%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX165^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:40:37 AM UTC 2026
% Result : Theorem 3.49s 0.95s
% Output : Refutation 3.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX165^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n016.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:14:20 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.49/0.42 % (538752)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.42 % (538768)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1861601220:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.42 % (538768)Instruction limit reached!
% 0.49/0.42 % (538768)------------------------------
% 0.49/0.42 % (538768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (538768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (538768)CaDiCaL version: 2.1.3
% 0.49/0.42 % (538768)Termination reason: Instruction limit
% 0.49/0.42 % (538768)Termination phase: shuffling
% 0.49/0.42 % (538768)Time elapsed: 0.001 s
% 0.49/0.42 % (538768)Peak memory usage: 9 MB
% 0.49/0.42 % (538768)Instructions burned: 3 (million)
% 0.49/0.42 % (538772)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.42 % (538772)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
% 0.49/0.42 % (538767)lrs+10_16_si=on:nwc=1.5:random_seed=3728095077:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.42 % (538771)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4118257770:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.42 % (538769)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=92398154: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)
% 0.49/0.42 % (538770)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=731796261:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.42 % (538772)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=3042562973:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.42 % (538766)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3161597472:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.42 % (538777)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=333910528:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.42 % (538777)Instruction limit reached!
% 0.49/0.42 % (538777)------------------------------
% 0.49/0.42 % (538777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (538777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (538777)CaDiCaL version: 2.1.3
% 0.49/0.42 % (538777)Termination reason: Instruction limit
% 0.49/0.42 % (538777)Termination phase: shuffling
% 0.49/0.42 % (538777)Time elapsed: 0.002 s
% 0.49/0.42 % (538777)Peak memory usage: 10 MB
% 0.49/0.42 % (538777)Instructions burned: 10 (million)
% 0.49/0.42 % (538767)Instruction limit reached!
% 0.49/0.42 % (538767)------------------------------
% 0.49/0.42 % (538767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (538767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (538767)CaDiCaL version: 2.1.3
% 0.49/0.42 % (538767)Termination reason: Instruction limit
% 0.49/0.42 % (538767)Termination phase: shuffling
% 0.49/0.42 % (538767)Time elapsed: 0.009 s
% 0.49/0.42 % (538767)Peak memory usage: 10 MB
% 0.49/0.42 % (538767)Instructions burned: 19 (million)
% 0.49/0.42 % (538770)Instruction limit reached!
% 0.49/0.42 % (538770)------------------------------
% 0.49/0.42 % (538770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.42 % (538770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.42 % (538770)CaDiCaL version: 2.1.3
% 0.49/0.42 % (538770)Termination reason: Instruction limit
% 0.49/0.42 % (538770)Termination phase: Property scanning
% 0.49/0.42 % (538770)Time elapsed: 0.011 s
% 0.49/0.42 % (538770)Peak memory usage: 10 MB
% 0.49/0.42 % (538770)Instructions burned: 25 (million)
% 0.49/0.42 % (538791)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1400900413:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.42 % (538791)Instruction limit reached!
% 0.49/0.47 % (538791)------------------------------
% 0.49/0.47 % (538791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538791)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538791)Termination reason: Instruction limit
% 0.49/0.47 % (538791)Termination phase: shuffling
% 0.49/0.47 % (538791)Time elapsed: 0.003 s
% 0.49/0.47 % (538791)Peak memory usage: 10 MB
% 0.49/0.47 % (538791)Instructions burned: 12 (million)
% 0.49/0.47 % (538793)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.47 % (538801)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
% 0.49/0.47 % (538801)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.47 % (538793)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2398715928:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.47 % (538795)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=258024598:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.49/0.47 % (538801)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2423846665:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.49/0.47 % (538771)Instruction limit reached!
% 0.49/0.47 % (538771)------------------------------
% 0.49/0.47 % (538771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538771)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538771)Termination reason: Instruction limit
% 0.49/0.47 % (538771)Termination phase: Preprocessing 3
% 0.49/0.47 % (538771)Time elapsed: 0.034 s
% 0.49/0.47 % (538771)Peak memory usage: 12 MB
% 0.49/0.47 % (538771)Instructions burned: 76 (million)
% 0.49/0.47 % (538793)Instruction limit reached!
% 0.49/0.47 % (538793)------------------------------
% 0.49/0.47 % (538793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538793)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538793)Termination reason: Instruction limit
% 0.49/0.47 % (538793)Termination phase: shuffling
% 0.49/0.47 % (538793)Time elapsed: 0.004 s
% 0.49/0.47 % (538793)Peak memory usage: 10 MB
% 0.49/0.47 % (538793)Instructions burned: 8 (million)
% 0.49/0.47 % (538795)Instruction limit reached!
% 0.49/0.47 % (538795)------------------------------
% 0.49/0.47 % (538795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538795)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538795)Termination reason: Instruction limit
% 0.49/0.47 % (538795)Termination phase: shuffling
% 0.49/0.47 % (538795)Time elapsed: 0.006 s
% 0.49/0.47 % (538795)Peak memory usage: 10 MB
% 0.49/0.47 % (538795)Instructions burned: 13 (million)
% 0.49/0.47 % (538801)Instruction limit reached!
% 0.49/0.47 % (538801)------------------------------
% 0.49/0.47 % (538801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538801)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538801)Termination reason: Instruction limit
% 0.49/0.47 % (538801)Termination phase: shuffling
% 0.49/0.47 % (538801)Time elapsed: 0.007 s
% 0.49/0.47 % (538801)Peak memory usage: 10 MB
% 0.49/0.47 % (538801)Instructions burned: 31 (million)
% 0.49/0.47 % (538766)Instruction limit reached!
% 0.49/0.47 % (538766)------------------------------
% 0.49/0.47 % (538766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.47 % (538766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.47 % (538766)CaDiCaL version: 2.1.3
% 0.49/0.47 % (538766)Termination reason: Instruction limit
% 0.49/0.47 % (538766)Termination phase: Preprocessing 3
% 0.49/0.47 % (538766)Time elapsed: 0.041 s
% 0.49/0.47 % (538766)Peak memory usage: 12 MB
% 1.23/0.50 % (538766)Instructions burned: 88 (million)
% 1.23/0.50 % (538816)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3706180067:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.23/0.50 % (538814)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.23/0.50 % (538811)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=2891490658:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.23/0.50 % (538812)lrs+10_1_si=on:cs=on:random_seed=1177993485:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.23/0.50 % (538814)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=1343234254:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.23/0.50 % (538812)Instruction limit reached!
% 1.23/0.50 % (538812)------------------------------
% 1.23/0.50 % (538812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.50 % (538812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.50 % (538812)CaDiCaL version: 2.1.3
% 1.23/0.50 % (538812)Termination reason: Instruction limit
% 1.23/0.50 % (538812)Termination phase: shuffling
% 1.23/0.50 % (538812)Time elapsed: 0.004 s
% 1.23/0.50 % (538812)Peak memory usage: 9 MB
% 1.23/0.50 % (538812)Instructions burned: 9 (million)
% 1.23/0.50 % (538814)Instruction limit reached!
% 1.23/0.50 % (538814)------------------------------
% 1.23/0.50 % (538814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.50 % (538814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.50 % (538814)CaDiCaL version: 2.1.3
% 1.23/0.50 % (538814)Termination reason: Instruction limit
% 1.23/0.50 % (538814)Termination phase: shuffling
% 1.23/0.50 % (538814)Time elapsed: 0.002 s
% 1.23/0.50 % (538814)Peak memory usage: 9 MB
% 1.23/0.50 % (538814)Instructions burned: 5 (million)
% 1.23/0.50 % (538816)Instruction limit reached!
% 1.23/0.50 % (538816)------------------------------
% 1.23/0.50 % (538816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.50 % (538816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.50 % (538816)CaDiCaL version: 2.1.3
% 1.23/0.50 % (538816)Termination reason: Instruction limit
% 1.23/0.50 % (538816)Termination phase: Saturation
% 1.23/0.50 % (538816)Time elapsed: 0.010 s
% 1.23/0.50 % (538816)Peak memory usage: 12 MB
% 1.23/0.50 % (538816)Instructions burned: 40 (million)
% 1.23/0.50 % (538820)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2155575376:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.23/0.50 % (538772)Instruction limit reached!
