%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX159^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:35 AM UTC 2026
% Result : Theorem 2.19s 0.59s
% Output : Refutation 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX159^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 16:09:18 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/0.40 % (3053520)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.73/0.40 % (3053526)lrs+10_16_si=on:nwc=1.5:random_seed=2432135436:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.73/0.40 % (3053531)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.73/0.40 % (3053531)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
% 0.73/0.40 % (3053526)Instruction limit reached!
% 0.73/0.40 % (3053526)------------------------------
% 0.73/0.40 % (3053526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (3053526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (3053526)CaDiCaL version: 2.1.3
% 0.73/0.40 % (3053526)Termination reason: Instruction limit
% 0.73/0.40 % (3053526)Termination phase: shuffling
% 0.73/0.40 % (3053526)Time elapsed: 0.004 s
% 0.73/0.40 % (3053526)Peak memory usage: 10 MB
% 0.73/0.40 % (3053526)Instructions burned: 20 (million)
% 0.73/0.40 % (3053525)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=665458101:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.73/0.40 % (3053527)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4171938246:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.73/0.40 % (3053530)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2394643523:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.73/0.40 % (3053529)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=318919825:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.73/0.40 % (3053528)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=2428472673: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)
% 0.73/0.40 % (3053531)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=1474701711:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.73/0.40 % (3053527)Instruction limit reached!
% 0.73/0.40 % (3053527)------------------------------
% 0.73/0.40 % (3053527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (3053527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (3053527)CaDiCaL version: 2.1.3
% 0.73/0.40 % (3053527)Termination reason: Instruction limit
% 0.73/0.40 % (3053527)Termination phase: shuffling
% 0.73/0.40 % (3053527)Time elapsed: 0.002 s
% 0.73/0.40 % (3053527)Peak memory usage: 9 MB
% 0.73/0.40 % (3053527)Instructions burned: 5 (million)
% 0.73/0.40 % (3053533)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=760720466:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.40 % (3053533)Instruction limit reached!
% 0.73/0.40 % (3053533)------------------------------
% 0.73/0.40 % (3053533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (3053533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (3053533)CaDiCaL version: 2.1.3
% 0.73/0.40 % (3053533)Termination reason: Instruction limit
% 0.73/0.40 % (3053533)Termination phase: shuffling
% 0.73/0.40 % (3053533)Time elapsed: 0.0000 s
% 0.73/0.40 % (3053533)Peak memory usage: 9 MB
% 0.73/0.40 % (3053533)Instructions burned: 2 (million)
% 0.73/0.40 % (3053529)Instruction limit reached!
% 0.73/0.40 % (3053529)------------------------------
% 0.73/0.40 % (3053529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.40 % (3053529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.40 % (3053529)CaDiCaL version: 2.1.3
% 0.73/0.40 % (3053529)Termination reason: Instruction limit
% 0.73/0.40 % (3053529)Termination phase: Property scanning
% 0.73/0.40 % (3053529)Time elapsed: 0.011 s
% 0.73/0.40 % (3053529)Peak memory usage: 10 MB
% 0.73/0.40 % (3053529)Instructions burned: 24 (million)
% 0.73/0.40 % (3053542)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.43 % (3053542)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3873877625:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.73/0.43 % (3053540)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1861675610:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.73/0.43 % (3053542)Instruction limit reached!
% 0.73/0.43 % (3053542)------------------------------
% 0.73/0.43 % (3053542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.43 % (3053542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.43 % (3053542)CaDiCaL version: 2.1.3
% 0.73/0.43 % (3053542)Termination reason: Instruction limit
% 0.73/0.43 % (3053542)Termination phase: shuffling
% 0.73/0.43 % (3053542)Time elapsed: 0.002 s
% 0.73/0.43 % (3053542)Peak memory usage: 10 MB
% 0.73/0.43 % (3053542)Instructions burned: 9 (million)
% 0.73/0.43 % (3053540)Instruction limit reached!
% 0.73/0.43 % (3053540)------------------------------
% 0.73/0.43 % (3053540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.43 % (3053540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.43 % (3053540)CaDiCaL version: 2.1.3
% 0.73/0.43 % (3053540)Termination reason: Instruction limit
% 0.73/0.43 % (3053540)Termination phase: shuffling
% 0.73/0.43 % (3053540)Time elapsed: 0.003 s
% 0.73/0.43 % (3053540)Peak memory usage: 10 MB
% 0.73/0.43 % (3053540)Instructions burned: 6 (million)
% 0.73/0.43 % (3053543)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1977991492:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.73/0.43 % (3053546)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
% 0.73/0.43 % (3053546)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.73/0.43 % (3053546)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=41986784:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.73/0.43 % (3053530)Instruction limit reached!
% 0.73/0.43 % (3053530)------------------------------
% 0.73/0.43 % (3053530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.43 % (3053530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.43 % (3053530)CaDiCaL version: 2.1.3
% 0.73/0.43 % (3053530)Termination reason: Instruction limit
% 0.73/0.43 % (3053530)Termination phase: Preprocessing 3
% 0.73/0.43 % (3053530)Time elapsed: 0.033 s
% 0.73/0.43 % (3053530)Peak memory usage: 12 MB
% 0.73/0.43 % (3053530)Instructions burned: 76 (million)
% 0.73/0.43 % (3053543)Instruction limit reached!
% 0.73/0.43 % (3053543)------------------------------
% 0.73/0.43 % (3053543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.43 % (3053543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.43 % (3053543)CaDiCaL version: 2.1.3
% 0.73/0.43 % (3053543)Termination reason: Instruction limit
% 0.73/0.43 % (3053543)Termination phase: shuffling
% 0.73/0.43 % (3053543)Time elapsed: 0.006 s
% 0.73/0.43 % (3053543)Peak memory usage: 10 MB
% 0.73/0.43 % (3053543)Instructions burned: 14 (million)
% 0.73/0.43 % (3053546)Instruction limit reached!
% 0.73/0.43 % (3053546)------------------------------
% 0.73/0.43 % (3053546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.43 % (3053546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.43 % (3053546)CaDiCaL version: 2.1.3
% 0.73/0.43 % (3053546)Termination reason: Instruction limit
% 0.73/0.43 % (3053546)Termination phase: Property scanning
% 0.73/0.43 % (3053546)Time elapsed: 0.007 s
% 0.73/0.43 % (3053546)Peak memory usage: 10 MB
% 0.73/0.43 % (3053546)Instructions burned: 32 (million)
% 0.73/0.43 % (3053547)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=1149468382:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.73/0.43 % (3053552)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1576162236:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.73/0.47 % (3053551)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.73/0.47 % (3053550)lrs+10_1_si=on:cs=on:random_seed=933692331:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.73/0.47 % (3053551)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=3977560092:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.73/0.47 % (3053550)Instruction limit reached!
% 0.73/0.47 % (3053550)------------------------------
% 0.73/0.47 % (3053550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053550)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053550)Termination reason: Instruction limit
% 0.73/0.47 % (3053550)Termination phase: shuffling
% 0.73/0.47 % (3053550)Time elapsed: 0.004 s
% 0.73/0.47 % (3053550)Peak memory usage: 10 MB
% 0.73/0.47 % (3053550)Instructions burned: 9 (million)
% 0.73/0.47 % (3053551)Instruction limit reached!
% 0.73/0.47 % (3053551)------------------------------
% 0.73/0.47 % (3053551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053551)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053551)Termination reason: Instruction limit
% 0.73/0.47 % (3053551)Termination phase: shuffling
% 0.73/0.47 % (3053551)Time elapsed: 0.002 s
% 0.73/0.47 % (3053551)Peak memory usage: 10 MB
% 0.73/0.47 % (3053551)Instructions burned: 4 (million)
% 0.73/0.47 % (3053552)Refutation not found, incomplete strategy
% 0.73/0.47 % (3053552)------------------------------
% 0.73/0.47 % (3053552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053552)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053552)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.47 % (3053552)Time elapsed: 0.009 s
% 0.73/0.47 % (3053552)Peak memory usage: 12 MB
% 0.73/0.47 % (3053552)Instructions burned: 38 (million)
% 0.73/0.47 % (3053552)------------------------------
% 0.73/0.47 % (3053552)------------------------------
% 0.73/0.47 % (3053531)Instruction limit reached!
% 0.73/0.47 % (3053531)------------------------------
% 0.73/0.47 % (3053531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053531)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053531)Termination reason: Instruction limit
% 0.73/0.47 % (3053531)Termination phase: Property scanning
% 0.73/0.47 % (3053531)Time elapsed: 0.069 s
% 0.73/0.47 % (3053531)Peak memory usage: 13 MB
% 0.73/0.47 % (3053531)Instructions burned: 159 (million)
% 0.73/0.47 % (3053525)Instruction limit reached!
% 0.73/0.47 % (3053525)------------------------------
% 0.73/0.47 % (3053525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053525)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053525)Termination reason: Instruction limit
% 0.73/0.47 % (3053525)Termination phase: Preprocessing 3
% 0.73/0.47 % (3053525)Time elapsed: 0.071 s
% 0.73/0.47 % (3053525)Peak memory usage: 13 MB
% 0.73/0.47 % (3053525)Instructions burned: 88 (million)
% 0.73/0.47 % (3053559)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3527963252:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.73/0.47 % (3053559)Instruction limit reached!
% 0.73/0.47 % (3053559)------------------------------
% 0.73/0.47 % (3053559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.47 % (3053559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.47 % (3053559)CaDiCaL version: 2.1.3
% 0.73/0.47 % (3053559)Termination reason: Instruction limit
% 0.73/0.47 % (3053559)Termination phase: shuffling
% 0.73/0.47 % (3053559)Time elapsed: 0.003 s
% 0.73/0.47 % (3053559)Peak memory usage: 10 MB
% 0.73/0.47 % (3053559)Instructions burned: 16 (million)
% 0.73/0.47 % (3053557)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3292393814:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.36/0.53 % (3053558)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=379902267:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.36/0.53 % (3053547)Instruction limit reached!
% 1.36/0.53 % (3053547)------------------------------
% 1.36/0.53 % (3053547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (3053547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (3053547)CaDiCaL version: 2.1.3
% 1.36/0.53 % (3053547)Termination reason: Instruction limit
% 1.36/0.53 % (3053547)Termination phase: Saturation
% 1.36/0.53 % (3053547)Time elapsed: 0.036 s
% 1.36/0.53 % (3053547)Peak memory usage: 12 MB
% 1.36/0.53 % (3053547)Instructions burned: 88 (million)
% 1.36/0.53 % (3053563)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=28081420: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)
% 1.36/0.53 % (3053563)Instruction limit reached!
% 1.36/0.53 % (3053563)------------------------------
% 1.36/0.53 % (3053563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (3053563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (3053563)CaDiCaL version: 2.1.3
% 1.36/0.53 % (3053563)Termination reason: Instruction limit
% 1.36/0.53 % (3053563)Termination phase: shuffling
% 1.36/0.53 % (3053563)Time elapsed: 0.001 s
% 1.36/0.53 % (3053563)Peak memory usage: 9 MB
% 1.36/0.53 % (3053563)Instructions burned: 5 (million)
% 1.36/0.53 % (3053560)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2773881179:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.36/0.53 % (3053558)Instruction limit reached!
% 1.36/0.53 % (3053558)------------------------------
% 1.36/0.53 % (3053558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (3053558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (3053558)CaDiCaL version: 2.1.3
% 1.36/0.53 % (3053558)Termination reason: Instruction limit
% 1.36/0.53 % (3053558)Termination phase: Property scanning
% 1.36/0.53 % (3053558)Time elapsed: 0.012 s
% 1.36/0.53 % (3053558)Peak memory usage: 10 MB
% 1.36/0.53 % (3053558)Instructions burned: 27 (million)
% 1.36/0.53 % (3053562)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=182728835:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.36/0.53 % (3053568)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3311036699:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.36/0.53 % (3053562)Instruction limit reached!
% 1.36/0.53 % (3053562)------------------------------
% 1.36/0.53 % (3053562)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (3053562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (3053562)CaDiCaL version: 2.1.3
% 1.36/0.53 % (3053562)Termination reason: Instruction limit
% 1.36/0.53 % (3053562)Termination phase: shuffling
% 1.36/0.53 % (3053562)Time elapsed: 0.006 s
% 1.36/0.53 % (3053562)Peak memory usage: 10 MB
% 1.36/0.53 % (3053562)Instructions burned: 14 (million)
% 1.36/0.53 % (3053566)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3067899687:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.36/0.53 % (3053568)Instruction limit reached!
% 1.36/0.53 % (3053568)------------------------------
% 1.36/0.53 % (3053568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.53 % (3053568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.53 % (3053568)CaDiCaL version: 2.1.3
% 1.36/0.53 % (3053568)Termination reason: Instruction limit
% 1.36/0.53 % (3053568)Termination phase: Property scanning
% 1.36/0.53 % (3053568)Time elapsed: 0.006 s
% 1.36/0.53 % (3053568)Peak memory usage: 10 MB
% 1.36/0.53 % (3053568)Instructions burned: 26 (million)
% 1.36/0.53 % (3053570)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2357812419:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.36/0.53 % (3053575)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.36/0.53 % (3053566)Instruction limit reached!
% 1.36/0.53 % (3053566)------------------------------
% 1.36/0.53 % (3053566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053566)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053566)Termination reason: Instruction limit
% 1.36/0.59 % (3053566)Termination phase: shuffling
% 1.36/0.59 % (3053566)Time elapsed: 0.011 s
% 1.36/0.59 % (3053566)Peak memory usage: 10 MB
% 1.36/0.59 % (3053566)Instructions burned: 27 (million)
% 1.36/0.59 % (3053575)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=3073164067:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.36/0.59 % (3053573)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
% 1.36/0.59 % (3053573)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.36/0.59 % (3053575)Instruction limit reached!
% 1.36/0.59 % (3053575)------------------------------
% 1.36/0.59 % (3053575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053575)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053575)Termination reason: Instruction limit
% 1.36/0.59 % (3053575)Termination phase: shuffling
% 1.36/0.59 % (3053575)Time elapsed: 0.002 s
% 1.36/0.59 % (3053575)Peak memory usage: 10 MB
% 1.36/0.59 % (3053575)Instructions burned: 9 (million)
% 1.36/0.59 % (3053573)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=895553217:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.36/0.59 % (3053573)Instruction limit reached!
% 1.36/0.59 % (3053573)------------------------------
% 1.36/0.59 % (3053573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053573)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053573)Termination reason: Instruction limit
% 1.36/0.59 % (3053573)Termination phase: shuffling
% 1.36/0.59 % (3053573)Time elapsed: 0.006 s
% 1.36/0.59 % (3053573)Peak memory usage: 10 MB
% 1.36/0.59 % (3053573)Instructions burned: 15 (million)
% 1.36/0.59 % (3053579)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=172450833:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.36/0.59 % (3053579)Instruction limit reached!
% 1.36/0.59 % (3053579)------------------------------
% 1.36/0.59 % (3053579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053579)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053579)Termination reason: Instruction limit
% 1.36/0.59 % (3053579)Termination phase: shuffling
% 1.36/0.59 % (3053579)Time elapsed: 0.002 s
% 1.36/0.59 % (3053579)Peak memory usage: 10 MB
% 1.36/0.59 % (3053579)Instructions burned: 11 (million)
% 1.36/0.59 % (3053577)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=2951682007:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.36/0.59 % (3053570)Instruction limit reached!
% 1.36/0.59 % (3053570)------------------------------
% 1.36/0.59 % (3053570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053570)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053570)Termination reason: Instruction limit
% 1.36/0.59 % (3053570)Termination phase: Preprocessing 3
% 1.36/0.59 % (3053570)Time elapsed: 0.027 s
% 1.36/0.59 % (3053570)Peak memory usage: 11 MB
% 1.36/0.59 % (3053570)Instructions burned: 61 (million)
% 1.36/0.59 % (3053583)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2150138541:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.36/0.59 % (3053583)Instruction limit reached!
% 1.36/0.59 % (3053583)------------------------------
% 1.36/0.59 % (3053583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053583)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053583)Termination reason: Instruction limit
% 1.36/0.59 % (3053583)Termination phase: shuffling
% 1.36/0.59 % (3053583)Time elapsed: 0.004 s
% 1.36/0.59 % (3053583)Peak memory usage: 10 MB
% 1.36/0.59 % (3053583)Instructions burned: 21 (million)
% 1.36/0.59 % (3053577)Instruction limit reached!
% 1.36/0.59 % (3053577)------------------------------
% 1.36/0.59 % (3053577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053577)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053577)Termination reason: Instruction limit
% 1.36/0.59 % (3053577)Termination phase: Property scanning
% 1.36/0.59 % (3053577)Time elapsed: 0.014 s
% 1.36/0.59 % (3053577)Peak memory usage: 10 MB
% 1.36/0.59 % (3053577)Instructions burned: 31 (million)
% 1.36/0.59 % (3053581)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=85707816:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.36/0.59 % (3053587)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3876014754:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.36/0.59 % (3053585)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4230361261:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.36/0.59 % (3053581)Instruction limit reached!
% 1.36/0.59 % (3053581)------------------------------
% 1.36/0.59 % (3053581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053581)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053581)Termination reason: Instruction limit
% 1.36/0.59 % (3053581)Termination phase: shuffling
% 1.36/0.59 % (3053581)Time elapsed: 0.014 s
% 1.36/0.59 % (3053581)Peak memory usage: 10 MB
% 1.36/0.59 % (3053581)Instructions burned: 23 (million)
% 1.36/0.59 % (3053588)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3379780223:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.36/0.59 % (3053557)Instruction limit reached!
% 1.36/0.59 % (3053557)------------------------------
% 1.36/0.59 % (3053557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053557)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053557)Termination reason: Instruction limit
% 1.36/0.59 % (3053557)Termination phase: Saturation
% 1.36/0.59 % (3053557)Time elapsed: 0.110 s
% 1.36/0.59 % (3053557)Peak memory usage: 15 MB
% 1.36/0.59 % (3053557)Instructions burned: 250 (million)
% 1.36/0.59 % (3053593)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2319075451:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.36/0.59 % (3053587)Instruction limit reached!
% 1.36/0.59 % (3053587)------------------------------
% 1.36/0.59 % (3053587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053587)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053587)Termination reason: Instruction limit
% 1.36/0.59 % (3053587)Termination phase: Property scanning
% 1.36/0.59 % (3053587)Time elapsed: 0.041 s
% 1.36/0.59 % (3053587)Peak memory usage: 13 MB
% 1.36/0.59 % (3053587)Instructions burned: 146 (million)
% 1.36/0.59 % (3053595)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.36/0.59 % (3053596)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1827953086:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.36/0.59 % (3053595)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1410213552:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.36/0.59 % (3053595)Instruction limit reached!
% 1.36/0.59 % (3053595)------------------------------
% 1.36/0.59 % (3053595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053595)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053595)Termination reason: Instruction limit
% 1.36/0.59 % (3053595)Termination phase: shuffling
% 1.36/0.59 % (3053595)Time elapsed: 0.004 s
% 1.36/0.59 % (3053595)Peak memory usage: 9 MB
% 1.36/0.59 % (3053595)Instructions burned: 9 (million)
% 1.36/0.59 % (3053560) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3053520-3053560"...
% 1.36/0.59 % (3053596)Refutation not found, incomplete strategy
% 1.36/0.59 % (3053596)------------------------------
% 1.36/0.59 % (3053596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053596)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053596)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.59 % (3053596)Time elapsed: 0.011 s
% 1.36/0.59 % (3053596)Peak memory usage: 13 MB
% 1.36/0.59 % (3053596)Instructions burned: 46 (million)
% 1.36/0.59 % (3053596)------------------------------
% 1.36/0.59 % (3053596)------------------------------
% 1.36/0.59 % (3053593)Instruction limit reached!
% 1.36/0.59 % (3053593)------------------------------
% 1.36/0.59 % (3053593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053593)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053593)Termination reason: Instruction limit
% 1.36/0.59 % (3053593)Termination phase: Preprocessing 1
% 1.36/0.59 % (3053593)Time elapsed: 0.035 s
% 1.36/0.59 % (3053593)Peak memory usage: 11 MB
% 1.36/0.59 % (3053593)Instructions burned: 42 (million)
% 1.36/0.59 % (3053600)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.36/0.59 % (3053600)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3379359020:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.36/0.59 % (3053599)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=508083906:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.36/0.59 % (3053600)Instruction limit reached!
% 1.36/0.59 % (3053600)------------------------------
% 1.36/0.59 % (3053600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053600)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053600)Termination reason: Instruction limit
% 1.36/0.59 % (3053600)Termination phase: shuffling
% 1.36/0.59 % (3053600)Time elapsed: 0.003 s
% 1.36/0.59 % (3053600)Peak memory usage: 10 MB
% 1.36/0.59 % (3053600)Instructions burned: 13 (million)
% 1.36/0.59 % (3053604)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3840312882:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.36/0.59 % (3053588)Instruction limit reached!
% 1.36/0.59 % (3053588)------------------------------
% 1.36/0.59 % (3053588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053588)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053588)Termination reason: Instruction limit
% 1.36/0.59 % (3053588)Termination phase: Saturation
% 1.36/0.59 % (3053588)Time elapsed: 0.082 s
% 1.36/0.59 % (3053588)Peak memory usage: 13 MB
% 1.36/0.59 % (3053588)Instructions burned: 193 (million)
% 1.36/0.59 % (3053604)Instruction limit reached!
% 1.36/0.59 % (3053604)------------------------------
% 1.36/0.59 % (3053604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.36/0.59 % (3053604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.36/0.59 % (3053604)CaDiCaL version: 2.1.3
% 1.36/0.59 % (3053604)Termination reason: Instruction limit
% 1.36/0.59 % (3053604)Termination phase: shuffling
% 1.36/0.59 % (3053604)Time elapsed: 0.004 s
% 1.36/0.59 % (3053604)Peak memory usage: 10 MB
% 1.36/0.59 % (3053604)Instructions burned: 20 (million)
% 1.36/0.59 % (3053601)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=797462856:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.36/0.59 % (3053601)Instruction limit reached!
% 1.36/0.59 % (3053601)------------------------------
% 1.36/0.59 % (3053601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.59 % (3053601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.59 % (3053601)CaDiCaL version: 2.1.3
% 2.19/0.59 % (3053601)Termination reason: Instruction limit
% 2.19/0.59 % (3053601)Termination phase: shuffling
% 2.19/0.59 % (3053601)Time elapsed: 0.005 s
% 2.19/0.59 % (3053601)Peak memory usage: 10 MB
% 2.19/0.59 % (3053601)Instructions burned: 23 (million)
% 2.19/0.59 % (3053560)...printing done.
% 2.19/0.59 % (3053606)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1247259979:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.19/0.59 % (3053609)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1410987223:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.19/0.59 % (3053607)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1193054797:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.19/0.59 % (3053560)Refutation found. Thanks to Tanya!
% 2.19/0.59 % SZS status Theorem for theBenchmark
% 2.19/0.59 % SZS output start Proof for theBenchmark
% 2.19/0.59 thf(type_def_5, type, term: $tType).
% 2.19/0.59 thf(type_def_6, type, subst: $tType).
% 2.19/0.59 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 2.19/0.59 thf(type_def_8, type, d_term: $tType).
% 2.19/0.59 thf(type_def_9, type, d_subst: $tType).
% 2.19/0.59 thf(func_def_0, type, one: term).
% 2.19/0.59 thf(func_def_1, type, ap: (term > term > term)).
% 2.19/0.59 thf(func_def_2, type, lam: (term > term)).
% 2.19/0.59 thf(func_def_3, type, sub: (term > subst > term)).
% 2.19/0.59 thf(func_def_4, type, id: subst).
% 2.19/0.59 thf(func_def_5, type, sh: subst).
% 2.19/0.59 thf(func_def_6, type, push: (term > subst > subst)).
% 2.19/0.59 thf(func_def_7, type, comp: (subst > subst > subst)).
% 2.19/0.59 thf(func_def_8, type, var: (term > $o)).
% 2.19/0.59 thf(func_def_9, type, pushprop_lem1v2: $o).
% 2.19/0.59 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 2.19/0.59 thf(func_def_11, type, axmap: $o).
% 2.19/0.59 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 2.19/0.59 thf(func_def_13, type, shinj: $o).
% 2.19/0.59 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 2.19/0.59 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 2.19/0.59 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 2.19/0.59 thf(func_def_17, type, induction2lem: $o).
% 2.19/0.59 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 2.19/0.59 thf(func_def_19, type, axvarshift: $o).
% 2.19/0.59 thf(func_def_20, type, hoasapinj2: $o).
% 2.19/0.59 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 2.19/0.59 thf(func_def_22, type, hoasapinj1: $o).
% 2.19/0.59 thf(func_def_23, type, ulamvar1: $o).
% 2.19/0.59 thf(func_def_24, type, induction2lem_lthm: $o).
% 2.19/0.59 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 2.19/0.59 thf(func_def_26, type, apnotvar: $o).
% 2.19/0.59 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 2.19/0.59 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 2.19/0.59 thf(func_def_29, type, hoasinduction_lthm: $o).
% 2.19/0.59 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 2.19/0.59 thf(func_def_31, type, hoaslaminj: $o).
% 2.19/0.59 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 2.19/0.59 thf(func_def_33, type, induction2lem_gthm: $o).
% 2.19/0.59 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 2.19/0.59 thf(func_def_35, type, hoasinduction_lem3: $o).
% 2.19/0.59 thf(func_def_36, type, hoasinduction_lem2: $o).
% 2.19/0.59 thf(func_def_37, type, termmset_lthm: $o).
% 2.19/0.59 thf(func_def_38, type, hoasinduction_lem1: $o).
% 2.19/0.59 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 2.19/0.59 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 2.19/0.59 thf(func_def_41, type, hoasapnotvar: $o).
% 2.19/0.59 thf(func_def_42, type, hoasinduction_lem0: $o).
% 2.19/0.59 thf(func_def_43, type, hoasinduction: $o).
% 2.19/0.59 thf(func_def_44, type, hoasinduction_gthm: $o).
% 2.19/0.59 thf(func_def_45, type, axapp: $o).
% 2.19/0.59 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 2.19/0.59 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 2.19/0.59 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 2.19/0.59 thf(func_def_49, type, ulamvarind: $o).
% 2.19/0.59 thf(func_def_50, type, induction: $o).
% 2.19/0.59 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 2.19/0.59 thf(func_def_52, type, termmset_gthm: $o).
% 2.19/0.59 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 2.19/0.59 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 2.19/0.59 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 2.19/0.59 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 2.19/0.59 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 2.19/0.59 thf(func_def_58, type, pushprop_lem2v2: $o).
% 2.19/0.59 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 2.19/0.59 thf(func_def_60, type, axclos: $o).
% 2.19/0.59 thf(func_def_61, type, axassoc: $o).
% 2.19/0.59 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 2.19/0.59 thf(func_def_63, type, pushprop_lthm: $o).
% 2.19/0.59 thf(func_def_64, type, apinj2: $o).
% 2.19/0.59 thf(func_def_65, type, apinj1: $o).
% 2.19/0.59 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 2.19/0.59 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 2.19/0.59 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 2.19/0.59 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 2.19/0.59 thf(func_def_70, type, axvarcons: $o).
% 2.19/0.59 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 2.19/0.59 thf(func_def_72, type, axscons: $o).
% 2.19/0.59 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 2.19/0.59 thf(func_def_74, type, axidr: $o).
% 2.19/0.59 thf(func_def_75, type, pushprop_lem1: $o).
% 2.19/0.59 thf(func_def_76, type, laminj: $o).
% 2.19/0.59 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 2.19/0.59 thf(func_def_78, type, pushprop_lem0: $o).
% 2.19/0.59 thf(func_def_79, type, pushprop_gthm: $o).
% 2.19/0.59 thf(func_def_80, type, axabs: $o).
% 2.19/0.59 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 2.19/0.59 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 2.19/0.59 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 2.19/0.59 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 2.19/0.59 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 2.19/0.59 thf(func_def_86, type, lamnotap: $o).
% 2.19/0.59 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 2.19/0.59 thf(func_def_88, type, hoaslamnotvar: $o).
% 2.19/0.59 thf(func_def_89, type, axidl: $o).
% 2.19/0.59 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 2.19/0.59 thf(func_def_91, type, induction2_lthm: $o).
% 2.19/0.59 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 2.19/0.59 thf(func_def_93, type, substmonoid_lthm: $o).
% 2.19/0.59 thf(func_def_94, type, pushprop: $o).
% 2.19/0.59 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 2.19/0.59 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 2.19/0.59 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 2.19/0.59 thf(func_def_98, type, substmonoid: $o).
% 2.19/0.59 thf(func_def_99, type, lamnotvar: $o).
% 2.19/0.59 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 2.19/0.59 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 2.19/0.59 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 2.19/0.59 thf(func_def_103, type, induction2_gthm: $o).
% 2.19/0.59 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 2.19/0.59 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 2.19/0.59 thf(func_def_106, type, hoaslamnotap: $o).
% 2.19/0.59 thf(func_def_107, type, substmonoid_gthm: $o).
% 2.19/0.59 thf(func_def_108, type, ulamvarsh: $o).
% 2.19/0.59 thf(func_def_109, type, induction2: $o).
% 2.19/0.59 thf(func_def_110, type, pushprop_lem3v2: $o).
% 2.19/0.59 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 2.19/0.59 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 2.19/0.59 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 2.19/0.59 thf(func_def_114, type, axshiftcons: $o).
% 2.19/0.59 thf(func_def_115, type, termmset: $o).
% 2.19/0.59 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 2.19/0.59 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 2.19/0.59 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 2.19/0.59 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 2.19/0.59 thf(func_def_120, type, axvarid: $o).
% 2.19/0.59 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 2.19/0.59 thf(func_def_122, type, d2term: (d_term > term)).
% 2.19/0.59 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 2.19/0.59 thf(func_def_124, type, d_one: d_term).
% 2.19/0.59 thf(func_def_125, type, d_id: d_subst).
% 2.19/0.59 thf(func_def_127, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.19/0.59 thf(func_def_128, type, vIMP: ($o > $o > $o)).
% 2.19/0.59 thf(func_def_129, type, db1: !>[X0: $tType]:(X0)).
% 2.19/0.59 thf(func_def_130, type, db2: !>[X0: $tType]:(X0)).
% 2.19/0.59 thf(func_def_131, type, db3: !>[X0: $tType]:(X0)).
% 2.19/0.59 thf(func_def_132, type, db0: !>[X0: $tType]:(X0)).
% 2.19/0.59 thf(func_def_133, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.19/0.59 thf(func_def_134, type, db4: !>[X0: $tType]:(X0)).
% 2.19/0.59 thf(func_def_137, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.19/0.59 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_139, type, sP1: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_140, type, sP2: $o).
% 2.19/0.59 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_142, type, sP4: $o).
% 2.19/0.59 thf(func_def_143, type, sP5: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_145, type, sP7: $o).
% 2.19/0.59 thf(func_def_146, type, sP8: $o).
% 2.19/0.59 thf(func_def_147, type, sP9: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_148, type, sP10: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_149, type, sP11: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_150, type, sP12: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_151, type, sP13: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_152, type, sP14: $o).
% 2.19/0.59 thf(func_def_153, type, sP15: $o).
% 2.19/0.59 thf(func_def_154, type, sP16: $o).
% 2.19/0.59 thf(func_def_155, type, sP17: $o).
% 2.19/0.59 thf(func_def_156, type, sP18: $o).
% 2.19/0.59 thf(func_def_157, type, sP19: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_158, type, sP20: $o).
% 2.19/0.59 thf(func_def_159, type, sP21: $o).
% 2.19/0.59 thf(func_def_160, type, sP22: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_161, type, sP23: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_162, type, sP24: $o).
% 2.19/0.59 thf(func_def_163, type, sP25: $o).
% 2.19/0.59 thf(func_def_164, type, sP26: $o).
% 2.19/0.59 thf(func_def_165, type, sP27: $o).
% 2.19/0.59 thf(func_def_166, type, sP28: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_167, type, sP29: $o).
% 2.19/0.59 thf(func_def_168, type, sP30: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_169, type, sP31: $o).
% 2.19/0.59 thf(func_def_170, type, sP32: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_171, type, sP33: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_172, type, sP34: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_173, type, sP35: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_174, type, sP36: $o).
% 2.19/0.59 thf(func_def_175, type, sP37: $o).
% 2.19/0.59 thf(func_def_176, type, sP38: $o).
% 2.19/0.59 thf(func_def_177, type, sP39: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_178, type, sP40: $o).
% 2.19/0.59 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_180, type, sP42: $o).
% 2.19/0.59 thf(func_def_181, type, sP43: $o).
% 2.19/0.59 thf(func_def_182, type, sP44: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_183, type, sP45: $o).
% 2.19/0.59 thf(func_def_184, type, sP46: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_185, type, sP47: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_186, type, sP48: $o).
% 2.19/0.59 thf(func_def_187, type, sP49: $o).
% 2.19/0.59 thf(func_def_188, type, sP50: $o).
% 2.19/0.59 thf(func_def_189, type, sP51: $o).
% 2.19/0.59 thf(func_def_190, type, sP52: $o).
% 2.19/0.59 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 2.19/0.59 thf(func_def_192, type, sP54: $o).
% 2.19/0.59 thf(func_def_193, type, sP55: ((term > $o) > $o)).
% 2.19/0.59 thf(func_def_194, type, sP56: $o).
% 2.19/0.59 thf(func_def_195, type, sP57: $o).
% 2.19/0.59 thf(func_def_196, type, sP58: $o).
% 2.19/0.59 thf(func_def_197, type, sK59: (subst > term > subst > $o)).
% 2.19/0.59 thf(func_def_198, type, sK60: term).
% 2.19/0.59 thf(func_def_199, type, sK61: ((subst > term > term) > term)).
% 2.19/0.59 thf(func_def_200, type, sK62: ((subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_201, type, sK63: ((subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_202, type, sK64: ((subst > term > term) > term)).
% 2.19/0.59 thf(func_def_203, type, sK65: (term > (subst > term > subst > $o) > term)).
% 2.19/0.59 thf(func_def_204, type, sK66: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.59 thf(func_def_205, type, sK67: (term > $o)).
% 2.19/0.59 thf(func_def_206, type, sK68: (subst > term > subst > $o)).
% 2.19/0.59 thf(func_def_207, type, sK69: term).
% 2.19/0.59 thf(func_def_208, type, sK70: ((subst > term > term) > term)).
% 2.19/0.59 thf(func_def_209, type, sK71: ((subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_210, type, sK72: ((subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_211, type, sK73: ((subst > term > term) > term)).
% 2.19/0.59 thf(func_def_212, type, sK74: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.19/0.59 thf(func_def_213, type, sK75: (term > (term > $o) > term)).
% 2.19/0.59 thf(func_def_214, type, sK76: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.59 thf(func_def_215, type, sK77: (subst > term > subst > $o)).
% 2.19/0.59 thf(func_def_216, type, sK78: term).
% 2.19/0.59 thf(func_def_217, type, sK79: (term > (subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_218, type, sK80: (term > (subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_219, type, sK81: (term > (subst > term > term) > term)).
% 2.19/0.59 thf(func_def_220, type, sK82: ((subst > term > term) > term)).
% 2.19/0.59 thf(func_def_221, type, sK83: (term > (subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_222, type, sK84: (term > (subst > term > term) > subst)).
% 2.19/0.59 thf(func_def_223, type, sK85: (term > (subst > term > term) > term)).
% 2.19/0.59 thf(func_def_224, type, sK86: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.59 thf(func_def_225, type, sK87: ((subst > term > subst > $o) > term)).
% 2.19/0.59 thf(func_def_226, type, sK88: (term > (subst > term > subst > $o) > term)).
% 2.19/0.59 thf(func_def_227, type, sK89: ((term > $o) > term)).
% 2.19/0.59 thf(func_def_228, type, sK90: ((term > $o) > term)).
% 2.19/0.59 thf(func_def_229, type, sK91: term).
% 2.19/0.59 thf(func_def_230, type, sK92: (subst > term > subst > $o)).
% 2.19/0.59 thf(func_def_231, type, sK93: term).
% 2.19/0.59 thf(func_def_232, type, sK94: ((subst > term > subst > $o) > term)).
% 2.19/0.59 thf(func_def_233, type, sK95: ((subst > term > subst > $o) > subst)).
% 2.19/0.59 thf(func_def_234, type, sK96: ((subst > term > subst > $o) > subst)).
% 2.19/0.59 thf(func_def_235, type, sK97: ((subst > term > subst > $o) > subst)).
% 2.19/0.59 thf(func_def_236, type, sK98: ((subst > term > subst > $o) > term)).
% 2.19/0.59 thf(func_def_237, type, sK99: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_238, type, sK100: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_239, type, sK101: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_240, type, sK102: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_241, type, sK103: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_242, type, sK104: term).
% 2.19/0.60 thf(func_def_243, type, sK105: (term > $o)).
% 2.19/0.60 thf(func_def_244, type, sK106: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_245, type, sK107: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_246, type, sK108: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_247, type, sK109: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_248, type, sK110: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_249, type, sK111: (term > subst > term > term)).
% 2.19/0.60 thf(func_def_250, type, sK112: ((term > $o) > term > term)).
% 2.19/0.60 thf(func_def_251, type, sK113: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_252, type, sK114: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.19/0.60 thf(func_def_253, type, sK115: term).
% 2.19/0.60 thf(func_def_254, type, sK116: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_255, type, sK117: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_256, type, sK118: term).
% 2.19/0.60 thf(func_def_257, type, sK119: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_258, type, sK120: term).
% 2.19/0.60 thf(func_def_259, type, sK121: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_260, type, sK122: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_261, type, sK123: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_262, type, sK124: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_263, type, sK125: (term > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_264, type, sK126: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_265, type, sK127: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_266, type, sK128: term).
% 2.19/0.60 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > term > $o)).
% 2.19/0.60 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_270, type, sK132: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_271, type, sK133: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_272, type, sK134: term).
% 2.19/0.60 thf(func_def_273, type, sK135: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_274, type, sK136: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_275, type, sK137: term).
% 2.19/0.60 thf(func_def_276, type, sK138: (term > $o)).
% 2.19/0.60 thf(func_def_277, type, sK139: (term > term)).
% 2.19/0.60 thf(func_def_278, type, sK140: ((term > $o) > term > term)).
% 2.19/0.60 thf(func_def_279, type, sK141: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_280, type, sK142: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_281, type, sK143: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_282, type, sK144: term).
% 2.19/0.60 thf(func_def_283, type, sK145: (term > $o)).
% 2.19/0.60 thf(func_def_284, type, sK146: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_285, type, sK147: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_286, type, sK148: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_287, type, sK149: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_288, type, sK150: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_290, type, sK152: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_291, type, sK153: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_293, type, sK155: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_294, type, sK156: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_295, type, sK157: (term > $o)).
% 2.19/0.60 thf(func_def_296, type, sK158: term).
% 2.19/0.60 thf(func_def_297, type, sK159: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_298, type, sK160: term).
% 2.19/0.60 thf(func_def_299, type, sK161: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_300, type, sK162: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_301, type, sK163: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_302, type, sK164: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_303, type, sK165: (term > (term > $o) > term)).
% 2.19/0.60 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_305, type, sK167: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_306, type, sK168: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_307, type, sK169: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_308, type, sK170: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.19/0.60 thf(func_def_309, type, sK171: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_310, type, sK172: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_311, type, sK173: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_312, type, sK174: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_313, type, sK175: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_314, type, sK176: term).
% 2.19/0.60 thf(func_def_315, type, sK177: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_316, type, sK178: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_317, type, sK179: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_318, type, sK180: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_319, type, sK181: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_320, type, sK182: ((subst > term > subst > $o) > term > term)).
% 2.19/0.60 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_322, type, sK184: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_323, type, sK185: (term > $o)).
% 2.19/0.60 thf(func_def_324, type, sK186: term).
% 2.19/0.60 thf(func_def_325, type, sK187: term).
% 2.19/0.60 thf(func_def_326, type, sK188: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_327, type, sK189: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_328, type, sK190: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_329, type, sK191: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_330, type, sK192: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_331, type, sK193: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_332, type, sK194: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_333, type, sK195: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_334, type, sK196: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_335, type, sK197: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_336, type, sK198: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_337, type, sK199: term).
% 2.19/0.60 thf(func_def_338, type, sK200: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_339, type, sK201: ((subst > term > subst > $o) > term > term)).
% 2.19/0.60 thf(func_def_340, type, sK202: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_341, type, sK203: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_342, type, sK204: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_343, type, sK205: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_344, type, sK206: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_345, type, sK207: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_347, type, sK209: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_348, type, sK210: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_349, type, sK211: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_350, type, sK212: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_351, type, sK213: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_352, type, sK214: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_353, type, sK215: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_354, type, sK216: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_355, type, sK217: ((subst > term > subst > $o) > term > $o)).
% 2.19/0.60 thf(func_def_356, type, sK218: term).
% 2.19/0.60 thf(func_def_357, type, sK219: (term > $o)).
% 2.19/0.60 thf(func_def_358, type, sK220: (term > term)).
% 2.19/0.60 thf(func_def_359, type, sK221: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_360, type, sK222: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_361, type, sK223: term).
% 2.19/0.60 thf(func_def_362, type, sK224: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_363, type, sK225: term).
% 2.19/0.60 thf(func_def_364, type, sK226: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_365, type, sK227: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_366, type, sK228: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_367, type, sK229: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_368, type, sK230: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_369, type, sK231: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_370, type, sK232: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_371, type, sK233: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_372, type, sK234: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_373, type, sK235: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_374, type, sK236: ((term > $o) > term > term)).
% 2.19/0.60 thf(func_def_375, type, sK237: ((term > $o) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_376, type, sK238: term).
% 2.19/0.60 thf(func_def_377, type, sK239: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_378, type, sK240: (term > $o)).
% 2.19/0.60 thf(func_def_379, type, sK241: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_380, type, sK242: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_381, type, sK243: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_382, type, sK244: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_383, type, sK245: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_384, type, sK246: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_386, type, sK248: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_387, type, sK249: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_388, type, sK250: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_389, type, sK251: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_390, type, sK252: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_391, type, sK253: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_392, type, sK254: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_393, type, sK255: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_394, type, sK256: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_395, type, sK257: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_397, type, sK259: term).
% 2.19/0.60 thf(func_def_398, type, sK260: (term > $o)).
% 2.19/0.60 thf(func_def_399, type, sK261: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_400, type, sK262: ((term > $o) > term > term)).
% 2.19/0.60 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_403, type, sK265: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_404, type, sK266: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_405, type, sK267: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_406, type, sK268: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_407, type, sK269: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_408, type, sK270: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_409, type, sK271: ((subst > term > subst > $o) > (term > $o) > term)).
% 2.19/0.60 thf(func_def_410, type, sK272: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_411, type, sK273: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_412, type, sK274: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_413, type, sK275: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_414, type, sK276: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_415, type, sK277: (term > $o)).
% 2.19/0.60 thf(func_def_416, type, sK278: term).
% 2.19/0.60 thf(func_def_417, type, sK279: subst).
% 2.19/0.60 thf(func_def_418, type, sK280: (term > term)).
% 2.19/0.60 thf(func_def_419, type, sK281: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_420, type, sK282: (subst > (term > $o) > term)).
% 2.19/0.60 thf(func_def_421, type, sK283: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_422, type, sK284: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_423, type, sK285: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_424, type, sK286: term).
% 2.19/0.60 thf(func_def_425, type, sK287: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_426, type, sK288: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_427, type, sK289: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_428, type, sK290: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_429, type, sK291: term).
% 2.19/0.60 thf(func_def_430, type, sK292: (term > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_431, type, sK293: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_432, type, sK294: (term > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_433, type, sK295: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_434, type, sK296: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_435, type, sK297: term).
% 2.19/0.60 thf(func_def_436, type, sK298: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_437, type, sK299: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_438, type, sK300: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_439, type, sK301: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_440, type, sK302: ((term > $o) > subst > term)).
% 2.19/0.60 thf(func_def_441, type, sK303: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_442, type, sK304: term).
% 2.19/0.60 thf(func_def_443, type, sK305: term).
% 2.19/0.60 thf(func_def_444, type, sK306: subst).
% 2.19/0.60 thf(func_def_445, type, sK307: (term > $o)).
% 2.19/0.60 thf(func_def_446, type, sK308: (term > term)).
% 2.19/0.60 thf(func_def_447, type, sK309: (term > $o)).
% 2.19/0.60 thf(func_def_448, type, sK310: term).
% 2.19/0.60 thf(func_def_449, type, sK311: (term > term)).
% 2.19/0.60 thf(func_def_450, type, sK312: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_451, type, sK313: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_452, type, sK314: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_453, type, sK315: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_454, type, sK316: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_455, type, sK317: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_456, type, sK318: term).
% 2.19/0.60 thf(func_def_457, type, sK319: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_458, type, sK320: term).
% 2.19/0.60 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_460, type, sK322: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_461, type, sK323: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_462, type, sK324: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_463, type, sK325: ((subst > term > subst > $o) > term > term)).
% 2.19/0.60 thf(func_def_464, type, sK326: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_465, type, sK327: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_466, type, sK328: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_467, type, sK329: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_469, type, sK331: (term > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_470, type, sK332: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_471, type, sK333: term).
% 2.19/0.60 thf(func_def_472, type, sK334: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_473, type, sK335: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_474, type, sK336: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_475, type, sK337: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_476, type, sK338: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_477, type, sK339: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_478, type, sK340: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_479, type, sK341: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_480, type, sK342: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_481, type, sK343: (subst > term > term)).
% 2.19/0.60 thf(func_def_482, type, sK344: (subst > term > term)).
% 2.19/0.60 thf(func_def_483, type, sK345: subst).
% 2.19/0.60 thf(func_def_484, type, sK346: term).
% 2.19/0.60 thf(func_def_485, type, sK347: subst).
% 2.19/0.60 thf(func_def_486, type, sK348: term).
% 2.19/0.60 thf(func_def_487, type, sK349: subst).
% 2.19/0.60 thf(func_def_488, type, sK350: term).
% 2.19/0.60 thf(func_def_489, type, sK351: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_490, type, sK352: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_491, type, sK353: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_492, type, sK354: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_493, type, sK355: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_494, type, sK356: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_495, type, sK357: term).
% 2.19/0.60 thf(func_def_496, type, sK358: term).
% 2.19/0.60 thf(func_def_497, type, sK359: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_498, type, sK360: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_499, type, sK361: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_503, type, sK365: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_504, type, sK366: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_505, type, sK367: term).
% 2.19/0.60 thf(func_def_506, type, sK368: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_507, type, sK369: term).
% 2.19/0.60 thf(func_def_508, type, sK370: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_509, type, sK371: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_510, type, sK372: (term > $o)).
% 2.19/0.60 thf(func_def_511, type, sK373: term).
% 2.19/0.60 thf(func_def_512, type, sK374: (term > term)).
% 2.19/0.60 thf(func_def_513, type, sK375: term).
% 2.19/0.60 thf(func_def_514, type, sK376: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_520, type, sK382: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_521, type, sK383: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_522, type, sK384: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_523, type, sK385: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_524, type, sK386: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_526, type, sK388: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_527, type, sK389: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_529, type, sK391: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_530, type, sK392: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_531, type, sK393: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_532, type, sK394: (term > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_533, type, sK395: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_534, type, sK396: term).
% 2.19/0.60 thf(func_def_535, type, sK397: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_536, type, sK398: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_537, type, sK399: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_538, type, sK400: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_539, type, sK401: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_540, type, sK402: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_541, type, sK403: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_542, type, sK404: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_543, type, sK405: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_544, type, sK406: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_545, type, sK407: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_546, type, sK408: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_547, type, sK409: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_548, type, sK410: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_549, type, sK411: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_550, type, sK412: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_551, type, sK413: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_552, type, sK414: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_553, type, sK415: (term > $o)).
% 2.19/0.60 thf(func_def_554, type, sK416: term).
% 2.19/0.60 thf(func_def_555, type, sK417: subst).
% 2.19/0.60 thf(func_def_556, type, sK418: subst).
% 2.19/0.60 thf(func_def_557, type, sK419: term).
% 2.19/0.60 thf(func_def_558, type, sK420: subst).
% 2.19/0.60 thf(func_def_559, type, sK421: term).
% 2.19/0.60 thf(func_def_560, type, sK422: term).
% 2.19/0.60 thf(func_def_561, type, sK423: (term > $o)).
% 2.19/0.60 thf(func_def_562, type, sK424: subst).
% 2.19/0.60 thf(func_def_563, type, sK425: (term > term)).
% 2.19/0.60 thf(func_def_564, type, sK426: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_565, type, sK427: (subst > (term > $o) > term)).
% 2.19/0.60 thf(func_def_566, type, sK428: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_567, type, sK429: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_568, type, sK430: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_569, type, sK431: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_570, type, sK432: term).
% 2.19/0.60 thf(func_def_571, type, sK433: (term > $o)).
% 2.19/0.60 thf(func_def_572, type, sK434: (term > term)).
% 2.19/0.60 thf(func_def_573, type, sK435: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_574, type, sK436: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_575, type, sK437: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_576, type, sK438: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_577, type, sK439: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_578, type, sK440: term).
% 2.19/0.60 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_583, type, sK445: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_584, type, sK446: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_585, type, sK447: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_586, type, sK448: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > subst)).
% 2.19/0.60 thf(func_def_588, type, sK450: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_589, type, sK451: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_590, type, sK452: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_591, type, sK453: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_592, type, sK454: ((subst > term > subst > $o) > subst > term > term)).
% 2.19/0.60 thf(func_def_593, type, sK455: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_594, type, sK456: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_595, type, sK457: subst).
