induction = $true) | ? [X86 : term,X87 : (term > $o)] : (! [X88 : term] : ((((X87 @ (lam @ X88))) = $true) | (((X87 @ X88)) != $true)) & ! [X89 : term] : (($true != ((var @ X89))) | (((X87 @ X89)) = $true)) & ($true != ((sP39 @ X87))) & ($true != ((X87 @ X86))))) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2lem = $true) | ($true != sP36)) & (($true = sP36) | (induction2lem != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X90 : term] : ! [X91 : (subst > term > term)] : ? [X92 : term,X93 : subst] : (((X91 @ X93 @ X92)) != ((sub @ X90 @ (push @ X92 @ X93))))) & (! [X94 : term] : ? [X95 : (subst > term > term)] : ! [X96 : term,X97 : subst] : (((sub @ X94 @ (push @ X96 @ X97))) = ((X95 @ X97 @ X96))) | (hoasinduction_lem3v2_f != $true)) & ((hoasapinj1 = $true) | ? [X98 : term,X99 : term,X100 : term,X101 : term] : ((X98 != X100) & (((ap @ (sub @ X98 @ id) @ X99)) = ((ap @ (sub @ X100 @ id) @ X101))))) & (! [X102 : term,X103 : term,X104 : term,X105 : term] : ((X102 = X104) | (((ap @ (sub @ X104 @ id) @ X105)) != ((ap @ (sub @ X102 @ id) @ X103)))) | (hoasapinj1 != $true)) & ((axshiftcons = $true) | ? [X106 : subst,X107 : term] : (((comp @ sh @ (push @ X107 @ X106))) != X106)) & (! [X108 : subst,X109 : term] : (((comp @ sh @ (push @ X109 @ X108))) = X108) | (axshiftcons != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X110 : term] : ? [X111 : (subst > term > term)] : ! [X112 : subst,X113 : term] : (((sub @ X110 @ (push @ X113 @ X112))) = ((X111 @ X112 @ X113))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X114 : term] : ! [X115 : (subst > term > term)] : ? [X116 : subst,X117 : term] : (((sub @ X114 @ (push @ X117 @ X116))) != ((X115 @ X116 @ X117)))) & (pushprop_lem3v2_lthm = $true) & (! [X118 : term] : (((sub @ X118 @ id)) = X118) | (axvarid != $true)) & ((axvarid = $true) | ? [X119 : term] : (((sub @ X119 @ id)) != X119)) & (hoasinduction_gthm = $true) & (($true = sP34) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP34)) & ((hoasinduction_lem3v2_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (! [X120 : term,X121 : (subst > term > term),X122 : (subst > term > term),X123 : subst] : (? [X124 : subst,X125 : subst,X126 : term] : (((sub @ (X122 @ X124 @ X126) @ X125)) != ((X122 @ (comp @ X124 @ X125) @ (sub @ X126 @ X125)))) | (((lam @ (X121 @ sh @ one))) != ((lam @ (X122 @ sh @ one)))) | (((X122 @ X123 @ X120)) = ((X121 @ X123 @ X120))) | ? [X127 : term,X128 : subst,X129 : subst] : (((sub @ (X121 @ X129 @ X127) @ X128)) != ((X121 @ (comp @ X129 @ X128) @ (sub @ X127 @ X128))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X130 : term,X131 : (subst > term > term),X132 : (subst > term > term),X133 : subst] : (! [X134 : subst,X135 : subst,X136 : term] : (((sub @ (X132 @ X134 @ X136) @ X135)) = ((X132 @ (comp @ X134 @ X135) @ (sub @ X136 @ X135)))) & (((lam @ (X131 @ sh @ one))) = ((lam @ (X132 @ sh @ one)))) & (((X131 @ X133 @ X130)) != ((X132 @ X133 @ X130))) & ! [X137 : term,X138 : subst,X139 : subst] : (((X131 @ (comp @ X139 @ X138) @ (sub @ X137 @ X138))) = ((sub @ (X131 @ X139 @ X137) @ X138))))) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X140 : subst] : (((comp @ id @ X140)) = X140) & ! [X141 : subst] : (((comp @ X141 @ id)) = X141)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X142 : subst] : (((comp @ id @ X142)) != X142) | ? [X143 : subst] : (((comp @ X143 @ id)) != X143)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) | ? [X144 : term] : ! [X145 : (subst > term > term)] : (((sub @ X144 @ (push @ one @ sh))) != ((X145 @ sh @ one)))) & (! [X146 : term] : ? [X147 : (subst > term > term)] : (((sub @ X146 @ (push @ one @ sh))) = ((X147 @ sh @ one))) | (hoasinduction_lem3b != $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)))))))))))) & (hoaslamnotvar = $true) & ! [X148 : d_subst] : (d_id = X148) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((laminj = $true) | ? [X149 : term,X150 : term] : ((X149 != X150) & (((lam @ X149)) = ((lam @ X150))))) & (! [X151 : term,X152 : term] : ((X151 = X152) | (((lam @ X151)) != ((lam @ X152)))) | (laminj != $true)) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X153 : term] : ? [X154 : d_term] : (((d2term @ X154)) = X153) & ((hoasinduction_lem2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2 != $true)) & ((axidl = $true) | ? [X155 : subst] : (((comp @ id @ X155)) != X155)) & (! [X156 : subst] : (((comp @ id @ X156)) = X156) | (axidl != $true)) & (($true = sP29) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP29)) & (($true = sP28) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP28)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X157 : subst] : (((comp @ X157 @ id)) = X157) | (axidr != $true)) & ((axidr = $true) | ? [X158 : subst] : (((comp @ X158 @ id)) != X158)) & (pushprop_gthm = $true) & (! [X159 : term,X160 : term,X161 : term,X162 : term] : ((X159 = X161) | (((ap @ (sub @ X162 @ id) @ X159)) != ((ap @ (sub @ X160 @ id) @ X161)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X163 : term,X164 : term,X165 : term,X166 : term] : ((X163 != X165) & (((ap @ (sub @ X164 @ id) @ X165)) = ((ap @ (sub @ X166 @ id) @ X163))))) & ! [X167 : d_term] : (d_one = X167) & ((axvarcons = $true) | ? [X168 : term,X169 : subst] : (((sub @ one @ (push @ X168 @ X169))) != X168)) & (! [X170 : term,X171 : subst] : (((sub @ one @ (push @ X170 @ X171))) = X170) | (axvarcons != $true)) & (($true = sP18) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP18)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2_lthm = $true) | (? [X172 : term,X173 : term,X174 : term,X175 : term] : ((X174 != X175) & (((ap @ (sub @ X173 @ id) @ X174)) = ((ap @ (sub @ X172 @ id) @ X175)))) & ! [X176 : term,X177 : term,X178 : term,X179 : term] : ((X177 = X178) | (((ap @ X176 @ X177)) != ((ap @ X179 @ X178)))))) & (! [X180 : term,X181 : term,X182 : term,X183 : term] : ((X182 = X183) | (((ap @ (sub @ X180 @ id) @ X183)) != ((ap @ (sub @ X181 @ id) @ X182)))) | ? [X184 : term,X185 : term,X186 : term,X187 : term] : ((X185 != X186) & (((ap @ X187 @ X186)) = ((ap @ X184 @ X185)))) | (hoasapinj2_lthm != $true)) & ((axscons = $true) | ? [X188 : subst] : (((push @ (sub @ one @ X188) @ (comp @ sh @ X188))) != X188)) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) | (axscons != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem0 = $true) | ? [X190 : (subst > term > subst > $o)] : ! [X191 : (term > $o)] : ? [X192 : term] : (((X191 @ X192)) != ((X190 @ id @ X192 @ id)))) & (! [X193 : (subst > term > subst > $o)] : ? [X194 : (term > $o)] : ! [X195 : term] : (((X194 @ X195)) = ((X193 @ id @ X195 @ id))) | (hoasinduction_lem0 != $true)) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X196 : subst] : ? [X197 : d_subst] : (((d2subst @ X197)) = X196) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3v2a != $true)) & (axclos = $true) & ((sP6 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP6 != $true)) & (! [X198 : (term > $o),X199 : term,X200 : (term > $o),X201 : subst] : (($true = ((X200 @ one))) | ? [X202 : term] : (((X198 @ (sub @ X202 @ (push @ X199 @ X201)))) != ((X200 @ X202))) | ($true != ((X198 @ X199)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X203 : (term > $o),X204 : term,X205 : (term > $o),X206 : subst] : (($true != ((X205 @ one))) & ! [X207 : term] : (((X203 @ (sub @ X207 @ (push @ X204 @ X206)))) = ((X205 @ X207))) & ($true = ((X203 @ X204))))) & ! [X208 : d_subst,X209 : d_subst] : ((((d2subst @ X209)) != ((d2subst @ X208))) | (X208 = X209)) & (termmset_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X210 : term] : ! [X211 : (subst > term > term)] : (((sub @ X210 @ (push @ one @ sh))) != ((X211 @ sh @ one)))) & (! [X212 : term] : ? [X213 : (subst > term > term)] : (((X213 @ sh @ one)) = ((sub @ X212 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X214 : d_term,X215 : d_term] : ((((d2term @ X215)) != ((d2term @ X214))) | (X214 = X215)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) | ($true != sP3)) & (($true = sP3) | (hoasinduction_lem3 != $true)) & (! [X216 : term,X217 : term] : ((((sub @ X217 @ sh)) != ((sub @ X216 @ sh))) | (X216 = X217)) | (shinj != $true)) & ((shinj = $true) | ? [X218 : term,X219 : term] : ((((sub @ X218 @ sh)) = ((sub @ X219 @ sh))) & (X218 != X219))) & (pushprop = $true) & (! [X220 : term,X221 : (subst > term > subst > $o)] : (($true = ((X221 @ id @ X220 @ id))) | ? [X222 : term,X223 : term] : (($true != ((X221 @ id @ (ap @ (sub @ X222 @ id) @ X223) @ id))) & ($true = ((X221 @ id @ X223 @ id))) & ($true = ((X221 @ id @ X222 @ id)))) | ($true = ((sP1 @ X221)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X224 : term,X225 : (subst > term > subst > $o)] : (($true != ((X225 @ id @ X224 @ id))) & ! [X226 : term,X227 : term] : (($true = ((X225 @ id @ (ap @ (sub @ X226 @ id) @ X227) @ id))) | ($true != ((X225 @ id @ X227 @ id))) | ($true != ((X225 @ id @ X226 @ id)))) & ($true != ((sP1 @ X225))))) & (hoasapinj2_gthm = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & (? [X228 : term] : (((sub @ X228 @ id)) != X228) | ? [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 != X230) & (((ap @ X230 @ X231)) = ((ap @ X229 @ X232)))) | ! [X233 : term,X234 : term,X235 : term,X236 : term] : ((X233 = X234) | (((ap @ (sub @ X234 @ id) @ X236)) != ((ap @ (sub @ X233 @ id) @ X235)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X237 : term] : (((sub @ X237 @ id)) = X237) & ! [X238 : term,X239 : term,X240 : term,X241 : term] : ((X238 = X239) | (((ap @ X238 @ X241)) != ((ap @ X239 @ X240)))) & ? [X242 : term,X243 : term,X244 : term,X245 : term] : ((X242 != X243) & (((ap @ (sub @ X243 @ id) @ X245)) = ((ap @ (sub @ X242 @ id) @ X244)))))) & (pushprop_lthm = $true) & (? [X246 : subst,X247 : term] : (((comp @ sh @ (push @ X247 @ X246))) != X246) | ! [X248 : term,X249 : (term > $o),X250 : (term > $o),X251 : term,X252 : subst] : (($true != ((X249 @ X248))) | (((X250 @ (sub @ X248 @ (push @ X251 @ X252)))) = $true)) | ? [X253 : subst,X254 : term] : (((sub @ one @ (push @ X254 @ X253))) != X254) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X255 : subst,X256 : term] : (((comp @ sh @ (push @ X256 @ X255))) = X255) & ? [X257 : term,X258 : (term > $o),X259 : (term > $o),X260 : term,X261 : subst] : (($true = ((X258 @ X257))) & ($true != ((X259 @ (sub @ X257 @ (push @ X260 @ X261)))))) & ! [X262 : subst,X263 : term] : (((sub @ one @ (push @ X263 @ X262))) = X263))) & (axassoc = $true) & (hoasapnotvar = $true) & (! [X264 : term,X265 : (term > $o),X266 : subst] : ? [X267 : (term > $o)] : ! [X268 : term] : (((X265 @ (sub @ X268 @ (push @ X264 @ X266)))) = ((X267 @ X268))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X269 : term,X270 : (term > $o),X271 : subst] : ! [X272 : (term > $o)] : ? [X273 : term] : (((X270 @ (sub @ X273 @ (push @ X269 @ X271)))) != ((X272 @ X273))))),
% 1.42/0.51 inference(rectify,[],[f261])).