% 1.23/0.50 % (538772)------------------------------
% 1.23/0.50 % (538772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.50 % (538772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.50 % (538772)CaDiCaL version: 2.1.3
% 1.23/0.50 % (538772)Termination reason: Instruction limit
% 1.23/0.50 % (538772)Termination phase: Property scanning
% 1.23/0.50 % (538772)Time elapsed: 0.070 s
% 1.23/0.50 % (538772)Peak memory usage: 13 MB
% 1.23/0.50 % (538772)Instructions burned: 158 (million)
% 1.23/0.50 % (538836)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=624441700:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.23/0.50 % (538831)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1296374446:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.23/0.50 % (538833)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3592332618:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.23/0.50 % (538833)Instruction limit reached!
% 1.23/0.50 % (538833)------------------------------
% 1.23/0.50 % (538833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.50 % (538833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.50 % (538833)CaDiCaL version: 2.1.3
% 1.23/0.50 % (538833)Termination reason: Instruction limit
% 1.23/0.50 % (538833)Termination phase: shuffling
% 1.23/0.50 % (538833)Time elapsed: 0.007 s
% 1.23/0.55 % (538833)Peak memory usage: 10 MB
% 1.23/0.55 % (538833)Instructions burned: 16 (million)
% 1.23/0.55 % (538831)Instruction limit reached!
% 1.23/0.55 % (538831)------------------------------
% 1.23/0.55 % (538831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538831)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538831)Termination reason: Instruction limit
% 1.23/0.55 % (538831)Termination phase: Property scanning
% 1.23/0.55 % (538831)Time elapsed: 0.011 s
% 1.23/0.55 % (538831)Peak memory usage: 10 MB
% 1.23/0.55 % (538831)Instructions burned: 25 (million)
% 1.23/0.55 % (538811)Instruction limit reached!
% 1.23/0.55 % (538811)------------------------------
% 1.23/0.55 % (538811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538846)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3441610405:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.23/0.55 % (538811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538811)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538811)Termination reason: Instruction limit
% 1.23/0.55 % (538811)Termination phase: Saturation
% 1.23/0.55 % (538811)Time elapsed: 0.037 s
% 1.23/0.55 % (538811)Peak memory usage: 12 MB
% 1.23/0.55 % (538811)Instructions burned: 87 (million)
% 1.23/0.55 % (538846)Instruction limit reached!
% 1.23/0.55 % (538846)------------------------------
% 1.23/0.55 % (538846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538846)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538846)Termination reason: Instruction limit
% 1.23/0.55 % (538846)Termination phase: shuffling
% 1.23/0.55 % (538846)Time elapsed: 0.009 s
% 1.23/0.55 % (538846)Peak memory usage: 10 MB
% 1.23/0.55 % (538846)Instructions burned: 19 (million)
% 1.23/0.55 % (538853)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3711381782: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)
% 1.23/0.55 % (538857)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3439271068:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.23/0.55 % (538853)Instruction limit reached!
% 1.23/0.55 % (538853)------------------------------
% 1.23/0.55 % (538853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538853)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538853)Termination reason: Instruction limit
% 1.23/0.55 % (538853)Termination phase: shuffling
% 1.23/0.55 % (538853)Time elapsed: 0.002 s
% 1.23/0.55 % (538853)Peak memory usage: 9 MB
% 1.23/0.55 % (538853)Instructions burned: 5 (million)
% 1.23/0.55 % (538855)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=115883528:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.23/0.55 % (538859)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=990815392:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.23/0.55 % (538857)Instruction limit reached!
% 1.23/0.55 % (538857)------------------------------
% 1.23/0.55 % (538857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538857)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538857)Termination reason: Instruction limit
% 1.23/0.55 % (538857)Termination phase: shuffling
% 1.23/0.55 % (538857)Time elapsed: 0.010 s
% 1.23/0.55 % (538857)Peak memory usage: 10 MB
% 1.23/0.55 % (538857)Instructions burned: 23 (million)
% 1.23/0.55 % (538855)Instruction limit reached!
% 1.23/0.55 % (538855)------------------------------
% 1.23/0.55 % (538855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.55 % (538855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.55 % (538855)CaDiCaL version: 2.1.3
% 1.23/0.55 % (538855)Termination reason: Instruction limit
% 1.23/0.55 % (538855)Termination phase: shuffling
% 1.23/0.55 % (538855)Time elapsed: 0.013 s
% 1.23/0.55 % (538855)Peak memory usage: 10 MB
% 1.23/0.55 % (538855)Instructions burned: 27 (million)
% 1.23/0.55 % (538862)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 2.12/0.61 % (538862)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.12/0.61 % (538862)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=2098032334:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.12/0.61 % (538862)Instruction limit reached!
% 2.12/0.61 % (538862)------------------------------
% 2.12/0.61 % (538862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.61 % (538862)CaDiCaL version: 2.1.3
% 2.12/0.61 % (538862)Termination reason: Instruction limit
% 2.12/0.61 % (538862)Termination phase: shuffling
% 2.12/0.61 % (538862)Time elapsed: 0.008 s
% 2.12/0.61 % (538862)Peak memory usage: 10 MB
% 2.12/0.61 % (538862)Instructions burned: 16 (million)
% 2.12/0.61 % (538867)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.12/0.61 % (538867)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=4109291504:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.12/0.61 % (538859)Instruction limit reached!
% 2.12/0.61 % (538859)------------------------------
% 2.12/0.61 % (538859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538869)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=4099660373:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.12/0.61 % (538859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.61 % (538859)CaDiCaL version: 2.1.3
% 2.12/0.61 % (538859)Termination reason: Instruction limit
% 2.12/0.61 % (538859)Termination phase: Preprocessing 3
% 2.12/0.61 % (538859)Time elapsed: 0.027 s
% 2.12/0.61 % (538859)Peak memory usage: 11 MB
% 2.12/0.61 % (538859)Instructions burned: 61 (million)
% 2.12/0.61 % (538867)Instruction limit reached!
% 2.12/0.61 % (538867)------------------------------
% 2.12/0.61 % (538867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.61 % (538867)CaDiCaL version: 2.1.3
% 2.12/0.61 % (538867)Termination reason: Instruction limit
% 2.12/0.61 % (538867)Termination phase: shuffling
% 2.12/0.61 % (538867)Time elapsed: 0.004 s
% 2.12/0.61 % (538867)Peak memory usage: 10 MB
% 2.12/0.61 % (538867)Instructions burned: 9 (million)
% 2.12/0.61 % (538836)Instruction limit reached!
% 2.12/0.61 % (538836)------------------------------
% 2.12/0.61 % (538836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.61 % (538836)CaDiCaL version: 2.1.3
% 2.12/0.61 % (538836)Termination reason: Instruction limit
% 2.12/0.61 % (538836)Termination phase: Saturation
% 2.12/0.61 % (538836)Time elapsed: 0.081 s
% 2.12/0.61 % (538836)Peak memory usage: 16 MB
% 2.12/0.61 % (538836)Instructions burned: 330 (million)
% 2.12/0.61 % (538874)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3703028183:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.12/0.61 % (538869)Instruction limit reached!
% 2.12/0.61 % (538869)------------------------------
% 2.12/0.61 % (538869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.12/0.61 % (538869)CaDiCaL version: 2.1.3
% 2.12/0.61 % (538869)Termination reason: Instruction limit
% 2.12/0.61 % (538869)Termination phase: shuffling
% 2.12/0.61 % (538869)Time elapsed: 0.013 s
% 2.12/0.61 % (538869)Peak memory usage: 10 MB
% 2.12/0.61 % (538869)Instructions burned: 31 (million)
% 2.12/0.61 % (538874)Instruction limit reached!
% 2.12/0.61 % (538874)------------------------------
% 2.12/0.61 % (538874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.12/0.61 % (538874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538874)CaDiCaL version: 2.1.3
% 2.40/0.68 % (538874)Termination reason: Instruction limit
% 2.40/0.68 % (538874)Termination phase: shuffling
% 2.40/0.68 % (538874)Time elapsed: 0.003 s
% 2.40/0.68 % (538874)Peak memory usage: 9 MB
% 2.40/0.68 % (538874)Instructions burned: 7 (million)
% 2.40/0.68 % (538879)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1362396247:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.40/0.68 % (538881)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3236758196:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.40/0.68 % (538891)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3672095591:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.40/0.68 % (538883)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3844649364:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.40/0.68 % (538879)Instruction limit reached!