% 2.19/0.60 thf(func_def_596, type, sK458: term).
% 2.19/0.60 thf(func_def_597, type, sK459: subst).
% 2.19/0.60 thf(func_def_598, type, sK460: term).
% 2.19/0.60 thf(func_def_599, type, sK461: term).
% 2.19/0.60 thf(func_def_600, type, sK462: subst).
% 2.19/0.60 thf(func_def_601, type, sK463: (term > $o)).
% 2.19/0.60 thf(func_def_602, type, sK464: (term > $o)).
% 2.19/0.60 thf(func_def_603, type, sK465: term).
% 2.19/0.60 thf(func_def_604, type, sK466: term).
% 2.19/0.60 thf(func_def_605, type, sK467: (term > d_term)).
% 2.19/0.60 thf(func_def_606, type, sK468: term).
% 2.19/0.60 thf(func_def_607, type, sK469: (term > $o)).
% 2.19/0.60 thf(func_def_608, type, sK470: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_609, type, sK471: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_610, type, sK472: (term > subst > term > term)).
% 2.19/0.60 thf(func_def_611, type, sK473: term).
% 2.19/0.60 thf(func_def_612, type, sK474: (term > $o)).
% 2.19/0.60 thf(func_def_613, type, sK475: (term > $o)).
% 2.19/0.60 thf(func_def_614, type, sK476: term).
% 2.19/0.60 thf(func_def_615, type, sK477: subst).
% 2.19/0.60 thf(func_def_616, type, sK478: (subst > term > (term > $o) > (term > $o) > term)).
% 2.19/0.60 thf(func_def_617, type, sK479: subst).
% 2.19/0.60 thf(func_def_618, type, sK480: term).
% 2.19/0.60 thf(func_def_619, type, sK481: subst).
% 2.19/0.60 thf(func_def_620, type, sK482: subst).
% 2.19/0.60 thf(func_def_621, type, sK483: subst).
% 2.19/0.60 thf(func_def_622, type, sK484: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_623, type, sK485: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_624, type, sK486: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_625, type, sK487: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_626, type, sK488: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_627, type, sK489: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_628, type, sK490: (subst > term > term)).
% 2.19/0.60 thf(func_def_629, type, sK491: subst).
% 2.19/0.60 thf(func_def_630, type, sK492: (subst > term > term)).
% 2.19/0.60 thf(func_def_631, type, sK493: term).
% 2.19/0.60 thf(func_def_632, type, sK494: term).
% 2.19/0.60 thf(func_def_633, type, sK495: term).
% 2.19/0.60 thf(func_def_634, type, sK496: term).
% 2.19/0.60 thf(func_def_635, type, sK497: term).
% 2.19/0.60 thf(func_def_636, type, sK498: term).
% 2.19/0.60 thf(func_def_637, type, sK499: subst).
% 2.19/0.60 thf(func_def_638, type, sK500: term).
% 2.19/0.60 thf(func_def_639, type, sK501: term).
% 2.19/0.60 thf(func_def_640, type, sK502: subst).
% 2.19/0.60 thf(func_def_641, type, sK503: term).
% 2.19/0.60 thf(func_def_642, type, sK504: subst).
% 2.19/0.60 thf(func_def_643, type, sK505: (term > $o)).
% 2.19/0.60 thf(func_def_644, type, sK506: (term > $o)).
% 2.19/0.60 thf(func_def_645, type, sK507: term).
% 2.19/0.60 thf(func_def_646, type, sK508: term).
% 2.19/0.60 thf(func_def_647, type, sK509: term).
% 2.19/0.60 thf(func_def_648, type, sK510: (term > subst > term > term)).
% 2.19/0.60 thf(func_def_649, type, sK511: term).
% 2.19/0.60 thf(func_def_650, type, sK512: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_651, type, sK513: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_652, type, sK514: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_653, type, sK515: ((subst > term > subst > $o) > term)).
% 2.19/0.60 thf(func_def_654, type, sK516: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_655, type, sK517: term).
% 2.19/0.60 thf(func_def_656, type, sK518: ((subst > term > subst > $o) > term > $o)).
% 2.19/0.60 thf(func_def_657, type, sK519: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_658, type, sK520: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_659, type, sK521: (subst > term > subst > $o)).
% 2.19/0.60 thf(func_def_660, type, sK522: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_661, type, sK523: ((subst > term > subst > $o) > term > $o)).
% 2.19/0.60 thf(func_def_662, type, sK524: term).
% 2.19/0.60 thf(func_def_663, type, sK525: term).
% 2.19/0.60 thf(func_def_664, type, sK526: term).
% 2.19/0.60 thf(func_def_665, type, sK527: term).
% 2.19/0.60 thf(func_def_666, type, sK528: term).
% 2.19/0.60 thf(func_def_667, type, sK529: term).
% 2.19/0.60 thf(func_def_668, type, sK530: term).
% 2.19/0.60 thf(func_def_669, type, sK531: term).
% 2.19/0.60 thf(func_def_670, type, sK532: term).
% 2.19/0.60 thf(func_def_671, type, sK533: term).
% 2.19/0.60 thf(func_def_672, type, sK534: term).
% 2.19/0.60 thf(func_def_673, type, sK535: (term > subst > term > term)).
% 2.19/0.60 thf(func_def_674, type, sK536: term).
% 2.19/0.60 thf(func_def_675, type, sK537: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_676, type, sK538: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_677, type, sK539: (term > subst > term > term)).
% 2.19/0.60 thf(func_def_678, type, sK540: subst).
% 2.19/0.60 thf(func_def_679, type, sK541: term).
% 2.19/0.60 thf(func_def_680, type, sK542: term).
% 2.19/0.60 thf(func_def_681, type, sK543: term).
% 2.19/0.60 thf(func_def_682, type, sK544: term).
% 2.19/0.60 thf(func_def_683, type, sK545: term).
% 2.19/0.60 thf(func_def_684, type, sK546: term).
% 2.19/0.60 thf(func_def_685, type, sK547: term).
% 2.19/0.60 thf(func_def_686, type, sK548: term).
% 2.19/0.60 thf(func_def_687, type, sK549: term).
% 2.19/0.60 thf(func_def_688, type, sK550: (term > subst > (term > $o) > term > $o)).
% 2.19/0.60 thf(func_def_689, type, sK551: (term > $o)).
% 2.19/0.60 thf(func_def_690, type, sK552: subst).
% 2.19/0.60 thf(func_def_691, type, sK553: term).
% 2.19/0.60 thf(func_def_692, type, sK554: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_693, type, sK555: subst).
% 2.19/0.60 thf(func_def_694, type, sK556: subst).
% 2.19/0.60 thf(func_def_695, type, sK557: subst).
% 2.19/0.60 thf(func_def_696, type, sK558: subst).
% 2.19/0.60 thf(func_def_697, type, sK559: (subst > d_subst)).
% 2.19/0.60 thf(func_def_698, type, sK560: term).
% 2.19/0.60 thf(func_def_699, type, sK561: term).
% 2.19/0.60 thf(func_def_700, type, sK562: subst).
% 2.19/0.60 thf(func_def_701, type, sK563: term).
% 2.19/0.60 thf(func_def_702, type, sK564: term).
% 2.19/0.60 thf(func_def_703, type, sK565: term).
% 2.19/0.60 thf(func_def_704, type, sK566: term).
% 2.19/0.60 thf(func_def_705, type, sK567: term).
% 2.19/0.60 thf(func_def_706, type, sK568: term).
% 2.19/0.60 thf(func_def_707, type, sK569: term).
% 2.19/0.60 thf(func_def_708, type, sK570: term).
% 2.19/0.60 thf(func_def_709, type, sK571: (subst > term > (term > $o) > term > $o)).
% 2.19/0.60 thf(func_def_710, type, sK572: (term > $o)).
% 2.19/0.60 thf(func_def_711, type, sK573: term).
% 2.19/0.60 thf(func_def_712, type, sK574: subst).
% 2.19/0.60 thf(func_def_713, type, sK575: ((term > $o) > term)).
% 2.19/0.60 thf(func_def_714, type, sK576: subst).
% 2.19/0.60 thf(func_def_715, type, sK577: (term > $o)).
% 2.19/0.60 thf(func_def_716, type, sK578: term).
% 2.19/0.60 thf(func_def_717, type, sK579: (term > $o)).
% 2.19/0.60 thf(func_def_718, type, sK580: ((term > $o) > term > (term > $o) > subst > term)).
% 2.19/0.60 thf(func_def_719, type, sK581: term).
% 2.19/0.60 thf(func_def_720, type, sK582: term).
% 2.19/0.60 thf(func_def_721, type, sK583: term).
% 2.19/0.60 thf(func_def_722, type, sK584: term).
% 2.19/0.60 thf(func_def_723, type, sK585: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_724, type, sK586: ((subst > term > term) > subst)).
% 2.19/0.60 thf(func_def_725, type, sK587: ((subst > term > term) > term)).
% 2.19/0.60 thf(func_def_726, type, sK588: term).
% 2.19/0.60 thf(func_def_727, type, sK589: term).
% 2.19/0.60 thf(func_def_728, type, sK590: (subst > term > term)).
% 2.19/0.60 thf(func_def_729, type, vNOT: ($o > $o)).
% 2.19/0.60 thf(func_def_730, type, sK591: (term > $o)).
% 2.19/0.60 thf(func_def_731, type, db5: !>[X0: $tType]:(X0)).
% 2.19/0.60 thf(func_def_732, type, sK592: subst).
% 2.19/0.60 thf(func_def_733, type, sK593: term).
% 2.19/0.60 thf(func_def_734, type, sK594: (term > $o)).
% 2.19/0.60 thf(func_def_735, type, sK595: term).
% 2.19/0.60 thf(f1,axiom,(
% 2.19/0.60 ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & hoaslaminj_gthm & hoasinduction_gthm & ~lamnotap & (id = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & (! [X46 : term,X18 : (subst > term > term),X47 : term] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47)))) <=> hoaslamnotap) & hoasinduction_lem3a_gthm & hoasinduction_lem3_gthm & (pushprop_lem0 <=> ! [X13 : term,X14 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & pushprop_gthm & (pushprop_lem0_lthm <=> ! [X13 : term,X10 : (term > $o),X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & hoasapinj2_gthm & hoasinduction_lem1v2_gthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X21 : term,X10 : (term > $o)] : ((X10 @ X21) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)))) => ! [X17 : subst,X10 : (term > $o),X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13)))))))) <=> induction2lem_lthm) & pushprop_lem2v2_lthm & (pushprop_lem1v2 <=> ! [X13 : term,X14 : subst,X11 : (term > $o),X10 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X15 : term,X13 : term,X10 : (term > $o),X14 : subst,X26 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))))) & (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))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X29 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))))) & (hoasinduction <=> ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id))) & pushprop_lem1v2_gthm & ulamvarind & hoasapnotvar & (! [X15 : term,X20 : term,X13 : term,X19 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj2) & axvarshift & (pushprop_lem1 <=> ! [X13 : term,X15 : term,X14 : subst,X26 : (term > $o),X10 : (term > $o)] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13))) & hoasinduction_lem1_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) <=> axvarcons) & hoaslamnotap_gthm & hoasinduction_lem3b_gthm & (hoasapinj1 <=> ! [X15 : term,X13 : term,X20 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & pushprop_lem2v2_gthm & axassoc & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X11 : (term > $o),X29 : term,X10 : (subst > term > subst > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [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)) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))))))) & (hoasinduction_lem3aa <=> ! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))) & (axvarid <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & induction2_gthm & axapp & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X19 : term,X13 : term,X15 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X19 : term,X20 : term,X15 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X13 = X15)))) <=> hoasapinj1_lthm) & (hoasinduction_lem3v2a <=> ! [X29 : term,X11 : (term > $o),X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)))) & ~ulamvar1 & (hoasinduction_lem2 <=> ! [X24 : term,X23 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X24 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id))) & ((! [X15 : term,X19 : term,X20 : term,X13 : term] : ((X19 = X20) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) => ! [X20 : term,X19 : term,X13 : term,X15 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) <=> hoasapinj2_lthm) & (induction2lem <=> ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)))) & ~(var @ (d2term @ d_one)) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X13 : term,X20 : term,X15 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) <=> apinj1) & (hoasinduction_lthm <=> (! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X24 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ 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))) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) => (! [X27 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X25 : subst,X26 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X14 : subst,X25 : subst,X26 : 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 : (subst > term > subst > $o),X28 : term] : (~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))))))) & (hoasinduction_p_and_p_prime = (^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (sh = ((d2subst @ d_id))) & hoasinduction_lem2_gthm & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & hoaslamnotvar_lthm & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & induction2lem_gthm & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X48 : term,X10 : (subst > term > subst > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | (X11 @ (lam @ X48)) | ~ ! [X15 : term] : ((X11 @ (sub @ X48 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) & (laminj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15))))) & apnotvar & ! [X7 : d_subst,X6 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) <=> termmset_lthm) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) => ! [X43 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [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)))))) <=> hoasinduction_lem3a_lthm) & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (hoaslaminj_lthm <=> (! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X13 : term,X15 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X32 : subst,X18 : (subst > term > term),X31 : (subst > term > term),X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))) & pushprop_lem3v2 & (hoasapinj2 <=> ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) & termmset_gthm & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13)))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & pushprop_lem0_gthm & hoasapnotvar_lthm & (! [X45 : term,X44 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X11 @ X44) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem2v2) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axclos & pushprop_lem3v2_lthm & hoaslamnotvar_gthm & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))))) & hoasinduction_lem1 & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & (! [X15 : term,X13 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & pushprop_lthm & hoasinduction_lem1_gthm & (induction <=> ! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))) & axabs & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (pushprop_lem1v2_lthm <=> (! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X14 : subst,X11 : (term > $o),X13 : term,X10 : (term > $o)] : ((X11 @ one) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13)))) & (hoasinduction_lem3aaa <=> ! [X34 : term,X10 : (subst > term > subst > $o)] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X40 : term,X39 : subst,X41 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X38 : subst,X37 : term,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)))) & pushprop_lthm_orig & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | (X10 @ X22) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $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))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : (~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (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)))))))))) <=> hoasinduction_lthm_3) & (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)))))))) & ! [X1 : d_term] : (X1 = d_one) & hoasapnotvar_gthm & pushprop & (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) <=> axshiftcons) & substmonoid_gthm & hoaslamnotvar & ! [X5 : d_subst] : (X5 = d_id) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (hoaslam = (^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one)))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & lamnotvar & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & (one = ((d2term @ d_one))) & (! [X48 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : (~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) <=> hoasinduction_lem3v2) & hoaslamnotap_lthm & (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)] : (~ ! [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)))) => ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) & axmap & hoasapinj1_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13))) <=> hoasinduction_lem3v2_f_lthm) & (hoasinduction_lem0 <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & pushprop_lem1_gthm & hoasinduction_lem2_lthm & hoasinduction_lem1v2 & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X27) @ id))) & (substmonoid_lthm <=> (! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id))))))) & (hoasinduction_lem3a <=> ! [X43 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id))) & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : ((X10 @ id @ X30 @ id) | ~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ 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)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & (hoaslaminj <=> ! [X18 : (subst > term > term),X31 : (subst > term > term),X32 : subst,X33 : term] : ((((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & ulamvarsh & (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm)),
% 2.19/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',alg444_1)).
% 2.19/0.60 thf(f2,conjecture,(
% 2.19/0.60 (! [X1 : (term > $o),X2 : term,X3 : subst,X0 : (term > $o)] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X4 : term] : ((var @ X4) => (X1 @ X4)) => ! [X4 : term] : ((var @ X4) => (X0 @ (sub @ X4 @ (push @ X2 @ X3)))))) = pushprop_lem3v2)),
% 2.19/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2)).
% 2.19/0.60 thf(f3,negated_conjecture,(
% 2.19/0.60 ~ (! [X1 : (term > $o),X2 : term,X3 : subst,X0 : (term > $o)] : ((pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1) => (! [X4 : term] : ((var @ X4) => (X1 @ X4)) => ! [X4 : term] : ((var @ X4) => (X0 @ (sub @ X4 @ (push @ X2 @ X3)))))) = pushprop_lem3v2)),
% 2.19/0.60 inference(negated_conjecture,[status(cth)],[f2])).
% 2.19/0.60 thf(f4,plain,(
% 2.19/0.60 ~ (! [X0 : (term > $o),X1 : term,X2 : subst,X3 : (term > $o)] : ((pushprop_p_and_p_prime @ X1 @ X2 @ X3 @ X0) => (! [X4 : term] : ((var @ X4) => (X0 @ X4)) => ! [X5 : term] : ((var @ X5) => (X3 @ (sub @ X5 @ (push @ X1 @ X2)))))) = pushprop_lem3v2)),
% 2.19/0.60 inference(rectify,[],[f3])).
% 2.19/0.60 thf(f5,plain,(
% 2.19/0.60 ~ (pushprop_lem3v2 = ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ (term > $o) @ (^[Y3 : term > $o]: ((pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3) => ((!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y3 @ Y4)))) => (!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y0 @ (sub @ Y4 @ (push @ Y2 @ Y1))))))))))))))))))),
% 2.19/0.60 inference(fool_elimination,[],[f4])).
% 2.19/0.60 thf(f6,plain,(
% 2.19/0.60 ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & hoaslaminj_gthm & hoasinduction_gthm & ~lamnotap & (id = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & (! [X2 : term,X3 : (subst > term > term),X4 : term] : (~ ! [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) <=> hoaslamnotap) & hoasinduction_lem3a_gthm & hoasinduction_lem3_gthm & (pushprop_lem0 <=> ! [X8 : term,X9 : subst,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9)))))) & pushprop_gthm & (pushprop_lem0_lthm <=> ! [X13 : term,X14 : (term > $o),X15 : subst] : ~ ! [X16 : (term > $o)] : ~ ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15)))))) & hoasapinj2_gthm & hoasinduction_lem1v2_gthm & ((! [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) = X19) => (! [X20 : subst,X21 : term] : (((comp @ sh @ (push @ X21 @ X20))) = X20) => (! [X22 : subst] : (((comp @ X22 @ id)) = X22) => (! [X23 : term,X24 : (term > $o)] : ((X24 @ X23) | ~ ! [X25 : term] : ((X24 @ (lam @ X25)) | ~(X24 @ X25)) | ~ ! [X26 : term] : ((X24 @ X26) | ~(var @ X26)) | ~ ! [X27 : term,X28 : term] : (~(X24 @ X27) | ~(X24 @ X28) | (X24 @ (ap @ X28 @ X27)))) => ! [X29 : subst,X30 : (term > $o),X31 : term] : ((X30 @ (sub @ X31 @ X29)) | ~ ! [X32 : term] : ((X30 @ (sub @ X32 @ X29)) | ~(var @ X32)) | ~ ! [X33 : term,X34 : term] : (~(X30 @ X34) | (X30 @ (ap @ X34 @ X33)) | ~(X30 @ X33)) | ~ ! [X35 : term] : (~ ! [X36 : term] : ((X30 @ (sub @ X35 @ (push @ X36 @ id))) | ~(X30 @ X36)) | (X30 @ (lam @ X35)))))))) <=> induction2lem_lthm) & pushprop_lem2v2_lthm & (pushprop_lem1v2 <=> ! [X37 : term,X38 : subst,X39 : (term > $o),X40 : (term > $o)] : (~ ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))) | ~(X40 @ X37) | (X39 @ one))) & (pushprop_lem1_lthm <=> (! [X42 : term,X43 : subst] : (((sub @ one @ (push @ X42 @ X43))) = X42) => (! [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) = X45) => ! [X46 : term,X47 : term,X48 : (term > $o),X49 : subst,X50 : (term > $o)] : ((X50 @ (sub @ X47 @ (push @ X46 @ X49))) | ~(X48 @ X47))))) & (hoasinduction_lem3v2a_lthm <=> (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X53 : term,X54 : subst] : (((sub @ X51 @ (push @ X53 @ X54))) = ((X52 @ X54 @ X53))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : (subst > term > term)] : (~ ! [X60 : term] : (~(X57 @ id @ X60 @ id) | (X57 @ id @ (X59 @ id @ X60) @ id)) | ~ ! [X61 : term,X62 : subst,X63 : subst] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63)))) | (X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) | (X56 @ (lam @ X58)) | ~ ! [X64 : term] : ((X56 @ (sub @ X58 @ (push @ X64 @ id))) | ~(X56 @ X64)) | ~ ! [X65 : term] : (((X57 @ id @ X65 @ id)) = ((X56 @ X65))))))) & (hoasinduction <=> ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : (subst > term > term)] : ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id) | ~ ! [X69 : term,X70 : subst,X71 : subst] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) | ~ ! [X72 : term] : ((X67 @ id @ (X68 @ id @ X72) @ id) | ~(X67 @ id @ X72 @ id))) | ~ ! [X73 : term,X74 : term] : (~(X67 @ id @ X74 @ id) | ~(X67 @ id @ X73 @ id) | (X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)) | ~ ! [X75 : term] : ((X67 @ id @ X75 @ id) | ~(var @ (sub @ X75 @ id))) | ~ ! [X76 : subst,X77 : subst,X78 : subst,X79 : term] : (~(X67 @ X76 @ X79 @ (comp @ X78 @ X77)) | (X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) | ~ ! [X80 : term,X81 : subst,X82 : subst,X83 : subst] : ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)) | ~(X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) | (X67 @ id @ X66 @ id))) & pushprop_lem1v2_gthm & ulamvarind & hoasapnotvar & (! [X84 : term,X85 : term,X86 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85)))) <=> apinj2) & axvarshift & (pushprop_lem1 <=> ! [X88 : term,X89 : term,X90 : subst,X91 : (term > $o),X92 : (term > $o)] : ((X91 @ (sub @ X88 @ (push @ X89 @ X90))) | ~(X92 @ X88))) & hoasinduction_lem1_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_f <=> ! [X93 : term] : ~ ! [X94 : (subst > term > term)] : ~ ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96))))) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> axvarcons) & hoaslamnotap_gthm & hoasinduction_lem3b_gthm & (hoasapinj1 <=> ! [X99 : term,X100 : term,X101 : term,X102 : term] : ((X99 = X100) | (((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))))) & pushprop_lem2v2_gthm & axassoc & (hoasinduction_no_psi_cond_lthm <=> (! [X103 : (subst > term > subst > $o)] : ~ ! [X104 : (term > $o)] : ~ ! [X105 : term] : (((X104 @ X105)) = ((X103 @ id @ X105 @ id))) => (! [X106 : term,X107 : (term > $o)] : (~ ! [X108 : term] : (~(var @ X108) | (X107 @ X108)) | ~ ! [X109 : term] : ((X107 @ (lam @ X109)) | ~ ! [X110 : term] : ((X107 @ (sub @ X109 @ (push @ X110 @ id))) | ~(X107 @ X110))) | (X107 @ X106) | ~ ! [X111 : term,X112 : term] : (~(X107 @ X111) | (X107 @ (ap @ X112 @ X111)) | ~(X107 @ X112))) => (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : (term > $o),X115 : term,X116 : (subst > term > subst > $o)] : ((X114 @ (lam @ X115)) | ~ ! [X117 : term] : ((X114 @ (sub @ X115 @ (push @ X117 @ id))) | ~(X114 @ X117)) | ~ ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))) | ~ ! [X119 : (subst > term > term)] : ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id) | ~ ! [X120 : subst,X121 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) = ((sub @ (X119 @ X121 @ X122) @ X120))) | ~ ! [X123 : term] : ((X116 @ id @ (X119 @ id @ X123) @ id) | ~(X116 @ id @ X123 @ id)))) => ! [X124 : term,X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : (~ ! [X127 : term] : ((X125 @ id @ (X126 @ id @ X127) @ id) | ~(X125 @ id @ X127 @ id)) | ~ ! [X128 : term,X129 : subst,X130 : subst] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) | (X125 @ id @ (lam @ (X126 @ sh @ one)) @ id)) | (X125 @ id @ X124 @ id) | ~ ! [X131 : term,X132 : term] : (~(X125 @ id @ X132 @ id) | (X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id) | ~(X125 @ id @ X131 @ id)))))))) & (hoasinduction_lem3aa <=> ! [X133 : term,X134 : (subst > term > subst > $o)] : (~ ! [X135 : term] : ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id) | ~(X134 @ id @ X135 @ id)) | (X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id) | ~ ! [X136 : (subst > term > term)] : (~ ! [X137 : term] : ((X134 @ id @ (X136 @ id @ X137) @ id) | ~(X134 @ id @ X137 @ id)) | ~ ! [X138 : subst,X139 : term,X140 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) | (X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)))) & (axvarid <=> ! [X141 : term] : (((sub @ X141 @ id)) = X141)) & induction2_gthm & axapp & ((! [X142 : term] : (((sub @ X142 @ id)) = X142) => (! [X143 : term,X144 : term,X145 : term,X146 : term] : ((((ap @ X145 @ X144)) != ((ap @ X146 @ X143))) | (X145 = X146)) => ! [X147 : term,X148 : term,X149 : term,X150 : term] : ((((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))) | (X149 = X150)))) <=> hoasapinj1_lthm) & (hoasinduction_lem3v2a <=> ! [X151 : term,X152 : (term > $o),X153 : (subst > term > subst > $o)] : (~ ! [X154 : term] : (((X152 @ X154)) = ((X153 @ id @ X154 @ id))) | ~ ! [X155 : (subst > term > term)] : ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id) | ~ ! [X156 : term,X157 : subst,X158 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) | ~ ! [X159 : term] : (~(X153 @ id @ X159 @ id) | (X153 @ id @ (X155 @ id @ X159) @ id))) | ~ ! [X160 : term] : ((X152 @ (sub @ X151 @ (push @ X160 @ id))) | ~(X152 @ X160)) | (X152 @ (lam @ X151)))) & ~ulamvar1 & (hoasinduction_lem2 <=> ! [X161 : term,X162 : term,X163 : (subst > term > subst > $o)] : (~ ! [X164 : subst,X165 : term,X166 : subst,X167 : subst] : ((X163 @ X164 @ X165 @ (comp @ X166 @ X167)) | ~(X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)) | ~(X163 @ id @ X161 @ id) | ~ ! [X168 : term,X169 : term] : (~(X163 @ id @ X169 @ id) | ~(X163 @ id @ X168 @ id) | (X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : (~(X163 @ X171 @ X173 @ (comp @ X170 @ X172)) | (X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172)) | (X163 @ id @ (ap @ X162 @ X161) @ id) | ~(X163 @ id @ X162 @ id))) & ((! [X174 : term,X175 : term,X176 : term,X177 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176)))) => ! [X178 : term,X179 : term,X180 : term,X181 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179))) <=> hoasapinj2_lthm) & (induction2lem <=> ! [X182 : (term > $o),X183 : subst,X184 : term] : (~ ! [X185 : term] : (~ ! [X186 : term] : ((X182 @ (sub @ X185 @ (push @ X186 @ id))) | ~(X182 @ X186)) | (X182 @ (lam @ X185))) | (X182 @ (sub @ X184 @ X183)) | ~ ! [X187 : term] : (~(var @ X187) | (X182 @ (sub @ X187 @ X183))) | ~ ! [X188 : term,X189 : term] : ((X182 @ (ap @ X188 @ X189)) | ~(X182 @ X189) | ~(X182 @ X188)))) & ~(var @ (d2term @ d_one)) & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one))) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (! [X190 : term,X191 : term,X192 : term,X193 : term] : ((((ap @ X190 @ X193)) != ((ap @ X192 @ X191))) | (X190 = X192)) <=> apinj1) & (hoasinduction_lthm <=> (! [X194 : term,X195 : (term > $o)] : ((X195 @ X194) | ~ ! [X196 : term,X197 : term] : ((X195 @ (ap @ X196 @ X197)) | ~(X195 @ X197) | ~(X195 @ X196)) | ~ ! [X198 : term] : (~ ! [X199 : term] : (~(X195 @ X199) | (X195 @ (sub @ X198 @ (push @ X199 @ id)))) | (X195 @ (lam @ X198))) | ~ ! [X200 : term] : (~(var @ X200) | (X195 @ X200))) => (! [X201 : (subst > term > subst > $o),X202 : term,X203 : term] : ((X201 @ id @ (ap @ X202 @ X203) @ id) | ~(X201 @ id @ X203 @ id) | ~ ! [X204 : term,X205 : term] : (~(X201 @ id @ X205 @ id) | ~(X201 @ id @ X204 @ id) | (X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)) | ~(X201 @ id @ X202 @ id) | ~ ! [X206 : term,X207 : subst,X208 : subst,X209 : subst] : (~(X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208) | (X201 @ X209 @ X206 @ (comp @ X207 @ X208))) | ~ ! [X210 : subst,X211 : subst,X212 : subst,X213 : term] : (~(X201 @ X211 @ X213 @ (comp @ X212 @ X210)) | (X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210))) => (! [X214 : term,X215 : (subst > term > subst > $o)] : ((X215 @ id @ (lam @ X214) @ id) | ~ ! [X216 : subst,X217 : subst,X218 : subst,X219 : term] : ((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217) | ~(X215 @ X216 @ X219 @ (comp @ X218 @ X217))) | ~ ! [X220 : (subst > term > term)] : ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id) | ~ ! [X221 : subst,X222 : subst,X223 : term] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) = ((sub @ (X220 @ X222 @ X223) @ X221))) | ~ ! [X224 : term] : ((X215 @ id @ (X220 @ id @ X224) @ id) | ~(X215 @ id @ X224 @ id))) | ~ ! [X225 : subst,X226 : subst,X227 : subst,X228 : term] : (~(X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226) | (X215 @ X225 @ X228 @ (comp @ X227 @ X226))) | ~ ! [X229 : term] : ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id) | ~(X215 @ id @ X229 @ id))) => ! [X230 : (subst > term > subst > $o),X231 : term] : (~ ! [X232 : term,X233 : term] : ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id) | ~(X230 @ id @ X233 @ id) | ~(X230 @ id @ X232 @ id)) | (X230 @ id @ X231 @ id) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (~(X230 @ id @ X235 @ id) | (X230 @ id @ (X234 @ id @ X235) @ id)) | ~ ! [X236 : term,X237 : subst,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)))) | (X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : ((X230 @ X242 @ X241 @ (comp @ X239 @ X240)) | ~(X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240)) | ~ ! [X243 : term] : (~(var @ (sub @ X243 @ id)) | (X230 @ id @ X243 @ id)) | ~ ! [X244 : term,X245 : subst,X246 : subst,X247 : subst] : (~(X230 @ X246 @ X244 @ (comp @ X245 @ X247)) | (X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247))))))) & (hoasinduction_p_and_p_prime = (^[X248 : (subst > term > subst > $o), X249 : (term > $o)] : (! [X250 : term] : (((X248 @ id @ X250 @ id)) = ((X249 @ X250)))))) & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & (sh = ((d2subst @ d_id))) & hoasinduction_lem2_gthm & (! [X251 : subst] : (((comp @ id @ X251)) = X251) <=> axidl) & hoaslamnotvar_lthm & (termmset <=> ! [X252 : term] : (((sub @ X252 @ id)) = X252)) & induction2lem_gthm & (hoasinduction_lem3v2_lthm <=> (! [X253 : term] : (((sub @ X253 @ id)) = X253) => ! [X254 : (term > $o),X255 : term,X256 : (subst > term > subst > $o)] : (~ ! [X257 : term] : (((X256 @ id @ X257 @ id)) = ((X254 @ X257))) | (X254 @ (lam @ X255)) | ~ ! [X258 : term] : ((X254 @ (sub @ X255 @ (push @ X258 @ id))) | ~(X254 @ X258)) | ~ ! [X259 : (subst > term > term)] : (~ ! [X260 : subst,X261 : term,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) | (X256 @ id @ (lam @ (X259 @ sh @ one)) @ id) | ~ ! [X263 : term] : (~(X256 @ id @ X263 @ id) | (X256 @ id @ (X259 @ id @ X263) @ id))) | ~ ! [X264 : subst,X265 : subst,X266 : subst,X267 : term] : ((X256 @ X265 @ X267 @ (comp @ X264 @ X266)) | ~(X256 @ (comp @ X265 @ X264) @ (sub @ X267 @ X264) @ X266)) | ~ ! [X268 : subst,X269 : subst,X270 : subst,X271 : term] : ((X256 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269) | ~(X256 @ X270 @ X271 @ (comp @ X268 @ X269)))))) & (laminj <=> ! [X272 : term,X273 : term] : ((X272 = X273) | (((lam @ X272)) != ((lam @ X273))))) & apnotvar & ! [X274 : d_subst,X275 : d_subst] : ((((d2subst @ X274)) = ((d2subst @ X275))) => (X274 = X275)) & ((! [X276 : term] : (((sub @ X276 @ id)) = X276) => ! [X277 : term] : (((sub @ X277 @ id)) = X277)) <=> termmset_lthm) & ((! [X278 : term] : (((sub @ X278 @ id)) = X278) => (! [X279 : (subst > term > subst > $o),X280 : term] : (~ ! [X281 : term] : (~(X279 @ id @ X281 @ id) | (X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)) | (X279 @ id @ (lam @ (sub @ X280 @ (push @ one @ sh))) @ id) | ~ ! [X282 : (subst > term > term)] : ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id) | ~ ! [X283 : term] : (~(X279 @ id @ X283 @ id) | (X279 @ id @ (X282 @ id @ X283) @ id)) | ~ ! [X284 : subst,X285 : subst,X286 : term] : (((X282 @ (comp @ X284 @ X285) @ (sub @ X286 @ X285))) = ((sub @ (X282 @ X284 @ X286) @ X285))))) => ! [X287 : term,X288 : (subst > term > subst > $o)] : ((X288 @ id @ (lam @ X287) @ id) | ~ ! [X289 : term] : ((X288 @ id @ (sub @ X287 @ (push @ X289 @ id)) @ id) | ~(X288 @ id @ X289 @ id)) | ~ ! [X290 : (subst > term > term)] : (~ ! [X291 : subst,X292 : subst,X293 : term] : (((sub @ (X290 @ X291 @ X293) @ X292)) = ((X290 @ (comp @ X291 @ X292) @ (sub @ X293 @ X292)))) | (X288 @ id @ (lam @ (X290 @ sh @ one)) @ id) | ~ ! [X294 : term] : (~(X288 @ id @ X294 @ id) | (X288 @ id @ (X290 @ id @ X294) @ id)))))) <=> hoasinduction_lem3a_lthm) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : (((X296 @ sh @ one)) != ((sub @ X295 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (hoaslaminj_lthm <=> (! [X297 : term,X298 : subst] : (((sub @ one @ (push @ X297 @ X298))) = X297) => (! [X299 : subst,X300 : term] : (((comp @ sh @ (push @ X300 @ X299))) = X299) => (! [X301 : term,X302 : term] : ((((lam @ X301)) != ((lam @ X302))) | (X301 = X302)) => ! [X303 : subst,X304 : (subst > term > term),X305 : (subst > term > term),X306 : term] : ((((X305 @ X303 @ X306)) = ((X304 @ X303 @ X306))) | ~ ! [X307 : subst,X308 : term,X309 : subst] : (((X304 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309))) = ((sub @ (X304 @ X307 @ X308) @ X309))) | (((lam @ (X305 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ~ ! [X310 : subst,X311 : subst,X312 : term] : (((sub @ (X305 @ X311 @ X312) @ X310)) = ((X305 @ (comp @ X311 @ X310) @ (sub @ X312 @ X310))))))))) & pushprop_lem3v2 & (hoasapinj2 <=> ! [X313 : term,X314 : term,X315 : term,X316 : term] : ((((ap @ (sub @ X314 @ id) @ X313)) != ((ap @ (sub @ X315 @ id) @ X316))) | (X313 = X316))) & termmset_gthm & (induction2_lthm <=> (! [X317 : term] : (((sub @ X317 @ id)) = X317) => (! [X318 : (term > $o),X319 : subst,X320 : term] : ((X318 @ (sub @ X320 @ X319)) | ~ ! [X321 : term,X322 : term] : (~(X318 @ X322) | (X318 @ (ap @ X321 @ X322)) | ~(X318 @ X321)) | ~ ! [X323 : term] : (~(var @ X323) | (X318 @ (sub @ X323 @ X319))) | ~ ! [X324 : term] : (~ ! [X325 : term] : (~(X318 @ X325) | (X318 @ (sub @ X324 @ (push @ X325 @ id)))) | (X318 @ (lam @ X324)))) => ! [X326 : term,X327 : (term > $o)] : (~ ! [X328 : term] : ((X327 @ (lam @ X328)) | ~ ! [X329 : term] : ((X327 @ (sub @ X328 @ (push @ X329 @ id))) | ~(X327 @ X329))) | ~ ! [X330 : term,X331 : term] : (~(X327 @ X331) | ~(X327 @ X330) | (X327 @ (ap @ X331 @ X330))) | (X327 @ X326) | ~ ! [X332 : term] : (~(var @ X332) | (X327 @ X332)))))) & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoasinduction_lem2v2_gthm & pushprop_lem2v2 & pushprop_lem0_gthm & hoasapnotvar_lthm & (! [X333 : term,X334 : term,X335 : (subst > term > subst > $o),X336 : (term > $o)] : (~ ! [X337 : subst,X338 : subst,X339 : subst,X340 : term] : ((X335 @ (comp @ X337 @ X338) @ (sub @ X340 @ X338) @ X339) | ~(X335 @ X337 @ X340 @ (comp @ X338 @ X339))) | ~ ! [X341 : subst,X342 : subst,X343 : term,X344 : subst] : ((X335 @ X344 @ X343 @ (comp @ X342 @ X341)) | ~(X335 @ (comp @ X344 @ X342) @ (sub @ X343 @ X342) @ X341)) | ~(X336 @ X334) | (X336 @ (ap @ X334 @ X333)) | ~(X336 @ X333) | ~ ! [X345 : term,X346 : term] : (~(X335 @ id @ X345 @ id) | ~(X335 @ id @ X346 @ id) | (X335 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id)) | ~ ! [X347 : term] : (((X335 @ id @ X347 @ id)) = ((X336 @ X347)))) <=> hoasinduction_lem2v2) & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & axclos & pushprop_lem3v2_lthm & hoaslamnotvar_gthm & (induction2 <=> ! [X348 : term,X349 : (term > $o)] : (~ ! [X350 : term] : ((X349 @ X350) | ~(var @ X350)) | ~ ! [X351 : term,X352 : term] : (~(X349 @ X352) | (X349 @ (ap @ X352 @ X351)) | ~(X349 @ X351)) | (X349 @ X348) | ~ ! [X353 : term] : ((X349 @ (lam @ X353)) | ~ ! [X354 : term] : ((X349 @ (sub @ X353 @ (push @ X354 @ id))) | ~(X349 @ X354))))) & hoasinduction_lem1 & (substmonoid <=> (! [X355 : subst] : (((comp @ X355 @ id)) = X355) & ! [X356 : subst] : (((comp @ id @ X356)) = X356))) & (! [X357 : term,X358 : term] : ((((sub @ X358 @ sh)) != ((sub @ X357 @ sh))) | (X357 = X358)) <=> shinj) & pushprop_lthm & hoasinduction_lem1_gthm & (induction <=> ! [X359 : (term > $o),X360 : term] : ((X359 @ X360) | ~ ! [X361 : term] : (~(X359 @ X361) | (X359 @ (lam @ X361))) | ~ ! [X362 : term,X363 : term] : (~(X359 @ X363) | ~(X359 @ X362) | (X359 @ (ap @ X362 @ X363))) | ~ ! [X364 : term] : (~(var @ X364) | (X359 @ X364)))) & axabs & (hoasinduction_lem0_lthm <=> ! [X365 : (subst > term > subst > $o)] : ~ ! [X366 : (term > $o)] : ~ ! [X367 : term] : (((X366 @ X367)) = ((X365 @ id @ X367 @ id)))) & (pushprop_lem1v2_lthm <=> (! [X368 : subst,X369 : term] : (((sub @ one @ (push @ X369 @ X368))) = X369) => ! [X370 : subst,X371 : (term > $o),X372 : term,X373 : (term > $o)] : ((X371 @ one) | ~ ! [X374 : term] : (((X371 @ X374)) = ((X373 @ (sub @ X374 @ (push @ X372 @ X370))))) | ~(X373 @ X372)))) & (hoasinduction_lem3aaa <=> ! [X375 : term,X376 : (subst > term > subst > $o)] : (~ ! [X377 : term] : ((X376 @ id @ (sub @ X375 @ (push @ X377 @ id)) @ id) | ~(X376 @ id @ X377 @ id)) | (X376 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id) | ~ ! [X378 : (subst > term > term),X379 : term] : (~ ! [X380 : term] : ((X376 @ id @ (X378 @ id @ X380) @ id) | ~(X376 @ id @ X380 @ id)) | ~ ! [X381 : term,X382 : subst,X383 : subst] : (((X378 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ X379 @ (push @ (sub @ X381 @ X383) @ (comp @ X382 @ X383))))) | ~ ! [X384 : subst,X385 : term,X386 : subst] : (((sub @ (X378 @ X386 @ X385) @ X384)) = ((sub @ (sub @ X379 @ (push @ X385 @ X386)) @ X384))) | (X376 @ id @ (lam @ (X378 @ sh @ one)) @ id)))) & pushprop_lthm_orig & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & ((! [X387 : (subst > term > subst > $o)] : ~ ! [X388 : (term > $o)] : ~ ! [X389 : term] : (((X387 @ id @ X389 @ id)) = ((X388 @ X389))) => (! [X390 : term,X391 : (term > $o)] : (~ ! [X392 : term] : (~ ! [X393 : term] : ((X391 @ (sub @ X392 @ (push @ X393 @ id))) | ~(X391 @ X393)) | (X391 @ (lam @ X392))) | (X391 @ X390) | ~ ! [X394 : term] : (~(var @ X394) | (X391 @ X394)) | ~ ! [X395 : term,X396 : term] : ((X391 @ (ap @ X395 @ X396)) | ~(X391 @ X395) | ~(X391 @ X396))) => (! [X397 : term] : (((sub @ X397 @ id)) = X397) => (! [X398 : (subst > term > subst > $o),X399 : term,X400 : (term > $o)] : (~ ! [X401 : (subst > term > term)] : ((X398 @ id @ (lam @ (X401 @ sh @ one)) @ id) | ~ ! [X402 : subst,X403 : term,X404 : subst] : (((X401 @ (comp @ X404 @ X402) @ (sub @ X403 @ X402))) = ((sub @ (X401 @ X404 @ X403) @ X402))) | ~ ! [X405 : term] : ((X398 @ id @ (X401 @ id @ X405) @ id) | ~(X398 @ id @ X405 @ id))) | (X400 @ (lam @ X399)) | ~ ! [X406 : term] : ((X400 @ (sub @ X399 @ (push @ X406 @ id))) | ~(X400 @ X406)) | ~ ! [X407 : term] : (((X398 @ id @ X407 @ id)) = ((X400 @ X407)))) => ! [X408 : (subst > term > subst > $o),X409 : term] : (~ ! [X410 : subst,X411 : term,X412 : subst,X413 : subst] : ((X408 @ X412 @ X411 @ (comp @ X410 @ X413)) | ~(X408 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410) @ X413)) | ~ ! [X414 : term] : (~(var @ (sub @ X414 @ id)) | (X408 @ id @ X414 @ id)) | ~ ! [X415 : subst,X416 : subst,X417 : subst,X418 : term] : ((X408 @ (comp @ X417 @ X416) @ (sub @ X418 @ X416) @ X415) | ~(X408 @ X417 @ X418 @ (comp @ X416 @ X415))) | (X408 @ id @ X409 @ id) | ~ ! [X419 : term,X420 : term] : ((X408 @ id @ (ap @ (sub @ X419 @ id) @ X420) @ id) | ~(X408 @ id @ X419 @ id) | ~(X408 @ id @ X420 @ id)) | ~ ! [X421 : (subst > term > term)] : (~ ! [X422 : term] : ((X408 @ id @ (X421 @ id @ X422) @ id) | ~(X408 @ id @ X422 @ id)) | (X408 @ id @ (lam @ (X421 @ sh @ one)) @ id) | ~ ! [X423 : subst,X424 : term,X425 : subst] : (((X421 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423))) = ((sub @ (X421 @ X425 @ X424) @ X423))))))))) <=> hoasinduction_lthm_3) & (pushprop_p_and_p_prime = (^[X426 : term, X427 : subst, X428 : (term > $o), X429 : (term > $o)] : (! [X430 : term] : (((X428 @ (sub @ X430 @ (push @ X426 @ X427)))) = ((X429 @ X430)))))) & ! [X431 : d_term] : (d_one = X431) & hoasapnotvar_gthm & pushprop & (! [X432 : subst,X433 : term] : (((comp @ sh @ (push @ X433 @ X432))) = X432) <=> axshiftcons) & substmonoid_gthm & hoaslamnotvar & ! [X434 : d_subst] : (d_id = X434) & (hoasinduction_lem3b_lthm <=> ! [X435 : term] : ~ ! [X436 : (subst > term > term)] : (((X436 @ sh @ one)) != ((sub @ X435 @ (push @ one @ sh))))) & (hoaslam = (^[X437 : subst, X438 : (subst > term > term)] : ((d2term @ d_one)))) & ! [X439 : term] : ? [X440 : d_term] : (((d2term @ X440)) = X439) & lamnotvar & (! [X441 : subst] : (((push @ (sub @ one @ X441) @ (comp @ sh @ X441))) = X441) <=> axscons) & (one = ((d2term @ d_one))) & (! [X442 : term,X443 : (subst > term > subst > $o),X444 : (term > $o)] : (~ ! [X445 : term] : (~(X444 @ X445) | (X444 @ (sub @ X442 @ (push @ X445 @ id)))) | ~ ! [X446 : term,X447 : subst,X448 : subst,X449 : subst] : (~(X443 @ (comp @ X449 @ X448) @ (sub @ X446 @ X448) @ X447) | (X443 @ X449 @ X446 @ (comp @ X448 @ X447))) | ~ ! [X450 : subst,X451 : subst,X452 : term,X453 : subst] : (~(X443 @ X451 @ X452 @ (comp @ X453 @ X450)) | (X443 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453) @ X450)) | ~ ! [X454 : (subst > term > term)] : ((X443 @ id @ (lam @ (X454 @ sh @ one)) @ id) | ~ ! [X455 : subst,X456 : subst,X457 : term] : (((X454 @ (comp @ X456 @ X455) @ (sub @ X457 @ X455))) = ((sub @ (X454 @ X456 @ X457) @ X455))) | ~ ! [X458 : term] : (~(X443 @ id @ X458 @ id) | (X443 @ id @ (X454 @ id @ X458) @ id))) | (X444 @ (lam @ X442)) | ~ ! [X459 : term] : (((X444 @ X459)) = ((X443 @ id @ X459 @ id)))) <=> hoasinduction_lem3v2) & hoaslamnotap_lthm & (hoasinduction_lem3_lthm <=> (! [X460 : term] : (((sub @ X460 @ id)) = X460) => (! [X461 : term,X462 : (subst > term > subst > $o)] : ((X462 @ id @ (lam @ (sub @ X461 @ (push @ one @ sh))) @ id) | ~ ! [X463 : term] : (~(X462 @ id @ X463 @ id) | (X462 @ id @ (sub @ X461 @ (push @ X463 @ id)) @ id)) | ~ ! [X464 : (subst > term > term)] : (~ ! [X465 : subst,X466 : subst,X467 : term] : (((X464 @ (comp @ X465 @ X466) @ (sub @ X467 @ X466))) = ((sub @ (X464 @ X465 @ X467) @ X466))) | (X462 @ id @ (lam @ (X464 @ sh @ one)) @ id) | ~ ! [X468 : term] : (~(X462 @ id @ X468 @ id) | (X462 @ id @ (X464 @ id @ X468) @ id)))) => ! [X469 : term,X470 : (subst > term > subst > $o)] : (~ ! [X471 : (subst > term > term)] : (~ ! [X472 : term] : (~(X470 @ id @ X472 @ id) | (X470 @ id @ (X471 @ id @ X472) @ id)) | ~ ! [X473 : subst,X474 : term,X475 : subst] : (((sub @ (X471 @ X473 @ X474) @ X475)) = ((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475)))) | (X470 @ id @ (lam @ (X471 @ sh @ one)) @ id)) | ~ ! [X476 : subst,X477 : subst,X478 : term,X479 : subst] : ((X470 @ (comp @ X477 @ X476) @ (sub @ X478 @ X476) @ X479) | ~(X470 @ X477 @ X478 @ (comp @ X476 @ X479))) | (X470 @ id @ (lam @ X469) @ id) | ~ ! [X480 : term] : (~(X470 @ id @ X480 @ id) | (X470 @ id @ (sub @ X469 @ (push @ X480 @ id)) @ id)) | ~ ! [X481 : subst,X482 : subst,X483 : subst,X484 : term] : (~(X470 @ (comp @ X481 @ X482) @ (sub @ X484 @ X482) @ X483) | (X470 @ X481 @ X484 @ (comp @ X482 @ X483))))))) & axmap & hoasapinj1_gthm & (! [X485 : term] : ~ ! [X486 : (subst > term > term)] : ~ ! [X487 : term,X488 : subst] : (((sub @ X485 @ (push @ X487 @ X488))) = ((X486 @ X488 @ X487))) <=> hoasinduction_lem3v2_f_lthm) & (hoasinduction_lem0 <=> ! [X489 : (subst > term > subst > $o)] : ~ ! [X490 : (term > $o)] : ~ ! [X491 : term] : (((X489 @ id @ X491 @ id)) = ((X490 @ X491)))) & pushprop_lem1_gthm & hoasinduction_lem2_lthm & hoasinduction_lem1v2 & ! [X492 : d_term,X493 : d_term] : ((((d2term @ X493)) = ((d2term @ X492))) => (X492 = X493)) & (hoasinduction_lem3 <=> ! [X494 : term,X495 : (subst > term > subst > $o)] : (~ ! [X496 : subst,X497 : term,X498 : subst,X499 : subst] : ((X495 @ X496 @ X497 @ (comp @ X498 @ X499)) | ~(X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498) @ X499)) | ~ ! [X500 : subst,X501 : term,X502 : subst,X503 : subst] : ((X495 @ (comp @ X502 @ X500) @ (sub @ X501 @ X500) @ X503) | ~(X495 @ X502 @ X501 @ (comp @ X500 @ X503))) | ~ ! [X504 : (subst > term > term)] : (~ ! [X505 : term,X506 : subst,X507 : subst] : (((sub @ (X504 @ X506 @ X505) @ X507)) = ((X504 @ (comp @ X506 @ X507) @ (sub @ X505 @ X507)))) | (X495 @ id @ (lam @ (X504 @ sh @ one)) @ id) | ~ ! [X508 : term] : ((X495 @ id @ (X504 @ id @ X508) @ id) | ~(X495 @ id @ X508 @ id))) | ~ ! [X509 : term] : ((X495 @ id @ (sub @ X494 @ (push @ X509 @ id)) @ id) | ~(X495 @ id @ X509 @ id)) | (X495 @ id @ (lam @ X494) @ id))) & (substmonoid_lthm <=> (! [X510 : subst] : (((comp @ id @ X510)) = X510) => (! [X511 : subst] : (((comp @ X511 @ id)) = X511) => (! [X512 : subst] : (((comp @ id @ X512)) = X512) & ! [X513 : subst] : (((comp @ X513 @ id)) = X513))))) & (hoasinduction_lem3a <=> ! [X514 : term,X515 : (subst > term > subst > $o)] : (~ ! [X516 : (subst > term > term)] : (~ ! [X517 : subst,X518 : subst,X519 : term] : (((X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X516 @ X518 @ X519) @ X517))) | ~ ! [X520 : term] : ((X515 @ id @ (X516 @ id @ X520) @ id) | ~(X515 @ id @ X520 @ id)) | (X515 @ id @ (lam @ (X516 @ sh @ one)) @ id)) | ~ ! [X521 : term] : ((X515 @ id @ (sub @ X514 @ (push @ X521 @ id)) @ id) | ~(X515 @ id @ X521 @ id)) | (X515 @ id @ (lam @ X514) @ id))) & (hoasinduction_no_psi_cond <=> ! [X522 : (subst > term > subst > $o),X523 : term] : ((X522 @ id @ X523 @ id) | ~ ! [X524 : term,X525 : term] : (~(X522 @ id @ X524 @ id) | (X522 @ id @ (ap @ (sub @ X524 @ id) @ X525) @ id) | ~(X522 @ id @ X525 @ id)) | ~ ! [X526 : (subst > term > term)] : ((X522 @ id @ (lam @ (X526 @ sh @ one)) @ id) | ~ ! [X527 : term] : (~(X522 @ id @ X527 @ id) | (X522 @ id @ (X526 @ id @ X527) @ id)) | ~ ! [X528 : subst,X529 : term,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530)))))) & (axidr <=> ! [X531 : subst] : (((comp @ X531 @ id)) = X531)) & (hoaslaminj <=> ! [X532 : (subst > term > term),X533 : (subst > term > term),X534 : subst,X535 : term] : ((((X533 @ X534 @ X535)) = ((X532 @ X534 @ X535))) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((X533 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537))) = ((sub @ (X533 @ X536 @ X538) @ X537))) | (((lam @ (X532 @ sh @ one))) != ((lam @ (X533 @ sh @ one)))) | ~ ! [X539 : term,X540 : subst,X541 : subst] : (((sub @ (X532 @ X540 @ X539) @ X541)) = ((X532 @ (comp @ X540 @ X541) @ (sub @ X539 @ X541)))))) & ulamvarsh & (! [X542 : (subst > term > subst > $o),X543 : term] : (~ ! [X544 : (subst > term > term)] : (~ ! [X545 : term] : ((X542 @ id @ (X544 @ id @ X545) @ id) | ~(X542 @ id @ X545 @ id)) | (X542 @ id @ (lam @ (X544 @ sh @ one)) @ id) | ~ ! [X546 : term,X547 : subst,X548 : subst] : (((sub @ (X544 @ X547 @ X546) @ X548)) = ((X544 @ (comp @ X547 @ X548) @ (sub @ X546 @ X548))))) | ~ ! [X549 : term] : (~(X542 @ id @ X549 @ id) | (X542 @ id @ (sub @ X543 @ (push @ X549 @ id)) @ id)) | (X542 @ id @ (lam @ (sub @ X543 @ (push @ one @ sh))) @ id)) <=> hoasinduction_lem3aa_lthm)),
% 2.19/0.60 inference(rectify,[],[f1])).