% 1.42/0.51 thf(f263,plain,(
% 1.42/0.51 (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((sP58 = $true) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | (sP58 != $true)) & ((termmset = $true) | (sK457 != ((sub @ sK457 @ id)))) & (! [X1 : term] : (((sub @ X1 @ id)) = X1) | (termmset != $true)) & (axapp = $true) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (hoasinduction_lem1v2 = $true) & ((pushprop_lem1v2_lthm = $true) | (! [X2 : term,X3 : subst] : (((sub @ one @ (push @ X2 @ X3))) = X2) & (($true != ((sK460 @ one))) & ! [X8 : term] : (((sK459 @ (sub @ X8 @ (push @ sK458 @ sK461)))) = ((sK460 @ X8))) & ($true = ((sK459 @ sK458)))))) & ((sK462 != ((sub @ one @ (push @ sK462 @ sK463)))) | ! [X11 : term,X12 : (term > $o),X13 : (term > $o),X14 : subst] : (($true = ((X13 @ one))) | (((X13 @ (sK464 @ X14 @ X13 @ X12 @ X11))) != ((X12 @ (sub @ (sK464 @ X14 @ X13 @ X12 @ X11) @ (push @ X11 @ X14))))) | ($true != ((X12 @ X11)))) | (pushprop_lem1v2_lthm != $true)) & (($true = sP56) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP56)) & ((apinj1 = $true) | ((((ap @ sK467 @ sK466)) = ((ap @ sK465 @ sK468))) & (sK465 != sK467))) & (! [X20 : term,X21 : term,X22 : term,X23 : term] : ((((ap @ X20 @ X23)) != ((ap @ X22 @ X21))) | (X20 = X22)) | (apinj1 != $true)) & (hoasinduction_lem2_lthm = $true) & (lamnotap != $true) & ((induction2lem_lthm = $true) | ($true != sP54)) & (($true = sP54) | (induction2lem_lthm != $true)) & ((termmset_lthm = $true) | ((sK469 != ((sub @ sK469 @ id))) & ! [X25 : term] : (((sub @ X25 @ id)) = X25))) & (! [X26 : term] : (((sub @ X26 @ id)) = X26) | (((sub @ sK470 @ id)) != sK470) | (termmset_lthm != $true)) & (((var @ (d2term @ d_one))) != $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoaslaminj_lthm = $true) | ($true != sP50)) & (($true = sP50) | (hoaslaminj_lthm != $true)) & (hoasinduction_lem3_gthm = $true) & (! [X28 : term,X29 : term,X30 : term,X31 : term] : ((((ap @ X29 @ X30)) != ((ap @ X28 @ X31))) | (X30 = X31)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK471 @ sK474)) = ((ap @ sK472 @ sK473))) & (sK474 != sK473))) & (! [X36 : (term > $o),X37 : subst,X38 : term] : ! [X40 : term] : (((sK475 @ X38 @ X37 @ X36 @ X40)) = ((X36 @ (sub @ X40 @ (push @ X38 @ X37))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X44 : (term > $o)] : (((X44 @ (sK479 @ X44))) != ((sK476 @ (sub @ (sK479 @ X44) @ (push @ sK478 @ sK477)))))) & (hoasapnotvar_gthm = $true) & (! [X46 : term,X47 : (term > $o),X48 : (term > $o),X49 : subst,X50 : term] : (($true != ((X48 @ X50))) | ($true = ((X47 @ (sub @ X50 @ (push @ X46 @ X49)))))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK482 @ sK484)) = $true) & ($true != ((sK481 @ (sub @ sK484 @ (push @ sK480 @ sK483))))))) & (($true = sP49) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP49)) & (! [X56 : term,X57 : term,X58 : (subst > term > term)] : ((((sub @ (X58 @ (sK486 @ X58) @ (sK485 @ X58)) @ (sK487 @ X58))) != ((X58 @ (comp @ (sK486 @ X58) @ (sK487 @ X58)) @ (sub @ (sK485 @ X58) @ (sK487 @ X58))))) | (((ap @ (sub @ X56 @ id) @ X57)) != ((lam @ (X58 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X65 : term,X66 : subst,X67 : subst] : (((sub @ (sK490 @ X66 @ X65) @ X67)) = ((sK490 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67)))) & (((ap @ (sub @ sK488 @ id) @ sK489)) = ((lam @ (sK490 @ sh @ one)))))) & (apnotvar = $true) & ((substmonoid_lthm = $true) | (((sK491 != ((comp @ id @ sK491))) | (((comp @ sK492 @ id)) != sK492)) & ! [X70 : subst] : (((comp @ id @ X70)) = X70) & ! [X71 : subst] : (((comp @ X71 @ id)) = X71))) & ((! [X72 : subst] : (((comp @ id @ X72)) = X72) & ! [X73 : subst] : (((comp @ X73 @ id)) = X73)) | (((comp @ id @ sK493)) != sK493) | (((comp @ sK494 @ id)) != sK494) | (substmonoid_lthm != $true)) & (! [X76 : (subst > term > subst > $o)] : ! [X78 : term] : (((X76 @ id @ X78 @ id)) = ((sK495 @ X76 @ X78))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X80 : (term > $o)] : (((X80 @ (sK497 @ X80))) != ((sK496 @ id @ (sK497 @ X80) @ id)))) & ((hoasinduction_lthm_3 = $true) | (sP48 != $true)) & ((sP48 = $true) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lem3_lthm = $true) | (sP42 != $true)) & ((sP42 = $true) | (hoasinduction_lem3_lthm != $true)) & (hoaslaminj_gthm = $true) & (! [X82 : term,X83 : (term > $o)] : ((($true != ((X83 @ (lam @ (sK498 @ X83))))) & (((X83 @ (sK498 @ X83))) = $true)) | (($true = ((var @ (sK499 @ X83)))) & (((X83 @ (sK499 @ X83))) != $true)) | ($true = ((sP39 @ X83))) | ($true = ((X83 @ X82)))) | (induction != $true)) & ((induction = $true) | (! [X88 : term] : (($true = ((sK501 @ (lam @ X88)))) | (((sK501 @ X88)) != $true)) & ! [X89 : term] : (($true != ((var @ X89))) | ($true = ((sK501 @ X89)))) & ($true != ((sP39 @ sK501))) & (((sK501 @ sK500)) != $true))) & (substmonoid_gthm = $true) & (pushprop_lem2v2_lthm = $true) & ((sP38 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP38 != $true)) & (hoasinduction_lem1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((induction2lem = $true) | ($true != sP36)) & (($true = sP36) | (induction2lem != $true)) & (pushprop_lem2v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & (ulamvarind = $true) & (hoasinduction_lem2v2_gthm = $true) & (((d2subst @ d_id)) = sh) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X91 : (subst > term > term)] : (((sub @ sK502 @ (push @ (sK503 @ X91) @ (sK504 @ X91)))) != ((X91 @ (sK504 @ X91) @ (sK503 @ X91))))) & (! [X94 : term] : ! [X96 : term,X97 : subst] : (((sub @ X94 @ (push @ X96 @ X97))) = ((sK505 @ X94 @ X97 @ X96))) | (hoasinduction_lem3v2_f != $true)) & ((hoasapinj1 = $true) | ((sK506 != sK508) & (((ap @ (sub @ sK508 @ id) @ sK509)) = ((ap @ (sub @ sK506 @ id) @ sK507))))) & (! [X102 : term,X103 : term,X104 : term,X105 : term] : ((X102 = X104) | (((ap @ (sub @ X104 @ id) @ X105)) != ((ap @ (sub @ X102 @ id) @ X103)))) | (hoasapinj1 != $true)) & ((axshiftcons = $true) | (((comp @ sh @ (push @ sK511 @ sK510))) != sK510)) & (! [X108 : subst,X109 : term] : (((comp @ sh @ (push @ X109 @ X108))) = X108) | (axshiftcons != $true)) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (! [X110 : term] : ! [X112 : subst,X113 : term] : (((sub @ X110 @ (push @ X113 @ X112))) = ((sK512 @ X110 @ X112 @ X113))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X115 : (subst > term > term)] : (((X115 @ (sK514 @ X115) @ (sK515 @ X115))) != ((sub @ sK513 @ (push @ (sK515 @ X115) @ (sK514 @ X115)))))) & (pushprop_lem3v2_lthm = $true) & (! [X118 : term] : (((sub @ X118 @ id)) = X118) | (axvarid != $true)) & ((axvarid = $true) | (sK516 != ((sub @ sK516 @ id)))) & (hoasinduction_gthm = $true) & (($true = sP34) | (hoasinduction_lem3aa != $true)) & ((hoasinduction_lem3aa = $true) | ($true != sP34)) & ((hoasinduction_lem3v2_lthm = $true) | (sP33 != $true)) & ((sP33 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (axvarshift = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lthm_orig = $true) & (pushprop_lem0_gthm = $true) & (! [X120 : term,X121 : (subst > term > term),X122 : (subst > term > term),X123 : subst] : ((((sub @ (X122 @ (sK517 @ X122) @ (sK519 @ X122)) @ (sK518 @ X122))) != ((X122 @ (comp @ (sK517 @ X122) @ (sK518 @ X122)) @ (sub @ (sK519 @ X122) @ (sK518 @ X122))))) | (((lam @ (X121 @ sh @ one))) != ((lam @ (X122 @ sh @ one)))) | (((X122 @ X123 @ X120)) = ((X121 @ X123 @ X120))) | (((sub @ (X121 @ (sK522 @ X121) @ (sK520 @ X121)) @ (sK521 @ X121))) != ((X121 @ (comp @ (sK522 @ X121) @ (sK521 @ X121)) @ (sub @ (sK520 @ X121) @ (sK521 @ X121)))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X134 : subst,X135 : subst,X136 : term] : (((sub @ (sK525 @ X134 @ X136) @ X135)) = ((sK525 @ (comp @ X134 @ X135) @ (sub @ X136 @ X135)))) & (((lam @ (sK525 @ sh @ one))) = ((lam @ (sK524 @ sh @ one)))) & (((sK524 @ sK526 @ sK523)) != ((sK525 @ sK526 @ sK523))) & ! [X137 : term,X138 : subst,X139 : subst] : (((sub @ (sK524 @ X139 @ X137) @ X138)) = ((sK524 @ (comp @ X139 @ X138) @ (sub @ X137 @ X138)))))) & (induction2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & ((! [X140 : subst] : (((comp @ id @ X140)) = X140) & ! [X141 : subst] : (((comp @ X141 @ id)) = X141)) | (substmonoid != $true)) & ((substmonoid = $true) | (((comp @ id @ sK527)) != sK527) | (sK528 != ((comp @ sK528 @ id)))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axmap = $true) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) | ! [X145 : (subst > term > term)] : (((sub @ sK529 @ (push @ one @ sh))) != ((X145 @ sh @ one)))) & (! [X146 : term] : (((sub @ X146 @ (push @ one @ sh))) = ((sK530 @ X146 @ sh @ one))) | (hoasinduction_lem3b != $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)))))))))))) & (hoaslamnotvar = $true) & ! [X148 : d_subst] : (d_id = X148) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((laminj = $true) | ((sK532 != sK531) & (((lam @ sK532)) = ((lam @ sK531))))) & (! [X151 : term,X152 : term] : ((X151 = X152) | (((lam @ X151)) != ((lam @ X152)))) | (laminj != $true)) & (ulamvarsh = $true) & (((d2subst @ d_id)) = id) & (pushprop_lem3v2 = $true) & ! [X153 : term] : (((d2term @ (sK533 @ X153))) = X153) & ((hoasinduction_lem2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2 != $true)) & ((axidl = $true) | (((comp @ id @ sK534)) != sK534)) & (! [X156 : subst] : (((comp @ id @ X156)) = X156) | (axidl != $true)) & (($true = sP29) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP29)) & (($true = sP28) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP28)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP24)) & (($true = sP24) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP19)) & (($true = sP19) | (hoasinduction_lem3aaa != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem1v2_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (! [X157 : subst] : (((comp @ X157 @ id)) = X157) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK535 @ id)) != sK535)) & (pushprop_gthm = $true) & (! [X159 : term,X160 : term,X161 : term,X162 : term] : ((X159 = X161) | (((ap @ (sub @ X162 @ id) @ X159)) != ((ap @ (sub @ X160 @ id) @ X161)))) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ((sK538 != sK536) & (((ap @ (sub @ sK539 @ id) @ sK536)) = ((ap @ (sub @ sK537 @ id) @ sK538))))) & ! [X167 : d_term] : (d_one = X167) & ((axvarcons = $true) | (sK540 != ((sub @ one @ (push @ sK540 @ sK541))))) & (! [X170 : term,X171 : subst] : (((sub @ one @ (push @ X170 @ X171))) = X170) | (axvarcons != $true)) & (($true = sP18) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP18)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasapinj2_lthm = $true) | (((sK545 != sK544) & (((ap @ (sub @ sK543 @ id) @ sK544)) = ((ap @ (sub @ sK542 @ id) @ sK545)))) & ! [X176 : term,X177 : term,X178 : term,X179 : term] : ((X177 = X178) | (((ap @ X176 @ X177)) != ((ap @ X179 @ X178)))))) & (! [X180 : term,X181 : term,X182 : term,X183 : term] : ((X182 = X183) | (((ap @ (sub @ X180 @ id) @ X183)) != ((ap @ (sub @ X181 @ id) @ X182)))) | ((sK547 != sK548) & (((ap @ sK549 @ sK548)) = ((ap @ sK546 @ sK547)))) | (hoasapinj2_lthm != $true)) & ((axscons = $true) | (((push @ (sub @ one @ sK550) @ (comp @ sh @ sK550))) != sK550)) & (! [X189 : subst] : (((push @ (sub @ one @ X189) @ (comp @ sh @ X189))) = X189) | (axscons != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP9 != $true)) & ((sP9 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem0 = $true) | ! [X191 : (term > $o)] : (((X191 @ (sK552 @ X191))) != ((sK551 @ id @ (sK552 @ X191) @ id)))) & (! [X193 : (subst > term > subst > $o)] : ! [X195 : term] : (((sK553 @ X193 @ X195)) = ((X193 @ id @ X195 @ id))) | (hoasinduction_lem0 != $true)) & (pushprop_lem1v2_gthm = $true) & (ulamvar1 != $true) & (hoasapnotvar_lthm = $true) & (induction2lem_gthm = $true) & ! [X196 : subst] : (((d2subst @ (sK554 @ X196))) = X196) & (one = ((d2term @ d_one))) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3v2a = $true) | (sP7 != $true)) & ((sP7 = $true) | (hoasinduction_lem3v2a != $true)) & (axclos = $true) & ((sP6 = $true) | (hoasinduction != $true)) & ((hoasinduction = $true) | (sP6 != $true)) & (! [X198 : (term > $o),X199 : term,X200 : (term > $o),X201 : subst] : (($true = ((X200 @ one))) | (((X198 @ (sub @ (sK555 @ X201 @ X200 @ X199 @ X198) @ (push @ X199 @ X201)))) != ((X200 @ (sK555 @ X201 @ X200 @ X199 @ X198)))) | ($true != ((X198 @ X199)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (($true != ((sK558 @ one))) & ! [X207 : term] : (((sK556 @ (sub @ X207 @ (push @ sK557 @ sK559)))) = ((sK558 @ X207))) & ($true = ((sK556 @ sK557))))) & ! [X208 : d_subst,X209 : d_subst] : ((((d2subst @ X209)) != ((d2subst @ X208))) | (X208 = X209)) & (termmset_gthm = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X211 : (subst > term > term)] : (((X211 @ sh @ one)) != ((sub @ sK560 @ (push @ one @ sh))))) & (! [X212 : term] : (((sK561 @ X212 @ sh @ one)) = ((sub @ X212 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (axabs = $true) & ! [X214 : d_term,X215 : d_term] : ((((d2term @ X215)) != ((d2term @ X214))) | (X214 = X215)) & (hoasapinj1_gthm = $true) & (pushprop_lem1_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3 = $true) | ($true != sP3)) & (($true = sP3) | (hoasinduction_lem3 != $true)) & (! [X216 : term,X217 : term] : ((((sub @ X217 @ sh)) != ((sub @ X216 @ sh))) | (X216 = X217)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK563 @ sh)) = ((sub @ sK562 @ sh))) & (sK562 != sK563))) & (pushprop = $true) & (! [X220 : term,X221 : (subst > term > subst > $o)] : (($true = ((X221 @ id @ X220 @ id))) | (($true != ((X221 @ id @ (ap @ (sub @ (sK564 @ X221) @ id) @ (sK565 @ X221)) @ id))) & ($true = ((X221 @ id @ (sK565 @ X221) @ id))) & ($true = ((X221 @ id @ (sK564 @ X221) @ id)))) | ($true = ((sP1 @ X221)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (($true != ((sK567 @ id @ sK566 @ id))) & ! [X226 : term,X227 : term] : (($true = ((sK567 @ id @ (ap @ (sub @ X226 @ id) @ X227) @ id))) | (((sK567 @ id @ X227 @ id)) != $true) | (((sK567 @ id @ X226 @ id)) != $true)) & ($true != ((sP1 @ sK567))))) & (hoasapinj2_gthm = $true) & (($true = sP0) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP0)) & ((sK568 != ((sub @ sK568 @ id))) | ((sK570 != sK569) & (((ap @ sK569 @ sK572)) = ((ap @ sK570 @ sK571)))) | ! [X233 : term,X234 : term,X235 : term,X236 : term] : ((X233 = X234) | (((ap @ (sub @ X234 @ id) @ X236)) != ((ap @ (sub @ X233 @ id) @ X235)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X237 : term] : (((sub @ X237 @ id)) = X237) & ! [X238 : term,X239 : term,X240 : term,X241 : term] : ((X238 = X239) | (((ap @ X238 @ X241)) != ((ap @ X239 @ X240)))) & ((sK573 != sK574) & (((ap @ (sub @ sK574 @ id) @ sK576)) = ((ap @ (sub @ sK573 @ id) @ sK575)))))) & (pushprop_lthm = $true) & ((((comp @ sh @ (push @ sK578 @ sK577))) != sK577) | ! [X248 : term,X249 : (term > $o),X250 : (term > $o),X251 : term,X252 : subst] : (($true != ((X249 @ X248))) | (((X250 @ (sub @ X248 @ (push @ X251 @ X252)))) = $true)) | (((sub @ one @ (push @ sK580 @ sK579))) != sK580) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X255 : subst,X256 : term] : (((comp @ sh @ (push @ X256 @ X255))) = X255) & (($true = ((sK582 @ sK581))) & (((sK583 @ (sub @ sK581 @ (push @ sK584 @ sK585)))) != $true)) & ! [X262 : subst,X263 : term] : (((sub @ one @ (push @ X263 @ X262))) = X263))) & (axassoc = $true) & (hoasapnotvar = $true) & (! [X264 : term,X265 : (term > $o),X266 : subst] : ! [X268 : term] : (((X265 @ (sub @ X268 @ (push @ X264 @ X266)))) = ((sK586 @ X266 @ X265 @ X264 @ X268))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X272 : (term > $o)] : (((X272 @ (sK590 @ X272))) != ((sK588 @ (sub @ (sK590 @ X272) @ (push @ sK587 @ sK589))))))),
% 1.42/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,vAPP,sK465,sK466,sK467,sK468,sK469,sK470,sK471,sK472,sK473,sK474,vAPP,sK476,sK477,sK478,vAPP,sK480,sK481,sK482,sK483,sK484,vAPP,vAPP,vAPP,sK488,sK489,sK490,sK491,sK492,sK493,sK494,vAPP,sK496,vAPP,vAPP,vAPP,sK500,sK501,sK502,vAPP,vAPP,vAPP,sK506,sK507,sK508,sK509,sK510,sK511,vAPP,sK513,vAPP,vAPP,sK516,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK523,sK524,sK525,sK526,sK527,sK528,sK529,vAPP,sK531,sK532,vAPP,sK534,sK535,sK536,sK537,sK538,sK539,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,sK550,sK551,vAPP,vAPP,vAPP,vAPP,sK556,sK557,sK558,sK559,sK560,vAPP,sK562,sK563,vAPP,vAPP,sK566,sK567,sK568,sK569,sK570,sK571,sK572,sK573,sK574,sK575,sK576,sK577,sK578,sK579,sK580,sK581,sK582,sK583,sK584,sK585,vAPP,sK587,sK588,sK589,vAPP]),skolemize(X0,sK457),skolemize(X4,sK458),skolemize(X5,sK459),skolemize(X6,sK460),skolemize(X7,sK461),skolemize(X9,sK462),skolemize(X10,sK463),skolemize(X25,sK71 @ X15),skolemize(X16,sK465),skolemize(X17,sK466),skolemize(X18,sK467),skolemize(X19,sK468),skolemize(X24,sK469),skolemize(X27,sK470),skolemize(X32,sK471),skolemize(X33,sK472),skolemize(X34,sK473),skolemize(X35,sK474),skolemize(X25,sK71 @ X15),skolemize(X41,sK476),skolemize(X42,sK477),skolemize(X43,sK478),skolemize(X25,sK71 @ X15),skolemize(X51,sK480),skolemize(X52,sK481),skolemize(X53,sK482),skolemize(X54,sK483),skolemize(X55,sK484),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X62,sK488),skolemize(X63,sK489),skolemize(X64,sK490),skolemize(X68,sK491),skolemize(X69,sK492),skolemize(X74,sK493),skolemize(X75,sK494),skolemize(X25,sK71 @ X15),skolemize(X79,sK496),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X86,sK500),skolemize(X87,sK501),skolemize(X90,sK502),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X98,sK506),skolemize(X99,sK507),skolemize(X100,sK508),skolemize(X101,sK509),skolemize(X106,sK510),skolemize(X107,sK511),skolemize(X25,sK71 @ X15),skolemize(X114,sK513),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X119,sK516),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X130,sK523),skolemize(X131,sK524),skolemize(X132,sK525),skolemize(X133,sK526),skolemize(X142,sK527),skolemize(X143,sK528),skolemize(X144,sK529),skolemize(X25,sK71 @ X15),skolemize(X149,sK531),skolemize(X150,sK532),skolemize(X25,sK71 @ X15),skolemize(X155,sK534),skolemize(X158,sK535),skolemize(X163,sK536),skolemize(X164,sK537),skolemize(X165,sK538),skolemize(X166,sK539),skolemize(X168,sK540),skolemize(X169,sK541),skolemize(X172,sK542),skolemize(X173,sK543),skolemize(X174,sK544),skolemize(X175,sK545),skolemize(X184,sK546),skolemize(X185,sK547),skolemize(X186,sK548),skolemize(X187,sK549),skolemize(X188,sK550),skolemize(X190,sK551),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X203,sK556),skolemize(X204,sK557),skolemize(X205,sK558),skolemize(X206,sK559),skolemize(X210,sK560),skolemize(X25,sK71 @ X15),skolemize(X218,sK562),skolemize(X219,sK563),skolemize(X25,sK71 @ X15),skolemize(X25,sK71 @ X15),skolemize(X224,sK566),skolemize(X225,sK567),skolemize(X228,sK568),skolemize(X229,sK569),skolemize(X230,sK570),skolemize(X231,sK571),skolemize(X232,sK572),skolemize(X242,sK573),skolemize(X243,sK574),skolemize(X244,sK575),skolemize(X245,sK576),skolemize(X246,sK577),skolemize(X247,sK578),skolemize(X253,sK579),skolemize(X254,sK580),skolemize(X257,sK581),skolemize(X258,sK582),skolemize(X259,sK583),skolemize(X260,sK584),skolemize(X261,sK585),skolemize(X25,sK71 @ X15),skolemize(X269,sK587),skolemize(X270,sK588),skolemize(X271,sK589),skolemize(X25,sK71 @ X15)],[f262])).