% 2.40/0.68 % (538879)------------------------------
% 2.40/0.68 % (538879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.68 % (538879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538879)CaDiCaL version: 2.1.3
% 2.40/0.68 % (538879)Termination reason: Instruction limit
% 2.40/0.68 % (538879)Termination phase: shuffling
% 2.40/0.68 % (538879)Time elapsed: 0.010 s
% 2.40/0.68 % (538879)Peak memory usage: 10 MB
% 2.40/0.68 % (538879)Instructions burned: 23 (million)
% 2.40/0.68 % (538889)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2738600565:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.40/0.68 % (538820)Instruction limit reached!
% 2.40/0.68 % (538820)------------------------------
% 2.40/0.68 % (538820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.68 % (538820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538820)CaDiCaL version: 2.1.3
% 2.40/0.68 % (538820)Termination reason: Instruction limit
% 2.40/0.68 % (538820)Termination phase: Saturation
% 2.40/0.68 % (538820)Time elapsed: 0.114 s
% 2.40/0.68 % (538820)Peak memory usage: 15 MB
% 2.40/0.68 % (538820)Instructions burned: 249 (million)
% 2.40/0.68 % (538881)Instruction limit reached!
% 2.40/0.68 % (538881)------------------------------
% 2.40/0.68 % (538881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.68 % (538881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538881)CaDiCaL version: 2.1.3
% 2.40/0.68 % (538881)Termination reason: Instruction limit
% 2.40/0.68 % (538881)Termination phase: shuffling
% 2.40/0.68 % (538881)Time elapsed: 0.017 s
% 2.40/0.68 % (538881)Peak memory usage: 10 MB
% 2.40/0.68 % (538881)Instructions burned: 20 (million)
% 2.40/0.68 % (538900)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.40/0.68 % (538898)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2598729249:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.40/0.68 % (538900)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2813119299:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.40/0.68 % (538900)Instruction limit reached!
% 2.40/0.68 % (538900)------------------------------
% 2.40/0.68 % (538900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.68 % (538900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538900)CaDiCaL version: 2.1.3
% 2.40/0.68 % (538900)Termination reason: Instruction limit
% 2.40/0.68 % (538900)Termination phase: shuffling
% 2.40/0.68 % (538900)Time elapsed: 0.003 s
% 2.40/0.68 % (538900)Peak memory usage: 10 MB
% 2.40/0.68 % (538900)Instructions burned: 7 (million)
% 2.40/0.68 % (538901)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4263866713:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.40/0.68 % (538898)Instruction limit reached!
% 2.40/0.68 % (538898)------------------------------
% 2.40/0.68 % (538898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.40/0.68 % (538898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.68 % (538898)CaDiCaL version: 2.1.3
% 2.60/0.75 % (538898)Termination reason: Instruction limit
% 2.60/0.75 % (538898)Termination phase: Naming
% 2.60/0.75 % (538898)Time elapsed: 0.020 s
% 2.60/0.75 % (538898)Peak memory usage: 11 MB
% 2.60/0.75 % (538898)Instructions burned: 44 (million)
% 2.60/0.75 % (538906)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=787914756:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.60/0.75 % (538891)Instruction limit reached!
% 2.60/0.75 % (538891)------------------------------
% 2.60/0.75 % (538891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.75 % (538891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.75 % (538891)CaDiCaL version: 2.1.3
% 2.60/0.75 % (538891)Termination reason: Instruction limit
% 2.60/0.75 % (538891)Termination phase: Saturation
% 2.60/0.75 % (538891)Time elapsed: 0.051 s
% 2.60/0.75 % (538891)Peak memory usage: 13 MB
% 2.60/0.75 % (538891)Instructions burned: 197 (million)
% 2.60/0.75 % (538913)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.60/0.75 % (538920)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1745767741:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.60/0.75 % (538913)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=410753677:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.60/0.75 % (538913)Instruction limit reached!
% 2.60/0.75 % (538913)------------------------------
% 2.60/0.75 % (538913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.75 % (538913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.75 % (538913)CaDiCaL version: 2.1.3
% 2.60/0.75 % (538913)Termination reason: Instruction limit
% 2.60/0.75 % (538913)Termination phase: shuffling
% 2.60/0.75 % (538913)Time elapsed: 0.004 s
% 2.60/0.75 % (538913)Peak memory usage: 10 MB
% 2.60/0.75 % (538913)Instructions burned: 7 (million)
% 2.60/0.75 % (538920)Instruction limit reached!
% 2.60/0.75 % (538920)------------------------------
% 2.60/0.75 % (538920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.75 % (538920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.75 % (538920)CaDiCaL version: 2.1.3
% 2.60/0.75 % (538920)Termination reason: Instruction limit
% 2.60/0.75 % (538920)Termination phase: shuffling
% 2.60/0.75 % (538920)Time elapsed: 0.005 s
% 2.60/0.75 % (538920)Peak memory usage: 10 MB
% 2.60/0.75 % (538920)Instructions burned: 22 (million)
% 2.60/0.75 % (538889)Instruction limit reached!
% 2.60/0.75 % (538889)------------------------------
% 2.60/0.75 % (538889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.75 % (538889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.75 % (538889)CaDiCaL version: 2.1.3
% 2.60/0.75 % (538889)Termination reason: Instruction limit
% 2.60/0.75 % (538889)Termination phase: Function definition elimination
% 2.60/0.75 % (538889)Time elapsed: 0.064 s
% 2.60/0.75 % (538889)Peak memory usage: 13 MB
% 2.60/0.75 % (538889)Instructions burned: 145 (million)
% 2.60/0.75 % (538928)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=1203269866:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.60/0.75 % (538927)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3610830299:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.60/0.75 % (538929)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=1463645867:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.60/0.75 % (538927)Instruction limit reached!
% 2.60/0.75 % (538927)------------------------------
% 2.60/0.75 % (538927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.60/0.75 % (538927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/0.75 % (538927)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538927)Termination reason: Instruction limit
% 3.31/0.85 % (538927)Termination phase: shuffling
% 3.31/0.85 % (538927)Time elapsed: 0.010 s
% 3.31/0.85 % (538927)Peak memory usage: 10 MB
% 3.31/0.85 % (538927)Instructions burned: 20 (million)
% 3.31/0.85 % (538901)Refutation not found, incomplete strategy
% 3.31/0.85 % (538901)------------------------------
% 3.31/0.85 % (538901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538901)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538901)Termination reason: Refutation not found, incomplete strategy
% 3.31/0.85 % (538901)Time elapsed: 0.062 s
% 3.31/0.85 % (538901)Peak memory usage: 13 MB
% 3.31/0.85 % (538901)Instructions burned: 130 (million)
% 3.31/0.85 % (538901)------------------------------
% 3.31/0.85 % (538901)------------------------------
% 3.31/0.85 % (538937)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=3880155436: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)
% 3.31/0.85 % (538938)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=4233159916:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 3.31/0.85 % (538906)Instruction limit reached!
% 3.31/0.85 % (538906)------------------------------
% 3.31/0.85 % (538906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538906)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538906)Termination reason: Instruction limit
% 3.31/0.85 % (538906)Termination phase: Property scanning
% 3.31/0.85 % (538906)Time elapsed: 0.079 s
% 3.31/0.85 % (538906)Peak memory usage: 13 MB
% 3.31/0.85 % (538906)Instructions burned: 170 (million)
% 3.31/0.85 % (538937)Instruction limit reached!
% 3.31/0.85 % (538937)------------------------------
% 3.31/0.85 % (538937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538937)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538937)Termination reason: Instruction limit
% 3.31/0.85 % (538937)Termination phase: SInE selection
% 3.31/0.85 % (538937)Time elapsed: 0.019 s
% 3.31/0.85 % (538937)Peak memory usage: 10 MB
% 3.31/0.85 % (538937)Instructions burned: 45 (million)
% 3.31/0.85 % (538947)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1029508823:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.31/0.85 % (538949)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.31/0.85 % (538769)Instruction limit reached!
% 3.31/0.85 % (538769)------------------------------
% 3.31/0.85 % (538769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538769)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538769)Termination reason: Instruction limit
% 3.31/0.85 % (538769)Termination phase: Saturation
% 3.31/0.85 % (538769)Time elapsed: 0.329 s
% 3.31/0.85 % (538769)Peak memory usage: 18 MB
% 3.31/0.85 % (538769)Instructions burned: 634 (million)
% 3.31/0.85 % (538949)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3420319925:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.31/0.85 % (538947)Instruction limit reached!