% 2.19/0.60 thf(f7,plain,(
% 2.19/0.60 ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & (hoaslaminj_gthm = $true) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X2 : term,X4 : term,X3 : (subst > term > term)] : (~ ! [X6 : subst,X7 : term,X5 : subst] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one)))))) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X9 : subst,X8 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & (pushprop_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X15 : subst,X14 : (term > $o),X13 : term] : ~ ! [X16 : (term > $o)] : ~ ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15)))))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) = X19) => (! [X21 : term,X20 : subst] : (((comp @ sh @ (push @ X21 @ X20))) = X20) => (! [X22 : subst] : (((comp @ X22 @ id)) = X22) => (! [X23 : term,X24 : (term > $o)] : (($true = ((X24 @ X23))) | ~ ! [X25 : term] : (($true = ((X24 @ (lam @ X25)))) | ~ (((X24 @ X25)) = $true)) | ~ ! [X26 : term] : (($true = ((X24 @ X26))) | ~ ($true = ((var @ X26)))) | ~ ! [X27 : term,X28 : term] : (~ ($true = ((X24 @ X27))) | ~ ($true = ((X24 @ X28))) | ($true = ((X24 @ (ap @ X28 @ X27)))))) => ! [X29 : subst,X30 : (term > $o),X31 : term] : (($true = ((X30 @ (sub @ X31 @ X29)))) | ~ ! [X32 : term] : (($true = ((X30 @ (sub @ X32 @ X29)))) | ~ ($true = ((var @ X32)))) | ~ ! [X33 : term,X34 : term] : (~ ($true = ((X30 @ X34))) | ($true = ((X30 @ (ap @ X34 @ X33)))) | ~ ($true = ((X30 @ X33)))) | ~ ! [X35 : term] : (~ ! [X36 : term] : (($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id))))) | ~ ($true = ((X30 @ X36)))) | (((X30 @ (lam @ X35))) = $true))))))) <=> (induction2lem_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X37 : term,X38 : subst,X39 : (term > $o),X40 : (term > $o)] : (~ ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))) | ~ (((X40 @ X37)) = $true) | ($true = ((X39 @ one))))) & ((pushprop_lem1_lthm = $true) <=> (! [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) = X42) => (! [X45 : subst,X44 : term] : (((comp @ sh @ (push @ X44 @ X45))) = X45) => ! [X46 : term,X47 : term,X48 : (term > $o),X49 : subst,X50 : (term > $o)] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ~ ($true = ((X48 @ X47))))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((sub @ X51 @ (push @ X53 @ X54))) = ((X52 @ X54 @ X53))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : (subst > term > term)] : (~ ! [X60 : term] : (~ ($true = ((X57 @ id @ X60 @ id))) | ($true = ((X57 @ id @ (X59 @ id @ X60) @ id)))) | ~ ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63)))) | (((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) = $true)) | ($true = ((X56 @ (lam @ X58)))) | ~ ! [X64 : term] : (($true = ((X56 @ (sub @ X58 @ (push @ X64 @ id))))) | ~ ($true = ((X56 @ X64)))) | ~ ! [X65 : term] : (((X57 @ id @ X65 @ id)) = ((X56 @ X65))))))) & ((hoasinduction = $true) <=> ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : (subst > term > term)] : (($true = ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id))) | ~ ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) | ~ ! [X72 : term] : (($true = ((X67 @ id @ (X68 @ id @ X72) @ id))) | ~ ($true = ((X67 @ id @ X72 @ id))))) | ~ ! [X73 : term,X74 : term] : (~ ($true = ((X67 @ id @ X74 @ id))) | ~ ($true = ((X67 @ id @ X73 @ id))) | ($true = ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))) | ~ ! [X75 : term] : (($true = ((X67 @ id @ X75 @ id))) | ~ ($true = ((var @ (sub @ X75 @ id))))) | ~ ! [X76 : subst,X77 : subst,X78 : subst,X79 : term] : (~ ($true = ((X67 @ X76 @ X79 @ (comp @ X78 @ X77)))) | (((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) = $true)) | ~ ! [X80 : term,X81 : subst,X82 : subst,X83 : subst] : (($true = ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)))) | ~ (((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) = $true)) | ($true = ((X67 @ id @ X66 @ id))))) & (pushprop_lem1v2_gthm = $true) & (ulamvarind = $true) & (hoasapnotvar = $true) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (axvarshift = $true) & ((pushprop_lem1 = $true) <=> ! [X88 : term,X89 : term,X90 : subst,X91 : (term > $o),X92 : (term > $o)] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ~ ($true = ((X92 @ X88))))) & (hoasinduction_lem1_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X93 : term] : ~ ! [X94 : (subst > term > term)] : ~ ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (pushprop_lem2v2_gthm = $true) & (axassoc = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X103 : (subst > term > subst > $o)] : ~ ! [X104 : (term > $o)] : ~ ! [X105 : term] : (((X104 @ X105)) = ((X103 @ id @ X105 @ id))) => (! [X106 : term,X107 : (term > $o)] : (~ ! [X108 : term] : (~ ($true = ((var @ X108))) | ($true = ((X107 @ X108)))) | ~ ! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ~ ! [X110 : term] : (($true = ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) | ~ ($true = ((X107 @ X110))))) | ($true = ((X107 @ X106))) | ~ ! [X111 : term,X112 : term] : (~ ($true = ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111)))) | ~ ($true = ((X107 @ X112))))) => (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : (term > $o),X115 : term,X116 : (subst > term > subst > $o)] : (($true = ((X114 @ (lam @ X115)))) | ~ ! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | ~ (((X114 @ X117)) = $true)) | ~ ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))) | ~ ! [X119 : (subst > term > term)] : (($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id))) | ~ ! [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) = ((sub @ (X119 @ X121 @ X122) @ X120))) | ~ ! [X123 : term] : (($true = ((X116 @ id @ (X119 @ id @ X123) @ id))) | ~ ($true = ((X116 @ id @ X123 @ id)))))) => ! [X124 : term,X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : (~ ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ~ ($true = ((X125 @ id @ X127 @ id)))) | ~ ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) | ($true = ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id)))) | ($true = ((X125 @ id @ X124 @ id))) | ~ ! [X131 : term,X132 : term] : (~ ($true = ((X125 @ id @ X132 @ id))) | ($true = ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ~ ($true = ((X125 @ id @ X131 @ id)))))))))) & ((hoasinduction_lem3aa = $true) <=> ! [X133 : term,X134 : (subst > term > subst > $o)] : (~ ! [X135 : term] : (($true = ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) | ~ (((X134 @ id @ X135 @ id)) = $true)) | (((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X136 : (subst > term > term)] : (~ ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ~ ($true = ((X134 @ id @ X137 @ id)))) | ~ ! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) | (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) = $true)))) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & (induction2_gthm = $true) & (axapp = $true) & ((hoasapinj1_lthm = $true) <=> (! [X142 : term] : (((sub @ X142 @ id)) = X142) => (! [X144 : term,X146 : term,X143 : term,X145 : term] : ((X145 = X146) | (((ap @ X145 @ X144)) != ((ap @ X146 @ X143)))) => ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X151 : term,X152 : (term > $o),X153 : (subst > term > subst > $o)] : (~ ! [X154 : term] : (((X152 @ X154)) = ((X153 @ id @ X154 @ id))) | ~ ! [X155 : (subst > term > term)] : (($true = ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id))) | ~ ! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) | ~ ! [X159 : term] : (~ (((X153 @ id @ X159 @ id)) = $true) | ($true = ((X153 @ id @ (X155 @ id @ X159) @ id))))) | ~ ! [X160 : term] : (($true = ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) | ~ ($true = ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true))) & ~ (ulamvar1 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X161 : term,X162 : term,X163 : (subst > term > subst > $o)] : (~ ! [X164 : subst,X165 : term,X166 : subst,X167 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) = $true) | ~ ($true = ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | ~ (((X163 @ id @ X161 @ id)) = $true) | ~ ! [X168 : term,X169 : term] : (~ ($true = ((X163 @ id @ X169 @ id))) | ~ ($true = ((X163 @ id @ X168 @ id))) | (((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) = $true)) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : (~ (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) = $true) | ($true = ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172)))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ~ ($true = ((X163 @ id @ X162 @ id))))) & ((! [X174 : term,X176 : term,X175 : term,X177 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176)))) => ! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179))) <=> (hoasapinj2_lthm = $true)) & ((induction2lem = $true) <=> ! [X182 : (term > $o),X183 : subst,X184 : term] : (~ ! [X185 : term] : (~ ! [X186 : term] : (($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id))))) | ~ ($true = ((X182 @ X186)))) | ($true = ((X182 @ (lam @ X185))))) | (((X182 @ (sub @ X184 @ X183))) = $true) | ~ ! [X187 : term] : (~ ($true = ((var @ X187))) | ($true = ((X182 @ (sub @ X187 @ X183))))) | ~ ! [X188 : term,X189 : term] : (($true = ((X182 @ (ap @ X188 @ X189)))) | ~ ($true = ((X182 @ X189))) | ~ ($true = ((X182 @ X188)))))) & ~ (((var @ (d2term @ d_one))) = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & ((hoasinduction_lthm = $true) <=> (! [X194 : term,X195 : (term > $o)] : ((((X195 @ X194)) = $true) | ~ ! [X196 : term,X197 : term] : (($true = ((X195 @ (ap @ X196 @ X197)))) | ~ ($true = ((X195 @ X197))) | ~ ($true = ((X195 @ X196)))) | ~ ! [X198 : term] : (~ ! [X199 : term] : (~ (((X195 @ X199)) = $true) | ($true = ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true)) | ~ ! [X200 : term] : (~ ($true = ((var @ X200))) | ($true = ((X195 @ X200))))) => (! [X201 : (subst > term > subst > $o),X202 : term,X203 : term] : ((((X201 @ id @ (ap @ X202 @ X203) @ id)) = $true) | ~ (((X201 @ id @ X203 @ id)) = $true) | ~ ! [X204 : term,X205 : term] : (~ ($true = ((X201 @ id @ X205 @ id))) | ~ ($true = ((X201 @ id @ X204 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)))) | ~ ($true = ((X201 @ id @ X202 @ id))) | ~ ! [X206 : term,X207 : subst,X208 : subst,X209 : subst] : (~ (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) = $true) | (((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true)) | ~ ! [X210 : subst,X211 : subst,X212 : subst,X213 : term] : (~ ($true = ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210))))) => (! [X214 : term,X215 : (subst > term > subst > $o)] : (($true = ((X215 @ id @ (lam @ X214) @ id))) | ~ ! [X216 : subst,X217 : subst,X218 : subst,X219 : term] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ~ ($true = ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) | ~ ! [X220 : (subst > term > term)] : (($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ~ ! [X221 : subst,X223 : term,X222 : subst] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) = ((sub @ (X220 @ X222 @ X223) @ X221))) | ~ ! [X224 : term] : (($true = ((X215 @ id @ (X220 @ id @ X224) @ id))) | ~ ($true = ((X215 @ id @ X224 @ id))))) | ~ ! [X225 : subst,X226 : subst,X227 : subst,X228 : term] : (~ ($true = ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226))) | ($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226))))) | ~ ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ~ ($true = ((X215 @ id @ X229 @ id))))) => ! [X230 : (subst > term > subst > $o),X231 : term] : (~ ! [X232 : term,X233 : term] : (($true = ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id))) | ~ ($true = ((X230 @ id @ X233 @ id))) | ~ ($true = ((X230 @ id @ X232 @ id)))) | (((X230 @ id @ X231 @ id)) = $true) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (~ ($true = ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) | ~ ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)))) | (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) = $true)) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : (($true = ((X230 @ X242 @ X241 @ (comp @ X239 @ X240)))) | ~ ($true = ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240)))) | ~ ! [X243 : term] : (~ ($true = ((var @ (sub @ X243 @ id)))) | ($true = ((X230 @ id @ X243 @ id)))) | ~ ! [X244 : term,X245 : subst,X246 : subst,X247 : subst] : (~ ($true = ((X230 @ X246 @ X244 @ (comp @ X245 @ X247)))) | (((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) = $true))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2_gthm = $true) & (! [X251 : subst] : (((comp @ id @ X251)) = X251) <=> (axidl = $true)) & (hoaslamnotvar_lthm = $true) & ((termmset = $true) <=> ! [X252 : term] : (((sub @ X252 @ id)) = X252)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X253 : term] : (((sub @ X253 @ id)) = X253) => ! [X254 : (term > $o),X255 : term,X256 : (subst > term > subst > $o)] : (~ ! [X257 : term] : (((X256 @ id @ X257 @ id)) = ((X254 @ X257))) | ($true = ((X254 @ (lam @ X255)))) | ~ ! [X258 : term] : (($true = ((X254 @ (sub @ X255 @ (push @ X258 @ id))))) | ~ (((X254 @ X258)) = $true)) | ~ ! [X259 : (subst > term > term)] : (~ ! [X260 : subst,X261 : term,X262 : subst] : (((X259 @ (comp @ X260 @ X262) @ (sub @ X261 @ X262))) = ((sub @ (X259 @ X260 @ X261) @ X262))) | ($true = ((X256 @ id @ (lam @ (X259 @ sh @ one)) @ id))) | ~ ! [X263 : term] : (~ ($true = ((X256 @ id @ X263 @ id))) | ($true = ((X256 @ id @ (X259 @ id @ X263) @ id))))) | ~ ! [X264 : subst,X265 : subst,X266 : subst,X267 : term] : (($true = ((X256 @ X265 @ X267 @ (comp @ X264 @ X266)))) | ~ ($true = ((X256 @ (comp @ X265 @ X264) @ (sub @ X267 @ X264) @ X266)))) | ~ ! [X268 : subst,X269 : subst,X270 : subst,X271 : term] : (($true = ((X256 @ (comp @ X270 @ X268) @ (sub @ X271 @ X268) @ X269))) | ~ (((X256 @ X270 @ X271 @ (comp @ X268 @ X269))) = $true))))) & ((laminj = $true) <=> ! [X272 : term,X273 : term] : ((X272 = X273) | (((lam @ X272)) != ((lam @ X273))))) & (apnotvar = $true) & ! [X274 : d_subst,X275 : d_subst] : ((((d2subst @ X274)) = ((d2subst @ X275))) => (X274 = X275)) & ((! [X276 : term] : (((sub @ X276 @ id)) = X276) => ! [X277 : term] : (((sub @ X277 @ id)) = X277)) <=> (termmset_lthm = $true)) & ((! [X278 : term] : (((sub @ X278 @ id)) = X278) => (! [X279 : (subst > term > subst > $o),X280 : term] : (~ ! [X281 : term] : (~ ($true = ((X279 @ id @ X281 @ id))) | ($true = ((X279 @ id @ (sub @ X280 @ (push @ X281 @ id)) @ id)))) | (((X279 @ id @ (lam @ (sub @ X280 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X282 : (subst > term > term)] : (($true = ((X279 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ~ ! [X283 : term] : (~ ($true = ((X279 @ id @ X283 @ id))) | (((X279 @ id @ (X282 @ id @ X283) @ id)) = $true)) | ~ ! [X284 : subst,X285 : subst,X286 : term] : (((X282 @ (comp @ X284 @ X285) @ (sub @ X286 @ X285))) = ((sub @ (X282 @ X284 @ X286) @ X285))))) => ! [X287 : term,X288 : (subst > term > subst > $o)] : (($true = ((X288 @ id @ (lam @ X287) @ id))) | ~ ! [X289 : term] : (($true = ((X288 @ id @ (sub @ X287 @ (push @ X289 @ id)) @ id))) | ~ (((X288 @ id @ X289 @ id)) = $true)) | ~ ! [X290 : (subst > term > term)] : (~ ! [X291 : subst,X292 : subst,X293 : term] : (((sub @ (X290 @ X291 @ X293) @ X292)) = ((X290 @ (comp @ X291 @ X292) @ (sub @ X293 @ X292)))) | ($true = ((X288 @ id @ (lam @ (X290 @ sh @ one)) @ id))) | ~ ! [X294 : term] : (~ ($true = ((X288 @ id @ X294 @ id))) | ($true = ((X288 @ id @ (X290 @ id @ X294) @ id)))))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X295 : term] : ~ ! [X296 : (subst > term > term)] : (((X296 @ sh @ one)) != ((sub @ X295 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X297 : term,X298 : subst] : (((sub @ one @ (push @ X297 @ X298))) = X297) => (! [X299 : subst,X300 : term] : (((comp @ sh @ (push @ X300 @ X299))) = X299) => (! [X301 : term,X302 : term] : ((((lam @ X301)) != ((lam @ X302))) | (X301 = X302)) => ! [X303 : subst,X304 : (subst > term > term),X305 : (subst > term > term),X306 : term] : ((((X305 @ X303 @ X306)) = ((X304 @ X303 @ X306))) | ~ ! [X307 : subst,X308 : term,X309 : subst] : (((X304 @ (comp @ X307 @ X309) @ (sub @ X308 @ X309))) = ((sub @ (X304 @ X307 @ X308) @ X309))) | (((lam @ (X305 @ sh @ one))) != ((lam @ (X304 @ sh @ one)))) | ~ ! [X310 : subst,X311 : subst,X312 : term] : (((sub @ (X305 @ X311 @ X312) @ X310)) = ((X305 @ (comp @ X311 @ X310) @ (sub @ X312 @ X310))))))))) & (pushprop_lem3v2 = $true) & ((hoasapinj2 = $true) <=> ! [X313 : term,X314 : term,X315 : term,X316 : term] : ((((ap @ (sub @ X314 @ id) @ X313)) != ((ap @ (sub @ X315 @ id) @ X316))) | (X313 = X316))) & (termmset_gthm = $true) & ((induction2_lthm = $true) <=> (! [X317 : term] : (((sub @ X317 @ id)) = X317) => (! [X318 : (term > $o),X319 : subst,X320 : term] : ((((X318 @ (sub @ X320 @ X319))) = $true) | ~ ! [X321 : term,X322 : term] : (~ ($true = ((X318 @ X322))) | ($true = ((X318 @ (ap @ X321 @ X322)))) | ~ ($true = ((X318 @ X321)))) | ~ ! [X323 : term] : (~ ($true = ((var @ X323))) | (((X318 @ (sub @ X323 @ X319))) = $true)) | ~ ! [X324 : term] : (~ ! [X325 : term] : (~ ($true = ((X318 @ X325))) | ($true = ((X318 @ (sub @ X324 @ (push @ X325 @ id)))))) | ($true = ((X318 @ (lam @ X324)))))) => ! [X326 : term,X327 : (term > $o)] : (~ ! [X328 : term] : (($true = ((X327 @ (lam @ X328)))) | ~ ! [X329 : term] : (($true = ((X327 @ (sub @ X328 @ (push @ X329 @ id))))) | ~ (((X327 @ X329)) = $true))) | ~ ! [X330 : term,X331 : term] : (~ ($true = ((X327 @ X331))) | ~ ($true = ((X327 @ X330))) | ($true = ((X327 @ (ap @ X331 @ X330))))) | ($true = ((X327 @ X326))) | ~ ! [X332 : term] : (~ (((var @ X332)) = $true) | ($true = ((X327 @ X332)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X333 : term,X334 : term,X335 : (subst > term > subst > $o),X336 : (term > $o)] : (~ ! [X337 : subst,X338 : subst,X339 : subst,X340 : term] : (($true = ((X335 @ (comp @ X337 @ X338) @ (sub @ X340 @ X338) @ X339))) | ~ ($true = ((X335 @ X337 @ X340 @ (comp @ X338 @ X339))))) | ~ ! [X341 : subst,X342 : subst,X343 : term,X344 : subst] : ((((X335 @ X344 @ X343 @ (comp @ X342 @ X341))) = $true) | ~ ($true = ((X335 @ (comp @ X344 @ X342) @ (sub @ X343 @ X342) @ X341)))) | ~ ($true = ((X336 @ X334))) | (((X336 @ (ap @ X334 @ X333))) = $true) | ~ ($true = ((X336 @ X333))) | ~ ! [X345 : term,X346 : term] : (~ (((X335 @ id @ X345 @ id)) = $true) | ~ (((X335 @ id @ X346 @ id)) = $true) | ($true = ((X335 @ id @ (ap @ (sub @ X345 @ id) @ X346) @ id)))) | ~ ! [X347 : term] : (((X335 @ id @ X347 @ id)) = ((X336 @ X347)))) <=> (hoasinduction_lem2v2 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axclos = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) <=> ! [X348 : term,X349 : (term > $o)] : (~ ! [X350 : term] : (($true = ((X349 @ X350))) | ~ ($true = ((var @ X350)))) | ~ ! [X351 : term,X352 : term] : (~ ($true = ((X349 @ X352))) | ($true = ((X349 @ (ap @ X352 @ X351)))) | ~ ($true = ((X349 @ X351)))) | ($true = ((X349 @ X348))) | ~ ! [X353 : term] : ((((X349 @ (lam @ X353))) = $true) | ~ ! [X354 : term] : (($true = ((X349 @ (sub @ X353 @ (push @ X354 @ id))))) | ~ (((X349 @ X354)) = $true))))) & (hoasinduction_lem1 = $true) & ((substmonoid = $true) <=> (! [X355 : subst] : (((comp @ X355 @ id)) = X355) & ! [X356 : subst] : (((comp @ id @ X356)) = X356))) & (! [X357 : term,X358 : term] : ((((sub @ X358 @ sh)) != ((sub @ X357 @ sh))) | (X357 = X358)) <=> (shinj = $true)) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((induction = $true) <=> ! [X359 : (term > $o),X360 : term] : ((((X359 @ X360)) = $true) | ~ ! [X361 : term] : (~ ($true = ((X359 @ X361))) | (((X359 @ (lam @ X361))) = $true)) | ~ ! [X362 : term,X363 : term] : (~ ($true = ((X359 @ X363))) | ~ ($true = ((X359 @ X362))) | ($true = ((X359 @ (ap @ X362 @ X363))))) | ~ ! [X364 : term] : (~ (((var @ X364)) = $true) | ($true = ((X359 @ X364)))))) & (axabs = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X365 : (subst > term > subst > $o)] : ~ ! [X366 : (term > $o)] : ~ ! [X367 : term] : (((X366 @ X367)) = ((X365 @ id @ X367 @ id)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X368 : subst,X369 : term] : (((sub @ one @ (push @ X369 @ X368))) = X369) => ! [X370 : subst,X371 : (term > $o),X372 : term,X373 : (term > $o)] : (($true = ((X371 @ one))) | ~ ! [X374 : term] : (((X371 @ X374)) = ((X373 @ (sub @ X374 @ (push @ X372 @ X370))))) | ~ ($true = ((X373 @ X372)))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X375 : term,X376 : (subst > term > subst > $o)] : (~ ! [X377 : term] : (($true = ((X376 @ id @ (sub @ X375 @ (push @ X377 @ id)) @ id))) | ~ (((X376 @ id @ X377 @ id)) = $true)) | ($true = ((X376 @ id @ (lam @ (sub @ X375 @ (push @ one @ sh))) @ id))) | ~ ! [X378 : (subst > term > term),X379 : term] : (~ ! [X380 : term] : (($true = ((X376 @ id @ (X378 @ id @ X380) @ id))) | ~ ($true = ((X376 @ id @ X380 @ id)))) | ~ ! [X381 : term,X382 : subst,X383 : subst] : (((X378 @ (comp @ X382 @ X383) @ (sub @ X381 @ X383))) = ((sub @ X379 @ (push @ (sub @ X381 @ X383) @ (comp @ X382 @ X383))))) | ~ ! [X384 : subst,X385 : term,X386 : subst] : (((sub @ (X378 @ X386 @ X385) @ X384)) = ((sub @ (sub @ X379 @ (push @ X385 @ X386)) @ X384))) | (((X376 @ id @ (lam @ (X378 @ sh @ one)) @ id)) = $true)))) & (pushprop_lthm_orig = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X387 : (subst > term > subst > $o)] : ~ ! [X388 : (term > $o)] : ~ ! [X389 : term] : (((X387 @ id @ X389 @ id)) = ((X388 @ X389))) => (! [X390 : term,X391 : (term > $o)] : (~ ! [X392 : term] : (~ ! [X393 : term] : (($true = ((X391 @ (sub @ X392 @ (push @ X393 @ id))))) | ~ ($true = ((X391 @ X393)))) | ($true = ((X391 @ (lam @ X392))))) | ($true = ((X391 @ X390))) | ~ ! [X394 : term] : (~ ($true = ((var @ X394))) | ($true = ((X391 @ X394)))) | ~ ! [X395 : term,X396 : term] : ((((X391 @ (ap @ X395 @ X396))) = $true) | ~ ($true = ((X391 @ X395))) | ~ (((X391 @ X396)) = $true))) => (! [X397 : term] : (((sub @ X397 @ id)) = X397) => (! [X398 : (subst > term > subst > $o),X399 : term,X400 : (term > $o)] : (~ ! [X401 : (subst > term > term)] : (($true = ((X398 @ id @ (lam @ (X401 @ sh @ one)) @ id))) | ~ ! [X402 : subst,X403 : term,X404 : subst] : (((X401 @ (comp @ X404 @ X402) @ (sub @ X403 @ X402))) = ((sub @ (X401 @ X404 @ X403) @ X402))) | ~ ! [X405 : term] : (($true = ((X398 @ id @ (X401 @ id @ X405) @ id))) | ~ ($true = ((X398 @ id @ X405 @ id))))) | ($true = ((X400 @ (lam @ X399)))) | ~ ! [X406 : term] : ((((X400 @ (sub @ X399 @ (push @ X406 @ id)))) = $true) | ~ ($true = ((X400 @ X406)))) | ~ ! [X407 : term] : (((X398 @ id @ X407 @ id)) = ((X400 @ X407)))) => ! [X408 : (subst > term > subst > $o),X409 : term] : (~ ! [X410 : subst,X411 : term,X412 : subst,X413 : subst] : (($true = ((X408 @ X412 @ X411 @ (comp @ X410 @ X413)))) | ~ (((X408 @ (comp @ X412 @ X410) @ (sub @ X411 @ X410) @ X413)) = $true)) | ~ ! [X414 : term] : (~ ($true = ((var @ (sub @ X414 @ id)))) | ($true = ((X408 @ id @ X414 @ id)))) | ~ ! [X415 : subst,X416 : subst,X417 : subst,X418 : term] : (($true = ((X408 @ (comp @ X417 @ X416) @ (sub @ X418 @ X416) @ X415))) | ~ ($true = ((X408 @ X417 @ X418 @ (comp @ X416 @ X415))))) | ($true = ((X408 @ id @ X409 @ id))) | ~ ! [X419 : term,X420 : term] : (($true = ((X408 @ id @ (ap @ (sub @ X419 @ id) @ X420) @ id))) | ~ (((X408 @ id @ X419 @ id)) = $true) | ~ ($true = ((X408 @ id @ X420 @ id)))) | ~ ! [X421 : (subst > term > term)] : (~ ! [X422 : term] : (($true = ((X408 @ id @ (X421 @ id @ X422) @ id))) | ~ ($true = ((X408 @ id @ X422 @ id)))) | ($true = ((X408 @ id @ (lam @ (X421 @ sh @ one)) @ id))) | ~ ! [X423 : subst,X424 : term,X425 : subst] : (((X421 @ (comp @ X425 @ X423) @ (sub @ X424 @ X423))) = ((sub @ (X421 @ X425 @ X424) @ X423))))))))) <=> (hoasinduction_lthm_3 = $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)))))))))))) & ! [X431 : d_term] : (d_one = X431) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & (! [X432 : subst,X433 : term] : (((comp @ sh @ (push @ X433 @ X432))) = X432) <=> (axshiftcons = $true)) & (substmonoid_gthm = $true) & (hoaslamnotvar = $true) & ! [X434 : d_subst] : (d_id = X434) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X435 : term] : ~ ! [X436 : (subst > term > term)] : (((X436 @ sh @ one)) != ((sub @ X435 @ (push @ one @ sh))))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X439 : term] : ? [X440 : d_term] : (((d2term @ X440)) = X439) & (lamnotvar = $true) & (! [X441 : subst] : (((push @ (sub @ one @ X441) @ (comp @ sh @ X441))) = X441) <=> (axscons = $true)) & (one = ((d2term @ d_one))) & (! [X442 : term,X443 : (subst > term > subst > $o),X444 : (term > $o)] : (~ ! [X445 : term] : (~ ($true = ((X444 @ X445))) | ($true = ((X444 @ (sub @ X442 @ (push @ X445 @ id)))))) | ~ ! [X446 : term,X447 : subst,X448 : subst,X449 : subst] : (~ ($true = ((X443 @ (comp @ X449 @ X448) @ (sub @ X446 @ X448) @ X447))) | (((X443 @ X449 @ X446 @ (comp @ X448 @ X447))) = $true)) | ~ ! [X450 : subst,X451 : subst,X452 : term,X453 : subst] : (~ ($true = ((X443 @ X451 @ X452 @ (comp @ X453 @ X450)))) | (((X443 @ (comp @ X451 @ X453) @ (sub @ X452 @ X453) @ X450)) = $true)) | ~ ! [X454 : (subst > term > term)] : (($true = ((X443 @ id @ (lam @ (X454 @ sh @ one)) @ id))) | ~ ! [X455 : subst,X456 : subst,X457 : term] : (((X454 @ (comp @ X456 @ X455) @ (sub @ X457 @ X455))) = ((sub @ (X454 @ X456 @ X457) @ X455))) | ~ ! [X458 : term] : (~ (((X443 @ id @ X458 @ id)) = $true) | (((X443 @ id @ (X454 @ id @ X458) @ id)) = $true))) | ($true = ((X444 @ (lam @ X442)))) | ~ ! [X459 : term] : (((X444 @ X459)) = ((X443 @ id @ X459 @ id)))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X460 : term] : (((sub @ X460 @ id)) = X460) => (! [X461 : term,X462 : (subst > term > subst > $o)] : (($true = ((X462 @ id @ (lam @ (sub @ X461 @ (push @ one @ sh))) @ id))) | ~ ! [X463 : term] : (~ ($true = ((X462 @ id @ X463 @ id))) | ($true = ((X462 @ id @ (sub @ X461 @ (push @ X463 @ id)) @ id)))) | ~ ! [X464 : (subst > term > term)] : (~ ! [X465 : subst,X466 : subst,X467 : term] : (((X464 @ (comp @ X465 @ X466) @ (sub @ X467 @ X466))) = ((sub @ (X464 @ X465 @ X467) @ X466))) | ($true = ((X462 @ id @ (lam @ (X464 @ sh @ one)) @ id))) | ~ ! [X468 : term] : (~ ($true = ((X462 @ id @ X468 @ id))) | (((X462 @ id @ (X464 @ id @ X468) @ id)) = $true)))) => ! [X469 : term,X470 : (subst > term > subst > $o)] : (~ ! [X471 : (subst > term > term)] : (~ ! [X472 : term] : (~ ($true = ((X470 @ id @ X472 @ id))) | ($true = ((X470 @ id @ (X471 @ id @ X472) @ id)))) | ~ ! [X473 : subst,X474 : term,X475 : subst] : (((sub @ (X471 @ X473 @ X474) @ X475)) = ((X471 @ (comp @ X473 @ X475) @ (sub @ X474 @ X475)))) | ($true = ((X470 @ id @ (lam @ (X471 @ sh @ one)) @ id)))) | ~ ! [X476 : subst,X477 : subst,X478 : term,X479 : subst] : (($true = ((X470 @ (comp @ X477 @ X476) @ (sub @ X478 @ X476) @ X479))) | ~ (((X470 @ X477 @ X478 @ (comp @ X476 @ X479))) = $true)) | ($true = ((X470 @ id @ (lam @ X469) @ id))) | ~ ! [X480 : term] : (~ (((X470 @ id @ X480 @ id)) = $true) | ($true = ((X470 @ id @ (sub @ X469 @ (push @ X480 @ id)) @ id)))) | ~ ! [X481 : subst,X482 : subst,X483 : subst,X484 : term] : (~ ($true = ((X470 @ (comp @ X481 @ X482) @ (sub @ X484 @ X482) @ X483))) | ($true = ((X470 @ X481 @ X484 @ (comp @ X482 @ X483))))))))) & (axmap = $true) & (hoasapinj1_gthm = $true) & (! [X485 : term] : ~ ! [X486 : (subst > term > term)] : ~ ! [X487 : term,X488 : subst] : (((sub @ X485 @ (push @ X487 @ X488))) = ((X486 @ X488 @ X487))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X489 : (subst > term > subst > $o)] : ~ ! [X490 : (term > $o)] : ~ ! [X491 : term] : (((X489 @ id @ X491 @ id)) = ((X490 @ X491)))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ! [X492 : d_term,X493 : d_term] : ((((d2term @ X493)) = ((d2term @ X492))) => (X492 = X493)) & ((hoasinduction_lem3 = $true) <=> ! [X494 : term,X495 : (subst > term > subst > $o)] : (~ ! [X496 : subst,X497 : term,X498 : subst,X499 : subst] : (($true = ((X495 @ X496 @ X497 @ (comp @ X498 @ X499)))) | ~ (((X495 @ (comp @ X496 @ X498) @ (sub @ X497 @ X498) @ X499)) = $true)) | ~ ! [X500 : subst,X501 : term,X502 : subst,X503 : subst] : (($true = ((X495 @ (comp @ X502 @ X500) @ (sub @ X501 @ X500) @ X503))) | ~ ($true = ((X495 @ X502 @ X501 @ (comp @ X500 @ X503))))) | ~ ! [X504 : (subst > term > term)] : (~ ! [X505 : term,X506 : subst,X507 : subst] : (((sub @ (X504 @ X506 @ X505) @ X507)) = ((X504 @ (comp @ X506 @ X507) @ (sub @ X505 @ X507)))) | ($true = ((X495 @ id @ (lam @ (X504 @ sh @ one)) @ id))) | ~ ! [X508 : term] : (($true = ((X495 @ id @ (X504 @ id @ X508) @ id))) | ~ ($true = ((X495 @ id @ X508 @ id))))) | ~ ! [X509 : term] : (($true = ((X495 @ id @ (sub @ X494 @ (push @ X509 @ id)) @ id))) | ~ (((X495 @ id @ X509 @ id)) = $true)) | ($true = ((X495 @ id @ (lam @ X494) @ id))))) & ((substmonoid_lthm = $true) <=> (! [X510 : subst] : (((comp @ id @ X510)) = X510) => (! [X511 : subst] : (((comp @ X511 @ id)) = X511) => (! [X512 : subst] : (((comp @ id @ X512)) = X512) & ! [X513 : subst] : (((comp @ X513 @ id)) = X513))))) & ((hoasinduction_lem3a = $true) <=> ! [X514 : term,X515 : (subst > term > subst > $o)] : (~ ! [X516 : (subst > term > term)] : (~ ! [X517 : subst,X518 : subst,X519 : term] : (((X516 @ (comp @ X518 @ X517) @ (sub @ X519 @ X517))) = ((sub @ (X516 @ X518 @ X519) @ X517))) | ~ ! [X520 : term] : ((((X515 @ id @ (X516 @ id @ X520) @ id)) = $true) | ~ ($true = ((X515 @ id @ X520 @ id)))) | (((X515 @ id @ (lam @ (X516 @ sh @ one)) @ id)) = $true)) | ~ ! [X521 : term] : ((((X515 @ id @ (sub @ X514 @ (push @ X521 @ id)) @ id)) = $true) | ~ ($true = ((X515 @ id @ X521 @ id)))) | ($true = ((X515 @ id @ (lam @ X514) @ id))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X522 : (subst > term > subst > $o),X523 : term] : (($true = ((X522 @ id @ X523 @ id))) | ~ ! [X524 : term,X525 : term] : (~ ($true = ((X522 @ id @ X524 @ id))) | ($true = ((X522 @ id @ (ap @ (sub @ X524 @ id) @ X525) @ id))) | ~ ($true = ((X522 @ id @ X525 @ id)))) | ~ ! [X526 : (subst > term > term)] : (($true = ((X522 @ id @ (lam @ (X526 @ sh @ one)) @ id))) | ~ ! [X527 : term] : (~ ($true = ((X522 @ id @ X527 @ id))) | (((X522 @ id @ (X526 @ id @ X527) @ id)) = $true)) | ~ ! [X528 : subst,X529 : term,X530 : subst] : (((X526 @ (comp @ X528 @ X530) @ (sub @ X529 @ X530))) = ((sub @ (X526 @ X528 @ X529) @ X530)))))) & ((axidr = $true) <=> ! [X531 : subst] : (((comp @ X531 @ id)) = X531)) & ((hoaslaminj = $true) <=> ! [X532 : (subst > term > term),X533 : (subst > term > term),X534 : subst,X535 : term] : ((((X533 @ X534 @ X535)) = ((X532 @ X534 @ X535))) | ~ ! [X536 : subst,X537 : subst,X538 : term] : (((X533 @ (comp @ X536 @ X537) @ (sub @ X538 @ X537))) = ((sub @ (X533 @ X536 @ X538) @ X537))) | (((lam @ (X532 @ sh @ one))) != ((lam @ (X533 @ sh @ one)))) | ~ ! [X539 : term,X540 : subst,X541 : subst] : (((sub @ (X532 @ X540 @ X539) @ X541)) = ((X532 @ (comp @ X540 @ X541) @ (sub @ X539 @ X541)))))) & (ulamvarsh = $true) & (! [X542 : (subst > term > subst > $o),X543 : term] : (~ ! [X544 : (subst > term > term)] : (~ ! [X545 : term] : (($true = ((X542 @ id @ (X544 @ id @ X545) @ id))) | ~ ($true = ((X542 @ id @ X545 @ id)))) | ($true = ((X542 @ id @ (lam @ (X544 @ sh @ one)) @ id))) | ~ ! [X546 : term,X547 : subst,X548 : subst] : (((sub @ (X544 @ X547 @ X546) @ X548)) = ((X544 @ (comp @ X547 @ X548) @ (sub @ X546 @ X548))))) | ~ ! [X549 : term] : (~ ($true = ((X542 @ id @ X549 @ id))) | (((X542 @ id @ (sub @ X543 @ (push @ X549 @ id)) @ id)) = $true)) | ($true = ((X542 @ id @ (lam @ (sub @ X543 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true))),
% 2.19/0.60 inference(fool_elimination,[],[f6])).
% 2.19/0.60 thf(f8,plain,(
% 2.19/0.60 (pushprop_lem3v2 != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ (term > $o) @ (^[Y3 : term > $o]: ((pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3) => ((!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y3 @ Y4)))) => (!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y0 @ (sub @ Y4 @ (push @ Y2 @ Y1))))))))))))))))))),
% 2.19/0.60 inference(flattening,[],[f5])).