% 1.42/0.52 thf(f264,plain,(
% 1.42/0.52 (hoaslaminj != ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => (((hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))))))),
% 1.42/0.52 inference(cnf_transformation,[],[f8])).
% 1.42/0.52 thf(f829,plain,(
% 1.42/0.52 ( ! [X167 : d_term] : ((d_one = X167)) )),
% 1.42/0.52 inference(cnf_transformation,[],[f263])).
% 1.42/0.52 thf(f851,plain,(
% 1.42/0.52 ( ! [X153 : term] : ((((d2term @ (sK533 @ X153))) = X153)) )),
% 1.42/0.52 inference(cnf_transformation,[],[f263])).
% 1.42/0.52 thf(f858,plain,(
% 1.42/0.52 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 1.42/0.52 inference(cnf_transformation,[],[f263])).
% 1.42/0.52 thf(f873,plain,(
% 1.42/0.52 (hoaslaminj = $true) | (((sK524 @ sK526 @ sK523)) != ((sK525 @ sK526 @ sK523)))),
% 1.42/0.52 inference(cnf_transformation,[],[f263])).
% 1.42/0.52 thf(f981,plain,(
% 1.42/0.52 (hoaslaminj != ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))))))),
% 1.42/0.52 inference(definition_unfolding,[],[f264,f858,f858])).
% 1.42/0.52 thf(f1021,plain,(
% 1.42/0.52 (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))))) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(xor_proxy_clausification,[],[f981])).
% 1.42/0.52 thf(f1022,plain,(
% 1.42/0.52 (hoaslaminj = $false) | ((((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y2 @ Y1) @ Y3) = (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3))))))))) => (!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ term @ (^[Y4 : term]: ((Y1 @ (comp @ Y2 @ Y3) @ (sub @ Y4 @ Y3)) = (sub @ (Y1 @ Y2 @ Y4) @ Y3)))))))) => ((((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) = ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (d2term @ d_one)))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y0 @ Y2 @ Y3)))))) => (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ Y2 @ Y3) = (Y1 @ Y2 @ Y3)))))))))))) @ sK591)) = $false)),
% 1.42/0.52 inference(sigma_proxy_clausification,[],[f1021])).
% 1.42/0.52 thf(f1023,plain,(
% 1.42/0.52 ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK591 @ Y1 @ Y0) @ Y2) = (sK591 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2))))))))) => (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => (((d2term @ d_one) = (d2term @ d_one)) => (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sK591 @ Y1 @ Y2) = (Y0 @ Y1 @ Y2)))))))))))) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(beta-eta_normalization,[],[f1022])).
% 1.42/0.52 thf(f1024,plain,(
% 1.42/0.52 (hoaslaminj = $false) | (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => (((d2term @ d_one) = (d2term @ d_one)) => (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sK591 @ Y1 @ Y2) = (Y0 @ Y1 @ Y2))))))))))) = $false)),
% 1.42/0.52 inference(imp_proxy_clausification,[],[f1023])).
% 1.42/0.52 thf(f1033,plain,(
% 1.42/0.52 ((((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: ((Y0 @ (comp @ Y1 @ Y2) @ (sub @ Y3 @ Y2)) = (sub @ (Y0 @ Y1 @ Y3) @ Y2)))))))) => (((d2term @ d_one) = (d2term @ d_one)) => (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sK591 @ Y1 @ Y2) = (Y0 @ Y1 @ Y2))))))))) @ sK592)) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(sigma_proxy_clausification,[],[f1024])).
% 1.42/0.52 thf(f1034,plain,(
% 1.42/0.52 ((((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: ((sK592 @ (comp @ Y0 @ Y1) @ (sub @ Y2 @ Y1)) = (sub @ (sK592 @ Y0 @ Y2) @ Y1)))))))) => (((d2term @ d_one) = (d2term @ d_one)) => (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sK591 @ Y0 @ Y1) = (sK592 @ Y0 @ Y1))))))))) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(beta-eta_normalization,[],[f1033])).
% 1.42/0.52 thf(f1035,plain,(
% 1.42/0.52 (((((d2term @ d_one) = (d2term @ d_one)) => (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sK591 @ Y0 @ Y1) = (sK592 @ Y0 @ Y1)))))))) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(imp_proxy_clausification,[],[f1034])).
% 1.42/0.52 thf(f1044,plain,(
% 1.42/0.52 (hoaslaminj = $false) | (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sK591 @ Y0 @ Y1) = (sK592 @ Y0 @ Y1))))))) = $false)),
% 1.42/0.52 inference(imp_proxy_clausification,[],[f1035])).
% 1.42/0.52 thf(f1047,plain,(
% 1.42/0.52 ((((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: ((sK591 @ Y0 @ Y1) = (sK592 @ Y0 @ Y1))))) @ sK593)) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(sigma_proxy_clausification,[],[f1044])).
% 1.42/0.52 thf(f1048,plain,(
% 1.42/0.52 (((!! @ term @ (^[Y0 : term]: ((sK591 @ sK593 @ Y0) = (sK592 @ sK593 @ Y0))))) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(beta-eta_normalization,[],[f1047])).
% 1.42/0.52 thf(f1049,plain,(
% 1.42/0.52 ((((^[Y0 : term]: ((sK591 @ sK593 @ Y0) = (sK592 @ sK593 @ Y0))) @ sK594)) = $false) | (hoaslaminj = $false)),
% 1.42/0.52 inference(sigma_proxy_clausification,[],[f1048])).
% 1.42/0.52 thf(f1050,plain,(
% 1.42/0.52 (hoaslaminj = $false) | ((((sK591 @ sK593 @ sK594) = (sK592 @ sK593 @ sK594))) = $false)),
% 1.42/0.52 inference(beta-eta_normalization,[],[f1049])).
% 1.42/0.52 thf(f1051,plain,(
% 1.42/0.52 (hoaslaminj = $false) | (((sK592 @ sK593 @ sK594)) != ((sK591 @ sK593 @ sK594)))),
% 1.42/0.52 inference(equality_proxy_clausification,[],[f1050])).
% 1.42/0.52 thf(f1615,definition,(
% 1.42/0.52 spl601_104 <=> (hoaslaminj = $true)),
% 1.42/0.52 introduced(definition,[new_symbols(definition,[spl601_104])],[avatar_definition])).