% 3.31/0.85 % (538947)------------------------------
% 3.31/0.85 % (538947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538947)CaDiCaL version: 2.1.3
% 3.31/0.85 % (538947)Termination reason: Instruction limit
% 3.31/0.85 % (538947)Termination phase: shuffling
% 3.31/0.85 % (538947)Time elapsed: 0.009 s
% 3.31/0.85 % (538947)Peak memory usage: 10 MB
% 3.31/0.85 % (538947)Instructions burned: 21 (million)
% 3.31/0.85 % (538928)Instruction limit reached!
% 3.31/0.85 % (538928)------------------------------
% 3.31/0.85 % (538928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.31/0.85 % (538928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/0.85 % (538928)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538928)Termination reason: Instruction limit
% 3.49/0.95 % (538928)Termination phase: Saturation
% 3.49/0.95 % (538928)Time elapsed: 0.094 s
% 3.49/0.95 % (538928)Peak memory usage: 15 MB
% 3.49/0.95 % (538928)Instructions burned: 318 (million)
% 3.49/0.95 % (538965)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=642294940:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.49/0.95 % (538959)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=736522902:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.49/0.95 % (538960)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3842231212:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.49/0.95 % (538959)Instruction limit reached!
% 3.49/0.95 % (538959)------------------------------
% 3.49/0.95 % (538959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538959)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538959)Termination reason: Instruction limit
% 3.49/0.95 % (538959)Termination phase: shuffling
% 3.49/0.95 % (538959)Time elapsed: 0.007 s
% 3.49/0.95 % (538959)Peak memory usage: 10 MB
% 3.49/0.95 % (538959)Instructions burned: 13 (million)
% 3.49/0.95 % (538965)Instruction limit reached!
% 3.49/0.95 % (538965)------------------------------
% 3.49/0.95 % (538965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538965)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538965)Termination reason: Instruction limit
% 3.49/0.95 % (538965)Termination phase: Preprocessing 3
% 3.49/0.95 % (538965)Time elapsed: 0.013 s
% 3.49/0.95 % (538965)Peak memory usage: 11 MB
% 3.49/0.95 % (538965)Instructions burned: 57 (million)
% 3.49/0.95 % (538971)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1992141237:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 3.49/0.95 % (538971)Instruction limit reached!
% 3.49/0.95 % (538971)------------------------------
% 3.49/0.95 % (538971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538971)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538971)Termination reason: Instruction limit
% 3.49/0.95 % (538971)Termination phase: Property scanning
% 3.49/0.95 % (538971)Time elapsed: 0.007 s
% 3.49/0.95 % (538971)Peak memory usage: 10 MB
% 3.49/0.95 % (538971)Instructions burned: 34 (million)
% 3.49/0.95 % (538973)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3356589280:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.49/0.95 % (538960)Instruction limit reached!
% 3.49/0.95 % (538960)------------------------------
% 3.49/0.95 % (538960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538960)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538960)Termination reason: Instruction limit
% 3.49/0.95 % (538960)Termination phase: Property scanning
% 3.49/0.95 % (538960)Time elapsed: 0.029 s
% 3.49/0.95 % (538960)Peak memory usage: 11 MB
% 3.49/0.95 % (538960)Instructions burned: 68 (million)
% 3.49/0.95 % (538978)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=552007661:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.49/0.95 % (538978)Instruction limit reached!
% 3.49/0.95 % (538978)------------------------------
% 3.49/0.95 % (538978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538978)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538978)Termination reason: Instruction limit
% 3.49/0.95 % (538978)Termination phase: Property scanning
% 3.49/0.95 % (538978)Time elapsed: 0.008 s
% 3.49/0.95 % (538978)Peak memory usage: 10 MB
% 3.49/0.95 % (538978)Instructions burned: 35 (million)
% 3.49/0.95 % (538982)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.49/0.95 % (538980)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1995444862:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.49/0.95 % (538982)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2072838547:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.49/0.95 % (538938)Refutation not found, incomplete strategy
% 3.49/0.95 % (538938)------------------------------
% 3.49/0.95 % (538938)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538938)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538938)Termination reason: Refutation not found, incomplete strategy
% 3.49/0.95 % (538938)Time elapsed: 0.126 s
% 3.49/0.95 % (538938)Peak memory usage: 16 MB
% 3.49/0.95 % (538938)Instructions burned: 275 (million)
% 3.49/0.95 % (538938)------------------------------
% 3.49/0.95 % (538938)------------------------------
% 3.49/0.95 % (538949)Instruction limit reached!
% 3.49/0.95 % (538949)------------------------------
% 3.49/0.95 % (538949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538949)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538949)Termination reason: Instruction limit
% 3.49/0.95 % (538949)Termination phase: Saturation
% 3.49/0.95 % (538949)Time elapsed: 0.099 s
% 3.49/0.95 % (538949)Peak memory usage: 14 MB
% 3.49/0.95 % (538949)Instructions burned: 201 (million)
% 3.49/0.95 % (538985)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1740023546:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.49/0.95 % (538986)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=403021234:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.49/0.95 % (538980)Instruction limit reached!
% 3.49/0.95 % (538980)------------------------------
% 3.49/0.95 % (538980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538980)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538980)Termination reason: Instruction limit
% 3.49/0.95 % (538980)Termination phase: Preprocessing 3
% 3.49/0.95 % (538980)Time elapsed: 0.032 s
% 3.49/0.95 % (538980)Peak memory usage: 12 MB
% 3.49/0.95 % (538980)Instructions burned: 69 (million)
% 3.49/0.95 % (538973)Instruction limit reached!
% 3.49/0.95 % (538973)------------------------------
% 3.49/0.95 % (538973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538973)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538973)Termination reason: Instruction limit
% 3.49/0.95 % (538973)Termination phase: Function definition elimination
% 3.49/0.95 % (538973)Time elapsed: 0.061 s
% 3.49/0.95 % (538973)Peak memory usage: 13 MB
% 3.49/0.95 % (538973)Instructions burned: 137 (million)
% 3.49/0.95 % (538982)Instruction limit reached!
% 3.49/0.95 % (538982)------------------------------
% 3.49/0.95 % (538982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538982)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538982)Termination reason: Instruction limit
% 3.49/0.95 % (538982)Termination phase: Saturation
% 3.49/0.95 % (538982)Time elapsed: 0.040 s
% 3.49/0.95 % (538982)Peak memory usage: 12 MB
% 3.49/0.95 % (538982)Instructions burned: 185 (million)
% 3.49/0.95 % (538994)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4051139906:i=427:sd=1:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/427Mi)
% 3.49/0.95 % (538996)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1305995748:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 3.49/0.95 % (538995)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1382627211:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 3.49/0.95 % (538986)Instruction limit reached!
% 3.49/0.95 % (538986)------------------------------
% 3.49/0.95 % (538986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538986)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538986)Termination reason: Instruction limit
% 3.49/0.95 % (538986)Termination phase: Property scanning
% 3.49/0.95 % (538986)Time elapsed: 0.063 s
% 3.49/0.95 % (538986)Peak memory usage: 13 MB
% 3.49/0.95 % (538986)Instructions burned: 96 (million)
% 3.49/0.95 % (539016)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3549263719:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 3.49/0.95 % (538929) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-538752-538929"...
% 3.49/0.95 % (538996) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-538752-538996"...
% 3.49/0.95 % (538985)Instruction limit reached!
% 3.49/0.95 % (538985)------------------------------
% 3.49/0.95 % (538985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.95 % (538985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.95 % (538985)CaDiCaL version: 2.1.3
% 3.49/0.95 % (538985)Termination reason: Instruction limit
% 3.49/0.95 % (538985)Termination phase: Saturation
% 3.49/0.95 % (538985)Time elapsed: 0.156 s
% 3.49/0.95 % (538985)Peak memory usage: 15 MB
% 3.49/0.95 % (538985)Instructions burned: 247 (million)
% 3.49/0.95 % (538996)...printing done.
% 3.49/0.95 % (538996)Refutation found. Thanks to Tanya!
% 3.49/0.95 % SZS status Theorem for theBenchmark
% 3.49/0.95 % SZS output start Proof for theBenchmark
% 3.49/0.95 thf(type_def_5, type, term: $tType).
% 3.49/0.95 thf(type_def_6, type, subst: $tType).
% 3.49/0.95 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 3.49/0.95 thf(type_def_8, type, d_term: $tType).
% 3.49/0.95 thf(type_def_9, type, d_subst: $tType).