% 2.19/0.60 thf(f9,plain,(
% 2.19/0.60 ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & (hoaslaminj_gthm = $true) & (hoasinduction_gthm = $true) & ~ (lamnotap = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3v2_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X2 : term,X4 : term,X3 : (subst > term > term)] : (~ ! [X6 : subst,X7 : term,X5 : subst] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one)))))) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (! [X9 : subst,X8 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & (pushprop_gthm = $true) & ((pushprop_lem0_lthm = $true) <=> ! [X15 : subst,X14 : (term > $o),X13 : term] : ~ ! [X16 : (term > $o)] : ~ ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15)))))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) = X19) => (! [X21 : term,X20 : subst] : (((comp @ sh @ (push @ X21 @ X20))) = X20) => (! [X22 : subst] : (((comp @ X22 @ id)) = X22) => (! [X23 : term,X24 : (term > $o)] : (($true = ((X24 @ X23))) | ~ ! [X25 : term] : (($true = ((X24 @ (lam @ X25)))) | ~ (((X24 @ X25)) = $true)) | ~ ! [X26 : term] : (($true = ((X24 @ X26))) | ~ ($true = ((var @ X26)))) | ~ ! [X27 : term,X28 : term] : (~ ($true = ((X24 @ X27))) | ~ ($true = ((X24 @ X28))) | ($true = ((X24 @ (ap @ X28 @ X27)))))) => ! [X29 : subst,X30 : (term > $o),X31 : term] : (($true = ((X30 @ (sub @ X31 @ X29)))) | ~ ! [X32 : term] : (($true = ((X30 @ (sub @ X32 @ X29)))) | ~ ($true = ((var @ X32)))) | ~ ! [X33 : term,X34 : term] : (~ ($true = ((X30 @ X34))) | ($true = ((X30 @ (ap @ X34 @ X33)))) | ~ ($true = ((X30 @ X33)))) | ~ ! [X35 : term] : (~ ! [X36 : term] : (($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id))))) | ~ ($true = ((X30 @ X36)))) | (((X30 @ (lam @ X35))) = $true))))))) <=> (induction2lem_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X37 : term,X38 : subst,X39 : (term > $o),X40 : (term > $o)] : (~ ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))) | ~ (((X40 @ X37)) = $true) | ($true = ((X39 @ one))))) & ((pushprop_lem1_lthm = $true) <=> (! [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) = X42) => (! [X45 : subst,X44 : term] : (((comp @ sh @ (push @ X44 @ X45))) = X45) => ! [X46 : term,X47 : term,X48 : (term > $o),X49 : subst,X50 : (term > $o)] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ~ ($true = ((X48 @ X47))))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((sub @ X51 @ (push @ X53 @ X54))) = ((X52 @ X54 @ X53))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : (subst > term > term)] : (~ ! [X60 : term] : (~ ($true = ((X57 @ id @ X60 @ id))) | ($true = ((X57 @ id @ (X59 @ id @ X60) @ id)))) | ~ ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63)))) | (((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) = $true)) | ($true = ((X56 @ (lam @ X58)))) | ~ ! [X64 : term] : (($true = ((X56 @ (sub @ X58 @ (push @ X64 @ id))))) | ~ ($true = ((X56 @ X64)))) | ~ ! [X65 : term] : (((X57 @ id @ X65 @ id)) = ((X56 @ X65))))))) & ((hoasinduction = $true) <=> ! [X66 : term,X67 : (subst > term > subst > $o)] : (~ ! [X68 : (subst > term > term)] : (($true = ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id))) | ~ ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) | ~ ! [X72 : term] : (($true = ((X67 @ id @ (X68 @ id @ X72) @ id))) | ~ ($true = ((X67 @ id @ X72 @ id))))) | ~ ! [X73 : term,X74 : term] : (~ ($true = ((X67 @ id @ X74 @ id))) | ~ ($true = ((X67 @ id @ X73 @ id))) | ($true = ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))) | ~ ! [X75 : term] : (($true = ((X67 @ id @ X75 @ id))) | ~ ($true = ((var @ (sub @ X75 @ id))))) | ~ ! [X76 : subst,X77 : subst,X78 : subst,X79 : term] : (~ ($true = ((X67 @ X76 @ X79 @ (comp @ X78 @ X77)))) | (((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) = $true)) | ~ ! [X80 : term,X81 : subst,X82 : subst,X83 : subst] : (($true = ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)))) | ~ (((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) = $true)) | ($true = ((X67 @ id @ X66 @ id))))) & (pushprop_lem1v2_gthm = $true) & (ulamvarind = $true) & (hoasapnotvar = $true) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (axvarshift = $true) & ((pushprop_lem1 = $true) <=> ! [X88 : term,X89 : term,X90 : subst,X91 : (term > $o),X92 : (term > $o)] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ~ ($true = ((X92 @ X88))))) & (hoasinduction_lem1_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X93 : term] : ~ ! [X94 : (subst > term > term)] : ~ ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & (hoaslamnotap_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (pushprop_lem2v2_gthm = $true) & (axassoc = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X103 : (subst > term > subst > $o)] : ~ ! [X104 : (term > $o)] : ~ ! [X105 : term] : (((X104 @ X105)) = ((X103 @ id @ X105 @ id))) => (! [X106 : term,X107 : (term > $o)] : (~ ! [X108 : term] : (~ ($true = ((var @ X108))) | ($true = ((X107 @ X108)))) | ~ ! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ~ ! [X110 : term] : (($true = ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) | ~ ($true = ((X107 @ X110))))) | ($true = ((X107 @ X106))) | ~ ! [X111 : term,X112 : term] : (~ ($true = ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111)))) | ~ ($true = ((X107 @ X112))))) => (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : (term > $o),X115 : term,X116 : (subst > term > subst > $o)] : (($true = ((X114 @ (lam @ X115)))) | ~ ! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | ~ (((X114 @ X117)) = $true)) | ~ ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))) | ~ ! [X119 : (subst > term > term)] : (($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id))) | ~ ! [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) = ((sub @ (X119 @ X121 @ X122) @ X120))) | ~ ! [X123 : term] : (($true = ((X116 @ id @ (X119 @ id @ X123) @ id))) | ~ ($true = ((X116 @ id @ X123 @ id)))))) => ! [X124 : term,X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : (~ ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ~ ($true = ((X125 @ id @ X127 @ id)))) | ~ ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) | ($true = ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id)))) | ($true = ((X125 @ id @ X124 @ id))) | ~ ! [X131 : term,X132 : term] : (~ ($true = ((X125 @ id @ X132 @ id))) | ($true = ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ~ ($true = ((X125 @ id @ X131 @ id)))))))))) & ((hoasinduction_lem3aa = $true) <=> ! [X133 : term,X134 : (subst > term > subst > $o)] : (~ ! [X135 : term] : (($true = ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) | ~ (((X134 @ id @ X135 @ id)) = $true)) | (((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X136 : (subst > term > term)] : (~ ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ~ ($true = ((X134 @ id @ X137 @ id)))) | ~ ! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) | (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) = $true)))) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & (induction2_gthm = $true) & (axapp = $true) & ((hoasapinj1_lthm = $true) <=> (! [X142 : term] : (((sub @ X142 @ id)) = X142) => (! [X144 : term,X146 : term,X143 : term,X145 : term] : ((X145 = X146) | (((ap @ X145 @ X144)) != ((ap @ X146 @ X143)))) => ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X151 : term,X152 : (term > $o),X153 : (subst > term > subst > $o)] : (~ ! [X154 : term] : (((X152 @ X154)) = ((X153 @ id @ X154 @ id))) | ~ ! [X155 : (subst > term > term)] : (($true = ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id))) | ~ ! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) | ~ ! [X159 : term] : (~ (((X153 @ id @ X159 @ id)) = $true) | ($true = ((X153 @ id @ (X155 @ id @ X159) @ id))))) | ~ ! [X160 : term] : (($true = ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) | ~ ($true = ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true))) & ~ (ulamvar1 = $true) & ((hoasinduction_lem2 = $true) <=> ! [X161 : term,X162 : term,X163 : (subst > term > subst > $o)] : (~ ! [X164 : subst,X165 : term,X166 : subst,X167 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) = $true) | ~ ($true = ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | ~ (((X163 @ id @ X161 @ id)) = $true) | ~ ! [X168 : term,X169 : term] : (~ ($true = ((X163 @ id @ X169 @ id))) | ~ ($true = ((X163 @ id @ X168 @ id))) | (((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) = $true)) | ~ ! [X170 : subst,X171 : subst,X172 : subst,X173 : term] : (~ (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) = $true) | ($true = ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172)))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ~ ($true = ((X163 @ id @ X162 @ id))))) & ((! [X174 : term,X176 : term,X175 : term,X177 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176)))) => ! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179))) <=> (hoasapinj2_lthm = $true)) & ((induction2lem = $true) <=> ! [X182 : (term > $o),X183 : subst,X184 : term] : (~ ! [X185 : term] : (~ ! [X186 : term] : (($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id))))) | ~ ($true = ((X182 @ X186)))) | ($true = ((X182 @ (lam @ X185))))) | (((X182 @ (sub @ X184 @ X183))) = $true) | ~ ! [X187 : term] : (~ ($true = ((var @ X187))) | ($true = ((X182 @ (sub @ X187 @ X183))))) | ~ ! [X188 : term,X189 : term] : (($true = ((X182 @ (ap @ X188 @ X189)))) | ~ ($true = ((X182 @ X189))) | ~ ($true = ((X182 @ X188)))))) & ~ (((var @ (d2term @ d_one))) = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & ((hoasinduction_lthm = $true) <=> (! [X194 : term,X195 : (term > $o)] : ((((X195 @ X194)) = $true) | ~ ! [X196 : term,X197 : term] : (($true = ((X195 @ (ap @ X196 @ X197)))) | ~ ($true = ((X195 @ X197))) | ~ ($true = ((X195 @ X196)))) | ~ ! [X198 : term] : (~ ! [X199 : term] : (~ (((X195 @ X199)) = $true) | ($true = ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true)) | ~ ! [X200 : term] : (~ ($true = ((var @ X200))) | ($true = ((X195 @ X200))))) => (! [X201 : (subst > term > subst > $o),X202 : term,X203 : term] : ((((X201 @ id @ (ap @ X202 @ X203) @ id)) = $true) | ~ (((X201 @ id @ X203 @ id)) = $true) | ~ ! [X204 : term,X205 : term] : (~ ($true = ((X201 @ id @ X205 @ id))) | ~ ($true = ((X201 @ id @ X204 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)))) | ~ ($true = ((X201 @ id @ X202 @ id))) | ~ ! [X206 : term,X207 : subst,X208 : subst,X209 : subst] : (~ (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) = $true) | (((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true)) | ~ ! [X210 : subst,X211 : subst,X212 : subst,X213 : term] : (~ ($true = ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210))))) => (! [X214 : term,X215 : (subst > term > subst > $o)] : (($true = ((X215 @ id @ (lam @ X214) @ id))) | ~ ! [X216 : subst,X217 : subst,X218 : subst,X219 : term] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ~ ($true = ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) | ~ ! [X220 : (subst > term > term)] : (($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ~ ! [X221 : subst,X223 : term,X222 : subst] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) = ((sub @ (X220 @ X222 @ X223) @ X221))) | ~ ! [X224 : term] : (($true = ((X215 @ id @ (X220 @ id @ X224) @ id))) | ~ ($true = ((X215 @ id @ X224 @ id))))) | ~ ! [X225 : subst,X226 : subst,X227 : subst,X228 : term] : (~ ($true = ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226))) | ($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226))))) | ~ ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ~ ($true = ((X215 @ id @ X229 @ id))))) => ! [X230 : (subst > term > subst > $o),X231 : term] : (~ ! [X232 : term,X233 : term] : (($true = ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id))) | ~ ($true = ((X230 @ id @ X233 @ id))) | ~ ($true = ((X230 @ id @ X232 @ id)))) | (((X230 @ id @ X231 @ id)) = $true) | ~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (~ ($true = ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) | ~ ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)))) | (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) = $true)) | ~ ! [X239 : subst,X240 : subst,X241 : term,X242 : subst] : (($true = ((X230 @ X242 @ X241 @ (comp @ X239 @ X240)))) | ~ ($true = ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240)))) | ~ ! [X243 : term] : (~ ($true = ((var @ (sub @ X243 @ id)))) | ($true = ((X230 @ id @ X243 @ id)))) | ~ ! [X244 : term,X245 : subst,X246 : subst,X247 : subst] : (~ ($true = ((X230 @ X246 @ X244 @ (comp @ X245 @ X247)))) | (((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) = $true))))))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (((d2subst @ d_id)) = sh) & (hoasinduction_lem2_gthm = $true) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) <=> (axidl = $true)) & (hoaslamnotvar_lthm = $true) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) <=> (termmset = $true)) & (induction2lem_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X250 : term] : (((sub @ X250 @ id)) = X250) => ! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o)] : (~ ! [X254 : term] : (((X251 @ X254)) = ((X253 @ id @ X254 @ id))) | ($true = ((X251 @ (lam @ X252)))) | ~ ! [X255 : term] : (($true = ((X251 @ (sub @ X252 @ (push @ X255 @ id))))) | ~ (((X251 @ X255)) = $true)) | ~ ! [X256 : (subst > term > term)] : (~ ! [X257 : subst,X259 : subst,X258 : term] : (((X256 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X257 @ X258) @ X259))) | ($true = ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id))) | ~ ! [X260 : term] : (~ (((X253 @ id @ X260 @ id)) = $true) | ($true = ((X253 @ id @ (X256 @ id @ X260) @ id))))) | ~ ! [X261 : subst,X262 : subst,X263 : subst,X264 : term] : ((((X253 @ X262 @ X264 @ (comp @ X261 @ X263))) = $true) | ~ ($true = ((X253 @ (comp @ X262 @ X261) @ (sub @ X264 @ X261) @ X263)))) | ~ ! [X265 : subst,X266 : subst,X267 : subst,X268 : term] : ((((X253 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true) | ~ (((X253 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true))))) & ((laminj = $true) <=> ! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270))) & (apnotvar = $true) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) = ((d2subst @ X271))) => (X271 = X272)) & ((termmset_lthm = $true) <=> (! [X273 : term] : (((sub @ X273 @ id)) = X273) => ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & ((! [X275 : term] : (((sub @ X275 @ id)) = X275) => (! [X276 : (subst > term > subst > $o),X277 : term] : (~ ! [X278 : term] : (~ ($true = ((X276 @ id @ X278 @ id))) | (((X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) = $true)) | (((X276 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X279 : (subst > term > term)] : (($true = ((X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ~ ! [X280 : term] : (~ ($true = ((X276 @ id @ X280 @ id))) | ($true = ((X276 @ id @ (X279 @ id @ X280) @ id)))) | ~ ! [X282 : subst,X283 : term,X281 : subst] : (((X279 @ (comp @ X281 @ X282) @ (sub @ X283 @ X282))) = ((sub @ (X279 @ X281 @ X283) @ X282))))) => ! [X284 : term,X285 : (subst > term > subst > $o)] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ~ ! [X286 : term] : (($true = ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) | ~ (((X285 @ id @ X286 @ id)) = $true)) | ~ ! [X287 : (subst > term > term)] : (~ ! [X289 : subst,X290 : term,X288 : subst] : (((X287 @ (comp @ X288 @ X289) @ (sub @ X290 @ X289))) = ((sub @ (X287 @ X288 @ X290) @ X289))) | ($true = ((X285 @ id @ (lam @ (X287 @ sh @ one)) @ id))) | ~ ! [X291 : term] : (~ ($true = ((X285 @ id @ X291 @ id))) | (((X285 @ id @ (X287 @ id @ X291) @ id)) = $true)))))) <=> (hoasinduction_lem3a_lthm = $true)) & (! [X292 : term] : ~ ! [X293 : (subst > term > term)] : (((X293 @ sh @ one)) != ((sub @ X292 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & ((! [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) = X294) => (! [X296 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X296))) = X296) => (! [X299 : term,X298 : term] : ((X298 = X299) | (((lam @ X299)) != ((lam @ X298)))) => ! [X300 : subst,X303 : term,X302 : (subst > term > term),X301 : (subst > term > term)] : ((((X302 @ X300 @ X303)) = ((X301 @ X300 @ X303))) | ~ ! [X307 : subst,X309 : term,X308 : subst] : (((X302 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307))) = ((sub @ (X302 @ X308 @ X309) @ X307))) | ~ ! [X304 : subst,X306 : subst,X305 : term] : (((X301 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))) = ((sub @ (X301 @ X304 @ X305) @ X306))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X301 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (pushprop_lem3v2 = $true) & ((hoasapinj2 = $true) <=> ! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313))))) & (termmset_gthm = $true) & ((induction2_lthm = $true) <=> (! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X315 : (term > $o),X316 : subst,X317 : term] : (($true = ((X315 @ (sub @ X317 @ X316)))) | ~ ! [X318 : term,X319 : term] : (~ (((X315 @ X319)) = $true) | ($true = ((X315 @ (ap @ X318 @ X319)))) | ~ ($true = ((X315 @ X318)))) | ~ ! [X320 : term] : (~ ($true = ((var @ X320))) | ($true = ((X315 @ (sub @ X320 @ X316))))) | ~ ! [X321 : term] : (~ ! [X322 : term] : (~ ($true = ((X315 @ X322))) | (((X315 @ (sub @ X321 @ (push @ X322 @ id)))) = $true)) | (((X315 @ (lam @ X321))) = $true))) => ! [X323 : term,X324 : (term > $o)] : (~ ! [X325 : term] : (($true = ((X324 @ (lam @ X325)))) | ~ ! [X326 : term] : (($true = ((X324 @ (sub @ X325 @ (push @ X326 @ id))))) | ~ ($true = ((X324 @ X326))))) | ~ ! [X327 : term,X328 : term] : (~ ($true = ((X324 @ X328))) | ~ ($true = ((X324 @ X327))) | (((X324 @ (ap @ X328 @ X327))) = $true)) | ($true = ((X324 @ X323))) | ~ ! [X329 : term] : (~ (((var @ X329)) = $true) | ($true = ((X324 @ X329)))))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem2v2 = $true) & (pushprop_lem0_gthm = $true) & (hoasapnotvar_lthm = $true) & (! [X330 : term,X331 : term,X332 : (subst > term > subst > $o),X333 : (term > $o)] : (~ ! [X334 : subst,X335 : subst,X336 : subst,X337 : term] : ((((X332 @ (comp @ X334 @ X335) @ (sub @ X337 @ X335) @ X336)) = $true) | ~ ($true = ((X332 @ X334 @ X337 @ (comp @ X335 @ X336))))) | ~ ! [X338 : subst,X339 : subst,X340 : term,X341 : subst] : (($true = ((X332 @ X341 @ X340 @ (comp @ X339 @ X338)))) | ~ (((X332 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339) @ X338)) = $true)) | ~ (((X333 @ X331)) = $true) | (((X333 @ (ap @ X331 @ X330))) = $true) | ~ ($true = ((X333 @ X330))) | ~ ! [X342 : term,X343 : term] : (~ (((X332 @ id @ X342 @ id)) = $true) | ~ ($true = ((X332 @ id @ X343 @ id))) | ($true = ((X332 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id)))) | ~ ! [X344 : term] : (((X333 @ X344)) = ((X332 @ id @ X344 @ id)))) <=> (hoasinduction_lem2v2 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (axclos = $true) & (pushprop_lem3v2_lthm = $true) & (hoaslamnotvar_gthm = $true) & ((induction2 = $true) <=> ! [X345 : term,X346 : (term > $o)] : (~ ! [X347 : term] : (($true = ((X346 @ X347))) | ~ ($true = ((var @ X347)))) | ~ ! [X348 : term,X349 : term] : (~ ($true = ((X346 @ X349))) | ($true = ((X346 @ (ap @ X349 @ X348)))) | ~ ($true = ((X346 @ X348)))) | ($true = ((X346 @ X345))) | ~ ! [X350 : term] : ((((X346 @ (lam @ X350))) = $true) | ~ ! [X351 : term] : (($true = ((X346 @ (sub @ X350 @ (push @ X351 @ id))))) | ~ ($true = ((X346 @ X351))))))) & (hoasinduction_lem1 = $true) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) <=> (substmonoid = $true)) & ((shinj = $true) <=> ! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh))))) & (pushprop_lthm = $true) & (hoasinduction_lem1_gthm = $true) & ((induction = $true) <=> ! [X356 : (term > $o),X357 : term] : (($true = ((X356 @ X357))) | ~ ! [X358 : term] : (~ ($true = ((X356 @ X358))) | ($true = ((X356 @ (lam @ X358))))) | ~ ! [X359 : term,X360 : term] : (~ ($true = ((X356 @ X360))) | ~ (((X356 @ X359)) = $true) | ($true = ((X356 @ (ap @ X359 @ X360))))) | ~ ! [X361 : term] : (~ ($true = ((var @ X361))) | (((X356 @ X361)) = $true)))) & (axabs = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X362 : (subst > term > subst > $o)] : ~ ! [X363 : (term > $o)] : ~ ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X366 : term,X365 : subst] : (((sub @ one @ (push @ X366 @ X365))) = X366) => ! [X367 : subst,X368 : (term > $o),X369 : term,X370 : (term > $o)] : (($true = ((X368 @ one))) | ~ ! [X371 : term] : (((X368 @ X371)) = ((X370 @ (sub @ X371 @ (push @ X369 @ X367))))) | ~ ($true = ((X370 @ X369)))))) & ((hoasinduction_lem3aaa = $true) <=> ! [X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : term] : (($true = ((X373 @ id @ (sub @ X372 @ (push @ X374 @ id)) @ id))) | ~ ($true = ((X373 @ id @ X374 @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X372 @ (push @ one @ sh))) @ id))) | ~ ! [X375 : (subst > term > term),X376 : term] : (~ ! [X377 : term] : (($true = ((X373 @ id @ (X375 @ id @ X377) @ id))) | ~ ($true = ((X373 @ id @ X377 @ id)))) | ~ ! [X380 : subst,X379 : subst,X378 : term] : (((sub @ X376 @ (push @ (sub @ X378 @ X380) @ (comp @ X379 @ X380)))) = ((X375 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380)))) | ~ ! [X381 : subst,X383 : subst,X382 : term] : (((sub @ (X375 @ X383 @ X382) @ X381)) = ((sub @ (sub @ X376 @ (push @ X382 @ X383)) @ X381))) | ($true = ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id)))))) & (pushprop_lthm_orig = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((! [X384 : (subst > term > subst > $o)] : ~ ! [X385 : (term > $o)] : ~ ! [X386 : term] : (((X385 @ X386)) = ((X384 @ id @ X386 @ id))) => (! [X387 : term,X388 : (term > $o)] : (~ ! [X389 : term] : (~ ! [X390 : term] : (($true = ((X388 @ (sub @ X389 @ (push @ X390 @ id))))) | ~ (((X388 @ X390)) = $true)) | ($true = ((X388 @ (lam @ X389))))) | ($true = ((X388 @ X387))) | ~ ! [X391 : term] : (~ (((var @ X391)) = $true) | (((X388 @ X391)) = $true)) | ~ ! [X392 : term,X393 : term] : ((((X388 @ (ap @ X392 @ X393))) = $true) | ~ ($true = ((X388 @ X392))) | ~ (((X388 @ X393)) = $true))) => (! [X394 : term] : (((sub @ X394 @ id)) = X394) => (! [X395 : (subst > term > subst > $o),X396 : term,X397 : (term > $o)] : (~ ! [X398 : (subst > term > term)] : (($true = ((X395 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ~ ! [X400 : term,X399 : subst,X401 : subst] : (((X398 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X398 @ X401 @ X400) @ X399))) | ~ ! [X402 : term] : ((((X395 @ id @ (X398 @ id @ X402) @ id)) = $true) | ~ ($true = ((X395 @ id @ X402 @ id))))) | ($true = ((X397 @ (lam @ X396)))) | ~ ! [X403 : term] : (($true = ((X397 @ (sub @ X396 @ (push @ X403 @ id))))) | ~ ($true = ((X397 @ X403)))) | ~ ! [X404 : term] : (((X397 @ X404)) = ((X395 @ id @ X404 @ id)))) => ! [X405 : (subst > term > subst > $o),X406 : term] : (~ ! [X407 : subst,X408 : term,X409 : subst,X410 : subst] : (($true = ((X405 @ X409 @ X408 @ (comp @ X407 @ X410)))) | ~ ($true = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407) @ X410)))) | ~ ! [X411 : term] : (~ ($true = ((var @ (sub @ X411 @ id)))) | ($true = ((X405 @ id @ X411 @ id)))) | ~ ! [X412 : subst,X413 : subst,X414 : subst,X415 : term] : (($true = ((X405 @ (comp @ X414 @ X413) @ (sub @ X415 @ X413) @ X412))) | ~ ($true = ((X405 @ X414 @ X415 @ (comp @ X413 @ X412))))) | ($true = ((X405 @ id @ X406 @ id))) | ~ ! [X416 : term,X417 : term] : ((((X405 @ id @ (ap @ (sub @ X416 @ id) @ X417) @ id)) = $true) | ~ ($true = ((X405 @ id @ X416 @ id))) | ~ ($true = ((X405 @ id @ X417 @ id)))) | ~ ! [X418 : (subst > term > term)] : (~ ! [X419 : term] : ((((X405 @ id @ (X418 @ id @ X419) @ id)) = $true) | ~ ($true = ((X405 @ id @ X419 @ id)))) | ($true = ((X405 @ id @ (lam @ (X418 @ sh @ one)) @ id))) | ~ ! [X422 : subst,X420 : subst,X421 : term] : (((X418 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X418 @ X422 @ X421) @ X420))))))))) <=> (hoasinduction_lthm_3 = $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)))))))))))) & ! [X423 : d_term] : (d_one = X423) & (hoasapnotvar_gthm = $true) & (pushprop = $true) & ((axshiftcons = $true) <=> ! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424)) & (substmonoid_gthm = $true) & (hoaslamnotvar = $true) & ! [X426 : d_subst] : (d_id = X426) & (! [X427 : term] : ~ ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & (lamnotvar = $true) & ((axscons = $true) <=> ! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431)) & (one = ((d2term @ d_one))) & (! [X432 : term,X433 : (subst > term > subst > $o),X434 : (term > $o)] : (~ ! [X435 : term] : (~ ($true = ((X434 @ X435))) | ($true = ((X434 @ (sub @ X432 @ (push @ X435 @ id)))))) | ~ ! [X436 : term,X437 : subst,X438 : subst,X439 : subst] : (~ ($true = ((X433 @ (comp @ X439 @ X438) @ (sub @ X436 @ X438) @ X437))) | ($true = ((X433 @ X439 @ X436 @ (comp @ X438 @ X437))))) | ~ ! [X440 : subst,X441 : subst,X442 : term,X443 : subst] : (~ (((X433 @ X441 @ X442 @ (comp @ X443 @ X440))) = $true) | (((X433 @ (comp @ X441 @ X443) @ (sub @ X442 @ X443) @ X440)) = $true)) | ~ ! [X444 : (subst > term > term)] : (($true = ((X433 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ~ ! [X447 : term,X445 : subst,X446 : subst] : (((X444 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445))) = ((sub @ (X444 @ X446 @ X447) @ X445))) | ~ ! [X448 : term] : (~ ($true = ((X433 @ id @ X448 @ id))) | ($true = ((X433 @ id @ (X444 @ id @ X448) @ id))))) | ($true = ((X434 @ (lam @ X432)))) | ~ ! [X449 : term] : (((X433 @ id @ X449 @ id)) = ((X434 @ X449)))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotap_lthm = $true) & ((hoasinduction_lem3_lthm = $true) <=> (! [X450 : term] : (((sub @ X450 @ id)) = X450) => (! [X451 : term,X452 : (subst > term > subst > $o)] : (($true = ((X452 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id))) | ~ ! [X453 : term] : (~ ($true = ((X452 @ id @ X453 @ id))) | ($true = ((X452 @ id @ (sub @ X451 @ (push @ X453 @ id)) @ id)))) | ~ ! [X454 : (subst > term > term)] : (~ ! [X457 : term,X456 : subst,X455 : subst] : (((sub @ (X454 @ X455 @ X457) @ X456)) = ((X454 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) | (((X452 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ~ ! [X458 : term] : (~ ($true = ((X452 @ id @ X458 @ id))) | ($true = ((X452 @ id @ (X454 @ id @ X458) @ id)))))) => ! [X459 : term,X460 : (subst > term > subst > $o)] : (~ ! [X461 : (subst > term > term)] : (~ ! [X462 : term] : (~ ($true = ((X460 @ id @ X462 @ id))) | ($true = ((X460 @ id @ (X461 @ id @ X462) @ id)))) | ~ ! [X464 : term,X463 : subst,X465 : subst] : (((sub @ (X461 @ X463 @ X464) @ X465)) = ((X461 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465)))) | ($true = ((X460 @ id @ (lam @ (X461 @ sh @ one)) @ id)))) | ~ ! [X466 : subst,X467 : subst,X468 : term,X469 : subst] : (($true = ((X460 @ (comp @ X467 @ X466) @ (sub @ X468 @ X466) @ X469))) | ~ ($true = ((X460 @ X467 @ X468 @ (comp @ X466 @ X469))))) | ($true = ((X460 @ id @ (lam @ X459) @ id))) | ~ ! [X470 : term] : (~ ($true = ((X460 @ id @ X470 @ id))) | ($true = ((X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id)))) | ~ ! [X471 : subst,X472 : subst,X473 : subst,X474 : term] : (~ ($true = ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473))) | (((X460 @ X471 @ X474 @ (comp @ X472 @ X473))) = $true)))))) & (axmap = $true) & (hoasapinj1_gthm = $true) & (! [X475 : term] : ~ ! [X476 : (subst > term > term)] : ~ ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X479 : (subst > term > subst > $o)] : ~ ! [X480 : (term > $o)] : ~ ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_lem1v2 = $true) & ! [X482 : d_term,X483 : d_term] : ((((d2term @ X482)) = ((d2term @ X483))) => (X482 = X483)) & ((hoasinduction_lem3 = $true) <=> ! [X484 : term,X485 : (subst > term > subst > $o)] : (~ ! [X486 : subst,X487 : term,X488 : subst,X489 : subst] : (($true = ((X485 @ X486 @ X487 @ (comp @ X488 @ X489)))) | ~ ($true = ((X485 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X489)))) | ~ ! [X490 : subst,X491 : term,X492 : subst,X493 : subst] : ((((X485 @ (comp @ X492 @ X490) @ (sub @ X491 @ X490) @ X493)) = $true) | ~ ($true = ((X485 @ X492 @ X491 @ (comp @ X490 @ X493))))) | ~ ! [X494 : (subst > term > term)] : (~ ! [X495 : term,X497 : subst,X496 : subst] : (((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497))) = ((sub @ (X494 @ X496 @ X495) @ X497))) | ($true = ((X485 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ~ ! [X498 : term] : (($true = ((X485 @ id @ (X494 @ id @ X498) @ id))) | ~ ($true = ((X485 @ id @ X498 @ id))))) | ~ ! [X499 : term] : ((((X485 @ id @ (sub @ X484 @ (push @ X499 @ id)) @ id)) = $true) | ~ ($true = ((X485 @ id @ X499 @ id)))) | ($true = ((X485 @ id @ (lam @ X484) @ id))))) & ((substmonoid_lthm = $true) <=> (! [X500 : subst] : (((comp @ id @ X500)) = X500) => (! [X501 : subst] : (((comp @ X501 @ id)) = X501) => (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503))))) & ((hoasinduction_lem3a = $true) <=> ! [X504 : term,X505 : (subst > term > subst > $o)] : (~ ! [X506 : (subst > term > term)] : (~ ! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X506 @ X508 @ X509) @ X507)) = ((X506 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) | ~ ! [X510 : term] : (($true = ((X505 @ id @ (X506 @ id @ X510) @ id))) | ~ ($true = ((X505 @ id @ X510 @ id)))) | ($true = ((X505 @ id @ (lam @ (X506 @ sh @ one)) @ id)))) | ~ ! [X511 : term] : ((((X505 @ id @ (sub @ X504 @ (push @ X511 @ id)) @ id)) = $true) | ~ ($true = ((X505 @ id @ X511 @ id)))) | ($true = ((X505 @ id @ (lam @ X504) @ id))))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X512 : (subst > term > subst > $o),X513 : term] : (($true = ((X512 @ id @ X513 @ id))) | ~ ! [X514 : term,X515 : term] : (~ ($true = ((X512 @ id @ X514 @ id))) | ($true = ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) | ~ ($true = ((X512 @ id @ X515 @ id)))) | ~ ! [X516 : (subst > term > term)] : ((((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id)) = $true) | ~ ! [X517 : term] : (~ ($true = ((X512 @ id @ X517 @ id))) | (((X512 @ id @ (X516 @ id @ X517) @ id)) = $true)) | ~ ! [X519 : term,X518 : subst,X520 : subst] : (((sub @ (X516 @ X518 @ X519) @ X520)) = ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520))))))) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) <=> (axidr = $true)) & (! [X523 : (subst > term > term),X524 : subst,X522 : (subst > term > term),X525 : term] : (~ ! [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) = ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X523 @ X526 @ X528) @ X527))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525)))) <=> (hoaslaminj = $true)) & (ulamvarsh = $true) & (! [X532 : (subst > term > subst > $o),X533 : term] : (~ ! [X534 : (subst > term > term)] : (~ ! [X535 : term] : (($true = ((X532 @ id @ (X534 @ id @ X535) @ id))) | ~ ($true = ((X532 @ id @ X535 @ id)))) | ($true = ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id))) | ~ ! [X538 : subst,X537 : subst,X536 : term] : (((sub @ (X534 @ X537 @ X536) @ X538)) = ((X534 @ (comp @ X537 @ X538) @ (sub @ X536 @ X538))))) | ~ ! [X539 : term] : (~ ($true = ((X532 @ id @ X539 @ id))) | (((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id)) = $true)) | ($true = ((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aa_lthm = $true))),
% 2.19/0.60 inference(rectify,[],[f7])).
% 2.19/0.60 thf(f10,plain,(
% 2.19/0.60 (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X362 : (subst > term > subst > $o)] : ~ ! [X363 : (term > $o)] : ~ ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id)))) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & (pushprop_lem2v2_lthm = $true) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (($true = ((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id))) | ~ ! [X534 : (subst > term > term)] : (~ ! [X535 : term] : (($true = ((X532 @ id @ (X534 @ id @ X535) @ id))) | ($true != ((X532 @ id @ X535 @ id)))) | ($true = ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id))) | ~ ! [X538 : subst,X537 : subst,X536 : term] : (((sub @ (X534 @ X537 @ X536) @ X538)) = ((X534 @ (comp @ X537 @ X538) @ (sub @ X536 @ X538))))) | ~ ! [X539 : term] : ((((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id)) = $true) | ($true != ((X532 @ id @ X539 @ id)))))) & (pushprop_lthm_orig = $true) & ((axshiftcons = $true) <=> ! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424)) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & (pushprop_lthm = $true) & (! [X183 : subst,X182 : (term > $o),X184 : term] : (~ ! [X185 : term] : (~ ! [X186 : term] : (($true != ((X182 @ X186))) | ($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id)))))) | ($true = ((X182 @ (lam @ X185))))) | ~ ! [X187 : term] : (($true = ((X182 @ (sub @ X187 @ X183)))) | ($true != ((var @ X187)))) | ~ ! [X189 : term,X188 : term] : (($true != ((X182 @ X189))) | ($true = ((X182 @ (ap @ X188 @ X189)))) | ($true != ((X182 @ X188)))) | (((X182 @ (sub @ X184 @ X183))) = $true)) <=> (induction2lem = $true)) & (! [X523 : (subst > term > term),X524 : subst,X522 : (subst > term > term),X525 : term] : (~ ! [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) = ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | ~ ! [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X523 @ X526 @ X528) @ X527))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) <=> (axidr = $true)) & (((d2subst @ d_id)) = sh) & ((laminj = $true) <=> ! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270))) & (ulamvarsh = $true) & (axvarshift = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X433 : (subst > term > subst > $o),X432 : term,X434 : (term > $o)] : (~ ! [X435 : term] : (($true != ((X434 @ X435))) | ($true = ((X434 @ (sub @ X432 @ (push @ X435 @ id)))))) | ~ ! [X444 : (subst > term > term)] : (~ ! [X448 : term] : (($true = ((X433 @ id @ (X444 @ id @ X448) @ id))) | ($true != ((X433 @ id @ X448 @ id)))) | ($true = ((X433 @ id @ (lam @ (X444 @ sh @ one)) @ id))) | ~ ! [X447 : term,X445 : subst,X446 : subst] : (((X444 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445))) = ((sub @ (X444 @ X446 @ X447) @ X445)))) | ($true = ((X434 @ (lam @ X432)))) | ~ ! [X443 : subst,X441 : subst,X442 : term,X440 : subst] : ((((X433 @ X441 @ X442 @ (comp @ X443 @ X440))) != $true) | (((X433 @ (comp @ X441 @ X443) @ (sub @ X442 @ X443) @ X440)) = $true)) | ~ ! [X449 : term] : (((X433 @ id @ X449 @ id)) = ((X434 @ X449))) | ~ ! [X438 : subst,X437 : subst,X436 : term,X439 : subst] : (($true != ((X433 @ (comp @ X439 @ X438) @ (sub @ X436 @ X438) @ X437))) | ($true = ((X433 @ X439 @ X436 @ (comp @ X438 @ X437))))))) & (! [X427 : term] : ~ ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X426 : d_subst] : (d_id = X426) & (hoaslaminj_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem2 = $true) <=> ! [X163 : (subst > term > subst > $o),X162 : term,X161 : term] : (~ ! [X169 : term,X168 : term] : ((((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) = $true) | ($true != ((X163 @ id @ X168 @ id))) | ($true != ((X163 @ id @ X169 @ id)))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ~ ! [X173 : term,X172 : subst,X171 : subst,X170 : subst] : (($true = ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172))) | (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) != $true)) | ~ ! [X164 : subst,X167 : subst,X165 : term,X166 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) = $true) | ($true != ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | (((X163 @ id @ X161 @ id)) != $true) | ($true != ((X163 @ id @ X162 @ id))))) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((! [X174 : term,X176 : term,X175 : term,X177 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176)))) => ! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> (! [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) = X42) => (! [X45 : subst,X44 : term] : (((comp @ sh @ (push @ X44 @ X45))) = X45) => ! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47))))))) & (one = ((d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X275 : term] : (((sub @ X275 @ id)) = X275) => (! [X277 : term,X276 : (subst > term > subst > $o)] : ((((X276 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X279 : (subst > term > term)] : (~ ! [X282 : subst,X283 : term,X281 : subst] : (((X279 @ (comp @ X281 @ X282) @ (sub @ X283 @ X282))) = ((sub @ (X279 @ X281 @ X283) @ X282))) | ($true = ((X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ~ ! [X280 : term] : (($true != ((X276 @ id @ X280 @ id))) | ($true = ((X276 @ id @ (X279 @ id @ X280) @ id))))) | ~ ! [X278 : term] : ((((X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) = $true) | ($true != ((X276 @ id @ X278 @ id))))) => ! [X285 : (subst > term > subst > $o),X284 : term] : ((((X285 @ id @ (lam @ X284) @ id)) = $true) | ~ ! [X287 : (subst > term > term)] : (($true = ((X285 @ id @ (lam @ (X287 @ sh @ one)) @ id))) | ~ ! [X291 : term] : (($true != ((X285 @ id @ X291 @ id))) | (((X285 @ id @ (X287 @ id @ X291) @ id)) = $true)) | ~ ! [X289 : subst,X290 : term,X288 : subst] : (((X287 @ (comp @ X288 @ X289) @ (sub @ X290 @ X289))) = ((sub @ (X287 @ X288 @ X290) @ X289)))) | ~ ! [X286 : term] : (($true = ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) | (((X285 @ id @ X286 @ id)) != $true)))))) & (lamnotap != $true) & ((shinj = $true) <=> ! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh))))) & (hoasinduction_lem1v2_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) <=> (! [X500 : subst] : (((comp @ id @ X500)) = X500) => (! [X501 : subst] : (((comp @ X501 @ id)) = X501) => (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503))))) & ((hoasinduction_lem3 = $true) <=> ! [X484 : term,X485 : (subst > term > subst > $o)] : (~ ! [X486 : subst,X488 : subst,X487 : term,X489 : subst] : (($true != ((X485 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X489))) | ($true = ((X485 @ X486 @ X487 @ (comp @ X488 @ X489))))) | ($true = ((X485 @ id @ (lam @ X484) @ id))) | ~ ! [X499 : term] : (($true != ((X485 @ id @ X499 @ id))) | (((X485 @ id @ (sub @ X484 @ (push @ X499 @ id)) @ id)) = $true)) | ~ ! [X492 : subst,X493 : subst,X491 : term,X490 : subst] : (($true != ((X485 @ X492 @ X491 @ (comp @ X490 @ X493)))) | (((X485 @ (comp @ X492 @ X490) @ (sub @ X491 @ X490) @ X493)) = $true)) | ~ ! [X494 : (subst > term > term)] : (~ ! [X498 : term] : (($true = ((X485 @ id @ (X494 @ id @ X498) @ id))) | ($true != ((X485 @ id @ X498 @ id)))) | ($true = ((X485 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ~ ! [X495 : term,X497 : subst,X496 : subst] : (((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497))) = ((sub @ (X494 @ X496 @ X495) @ X497)))))) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) <=> (termmset = $true)) & ((! [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) = X19) => (! [X21 : term,X20 : subst] : (((comp @ sh @ (push @ X21 @ X20))) = X20) => (! [X22 : subst] : (((comp @ X22 @ id)) = X22) => (! [X23 : term,X24 : (term > $o)] : (~ ! [X27 : term,X28 : term] : (($true = ((X24 @ (ap @ X28 @ X27)))) | ($true != ((X24 @ X27))) | ($true != ((X24 @ X28)))) | ($true = ((X24 @ X23))) | ~ ! [X26 : term] : (($true = ((X24 @ X26))) | ($true != ((var @ X26)))) | ~ ! [X25 : term] : ((((X24 @ X25)) != $true) | ($true = ((X24 @ (lam @ X25)))))) => ! [X29 : subst,X30 : (term > $o),X31 : term] : (($true = ((X30 @ (sub @ X31 @ X29)))) | ~ ! [X34 : term,X33 : term] : (($true != ((X30 @ X34))) | ($true = ((X30 @ (ap @ X34 @ X33)))) | ($true != ((X30 @ X33)))) | ~ ! [X35 : term] : (~ ! [X36 : term] : (($true != ((X30 @ X36))) | ($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id)))))) | (((X30 @ (lam @ X35))) = $true)) | ~ ! [X32 : term] : (($true != ((var @ X32))) | ($true = ((X30 @ (sub @ X32 @ X29)))))))))) <=> (induction2lem_lthm = $true)) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) <=> (! [X273 : term] : (((sub @ X273 @ id)) = X273) => ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (pushprop_gthm = $true) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) <=> (substmonoid = $true)) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & ((pushprop_lem0_lthm = $true) <=> ! [X15 : subst,X14 : (term > $o),X13 : term] : ~ ! [X16 : (term > $o)] : ~ ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15)))))) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) = ((d2subst @ X271))) => (X271 = X272)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem3a = $true) <=> ! [X504 : term,X505 : (subst > term > subst > $o)] : (($true = ((X505 @ id @ (lam @ X504) @ id))) | ~ ! [X506 : (subst > term > term)] : (~ ! [X510 : term] : (($true = ((X505 @ id @ (X506 @ id @ X510) @ id))) | ($true != ((X505 @ id @ X510 @ id)))) | ~ ! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X506 @ X508 @ X509) @ X507)) = ((X506 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) | ($true = ((X505 @ id @ (lam @ (X506 @ sh @ one)) @ id)))) | ~ ! [X511 : term] : (($true != ((X505 @ id @ X511 @ id))) | (((X505 @ id @ (sub @ X504 @ (push @ X511 @ id)) @ id)) = $true)))) & ! [X423 : d_term] : (d_one = X423) & (axapp = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axabs = $true) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (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)))))))))))) & (apnotvar = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X133 : term,X134 : (subst > term > subst > $o)] : ((((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X135 : term] : (($true = ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) | (((X134 @ id @ X135 @ id)) != $true)) | ~ ! [X136 : (subst > term > term)] : (~ ! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) | ~ ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ($true != ((X134 @ id @ X137 @ id)))) | (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) = $true)))) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X40 : (term > $o),X39 : (term > $o),X38 : subst,X37 : term] : (~ ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))) | (((X40 @ X37)) != $true) | ($true = ((X39 @ one))))) & (! [X475 : term] : ~ ! [X476 : (subst > term > term)] : ~ ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X366 : term,X365 : subst] : (((sub @ one @ (push @ X366 @ X365))) = X366) => ! [X370 : (term > $o),X368 : (term > $o),X367 : subst,X369 : term] : (($true != ((X370 @ X369))) | ~ ! [X371 : term] : (((X368 @ X371)) = ((X370 @ (sub @ X371 @ (push @ X369 @ X367))))) | ($true = ((X368 @ one)))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lthm_3 = $true) <=> (! [X384 : (subst > term > subst > $o)] : ~ ! [X385 : (term > $o)] : ~ ! [X386 : term] : (((X385 @ X386)) = ((X384 @ id @ X386 @ id))) => (! [X387 : term,X388 : (term > $o)] : (~ ! [X391 : term] : ((((X388 @ X391)) = $true) | (((var @ X391)) != $true)) | ($true = ((X388 @ X387))) | ~ ! [X393 : term,X392 : term] : ((((X388 @ (ap @ X392 @ X393))) = $true) | ($true != ((X388 @ X392))) | (((X388 @ X393)) != $true)) | ~ ! [X389 : term] : (($true = ((X388 @ (lam @ X389)))) | ~ ! [X390 : term] : (($true = ((X388 @ (sub @ X389 @ (push @ X390 @ id))))) | (((X388 @ X390)) != $true)))) => (! [X394 : term] : (((sub @ X394 @ id)) = X394) => (! [X397 : (term > $o),X396 : term,X395 : (subst > term > subst > $o)] : (($true = ((X397 @ (lam @ X396)))) | ~ ! [X404 : term] : (((X397 @ X404)) = ((X395 @ id @ X404 @ id))) | ~ ! [X403 : term] : (($true = ((X397 @ (sub @ X396 @ (push @ X403 @ id))))) | ($true != ((X397 @ X403)))) | ~ ! [X398 : (subst > term > term)] : (($true = ((X395 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ~ ! [X400 : term,X399 : subst,X401 : subst] : (((X398 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) = ((sub @ (X398 @ X401 @ X400) @ X399))) | ~ ! [X402 : term] : ((((X395 @ id @ (X398 @ id @ X402) @ id)) = $true) | ($true != ((X395 @ id @ X402 @ id)))))) => ! [X406 : term,X405 : (subst > term > subst > $o)] : (~ ! [X411 : term] : (($true != ((var @ (sub @ X411 @ id)))) | ($true = ((X405 @ id @ X411 @ id)))) | ~ ! [X416 : term,X417 : term] : (($true != ((X405 @ id @ X416 @ id))) | ($true != ((X405 @ id @ X417 @ id))) | (((X405 @ id @ (ap @ (sub @ X416 @ id) @ X417) @ id)) = $true)) | ~ ! [X407 : subst,X410 : subst,X409 : subst,X408 : term] : (($true = ((X405 @ X409 @ X408 @ (comp @ X407 @ X410)))) | ($true != ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407) @ X410)))) | ~ ! [X415 : term,X413 : subst,X412 : subst,X414 : subst] : (($true = ((X405 @ (comp @ X414 @ X413) @ (sub @ X415 @ X413) @ X412))) | ($true != ((X405 @ X414 @ X415 @ (comp @ X413 @ X412))))) | ($true = ((X405 @ id @ X406 @ id))) | ~ ! [X418 : (subst > term > term)] : (($true = ((X405 @ id @ (lam @ (X418 @ sh @ one)) @ id))) | ~ ! [X419 : term] : ((((X405 @ id @ (X418 @ id @ X419) @ id)) = $true) | ($true != ((X405 @ id @ X419 @ id)))) | ~ ! [X422 : subst,X420 : subst,X421 : term] : (((X418 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X418 @ X422 @ X421) @ X420)))))))))) & ((! [X103 : (subst > term > subst > $o)] : ~ ! [X104 : (term > $o)] : ~ ! [X105 : term] : (((X104 @ X105)) = ((X103 @ id @ X105 @ id))) => (! [X106 : term,X107 : (term > $o)] : (~ ! [X112 : term,X111 : term] : (($true != ((X107 @ X112))) | ($true != ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111))))) | ($true = ((X107 @ X106))) | ~ ! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ~ ! [X110 : term] : (($true = ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) | ($true != ((X107 @ X110))))) | ~ ! [X108 : term] : (($true = ((X107 @ X108))) | ($true != ((var @ X108))))) => (! [X113 : term] : (((sub @ X113 @ id)) = X113) => (! [X114 : (term > $o),X115 : term,X116 : (subst > term > subst > $o)] : (~ ! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | (((X114 @ X117)) != $true)) | ~ ! [X119 : (subst > term > term)] : (~ ! [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) = ((sub @ (X119 @ X121 @ X122) @ X120))) | ~ ! [X123 : term] : (($true = ((X116 @ id @ (X119 @ id @ X123) @ id))) | ($true != ((X116 @ id @ X123 @ id)))) | ($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id)))) | ~ ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))) | ($true = ((X114 @ (lam @ X115))))) => ! [X124 : term,X125 : (subst > term > subst > $o)] : (~ ! [X126 : (subst > term > term)] : (($true = ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id))) | ~ ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ($true != ((X125 @ id @ X127 @ id)))) | ~ ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129)))) | ($true = ((X125 @ id @ X124 @ id))) | ~ ! [X132 : term,X131 : term] : (($true != ((X125 @ id @ X131 @ id))) | ($true = ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) | ($true != ((X125 @ id @ X132 @ id))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X151 : term,X152 : (term > $o),X153 : (subst > term > subst > $o)] : (~ ! [X160 : term] : (($true = ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) | ($true != ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true) | ~ ! [X155 : (subst > term > term)] : (~ ! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) | ~ ! [X159 : term] : (($true = ((X153 @ id @ (X155 @ id @ X159) @ id))) | (((X153 @ id @ X159 @ id)) != $true)) | ($true = ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id)))) | ~ ! [X154 : term] : (((X152 @ X154)) = ((X153 @ id @ X154 @ id)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem3a_gthm = $true) & ((! [X314 : term] : (((sub @ X314 @ id)) = X314) => (! [X316 : subst,X315 : (term > $o),X317 : term] : (~ ! [X320 : term] : (($true != ((var @ X320))) | ($true = ((X315 @ (sub @ X320 @ X316))))) | ($true = ((X315 @ (sub @ X317 @ X316)))) | ~ ! [X321 : term] : (~ ! [X322 : term] : (($true != ((X315 @ X322))) | (((X315 @ (sub @ X321 @ (push @ X322 @ id)))) = $true)) | (((X315 @ (lam @ X321))) = $true)) | ~ ! [X318 : term,X319 : term] : (($true != ((X315 @ X318))) | (((X315 @ X319)) != $true) | ($true = ((X315 @ (ap @ X318 @ X319)))))) => ! [X324 : (term > $o),X323 : term] : (~ ! [X325 : term] : (($true = ((X324 @ (lam @ X325)))) | ~ ! [X326 : term] : (($true = ((X324 @ (sub @ X325 @ (push @ X326 @ id))))) | ($true != ((X324 @ X326))))) | ~ ! [X329 : term] : (($true = ((X324 @ X329))) | (((var @ X329)) != $true)) | ~ ! [X327 : term,X328 : term] : ((((X324 @ (ap @ X328 @ X327))) = $true) | ($true != ((X324 @ X328))) | ($true != ((X324 @ X327)))) | ($true = ((X324 @ X323)))))) <=> (induction2_lthm = $true)) & (! [X512 : (subst > term > subst > $o),X513 : term] : (~ ! [X514 : term,X515 : term] : (($true != ((X512 @ id @ X514 @ id))) | ($true = ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) | ($true != ((X512 @ id @ X515 @ id)))) | ($true = ((X512 @ id @ X513 @ id))) | ~ ! [X516 : (subst > term > term)] : (~ ! [X519 : term,X518 : subst,X520 : subst] : (((sub @ (X516 @ X518 @ X519) @ X520)) = ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520)))) | ~ ! [X517 : term] : ((((X512 @ id @ (X516 @ id @ X517) @ id)) = $true) | ($true != ((X512 @ id @ X517 @ id)))) | (((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & ((! [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) = X294) => (! [X296 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X296))) = X296) => (! [X299 : term,X298 : term] : ((X298 = X299) | (((lam @ X299)) != ((lam @ X298)))) => ! [X300 : subst,X303 : term,X302 : (subst > term > term),X301 : (subst > term > term)] : ((((X302 @ X300 @ X303)) = ((X301 @ X300 @ X303))) | ~ ! [X307 : subst,X309 : term,X308 : subst] : (((X302 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307))) = ((sub @ (X302 @ X308 @ X309) @ X307))) | ~ ! [X304 : subst,X306 : subst,X305 : term] : (((X301 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))) = ((sub @ (X301 @ X304 @ X305) @ X306))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X301 @ sh @ one)))))))) <=> (hoaslaminj_lthm = $true)) & (axclos = $true) & (! [X356 : (term > $o),X357 : term] : (~ ! [X358 : term] : (($true != ((X356 @ X358))) | ($true = ((X356 @ (lam @ X358))))) | ~ ! [X361 : term] : ((((X356 @ X361)) = $true) | ($true != ((var @ X361)))) | ($true = ((X356 @ X357))) | ~ ! [X359 : term,X360 : term] : ((((X356 @ X359)) != $true) | ($true = ((X356 @ (ap @ X359 @ X360)))) | ($true != ((X356 @ X360))))) <=> (induction = $true)) & (hoasinduction_gthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & ((! [X450 : term] : (((sub @ X450 @ id)) = X450) => (! [X451 : term,X452 : (subst > term > subst > $o)] : (($true = ((X452 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id))) | ~ ! [X454 : (subst > term > term)] : (~ ! [X457 : term,X456 : subst,X455 : subst] : (((sub @ (X454 @ X455 @ X457) @ X456)) = ((X454 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456)))) | (((X452 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ~ ! [X458 : term] : (($true = ((X452 @ id @ (X454 @ id @ X458) @ id))) | ($true != ((X452 @ id @ X458 @ id))))) | ~ ! [X453 : term] : (($true != ((X452 @ id @ X453 @ id))) | ($true = ((X452 @ id @ (sub @ X451 @ (push @ X453 @ id)) @ id))))) => ! [X459 : term,X460 : (subst > term > subst > $o)] : (($true = ((X460 @ id @ (lam @ X459) @ id))) | ~ ! [X472 : subst,X471 : subst,X474 : term,X473 : subst] : ((((X460 @ X471 @ X474 @ (comp @ X472 @ X473))) = $true) | ($true != ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473)))) | ~ ! [X470 : term] : (($true != ((X460 @ id @ X470 @ id))) | ($true = ((X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id)))) | ~ ! [X461 : (subst > term > term)] : (($true = ((X460 @ id @ (lam @ (X461 @ sh @ one)) @ id))) | ~ ! [X464 : term,X463 : subst,X465 : subst] : (((sub @ (X461 @ X463 @ X464) @ X465)) = ((X461 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465)))) | ~ ! [X462 : term] : (($true != ((X460 @ id @ X462 @ id))) | ($true = ((X460 @ id @ (X461 @ id @ X462) @ id))))) | ~ ! [X468 : term,X469 : subst,X466 : subst,X467 : subst] : (($true = ((X460 @ (comp @ X467 @ X466) @ (sub @ X468 @ X466) @ X469))) | ($true != ((X460 @ X467 @ X468 @ (comp @ X466 @ X469)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (! [X345 : term,X346 : (term > $o)] : (~ ! [X350 : term] : ((((X346 @ (lam @ X350))) = $true) | ~ ! [X351 : term] : (($true = ((X346 @ (sub @ X350 @ (push @ X351 @ id))))) | ($true != ((X346 @ X351))))) | ($true = ((X346 @ X345))) | ~ ! [X347 : term] : (($true = ((X346 @ X347))) | ($true != ((var @ X347)))) | ~ ! [X348 : term,X349 : term] : (($true = ((X346 @ (ap @ X349 @ X348)))) | ($true != ((X346 @ X348))) | ($true != ((X346 @ X349))))) <=> (induction2 = $true)) & (! [X292 : term] : ~ ! [X293 : (subst > term > term)] : (((X293 @ sh @ one)) != ((sub @ X292 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) <=> (pushprop_lem1 = $true)) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & ((axscons = $true) <=> ! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X372 : term,X373 : (subst > term > subst > $o)] : (~ ! [X374 : term] : (($true = ((X373 @ id @ (sub @ X372 @ (push @ X374 @ id)) @ id))) | ($true != ((X373 @ id @ X374 @ id)))) | ~ ! [X375 : (subst > term > term),X376 : term] : (~ ! [X377 : term] : (($true = ((X373 @ id @ (X375 @ id @ X377) @ id))) | ($true != ((X373 @ id @ X377 @ id)))) | ~ ! [X381 : subst,X383 : subst,X382 : term] : (((sub @ (X375 @ X383 @ X382) @ X381)) = ((sub @ (sub @ X376 @ (push @ X382 @ X383)) @ X381))) | ($true = ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) | ~ ! [X380 : subst,X379 : subst,X378 : term] : (((sub @ X376 @ (push @ (sub @ X378 @ X380) @ (comp @ X379 @ X380)))) = ((X375 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380))))) | ($true = ((X373 @ id @ (lam @ (sub @ X372 @ (push @ one @ sh))) @ id))))) & (pushprop_lem3v2 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X330 : term,X331 : term,X332 : (subst > term > subst > $o),X333 : (term > $o)] : (~ ! [X334 : subst,X337 : term,X336 : subst,X335 : subst] : (($true != ((X332 @ X334 @ X337 @ (comp @ X335 @ X336)))) | (((X332 @ (comp @ X334 @ X335) @ (sub @ X337 @ X335) @ X336)) = $true)) | ~ ! [X338 : subst,X339 : subst,X340 : term,X341 : subst] : (($true = ((X332 @ X341 @ X340 @ (comp @ X339 @ X338)))) | (((X332 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339) @ X338)) != $true)) | ($true != ((X333 @ X330))) | (((X333 @ X331)) != $true) | ~ ! [X344 : term] : (((X333 @ X344)) = ((X332 @ id @ X344 @ id))) | (((X333 @ (ap @ X331 @ X330))) = $true) | ~ ! [X343 : term,X342 : term] : (($true != ((X332 @ id @ X343 @ id))) | (((X332 @ id @ X342 @ id)) != $true) | ($true = ((X332 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id))))) <=> (hoasinduction_lem2v2 = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X142 : term] : (((sub @ X142 @ id)) = X142) => (! [X144 : term,X146 : term,X143 : term,X145 : term] : ((X145 = X146) | (((ap @ X145 @ X144)) != ((ap @ X146 @ X143)))) => ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))))) & ((hoasapinj2 = $true) <=> ! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313))))) & (! [X9 : subst,X8 : term,X10 : (term > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X250 : term] : (((sub @ X250 @ id)) = X250) => ! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o)] : (~ ! [X255 : term] : (($true = ((X251 @ (sub @ X252 @ (push @ X255 @ id))))) | (((X251 @ X255)) != $true)) | ~ ! [X265 : subst,X267 : subst,X268 : term,X266 : subst] : ((((X253 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) = $true) | (((X253 @ X267 @ X268 @ (comp @ X265 @ X266))) != $true)) | ($true = ((X251 @ (lam @ X252)))) | ~ ! [X264 : term,X261 : subst,X262 : subst,X263 : subst] : ((((X253 @ X262 @ X264 @ (comp @ X261 @ X263))) = $true) | ($true != ((X253 @ (comp @ X262 @ X261) @ (sub @ X264 @ X261) @ X263)))) | ~ ! [X254 : term] : (((X251 @ X254)) = ((X253 @ id @ X254 @ id))) | ~ ! [X256 : (subst > term > term)] : (~ ! [X260 : term] : ((((X253 @ id @ X260 @ id)) != $true) | ($true = ((X253 @ id @ (X256 @ id @ X260) @ id)))) | ~ ! [X257 : subst,X259 : subst,X258 : term] : (((X256 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X257 @ X258) @ X259))) | ($true = ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id))))))) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X51 : term] : ~ ! [X52 : (subst > term > term)] : ~ ! [X54 : subst,X53 : term] : (((sub @ X51 @ (push @ X53 @ X54))) = ((X52 @ X54 @ X53))) => (! [X55 : term] : (((sub @ X55 @ id)) = X55) => ! [X56 : (term > $o),X58 : term,X57 : (subst > term > subst > $o)] : (~ ! [X65 : term] : (((X57 @ id @ X65 @ id)) = ((X56 @ X65))) | ~ ! [X59 : (subst > term > term)] : (~ ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63)))) | ~ ! [X60 : term] : (($true = ((X57 @ id @ (X59 @ id @ X60) @ id))) | ($true != ((X57 @ id @ X60 @ id)))) | (((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) = $true)) | ($true = ((X56 @ (lam @ X58)))) | ~ ! [X64 : term] : (($true = ((X56 @ (sub @ X58 @ (push @ X64 @ id))))) | ($true != ((X56 @ X64)))))))) & (! [X93 : term] : ~ ! [X94 : (subst > term > term)] : ~ ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & ((hoaslamnotap = $true) <=> ! [X2 : term,X4 : term,X3 : (subst > term > term)] : (~ ! [X6 : subst,X7 : term,X5 : subst] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one)))))) & (hoasapinj1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem1v2_gthm = $true) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (termmset_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem2v2 = $true) & ((! [X195 : (term > $o),X194 : term] : (~ ! [X200 : term] : (($true = ((X195 @ X200))) | ($true != ((var @ X200)))) | ~ ! [X197 : term,X196 : term] : (($true != ((X195 @ X196))) | ($true = ((X195 @ (ap @ X196 @ X197)))) | ($true != ((X195 @ X197)))) | ~ ! [X198 : term] : (~ ! [X199 : term] : ((((X195 @ X199)) != $true) | ($true = ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true)) | (((X195 @ X194)) = $true)) => (! [X202 : term,X201 : (subst > term > subst > $o),X203 : term] : ((((X201 @ id @ X203 @ id)) != $true) | (((X201 @ id @ (ap @ X202 @ X203) @ id)) = $true) | ~ ! [X211 : subst,X212 : subst,X213 : term,X210 : subst] : (($true != ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210)))) | ~ ! [X208 : subst,X209 : subst,X206 : term,X207 : subst] : ((((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true) | (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) != $true)) | ~ ! [X205 : term,X204 : term] : (($true != ((X201 @ id @ X204 @ id))) | ($true != ((X201 @ id @ X205 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)))) | ($true != ((X201 @ id @ X202 @ id)))) => (! [X215 : (subst > term > subst > $o),X214 : term] : (~ ! [X228 : term,X226 : subst,X225 : subst,X227 : subst] : (($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226)))) | ($true != ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226)))) | ~ ! [X217 : subst,X219 : term,X218 : subst,X216 : subst] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ($true != ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) | ~ ! [X220 : (subst > term > term)] : (~ ! [X224 : term] : (($true = ((X215 @ id @ (X220 @ id @ X224) @ id))) | ($true != ((X215 @ id @ X224 @ id)))) | ~ ! [X221 : subst,X223 : term,X222 : subst] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) = ((sub @ (X220 @ X222 @ X223) @ X221))) | ($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id)))) | ~ ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ($true != ((X215 @ id @ X229 @ id)))) | ($true = ((X215 @ id @ (lam @ X214) @ id)))) => ! [X231 : term,X230 : (subst > term > subst > $o)] : ((((X230 @ id @ X231 @ id)) = $true) | ~ ! [X245 : subst,X244 : term,X246 : subst,X247 : subst] : (($true != ((X230 @ X246 @ X244 @ (comp @ X245 @ X247)))) | (((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) = $true)) | ~ ! [X234 : (subst > term > term)] : (~ ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238)))) | ~ ! [X235 : term] : (($true != ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) | (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) = $true)) | ~ ! [X243 : term] : (($true != ((var @ (sub @ X243 @ id)))) | ($true = ((X230 @ id @ X243 @ id)))) | ~ ! [X233 : term,X232 : term] : (($true != ((X230 @ id @ X232 @ id))) | ($true != ((X230 @ id @ X233 @ id))) | ($true = ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id)))) | ~ ! [X242 : subst,X241 : term,X240 : subst,X239 : subst] : (($true != ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240))) | ($true = ((X230 @ X242 @ X241 @ (comp @ X239 @ X240))))))))) <=> (hoasinduction_lthm = $true)) & (lamnotvar = $true) & (pushprop_lem3v2_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar = $true) & ((hoasinduction = $true) <=> ! [X67 : (subst > term > subst > $o),X66 : term] : (~ ! [X76 : subst,X78 : subst,X77 : subst,X79 : term] : ((((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) = $true) | ($true != ((X67 @ X76 @ X79 @ (comp @ X78 @ X77))))) | ~ ! [X75 : term] : (($true = ((X67 @ id @ X75 @ id))) | ($true != ((var @ (sub @ X75 @ id))))) | ~ ! [X68 : (subst > term > term)] : (~ ! [X72 : term] : (($true != ((X67 @ id @ X72 @ id))) | ($true = ((X67 @ id @ (X68 @ id @ X72) @ id)))) | ~ ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) | ($true = ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id)))) | ($true = ((X67 @ id @ X66 @ id))) | ~ ! [X82 : subst,X81 : subst,X80 : term,X83 : subst] : ((((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) != $true) | ($true = ((X67 @ X82 @ X80 @ (comp @ X81 @ X83))))) | ~ ! [X73 : term,X74 : term] : (($true != ((X67 @ id @ X73 @ id))) | ($true != ((X67 @ id @ X74 @ id))) | ($true = ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))))) & (hoasapnotvar = $true) & (! [X479 : (subst > term > subst > $o)] : ~ ! [X480 : (term > $o)] : ~ ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) <=> (hoasinduction_lem0 = $true)) & (axmap = $true) & ! [X482 : d_term,X483 : d_term] : ((((d2term @ X482)) = ((d2term @ X483))) => (X482 = X483)) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true)),
% 2.19/0.60 inference(flattening,[],[f9])).