% 1.42/0.52 thf(f1617,plain,(
% 1.42/0.52 (hoaslaminj = $true) | ~spl601_104),
% 1.42/0.52 inference(avatar_component_clause,[],[f1615])).
% 1.42/0.52 thf(f1844,definition,(
% 1.42/0.52 spl601_158 <=> (((sK524 @ sK526 @ sK523)) = ((sK525 @ sK526 @ sK523)))),
% 1.42/0.52 introduced(definition,[new_symbols(definition,[spl601_158])],[avatar_definition])).
% 1.42/0.52 thf(f1846,plain,(
% 1.42/0.52 (((sK524 @ sK526 @ sK523)) != ((sK525 @ sK526 @ sK523))) | spl601_158),
% 1.42/0.52 inference(avatar_component_clause,[],[f1844])).
% 1.42/0.52 thf(f1847,plain,(
% 1.42/0.52 spl601_104 | ~spl601_158),
% 1.42/0.52 inference(avatar_split_clause,[],[f873,f1844,f1615])).
% 1.42/0.52 thf(f2048,definition,(
% 1.42/0.52 spl601_206 <=> (hoaslaminj = $false)),
% 1.42/0.52 introduced(definition,[new_symbols(definition,[spl601_206])],[avatar_definition])).
% 1.42/0.52 thf(f2050,plain,(
% 1.42/0.52 (hoaslaminj = $false) | ~spl601_206),
% 1.42/0.52 inference(avatar_component_clause,[],[f2048])).
% 1.42/0.52 thf(f2057,definition,(
% 1.42/0.52 spl601_208 <=> (((sK592 @ sK593 @ sK594)) = ((sK591 @ sK593 @ sK594)))),
% 1.42/0.52 introduced(definition,[new_symbols(definition,[spl601_208])],[avatar_definition])).
% 1.42/0.52 thf(f2059,plain,(
% 1.42/0.52 (((sK592 @ sK593 @ sK594)) != ((sK591 @ sK593 @ sK594))) | spl601_208),
% 1.42/0.52 inference(avatar_component_clause,[],[f2057])).
% 1.42/0.52 thf(f2060,plain,(
% 1.42/0.52 ~spl601_208 | spl601_206),
% 1.42/0.52 inference(avatar_split_clause,[],[f1051,f2048,f2057])).
% 1.42/0.52 thf(f3907,plain,(
% 1.42/0.52 ($true = $false) | (~spl601_104 | ~spl601_206)),
% 1.42/0.52 inference(forward_demodulation,[],[f1617,f2050])).
% 1.42/0.52 thf(f3908,plain,(
% 1.42/0.52 $false | (~spl601_104 | ~spl601_206)),
% 1.42/0.52 inference(trivial_inequality_removal,[],[f3907])).
% 1.42/0.52 thf(f3909,plain,(
% 1.42/0.52 ~spl601_104 | ~spl601_206),
% 1.42/0.52 inference(avatar_contradiction_clause,[],[f3908])).
% 1.42/0.52 thf(f4065,plain,(
% 1.42/0.52 ( ! [X153 : term] : ((((d2term @ d_one)) = X153)) )),
% 1.42/0.52 inference(forward_demodulation,[],[f851,f829])).
% 1.42/0.52 thf(f4078,plain,(
% 1.42/0.52 (((d2term @ d_one)) != ((sK591 @ sK593 @ sK594))) | spl601_208),
% 1.42/0.52 inference(superposition,[],[f2059,f4065])).
% 1.42/0.52 thf(f4081,plain,(
% 1.42/0.52 $false | spl601_208),
% 1.42/0.52 inference(forward_subsumption_resolution,[],[f4078,f4065])).
% 1.42/0.52 thf(f4082,plain,(
% 1.42/0.52 spl601_208),
% 1.42/0.52 inference(avatar_contradiction_clause,[],[f4081])).
% 1.42/0.52 thf(f4085,plain,(
% 1.42/0.52 (((d2term @ d_one)) != ((sK524 @ sK526 @ sK523))) | spl601_158),
% 1.42/0.52 inference(forward_demodulation,[],[f1846,f4065])).
% 1.42/0.52 thf(f4090,plain,(
% 1.42/0.52 $false | spl601_158),
% 1.42/0.52 inference(forward_subsumption_resolution,[],[f4085,f4065])).
% 1.42/0.52 thf(f4091,plain,(
% 1.42/0.52 spl601_158),
% 1.42/0.52 inference(avatar_contradiction_clause,[],[f4090])).
% 1.42/0.52 cnf(s107, plain, spl601_104 | ~spl601_158, inference(sat_conversion,[],[f1847])).
% 1.42/0.52 cnf(s154, plain, spl601_206 | ~spl601_208, inference(sat_conversion,[],[f2060])).
% 1.42/0.52 cnf(s607, plain, ~spl601_104 | ~spl601_206, inference(sat_conversion,[],[f3909])).
% 1.42/0.52 cnf(s608, plain, spl601_208, inference(sat_conversion,[],[f4082])).
% 1.42/0.52 cnf(s609, plain, spl601_158, inference(sat_conversion,[],[f4091])).
% 1.42/0.52 cnf(s610, plain, spl601_206, inference(rat,[],[s154,s608])).
% 1.42/0.52 cnf(s611, plain, ~spl601_104, inference(rat,[],[s607,s610])).
% 1.42/0.52 cnf(s614, plain, $false, inference(rat,[],[s107,s609,s611])).
% 1.42/0.52 thf(f4096,plain,(
% 1.42/0.52 $false),
% 1.42/0.52 inference(avatar_sat_refutation,[],[s614])).
% 1.42/0.52 % SZS output end Proof for theBenchmark
% 1.42/0.52 % (2300711)------------------------------
% 1.42/0.52 % (2300711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (2300711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (2300711)CaDiCaL version: 2.1.3
% 1.42/0.52 % (2300711)Termination reason: Refutation
% 1.42/0.52 % (2300711)Time elapsed: 0.098 s
% 1.42/0.52 % (2300711)Peak memory usage: 17 MB
% 1.42/0.52 % (2300711)Instructions burned: 416 (million)
% 1.42/0.52 % (2300672)Success in time 0.232 s
% 1.42/0.52 % Vampire exiting
%------------------------------------------------------------------------------