% 3.49/0.95 thf(func_def_0, type, one: term).
% 3.49/0.95 thf(func_def_1, type, ap: (term > term > term)).
% 3.49/0.95 thf(func_def_2, type, lam: (term > term)).
% 3.49/0.95 thf(func_def_3, type, sub: (term > subst > term)).
% 3.49/0.95 thf(func_def_4, type, id: subst).
% 3.49/0.95 thf(func_def_5, type, sh: subst).
% 3.49/0.95 thf(func_def_6, type, push: (term > subst > subst)).
% 3.49/0.95 thf(func_def_7, type, comp: (subst > subst > subst)).
% 3.49/0.95 thf(func_def_8, type, var: (term > $o)).
% 3.49/0.95 thf(func_def_9, type, pushprop_lem1v2: $o).
% 3.49/0.95 thf(func_def_10, type, pushprop_lem1_gthm: $o).
% 3.49/0.95 thf(func_def_11, type, axmap: $o).
% 3.49/0.95 thf(func_def_12, type, pushprop_lem0_gthm: $o).
% 3.49/0.95 thf(func_def_13, type, shinj: $o).
% 3.49/0.95 thf(func_def_14, type, hoasinduction_lem1v2: $o).
% 3.49/0.95 thf(func_def_15, type, hoasinduction_lem1v2_gthm: $o).
% 3.49/0.95 thf(func_def_16, type, hoasap: (subst > term > subst > term > term)).
% 3.49/0.95 thf(func_def_17, type, induction2lem: $o).
% 3.49/0.95 thf(func_def_18, type, hoasinduction_lem3v2_f: $o).
% 3.49/0.95 thf(func_def_19, type, axvarshift: $o).
% 3.49/0.95 thf(func_def_20, type, hoasapinj2: $o).
% 3.49/0.95 thf(func_def_21, type, hoasapnotvar_gthm: $o).
% 3.49/0.95 thf(func_def_22, type, hoasapinj1: $o).
% 3.49/0.95 thf(func_def_23, type, ulamvar1: $o).
% 3.49/0.95 thf(func_def_24, type, induction2lem_lthm: $o).
% 3.49/0.95 thf(func_def_25, type, hoasinduction_lem3v2_gthm: $o).
% 3.49/0.95 thf(func_def_26, type, apnotvar: $o).
% 3.49/0.95 thf(func_def_27, type, pushprop_lthm_orig: $o).
% 3.49/0.95 thf(func_def_28, type, hoasinduction_lem3v2_f_lthm: $o).
% 3.49/0.95 thf(func_def_29, type, hoasinduction_lthm: $o).
% 3.49/0.95 thf(func_def_30, type, hoasinduction_no_psi_cond_lthm: $o).
% 3.49/0.95 thf(func_def_31, type, hoaslaminj: $o).
% 3.49/0.95 thf(func_def_32, type, hoasinduction_lem3aaa: $o).
% 3.49/0.95 thf(func_def_33, type, induction2lem_gthm: $o).
% 3.49/0.95 thf(func_def_34, type, hoasinduction_lem3aa_lthm: $o).
% 3.49/0.95 thf(func_def_35, type, hoasinduction_lem3: $o).
% 3.49/0.95 thf(func_def_36, type, hoasinduction_lem2: $o).
% 3.49/0.95 thf(func_def_37, type, termmset_lthm: $o).
% 3.49/0.95 thf(func_def_38, type, hoasinduction_lem1: $o).
% 3.49/0.95 thf(func_def_39, type, hoaslamnotap_lthm: $o).
% 3.49/0.95 thf(func_def_40, type, pushprop_lem1v2_lthm: $o).
% 3.49/0.95 thf(func_def_41, type, hoasapnotvar: $o).
% 3.49/0.95 thf(func_def_42, type, hoasinduction_lem0: $o).
% 3.49/0.95 thf(func_def_43, type, hoasinduction: $o).
% 3.49/0.95 thf(func_def_44, type, hoasinduction_gthm: $o).
% 3.49/0.95 thf(func_def_45, type, axapp: $o).
% 3.49/0.95 thf(func_def_46, type, hoaslamnotvar_lthm: $o).
% 3.49/0.95 thf(func_def_47, type, pushprop_lem3v2_lthm: $o).
% 3.49/0.95 thf(func_def_48, type, hoasinduction_lem3b_lthm: $o).
% 3.49/0.95 thf(func_def_49, type, ulamvarind: $o).
% 3.49/0.95 thf(func_def_50, type, induction: $o).
% 3.49/0.95 thf(func_def_51, type, hoasinduction_lem3a_lthm: $o).
% 3.49/0.95 thf(func_def_52, type, termmset_gthm: $o).
% 3.49/0.95 thf(func_def_53, type, hoasinduction_lem3aa: $o).
% 3.49/0.95 thf(func_def_54, type, pushprop_lem1v2_gthm: $o).
% 3.49/0.95 thf(func_def_55, type, hoaslamnotap_gthm: $o).
% 3.49/0.95 thf(func_def_56, type, hoaslamnotvar_gthm: $o).
% 3.49/0.95 thf(func_def_57, type, hoasinduction_lem3b_gthm: $o).
% 3.49/0.95 thf(func_def_58, type, pushprop_lem2v2: $o).
% 3.49/0.95 thf(func_def_59, type, hoasinduction_lem3a_gthm: $o).
% 3.49/0.95 thf(func_def_60, type, axclos: $o).
% 3.49/0.95 thf(func_def_61, type, axassoc: $o).
% 3.49/0.95 thf(func_def_62, type, hoasinduction_lem2v2: $o).
% 3.49/0.95 thf(func_def_63, type, pushprop_lthm: $o).
% 3.49/0.95 thf(func_def_64, type, apinj2: $o).
% 3.49/0.95 thf(func_def_65, type, apinj1: $o).
% 3.49/0.95 thf(func_def_66, type, hoasapinj2_lthm: $o).
% 3.49/0.95 thf(func_def_67, type, hoasinduction_lem3v2a: $o).
% 3.49/0.95 thf(func_def_68, type, hoasapinj1_lthm: $o).
% 3.49/0.95 thf(func_def_69, type, hoaslaminj_lthm: $o).
% 3.49/0.95 thf(func_def_70, type, axvarcons: $o).
% 3.49/0.95 thf(func_def_71, type, hoaslam: (subst > (subst > term > term) > term)).
% 3.49/0.95 thf(func_def_72, type, axscons: $o).
% 3.49/0.95 thf(func_def_73, type, hoasinduction_lem2v2_gthm: $o).
% 3.49/0.95 thf(func_def_74, type, axidr: $o).
% 3.49/0.95 thf(func_def_75, type, pushprop_lem1: $o).
% 3.49/0.95 thf(func_def_76, type, laminj: $o).
% 3.49/0.95 thf(func_def_77, type, hoasinduction_lem3_lthm: $o).
% 3.49/0.95 thf(func_def_78, type, pushprop_lem0: $o).
% 3.49/0.95 thf(func_def_79, type, pushprop_gthm: $o).
% 3.49/0.95 thf(func_def_80, type, axabs: $o).
% 3.49/0.95 thf(func_def_81, type, hoasinduction_lem3v2a_lthm: $o).
% 3.49/0.95 thf(func_def_82, type, hoasinduction_lem2_lthm: $o).
% 3.49/0.95 thf(func_def_83, type, hoasapinj2_gthm: $o).
% 3.49/0.95 thf(func_def_84, type, hoasinduction_p_and_p_prime: ((subst > term > subst > $o) > (term > $o) > $o)).
% 3.49/0.95 thf(func_def_85, type, hoasinduction_lem1_lthm: $o).
% 3.49/0.95 thf(func_def_86, type, lamnotap: $o).
% 3.49/0.95 thf(func_def_87, type, hoasapinj1_gthm: $o).
% 3.49/0.95 thf(func_def_88, type, hoaslamnotvar: $o).
% 3.49/0.95 thf(func_def_89, type, axidl: $o).
% 3.49/0.95 thf(func_def_90, type, hoaslaminj_gthm: $o).
% 3.49/0.95 thf(func_def_91, type, induction2_lthm: $o).
% 3.49/0.95 thf(func_def_92, type, hoasinduction_lem0_lthm: $o).
% 3.49/0.95 thf(func_def_93, type, substmonoid_lthm: $o).
% 3.49/0.95 thf(func_def_94, type, pushprop: $o).