% 2.19/0.60 thf(f11,plain,(
% 2.19/0.60 (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X362 : (subst > term > subst > $o)] : ? [X363 : (term > $o)] : ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id)))) & (hoasinduction_lem1v2 = $true) & (axassoc = $true) & (pushprop_lem2v2_lthm = $true) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & (hoasinduction_lem1 = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (? [X539 : term] : (($true = ((X532 @ id @ X539 @ id))) & (((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id)) != $true)) | ? [X534 : (subst > term > term)] : (! [X538 : subst,X537 : subst,X536 : term] : (((sub @ (X534 @ X537 @ X536) @ X538)) = ((X534 @ (comp @ X537 @ X538) @ (sub @ X536 @ X538)))) & ($true != ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id))) & ! [X535 : term] : (($true = ((X532 @ id @ (X534 @ id @ X535) @ id))) | ($true != ((X532 @ id @ X535 @ id))))) | ($true = ((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id))))) & (pushprop_lthm_orig = $true) & ((axshiftcons = $true) <=> ! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424)) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & (pushprop_lthm = $true) & ((induction2lem = $true) <=> ! [X182 : (term > $o),X184 : term,X183 : subst] : ((((X182 @ (sub @ X184 @ X183))) = $true) | ? [X185 : term] : (($true != ((X182 @ (lam @ X185)))) & ! [X186 : term] : (($true != ((X182 @ X186))) | ($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id))))))) | ? [X187 : term] : (($true = ((var @ X187))) & ($true != ((X182 @ (sub @ X187 @ X183))))) | ? [X188 : term,X189 : term] : (($true = ((X182 @ X188))) & ($true != ((X182 @ (ap @ X188 @ X189)))) & ($true = ((X182 @ X189)))))) & (! [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (? [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) != ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525))) | ? [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) != ((sub @ (X523 @ X526 @ X528) @ X527)))) <=> (hoaslaminj = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) <=> (axidr = $true)) & (((d2subst @ d_id)) = sh) & ((laminj = $true) <=> ! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270))) & (ulamvarsh = $true) & (axvarshift = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X432 : term,X434 : (term > $o),X433 : (subst > term > subst > $o)] : (? [X435 : term] : (($true = ((X434 @ X435))) & ($true != ((X434 @ (sub @ X432 @ (push @ X435 @ id)))))) | ? [X437 : subst,X436 : term,X438 : subst,X439 : subst] : (($true != ((X433 @ X439 @ X436 @ (comp @ X438 @ X437)))) & ($true = ((X433 @ (comp @ X439 @ X438) @ (sub @ X436 @ X438) @ X437)))) | ? [X443 : subst,X442 : term,X441 : subst,X440 : subst] : ((((X433 @ (comp @ X441 @ X443) @ (sub @ X442 @ X443) @ X440)) != $true) & (((X433 @ X441 @ X442 @ (comp @ X443 @ X440))) = $true)) | ($true = ((X434 @ (lam @ X432)))) | ? [X444 : (subst > term > term)] : (! [X447 : term,X445 : subst,X446 : subst] : (((X444 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445))) = ((sub @ (X444 @ X446 @ X447) @ X445))) & ($true != ((X433 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X433 @ id @ (X444 @ id @ X448) @ id))) | ($true != ((X433 @ id @ X448 @ id))))) | ? [X449 : term] : (((X433 @ id @ X449 @ id)) != ((X434 @ X449))))) & (! [X427 : term] : ? [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) = ((X428 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & ! [X426 : d_subst] : (d_id = X426) & (hoaslaminj_gthm = $true) & (pushprop = $true) & (! [X161 : term,X163 : (subst > term > subst > $o),X162 : term] : ((((X163 @ id @ X161 @ id)) != $true) | ? [X168 : term,X169 : term] : (($true = ((X163 @ id @ X168 @ id))) & (((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) != $true) & ($true = ((X163 @ id @ X169 @ id)))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ($true != ((X163 @ id @ X162 @ id))) | ? [X165 : term,X167 : subst,X164 : subst,X166 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) != $true) & ($true = ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | ? [X173 : term,X170 : subst,X172 : subst,X171 : subst] : (($true != ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172))) & (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) = $true))) <=> (hoasinduction_lem2 = $true)) & (hoasapnotvar_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179)) | ? [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 != X176) & (((ap @ X177 @ X175)) = ((ap @ X174 @ X176))))) <=> (hoasapinj2_lthm = $true)) & ((pushprop_lem1_lthm = $true) <=> ((! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47)))) | ? [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) != X45)) | ? [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) != X42))) & (one = ((d2term @ d_one))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X285 : (subst > term > subst > $o),X284 : term] : (? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & (((X285 @ id @ X286 @ id)) = $true)) | ? [X287 : (subst > term > term)] : (! [X289 : subst,X290 : term,X288 : subst] : (((X287 @ (comp @ X288 @ X289) @ (sub @ X290 @ X289))) = ((sub @ (X287 @ X288 @ X290) @ X289))) & ! [X291 : term] : (($true != ((X285 @ id @ X291 @ id))) | (((X285 @ id @ (X287 @ id @ X291) @ id)) = $true)) & ($true != ((X285 @ id @ (lam @ (X287 @ sh @ one)) @ id)))) | (((X285 @ id @ (lam @ X284) @ id)) = $true)) | ? [X276 : (subst > term > subst > $o),X277 : term] : ((((X276 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id)) != $true) & ! [X278 : term] : ((((X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) = $true) | ($true != ((X276 @ id @ X278 @ id)))) & ! [X279 : (subst > term > term)] : (($true = ((X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X282 : subst,X283 : term,X281 : subst] : (((X279 @ (comp @ X281 @ X282) @ (sub @ X283 @ X282))) != ((sub @ (X279 @ X281 @ X283) @ X282))) | ? [X280 : term] : (($true = ((X276 @ id @ X280 @ id))) & ($true != ((X276 @ id @ (X279 @ id @ X280) @ id))))))) | ? [X275 : term] : (((sub @ X275 @ id)) != X275))) & (lamnotap != $true) & ((shinj = $true) <=> ! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh))))) & (hoasinduction_lem1v2_gthm = $true) & (induction2lem_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((d2subst @ d_id)) = id) & ((substmonoid_lthm = $true) <=> (((! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503)) | ? [X501 : subst] : (((comp @ X501 @ id)) != X501)) | ? [X500 : subst] : (((comp @ id @ X500)) != X500))) & (! [X484 : term,X485 : (subst > term > subst > $o)] : (? [X499 : term] : ((((X485 @ id @ (sub @ X484 @ (push @ X499 @ id)) @ id)) != $true) & ($true = ((X485 @ id @ X499 @ id)))) | ($true = ((X485 @ id @ (lam @ X484) @ id))) | ? [X488 : subst,X486 : subst,X489 : subst,X487 : term] : (($true != ((X485 @ X486 @ X487 @ (comp @ X488 @ X489)))) & ($true = ((X485 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X489)))) | ? [X494 : (subst > term > term)] : (($true != ((X485 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X498 : term] : (($true = ((X485 @ id @ (X494 @ id @ X498) @ id))) | ($true != ((X485 @ id @ X498 @ id)))) & ! [X495 : term,X497 : subst,X496 : subst] : (((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497))) = ((sub @ (X494 @ X496 @ X495) @ X497)))) | ? [X492 : subst,X493 : subst,X490 : subst,X491 : term] : ((((X485 @ (comp @ X492 @ X490) @ (sub @ X491 @ X490) @ X493)) != $true) & ($true = ((X485 @ X492 @ X491 @ (comp @ X490 @ X493)))))) <=> (hoasinduction_lem3 = $true)) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) <=> (termmset = $true)) & (((((! [X31 : term,X30 : (term > $o),X29 : subst] : (? [X35 : term] : (! [X36 : term] : (($true != ((X30 @ X36))) | ($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id)))))) & (((X30 @ (lam @ X35))) != $true)) | ? [X32 : term] : (($true = ((var @ X32))) & ($true != ((X30 @ (sub @ X32 @ X29))))) | ? [X34 : term,X33 : term] : (($true = ((X30 @ X33))) & ($true = ((X30 @ X34))) & ($true != ((X30 @ (ap @ X34 @ X33))))) | ($true = ((X30 @ (sub @ X31 @ X29))))) | ? [X24 : (term > $o),X23 : term] : (! [X25 : term] : ((((X24 @ X25)) != $true) | ($true = ((X24 @ (lam @ X25))))) & ! [X27 : term,X28 : term] : (($true = ((X24 @ (ap @ X28 @ X27)))) | ($true != ((X24 @ X27))) | ($true != ((X24 @ X28)))) & ($true != ((X24 @ X23))) & ! [X26 : term] : (($true = ((X24 @ X26))) | ($true != ((var @ X26)))))) | ? [X22 : subst] : (((comp @ X22 @ id)) != X22)) | ? [X20 : subst,X21 : term] : (((comp @ sh @ (push @ X21 @ X20))) != X20)) | ? [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) != X19)) <=> (induction2lem_lthm = $true)) & (substmonoid_gthm = $true) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (pushprop_gthm = $true) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) <=> (substmonoid = $true)) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & (! [X14 : (term > $o),X15 : subst,X13 : term] : ? [X16 : (term > $o)] : ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))) <=> (pushprop_lem0_lthm = $true)) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) != ((d2subst @ X271))) | (X271 = X272)) & (hoaslamnotvar_gthm = $true) & (! [X504 : term,X505 : (subst > term > subst > $o)] : (? [X511 : term] : ((((X505 @ id @ (sub @ X504 @ (push @ X511 @ id)) @ id)) != $true) & ($true = ((X505 @ id @ X511 @ id)))) | ($true = ((X505 @ id @ (lam @ X504) @ id))) | ? [X506 : (subst > term > term)] : (! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X506 @ X508 @ X509) @ X507)) = ((X506 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) & ! [X510 : term] : (($true = ((X505 @ id @ (X506 @ id @ X510) @ id))) | ($true != ((X505 @ id @ X510 @ id)))) & ($true != ((X505 @ id @ (lam @ (X506 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3a = $true)) & ! [X423 : d_term] : (d_one = X423) & (axapp = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (axabs = $true) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (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)))))))))))) & (apnotvar = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X134 : (subst > term > subst > $o),X133 : term] : ((((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ? [X135 : term] : (($true != ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) & (((X134 @ id @ X135 @ id)) = $true)) | ? [X136 : (subst > term > term)] : (! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) & ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ($true != ((X134 @ id @ X137 @ id)))) & (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) != $true)))) & (hoasinduction_lem2_lthm = $true) & ((pushprop_lem1v2 = $true) <=> ! [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) != $true) | ($true = ((X39 @ one))) | ? [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) != ((X39 @ X41))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X475 : term] : ? [X476 : (subst > term > term)] : ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477)))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true = ((X368 @ one))) | ($true != ((X370 @ X369))) | ? [X371 : term] : (((X368 @ X371)) != ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) | ? [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) != X366))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lthm_3 = $true) <=> ((((! [X405 : (subst > term > subst > $o),X406 : term] : (? [X416 : term,X417 : term] : ((((X405 @ id @ (ap @ (sub @ X416 @ id) @ X417) @ id)) != $true) & ($true = ((X405 @ id @ X416 @ id))) & ($true = ((X405 @ id @ X417 @ id)))) | ? [X411 : term] : (($true != ((X405 @ id @ X411 @ id))) & ($true = ((var @ (sub @ X411 @ id))))) | ? [X410 : subst,X409 : subst,X407 : subst,X408 : term] : (($true = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407) @ X410))) & ($true != ((X405 @ X409 @ X408 @ (comp @ X407 @ X410))))) | ? [X413 : subst,X414 : subst,X415 : term,X412 : subst] : (($true != ((X405 @ (comp @ X414 @ X413) @ (sub @ X415 @ X413) @ X412))) & ($true = ((X405 @ X414 @ X415 @ (comp @ X413 @ X412))))) | ? [X418 : (subst > term > term)] : (! [X422 : subst,X420 : subst,X421 : term] : (((X418 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X418 @ X422 @ X421) @ X420))) & ($true != ((X405 @ id @ (lam @ (X418 @ sh @ one)) @ id))) & ! [X419 : term] : ((((X405 @ id @ (X418 @ id @ X419) @ id)) = $true) | ($true != ((X405 @ id @ X419 @ id))))) | ($true = ((X405 @ id @ X406 @ id)))) | ? [X396 : term,X395 : (subst > term > subst > $o),X397 : (term > $o)] : (! [X398 : (subst > term > term)] : (($true = ((X395 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ? [X402 : term] : ((((X395 @ id @ (X398 @ id @ X402) @ id)) != $true) & ($true = ((X395 @ id @ X402 @ id)))) | ? [X400 : term,X401 : subst,X399 : subst] : (((X398 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X398 @ X401 @ X400) @ X399)))) & ($true != ((X397 @ (lam @ X396)))) & ! [X403 : term] : (($true = ((X397 @ (sub @ X396 @ (push @ X403 @ id))))) | ($true != ((X397 @ X403)))) & ! [X404 : term] : (((X397 @ X404)) = ((X395 @ id @ X404 @ id))))) | ? [X394 : term] : (((sub @ X394 @ id)) != X394)) | ? [X387 : term,X388 : (term > $o)] : (! [X391 : term] : ((((X388 @ X391)) = $true) | (((var @ X391)) != $true)) & ! [X389 : term] : (($true = ((X388 @ (lam @ X389)))) | ? [X390 : term] : ((((X388 @ X390)) = $true) & ($true != ((X388 @ (sub @ X389 @ (push @ X390 @ id))))))) & ($true != ((X388 @ X387))) & ! [X393 : term,X392 : term] : ((((X388 @ (ap @ X392 @ X393))) = $true) | ($true != ((X388 @ X392))) | (((X388 @ X393)) != $true)))) | ? [X384 : (subst > term > subst > $o)] : ! [X385 : (term > $o)] : ? [X386 : term] : (((X385 @ X386)) != ((X384 @ id @ X386 @ id))))) & (((((! [X125 : (subst > term > subst > $o),X124 : term] : (($true = ((X125 @ id @ X124 @ id))) | ? [X132 : term,X131 : term] : (($true = ((X125 @ id @ X131 @ id))) & ($true != ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X125 @ id @ X132 @ id)))) | ? [X126 : (subst > term > term)] : (($true != ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id))) & ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) & ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ($true != ((X125 @ id @ X127 @ id)))))) | ? [X116 : (subst > term > subst > $o),X115 : term,X114 : (term > $o)] : (! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | (((X114 @ X117)) != $true)) & ($true != ((X114 @ (lam @ X115)))) & ! [X119 : (subst > term > term)] : (($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id))) | ? [X123 : term] : (($true = ((X116 @ id @ X123 @ id))) & ($true != ((X116 @ id @ (X119 @ id @ X123) @ id)))) | ? [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) != ((sub @ (X119 @ X121 @ X122) @ X120)))) & ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113)) | ? [X106 : term,X107 : (term > $o)] : (! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ? [X110 : term] : (($true != ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) & ($true = ((X107 @ X110))))) & ! [X112 : term,X111 : term] : (($true != ((X107 @ X112))) | ($true != ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111))))) & ($true != ((X107 @ X106))) & ! [X108 : term] : (($true = ((X107 @ X108))) | ($true != ((var @ X108)))))) | ? [X103 : (subst > term > subst > $o)] : ! [X104 : (term > $o)] : ? [X105 : term] : (((X104 @ X105)) != ((X103 @ id @ X105 @ id)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (! [X152 : (term > $o),X153 : (subst > term > subst > $o),X151 : term] : (? [X154 : term] : (((X152 @ X154)) != ((X153 @ id @ X154 @ id))) | ? [X160 : term] : (($true != ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) & ($true = ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true) | ? [X155 : (subst > term > term)] : (! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) & ! [X159 : term] : (($true = ((X153 @ id @ (X155 @ id @ X159) @ id))) | (((X153 @ id @ X159 @ id)) != $true)) & ($true != ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem3a_gthm = $true) & (((! [X324 : (term > $o),X323 : term] : (($true = ((X324 @ X323))) | ? [X327 : term,X328 : term] : ((((X324 @ (ap @ X328 @ X327))) != $true) & ($true = ((X324 @ X327))) & ($true = ((X324 @ X328)))) | ? [X329 : term] : (($true != ((X324 @ X329))) & (((var @ X329)) = $true)) | ? [X325 : term] : (! [X326 : term] : (($true = ((X324 @ (sub @ X325 @ (push @ X326 @ id))))) | ($true != ((X324 @ X326)))) & ($true != ((X324 @ (lam @ X325)))))) | ? [X317 : term,X316 : subst,X315 : (term > $o)] : (! [X320 : term] : (($true != ((var @ X320))) | ($true = ((X315 @ (sub @ X320 @ X316))))) & ($true != ((X315 @ (sub @ X317 @ X316)))) & ! [X321 : term] : (? [X322 : term] : (($true = ((X315 @ X322))) & (((X315 @ (sub @ X321 @ (push @ X322 @ id)))) != $true)) | (((X315 @ (lam @ X321))) = $true)) & ! [X318 : term,X319 : term] : (($true != ((X315 @ X318))) | (((X315 @ X319)) != $true) | ($true = ((X315 @ (ap @ X318 @ X319))))))) | ? [X314 : term] : (((sub @ X314 @ id)) != X314)) <=> (induction2_lthm = $true)) & (! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : term,X515 : term] : (($true != ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) & ($true = ((X512 @ id @ X514 @ id))) & ($true = ((X512 @ id @ X515 @ id)))) | ? [X516 : (subst > term > term)] : ((((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id)) != $true) & ! [X517 : term] : ((((X512 @ id @ (X516 @ id @ X517) @ id)) = $true) | ($true != ((X512 @ id @ X517 @ id)))) & ! [X519 : term,X518 : subst,X520 : subst] : (((sub @ (X516 @ X518 @ X519) @ X520)) = ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520))))) | ($true = ((X512 @ id @ X513 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((((! [X302 : (subst > term > term),X301 : (subst > term > term),X300 : subst,X303 : term] : ((((X302 @ X300 @ X303)) = ((X301 @ X300 @ X303))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X301 @ sh @ one)))) | ? [X305 : term,X306 : subst,X304 : subst] : (((X301 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))) != ((sub @ (X301 @ X304 @ X305) @ X306))) | ? [X309 : term,X307 : subst,X308 : subst] : (((X302 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307))) != ((sub @ (X302 @ X308 @ X309) @ X307)))) | ? [X299 : term,X298 : term] : ((((lam @ X299)) = ((lam @ X298))) & (X298 != X299))) | ? [X296 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X296))) != X296)) | ? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294)) <=> (hoaslaminj_lthm = $true)) & (axclos = $true) & ((induction = $true) <=> ! [X357 : term,X356 : (term > $o)] : (($true = ((X356 @ X357))) | ? [X359 : term,X360 : term] : (($true != ((X356 @ (ap @ X359 @ X360)))) & ($true = ((X356 @ X360))) & (((X356 @ X359)) = $true)) | ? [X358 : term] : (($true != ((X356 @ (lam @ X358)))) & ($true = ((X356 @ X358)))) | ? [X361 : term] : ((((X356 @ X361)) != $true) & ($true = ((var @ X361)))))) & (hoasinduction_gthm = $true) & (hoaslamnotap_lthm = $true) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem1_gthm = $true) & (((var @ (d2term @ d_one))) != $true) & (((! [X459 : term,X460 : (subst > term > subst > $o)] : (? [X466 : subst,X467 : subst,X468 : term,X469 : subst] : (($true != ((X460 @ (comp @ X467 @ X466) @ (sub @ X468 @ X466) @ X469))) & ($true = ((X460 @ X467 @ X468 @ (comp @ X466 @ X469))))) | ? [X461 : (subst > term > term)] : (($true != ((X460 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : (($true != ((X460 @ id @ X462 @ id))) | ($true = ((X460 @ id @ (X461 @ id @ X462) @ id)))) & ! [X464 : term,X463 : subst,X465 : subst] : (((sub @ (X461 @ X463 @ X464) @ X465)) = ((X461 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465))))) | ($true = ((X460 @ id @ (lam @ X459) @ id))) | ? [X470 : term] : (($true != ((X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id))) & ($true = ((X460 @ id @ X470 @ id)))) | ? [X471 : subst,X474 : term,X472 : subst,X473 : subst] : ((((X460 @ X471 @ X474 @ (comp @ X472 @ X473))) != $true) & ($true = ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473))))) | ? [X452 : (subst > term > subst > $o),X451 : term] : (($true != ((X452 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id))) & ! [X454 : (subst > term > term)] : (? [X458 : term] : (($true = ((X452 @ id @ X458 @ id))) & ($true != ((X452 @ id @ (X454 @ id @ X458) @ id)))) | (((X452 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X456 : subst,X457 : term,X455 : subst] : (((sub @ (X454 @ X455 @ X457) @ X456)) != ((X454 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456))))) & ! [X453 : term] : (($true != ((X452 @ id @ X453 @ id))) | ($true = ((X452 @ id @ (sub @ X451 @ (push @ X453 @ id)) @ id)))))) | ? [X450 : term] : (((sub @ X450 @ id)) != X450)) <=> (hoasinduction_lem3_lthm = $true)) & (! [X345 : term,X346 : (term > $o)] : (($true = ((X346 @ X345))) | ? [X347 : term] : (($true = ((var @ X347))) & ($true != ((X346 @ X347)))) | ? [X350 : term] : ((((X346 @ (lam @ X350))) != $true) & ! [X351 : term] : (($true = ((X346 @ (sub @ X350 @ (push @ X351 @ id))))) | ($true != ((X346 @ X351))))) | ? [X348 : term,X349 : term] : (($true = ((X346 @ X349))) & ($true = ((X346 @ X348))) & ($true != ((X346 @ (ap @ X349 @ X348)))))) <=> (induction2 = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X292 : term] : ? [X293 : (subst > term > term)] : (((X293 @ sh @ one)) = ((sub @ X292 @ (push @ one @ sh))))) & (! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) <=> (pushprop_lem1 = $true)) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & ((axscons = $true) <=> ! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431)) & (hoasinduction_lem3b_gthm = $true) & ((hoasinduction_lem3aaa = $true) <=> ! [X373 : (subst > term > subst > $o),X372 : term] : (? [X375 : (subst > term > term),X376 : term] : (($true != ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X380 : subst,X379 : subst,X378 : term] : (((sub @ X376 @ (push @ (sub @ X378 @ X380) @ (comp @ X379 @ X380)))) = ((X375 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380)))) & ! [X377 : term] : (($true = ((X373 @ id @ (X375 @ id @ X377) @ id))) | ($true != ((X373 @ id @ X377 @ id)))) & ! [X381 : subst,X383 : subst,X382 : term] : (((sub @ (X375 @ X383 @ X382) @ X381)) = ((sub @ (sub @ X376 @ (push @ X382 @ X383)) @ X381)))) | ? [X374 : term] : (($true = ((X373 @ id @ X374 @ id))) & ($true != ((X373 @ id @ (sub @ X372 @ (push @ X374 @ id)) @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X372 @ (push @ one @ sh))) @ id))))) & (pushprop_lem3v2 = $true) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (! [X332 : (subst > term > subst > $o),X333 : (term > $o),X331 : term,X330 : term] : (($true != ((X333 @ X330))) | ? [X336 : subst,X335 : subst,X334 : subst,X337 : term] : ((((X332 @ (comp @ X334 @ X335) @ (sub @ X337 @ X335) @ X336)) != $true) & ($true = ((X332 @ X334 @ X337 @ (comp @ X335 @ X336))))) | ? [X344 : term] : (((X333 @ X344)) != ((X332 @ id @ X344 @ id))) | ? [X342 : term,X343 : term] : (($true = ((X332 @ id @ X343 @ id))) & ($true != ((X332 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id))) & (((X332 @ id @ X342 @ id)) = $true)) | ? [X338 : subst,X339 : subst,X340 : term,X341 : subst] : (($true != ((X332 @ X341 @ X340 @ (comp @ X339 @ X338)))) & (((X332 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339) @ X338)) = $true)) | (((X333 @ (ap @ X331 @ X330))) = $true) | (((X333 @ X331)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147)))) | ? [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 != X146) & (((ap @ X145 @ X144)) = ((ap @ X146 @ X143))))) | ? [X142 : term] : (((sub @ X142 @ id)) != X142))) & ((hoasapinj2 = $true) <=> ! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313))))) & (! [X10 : (term > $o),X8 : term,X9 : subst] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (hoasapinj2_gthm = $true) & (hoasinduction_lem1_gthm = $true) & (ulamvarind = $true) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X250 : term] : (((sub @ X250 @ id)) != X250) | ! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o)] : (? [X267 : subst,X266 : subst,X265 : subst,X268 : term] : ((((X253 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) != $true) & (((X253 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true)) | ? [X255 : term] : (($true != ((X251 @ (sub @ X252 @ (push @ X255 @ id))))) & (((X251 @ X255)) = $true)) | ($true = ((X251 @ (lam @ X252)))) | ? [X256 : (subst > term > term)] : (! [X257 : subst,X259 : subst,X258 : term] : (((X256 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X257 @ X258) @ X259))) & ! [X260 : term] : ((((X253 @ id @ X260 @ id)) != $true) | ($true = ((X253 @ id @ (X256 @ id @ X260) @ id)))) & ($true != ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id)))) | ? [X264 : term,X263 : subst,X262 : subst,X261 : subst] : (($true = ((X253 @ (comp @ X262 @ X261) @ (sub @ X264 @ X261) @ X263))) & (((X253 @ X262 @ X264 @ (comp @ X261 @ X263))) != $true)) | ? [X254 : term] : (((X251 @ X254)) != ((X253 @ id @ X254 @ id)))))) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X58 : term,X56 : (term > $o),X57 : (subst > term > subst > $o)] : (? [X64 : term] : (($true = ((X56 @ X64))) & ($true != ((X56 @ (sub @ X58 @ (push @ X64 @ id)))))) | ? [X59 : (subst > term > term)] : ((((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) != $true) & ! [X60 : term] : (($true = ((X57 @ id @ (X59 @ id @ X60) @ id))) | ($true != ((X57 @ id @ X60 @ id)))) & ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63))))) | ($true = ((X56 @ (lam @ X58)))) | ? [X65 : term] : (((X57 @ id @ X65 @ id)) != ((X56 @ X65)))) | ? [X55 : term] : (((sub @ X55 @ id)) != X55)) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X53 : term,X54 : subst] : (((sub @ X51 @ (push @ X53 @ X54))) != ((X52 @ X54 @ X53))))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & (! [X4 : term,X2 : term,X3 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) != ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (hoasapinj1_gthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (pushprop_lem1v2_gthm = $true) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (termmset_gthm = $true) & (induction2_gthm = $true) & (pushprop_lem2v2 = $true) & ((((! [X231 : term,X230 : (subst > term > subst > $o)] : (? [X241 : term,X240 : subst,X242 : subst,X239 : subst] : (($true = ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240))) & ($true != ((X230 @ X242 @ X241 @ (comp @ X239 @ X240))))) | ? [X247 : subst,X245 : subst,X244 : term,X246 : subst] : ((((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) != $true) & ($true = ((X230 @ X246 @ X244 @ (comp @ X245 @ X247))))) | (((X230 @ id @ X231 @ id)) = $true) | ? [X232 : term,X233 : term] : (($true = ((X230 @ id @ X233 @ id))) & ($true != ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id))) & ($true = ((X230 @ id @ X232 @ id)))) | ? [X234 : (subst > term > term)] : (! [X235 : term] : (($true != ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) & (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) != $true) & ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ? [X243 : term] : (($true = ((var @ (sub @ X243 @ id)))) & ($true != ((X230 @ id @ X243 @ id))))) | ? [X215 : (subst > term > subst > $o),X214 : term] : (($true != ((X215 @ id @ (lam @ X214) @ id))) & ! [X217 : subst,X219 : term,X218 : subst,X216 : subst] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ($true != ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) & ! [X228 : term,X226 : subst,X225 : subst,X227 : subst] : (($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226)))) | ($true != ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226)))) & ! [X220 : (subst > term > term)] : (? [X224 : term] : (($true != ((X215 @ id @ (X220 @ id @ X224) @ id))) & ($true = ((X215 @ id @ X224 @ id)))) | ($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ? [X221 : subst,X222 : subst,X223 : term] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) != ((sub @ (X220 @ X222 @ X223) @ X221)))) & ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ($true != ((X215 @ id @ X229 @ id)))))) | ? [X203 : term,X201 : (subst > term > subst > $o),X202 : term] : ((((X201 @ id @ X203 @ id)) = $true) & ($true = ((X201 @ id @ X202 @ id))) & (((X201 @ id @ (ap @ X202 @ X203) @ id)) != $true) & ! [X211 : subst,X212 : subst,X213 : term,X210 : subst] : (($true != ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210)))) & ! [X208 : subst,X209 : subst,X206 : term,X207 : subst] : ((((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true) | (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) != $true)) & ! [X205 : term,X204 : term] : (($true != ((X201 @ id @ X204 @ id))) | ($true != ((X201 @ id @ X205 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)))))) | ? [X195 : (term > $o),X194 : term] : (! [X197 : term,X196 : term] : (($true != ((X195 @ X196))) | ($true = ((X195 @ (ap @ X196 @ X197)))) | ($true != ((X195 @ X197)))) & ! [X200 : term] : (($true = ((X195 @ X200))) | ($true != ((var @ X200)))) & (((X195 @ X194)) != $true) & ! [X198 : term] : (? [X199 : term] : ((((X195 @ X199)) = $true) & ($true != ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true)))) <=> (hoasinduction_lthm = $true)) & (lamnotvar = $true) & (pushprop_lem3v2_lthm = $true) & (hoasapnotvar_lthm = $true) & (hoaslamnotvar = $true) & ((hoasinduction = $true) <=> ! [X67 : (subst > term > subst > $o),X66 : term] : (? [X76 : subst,X78 : subst,X77 : subst,X79 : term] : ((((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) != $true) & ($true = ((X67 @ X76 @ X79 @ (comp @ X78 @ X77))))) | ? [X75 : term] : (($true != ((X67 @ id @ X75 @ id))) & ($true = ((var @ (sub @ X75 @ id))))) | ? [X83 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)))) & (((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) = $true)) | ($true = ((X67 @ id @ X66 @ id))) | ? [X68 : (subst > term > term)] : (! [X72 : term] : (($true != ((X67 @ id @ X72 @ id))) | ($true = ((X67 @ id @ (X68 @ id @ X72) @ id)))) & ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) & ($true != ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id)))) | ? [X74 : term,X73 : term] : (($true = ((X67 @ id @ X73 @ id))) & ($true = ((X67 @ id @ X74 @ id))) & ($true != ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))))) & (hoasapnotvar = $true) & (! [X479 : (subst > term > subst > $o)] : ? [X480 : (term > $o)] : ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) <=> (hoasinduction_lem0 = $true)) & (axmap = $true) & ! [X483 : d_term,X482 : d_term] : ((X482 = X483) | (((d2term @ X482)) != ((d2term @ X483)))) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) <=> (axidl = $true)) & (hoaslamnotap_gthm = $true)),
% 2.19/0.60 inference(ennf_transformation,[],[f10])).