% 3.49/0.95 thf(func_def_95, type, hoasinduction_lem3_gthm: $o).
% 3.49/0.95 thf(func_def_96, type, hoasinduction_lem2_gthm: $o).
% 3.49/0.95 thf(func_def_97, type, hoasinduction_lem3b: $o).
% 3.49/0.95 thf(func_def_98, type, substmonoid: $o).
% 3.49/0.95 thf(func_def_99, type, lamnotvar: $o).
% 3.49/0.95 thf(func_def_100, type, hoasinduction_lem3a: $o).
% 3.49/0.95 thf(func_def_101, type, hoasinduction_lem1_gthm: $o).
% 3.49/0.95 thf(func_def_102, type, hoasinduction_no_psi_cond: $o).
% 3.49/0.95 thf(func_def_103, type, induction2_gthm: $o).
% 3.49/0.95 thf(func_def_104, type, pushprop_lem2v2_lthm: $o).
% 3.49/0.95 thf(func_def_105, type, hoasvar: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_106, type, hoaslamnotap: $o).
% 3.49/0.95 thf(func_def_107, type, substmonoid_gthm: $o).
% 3.49/0.95 thf(func_def_108, type, ulamvarsh: $o).
% 3.49/0.95 thf(func_def_109, type, induction2: $o).
% 3.49/0.95 thf(func_def_110, type, pushprop_lem3v2: $o).
% 3.49/0.95 thf(func_def_111, type, pushprop_lem2v2_gthm: $o).
% 3.49/0.95 thf(func_def_112, type, pushprop_lem1_lthm: $o).
% 3.49/0.95 thf(func_def_113, type, hoasinduction_lem3v2: $o).
% 3.49/0.95 thf(func_def_114, type, axshiftcons: $o).
% 3.49/0.95 thf(func_def_115, type, termmset: $o).
% 3.49/0.95 thf(func_def_116, type, pushprop_lem0_lthm: $o).
% 3.49/0.95 thf(func_def_117, type, hoasapnotvar_lthm: $o).
% 3.49/0.95 thf(func_def_118, type, hoasinduction_lem3v2_lthm: $o).
% 3.49/0.95 thf(func_def_119, type, pushprop_p_and_p_prime: (term > subst > (term > $o) > (term > $o) > $o)).
% 3.49/0.95 thf(func_def_120, type, axvarid: $o).
% 3.49/0.95 thf(func_def_121, type, hoasinduction_lthm_3: $o).
% 3.49/0.95 thf(func_def_122, type, d2term: (d_term > term)).
% 3.49/0.95 thf(func_def_123, type, d2subst: (d_subst > subst)).
% 3.49/0.95 thf(func_def_124, type, d_one: d_term).
% 3.49/0.95 thf(func_def_125, type, d_id: d_subst).
% 3.49/0.95 thf(func_def_129, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.49/0.95 thf(func_def_130, type, db1: !>[X0: $tType]:(X0)).
% 3.49/0.95 thf(func_def_131, type, db0: !>[X0: $tType]:(X0)).
% 3.49/0.95 thf(func_def_132, type, db2: !>[X0: $tType]:(X0)).
% 3.49/0.95 thf(func_def_133, type, db4: !>[X0: $tType]:(X0)).
% 3.49/0.95 thf(func_def_134, type, db3: !>[X0: $tType]:(X0)).
% 3.49/0.95 thf(func_def_135, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.49/0.95 thf(func_def_136, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.49/0.95 thf(func_def_137, type, vIMP: ($o > $o > $o)).
% 3.49/0.95 thf(func_def_138, type, sP0: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_139, type, sP1: $o).
% 3.49/0.95 thf(func_def_140, type, sP2: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_141, type, sP3: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_142, type, sP4: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_143, type, sP5: ((term > $o) > subst > $o)).
% 3.49/0.95 thf(func_def_144, type, sP6: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_145, type, sP7: $o).
% 3.49/0.95 thf(func_def_146, type, sP8: $o).
% 3.49/0.95 thf(func_def_147, type, sP9: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_148, type, sP10: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_149, type, sP11: $o).
% 3.49/0.95 thf(func_def_150, type, sP12: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_151, type, sP13: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_152, type, sP14: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_153, type, sP15: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_154, type, sP16: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_155, type, sP17: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_156, type, sP18: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_157, type, sP19: $o).
% 3.49/0.95 thf(func_def_158, type, sP20: $o).
% 3.49/0.95 thf(func_def_159, type, sP21: $o).
% 3.49/0.95 thf(func_def_160, type, sP22: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_161, type, sP23: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_162, type, sP24: ((term > $o) > term > $o)).
% 3.49/0.95 thf(func_def_163, type, sP25: $o).
% 3.49/0.95 thf(func_def_164, type, sP26: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_165, type, sP27: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_166, type, sP28: $o).
% 3.49/0.95 thf(func_def_167, type, sP29: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_168, type, sP30: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_169, type, sP31: $o).
% 3.49/0.95 thf(func_def_170, type, sP32: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_171, type, sP33: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_172, type, sP34: $o).
% 3.49/0.95 thf(func_def_173, type, sP35: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_174, type, sP36: $o).
% 3.49/0.95 thf(func_def_175, type, sP37: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_176, type, sP38: ((term > $o) > term > $o)).
% 3.49/0.95 thf(func_def_177, type, sP39: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_178, type, sP40: $o).
% 3.49/0.95 thf(func_def_179, type, sP41: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_180, type, sP42: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_181, type, sP43: (term > (subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_182, type, sP44: $o).
% 3.49/0.95 thf(func_def_183, type, sP45: $o).
% 3.49/0.95 thf(func_def_184, type, sP46: $o).
% 3.49/0.95 thf(func_def_185, type, sP47: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_186, type, sP48: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_187, type, sP49: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_188, type, sP50: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_189, type, sP51: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_190, type, sP52: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_191, type, sP53: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_192, type, sP54: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_193, type, sP55: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_194, type, sP56: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_195, type, sP57: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_196, type, sP58: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_197, type, sP59: $o).
% 3.49/0.95 thf(func_def_198, type, sP60: $o).
% 3.49/0.95 thf(func_def_199, type, sP61: $o).
% 3.49/0.95 thf(func_def_200, type, sP62: $o).
% 3.49/0.95 thf(func_def_201, type, sP63: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_202, type, sP64: $o).
% 3.49/0.95 thf(func_def_203, type, sP65: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_204, type, sP66: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_205, type, sP67: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_206, type, sP68: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_207, type, sP69: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_208, type, sP70: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_209, type, sP71: $o).
% 3.49/0.95 thf(func_def_210, type, sP72: $o).
% 3.49/0.95 thf(func_def_211, type, sP73: $o).
% 3.49/0.95 thf(func_def_212, type, sP74: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_213, type, sP75: $o).
% 3.49/0.95 thf(func_def_214, type, sP76: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_215, type, sP77: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_216, type, sP78: $o).
% 3.49/0.95 thf(func_def_217, type, sP79: $o).
% 3.49/0.95 thf(func_def_218, type, sP80: $o).
% 3.49/0.95 thf(func_def_219, type, sP81: $o).
% 3.49/0.95 thf(func_def_220, type, sP82: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_221, type, sP83: $o).
% 3.49/0.95 thf(func_def_222, type, sP84: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_223, type, sP85: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_224, type, sP86: $o).
% 3.49/0.95 thf(func_def_225, type, sP87: $o).
% 3.49/0.95 thf(func_def_226, type, sP88: $o).
% 3.49/0.95 thf(func_def_227, type, sP89: $o).
% 3.49/0.95 thf(func_def_228, type, sP90: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_229, type, sP91: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_230, type, sP92: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_231, type, sP93: $o).
% 3.49/0.95 thf(func_def_232, type, sP94: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_233, type, sP95: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_234, type, sP96: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_235, type, sP97: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_236, type, sP98: $o).
% 3.49/0.95 thf(func_def_237, type, sP99: $o).
% 3.49/0.95 thf(func_def_238, type, sP100: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_239, type, sP101: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_240, type, sP102: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_241, type, sP103: ((subst > term > subst > $o) > $o)).
% 3.49/0.95 thf(func_def_242, type, sP104: $o).
% 3.49/0.95 thf(func_def_243, type, sP105: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_244, type, sP106: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_245, type, sP107: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_246, type, sP108: ((term > $o) > $o)).
% 3.49/0.95 thf(func_def_247, type, sP109: $o).
% 3.49/0.95 thf(func_def_248, type, sP110: $o).
% 3.49/0.95 thf(func_def_249, type, sK111: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_250, type, sK112: (term > $o)).
% 3.49/0.95 thf(func_def_251, type, sK113: term).
% 3.49/0.95 thf(func_def_252, type, sK114: subst).
% 3.49/0.95 thf(func_def_253, type, sK115: (term > $o)).
% 3.49/0.95 thf(func_def_254, type, sK116: term).
% 3.49/0.95 thf(func_def_255, type, sK117: ((term > $o) > subst > term)).
% 3.49/0.95 thf(func_def_256, type, sK118: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_257, type, sK119: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_258, type, sK120: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_259, type, sK121: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_260, type, sK122: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_261, type, sK123: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_262, type, sK124: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_263, type, sK125: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_264, type, sK126: term).
% 3.49/0.95 thf(func_def_265, type, sK127: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_266, type, sK128: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_267, type, sK129: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_268, type, sK130: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_269, type, sK131: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_270, type, sK132: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_271, type, sK133: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_272, type, sK134: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_273, type, sK135: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_274, type, sK136: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_275, type, sK137: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_276, type, sK138: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_277, type, sK139: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_278, type, sK140: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_279, type, sK141: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_280, type, sK142: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_281, type, sK143: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_282, type, sK144: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_283, type, sK145: term).
% 3.49/0.95 thf(func_def_284, type, sK146: term).
% 3.49/0.95 thf(func_def_285, type, sK147: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_286, type, sK148: ((subst > term > subst > $o) > term > term)).
% 3.49/0.95 thf(func_def_287, type, sK149: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_288, type, sK150: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_289, type, sK151: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_290, type, sK152: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_291, type, sK153: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_292, type, sK154: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_293, type, sK155: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_294, type, sK156: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_295, type, sK157: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_296, type, sK158: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_297, type, sK159: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_298, type, sK160: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_299, type, sK161: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_300, type, sK162: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_301, type, sK163: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_302, type, sK164: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_303, type, sK165: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_304, type, sK166: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_305, type, sK167: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_306, type, sK168: (term > $o)).
% 3.49/0.95 thf(func_def_307, type, sK169: term).
% 3.49/0.95 thf(func_def_308, type, sK170: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_309, type, sK171: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_310, type, sK172: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_311, type, sK173: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_312, type, sK174: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_313, type, sK175: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_314, type, sK176: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_315, type, sK177: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_316, type, sK178: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_317, type, sK179: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_318, type, sK180: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_319, type, sK181: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_320, type, sK182: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_321, type, sK183: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_322, type, sK184: term).
% 3.49/0.95 thf(func_def_323, type, sK185: term).
% 3.49/0.95 thf(func_def_324, type, sK186: term).
% 3.49/0.95 thf(func_def_325, type, sK187: term).
% 3.49/0.95 thf(func_def_326, type, sK188: term).
% 3.49/0.95 thf(func_def_327, type, sK189: term).
% 3.49/0.95 thf(func_def_328, type, sK190: term).
% 3.49/0.95 thf(func_def_329, type, sK191: term).
% 3.49/0.95 thf(func_def_330, type, sK192: term).
% 3.49/0.95 thf(func_def_331, type, sK193: ((subst > term > subst > $o) > term > term)).
% 3.49/0.95 thf(func_def_332, type, sK194: term).
% 3.49/0.95 thf(func_def_333, type, sK195: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_334, type, sK196: term).
% 3.49/0.95 thf(func_def_335, type, sK197: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_336, type, sK198: ((subst > term > subst > $o) > term > term)).
% 3.49/0.95 thf(func_def_337, type, sK199: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_338, type, sK200: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_339, type, sK201: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_340, type, sK202: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_341, type, sK203: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_342, type, sK204: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_343, type, sK205: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_344, type, sK206: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_345, type, sK207: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_346, type, sK208: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_347, type, sK209: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_348, type, sK210: term).
% 3.49/0.95 thf(func_def_349, type, sK211: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_350, type, sK212: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_351, type, sK213: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_352, type, sK214: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_353, type, sK215: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_354, type, sK216: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_355, type, sK217: subst).
% 3.49/0.95 thf(func_def_356, type, sK218: subst).
% 3.49/0.95 thf(func_def_357, type, sK219: subst).
% 3.49/0.95 thf(func_def_358, type, sK220: subst).
% 3.49/0.95 thf(func_def_359, type, sK221: term).
% 3.49/0.95 thf(func_def_360, type, sK222: term).
% 3.49/0.95 thf(func_def_361, type, sK223: term).
% 3.49/0.95 thf(func_def_362, type, sK224: term).
% 3.49/0.95 thf(func_def_363, type, sK225: term).
% 3.49/0.95 thf(func_def_364, type, sK226: term).
% 3.49/0.95 thf(func_def_365, type, sK227: term).
% 3.49/0.95 thf(func_def_366, type, sK228: term).
% 3.49/0.95 thf(func_def_367, type, sK229: term).
% 3.49/0.95 thf(func_def_368, type, sK230: (term > $o)).
% 3.49/0.95 thf(func_def_369, type, sK231: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_370, type, sK232: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_371, type, sK233: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_372, type, sK234: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_373, type, sK235: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_374, type, sK236: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_375, type, sK237: term).
% 3.49/0.95 thf(func_def_376, type, sK238: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_377, type, sK239: (term > (subst > term > term) > term)).
% 3.49/0.95 thf(func_def_378, type, sK240: (term > (subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_379, type, sK241: (term > (subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_380, type, sK242: (term > (subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_381, type, sK243: (term > (subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_382, type, sK244: (term > (subst > term > term) > term)).
% 3.49/0.95 thf(func_def_383, type, sK245: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_384, type, sK246: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_385, type, sK247: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_386, type, sK248: (term > $o)).
% 3.49/0.95 thf(func_def_387, type, sK249: term).
% 3.49/0.95 thf(func_def_388, type, sK250: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.49/0.95 thf(func_def_389, type, sK251: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_390, type, sK252: (term > $o)).
% 3.49/0.95 thf(func_def_391, type, sK253: term).
% 3.49/0.95 thf(func_def_392, type, sK254: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_393, type, sK255: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_394, type, sK256: term).
% 3.49/0.95 thf(func_def_395, type, sK257: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_396, type, sK258: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_397, type, sK259: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_398, type, sK260: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_399, type, sK261: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_400, type, sK262: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_401, type, sK263: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_402, type, sK264: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_403, type, sK265: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_404, type, sK266: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_405, type, sK267: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_406, type, sK268: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_407, type, sK269: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_408, type, sK270: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_409, type, sK271: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_410, type, sK272: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_411, type, sK273: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_412, type, sK274: (term > $o)).
% 3.49/0.95 thf(func_def_413, type, sK275: term).
% 3.49/0.95 thf(func_def_414, type, sK276: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_415, type, sK277: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_416, type, sK278: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.49/0.95 thf(func_def_417, type, sK279: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_418, type, sK280: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_419, type, sK281: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_420, type, sK282: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_421, type, sK283: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_422, type, sK284: (term > $o)).
% 3.49/0.95 thf(func_def_423, type, sK285: term).
% 3.49/0.95 thf(func_def_424, type, sK286: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_425, type, sK287: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_426, type, sK288: term).
% 3.49/0.95 thf(func_def_427, type, sK289: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_428, type, sK290: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_429, type, sK291: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_430, type, sK292: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_431, type, sK293: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_432, type, sK294: term).
% 3.49/0.95 thf(func_def_433, type, sK295: term).
% 3.49/0.95 thf(func_def_434, type, sK296: term).
% 3.49/0.95 thf(func_def_435, type, sK297: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_436, type, sK298: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_437, type, sK299: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_438, type, sK300: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_439, type, sK301: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_440, type, sK302: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_441, type, sK303: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_442, type, sK304: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_443, type, sK305: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_444, type, sK306: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_445, type, sK307: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_446, type, sK308: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_447, type, sK309: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_448, type, sK310: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_449, type, sK311: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_450, type, sK312: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_451, type, sK313: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_452, type, sK314: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_453, type, sK315: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_454, type, sK316: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_455, type, sK317: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_456, type, sK318: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_457, type, sK319: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_458, type, sK320: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_459, type, sK321: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_460, type, sK322: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_461, type, sK323: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_462, type, sK324: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_463, type, sK325: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_464, type, sK326: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_465, type, sK327: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_466, type, sK328: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_467, type, sK329: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_468, type, sK330: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_469, type, sK331: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_470, type, sK332: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_471, type, sK333: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_472, type, sK334: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_473, type, sK335: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_474, type, sK336: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_475, type, sK337: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_476, type, sK338: term).