% 2.19/0.60 thf(f12,plain,(
% 2.19/0.60 (pushprop = $true) & ((axshiftcons = $true) <=> ! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424)) & (axmap = $true) & ((hoasinduction_lem3aa = $true) <=> ! [X134 : (subst > term > subst > $o),X133 : term] : ((((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ? [X135 : term] : (($true != ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) & (((X134 @ id @ X135 @ id)) = $true)) | ? [X136 : (subst > term > term)] : (! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) & ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ($true != ((X134 @ id @ X137 @ id)))) & (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) != $true)))) & (axapp = $true) & ((axscons = $true) <=> ! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431)) & ((shinj = $true) <=> ! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X483 : d_term,X482 : d_term] : ((X482 = X483) | (((d2term @ X482)) != ((d2term @ X483)))) & (hoasinduction_lem1_lthm = $true) & (! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (! [X152 : (term > $o),X153 : (subst > term > subst > $o),X151 : term] : (? [X154 : term] : (((X152 @ X154)) != ((X153 @ id @ X154 @ id))) | ? [X160 : term] : (($true != ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) & ($true = ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true) | ? [X155 : (subst > term > term)] : (! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) & ! [X159 : term] : (($true = ((X153 @ id @ (X155 @ id @ X159) @ id))) | (((X153 @ id @ X159 @ id)) != $true)) & ($true != ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3v2a = $true)) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & ((hoasinduction_lem3aaa = $true) <=> ! [X373 : (subst > term > subst > $o),X372 : term] : (? [X375 : (subst > term > term),X376 : term] : (($true != ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X380 : subst,X379 : subst,X378 : term] : (((sub @ X376 @ (push @ (sub @ X378 @ X380) @ (comp @ X379 @ X380)))) = ((X375 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380)))) & ! [X377 : term] : (($true = ((X373 @ id @ (X375 @ id @ X377) @ id))) | ($true != ((X373 @ id @ X377 @ id)))) & ! [X381 : subst,X383 : subst,X382 : term] : (((sub @ (X375 @ X383 @ X382) @ X381)) = ((sub @ (sub @ X376 @ (push @ X382 @ X383)) @ X381)))) | ? [X374 : term] : (($true = ((X373 @ id @ X374 @ id))) & ($true != ((X373 @ id @ (sub @ X372 @ (push @ X374 @ id)) @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X372 @ (push @ one @ sh))) @ id))))) & (hoasinduction_lem3a_gthm = $true) & ((induction = $true) <=> ! [X357 : term,X356 : (term > $o)] : (($true = ((X356 @ X357))) | ? [X359 : term,X360 : term] : (($true != ((X356 @ (ap @ X359 @ X360)))) & ($true = ((X356 @ X360))) & (((X356 @ X359)) = $true)) | ? [X358 : term] : (($true != ((X356 @ (lam @ X358)))) & ($true = ((X356 @ X358)))) | ? [X361 : term] : ((((X356 @ X361)) != $true) & ($true = ((var @ X361)))))) & (! [X427 : term] : ? [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) = ((X428 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (! [X161 : term,X163 : (subst > term > subst > $o),X162 : term] : ((((X163 @ id @ X161 @ id)) != $true) | ? [X168 : term,X169 : term] : (($true = ((X163 @ id @ X168 @ id))) & (((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) != $true) & ($true = ((X163 @ id @ X169 @ id)))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ($true != ((X163 @ id @ X162 @ id))) | ? [X165 : term,X167 : subst,X164 : subst,X166 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) != $true) & ($true = ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | ? [X173 : term,X170 : subst,X172 : subst,X171 : subst] : (($true != ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172))) & (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) = $true))) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X58 : term,X56 : (term > $o),X57 : (subst > term > subst > $o)] : (? [X64 : term] : (($true = ((X56 @ X64))) & ($true != ((X56 @ (sub @ X58 @ (push @ X64 @ id)))))) | ? [X59 : (subst > term > term)] : ((((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) != $true) & ! [X60 : term] : (($true = ((X57 @ id @ (X59 @ id @ X60) @ id))) | ($true != ((X57 @ id @ X60 @ id)))) & ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63))))) | ($true = ((X56 @ (lam @ X58)))) | ? [X65 : term] : (((X57 @ id @ X65 @ id)) != ((X56 @ X65)))) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X53 : term,X54 : subst] : (((sub @ X51 @ (push @ X53 @ X54))) != ((X52 @ X54 @ X53))) | ? [X55 : term] : (((sub @ X55 @ id)) != X55))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true = ((X368 @ one))) | ($true != ((X370 @ X369))) | ? [X371 : term] : (((X368 @ X371)) != ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) | ? [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) != X366))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (? [X539 : term] : (($true = ((X532 @ id @ X539 @ id))) & (((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id)) != $true)) | ? [X534 : (subst > term > term)] : (! [X538 : subst,X537 : subst,X536 : term] : (((sub @ (X534 @ X537 @ X536) @ X538)) = ((X534 @ (comp @ X537 @ X538) @ (sub @ X536 @ X538)))) & ($true != ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id))) & ! [X535 : term] : (($true = ((X532 @ id @ (X534 @ id @ X535) @ id))) | ($true != ((X532 @ id @ X535 @ id))))) | ($true = ((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id))))) & ! [X423 : d_term] : (d_one = X423) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) <=> (substmonoid = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) <=> (axidr = $true)) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & ((! [X125 : (subst > term > subst > $o),X124 : term] : (($true = ((X125 @ id @ X124 @ id))) | ? [X132 : term,X131 : term] : (($true = ((X125 @ id @ X131 @ id))) & ($true != ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X125 @ id @ X132 @ id)))) | ? [X126 : (subst > term > term)] : (($true != ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id))) & ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) & ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ($true != ((X125 @ id @ X127 @ id)))))) | ? [X103 : (subst > term > subst > $o)] : ! [X104 : (term > $o)] : ? [X105 : term] : (((X104 @ X105)) != ((X103 @ id @ X105 @ id))) | ? [X116 : (subst > term > subst > $o),X115 : term,X114 : (term > $o)] : (! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | (((X114 @ X117)) != $true)) & ($true != ((X114 @ (lam @ X115)))) & ! [X119 : (subst > term > term)] : (($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id))) | ? [X123 : term] : (($true = ((X116 @ id @ X123 @ id))) & ($true != ((X116 @ id @ (X119 @ id @ X123) @ id)))) | ? [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) != ((sub @ (X119 @ X121 @ X122) @ X120)))) & ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id)))) | ? [X113 : term] : (((sub @ X113 @ id)) != X113) | ? [X106 : term,X107 : (term > $o)] : (! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ? [X110 : term] : (($true != ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) & ($true = ((X107 @ X110))))) & ! [X112 : term,X111 : term] : (($true != ((X107 @ X112))) | ($true != ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111))))) & ($true != ((X107 @ X106))) & ! [X108 : term] : (($true = ((X107 @ X108))) | ($true != ((var @ X108)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasapinj1_gthm = $true) & (! [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (? [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) != ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525))) | ? [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) != ((sub @ (X523 @ X526 @ X528) @ X527)))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X250 : term] : (((sub @ X250 @ id)) != X250) | ! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o)] : (? [X267 : subst,X266 : subst,X265 : subst,X268 : term] : ((((X253 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) != $true) & (((X253 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true)) | ? [X255 : term] : (($true != ((X251 @ (sub @ X252 @ (push @ X255 @ id))))) & (((X251 @ X255)) = $true)) | ($true = ((X251 @ (lam @ X252)))) | ? [X256 : (subst > term > term)] : (! [X257 : subst,X259 : subst,X258 : term] : (((X256 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X257 @ X258) @ X259))) & ! [X260 : term] : ((((X253 @ id @ X260 @ id)) != $true) | ($true = ((X253 @ id @ (X256 @ id @ X260) @ id)))) & ($true != ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id)))) | ? [X264 : term,X263 : subst,X262 : subst,X261 : subst] : (($true = ((X253 @ (comp @ X262 @ X261) @ (sub @ X264 @ X261) @ X263))) & (((X253 @ X262 @ X264 @ (comp @ X261 @ X263))) != $true)) | ? [X254 : term] : (((X251 @ X254)) != ((X253 @ id @ X254 @ id)))))) & (! [X504 : term,X505 : (subst > term > subst > $o)] : (? [X511 : term] : ((((X505 @ id @ (sub @ X504 @ (push @ X511 @ id)) @ id)) != $true) & ($true = ((X505 @ id @ X511 @ id)))) | ($true = ((X505 @ id @ (lam @ X504) @ id))) | ? [X506 : (subst > term > term)] : (! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X506 @ X508 @ X509) @ X507)) = ((X506 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) & ! [X510 : term] : (($true = ((X505 @ id @ (X506 @ id @ X510) @ id))) | ($true != ((X505 @ id @ X510 @ id)))) & ($true != ((X505 @ id @ (lam @ (X506 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3a = $true)) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & (lamnotvar = $true) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47)))) | ? [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) != X42) | ? [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) != X45)) <=> (pushprop_lem1_lthm = $true)) & (((d2subst @ d_id)) = sh) & ((laminj = $true) <=> ! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (! [X332 : (subst > term > subst > $o),X333 : (term > $o),X331 : term,X330 : term] : (($true != ((X333 @ X330))) | ? [X336 : subst,X335 : subst,X334 : subst,X337 : term] : ((((X332 @ (comp @ X334 @ X335) @ (sub @ X337 @ X335) @ X336)) != $true) & ($true = ((X332 @ X334 @ X337 @ (comp @ X335 @ X336))))) | ? [X344 : term] : (((X333 @ X344)) != ((X332 @ id @ X344 @ id))) | ? [X342 : term,X343 : term] : (($true = ((X332 @ id @ X343 @ id))) & ($true != ((X332 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id))) & (((X332 @ id @ X342 @ id)) = $true)) | ? [X338 : subst,X339 : subst,X340 : term,X341 : subst] : (($true != ((X332 @ X341 @ X340 @ (comp @ X339 @ X338)))) & (((X332 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339) @ X338)) = $true)) | (((X333 @ (ap @ X331 @ X330))) = $true) | (((X333 @ X331)) != $true)) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) != ((d2subst @ X271))) | (X271 = X272)) & (! [X484 : term,X485 : (subst > term > subst > $o)] : (? [X499 : term] : ((((X485 @ id @ (sub @ X484 @ (push @ X499 @ id)) @ id)) != $true) & ($true = ((X485 @ id @ X499 @ id)))) | ($true = ((X485 @ id @ (lam @ X484) @ id))) | ? [X488 : subst,X486 : subst,X489 : subst,X487 : term] : (($true != ((X485 @ X486 @ X487 @ (comp @ X488 @ X489)))) & ($true = ((X485 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X489)))) | ? [X494 : (subst > term > term)] : (($true != ((X485 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X498 : term] : (($true = ((X485 @ id @ (X494 @ id @ X498) @ id))) | ($true != ((X485 @ id @ X498 @ id)))) & ! [X495 : term,X497 : subst,X496 : subst] : (((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497))) = ((sub @ (X494 @ X496 @ X495) @ X497)))) | ? [X492 : subst,X493 : subst,X490 : subst,X491 : term] : ((((X485 @ (comp @ X492 @ X490) @ (sub @ X491 @ X490) @ X493)) != $true) & ($true = ((X485 @ X492 @ X491 @ (comp @ X490 @ X493)))))) <=> (hoasinduction_lem3 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & ((? [X387 : term,X388 : (term > $o)] : (! [X391 : term] : ((((X388 @ X391)) = $true) | (((var @ X391)) != $true)) & ! [X389 : term] : (($true = ((X388 @ (lam @ X389)))) | ? [X390 : term] : ((((X388 @ X390)) = $true) & ($true != ((X388 @ (sub @ X389 @ (push @ X390 @ id))))))) & ($true != ((X388 @ X387))) & ! [X393 : term,X392 : term] : ((((X388 @ (ap @ X392 @ X393))) = $true) | ($true != ((X388 @ X392))) | (((X388 @ X393)) != $true))) | ! [X405 : (subst > term > subst > $o),X406 : term] : (? [X416 : term,X417 : term] : ((((X405 @ id @ (ap @ (sub @ X416 @ id) @ X417) @ id)) != $true) & ($true = ((X405 @ id @ X416 @ id))) & ($true = ((X405 @ id @ X417 @ id)))) | ? [X411 : term] : (($true != ((X405 @ id @ X411 @ id))) & ($true = ((var @ (sub @ X411 @ id))))) | ? [X410 : subst,X409 : subst,X407 : subst,X408 : term] : (($true = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407) @ X410))) & ($true != ((X405 @ X409 @ X408 @ (comp @ X407 @ X410))))) | ? [X413 : subst,X414 : subst,X415 : term,X412 : subst] : (($true != ((X405 @ (comp @ X414 @ X413) @ (sub @ X415 @ X413) @ X412))) & ($true = ((X405 @ X414 @ X415 @ (comp @ X413 @ X412))))) | ? [X418 : (subst > term > term)] : (! [X422 : subst,X420 : subst,X421 : term] : (((X418 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X418 @ X422 @ X421) @ X420))) & ($true != ((X405 @ id @ (lam @ (X418 @ sh @ one)) @ id))) & ! [X419 : term] : ((((X405 @ id @ (X418 @ id @ X419) @ id)) = $true) | ($true != ((X405 @ id @ X419 @ id))))) | ($true = ((X405 @ id @ X406 @ id)))) | ? [X396 : term,X395 : (subst > term > subst > $o),X397 : (term > $o)] : (! [X398 : (subst > term > term)] : (($true = ((X395 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ? [X402 : term] : ((((X395 @ id @ (X398 @ id @ X402) @ id)) != $true) & ($true = ((X395 @ id @ X402 @ id)))) | ? [X400 : term,X401 : subst,X399 : subst] : (((X398 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X398 @ X401 @ X400) @ X399)))) & ($true != ((X397 @ (lam @ X396)))) & ! [X403 : term] : (($true = ((X397 @ (sub @ X396 @ (push @ X403 @ id))))) | ($true != ((X397 @ X403)))) & ! [X404 : term] : (((X397 @ X404)) = ((X395 @ id @ X404 @ id)))) | ? [X384 : (subst > term > subst > $o)] : ! [X385 : (term > $o)] : ? [X386 : term] : (((X385 @ X386)) != ((X384 @ id @ X386 @ id))) | ? [X394 : term] : (((sub @ X394 @ id)) != X394)) <=> (hoasinduction_lthm_3 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : term,X515 : term] : (($true != ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) & ($true = ((X512 @ id @ X514 @ id))) & ($true = ((X512 @ id @ X515 @ id)))) | ? [X516 : (subst > term > term)] : ((((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id)) != $true) & ! [X517 : term] : ((((X512 @ id @ (X516 @ id @ X517) @ id)) = $true) | ($true != ((X512 @ id @ X517 @ id)))) & ! [X519 : term,X518 : subst,X520 : subst] : (((sub @ (X516 @ X518 @ X519) @ X520)) = ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520))))) | ($true = ((X512 @ id @ X513 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2 = $true) <=> ! [X432 : term,X434 : (term > $o),X433 : (subst > term > subst > $o)] : (? [X435 : term] : (($true = ((X434 @ X435))) & ($true != ((X434 @ (sub @ X432 @ (push @ X435 @ id)))))) | ? [X437 : subst,X436 : term,X438 : subst,X439 : subst] : (($true != ((X433 @ X439 @ X436 @ (comp @ X438 @ X437)))) & ($true = ((X433 @ (comp @ X439 @ X438) @ (sub @ X436 @ X438) @ X437)))) | ? [X443 : subst,X442 : term,X441 : subst,X440 : subst] : ((((X433 @ (comp @ X441 @ X443) @ (sub @ X442 @ X443) @ X440)) != $true) & (((X433 @ X441 @ X442 @ (comp @ X443 @ X440))) = $true)) | ($true = ((X434 @ (lam @ X432)))) | ? [X444 : (subst > term > term)] : (! [X447 : term,X445 : subst,X446 : subst] : (((X444 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445))) = ((sub @ (X444 @ X446 @ X447) @ X445))) & ($true != ((X433 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X433 @ id @ (X444 @ id @ X448) @ id))) | ($true != ((X433 @ id @ X448 @ id))))) | ? [X449 : term] : (((X433 @ id @ X449 @ id)) != ((X434 @ X449))))) & (! [X479 : (subst > term > subst > $o)] : ? [X480 : (term > $o)] : ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) <=> (hoasinduction_lem0 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X362 : (subst > term > subst > $o)] : ? [X363 : (term > $o)] : ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id)))) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & ((induction2lem = $true) <=> ! [X182 : (term > $o),X184 : term,X183 : subst] : ((((X182 @ (sub @ X184 @ X183))) = $true) | ? [X185 : term] : (($true != ((X182 @ (lam @ X185)))) & ! [X186 : term] : (($true != ((X182 @ X186))) | ($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id))))))) | ? [X187 : term] : (($true = ((var @ X187))) & ($true != ((X182 @ (sub @ X187 @ X183))))) | ? [X188 : term,X189 : term] : (($true = ((X182 @ X188))) & ($true != ((X182 @ (ap @ X188 @ X189)))) & ($true = ((X182 @ X189)))))) & (pushprop_lem1_gthm = $true) & ((? [X142 : term] : (((sub @ X142 @ id)) != X142) | ? [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 != X146) & (((ap @ X145 @ X144)) = ((ap @ X146 @ X143)))) | ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) <=> (termmset = $true)) & (hoasinduction_lem1 = $true) & ((? [X275 : term] : (((sub @ X275 @ id)) != X275) | ? [X276 : (subst > term > subst > $o),X277 : term] : ((((X276 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id)) != $true) & ! [X278 : term] : ((((X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) = $true) | ($true != ((X276 @ id @ X278 @ id)))) & ! [X279 : (subst > term > term)] : (($true = ((X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X282 : subst,X283 : term,X281 : subst] : (((X279 @ (comp @ X281 @ X282) @ (sub @ X283 @ X282))) != ((sub @ (X279 @ X281 @ X283) @ X282))) | ? [X280 : term] : (($true = ((X276 @ id @ X280 @ id))) & ($true != ((X276 @ id @ (X279 @ id @ X280) @ id)))))) | ! [X285 : (subst > term > subst > $o),X284 : term] : (? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & (((X285 @ id @ X286 @ id)) = $true)) | ? [X287 : (subst > term > term)] : (! [X289 : subst,X290 : term,X288 : subst] : (((X287 @ (comp @ X288 @ X289) @ (sub @ X290 @ X289))) = ((sub @ (X287 @ X288 @ X290) @ X289))) & ! [X291 : term] : (($true != ((X285 @ id @ X291 @ id))) | (((X285 @ id @ (X287 @ id @ X291) @ id)) = $true)) & ($true != ((X285 @ id @ (lam @ (X287 @ sh @ one)) @ id)))) | (((X285 @ id @ (lam @ X284) @ id)) = $true))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X292 : term] : ? [X293 : (subst > term > term)] : (((X293 @ sh @ one)) = ((sub @ X292 @ (push @ one @ sh))))) & ((! [X324 : (term > $o),X323 : term] : (($true = ((X324 @ X323))) | ? [X327 : term,X328 : term] : ((((X324 @ (ap @ X328 @ X327))) != $true) & ($true = ((X324 @ X327))) & ($true = ((X324 @ X328)))) | ? [X329 : term] : (($true != ((X324 @ X329))) & (((var @ X329)) = $true)) | ? [X325 : term] : (! [X326 : term] : (($true = ((X324 @ (sub @ X325 @ (push @ X326 @ id))))) | ($true != ((X324 @ X326)))) & ($true != ((X324 @ (lam @ X325)))))) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ? [X317 : term,X316 : subst,X315 : (term > $o)] : (! [X320 : term] : (($true != ((var @ X320))) | ($true = ((X315 @ (sub @ X320 @ X316))))) & ($true != ((X315 @ (sub @ X317 @ X316)))) & ! [X321 : term] : (? [X322 : term] : (($true = ((X315 @ X322))) & (((X315 @ (sub @ X321 @ (push @ X322 @ id)))) != $true)) | (((X315 @ (lam @ X321))) = $true)) & ! [X318 : term,X319 : term] : (($true != ((X315 @ X318))) | (((X315 @ X319)) != $true) | ($true = ((X315 @ (ap @ X318 @ X319))))))) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X475 : term] : ? [X476 : (subst > term > term)] : ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477)))) & (substmonoid_gthm = $true) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & (ulamvar1 != $true) & ((hoasinduction_lem3_lthm = $true) <=> (? [X452 : (subst > term > subst > $o),X451 : term] : (($true != ((X452 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id))) & ! [X454 : (subst > term > term)] : (? [X458 : term] : (($true = ((X452 @ id @ X458 @ id))) & ($true != ((X452 @ id @ (X454 @ id @ X458) @ id)))) | (((X452 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X456 : subst,X457 : term,X455 : subst] : (((sub @ (X454 @ X455 @ X457) @ X456)) != ((X454 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456))))) & ! [X453 : term] : (($true != ((X452 @ id @ X453 @ id))) | ($true = ((X452 @ id @ (sub @ X451 @ (push @ X453 @ id)) @ id))))) | ? [X450 : term] : (((sub @ X450 @ id)) != X450) | ! [X459 : term,X460 : (subst > term > subst > $o)] : (? [X466 : subst,X467 : subst,X468 : term,X469 : subst] : (($true != ((X460 @ (comp @ X467 @ X466) @ (sub @ X468 @ X466) @ X469))) & ($true = ((X460 @ X467 @ X468 @ (comp @ X466 @ X469))))) | ? [X461 : (subst > term > term)] : (($true != ((X460 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : (($true != ((X460 @ id @ X462 @ id))) | ($true = ((X460 @ id @ (X461 @ id @ X462) @ id)))) & ! [X464 : term,X463 : subst,X465 : subst] : (((sub @ (X461 @ X463 @ X464) @ X465)) = ((X461 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465))))) | ($true = ((X460 @ id @ (lam @ X459) @ id))) | ? [X470 : term] : (($true != ((X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id))) & ($true = ((X460 @ id @ X470 @ id)))) | ? [X471 : subst,X474 : term,X472 : subst,X473 : subst] : ((((X460 @ X471 @ X474 @ (comp @ X472 @ X473))) != $true) & ($true = ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473))))))) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> (? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ? [X296 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X296))) != X296) | ! [X302 : (subst > term > term),X301 : (subst > term > term),X300 : subst,X303 : term] : ((((X302 @ X300 @ X303)) = ((X301 @ X300 @ X303))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X301 @ sh @ one)))) | ? [X305 : term,X306 : subst,X304 : subst] : (((X301 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))) != ((sub @ (X301 @ X304 @ X305) @ X306))) | ? [X309 : term,X307 : subst,X308 : subst] : (((X302 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307))) != ((sub @ (X302 @ X308 @ X309) @ X307)))) | ? [X299 : term,X298 : term] : ((((lam @ X299)) = ((lam @ X298))) & (X298 != X299)))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & ((! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179)) | ? [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 != X176) & (((ap @ X177 @ X175)) = ((ap @ X174 @ X176))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (! [X14 : (term > $o),X15 : subst,X13 : term] : ? [X16 : (term > $o)] : ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))) <=> (pushprop_lem0_lthm = $true)) & ((substmonoid_lthm = $true) <=> (? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500) | (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503)))) & ((hoasinduction_lthm = $true) <=> (? [X203 : term,X201 : (subst > term > subst > $o),X202 : term] : ((((X201 @ id @ X203 @ id)) = $true) & ($true = ((X201 @ id @ X202 @ id))) & (((X201 @ id @ (ap @ X202 @ X203) @ id)) != $true) & ! [X211 : subst,X212 : subst,X213 : term,X210 : subst] : (($true != ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210)))) & ! [X208 : subst,X209 : subst,X206 : term,X207 : subst] : ((((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true) | (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) != $true)) & ! [X205 : term,X204 : term] : (($true != ((X201 @ id @ X204 @ id))) | ($true != ((X201 @ id @ X205 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id))))) | ? [X215 : (subst > term > subst > $o),X214 : term] : (($true != ((X215 @ id @ (lam @ X214) @ id))) & ! [X217 : subst,X219 : term,X218 : subst,X216 : subst] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ($true != ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) & ! [X228 : term,X226 : subst,X225 : subst,X227 : subst] : (($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226)))) | ($true != ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226)))) & ! [X220 : (subst > term > term)] : (? [X224 : term] : (($true != ((X215 @ id @ (X220 @ id @ X224) @ id))) & ($true = ((X215 @ id @ X224 @ id)))) | ($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ? [X221 : subst,X222 : subst,X223 : term] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) != ((sub @ (X220 @ X222 @ X223) @ X221)))) & ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ($true != ((X215 @ id @ X229 @ id))))) | ! [X231 : term,X230 : (subst > term > subst > $o)] : (? [X241 : term,X240 : subst,X242 : subst,X239 : subst] : (($true = ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240))) & ($true != ((X230 @ X242 @ X241 @ (comp @ X239 @ X240))))) | ? [X247 : subst,X245 : subst,X244 : term,X246 : subst] : ((((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) != $true) & ($true = ((X230 @ X246 @ X244 @ (comp @ X245 @ X247))))) | (((X230 @ id @ X231 @ id)) = $true) | ? [X232 : term,X233 : term] : (($true = ((X230 @ id @ X233 @ id))) & ($true != ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id))) & ($true = ((X230 @ id @ X232 @ id)))) | ? [X234 : (subst > term > term)] : (! [X235 : term] : (($true != ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) & (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) != $true) & ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))) | ? [X243 : term] : (($true = ((var @ (sub @ X243 @ id)))) & ($true != ((X230 @ id @ X243 @ id))))) | ? [X195 : (term > $o),X194 : term] : (! [X197 : term,X196 : term] : (($true != ((X195 @ X196))) | ($true = ((X195 @ (ap @ X196 @ X197)))) | ($true != ((X195 @ X197)))) & ! [X200 : term] : (($true = ((X195 @ X200))) | ($true != ((var @ X200)))) & (((X195 @ X194)) != $true) & ! [X198 : term] : (? [X199 : term] : ((((X195 @ X199)) = $true) & ($true != ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true))))) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) <=> (axidl = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj2 = $true) <=> ! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313))))) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (axabs = $true) & (hoaslamnotap_lthm = $true) & (! [X10 : (term > $o),X8 : term,X9 : subst] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) != $true) | ($true = ((X39 @ one))) | ? [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) != ((X39 @ X41))))) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (! [X31 : term,X30 : (term > $o),X29 : subst] : (? [X35 : term] : (! [X36 : term] : (($true != ((X30 @ X36))) | ($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id)))))) & (((X30 @ (lam @ X35))) != $true)) | ? [X32 : term] : (($true = ((var @ X32))) & ($true != ((X30 @ (sub @ X32 @ X29))))) | ? [X34 : term,X33 : term] : (($true = ((X30 @ X33))) & ($true = ((X30 @ X34))) & ($true != ((X30 @ (ap @ X34 @ X33))))) | ($true = ((X30 @ (sub @ X31 @ X29))))) | ? [X24 : (term > $o),X23 : term] : (! [X25 : term] : ((((X24 @ X25)) != $true) | ($true = ((X24 @ (lam @ X25))))) & ! [X27 : term,X28 : term] : (($true = ((X24 @ (ap @ X28 @ X27)))) | ($true != ((X24 @ X27))) | ($true != ((X24 @ X28)))) & ($true != ((X24 @ X23))) & ! [X26 : term] : (($true = ((X24 @ X26))) | ($true != ((var @ X26))))) | ? [X22 : subst] : (((comp @ X22 @ id)) != X22) | ? [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) != X19) | ? [X20 : subst,X21 : term] : (((comp @ sh @ (push @ X21 @ X20))) != X20))) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & (! [X345 : term,X346 : (term > $o)] : (($true = ((X346 @ X345))) | ? [X347 : term] : (($true = ((var @ X347))) & ($true != ((X346 @ X347)))) | ? [X350 : term] : ((((X346 @ (lam @ X350))) != $true) & ! [X351 : term] : (($true = ((X346 @ (sub @ X350 @ (push @ X351 @ id))))) | ($true != ((X346 @ X351))))) | ? [X348 : term,X349 : term] : (($true = ((X346 @ X349))) & ($true = ((X346 @ X348))) & ($true != ((X346 @ (ap @ X349 @ X348)))))) <=> (induction2 = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) <=> ! [X67 : (subst > term > subst > $o),X66 : term] : (? [X76 : subst,X78 : subst,X77 : subst,X79 : term] : ((((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) != $true) & ($true = ((X67 @ X76 @ X79 @ (comp @ X78 @ X77))))) | ? [X75 : term] : (($true != ((X67 @ id @ X75 @ id))) & ($true = ((var @ (sub @ X75 @ id))))) | ? [X83 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)))) & (((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) = $true)) | ($true = ((X67 @ id @ X66 @ id))) | ? [X68 : (subst > term > term)] : (! [X72 : term] : (($true != ((X67 @ id @ X72 @ id))) | ($true = ((X67 @ id @ (X68 @ id @ X72) @ id)))) & ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) & ($true != ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id)))) | ? [X74 : term,X73 : term] : (($true = ((X67 @ id @ X73 @ id))) & ($true = ((X67 @ id @ X74 @ id))) & ($true != ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))))) & (hoasinduction_lem1_gthm = $true) & ! [X426 : d_subst] : (d_id = X426) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (! [X4 : term,X2 : term,X3 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) != ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) <=> (hoaslamnotap = $true))),
% 2.19/0.60 inference(flattening,[],[f11])).
% 2.19/0.60 thf(f13,definition,(
% 2.19/0.60 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP0 @ X67))) <=> ? [X74 : term,X73 : term] : (($true = ((X67 @ id @ X73 @ id))) & ($true = ((X67 @ id @ X74 @ id))) & ($true != ((X67 @ id @ (ap @ (sub @ X73 @ id) @ X74) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f14,definition,(
% 2.19/0.60 ! [X67 : (subst > term > subst > $o)] : (($true = ((sP1 @ X67))) <=> ? [X68 : (subst > term > term)] : (! [X72 : term] : (($true != ((X67 @ id @ X72 @ id))) | ($true = ((X67 @ id @ (X68 @ id @ X72) @ id)))) & ! [X70 : subst,X71 : subst,X69 : term] : (((sub @ (X68 @ X71 @ X69) @ X70)) = ((X68 @ (comp @ X71 @ X70) @ (sub @ X69 @ X70)))) & ($true != ((X67 @ id @ (lam @ (X68 @ sh @ one)) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f15,definition,(
% 2.19/0.60 (sP2 = $true) <=> ! [X67 : (subst > term > subst > $o),X66 : term] : (? [X76 : subst,X78 : subst,X77 : subst,X79 : term] : ((((X67 @ (comp @ X76 @ X78) @ (sub @ X79 @ X78) @ X77)) != $true) & ($true = ((X67 @ X76 @ X79 @ (comp @ X78 @ X77))))) | ? [X75 : term] : (($true != ((X67 @ id @ X75 @ id))) & ($true = ((var @ (sub @ X75 @ id))))) | ? [X83 : subst,X80 : term,X82 : subst,X81 : subst] : (($true != ((X67 @ X82 @ X80 @ (comp @ X81 @ X83)))) & (((X67 @ (comp @ X82 @ X81) @ (sub @ X80 @ X81) @ X83)) = $true)) | ($true = ((X67 @ id @ X66 @ id))) | ($true = ((sP1 @ X67))) | ($true = ((sP0 @ X67))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f16,definition,(
% 2.19/0.60 ! [X346 : (term > $o)] : (($true = ((sP3 @ X346))) <=> ? [X348 : term,X349 : term] : (($true = ((X346 @ X349))) & ($true = ((X346 @ X348))) & ($true != ((X346 @ (ap @ X349 @ X348))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f17,definition,(
% 2.19/0.60 ($true = sP4) <=> ! [X345 : term,X346 : (term > $o)] : (($true = ((X346 @ X345))) | ? [X347 : term] : (($true = ((var @ X347))) & ($true != ((X346 @ X347)))) | ? [X350 : term] : ((((X346 @ (lam @ X350))) != $true) & ! [X351 : term] : (($true = ((X346 @ (sub @ X350 @ (push @ X351 @ id))))) | ($true != ((X346 @ X351))))) | ($true = ((sP3 @ X346))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f18,definition,(
% 2.19/0.60 ! [X24 : (term > $o)] : (($true = ((sP5 @ X24))) <=> ! [X27 : term,X28 : term] : (($true = ((X24 @ (ap @ X28 @ X27)))) | ($true != ((X24 @ X27))) | ($true != ((X24 @ X28)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f19,definition,(
% 2.19/0.60 ! [X30 : (term > $o)] : ((((sP6 @ X30)) = $true) <=> ? [X34 : term,X33 : term] : (($true = ((X30 @ X33))) & ($true = ((X30 @ X34))) & ($true != ((X30 @ (ap @ X34 @ X33))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f20,definition,(
% 2.19/0.60 ($true = sP7) <=> ! [X31 : term,X30 : (term > $o),X29 : subst] : (? [X35 : term] : (! [X36 : term] : (($true != ((X30 @ X36))) | ($true = ((X30 @ (sub @ X35 @ (push @ X36 @ id)))))) & (((X30 @ (lam @ X35))) != $true)) | ? [X32 : term] : (($true = ((var @ X32))) & ($true != ((X30 @ (sub @ X32 @ X29))))) | (((sP6 @ X30)) = $true) | ($true = ((X30 @ (sub @ X31 @ X29)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f21,definition,(
% 2.19/0.60 (sP8 = $true) <=> (($true = sP7) | ? [X24 : (term > $o),X23 : term] : (! [X25 : term] : ((((X24 @ X25)) != $true) | ($true = ((X24 @ (lam @ X25))))) & ($true = ((sP5 @ X24))) & ($true != ((X24 @ X23))) & ! [X26 : term] : (($true = ((X24 @ X26))) | ($true != ((var @ X26))))) | ? [X22 : subst] : (((comp @ X22 @ id)) != X22) | ? [X18 : subst,X19 : term] : (((sub @ one @ (push @ X19 @ X18))) != X19) | ? [X20 : subst,X21 : term] : (((comp @ sh @ (push @ X21 @ X20))) != X20))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f22,definition,(
% 2.19/0.60 ! [X195 : (term > $o)] : ((((sP9 @ X195)) = $true) <=> ! [X197 : term,X196 : term] : (($true != ((X195 @ X196))) | ($true = ((X195 @ (ap @ X196 @ X197)))) | ($true != ((X195 @ X197)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f23,definition,(
% 2.19/0.60 ! [X230 : (subst > term > subst > $o)] : (($true = ((sP10 @ X230))) <=> ? [X234 : (subst > term > term)] : (! [X235 : term] : (($true != ((X230 @ id @ X235 @ id))) | (((X230 @ id @ (X234 @ id @ X235) @ id)) = $true)) & (((X230 @ id @ (lam @ (X234 @ sh @ one)) @ id)) != $true) & ! [X237 : subst,X236 : term,X238 : subst] : (((sub @ (X234 @ X237 @ X236) @ X238)) = ((X234 @ (comp @ X237 @ X238) @ (sub @ X236 @ X238))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f24,definition,(
% 2.19/0.60 ! [X230 : (subst > term > subst > $o)] : ((((sP11 @ X230)) = $true) <=> ? [X232 : term,X233 : term] : (($true = ((X230 @ id @ X233 @ id))) & ($true != ((X230 @ id @ (ap @ (sub @ X232 @ id) @ X233) @ id))) & ($true = ((X230 @ id @ X232 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f25,definition,(
% 2.19/0.60 ! [X215 : (subst > term > subst > $o)] : (($true = ((sP12 @ X215))) <=> ! [X220 : (subst > term > term)] : (? [X224 : term] : (($true != ((X215 @ id @ (X220 @ id @ X224) @ id))) & ($true = ((X215 @ id @ X224 @ id)))) | ($true = ((X215 @ id @ (lam @ (X220 @ sh @ one)) @ id))) | ? [X221 : subst,X222 : subst,X223 : term] : (((X220 @ (comp @ X222 @ X221) @ (sub @ X223 @ X221))) != ((sub @ (X220 @ X222 @ X223) @ X221)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f26,definition,(
% 2.19/0.60 ! [X201 : (subst > term > subst > $o)] : (($true = ((sP13 @ X201))) <=> ! [X205 : term,X204 : term] : (($true != ((X201 @ id @ X204 @ id))) | ($true != ((X201 @ id @ X205 @ id))) | ($true = ((X201 @ id @ (ap @ (sub @ X204 @ id) @ X205) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f27,definition,(
% 2.19/0.60 ($true = sP14) <=> ? [X215 : (subst > term > subst > $o),X214 : term] : (($true != ((X215 @ id @ (lam @ X214) @ id))) & ! [X217 : subst,X219 : term,X218 : subst,X216 : subst] : ((((X215 @ (comp @ X216 @ X218) @ (sub @ X219 @ X218) @ X217)) = $true) | ($true != ((X215 @ X216 @ X219 @ (comp @ X218 @ X217))))) & ! [X228 : term,X226 : subst,X225 : subst,X227 : subst] : (($true = ((X215 @ X225 @ X228 @ (comp @ X227 @ X226)))) | ($true != ((X215 @ (comp @ X225 @ X227) @ (sub @ X228 @ X227) @ X226)))) & ($true = ((sP12 @ X215))) & ! [X229 : term] : (($true = ((X215 @ id @ (sub @ X214 @ (push @ X229 @ id)) @ id))) | ($true != ((X215 @ id @ X229 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f28,definition,(
% 2.19/0.60 ($true = sP15) <=> ! [X231 : term,X230 : (subst > term > subst > $o)] : (? [X241 : term,X240 : subst,X242 : subst,X239 : subst] : (($true = ((X230 @ (comp @ X242 @ X239) @ (sub @ X241 @ X239) @ X240))) & ($true != ((X230 @ X242 @ X241 @ (comp @ X239 @ X240))))) | ? [X247 : subst,X245 : subst,X244 : term,X246 : subst] : ((((X230 @ (comp @ X246 @ X245) @ (sub @ X244 @ X245) @ X247)) != $true) & ($true = ((X230 @ X246 @ X244 @ (comp @ X245 @ X247))))) | (((X230 @ id @ X231 @ id)) = $true) | (((sP11 @ X230)) = $true) | ($true = ((sP10 @ X230))) | ? [X243 : term] : (($true = ((var @ (sub @ X243 @ id)))) & ($true != ((X230 @ id @ X243 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f29,definition,(
% 2.19/0.60 ($true = sP16) <=> ? [X195 : (term > $o),X194 : term] : ((((sP9 @ X195)) = $true) & ! [X200 : term] : (($true = ((X195 @ X200))) | ($true != ((var @ X200)))) & (((X195 @ X194)) != $true) & ! [X198 : term] : (? [X199 : term] : ((((X195 @ X199)) = $true) & ($true != ((X195 @ (sub @ X198 @ (push @ X199 @ id)))))) | (((X195 @ (lam @ X198))) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f30,definition,(
% 2.19/0.60 ($true = sP17) <=> (? [X203 : term,X201 : (subst > term > subst > $o),X202 : term] : ((((X201 @ id @ X203 @ id)) = $true) & ($true = ((X201 @ id @ X202 @ id))) & (((X201 @ id @ (ap @ X202 @ X203) @ id)) != $true) & ! [X211 : subst,X212 : subst,X213 : term,X210 : subst] : (($true != ((X201 @ X211 @ X213 @ (comp @ X212 @ X210)))) | ($true = ((X201 @ (comp @ X211 @ X212) @ (sub @ X213 @ X212) @ X210)))) & ! [X208 : subst,X209 : subst,X206 : term,X207 : subst] : ((((X201 @ X209 @ X206 @ (comp @ X207 @ X208))) = $true) | (((X201 @ (comp @ X209 @ X207) @ (sub @ X206 @ X207) @ X208)) != $true)) & ($true = ((sP13 @ X201)))) | ($true = sP14) | ($true = sP15) | ($true = sP16))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f31,definition,(
% 2.19/0.60 ($true = sP18) <=> (? [X295 : subst,X294 : term] : (((sub @ one @ (push @ X294 @ X295))) != X294) | ? [X296 : subst,X297 : term] : (((comp @ sh @ (push @ X297 @ X296))) != X296) | ! [X302 : (subst > term > term),X301 : (subst > term > term),X300 : subst,X303 : term] : ((((X302 @ X300 @ X303)) = ((X301 @ X300 @ X303))) | (((lam @ (X302 @ sh @ one))) != ((lam @ (X301 @ sh @ one)))) | ? [X305 : term,X306 : subst,X304 : subst] : (((X301 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))) != ((sub @ (X301 @ X304 @ X305) @ X306))) | ? [X309 : term,X307 : subst,X308 : subst] : (((X302 @ (comp @ X308 @ X307) @ (sub @ X309 @ X307))) != ((sub @ (X302 @ X308 @ X309) @ X307)))) | ? [X299 : term,X298 : term] : ((((lam @ X299)) = ((lam @ X298))) & (X298 != X299)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f32,definition,(
% 2.19/0.60 ! [X460 : (subst > term > subst > $o)] : (($true = ((sP19 @ X460))) <=> ? [X461 : (subst > term > term)] : (($true != ((X460 @ id @ (lam @ (X461 @ sh @ one)) @ id))) & ! [X462 : term] : (($true != ((X460 @ id @ X462 @ id))) | ($true = ((X460 @ id @ (X461 @ id @ X462) @ id)))) & ! [X464 : term,X463 : subst,X465 : subst] : (((sub @ (X461 @ X463 @ X464) @ X465)) = ((X461 @ (comp @ X463 @ X465) @ (sub @ X464 @ X465))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f33,definition,(
% 2.19/0.60 ($true = sP20) <=> ? [X452 : (subst > term > subst > $o),X451 : term] : (($true != ((X452 @ id @ (lam @ (sub @ X451 @ (push @ one @ sh))) @ id))) & ! [X454 : (subst > term > term)] : (? [X458 : term] : (($true = ((X452 @ id @ X458 @ id))) & ($true != ((X452 @ id @ (X454 @ id @ X458) @ id)))) | (((X452 @ id @ (lam @ (X454 @ sh @ one)) @ id)) = $true) | ? [X456 : subst,X457 : term,X455 : subst] : (((sub @ (X454 @ X455 @ X457) @ X456)) != ((X454 @ (comp @ X455 @ X456) @ (sub @ X457 @ X456))))) & ! [X453 : term] : (($true != ((X452 @ id @ X453 @ id))) | ($true = ((X452 @ id @ (sub @ X451 @ (push @ X453 @ id)) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f34,definition,(
% 2.19/0.60 ($true = sP21) <=> (($true = sP20) | ? [X450 : term] : (((sub @ X450 @ id)) != X450) | ! [X459 : term,X460 : (subst > term > subst > $o)] : (? [X466 : subst,X467 : subst,X468 : term,X469 : subst] : (($true != ((X460 @ (comp @ X467 @ X466) @ (sub @ X468 @ X466) @ X469))) & ($true = ((X460 @ X467 @ X468 @ (comp @ X466 @ X469))))) | ($true = ((sP19 @ X460))) | ($true = ((X460 @ id @ (lam @ X459) @ id))) | ? [X470 : term] : (($true != ((X460 @ id @ (sub @ X459 @ (push @ X470 @ id)) @ id))) & ($true = ((X460 @ id @ X470 @ id)))) | ? [X471 : subst,X474 : term,X472 : subst,X473 : subst] : ((((X460 @ X471 @ X474 @ (comp @ X472 @ X473))) != $true) & ($true = ((X460 @ (comp @ X471 @ X472) @ (sub @ X474 @ X472) @ X473))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f35,definition,(
% 2.19/0.60 ! [X315 : (term > $o)] : ((((sP22 @ X315)) = $true) <=> ! [X318 : term,X319 : term] : (($true != ((X315 @ X318))) | (((X315 @ X319)) != $true) | ($true = ((X315 @ (ap @ X318 @ X319))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f36,definition,(
% 2.19/0.60 ! [X324 : (term > $o)] : (($true = ((sP23 @ X324))) <=> ? [X327 : term,X328 : term] : ((((X324 @ (ap @ X328 @ X327))) != $true) & ($true = ((X324 @ X327))) & ($true = ((X324 @ X328)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f37,definition,(
% 2.19/0.60 (sP24 = $true) <=> ! [X324 : (term > $o),X323 : term] : (($true = ((X324 @ X323))) | ($true = ((sP23 @ X324))) | ? [X329 : term] : (($true != ((X324 @ X329))) & (((var @ X329)) = $true)) | ? [X325 : term] : (! [X326 : term] : (($true = ((X324 @ (sub @ X325 @ (push @ X326 @ id))))) | ($true != ((X324 @ X326)))) & ($true != ((X324 @ (lam @ X325))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f38,definition,(
% 2.19/0.60 ($true = sP25) <=> ((sP24 = $true) | ? [X314 : term] : (((sub @ X314 @ id)) != X314) | ? [X317 : term,X316 : subst,X315 : (term > $o)] : (! [X320 : term] : (($true != ((var @ X320))) | ($true = ((X315 @ (sub @ X320 @ X316))))) & ($true != ((X315 @ (sub @ X317 @ X316)))) & ! [X321 : term] : (? [X322 : term] : (($true = ((X315 @ X322))) & (((X315 @ (sub @ X321 @ (push @ X322 @ id)))) != $true)) | (((X315 @ (lam @ X321))) = $true)) & (((sP22 @ X315)) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f39,definition,(
% 2.19/0.60 ($true = sP26) <=> ? [X276 : (subst > term > subst > $o),X277 : term] : ((((X276 @ id @ (lam @ (sub @ X277 @ (push @ one @ sh))) @ id)) != $true) & ! [X278 : term] : ((((X276 @ id @ (sub @ X277 @ (push @ X278 @ id)) @ id)) = $true) | ($true != ((X276 @ id @ X278 @ id)))) & ! [X279 : (subst > term > term)] : (($true = ((X276 @ id @ (lam @ (X279 @ sh @ one)) @ id))) | ? [X282 : subst,X283 : term,X281 : subst] : (((X279 @ (comp @ X281 @ X282) @ (sub @ X283 @ X282))) != ((sub @ (X279 @ X281 @ X283) @ X282))) | ? [X280 : term] : (($true = ((X276 @ id @ X280 @ id))) & ($true != ((X276 @ id @ (X279 @ id @ X280) @ id))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f40,definition,(
% 2.19/0.60 (sP27 = $true) <=> (? [X275 : term] : (((sub @ X275 @ id)) != X275) | ($true = sP26) | ! [X285 : (subst > term > subst > $o),X284 : term] : (? [X286 : term] : (($true != ((X285 @ id @ (sub @ X284 @ (push @ X286 @ id)) @ id))) & (((X285 @ id @ X286 @ id)) = $true)) | ? [X287 : (subst > term > term)] : (! [X289 : subst,X290 : term,X288 : subst] : (((X287 @ (comp @ X288 @ X289) @ (sub @ X290 @ X289))) = ((sub @ (X287 @ X288 @ X290) @ X289))) & ! [X291 : term] : (($true != ((X285 @ id @ X291 @ id))) | (((X285 @ id @ (X287 @ id @ X291) @ id)) = $true)) & ($true != ((X285 @ id @ (lam @ (X287 @ sh @ one)) @ id)))) | (((X285 @ id @ (lam @ X284) @ id)) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f41,definition,(
% 2.19/0.60 ! [X182 : (term > $o)] : (($true = ((sP28 @ X182))) <=> ? [X188 : term,X189 : term] : (($true = ((X182 @ X188))) & ($true != ((X182 @ (ap @ X188 @ X189)))) & ($true = ((X182 @ X189)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f42,definition,(
% 2.19/0.60 ($true = sP29) <=> ! [X182 : (term > $o),X184 : term,X183 : subst] : ((((X182 @ (sub @ X184 @ X183))) = $true) | ? [X185 : term] : (($true != ((X182 @ (lam @ X185)))) & ! [X186 : term] : (($true != ((X182 @ X186))) | ($true = ((X182 @ (sub @ X185 @ (push @ X186 @ id))))))) | ? [X187 : term] : (($true = ((var @ X187))) & ($true != ((X182 @ (sub @ X187 @ X183))))) | ($true = ((sP28 @ X182))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f43,definition,(
% 2.19/0.60 ! [X433 : (subst > term > subst > $o)] : (($true = ((sP30 @ X433))) <=> ? [X444 : (subst > term > term)] : (! [X447 : term,X445 : subst,X446 : subst] : (((X444 @ (comp @ X446 @ X445) @ (sub @ X447 @ X445))) = ((sub @ (X444 @ X446 @ X447) @ X445))) & ($true != ((X433 @ id @ (lam @ (X444 @ sh @ one)) @ id))) & ! [X448 : term] : (($true = ((X433 @ id @ (X444 @ id @ X448) @ id))) | ($true != ((X433 @ id @ X448 @ id))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f44,definition,(
% 2.19/0.60 ($true = sP31) <=> ! [X432 : term,X434 : (term > $o),X433 : (subst > term > subst > $o)] : (? [X435 : term] : (($true = ((X434 @ X435))) & ($true != ((X434 @ (sub @ X432 @ (push @ X435 @ id)))))) | ? [X437 : subst,X436 : term,X438 : subst,X439 : subst] : (($true != ((X433 @ X439 @ X436 @ (comp @ X438 @ X437)))) & ($true = ((X433 @ (comp @ X439 @ X438) @ (sub @ X436 @ X438) @ X437)))) | ? [X443 : subst,X442 : term,X441 : subst,X440 : subst] : ((((X433 @ (comp @ X441 @ X443) @ (sub @ X442 @ X443) @ X440)) != $true) & (((X433 @ X441 @ X442 @ (comp @ X443 @ X440))) = $true)) | ($true = ((X434 @ (lam @ X432)))) | ($true = ((sP30 @ X433))) | ? [X449 : term] : (((X433 @ id @ X449 @ id)) != ((X434 @ X449))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f45,definition,(
% 2.19/0.60 ! [X512 : (subst > term > subst > $o)] : (($true = ((sP32 @ X512))) <=> ? [X516 : (subst > term > term)] : ((((X512 @ id @ (lam @ (X516 @ sh @ one)) @ id)) != $true) & ! [X517 : term] : ((((X512 @ id @ (X516 @ id @ X517) @ id)) = $true) | ($true != ((X512 @ id @ X517 @ id)))) & ! [X519 : term,X518 : subst,X520 : subst] : (((sub @ (X516 @ X518 @ X519) @ X520)) = ((X516 @ (comp @ X518 @ X520) @ (sub @ X519 @ X520))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f46,definition,(
% 2.19/0.60 ! [X405 : (subst > term > subst > $o)] : (($true = ((sP33 @ X405))) <=> ? [X418 : (subst > term > term)] : (! [X422 : subst,X420 : subst,X421 : term] : (((X418 @ (comp @ X422 @ X420) @ (sub @ X421 @ X420))) = ((sub @ (X418 @ X422 @ X421) @ X420))) & ($true != ((X405 @ id @ (lam @ (X418 @ sh @ one)) @ id))) & ! [X419 : term] : ((((X405 @ id @ (X418 @ id @ X419) @ id)) = $true) | ($true != ((X405 @ id @ X419 @ id))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f47,definition,(
% 2.19/0.60 ! [X405 : (subst > term > subst > $o)] : (($true = ((sP34 @ X405))) <=> ? [X416 : term,X417 : term] : ((((X405 @ id @ (ap @ (sub @ X416 @ id) @ X417) @ id)) != $true) & ($true = ((X405 @ id @ X416 @ id))) & ($true = ((X405 @ id @ X417 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f48,definition,(
% 2.19/0.60 ! [X388 : (term > $o)] : (($true = ((sP35 @ X388))) <=> ! [X393 : term,X392 : term] : ((((X388 @ (ap @ X392 @ X393))) = $true) | ($true != ((X388 @ X392))) | (((X388 @ X393)) != $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f49,definition,(
% 2.19/0.60 ($true = sP36) <=> ? [X396 : term,X395 : (subst > term > subst > $o),X397 : (term > $o)] : (! [X398 : (subst > term > term)] : (($true = ((X395 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ? [X402 : term] : ((((X395 @ id @ (X398 @ id @ X402) @ id)) != $true) & ($true = ((X395 @ id @ X402 @ id)))) | ? [X400 : term,X401 : subst,X399 : subst] : (((X398 @ (comp @ X401 @ X399) @ (sub @ X400 @ X399))) != ((sub @ (X398 @ X401 @ X400) @ X399)))) & ($true != ((X397 @ (lam @ X396)))) & ! [X403 : term] : (($true = ((X397 @ (sub @ X396 @ (push @ X403 @ id))))) | ($true != ((X397 @ X403)))) & ! [X404 : term] : (((X397 @ X404)) = ((X395 @ id @ X404 @ id))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f50,definition,(
% 2.19/0.60 (sP37 = $true) <=> ! [X405 : (subst > term > subst > $o),X406 : term] : (($true = ((sP34 @ X405))) | ? [X411 : term] : (($true != ((X405 @ id @ X411 @ id))) & ($true = ((var @ (sub @ X411 @ id))))) | ? [X410 : subst,X409 : subst,X407 : subst,X408 : term] : (($true = ((X405 @ (comp @ X409 @ X407) @ (sub @ X408 @ X407) @ X410))) & ($true != ((X405 @ X409 @ X408 @ (comp @ X407 @ X410))))) | ? [X413 : subst,X414 : subst,X415 : term,X412 : subst] : (($true != ((X405 @ (comp @ X414 @ X413) @ (sub @ X415 @ X413) @ X412))) & ($true = ((X405 @ X414 @ X415 @ (comp @ X413 @ X412))))) | ($true = ((sP33 @ X405))) | ($true = ((X405 @ id @ X406 @ id))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f51,definition,(
% 2.19/0.60 ($true = sP38) <=> (? [X387 : term,X388 : (term > $o)] : (! [X391 : term] : ((((X388 @ X391)) = $true) | (((var @ X391)) != $true)) & ! [X389 : term] : (($true = ((X388 @ (lam @ X389)))) | ? [X390 : term] : ((((X388 @ X390)) = $true) & ($true != ((X388 @ (sub @ X389 @ (push @ X390 @ id))))))) & ($true != ((X388 @ X387))) & ($true = ((sP35 @ X388)))) | (sP37 = $true) | ($true = sP36) | ? [X384 : (subst > term > subst > $o)] : ! [X385 : (term > $o)] : ? [X386 : term] : (((X385 @ X386)) != ((X384 @ id @ X386 @ id))) | ? [X394 : term] : (((sub @ X394 @ id)) != X394))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f52,definition,(
% 2.19/0.60 ! [X485 : (subst > term > subst > $o)] : ((((sP39 @ X485)) = $true) <=> ? [X494 : (subst > term > term)] : (($true != ((X485 @ id @ (lam @ (X494 @ sh @ one)) @ id))) & ! [X498 : term] : (($true = ((X485 @ id @ (X494 @ id @ X498) @ id))) | ($true != ((X485 @ id @ X498 @ id)))) & ! [X495 : term,X497 : subst,X496 : subst] : (((X494 @ (comp @ X496 @ X497) @ (sub @ X495 @ X497))) = ((sub @ (X494 @ X496 @ X495) @ X497)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f53,definition,(
% 2.19/0.60 ($true = sP40) <=> ! [X484 : term,X485 : (subst > term > subst > $o)] : (? [X499 : term] : ((((X485 @ id @ (sub @ X484 @ (push @ X499 @ id)) @ id)) != $true) & ($true = ((X485 @ id @ X499 @ id)))) | ($true = ((X485 @ id @ (lam @ X484) @ id))) | ? [X488 : subst,X486 : subst,X489 : subst,X487 : term] : (($true != ((X485 @ X486 @ X487 @ (comp @ X488 @ X489)))) & ($true = ((X485 @ (comp @ X486 @ X488) @ (sub @ X487 @ X488) @ X489)))) | (((sP39 @ X485)) = $true) | ? [X492 : subst,X493 : subst,X490 : subst,X491 : term] : ((((X485 @ (comp @ X492 @ X490) @ (sub @ X491 @ X490) @ X493)) != $true) & ($true = ((X485 @ X492 @ X491 @ (comp @ X490 @ X493))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f54,definition,(
% 2.19/0.60 ! [X332 : (subst > term > subst > $o)] : (($true = ((sP41 @ X332))) <=> ? [X342 : term,X343 : term] : (($true = ((X332 @ id @ X343 @ id))) & ($true != ((X332 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id))) & (((X332 @ id @ X342 @ id)) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f55,definition,(
% 2.19/0.60 ($true = sP42) <=> ! [X332 : (subst > term > subst > $o),X333 : (term > $o),X331 : term,X330 : term] : (($true != ((X333 @ X330))) | ? [X336 : subst,X335 : subst,X334 : subst,X337 : term] : ((((X332 @ (comp @ X334 @ X335) @ (sub @ X337 @ X335) @ X336)) != $true) & ($true = ((X332 @ X334 @ X337 @ (comp @ X335 @ X336))))) | ? [X344 : term] : (((X333 @ X344)) != ((X332 @ id @ X344 @ id))) | ($true = ((sP41 @ X332))) | ? [X338 : subst,X339 : subst,X340 : term,X341 : subst] : (($true != ((X332 @ X341 @ X340 @ (comp @ X339 @ X338)))) & (((X332 @ (comp @ X341 @ X339) @ (sub @ X340 @ X339) @ X338)) = $true)) | (((X333 @ (ap @ X331 @ X330))) = $true) | (((X333 @ X331)) != $true))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f56,definition,(
% 2.19/0.60 ($true = sP43) <=> ! [X504 : term,X505 : (subst > term > subst > $o)] : (? [X511 : term] : ((((X505 @ id @ (sub @ X504 @ (push @ X511 @ id)) @ id)) != $true) & ($true = ((X505 @ id @ X511 @ id)))) | ($true = ((X505 @ id @ (lam @ X504) @ id))) | ? [X506 : (subst > term > term)] : (! [X507 : subst,X508 : subst,X509 : term] : (((sub @ (X506 @ X508 @ X509) @ X507)) = ((X506 @ (comp @ X508 @ X507) @ (sub @ X509 @ X507)))) & ! [X510 : term] : (($true = ((X505 @ id @ (X506 @ id @ X510) @ id))) | ($true != ((X505 @ id @ X510 @ id)))) & ($true != ((X505 @ id @ (lam @ (X506 @ sh @ one)) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f57,definition,(
% 2.19/0.60 ! [X253 : (subst > term > subst > $o)] : ((((sP44 @ X253)) = $true) <=> ? [X256 : (subst > term > term)] : (! [X257 : subst,X259 : subst,X258 : term] : (((X256 @ (comp @ X257 @ X259) @ (sub @ X258 @ X259))) = ((sub @ (X256 @ X257 @ X258) @ X259))) & ! [X260 : term] : ((((X253 @ id @ X260 @ id)) != $true) | ($true = ((X253 @ id @ (X256 @ id @ X260) @ id)))) & ($true != ((X253 @ id @ (lam @ (X256 @ sh @ one)) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f58,definition,(
% 2.19/0.60 (sP45 = $true) <=> (? [X250 : term] : (((sub @ X250 @ id)) != X250) | ! [X251 : (term > $o),X252 : term,X253 : (subst > term > subst > $o)] : (? [X267 : subst,X266 : subst,X265 : subst,X268 : term] : ((((X253 @ (comp @ X267 @ X265) @ (sub @ X268 @ X265) @ X266)) != $true) & (((X253 @ X267 @ X268 @ (comp @ X265 @ X266))) = $true)) | ? [X255 : term] : (($true != ((X251 @ (sub @ X252 @ (push @ X255 @ id))))) & (((X251 @ X255)) = $true)) | ($true = ((X251 @ (lam @ X252)))) | (((sP44 @ X253)) = $true) | ? [X264 : term,X263 : subst,X262 : subst,X261 : subst] : (($true = ((X253 @ (comp @ X262 @ X261) @ (sub @ X264 @ X261) @ X263))) & (((X253 @ X262 @ X264 @ (comp @ X261 @ X263))) != $true)) | ? [X254 : term] : (((X251 @ X254)) != ((X253 @ id @ X254 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f59,definition,(
% 2.19/0.60 ! [X107 : (term > $o)] : (($true = ((sP46 @ X107))) <=> ! [X112 : term,X111 : term] : (($true != ((X107 @ X112))) | ($true != ((X107 @ X111))) | ($true = ((X107 @ (ap @ X112 @ X111))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f60,definition,(
% 2.19/0.60 ! [X125 : (subst > term > subst > $o)] : (($true = ((sP47 @ X125))) <=> ? [X126 : (subst > term > term)] : (($true != ((X125 @ id @ (lam @ (X126 @ sh @ one)) @ id))) & ! [X130 : subst,X129 : subst,X128 : term] : (((X126 @ (comp @ X130 @ X129) @ (sub @ X128 @ X129))) = ((sub @ (X126 @ X130 @ X128) @ X129))) & ! [X127 : term] : (($true = ((X125 @ id @ (X126 @ id @ X127) @ id))) | ($true != ((X125 @ id @ X127 @ id))))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f61,definition,(
% 2.19/0.60 ($true = sP48) <=> ? [X116 : (subst > term > subst > $o),X115 : term,X114 : (term > $o)] : (! [X117 : term] : ((((X114 @ (sub @ X115 @ (push @ X117 @ id)))) = $true) | (((X114 @ X117)) != $true)) & ($true != ((X114 @ (lam @ X115)))) & ! [X119 : (subst > term > term)] : (($true = ((X116 @ id @ (lam @ (X119 @ sh @ one)) @ id))) | ? [X123 : term] : (($true = ((X116 @ id @ X123 @ id))) & ($true != ((X116 @ id @ (X119 @ id @ X123) @ id)))) | ? [X121 : subst,X120 : subst,X122 : term] : (((X119 @ (comp @ X121 @ X120) @ (sub @ X122 @ X120))) != ((sub @ (X119 @ X121 @ X122) @ X120)))) & ! [X118 : term] : (((X114 @ X118)) = ((X116 @ id @ X118 @ id))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f62,definition,(
% 2.19/0.60 (sP49 = $true) <=> ? [X106 : term,X107 : (term > $o)] : (! [X109 : term] : (($true = ((X107 @ (lam @ X109)))) | ? [X110 : term] : (($true != ((X107 @ (sub @ X109 @ (push @ X110 @ id))))) & ($true = ((X107 @ X110))))) & ($true = ((sP46 @ X107))) & ($true != ((X107 @ X106))) & ! [X108 : term] : (($true = ((X107 @ X108))) | ($true != ((var @ X108)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f63,definition,(
% 2.19/0.60 ($true = sP50) <=> (! [X125 : (subst > term > subst > $o),X124 : term] : (($true = ((X125 @ id @ X124 @ id))) | ? [X132 : term,X131 : term] : (($true = ((X125 @ id @ X131 @ id))) & ($true != ((X125 @ id @ (ap @ (sub @ X132 @ id) @ X131) @ id))) & ($true = ((X125 @ id @ X132 @ id)))) | ($true = ((sP47 @ X125)))) | ? [X103 : (subst > term > subst > $o)] : ! [X104 : (term > $o)] : ? [X105 : term] : (((X104 @ X105)) != ((X103 @ id @ X105 @ id))) | ($true = sP48) | ? [X113 : term] : (((sub @ X113 @ id)) != X113) | (sP49 = $true))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f64,definition,(
% 2.19/0.60 ($true = sP51) <=> ! [X532 : (subst > term > subst > $o),X533 : term] : (? [X539 : term] : (($true = ((X532 @ id @ X539 @ id))) & (((X532 @ id @ (sub @ X533 @ (push @ X539 @ id)) @ id)) != $true)) | ? [X534 : (subst > term > term)] : (! [X538 : subst,X537 : subst,X536 : term] : (((sub @ (X534 @ X537 @ X536) @ X538)) = ((X534 @ (comp @ X537 @ X538) @ (sub @ X536 @ X538)))) & ($true != ((X532 @ id @ (lam @ (X534 @ sh @ one)) @ id))) & ! [X535 : term] : (($true = ((X532 @ id @ (X534 @ id @ X535) @ id))) | ($true != ((X532 @ id @ X535 @ id))))) | ($true = ((X532 @ id @ (lam @ (sub @ X533 @ (push @ one @ sh))) @ id))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f65,definition,(
% 2.19/0.60 ($true = sP52) <=> (! [X58 : term,X56 : (term > $o),X57 : (subst > term > subst > $o)] : (? [X64 : term] : (($true = ((X56 @ X64))) & ($true != ((X56 @ (sub @ X58 @ (push @ X64 @ id)))))) | ? [X59 : (subst > term > term)] : ((((X57 @ id @ (lam @ (X59 @ sh @ one)) @ id)) != $true) & ! [X60 : term] : (($true = ((X57 @ id @ (X59 @ id @ X60) @ id))) | ($true != ((X57 @ id @ X60 @ id)))) & ! [X63 : subst,X62 : subst,X61 : term] : (((sub @ (X59 @ X62 @ X61) @ X63)) = ((X59 @ (comp @ X62 @ X63) @ (sub @ X61 @ X63))))) | ($true = ((X56 @ (lam @ X58)))) | ? [X65 : term] : (((X57 @ id @ X65 @ id)) != ((X56 @ X65)))) | ? [X51 : term] : ! [X52 : (subst > term > term)] : ? [X53 : term,X54 : subst] : (((sub @ X51 @ (push @ X53 @ X54))) != ((X52 @ X54 @ X53))) | ? [X55 : term] : (((sub @ X55 @ id)) != X55))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f66,definition,(
% 2.19/0.60 ! [X163 : (subst > term > subst > $o)] : (($true = ((sP53 @ X163))) <=> ? [X168 : term,X169 : term] : (($true = ((X163 @ id @ X168 @ id))) & (((X163 @ id @ (ap @ (sub @ X169 @ id) @ X168) @ id)) != $true) & ($true = ((X163 @ id @ X169 @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f67,definition,(
% 2.19/0.60 ($true = sP54) <=> ! [X161 : term,X163 : (subst > term > subst > $o),X162 : term] : ((((X163 @ id @ X161 @ id)) != $true) | ($true = ((sP53 @ X163))) | ($true = ((X163 @ id @ (ap @ X162 @ X161) @ id))) | ($true != ((X163 @ id @ X162 @ id))) | ? [X165 : term,X167 : subst,X164 : subst,X166 : subst] : ((((X163 @ X164 @ X165 @ (comp @ X166 @ X167))) != $true) & ($true = ((X163 @ (comp @ X164 @ X166) @ (sub @ X165 @ X166) @ X167)))) | ? [X173 : term,X170 : subst,X172 : subst,X171 : subst] : (($true != ((X163 @ (comp @ X171 @ X170) @ (sub @ X173 @ X170) @ X172))) & (((X163 @ X171 @ X173 @ (comp @ X170 @ X172))) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f68,definition,(
% 2.19/0.60 ! [X356 : (term > $o)] : (($true = ((sP55 @ X356))) <=> ? [X359 : term,X360 : term] : (($true != ((X356 @ (ap @ X359 @ X360)))) & ($true = ((X356 @ X360))) & (((X356 @ X359)) = $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f69,definition,(
% 2.19/0.60 ($true = sP56) <=> ! [X373 : (subst > term > subst > $o),X372 : term] : (? [X375 : (subst > term > term),X376 : term] : (($true != ((X373 @ id @ (lam @ (X375 @ sh @ one)) @ id))) & ! [X380 : subst,X379 : subst,X378 : term] : (((sub @ X376 @ (push @ (sub @ X378 @ X380) @ (comp @ X379 @ X380)))) = ((X375 @ (comp @ X379 @ X380) @ (sub @ X378 @ X380)))) & ! [X377 : term] : (($true = ((X373 @ id @ (X375 @ id @ X377) @ id))) | ($true != ((X373 @ id @ X377 @ id)))) & ! [X381 : subst,X383 : subst,X382 : term] : (((sub @ (X375 @ X383 @ X382) @ X381)) = ((sub @ (sub @ X376 @ (push @ X382 @ X383)) @ X381)))) | ? [X374 : term] : (($true = ((X373 @ id @ X374 @ id))) & ($true != ((X373 @ id @ (sub @ X372 @ (push @ X374 @ id)) @ id)))) | ($true = ((X373 @ id @ (lam @ (sub @ X372 @ (push @ one @ sh))) @ id))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f70,definition,(
% 2.19/0.60 ($true = sP57) <=> ! [X152 : (term > $o),X153 : (subst > term > subst > $o),X151 : term] : (? [X154 : term] : (((X152 @ X154)) != ((X153 @ id @ X154 @ id))) | ? [X160 : term] : (($true != ((X152 @ (sub @ X151 @ (push @ X160 @ id))))) & ($true = ((X152 @ X160)))) | (((X152 @ (lam @ X151))) = $true) | ? [X155 : (subst > term > term)] : (! [X156 : term,X158 : subst,X157 : subst] : (((X155 @ (comp @ X158 @ X157) @ (sub @ X156 @ X157))) = ((sub @ (X155 @ X158 @ X156) @ X157))) & ! [X159 : term] : (($true = ((X153 @ id @ (X155 @ id @ X159) @ id))) | (((X153 @ id @ X159 @ id)) != $true)) & ($true != ((X153 @ id @ (lam @ (X155 @ sh @ one)) @ id)))))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f71,definition,(
% 2.19/0.60 ($true = sP58) <=> ! [X134 : (subst > term > subst > $o),X133 : term] : ((((X134 @ id @ (lam @ (sub @ X133 @ (push @ one @ sh))) @ id)) = $true) | ? [X135 : term] : (($true != ((X134 @ id @ (sub @ X133 @ (push @ X135 @ id)) @ id))) & (((X134 @ id @ X135 @ id)) = $true)) | ? [X136 : (subst > term > term)] : (! [X139 : term,X140 : subst,X138 : subst] : (((sub @ (X136 @ X140 @ X139) @ X138)) = ((X136 @ (comp @ X140 @ X138) @ (sub @ X139 @ X138)))) & ! [X137 : term] : (($true = ((X134 @ id @ (X136 @ id @ X137) @ id))) | ($true != ((X134 @ id @ X137 @ id)))) & (((X134 @ id @ (lam @ (X136 @ sh @ one)) @ id)) != $true)))),
% 2.19/0.60 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 2.19/0.60 thf(f72,plain,(
% 2.19/0.60 (pushprop = $true) & ((axshiftcons = $true) <=> ! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424)) & (axmap = $true) & ((hoasinduction_lem3aa = $true) <=> ($true = sP58)) & (axapp = $true) & ((axscons = $true) <=> ! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431)) & ((shinj = $true) <=> ! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh))))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X483 : d_term,X482 : d_term] : ((X482 = X483) | (((d2term @ X482)) != ((d2term @ X483)))) & (hoasinduction_lem1_lthm = $true) & (! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) <=> (pushprop_lem1 = $true)) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP57) <=> (hoasinduction_lem3v2a = $true)) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP56)) & (hoasinduction_lem3a_gthm = $true) & ((induction = $true) <=> ! [X357 : term,X356 : (term > $o)] : (($true = ((X356 @ X357))) | ($true = ((sP55 @ X356))) | ? [X358 : term] : (($true != ((X356 @ (lam @ X358)))) & ($true = ((X356 @ X358)))) | ? [X361 : term] : ((((X356 @ X361)) != $true) & ($true = ((var @ X361)))))) & (! [X427 : term] : ? [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) = ((X428 @ sh @ one))) <=> (hoasinduction_lem3b_lthm = $true)) & (($true = sP54) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3v2a_lthm = $true) <=> ($true = sP52)) & ((pushprop_lem1v2_lthm = $true) <=> (! [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true = ((X368 @ one))) | ($true != ((X370 @ X369))) | ? [X371 : term] : (((X368 @ X371)) != ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) | ? [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) != X366))) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP51)) & ! [X423 : d_term] : (d_one = X423) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) <=> (substmonoid = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) <=> (axidr = $true)) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & (($true = sP50) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasapinj1_gthm = $true) & (! [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (? [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) != ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525))) | ? [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) != ((sub @ (X523 @ X526 @ X528) @ X527)))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2_lthm = $true) <=> (sP45 = $true)) & (($true = sP43) <=> (hoasinduction_lem3a = $true)) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) <=> (axvarid = $true)) & (lamnotvar = $true) & ((apinj1 = $true) <=> ! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191))))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47)))) | ? [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) != X42) | ? [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) != X45)) <=> (pushprop_lem1_lthm = $true)) & (((d2subst @ d_id)) = sh) & ((laminj = $true) <=> ! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) <=> (hoasinduction_lem3v2_f = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (($true = sP42) <=> (hoasinduction_lem2v2 = $true)) & (hoasinduction_lem1v2_gthm = $true) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) != ((d2subst @ X271))) | (X271 = X272)) & (($true = sP40) <=> (hoasinduction_lem3 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & (($true = sP38) <=> (hoasinduction_lthm_3 = $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : term,X515 : term] : (($true != ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) & ($true = ((X512 @ id @ X514 @ id))) & ($true = ((X512 @ id @ X515 @ id)))) | ($true = ((sP32 @ X512))) | ($true = ((X512 @ id @ X513 @ id)))) <=> (hoasinduction_no_psi_cond = $true)) & ((hoasinduction_lem3v2 = $true) <=> ($true = sP31)) & (! [X479 : (subst > term > subst > $o)] : ? [X480 : (term > $o)] : ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) <=> (hoasinduction_lem0 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X362 : (subst > term > subst > $o)] : ? [X363 : (term > $o)] : ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id)))) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & ((induction2lem = $true) <=> ($true = sP29)) & (pushprop_lem1_gthm = $true) & ((? [X142 : term] : (((sub @ X142 @ id)) != X142) | ? [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 != X146) & (((ap @ X145 @ X144)) = ((ap @ X146 @ X143)))) | ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))) <=> (hoasapinj1_lthm = $true)) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) <=> (termmset = $true)) & (hoasinduction_lem1 = $true) & ((sP27 = $true) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3b = $true) <=> ! [X292 : term] : ? [X293 : (subst > term > term)] : (((X293 @ sh @ one)) = ((sub @ X292 @ (push @ one @ sh))))) & (($true = sP25) <=> (induction2_lthm = $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X475 : term] : ? [X476 : (subst > term > term)] : ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477)))) & (substmonoid_gthm = $true) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) <=> (axvarcons = $true)) & (ulamvar1 != $true) & ((hoasinduction_lem3_lthm = $true) <=> ($true = sP21)) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) <=> ($true = sP18)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & ((! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179)) | ? [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 != X176) & (((ap @ X177 @ X175)) = ((ap @ X174 @ X176))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (! [X14 : (term > $o),X15 : subst,X13 : term] : ? [X16 : (term > $o)] : ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))) <=> (pushprop_lem0_lthm = $true)) & ((substmonoid_lthm = $true) <=> (? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500) | (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503)))) & ((hoasinduction_lthm = $true) <=> ($true = sP17)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) <=> (axidl = $true)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj2 = $true) <=> ! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313))))) & ((apinj2 = $true) <=> ! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85))))) & (axabs = $true) & (hoaslamnotap_lthm = $true) & (! [X10 : (term > $o),X8 : term,X9 : subst] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) <=> (pushprop_lem0 = $true)) & ((pushprop_lem1v2 = $true) <=> ! [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) != $true) | ($true = ((X39 @ one))) | ? [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) != ((X39 @ X41))))) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & ((induction2lem_lthm = $true) <=> (sP8 = $true)) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & (($true = sP4) <=> (induction2 = $true)) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) <=> (sP2 = $true)) & (hoasinduction_lem1_gthm = $true) & ! [X426 : d_subst] : (d_id = X426) & ((hoasapinj1 = $true) <=> ! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100))) & (! [X4 : term,X2 : term,X3 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) != ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) <=> (hoaslamnotap = $true))),
% 2.19/0.60 inference(definition_folding,[],[f12,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13])).
% 2.19/0.60 thf(f260,plain,(
% 2.19/0.60 (pushprop = $true) & (((axshiftcons = $true) | ? [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) != X424)) & (! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424) | (axshiftcons != $true))) & (axmap = $true) & (((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true))) & (axapp = $true) & (((axscons = $true) | ? [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) != X431)) & (! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431) | (axscons != $true))) & (((shinj = $true) | ? [X355 : term,X354 : term] : ((X354 != X355) & (((sub @ X355 @ sh)) = ((sub @ X354 @ sh))))) & (! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh)))) | (shinj != $true))) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X483 : d_term,X482 : d_term] : ((X482 = X483) | (((d2term @ X482)) != ((d2term @ X483)))) & (hoasinduction_lem1_lthm = $true) & ((! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true != ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) & ($true = ((X92 @ X88)))))) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & ((($true = sP57) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP57))) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & (((hoasinduction_lem3aaa = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3aaa != $true))) & (hoasinduction_lem3a_gthm = $true) & (((induction = $true) | ? [X357 : term,X356 : (term > $o)] : (($true != ((X356 @ X357))) & ($true != ((sP55 @ X356))) & ! [X358 : term] : (($true = ((X356 @ (lam @ X358)))) | ($true != ((X356 @ X358)))) & ! [X361 : term] : ((((X356 @ X361)) = $true) | ($true != ((var @ X361)))))) & (! [X357 : term,X356 : (term > $o)] : (($true = ((X356 @ X357))) | ($true = ((sP55 @ X356))) | ? [X358 : term] : (($true != ((X356 @ (lam @ X358)))) & ($true = ((X356 @ X358)))) | ? [X361 : term] : ((((X356 @ X361)) != $true) & ($true = ((var @ X361))))) | (induction != $true))) & ((! [X427 : term] : ? [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) = ((X428 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X427 : term] : ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one))))) & ((($true = sP54) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP54))) & (((hoasinduction_lem3v2a_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2a_lthm != $true))) & (((pushprop_lem1v2_lthm = $true) | (? [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true != ((X368 @ one))) & ($true = ((X370 @ X369))) & ! [X371 : term] : (((X368 @ X371)) = ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) & ! [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) = X366))) & ((! [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true = ((X368 @ one))) | ($true != ((X370 @ X369))) | ? [X371 : term] : (((X368 @ X371)) != ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) | ? [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) != X366)) | (pushprop_lem1v2_lthm != $true))) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3aa_lthm != $true))) & ! [X423 : d_term] : (d_one = X423) & (((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X352 : subst] : (((comp @ X352 @ id)) != X352) | ? [X353 : subst] : (((comp @ id @ X353)) != X353)))) & (hoasinduction_lem3_gthm = $true) & ((! [X521 : subst] : (((comp @ X521 @ id)) = X521) | (axidr != $true)) & ((axidr = $true) | ? [X521 : subst] : (((comp @ X521 @ id)) != X521))) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & ((($true = sP50) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP50))) & (hoasapinj1_gthm = $true) & ((! [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (? [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) != ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525))) | ? [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) != ((sub @ (X523 @ X526 @ X528) @ X527)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (! [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) = ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) & (((lam @ (X523 @ sh @ one))) = ((lam @ (X522 @ sh @ one)))) & (((X522 @ X524 @ X525)) != ((X523 @ X524 @ X525))) & ! [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X523 @ X526 @ X528) @ X527)))))) & (((hoasinduction_lem3v2_lthm = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lem3v2_lthm != $true))) & ((($true = sP43) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP43))) & ((! [X141 : term] : (((sub @ X141 @ id)) = X141) | (axvarid != $true)) & ((axvarid = $true) | ? [X141 : term] : (((sub @ X141 @ id)) != X141))) & (lamnotvar = $true) & (((apinj1 = $true) | ? [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 != X192) & (((ap @ X190 @ X193)) = ((ap @ X192 @ X191))))) & (! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191)))) | (apinj1 != $true))) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (((! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47)))) | ? [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) != X42) | ? [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) != X45)) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true != ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) & ($true = ((X48 @ X47)))) & ! [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) = X42) & ! [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) = X45)))) & (((d2subst @ d_id)) = sh) & (((laminj = $true) | ? [X270 : term,X269 : term] : ((((lam @ X270)) = ((lam @ X269))) & (X269 != X270))) & (! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270)) | (laminj != $true))) & ((! [X93 : term] : ? [X94 : (subst > term > term)] : ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X93 : term] : ! [X94 : (subst > term > term)] : ? [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) != ((sub @ X93 @ (push @ X95 @ X96)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & ((($true = sP42) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP42))) & (hoasinduction_lem1v2_gthm = $true) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) != ((d2subst @ X271))) | (X271 = X272)) & ((($true = sP40) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP40))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & ((($true = sP38) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP38))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & ((! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : term,X515 : term] : (($true != ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) & ($true = ((X512 @ id @ X514 @ id))) & ($true = ((X512 @ id @ X515 @ id)))) | ($true = ((sP32 @ X512))) | ($true = ((X512 @ id @ X513 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X512 : (subst > term > subst > $o),X513 : term] : (! [X514 : term,X515 : term] : (($true = ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) | ($true != ((X512 @ id @ X514 @ id))) | ($true != ((X512 @ id @ X515 @ id)))) & ($true != ((sP32 @ X512))) & ($true != ((X512 @ id @ X513 @ id)))))) & (((hoasinduction_lem3v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3v2 != $true))) & ((! [X479 : (subst > term > subst > $o)] : ? [X480 : (term > $o)] : ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X479 : (subst > term > subst > $o)] : ! [X480 : (term > $o)] : ? [X481 : term] : (((X479 @ id @ X481 @ id)) != ((X480 @ X481))))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasinduction_lem0_lthm = $true) | ? [X362 : (subst > term > subst > $o)] : ! [X363 : (term > $o)] : ? [X364 : term] : (((X363 @ X364)) != ((X362 @ id @ X364 @ id)))) & (! [X362 : (subst > term > subst > $o)] : ? [X363 : (term > $o)] : ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id))) | (hoasinduction_lem0_lthm != $true))) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & (((induction2lem = $true) | ($true != sP29)) & (($true = sP29) | (induction2lem != $true))) & (pushprop_lem1_gthm = $true) & (((? [X142 : term] : (((sub @ X142 @ id)) != X142) | ? [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 != X146) & (((ap @ X145 @ X144)) = ((ap @ X146 @ X143)))) | ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147))))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X142 : term] : (((sub @ X142 @ id)) = X142) & ! [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 = X146) | (((ap @ X145 @ X144)) != ((ap @ X146 @ X143)))) & ? [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 != X150) & (((ap @ (sub @ X149 @ id) @ X148)) = ((ap @ (sub @ X150 @ id) @ X147))))))) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & ((! [X249 : term] : (((sub @ X249 @ id)) = X249) | (termmset != $true)) & ((termmset = $true) | ? [X249 : term] : (((sub @ X249 @ id)) != X249))) & (hoasinduction_lem1 = $true) & (((sP27 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP27 != $true))) & (((hoasinduction_lem3b = $true) | ? [X292 : term] : ! [X293 : (subst > term > term)] : (((X293 @ sh @ one)) != ((sub @ X292 @ (push @ one @ sh))))) & (! [X292 : term] : ? [X293 : (subst > term > term)] : (((X293 @ sh @ one)) = ((sub @ X292 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & ((($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25))) & (hoasapnotvar = $true) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X475 : term] : ! [X476 : (subst > term > term)] : ? [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) != ((X476 @ X478 @ X477)))) & (! [X475 : term] : ? [X476 : (subst > term > term)] : ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477))) | (hoasinduction_lem3v2_f_lthm != $true))) & (substmonoid_gthm = $true) & ((! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) != X98))) & (ulamvar1 != $true) & (((hoasinduction_lem3_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3_lthm != $true))) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & (((hoaslaminj_lthm = $true) | ($true != sP18)) & (($true = sP18) | (hoaslaminj_lthm != $true))) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & (((! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179)) | ? [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 != X176) & (((ap @ X177 @ X175)) = ((ap @ X174 @ X176))))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) = ((ap @ (sub @ X180 @ id) @ X179))) & (X178 != X179)) & ! [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176))))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & ((! [X14 : (term > $o),X15 : subst,X13 : term] : ? [X16 : (term > $o)] : ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X14 : (term > $o),X15 : subst,X13 : term] : ! [X16 : (term > $o)] : ? [X17 : term] : (((X16 @ X17)) != ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))))) & (((substmonoid_lthm = $true) | (! [X501 : subst] : (((comp @ X501 @ id)) = X501) & ! [X500 : subst] : (((comp @ id @ X500)) = X500) & (? [X502 : subst] : (((comp @ id @ X502)) != X502) | ? [X503 : subst] : (((comp @ X503 @ id)) != X503)))) & ((? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500) | (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503))) | (substmonoid_lthm != $true))) & (((hoasinduction_lthm = $true) | ($true != sP17)) & (($true = sP17) | (hoasinduction_lthm != $true))) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & (((termmset_lthm = $true) | (! [X273 : term] : (((sub @ X273 @ id)) = X273) & ? [X274 : term] : (((sub @ X274 @ id)) != X274))) & ((? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274)) | (termmset_lthm != $true))) & ((! [X248 : subst] : (((comp @ id @ X248)) = X248) | (axidl != $true)) & ((axidl = $true) | ? [X248 : subst] : (((comp @ id @ X248)) != X248))) & (((var @ (d2term @ d_one))) != $true) & (((hoasapinj2 = $true) | ? [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 != X313) & (((ap @ (sub @ X311 @ id) @ X310)) = ((ap @ (sub @ X312 @ id) @ X313))))) & (! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313)))) | (hoasapinj2 != $true))) & (((apinj2 = $true) | ? [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 != X87) & (((ap @ X86 @ X87)) = ((ap @ X84 @ X85))))) & (! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85)))) | (apinj2 != $true))) & (axabs = $true) & (hoaslamnotap_lthm = $true) & ((! [X10 : (term > $o),X8 : term,X9 : subst] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X10 : (term > $o),X8 : term,X9 : subst] : ! [X11 : (term > $o)] : ? [X12 : term] : (((X11 @ X12)) != ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))))) & (((pushprop_lem1v2 = $true) | ? [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) = $true) & ($true != ((X39 @ one))) & ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))))) & (! [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) != $true) | ($true = ((X39 @ one))) | ? [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) != ((X39 @ X41)))) | (pushprop_lem1v2 != $true))) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & (((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true))) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & ((($true = sP4) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP4))) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & (((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true))) & (hoasinduction_lem1_gthm = $true) & ! [X426 : d_subst] : (d_id = X426) & (((hoasapinj1 = $true) | ? [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) = ((ap @ (sub @ X100 @ id) @ X102))) & (X99 != X100))) & (! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100)) | (hoasapinj1 != $true))) & ((! [X4 : term,X2 : term,X3 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) != ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X4 : term,X2 : term,X3 : (subst > term > term)] : (! [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) & (((ap @ (sub @ X2 @ id) @ X4)) = ((lam @ (X3 @ sh @ one)))))))),
% 2.19/0.60 inference(nnf_transformation,[],[f72])).
% 2.19/0.60 thf(f261,plain,(
% 2.19/0.60 (pushprop = $true) & ((axshiftcons = $true) | ? [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) != X424)) & (! [X424 : subst,X425 : term] : (((comp @ sh @ (push @ X425 @ X424))) = X424) | (axshiftcons != $true)) & (axmap = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (axapp = $true) & ((axscons = $true) | ? [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) != X431)) & (! [X431 : subst] : (((push @ (sub @ one @ X431) @ (comp @ sh @ X431))) = X431) | (axscons != $true)) & ((shinj = $true) | ? [X355 : term,X354 : term] : ((X354 != X355) & (((sub @ X355 @ sh)) = ((sub @ X354 @ sh))))) & (! [X355 : term,X354 : term] : ((X354 = X355) | (((sub @ X355 @ sh)) != ((sub @ X354 @ sh)))) | (shinj != $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X483 : d_term,X482 : d_term] : ((X482 = X483) | (((d2term @ X482)) != ((d2term @ X483)))) & (hoasinduction_lem1_lthm = $true) & (! [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true = ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) | ($true != ((X92 @ X88)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X90 : subst,X92 : (term > $o),X91 : (term > $o),X88 : term,X89 : term] : (($true != ((X91 @ (sub @ X88 @ (push @ X89 @ X90))))) & ($true = ((X92 @ X88))))) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP57) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP57)) & ! [X429 : term] : ? [X430 : d_term] : (((d2term @ X430)) = X429) & ((hoasinduction_lem3aaa = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem3a_gthm = $true) & ((induction = $true) | ? [X357 : term,X356 : (term > $o)] : (($true != ((X356 @ X357))) & ($true != ((sP55 @ X356))) & ! [X358 : term] : (($true = ((X356 @ (lam @ X358)))) | ($true != ((X356 @ X358)))) & ! [X361 : term] : ((((X356 @ X361)) = $true) | ($true != ((var @ X361)))))) & (! [X357 : term,X356 : (term > $o)] : (($true = ((X356 @ X357))) | ($true = ((sP55 @ X356))) | ? [X358 : term] : (($true != ((X356 @ (lam @ X358)))) & ($true = ((X356 @ X358)))) | ? [X361 : term] : ((((X356 @ X361)) != $true) & ($true = ((var @ X361))))) | (induction != $true)) & (! [X427 : term] : ? [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) = ((X428 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X427 : term] : ! [X428 : (subst > term > term)] : (((sub @ X427 @ (push @ one @ sh))) != ((X428 @ sh @ one)))) & (($true = sP54) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP54)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2a_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true != ((X368 @ one))) & ($true = ((X370 @ X369))) & ! [X371 : term] : (((X368 @ X371)) = ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) & ! [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) = X366))) & (! [X368 : (term > $o),X370 : (term > $o),X369 : term,X367 : subst] : (($true = ((X368 @ one))) | ($true != ((X370 @ X369))) | ? [X371 : term] : (((X368 @ X371)) != ((X370 @ (sub @ X371 @ (push @ X369 @ X367)))))) | ? [X365 : subst,X366 : term] : (((sub @ one @ (push @ X366 @ X365))) != X366) | (pushprop_lem1v2_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3aa_lthm != $true)) & ! [X423 : d_term] : (d_one = X423) & ((! [X352 : subst] : (((comp @ X352 @ id)) = X352) & ! [X353 : subst] : (((comp @ id @ X353)) = X353)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X352 : subst] : (((comp @ X352 @ id)) != X352) | ? [X353 : subst] : (((comp @ id @ X353)) != X353)) & (hoasinduction_lem3_gthm = $true) & (! [X521 : subst] : (((comp @ X521 @ id)) = X521) | (axidr != $true)) & ((axidr = $true) | ? [X521 : subst] : (((comp @ X521 @ id)) != X521)) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & (($true = sP50) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP50)) & (hoasapinj1_gthm = $true) & (! [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (? [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) != ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) | (((lam @ (X523 @ sh @ one))) != ((lam @ (X522 @ sh @ one)))) | (((X522 @ X524 @ X525)) = ((X523 @ X524 @ X525))) | ? [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) != ((sub @ (X523 @ X526 @ X528) @ X527)))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X522 : (subst > term > term),X524 : subst,X523 : (subst > term > term),X525 : term] : (! [X531 : subst,X530 : subst,X529 : term] : (((sub @ (X522 @ X530 @ X529) @ X531)) = ((X522 @ (comp @ X530 @ X531) @ (sub @ X529 @ X531)))) & (((lam @ (X523 @ sh @ one))) = ((lam @ (X522 @ sh @ one)))) & (((X522 @ X524 @ X525)) != ((X523 @ X524 @ X525))) & ! [X528 : term,X527 : subst,X526 : subst] : (((X523 @ (comp @ X526 @ X527) @ (sub @ X528 @ X527))) = ((sub @ (X523 @ X526 @ X528) @ X527))))) & ((hoasinduction_lem3v2_lthm = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (! [X141 : term] : (((sub @ X141 @ id)) = X141) | (axvarid != $true)) & ((axvarid = $true) | ? [X141 : term] : (((sub @ X141 @ id)) != X141)) & (lamnotvar = $true) & ((apinj1 = $true) | ? [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 != X192) & (((ap @ X190 @ X193)) = ((ap @ X192 @ X191))))) & (! [X190 : term,X193 : term,X191 : term,X192 : term] : ((X190 = X192) | (((ap @ X190 @ X193)) != ((ap @ X192 @ X191)))) | (apinj1 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true = ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) | ($true != ((X48 @ X47)))) | ? [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) != X42) | ? [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) != X45) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X47 : term,X49 : subst,X48 : (term > $o),X50 : (term > $o),X46 : term] : (($true != ((X50 @ (sub @ X47 @ (push @ X46 @ X49))))) & ($true = ((X48 @ X47)))) & ! [X43 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X43))) = X42) & ! [X44 : term,X45 : subst] : (((comp @ sh @ (push @ X44 @ X45))) = X45))) & (((d2subst @ d_id)) = sh) & ((laminj = $true) | ? [X270 : term,X269 : term] : ((((lam @ X270)) = ((lam @ X269))) & (X269 != X270))) & (! [X270 : term,X269 : term] : ((((lam @ X270)) != ((lam @ X269))) | (X269 = X270)) | (laminj != $true)) & (! [X93 : term] : ? [X94 : (subst > term > term)] : ! [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) = ((sub @ X93 @ (push @ X95 @ X96)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X93 : term] : ! [X94 : (subst > term > term)] : ? [X95 : term,X96 : subst] : (((X94 @ X96 @ X95)) != ((sub @ X93 @ (push @ X95 @ X96))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (($true = sP42) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP42)) & (hoasinduction_lem1v2_gthm = $true) & ! [X272 : d_subst,X271 : d_subst] : ((((d2subst @ X272)) != ((d2subst @ X271))) | (X271 = X272)) & (($true = sP40) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP40)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & (($true = sP38) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP38)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X512 : (subst > term > subst > $o),X513 : term] : (? [X514 : term,X515 : term] : (($true != ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) & ($true = ((X512 @ id @ X514 @ id))) & ($true = ((X512 @ id @ X515 @ id)))) | ($true = ((sP32 @ X512))) | ($true = ((X512 @ id @ X513 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X512 : (subst > term > subst > $o),X513 : term] : (! [X514 : term,X515 : term] : (($true = ((X512 @ id @ (ap @ (sub @ X514 @ id) @ X515) @ id))) | ($true != ((X512 @ id @ X514 @ id))) | ($true != ((X512 @ id @ X515 @ id)))) & ($true != ((sP32 @ X512))) & ($true != ((X512 @ id @ X513 @ id))))) & ((hoasinduction_lem3v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3v2 != $true)) & (! [X479 : (subst > term > subst > $o)] : ? [X480 : (term > $o)] : ! [X481 : term] : (((X479 @ id @ X481 @ id)) = ((X480 @ X481))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X479 : (subst > term > subst > $o)] : ! [X480 : (term > $o)] : ? [X481 : term] : (((X479 @ id @ X481 @ id)) != ((X480 @ X481)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) | ? [X362 : (subst > term > subst > $o)] : ! [X363 : (term > $o)] : ? [X364 : term] : (((X363 @ X364)) != ((X362 @ id @ X364 @ id)))) & (! [X362 : (subst > term > subst > $o)] : ? [X363 : (term > $o)] : ! [X364 : term] : (((X363 @ X364)) = ((X362 @ id @ X364 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & ((induction2lem = $true) | ($true != sP29)) & (($true = sP29) | (induction2lem != $true)) & (pushprop_lem1_gthm = $true) & (? [X142 : term] : (((sub @ X142 @ id)) != X142) | ? [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 != X146) & (((ap @ X145 @ X144)) = ((ap @ X146 @ X143)))) | ! [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 = X150) | (((ap @ (sub @ X149 @ id) @ X148)) != ((ap @ (sub @ X150 @ id) @ X147)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X142 : term] : (((sub @ X142 @ id)) = X142) & ! [X144 : term,X146 : term,X145 : term,X143 : term] : ((X145 = X146) | (((ap @ X145 @ X144)) != ((ap @ X146 @ X143)))) & ? [X148 : term,X147 : term,X150 : term,X149 : term] : ((X149 != X150) & (((ap @ (sub @ X149 @ id) @ X148)) = ((ap @ (sub @ X150 @ id) @ X147)))))) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (! [X249 : term] : (((sub @ X249 @ id)) = X249) | (termmset != $true)) & ((termmset = $true) | ? [X249 : term] : (((sub @ X249 @ id)) != X249)) & (hoasinduction_lem1 = $true) & ((sP27 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP27 != $true)) & ((hoasinduction_lem3b = $true) | ? [X292 : term] : ! [X293 : (subst > term > term)] : (((X293 @ sh @ one)) != ((sub @ X292 @ (push @ one @ sh))))) & (! [X292 : term] : ? [X293 : (subst > term > term)] : (((X293 @ sh @ one)) = ((sub @ X292 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X475 : term] : ! [X476 : (subst > term > term)] : ? [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) != ((X476 @ X478 @ X477)))) & (! [X475 : term] : ? [X476 : (subst > term > term)] : ! [X478 : subst,X477 : term] : (((sub @ X475 @ (push @ X477 @ X478))) = ((X476 @ X478 @ X477))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & (! [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) = X98) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X97 : subst,X98 : term] : (((sub @ one @ (push @ X98 @ X97))) != X98)) & (ulamvar1 != $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3_lthm != $true)) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP18)) & (($true = sP18) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & (! [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) != ((ap @ (sub @ X180 @ id) @ X179))) | (X178 = X179)) | ? [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 != X176) & (((ap @ X177 @ X175)) = ((ap @ X174 @ X176)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X180 : term,X179 : term,X181 : term,X178 : term] : ((((ap @ (sub @ X181 @ id) @ X178)) = ((ap @ (sub @ X180 @ id) @ X179))) & (X178 != X179)) & ! [X174 : term,X177 : term,X176 : term,X175 : term] : ((X175 = X176) | (((ap @ X177 @ X175)) != ((ap @ X174 @ X176)))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (! [X14 : (term > $o),X15 : subst,X13 : term] : ? [X16 : (term > $o)] : ! [X17 : term] : (((X16 @ X17)) = ((X14 @ (sub @ X17 @ (push @ X13 @ X15))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X14 : (term > $o),X15 : subst,X13 : term] : ! [X16 : (term > $o)] : ? [X17 : term] : (((X16 @ X17)) != ((X14 @ (sub @ X17 @ (push @ X13 @ X15)))))) & ((substmonoid_lthm = $true) | (! [X501 : subst] : (((comp @ X501 @ id)) = X501) & ! [X500 : subst] : (((comp @ id @ X500)) = X500) & (? [X502 : subst] : (((comp @ id @ X502)) != X502) | ? [X503 : subst] : (((comp @ X503 @ id)) != X503)))) & (? [X501 : subst] : (((comp @ X501 @ id)) != X501) | ? [X500 : subst] : (((comp @ id @ X500)) != X500) | (! [X502 : subst] : (((comp @ id @ X502)) = X502) & ! [X503 : subst] : (((comp @ X503 @ id)) = X503)) | (substmonoid_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP17)) & (($true = sP17) | (hoasinduction_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X0 : subst] : ? [X1 : d_subst] : (((d2subst @ X1)) = X0) & ((termmset_lthm = $true) | (! [X273 : term] : (((sub @ X273 @ id)) = X273) & ? [X274 : term] : (((sub @ X274 @ id)) != X274))) & (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274) | (termmset_lthm != $true)) & (! [X248 : subst] : (((comp @ id @ X248)) = X248) | (axidl != $true)) & ((axidl = $true) | ? [X248 : subst] : (((comp @ id @ X248)) != X248)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj2 = $true) | ? [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 != X313) & (((ap @ (sub @ X311 @ id) @ X310)) = ((ap @ (sub @ X312 @ id) @ X313))))) & (! [X310 : term,X312 : term,X313 : term,X311 : term] : ((X310 = X313) | (((ap @ (sub @ X311 @ id) @ X310)) != ((ap @ (sub @ X312 @ id) @ X313)))) | (hoasapinj2 != $true)) & ((apinj2 = $true) | ? [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 != X87) & (((ap @ X86 @ X87)) = ((ap @ X84 @ X85))))) & (! [X85 : term,X86 : term,X84 : term,X87 : term] : ((X85 = X87) | (((ap @ X86 @ X87)) != ((ap @ X84 @ X85)))) | (apinj2 != $true)) & (axabs = $true) & (hoaslamnotap_lthm = $true) & (! [X10 : (term > $o),X8 : term,X9 : subst] : ? [X11 : (term > $o)] : ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X8 @ X9))))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X10 : (term > $o),X8 : term,X9 : subst] : ! [X11 : (term > $o)] : ? [X12 : term] : (((X11 @ X12)) != ((X10 @ (sub @ X12 @ (push @ X8 @ X9)))))) & ((pushprop_lem1v2 = $true) | ? [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) = $true) & ($true != ((X39 @ one))) & ! [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) = ((X39 @ X41))))) & (! [X38 : subst,X40 : (term > $o),X37 : term,X39 : (term > $o)] : ((((X40 @ X37)) != $true) | ($true = ((X39 @ one))) | ? [X41 : term] : (((X40 @ (sub @ X41 @ (push @ X37 @ X38)))) != ((X39 @ X41)))) | (pushprop_lem1v2 != $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & (($true = sP4) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP4)) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & (hoasinduction_lem1_gthm = $true) & ! [X426 : d_subst] : (d_id = X426) & ((hoasapinj1 = $true) | ? [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) = ((ap @ (sub @ X100 @ id) @ X102))) & (X99 != X100))) & (! [X99 : term,X102 : term,X100 : term,X101 : term] : ((((ap @ (sub @ X99 @ id) @ X101)) != ((ap @ (sub @ X100 @ id) @ X102))) | (X99 = X100)) | (hoasapinj1 != $true)) & (! [X4 : term,X2 : term,X3 : (subst > term > term)] : (? [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) != ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) | (((ap @ (sub @ X2 @ id) @ X4)) != ((lam @ (X3 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X4 : term,X2 : term,X3 : (subst > term > term)] : (! [X5 : subst,X6 : subst,X7 : term] : (((sub @ (X3 @ X6 @ X7) @ X5)) = ((X3 @ (comp @ X6 @ X5) @ (sub @ X7 @ X5)))) & (((ap @ (sub @ X2 @ id) @ X4)) = ((lam @ (X3 @ sh @ one))))))),
% 2.19/0.60 inference(flattening,[],[f260])).
% 2.19/0.60 thf(f262,plain,(
% 2.19/0.60 (pushprop = $true) & ((axshiftcons = $true) | ? [X0 : subst,X1 : term] : (((comp @ sh @ (push @ X1 @ X0))) != X0)) & (! [X2 : subst,X3 : term] : (((comp @ sh @ (push @ X3 @ X2))) = X2) | (axshiftcons != $true)) & (axmap = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (axapp = $true) & ((axscons = $true) | ? [X4 : subst] : (((push @ (sub @ one @ X4) @ (comp @ sh @ X4))) != X4)) & (! [X5 : subst] : (((push @ (sub @ one @ X5) @ (comp @ sh @ X5))) = X5) | (axscons != $true)) & ((shinj = $true) | ? [X6 : term,X7 : term] : ((X6 != X7) & (((sub @ X7 @ sh)) = ((sub @ X6 @ sh))))) & (! [X8 : term,X9 : term] : ((X8 = X9) | (((sub @ X9 @ sh)) != ((sub @ X8 @ sh)))) | (shinj != $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X10 : d_term,X11 : d_term] : ((X10 = X11) | (((d2term @ X10)) != ((d2term @ X11)))) & (hoasinduction_lem1_lthm = $true) & (! [X12 : subst,X13 : (term > $o),X14 : (term > $o),X15 : term,X16 : term] : (($true = ((X14 @ (sub @ X15 @ (push @ X16 @ X12))))) | ($true != ((X13 @ X15)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ? [X17 : subst,X18 : (term > $o),X19 : (term > $o),X20 : term,X21 : term] : (($true != ((X19 @ (sub @ X20 @ (push @ X21 @ X17))))) & ($true = ((X18 @ X20))))) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP57) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP57)) & ! [X22 : term] : ? [X23 : d_term] : (((d2term @ X23)) = X22) & ((hoasinduction_lem3aaa = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem3a_gthm = $true) & ((induction = $true) | ? [X24 : term,X25 : (term > $o)] : ((((X25 @ X24)) != $true) & ($true != ((sP55 @ X25))) & ! [X26 : term] : (($true = ((X25 @ (lam @ X26)))) | ($true != ((X25 @ X26)))) & ! [X27 : term] : ((((X25 @ X27)) = $true) | ($true != ((var @ X27)))))) & (! [X28 : term,X29 : (term > $o)] : (($true = ((X29 @ X28))) | ($true = ((sP55 @ X29))) | ? [X30 : term] : ((((X29 @ (lam @ X30))) != $true) & ($true = ((X29 @ X30)))) | ? [X31 : term] : (($true != ((X29 @ X31))) & ($true = ((var @ X31))))) | (induction != $true)) & (! [X32 : term] : ? [X33 : (subst > term > term)] : (((sub @ X32 @ (push @ one @ sh))) = ((X33 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ? [X34 : term] : ! [X35 : (subst > term > term)] : (((sub @ X34 @ (push @ one @ sh))) != ((X35 @ sh @ one)))) & (($true = sP54) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP54)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2a_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X36 : (term > $o),X37 : (term > $o),X38 : term,X39 : subst] : ((((X36 @ one)) != $true) & ($true = ((X37 @ X38))) & ! [X40 : term] : (((X37 @ (sub @ X40 @ (push @ X38 @ X39)))) = ((X36 @ X40)))) & ! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42))) & (! [X43 : (term > $o),X44 : (term > $o),X45 : term,X46 : subst] : ((((X43 @ one)) = $true) | ($true != ((X44 @ X45))) | ? [X47 : term] : (((X44 @ (sub @ X47 @ (push @ X45 @ X46)))) != ((X43 @ X47)))) | ? [X48 : subst,X49 : term] : (((sub @ one @ (push @ X49 @ X48))) != X49) | (pushprop_lem1v2_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3aa_lthm != $true)) & ! [X50 : d_term] : (d_one = X50) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X52 : subst] : (((comp @ id @ X52)) = X52)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X53 : subst] : (((comp @ X53 @ id)) != X53) | ? [X54 : subst] : (((comp @ id @ X54)) != X54)) & (hoasinduction_lem3_gthm = $true) & (! [X55 : subst] : (((comp @ X55 @ id)) = X55) | (axidr != $true)) & ((axidr = $true) | ? [X56 : subst] : (((comp @ X56 @ id)) != X56)) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & (($true = sP50) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP50)) & (hoasapinj1_gthm = $true) & (! [X57 : (subst > term > term),X58 : subst,X59 : (subst > term > term),X60 : term] : (? [X61 : subst,X62 : subst,X63 : term] : (((X57 @ (comp @ X62 @ X61) @ (sub @ X63 @ X61))) != ((sub @ (X57 @ X62 @ X63) @ X61))) | (((lam @ (X59 @ sh @ one))) != ((lam @ (X57 @ sh @ one)))) | (((X57 @ X58 @ X60)) = ((X59 @ X58 @ X60))) | ? [X64 : term,X65 : subst,X66 : subst] : (((sub @ (X59 @ X66 @ X64) @ X65)) != ((X59 @ (comp @ X66 @ X65) @ (sub @ X64 @ X65))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X67 : (subst > term > term),X68 : subst,X69 : (subst > term > term),X70 : term] : (! [X71 : subst,X72 : subst,X73 : term] : (((sub @ (X67 @ X72 @ X73) @ X71)) = ((X67 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71)))) & (((lam @ (X69 @ sh @ one))) = ((lam @ (X67 @ sh @ one)))) & (((X69 @ X68 @ X70)) != ((X67 @ X68 @ X70))) & ! [X74 : term,X75 : subst,X76 : subst] : (((X69 @ (comp @ X76 @ X75) @ (sub @ X74 @ X75))) = ((sub @ (X69 @ X76 @ X74) @ X75))))) & ((hoasinduction_lem3v2_lthm = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (! [X77 : term] : (((sub @ X77 @ id)) = X77) | (axvarid != $true)) & ((axvarid = $true) | ? [X78 : term] : (((sub @ X78 @ id)) != X78)) & (lamnotvar = $true) & ((apinj1 = $true) | ? [X79 : term,X80 : term,X81 : term,X82 : term] : ((X79 != X82) & (((ap @ X79 @ X80)) = ((ap @ X82 @ X81))))) & (! [X83 : term,X84 : term,X85 : term,X86 : term] : ((X83 = X86) | (((ap @ X86 @ X85)) != ((ap @ X83 @ X84)))) | (apinj1 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X87 : term,X88 : subst,X89 : (term > $o),X90 : (term > $o),X91 : term] : (($true = ((X90 @ (sub @ X87 @ (push @ X91 @ X88))))) | ($true != ((X89 @ X87)))) | ? [X92 : subst,X93 : term] : (((sub @ one @ (push @ X93 @ X92))) != X93) | ? [X94 : term,X95 : subst] : (((comp @ sh @ (push @ X94 @ X95))) != X95) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (? [X96 : term,X97 : subst,X98 : (term > $o),X99 : (term > $o),X100 : term] : ((((X99 @ (sub @ X96 @ (push @ X100 @ X97)))) != $true) & ($true = ((X98 @ X96)))) & ! [X101 : subst,X102 : term] : (((sub @ one @ (push @ X102 @ X101))) = X102) & ! [X103 : term,X104 : subst] : (((comp @ sh @ (push @ X103 @ X104))) = X104))) & (((d2subst @ d_id)) = sh) & ((laminj = $true) | ? [X105 : term,X106 : term] : ((((lam @ X106)) = ((lam @ X105))) & (X105 != X106))) & (! [X107 : term,X108 : term] : ((((lam @ X108)) != ((lam @ X107))) | (X107 = X108)) | (laminj != $true)) & (! [X109 : term] : ? [X110 : (subst > term > term)] : ! [X111 : term,X112 : subst] : (((sub @ X109 @ (push @ X111 @ X112))) = ((X110 @ X112 @ X111))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ? [X113 : term] : ! [X114 : (subst > term > term)] : ? [X115 : term,X116 : subst] : (((sub @ X113 @ (push @ X115 @ X116))) != ((X114 @ X116 @ X115)))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (($true = sP42) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP42)) & (hoasinduction_lem1v2_gthm = $true) & ! [X117 : d_subst,X118 : d_subst] : ((((d2subst @ X117)) != ((d2subst @ X118))) | (X117 = X118)) & (($true = sP40) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP40)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & (($true = sP38) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP38)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X119 : (subst > term > subst > $o),X120 : term] : (? [X121 : term,X122 : term] : ((((X119 @ id @ (ap @ (sub @ X121 @ id) @ X122) @ id)) != $true) & ($true = ((X119 @ id @ X121 @ id))) & (((X119 @ id @ X122 @ id)) = $true)) | ($true = ((sP32 @ X119))) | ($true = ((X119 @ id @ X120 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X123 : (subst > term > subst > $o),X124 : term] : (! [X125 : term,X126 : term] : (($true = ((X123 @ id @ (ap @ (sub @ X125 @ id) @ X126) @ id))) | ($true != ((X123 @ id @ X125 @ id))) | ($true != ((X123 @ id @ X126 @ id)))) & (((sP32 @ X123)) != $true) & ($true != ((X123 @ id @ X124 @ id))))) & ((hoasinduction_lem3v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3v2 != $true)) & (! [X127 : (subst > term > subst > $o)] : ? [X128 : (term > $o)] : ! [X129 : term] : (((X128 @ X129)) = ((X127 @ id @ X129 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X130 : (subst > term > subst > $o)] : ! [X131 : (term > $o)] : ? [X132 : term] : (((X130 @ id @ X132 @ id)) != ((X131 @ X132)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) | ? [X133 : (subst > term > subst > $o)] : ! [X134 : (term > $o)] : ? [X135 : term] : (((X133 @ id @ X135 @ id)) != ((X134 @ X135)))) & (! [X136 : (subst > term > subst > $o)] : ? [X137 : (term > $o)] : ! [X138 : term] : (((X137 @ X138)) = ((X136 @ id @ X138 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & ((induction2lem = $true) | ($true != sP29)) & (($true = sP29) | (induction2lem != $true)) & (pushprop_lem1_gthm = $true) & (? [X139 : term] : (((sub @ X139 @ id)) != X139) | ? [X140 : term,X141 : term,X142 : term,X143 : term] : ((X141 != X142) & (((ap @ X141 @ X143)) = ((ap @ X142 @ X140)))) | ! [X144 : term,X145 : term,X146 : term,X147 : term] : ((X146 = X147) | (((ap @ (sub @ X146 @ id) @ X145)) != ((ap @ (sub @ X147 @ id) @ X144)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X148 : term] : (((sub @ X148 @ id)) = X148) & ! [X149 : term,X150 : term,X151 : term,X152 : term] : ((X150 = X151) | (((ap @ X151 @ X149)) != ((ap @ X150 @ X152)))) & ? [X153 : term,X154 : term,X155 : term,X156 : term] : ((X155 != X156) & (((ap @ (sub @ X155 @ id) @ X154)) = ((ap @ (sub @ X156 @ id) @ X153)))))) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (! [X157 : term] : (((sub @ X157 @ id)) = X157) | (termmset != $true)) & ((termmset = $true) | ? [X158 : term] : (((sub @ X158 @ id)) != X158)) & (hoasinduction_lem1 = $true) & ((sP27 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP27 != $true)) & ((hoasinduction_lem3b = $true) | ? [X159 : term] : ! [X160 : (subst > term > term)] : (((X160 @ sh @ one)) != ((sub @ X159 @ (push @ one @ sh))))) & (! [X161 : term] : ? [X162 : (subst > term > term)] : (((sub @ X161 @ (push @ one @ sh))) = ((X162 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X163 : term] : ! [X164 : (subst > term > term)] : ? [X165 : subst,X166 : term] : (((X164 @ X165 @ X166)) != ((sub @ X163 @ (push @ X166 @ X165))))) & (! [X167 : term] : ? [X168 : (subst > term > term)] : ! [X169 : subst,X170 : term] : (((sub @ X167 @ (push @ X170 @ X169))) = ((X168 @ X169 @ X170))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & (! [X171 : subst,X172 : term] : (((sub @ one @ (push @ X172 @ X171))) = X172) | (axvarcons != $true)) & ((axvarcons = $true) | ? [X173 : subst,X174 : term] : (((sub @ one @ (push @ X174 @ X173))) != X174)) & (ulamvar1 != $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3_lthm != $true)) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP18)) & (($true = sP18) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & (! [X175 : term,X176 : term,X177 : term,X178 : term] : ((((ap @ (sub @ X175 @ id) @ X176)) != ((ap @ (sub @ X177 @ id) @ X178))) | (X176 = X178)) | ? [X179 : term,X180 : term,X181 : term,X182 : term] : ((X181 != X182) & (((ap @ X179 @ X181)) = ((ap @ X180 @ X182)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (? [X183 : term,X184 : term,X185 : term,X186 : term] : ((((ap @ (sub @ X183 @ id) @ X184)) = ((ap @ (sub @ X185 @ id) @ X186))) & (X184 != X186)) & ! [X187 : term,X188 : term,X189 : term,X190 : term] : ((X189 = X190) | (((ap @ X188 @ X190)) != ((ap @ X187 @ X189)))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (! [X191 : (term > $o),X192 : subst,X193 : term] : ? [X194 : (term > $o)] : ! [X195 : term] : (((X194 @ X195)) = ((X191 @ (sub @ X195 @ (push @ X193 @ X192))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X196 : (term > $o),X197 : subst,X198 : term] : ! [X199 : (term > $o)] : ? [X200 : term] : (((X199 @ X200)) != ((X196 @ (sub @ X200 @ (push @ X198 @ X197)))))) & ((substmonoid_lthm = $true) | (! [X201 : subst] : (((comp @ X201 @ id)) = X201) & ! [X202 : subst] : (((comp @ id @ X202)) = X202) & (? [X203 : subst] : (((comp @ id @ X203)) != X203) | ? [X204 : subst] : (((comp @ X204 @ id)) != X204)))) & (? [X205 : subst] : (((comp @ X205 @ id)) != X205) | ? [X206 : subst] : (((comp @ id @ X206)) != X206) | (! [X207 : subst] : (((comp @ id @ X207)) = X207) & ! [X208 : subst] : (((comp @ X208 @ id)) = X208)) | (substmonoid_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP17)) & (($true = sP17) | (hoasinduction_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X209 : subst] : ? [X210 : d_subst] : (((d2subst @ X210)) = X209) & ((termmset_lthm = $true) | (! [X211 : term] : (((sub @ X211 @ id)) = X211) & ? [X212 : term] : (((sub @ X212 @ id)) != X212))) & (? [X213 : term] : (((sub @ X213 @ id)) != X213) | ! [X214 : term] : (((sub @ X214 @ id)) = X214) | (termmset_lthm != $true)) & (! [X215 : subst] : (((comp @ id @ X215)) = X215) | (axidl != $true)) & ((axidl = $true) | ? [X216 : subst] : (((comp @ id @ X216)) != X216)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj2 = $true) | ? [X217 : term,X218 : term,X219 : term,X220 : term] : ((X217 != X219) & (((ap @ (sub @ X220 @ id) @ X217)) = ((ap @ (sub @ X218 @ id) @ X219))))) & (! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X221 = X223) | (((ap @ (sub @ X224 @ id) @ X221)) != ((ap @ (sub @ X222 @ id) @ X223)))) | (hoasapinj2 != $true)) & ((apinj2 = $true) | ? [X225 : term,X226 : term,X227 : term,X228 : term] : ((X225 != X228) & (((ap @ X227 @ X225)) = ((ap @ X226 @ X228))))) & (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X232) | (((ap @ X231 @ X229)) != ((ap @ X230 @ X232)))) | (apinj2 != $true)) & (axabs = $true) & (hoaslamnotap_lthm = $true) & (! [X233 : (term > $o),X234 : term,X235 : subst] : ? [X236 : (term > $o)] : ! [X237 : term] : (((X233 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((X236 @ X237))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ? [X238 : (term > $o),X239 : term,X240 : subst] : ! [X241 : (term > $o)] : ? [X242 : term] : (((X238 @ (sub @ X242 @ (push @ X239 @ X240)))) != ((X241 @ X242)))) & ((pushprop_lem1v2 = $true) | ? [X243 : subst,X244 : (term > $o),X245 : term,X246 : (term > $o)] : ((((X244 @ X245)) = $true) & ($true != ((X246 @ one))) & ! [X247 : term] : (((X244 @ (sub @ X247 @ (push @ X245 @ X243)))) = ((X246 @ X247))))) & (! [X248 : subst,X249 : (term > $o),X250 : term,X251 : (term > $o)] : (($true != ((X249 @ X250))) | ($true = ((X251 @ one))) | ? [X252 : term] : (((X251 @ X252)) != ((X249 @ (sub @ X252 @ (push @ X250 @ X248)))))) | (pushprop_lem1v2 != $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & (($true = sP4) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP4)) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & (hoasinduction_lem1_gthm = $true) & ! [X253 : d_subst] : (d_id = X253) & ((hoasapinj1 = $true) | ? [X254 : term,X255 : term,X256 : term,X257 : term] : ((((ap @ (sub @ X256 @ id) @ X255)) = ((ap @ (sub @ X254 @ id) @ X257))) & (X254 != X256))) & (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((((ap @ (sub @ X258 @ id) @ X261)) != ((ap @ (sub @ X260 @ id) @ X259))) | (X258 = X260)) | (hoasapinj1 != $true)) & (! [X262 : term,X263 : term,X264 : (subst > term > term)] : (? [X265 : subst,X266 : subst,X267 : term] : (((X264 @ (comp @ X266 @ X265) @ (sub @ X267 @ X265))) != ((sub @ (X264 @ X266 @ X267) @ X265))) | (((ap @ (sub @ X263 @ id) @ X262)) != ((lam @ (X264 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X268 : term,X269 : term,X270 : (subst > term > term)] : (! [X271 : subst,X272 : subst,X273 : term] : (((sub @ (X270 @ X272 @ X273) @ X271)) = ((X270 @ (comp @ X272 @ X271) @ (sub @ X273 @ X271)))) & (((ap @ (sub @ X269 @ id) @ X268)) = ((lam @ (X270 @ sh @ one))))))),
% 2.19/0.60 inference(rectify,[],[f261])).
% 2.19/0.60 thf(f263,plain,(
% 2.19/0.60 (pushprop = $true) & ((axshiftcons = $true) | (sK457 != ((comp @ sh @ (push @ sK458 @ sK457))))) & (! [X2 : subst,X3 : term] : (((comp @ sh @ (push @ X3 @ X2))) = X2) | (axshiftcons != $true)) & (axmap = $true) & ((hoasinduction_lem3aa = $true) | ($true != sP58)) & (($true = sP58) | (hoasinduction_lem3aa != $true)) & (axapp = $true) & ((axscons = $true) | (((push @ (sub @ one @ sK459) @ (comp @ sh @ sK459))) != sK459)) & (! [X5 : subst] : (((push @ (sub @ one @ X5) @ (comp @ sh @ X5))) = X5) | (axscons != $true)) & ((shinj = $true) | ((sK460 != sK461) & (((sub @ sK460 @ sh)) = ((sub @ sK461 @ sh))))) & (! [X8 : term,X9 : term] : ((X8 = X9) | (((sub @ X9 @ sh)) != ((sub @ X8 @ sh)))) | (shinj != $true)) & (((d2subst @ d_id)) = id) & (hoasinduction_lem1v2 = $true) & (hoasinduction_lem2v2_gthm = $true) & ! [X10 : d_term,X11 : d_term] : ((X10 = X11) | (((d2term @ X10)) != ((d2term @ X11)))) & (hoasinduction_lem1_lthm = $true) & (! [X12 : subst,X13 : (term > $o),X14 : (term > $o),X15 : term,X16 : term] : (($true = ((X14 @ (sub @ X15 @ (push @ X16 @ X12))))) | ($true != ((X13 @ X15)))) | (pushprop_lem1 != $true)) & ((pushprop_lem1 = $true) | ((((sK464 @ (sub @ sK465 @ (push @ sK466 @ sK462)))) != $true) & ($true = ((sK463 @ sK465))))) & (pushprop_lem2v2 = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (($true = sP57) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP57)) & ! [X22 : term] : (((d2term @ (sK467 @ X22))) = X22) & ((hoasinduction_lem3aaa = $true) | ($true != sP56)) & (($true = sP56) | (hoasinduction_lem3aaa != $true)) & (hoasinduction_lem3a_gthm = $true) & ((induction = $true) | (($true != ((sK469 @ sK468))) & ($true != ((sP55 @ sK469))) & ! [X26 : term] : (($true = ((sK469 @ (lam @ X26)))) | ($true != ((sK469 @ X26)))) & ! [X27 : term] : (($true = ((sK469 @ X27))) | ($true != ((var @ X27)))))) & (! [X28 : term,X29 : (term > $o)] : (($true = ((X29 @ X28))) | ($true = ((sP55 @ X29))) | (($true != ((X29 @ (lam @ (sK470 @ X29))))) & ($true = ((X29 @ (sK470 @ X29))))) | (($true != ((X29 @ (sK471 @ X29)))) & ($true = ((var @ (sK471 @ X29)))))) | (induction != $true)) & (! [X32 : term] : (((sK472 @ X32 @ sh @ one)) = ((sub @ X32 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & ((hoasinduction_lem3b_lthm = $true) | ! [X35 : (subst > term > term)] : (((sub @ sK473 @ (push @ one @ sh))) != ((X35 @ sh @ one)))) & (($true = sP54) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP54)) & ((hoasinduction_lem3v2a_lthm = $true) | ($true != sP52)) & (($true = sP52) | (hoasinduction_lem3v2a_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((($true != ((sK474 @ one))) & (((sK475 @ sK476)) = $true) & ! [X40 : term] : (((sK475 @ (sub @ X40 @ (push @ sK476 @ sK477)))) = ((sK474 @ X40)))) & ! [X41 : subst,X42 : term] : (((sub @ one @ (push @ X42 @ X41))) = X42))) & (! [X43 : (term > $o),X44 : (term > $o),X45 : term,X46 : subst] : ((((X43 @ one)) = $true) | ($true != ((X44 @ X45))) | (((X43 @ (sK478 @ X46 @ X45 @ X44 @ X43))) != ((X44 @ (sub @ (sK478 @ X46 @ X45 @ X44 @ X43) @ (push @ X45 @ X46)))))) | (((sub @ one @ (push @ sK480 @ sK479))) != sK480) | (pushprop_lem1v2_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP51)) & (($true = sP51) | (hoasinduction_lem3aa_lthm != $true)) & ! [X50 : d_term] : (d_one = X50) & ((! [X51 : subst] : (((comp @ X51 @ id)) = X51) & ! [X52 : subst] : (((comp @ id @ X52)) = X52)) | (substmonoid != $true)) & ((substmonoid = $true) | (sK481 != ((comp @ sK481 @ id))) | (((comp @ id @ sK482)) != sK482)) & (hoasinduction_lem3_gthm = $true) & (! [X55 : subst] : (((comp @ X55 @ id)) = X55) | (axidr != $true)) & ((axidr = $true) | (sK483 != ((comp @ sK483 @ id)))) & (hoaslamnotvar_gthm = $true) & (apnotvar = $true) & (($true = sP50) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ($true != sP50)) & (hoasapinj1_gthm = $true) & (! [X57 : (subst > term > term),X58 : subst,X59 : (subst > term > term),X60 : term] : ((((X57 @ (comp @ (sK485 @ X57) @ (sK484 @ X57)) @ (sub @ (sK486 @ X57) @ (sK484 @ X57)))) != ((sub @ (X57 @ (sK485 @ X57) @ (sK486 @ X57)) @ (sK484 @ X57)))) | (((lam @ (X59 @ sh @ one))) != ((lam @ (X57 @ sh @ one)))) | (((X57 @ X58 @ X60)) = ((X59 @ X58 @ X60))) | (((sub @ (X59 @ (sK489 @ X59) @ (sK487 @ X59)) @ (sK488 @ X59))) != ((X59 @ (comp @ (sK489 @ X59) @ (sK488 @ X59)) @ (sub @ (sK487 @ X59) @ (sK488 @ X59)))))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X71 : subst,X72 : subst,X73 : term] : (((sub @ (sK490 @ X72 @ X73) @ X71)) = ((sK490 @ (comp @ X72 @ X71) @ (sub @ X73 @ X71)))) & (((lam @ (sK492 @ sh @ one))) = ((lam @ (sK490 @ sh @ one)))) & (((sK490 @ sK491 @ sK493)) != ((sK492 @ sK491 @ sK493))) & ! [X74 : term,X75 : subst,X76 : subst] : (((sK492 @ (comp @ X76 @ X75) @ (sub @ X74 @ X75))) = ((sub @ (sK492 @ X76 @ X74) @ X75))))) & ((hoasinduction_lem3v2_lthm = $true) | (sP45 != $true)) & ((sP45 = $true) | (hoasinduction_lem3v2_lthm != $true)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (! [X77 : term] : (((sub @ X77 @ id)) = X77) | (axvarid != $true)) & ((axvarid = $true) | (sK494 != ((sub @ sK494 @ id)))) & (lamnotvar = $true) & ((apinj1 = $true) | ((sK498 != sK495) & (((ap @ sK498 @ sK497)) = ((ap @ sK495 @ sK496))))) & (! [X83 : term,X84 : term,X85 : term,X86 : term] : ((X83 = X86) | (((ap @ X86 @ X85)) != ((ap @ X83 @ X84)))) | (apinj1 != $true)) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X87 : term,X88 : subst,X89 : (term > $o),X90 : (term > $o),X91 : term] : (($true = ((X90 @ (sub @ X87 @ (push @ X91 @ X88))))) | ($true != ((X89 @ X87)))) | (sK500 != ((sub @ one @ (push @ sK500 @ sK499)))) | (((comp @ sh @ (push @ sK501 @ sK502))) != sK502) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | ((($true != ((sK506 @ (sub @ sK503 @ (push @ sK507 @ sK504))))) & ($true = ((sK505 @ sK503)))) & ! [X101 : subst,X102 : term] : (((sub @ one @ (push @ X102 @ X101))) = X102) & ! [X103 : term,X104 : subst] : (((comp @ sh @ (push @ X103 @ X104))) = X104))) & (((d2subst @ d_id)) = sh) & ((laminj = $true) | ((((lam @ sK508)) = ((lam @ sK509))) & (sK508 != sK509))) & (! [X107 : term,X108 : term] : ((((lam @ X108)) != ((lam @ X107))) | (X107 = X108)) | (laminj != $true)) & (! [X109 : term] : ! [X111 : term,X112 : subst] : (((sK510 @ X109 @ X112 @ X111)) = ((sub @ X109 @ (push @ X111 @ X112)))) | (hoasinduction_lem3v2_f != $true)) & ((hoasinduction_lem3v2_f = $true) | ! [X114 : (subst > term > term)] : (((sub @ sK511 @ (push @ (sK512 @ X114) @ (sK513 @ X114)))) != ((X114 @ (sK513 @ X114) @ (sK512 @ X114))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (hoasinduction_gthm = $true) & (($true = sP42) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP42)) & (hoasinduction_lem1v2_gthm = $true) & ! [X117 : d_subst,X118 : d_subst] : ((((d2subst @ X117)) != ((d2subst @ X118))) | (X117 = X118)) & (($true = sP40) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP40)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (lamnotap != $true) & (($true = sP38) | (hoasinduction_lthm_3 != $true)) & ((hoasinduction_lthm_3 = $true) | ($true != sP38)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X119 : (subst > term > subst > $o),X120 : term] : ((($true != ((X119 @ id @ (ap @ (sub @ (sK514 @ X119) @ id) @ (sK515 @ X119)) @ id))) & ($true = ((X119 @ id @ (sK514 @ X119) @ id))) & ($true = ((X119 @ id @ (sK515 @ X119) @ id)))) | ($true = ((sP32 @ X119))) | ($true = ((X119 @ id @ X120 @ id)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | (! [X125 : term,X126 : term] : ((((sK516 @ id @ (ap @ (sub @ X125 @ id) @ X126) @ id)) = $true) | ($true != ((sK516 @ id @ X125 @ id))) | ($true != ((sK516 @ id @ X126 @ id)))) & (((sP32 @ sK516)) != $true) & (((sK516 @ id @ sK517 @ id)) != $true))) & ((hoasinduction_lem3v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem3v2 != $true)) & (! [X127 : (subst > term > subst > $o)] : ! [X129 : term] : (((sK518 @ X127 @ X129)) = ((X127 @ id @ X129 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X131 : (term > $o)] : (((X131 @ (sK520 @ X131))) != ((sK519 @ id @ (sK520 @ X131) @ id)))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem0_lthm = $true) | ! [X134 : (term > $o)] : (((sK521 @ id @ (sK522 @ X134) @ id)) != ((X134 @ (sK522 @ X134))))) & (! [X136 : (subst > term > subst > $o)] : ! [X138 : term] : (((sK523 @ X136 @ X138)) = ((X136 @ id @ X138 @ id))) | (hoasinduction_lem0_lthm != $true)) & (hoaslamnotap_gthm = $true) & (hoaslaminj_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (induction2lem_gthm = $true) & ((induction2lem = $true) | ($true != sP29)) & (($true = sP29) | (induction2lem != $true)) & (pushprop_lem1_gthm = $true) & ((((sub @ sK524 @ id)) != sK524) | ((sK527 != sK526) & (((ap @ sK527 @ sK525)) = ((ap @ sK526 @ sK528)))) | ! [X144 : term,X145 : term,X146 : term,X147 : term] : ((X146 = X147) | (((ap @ (sub @ X146 @ id) @ X145)) != ((ap @ (sub @ X147 @ id) @ X144)))) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | (! [X148 : term] : (((sub @ X148 @ id)) = X148) & ! [X149 : term,X150 : term,X151 : term,X152 : term] : ((X150 = X151) | (((ap @ X151 @ X149)) != ((ap @ X150 @ X152)))) & ((sK532 != sK531) & (((ap @ (sub @ sK531 @ id) @ sK530)) = ((ap @ (sub @ sK532 @ id) @ sK529)))))) & (pushprop_lem3v2_lthm = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (axassoc = $true) & (! [X157 : term] : (((sub @ X157 @ id)) = X157) | (termmset != $true)) & ((termmset = $true) | (((sub @ sK533 @ id)) != sK533)) & (hoasinduction_lem1 = $true) & ((sP27 = $true) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (sP27 != $true)) & ((hoasinduction_lem3b = $true) | ! [X160 : (subst > term > term)] : (((X160 @ sh @ one)) != ((sub @ sK534 @ (push @ one @ sh))))) & (! [X161 : term] : (((sub @ X161 @ (push @ one @ sh))) = ((sK535 @ X161 @ sh @ one))) | (hoasinduction_lem3b != $true)) & (($true = sP25) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ($true != sP25)) & (hoasapnotvar = $true) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X164 : (subst > term > term)] : (((sub @ sK536 @ (push @ (sK538 @ X164) @ (sK537 @ X164)))) != ((X164 @ (sK537 @ X164) @ (sK538 @ X164))))) & (! [X167 : term] : ! [X169 : subst,X170 : term] : (((sub @ X167 @ (push @ X170 @ X169))) = ((sK539 @ X167 @ X169 @ X170))) | (hoasinduction_lem3v2_f_lthm != $true)) & (substmonoid_gthm = $true) & (! [X171 : subst,X172 : term] : (((sub @ one @ (push @ X172 @ X171))) = X172) | (axvarcons != $true)) & ((axvarcons = $true) | (sK541 != ((sub @ one @ (push @ sK541 @ sK540))))) & (ulamvar1 != $true) & ((hoasinduction_lem3_lthm = $true) | ($true != sP21)) & (($true = sP21) | (hoasinduction_lem3_lthm != $true)) & (termmset_gthm = $true) & (pushprop_lem0_gthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (pushprop_gthm = $true) & (hoasapinj2_gthm = $true) & ((hoaslaminj_lthm = $true) | ($true != sP18)) & (($true = sP18) | (hoaslaminj_lthm != $true)) & (pushprop_lem2v2_lthm = $true) & (hoasinduction_lem3v2_gthm = $true) & (ulamvarind = $true) & (! [X175 : term,X176 : term,X177 : term,X178 : term] : ((((ap @ (sub @ X175 @ id) @ X176)) != ((ap @ (sub @ X177 @ id) @ X178))) | (X176 = X178)) | ((sK545 != sK544) & (((ap @ sK542 @ sK544)) = ((ap @ sK543 @ sK545)))) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (((((ap @ (sub @ sK548 @ id) @ sK549)) = ((ap @ (sub @ sK546 @ id) @ sK547))) & (sK547 != sK549)) & ! [X187 : term,X188 : term,X189 : term,X190 : term] : ((X189 = X190) | (((ap @ X188 @ X190)) != ((ap @ X187 @ X189)))))) & (pushprop_lem2v2_gthm = $true) & (pushprop_lthm = $true) & (! [X191 : (term > $o),X192 : subst,X193 : term] : ! [X195 : term] : (((sK550 @ X193 @ X192 @ X191 @ X195)) = ((X191 @ (sub @ X195 @ (push @ X193 @ X192))))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X199 : (term > $o)] : (((sK551 @ (sub @ (sK554 @ X199) @ (push @ sK553 @ sK552)))) != ((X199 @ (sK554 @ X199))))) & ((substmonoid_lthm = $true) | (! [X201 : subst] : (((comp @ X201 @ id)) = X201) & ! [X202 : subst] : (((comp @ id @ X202)) = X202) & ((sK555 != ((comp @ id @ sK555))) | (((comp @ sK556 @ id)) != sK556)))) & ((((comp @ sK557 @ id)) != sK557) | (sK558 != ((comp @ id @ sK558))) | (! [X207 : subst] : (((comp @ id @ X207)) = X207) & ! [X208 : subst] : (((comp @ X208 @ id)) = X208)) | (substmonoid_lthm != $true)) & ((hoasinduction_lthm = $true) | ($true != sP17)) & (($true = sP17) | (hoasinduction_lthm != $true)) & (pushprop_lem1v2_gthm = $true) & (hoasapnotvar_lthm = $true) & ! [X209 : subst] : (((d2subst @ (sK559 @ X209))) = X209) & ((termmset_lthm = $true) | (! [X211 : term] : (((sub @ X211 @ id)) = X211) & (sK560 != ((sub @ sK560 @ id))))) & ((((sub @ sK561 @ id)) != sK561) | ! [X214 : term] : (((sub @ X214 @ id)) = X214) | (termmset_lthm != $true)) & (! [X215 : subst] : (((comp @ id @ X215)) = X215) | (axidl != $true)) & ((axidl = $true) | (((comp @ id @ sK562)) != sK562)) & (((var @ (d2term @ d_one))) != $true) & ((hoasapinj2 = $true) | ((sK563 != sK565) & (((ap @ (sub @ sK566 @ id) @ sK563)) = ((ap @ (sub @ sK564 @ id) @ sK565))))) & (! [X221 : term,X222 : term,X223 : term,X224 : term] : ((X221 = X223) | (((ap @ (sub @ X224 @ id) @ X221)) != ((ap @ (sub @ X222 @ id) @ X223)))) | (hoasapinj2 != $true)) & ((apinj2 = $true) | ((sK567 != sK570) & (((ap @ sK569 @ sK567)) = ((ap @ sK568 @ sK570))))) & (! [X229 : term,X230 : term,X231 : term,X232 : term] : ((X229 = X232) | (((ap @ X231 @ X229)) != ((ap @ X230 @ X232)))) | (apinj2 != $true)) & (axabs = $true) & (hoaslamnotap_lthm = $true) & (! [X233 : (term > $o),X234 : term,X235 : subst] : ! [X237 : term] : (((X233 @ (sub @ X237 @ (push @ X234 @ X235)))) = ((sK571 @ X235 @ X234 @ X233 @ X237))) | (pushprop_lem0 != $true)) & ((pushprop_lem0 = $true) | ! [X241 : (term > $o)] : (((sK572 @ (sub @ (sK575 @ X241) @ (push @ sK573 @ sK574)))) != ((X241 @ (sK575 @ X241))))) & ((pushprop_lem1v2 = $true) | (($true = ((sK577 @ sK578))) & ($true != ((sK579 @ one))) & ! [X247 : term] : (((sK577 @ (sub @ X247 @ (push @ sK578 @ sK576)))) = ((sK579 @ X247))))) & (! [X248 : subst,X249 : (term > $o),X250 : term,X251 : (term > $o)] : (($true != ((X249 @ X250))) | ($true = ((X251 @ one))) | (((X249 @ (sub @ (sK580 @ X251 @ X250 @ X249 @ X248) @ (push @ X250 @ X248)))) != ((X251 @ (sK580 @ X251 @ X250 @ X249 @ X248))))) | (pushprop_lem1v2 != $true)) & (one = ((d2term @ d_one))) & (hoasapnotvar_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (axclos = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoaslamnotvar_lthm = $true) & ((induction2lem_lthm = $true) | (sP8 != $true)) & ((sP8 = $true) | (induction2lem_lthm != $true)) & (hoasinduction_lem2_lthm = $true) & (ulamvarsh = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) = (Y1 @ Y2)))))))) & (hoaslamnotvar = $true) & (($true = sP4) | (induction2 != $true)) & ((induction2 = $true) | ($true != sP4)) & (pushprop_lthm_orig = $true) & (pushprop_lem3v2 = $true) & ((hoasinduction = $true) | (sP2 != $true)) & ((sP2 = $true) | (hoasinduction != $true)) & (hoasinduction_lem1_gthm = $true) & ! [X253 : d_subst] : (d_id = X253) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK583 @ id) @ sK582)) = ((ap @ (sub @ sK581 @ id) @ sK584))) & (sK583 != sK581))) & (! [X258 : term,X259 : term,X260 : term,X261 : term] : ((((ap @ (sub @ X258 @ id) @ X261)) != ((ap @ (sub @ X260 @ id) @ X259))) | (X258 = X260)) | (hoasapinj1 != $true)) & (! [X262 : term,X263 : term,X264 : (subst > term > term)] : ((((X264 @ (comp @ (sK586 @ X264) @ (sK585 @ X264)) @ (sub @ (sK587 @ X264) @ (sK585 @ X264)))) != ((sub @ (X264 @ (sK586 @ X264) @ (sK587 @ X264)) @ (sK585 @ X264)))) | (((ap @ (sub @ X263 @ id) @ X262)) != ((lam @ (X264 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X271 : subst,X272 : subst,X273 : term] : (((sub @ (sK590 @ X272 @ X273) @ X271)) = ((sK590 @ (comp @ X272 @ X271) @ (sub @ X273 @ X271)))) & (((lam @ (sK590 @ sh @ one))) = ((ap @ (sub @ sK589 @ id) @ sK588)))))),
% 2.19/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK457,sK458,sK459,sK460,sK461,sK462,sK463,sK464,sK465,sK466,vAPP,sK468,sK469,vAPP,vAPP,vAPP,sK473,sK474,sK475,sK476,sK477,vAPP,sK479,sK480,sK481,sK482,sK483,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK490,sK491,sK492,sK493,sK494,sK495,sK496,sK497,sK498,sK499,sK500,sK501,sK502,sK503,sK504,sK505,sK506,sK507,sK508,sK509,vAPP,sK511,vAPP,vAPP,vAPP,vAPP,sK516,sK517,vAPP,sK519,vAPP,sK521,vAPP,vAPP,sK524,sK525,sK526,sK527,sK528,sK529,sK530,sK531,sK532,sK533,sK534,vAPP,sK536,vAPP,vAPP,vAPP,sK540,sK541,sK542,sK543,sK544,sK545,sK546,sK547,sK548,sK549,vAPP,sK551,sK552,sK553,vAPP,sK555,sK556,sK557,sK558,vAPP,sK560,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,sK569,sK570,vAPP,sK572,sK573,sK574,vAPP,sK576,sK577,sK578,sK579,vAPP,sK581,sK582,sK583,sK584,vAPP,vAPP,vAPP,sK588,sK589,sK590]),skolemize(X0,sK457),skolemize(X1,sK458),skolemize(X4,sK459),skolemize(X6,sK460),skolemize(X7,sK461),skolemize(X17,sK462),skolemize(X18,sK463),skolemize(X19,sK464),skolemize(X20,sK465),skolemize(X21,sK466),skolemize(X11,sK66 @ X8),skolemize(X24,sK468),skolemize(X25,sK469),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X34,sK473),skolemize(X36,sK474),skolemize(X37,sK475),skolemize(X38,sK476),skolemize(X39,sK477),skolemize(X11,sK66 @ X8),skolemize(X48,sK479),skolemize(X49,sK480),skolemize(X53,sK481),skolemize(X54,sK482),skolemize(X56,sK483),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X67,sK490),skolemize(X68,sK491),skolemize(X69,sK492),skolemize(X70,sK493),skolemize(X78,sK494),skolemize(X79,sK495),skolemize(X80,sK496),skolemize(X81,sK497),skolemize(X82,sK498),skolemize(X92,sK499),skolemize(X93,sK500),skolemize(X94,sK501),skolemize(X95,sK502),skolemize(X96,sK503),skolemize(X97,sK504),skolemize(X98,sK505),skolemize(X99,sK506),skolemize(X100,sK507),skolemize(X105,sK508),skolemize(X106,sK509),skolemize(X11,sK66 @ X8),skolemize(X113,sK511),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X123,sK516),skolemize(X124,sK517),skolemize(X11,sK66 @ X8),skolemize(X130,sK519),skolemize(X11,sK66 @ X8),skolemize(X133,sK521),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X139,sK524),skolemize(X140,sK525),skolemize(X141,sK526),skolemize(X142,sK527),skolemize(X143,sK528),skolemize(X153,sK529),skolemize(X154,sK530),skolemize(X155,sK531),skolemize(X156,sK532),skolemize(X158,sK533),skolemize(X159,sK534),skolemize(X11,sK66 @ X8),skolemize(X163,sK536),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X173,sK540),skolemize(X174,sK541),skolemize(X179,sK542),skolemize(X180,sK543),skolemize(X181,sK544),skolemize(X182,sK545),skolemize(X183,sK546),skolemize(X184,sK547),skolemize(X185,sK548),skolemize(X186,sK549),skolemize(X11,sK66 @ X8),skolemize(X196,sK551),skolemize(X197,sK552),skolemize(X198,sK553),skolemize(X11,sK66 @ X8),skolemize(X203,sK555),skolemize(X204,sK556),skolemize(X205,sK557),skolemize(X206,sK558),skolemize(X11,sK66 @ X8),skolemize(X212,sK560),skolemize(X213,sK561),skolemize(X216,sK562),skolemize(X217,sK563),skolemize(X218,sK564),skolemize(X219,sK565),skolemize(X220,sK566),skolemize(X225,sK567),skolemize(X226,sK568),skolemize(X227,sK569),skolemize(X228,sK570),skolemize(X11,sK66 @ X8),skolemize(X238,sK572),skolemize(X239,sK573),skolemize(X240,sK574),skolemize(X11,sK66 @ X8),skolemize(X243,sK576),skolemize(X244,sK577),skolemize(X245,sK578),skolemize(X246,sK579),skolemize(X11,sK66 @ X8),skolemize(X254,sK581),skolemize(X255,sK582),skolemize(X256,sK583),skolemize(X257,sK584),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X11,sK66 @ X8),skolemize(X268,sK588),skolemize(X269,sK589),skolemize(X270,sK590)],[f262])).
% 2.19/0.60 thf(f264,plain,(
% 2.19/0.60 (pushprop_lem3v2 != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ (term > $o) @ (^[Y3 : term > $o]: ((pushprop_p_and_p_prime @ Y2 @ Y1 @ Y0 @ Y3) => ((!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y3 @ Y4)))) => (!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y0 @ (sub @ Y4 @ (push @ Y2 @ Y1))))))))))))))))))),
% 2.19/0.60 inference(cnf_transformation,[],[f8])).
% 2.19/0.60 thf(f764,plain,(
% 2.19/0.60 (pushprop_lem3v2 = $true)),
% 2.19/0.60 inference(cnf_transformation,[],[f263])).
% 2.19/0.60 thf(f860,plain,(
% 2.19/0.60 (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4))))))))))))),
% 2.19/0.60 inference(cnf_transformation,[],[f263])).
% 2.19/0.60 thf(f981,plain,(
% 2.19/0.60 ($true != ((!! @ (term > $o) @ (^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ (term > $o) @ (^[Y3 : term > $o]: (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))) = (Y7 @ Y8))))))))))) @ Y2 @ Y1 @ Y0 @ Y3) => ((!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y3 @ Y4)))) => (!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y0 @ (sub @ Y4 @ (push @ Y2 @ Y1))))))))))))))))))),
% 2.19/0.60 inference(definition_unfolding,[],[f264,f764,f860])).
% 2.19/0.60 thf(f990,plain,(
% 2.19/0.60 ($false = (((^[Y0 : term > $o]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ (term > $o) @ (^[Y3 : term > $o]: (((^[Y4 : term]: ((^[Y5 : subst]: ((^[Y6 : term > $o]: ((^[Y7 : term > $o]: (!! @ term @ (^[Y8 : term]: ((Y6 @ (sub @ Y8 @ (push @ Y4 @ Y5))) = (Y7 @ Y8))))))))))) @ Y2 @ Y1 @ Y0 @ Y3) => ((!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y3 @ Y4)))) => (!! @ term @ (^[Y4 : term]: ((var @ Y4) => (Y0 @ (sub @ Y4 @ (push @ Y2 @ Y1))))))))))))))) @ sK591)))),
% 2.19/0.60 inference(sigma_proxy_clausification,[],[f981])).
% 2.19/0.60 thf(f991,plain,(
% 2.19/0.60 ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: ((!! @ term @ (^[Y3 : term]: ((sK591 @ (sub @ Y3 @ (push @ Y1 @ Y0))) = (Y2 @ Y3)))) => ((!! @ term @ (^[Y3 : term]: ((var @ Y3) => (Y2 @ Y3)))) => (!! @ term @ (^[Y3 : term]: ((var @ Y3) => (sK591 @ (sub @ Y3 @ (push @ Y1 @ Y0))))))))))))))))),
% 2.19/0.60 inference(beta-eta_normalization,[],[f990])).
% 2.19/0.60 thf(f992,plain,(
% 2.19/0.60 ($false = (((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ (term > $o) @ (^[Y2 : term > $o]: ((!! @ term @ (^[Y3 : term]: ((sK591 @ (sub @ Y3 @ (push @ Y1 @ Y0))) = (Y2 @ Y3)))) => ((!! @ term @ (^[Y3 : term]: ((var @ Y3) => (Y2 @ Y3)))) => (!! @ term @ (^[Y3 : term]: ((var @ Y3) => (sK591 @ (sub @ Y3 @ (push @ Y1 @ Y0))))))))))))) @ sK592)))),
% 2.19/0.60 inference(sigma_proxy_clausification,[],[f991])).
% 2.19/0.60 thf(f993,plain,(
% 2.19/0.60 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ term @ (^[Y2 : term]: ((sK591 @ (sub @ Y2 @ (push @ Y0 @ sK592))) = (Y1 @ Y2)))) => ((!! @ term @ (^[Y2 : term]: ((var @ Y2) => (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((var @ Y2) => (sK591 @ (sub @ Y2 @ (push @ Y0 @ sK592))))))))))))))),
% 2.19/0.60 inference(beta-eta_normalization,[],[f992])).
% 2.19/0.60 thf(f994,plain,(
% 2.19/0.60 ($false = (((^[Y0 : term]: (!! @ (term > $o) @ (^[Y1 : term > $o]: ((!! @ term @ (^[Y2 : term]: ((sK591 @ (sub @ Y2 @ (push @ Y0 @ sK592))) = (Y1 @ Y2)))) => ((!! @ term @ (^[Y2 : term]: ((var @ Y2) => (Y1 @ Y2)))) => (!! @ term @ (^[Y2 : term]: ((var @ Y2) => (sK591 @ (sub @ Y2 @ (push @ Y0 @ sK592))))))))))) @ sK593)))),
% 2.19/0.60 inference(sigma_proxy_clausification,[],[f993])).
% 2.19/0.60 thf(f995,plain,(
% 2.19/0.60 ($false = ((!! @ (term > $o) @ (^[Y0 : term > $o]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ (sub @ Y1 @ (push @ sK593 @ sK592))) = (Y0 @ Y1)))) => ((!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (sK591 @ (sub @ Y1 @ (push @ sK593 @ sK592))))))))))))),
% 2.19/0.60 inference(beta-eta_normalization,[],[f994])).
% 2.19/0.60 thf(f996,plain,(
% 2.19/0.60 ($false = (((^[Y0 : term > $o]: ((!! @ term @ (^[Y1 : term]: ((sK591 @ (sub @ Y1 @ (push @ sK593 @ sK592))) = (Y0 @ Y1)))) => ((!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ Y1)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (sK591 @ (sub @ Y1 @ (push @ sK593 @ sK592))))))))) @ sK594)))),
% 2.19/0.60 inference(sigma_proxy_clausification,[],[f995])).
% 2.19/0.60 thf(f997,plain,(
% 2.19/0.60 ($false = (((!! @ term @ (^[Y0 : term]: ((sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))) = (sK594 @ Y0)))) => ((!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK594 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))))))))))),
% 2.19/0.60 inference(beta-eta_normalization,[],[f996])).
% 2.19/0.60 thf(f998,plain,(
% 2.19/0.60 ($false = (((!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK594 @ Y0)))) => (!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592)))))))))),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f997])).
% 2.19/0.60 thf(f999,plain,(
% 2.19/0.60 ($true = ((!! @ term @ (^[Y0 : term]: ((sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))) = (sK594 @ Y0))))))),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f997])).
% 2.19/0.60 thf(f1000,plain,(
% 2.19/0.60 ( ! [X1 : term] : (($true = (((^[Y0 : term]: ((sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))) = (sK594 @ Y0))) @ X1)))) )),
% 2.19/0.60 inference(pi_proxy_clausification,[],[f999])).
% 2.19/0.60 thf(f1001,plain,(
% 2.19/0.60 ( ! [X1 : term] : (($true = (((sK591 @ (sub @ X1 @ (push @ sK593 @ sK592))) = (sK594 @ X1))))) )),
% 2.19/0.60 inference(beta-eta_normalization,[],[f1000])).
% 2.19/0.60 thf(f1002,plain,(
% 2.19/0.60 ( ! [X1 : term] : ((((sK594 @ X1)) = ((sK591 @ (sub @ X1 @ (push @ sK593 @ sK592)))))) )),
% 2.19/0.60 inference(equality_proxy_clausification,[],[f1001])).
% 2.19/0.60 thf(f1004,plain,(
% 2.19/0.60 ( ! [X1 : term] : (($true = ((sK591 @ (sub @ X1 @ (push @ sK593 @ sK592))))) | ($false = ((sK594 @ X1)))) )),
% 2.19/0.60 inference(iff_proxy_clausification,[],[f1002])).
% 2.19/0.60 thf(f1005,plain,(
% 2.19/0.60 ($false = ((!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))))))))),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f998])).
% 2.19/0.60 thf(f1006,plain,(
% 2.19/0.60 (((!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK594 @ Y0))))) = $true)),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f998])).
% 2.19/0.60 thf(f1007,plain,(
% 2.19/0.60 ( ! [X1 : term] : (($true = (((^[Y0 : term]: ((var @ Y0) => (sK594 @ Y0))) @ X1)))) )),
% 2.19/0.60 inference(pi_proxy_clausification,[],[f1006])).
% 2.19/0.60 thf(f1008,plain,(
% 2.19/0.60 ( ! [X1 : term] : (((((var @ X1) => (sK594 @ X1))) = $true)) )),
% 2.19/0.60 inference(beta-eta_normalization,[],[f1007])).
% 2.19/0.60 thf(f1009,plain,(
% 2.19/0.60 ( ! [X1 : term] : (($true = ((sK594 @ X1))) | ($false = ((var @ X1)))) )),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f1008])).
% 2.19/0.60 thf(f1010,plain,(
% 2.19/0.60 ($false = (((^[Y0 : term]: ((var @ Y0) => (sK591 @ (sub @ Y0 @ (push @ sK593 @ sK592))))) @ sK595)))),
% 2.19/0.60 inference(sigma_proxy_clausification,[],[f1005])).
% 2.19/0.60 thf(f1011,plain,(
% 2.19/0.60 ($false = (((var @ sK595) => (sK591 @ (sub @ sK595 @ (push @ sK593 @ sK592))))))),
% 2.19/0.60 inference(beta-eta_normalization,[],[f1010])).
% 2.19/0.60 thf(f1012,plain,(
% 2.19/0.60 ($false = ((sK591 @ (sub @ sK595 @ (push @ sK593 @ sK592)))))),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f1011])).
% 2.19/0.60 thf(f1013,plain,(
% 2.19/0.60 (((var @ sK595)) = $true)),
% 2.19/0.60 inference(imp_proxy_clausification,[],[f1011])).
% 2.19/0.60 thf(f3850,plain,(
% 2.19/0.60 ($false = $true) | ($false = ((sK594 @ sK595)))),
% 2.19/0.60 inference(superposition,[],[f1004,f1012])).
% 2.19/0.60 thf(f3855,plain,(
% 2.19/0.60 ($false = ((sK594 @ sK595)))),
% 2.19/0.60 inference(trivial_inequality_removal,[],[f3850])).
% 2.19/0.60 thf(f3859,plain,(
% 2.19/0.60 ($false = ((var @ sK595))) | ($false = $true)),
% 2.19/0.60 inference(superposition,[],[f1009,f3855])).
% 2.19/0.60 thf(f3860,plain,(
% 2.19/0.60 ($false = ((var @ sK595)))),
% 2.19/0.60 inference(trivial_inequality_removal,[],[f3859])).
% 2.19/0.60 thf(f3873,plain,(
% 2.19/0.60 ($false = $true)),
% 2.19/0.60 inference(superposition,[],[f3860,f1013])).
% 2.19/0.60 thf(f3875,plain,(
% 2.19/0.60 $false),
% 2.19/0.60 inference(trivial_inequality_removal,[],[f3873])).
% 2.19/0.60 % SZS output end Proof for theBenchmark
% 2.19/0.60 % (3053560)------------------------------
% 2.19/0.60 % (3053560)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.19/0.60 % (3053560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/0.60 % (3053560)CaDiCaL version: 2.1.3
% 2.19/0.60 % (3053560)Termination reason: Refutation
% 2.19/0.60 % (3053560)Time elapsed: 0.174 s
% 2.19/0.60 % (3053560)Peak memory usage: 16 MB
% 2.19/0.60 % (3053560)Instructions burned: 397 (million)
% 2.19/0.60 % (3053520)Success in time 0.328 s
% 2.19/0.60 % Vampire exiting
%------------------------------------------------------------------------------