% 3.49/0.95 thf(func_def_477, type, sK339: term).
% 3.49/0.95 thf(func_def_478, type, sK340: term).
% 3.49/0.95 thf(func_def_479, type, sK341: subst).
% 3.49/0.95 thf(func_def_480, type, sK342: subst).
% 3.49/0.95 thf(func_def_481, type, sK343: term).
% 3.49/0.95 thf(func_def_482, type, sK344: (subst > term > term)).
% 3.49/0.95 thf(func_def_483, type, sK345: (subst > term > term)).
% 3.49/0.95 thf(func_def_484, type, sK346: term).
% 3.49/0.95 thf(func_def_485, type, sK347: subst).
% 3.49/0.95 thf(func_def_486, type, sK348: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_487, type, sK349: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_488, type, sK350: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_489, type, sK351: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_490, type, sK352: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_491, type, sK353: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_492, type, sK354: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_493, type, sK355: term).
% 3.49/0.95 thf(func_def_494, type, sK356: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_495, type, sK357: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_496, type, sK358: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_497, type, sK359: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_498, type, sK360: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_499, type, sK361: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_500, type, sK362: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_501, type, sK363: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_502, type, sK364: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_503, type, sK365: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_504, type, sK366: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_505, type, sK367: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_506, type, sK368: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_507, type, sK369: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_508, type, sK370: term).
% 3.49/0.95 thf(func_def_509, type, sK371: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_510, type, sK372: (term > $o)).
% 3.49/0.95 thf(func_def_511, type, sK373: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_512, type, sK374: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_513, type, sK375: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_514, type, sK376: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_515, type, sK377: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_516, type, sK378: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_517, type, sK379: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_518, type, sK380: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_519, type, sK381: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_520, type, sK382: ((term > $o) > term > term)).
% 3.49/0.95 thf(func_def_521, type, sK383: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_522, type, sK384: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_523, type, sK385: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_524, type, sK386: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_525, type, sK387: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_526, type, sK388: term).
% 3.49/0.95 thf(func_def_527, type, sK389: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_528, type, sK390: ((subst > term > subst > $o) > term > term)).
% 3.49/0.95 thf(func_def_529, type, sK391: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_530, type, sK392: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_531, type, sK393: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_532, type, sK394: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_533, type, sK395: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_534, type, sK396: (term > $o)).
% 3.49/0.95 thf(func_def_535, type, sK397: term).
% 3.49/0.95 thf(func_def_536, type, sK398: subst).
% 3.49/0.95 thf(func_def_537, type, sK399: (subst > (term > $o) > term)).
% 3.49/0.95 thf(func_def_538, type, sK400: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_539, type, sK401: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_540, type, sK402: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_541, type, sK403: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_542, type, sK404: (term > $o)).
% 3.49/0.95 thf(func_def_543, type, sK405: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_544, type, sK406: term).
% 3.49/0.95 thf(func_def_545, type, sK407: term).
% 3.49/0.95 thf(func_def_546, type, sK408: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_547, type, sK409: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_548, type, sK410: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_549, type, sK411: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_550, type, sK412: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.49/0.95 thf(func_def_551, type, sK413: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_552, type, sK414: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_553, type, sK415: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_554, type, sK416: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_555, type, sK417: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_556, type, sK418: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_557, type, sK419: term).
% 3.49/0.95 thf(func_def_558, type, sK420: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_559, type, sK421: term).
% 3.49/0.95 thf(func_def_560, type, sK422: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_561, type, sK423: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_562, type, sK424: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_563, type, sK425: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_564, type, sK426: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_565, type, sK427: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_566, type, sK428: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_567, type, sK429: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_568, type, sK430: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_569, type, sK431: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_570, type, sK432: (term > $o)).
% 3.49/0.95 thf(func_def_571, type, sK433: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_572, type, sK434: term).
% 3.49/0.95 thf(func_def_573, type, sK435: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_574, type, sK436: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_575, type, sK437: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_576, type, sK438: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_577, type, sK439: ((subst > term > subst > $o) > (term > $o) > term)).
% 3.49/0.95 thf(func_def_578, type, sK440: ((term > $o) > term > term)).
% 3.49/0.95 thf(func_def_579, type, sK441: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_580, type, sK442: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_581, type, sK443: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_582, type, sK444: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_583, type, sK445: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_584, type, sK446: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_585, type, sK447: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_586, type, sK448: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_587, type, sK449: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_588, type, sK450: ((term > $o) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_589, type, sK451: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_590, type, sK452: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_591, type, sK453: (term > $o)).
% 3.49/0.95 thf(func_def_592, type, sK454: term).
% 3.49/0.95 thf(func_def_593, type, sK455: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_594, type, sK456: term).
% 3.49/0.95 thf(func_def_595, type, sK457: (term > $o)).
% 3.49/0.95 thf(func_def_596, type, sK458: term).
% 3.49/0.95 thf(func_def_597, type, sK459: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_598, type, sK460: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_599, type, sK461: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_600, type, sK462: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_601, type, sK463: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_602, type, sK464: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_603, type, sK465: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_604, type, sK466: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_605, type, sK467: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_606, type, sK468: ((subst > term > subst > $o) > subst)).
% 3.49/0.95 thf(func_def_607, type, sK469: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_608, type, sK470: ((subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_609, type, sK471: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_610, type, sK472: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_611, type, sK473: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_612, type, sK474: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_613, type, sK475: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_614, type, sK476: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_615, type, sK477: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_616, type, sK478: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_617, type, sK479: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_618, type, sK480: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_619, type, sK481: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_620, type, sK482: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_621, type, sK483: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_622, type, sK484: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_623, type, sK485: term).
% 3.49/0.95 thf(func_def_624, type, sK486: (term > $o)).
% 3.49/0.95 thf(func_def_625, type, sK487: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_626, type, sK488: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_627, type, sK489: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_628, type, sK490: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_629, type, sK491: subst).
% 3.49/0.95 thf(func_def_630, type, sK492: term).
% 3.49/0.95 thf(func_def_631, type, sK493: (term > $o)).
% 3.49/0.95 thf(func_def_632, type, sK494: (term > $o)).
% 3.49/0.95 thf(func_def_633, type, sK495: term).
% 3.49/0.95 thf(func_def_634, type, sK496: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_635, type, sK497: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_636, type, sK498: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_637, type, sK499: ((term > $o) > subst > term)).
% 3.49/0.95 thf(func_def_638, type, sK500: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_639, type, sK501: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_640, type, sK502: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_641, type, sK503: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_642, type, sK504: (term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_643, type, sK505: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_644, type, sK506: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_645, type, sK507: term).
% 3.49/0.95 thf(func_def_646, type, sK508: (term > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_647, type, sK509: ((subst > term > term) > (subst > term > subst > $o) > term)).
% 3.49/0.95 thf(func_def_648, type, sK510: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_649, type, sK511: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_650, type, sK512: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_651, type, sK513: ((subst > term > subst > $o) > subst > term > term)).
% 3.49/0.95 thf(func_def_652, type, sK514: term).
% 3.49/0.95 thf(func_def_653, type, sK515: subst).
% 3.49/0.95 thf(func_def_654, type, sK516: (subst > (term > $o) > (term > $o) > term > term)).
% 3.49/0.95 thf(func_def_655, type, sK517: term).
% 3.49/0.95 thf(func_def_656, type, sK518: (term > $o)).
% 3.49/0.95 thf(func_def_657, type, sK519: (term > $o)).
% 3.49/0.95 thf(func_def_658, type, sK520: subst).
% 3.49/0.95 thf(func_def_659, type, sK521: (term > $o)).
% 3.49/0.95 thf(func_def_660, type, sK522: term).
% 3.49/0.95 thf(func_def_661, type, sK523: subst).
% 3.49/0.95 thf(func_def_662, type, sK524: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_663, type, sK525: (subst > term > (term > $o) > term > $o)).
% 3.49/0.95 thf(func_def_664, type, sK526: term).
% 3.49/0.95 thf(func_def_665, type, sK527: subst).
% 3.49/0.95 thf(func_def_666, type, sK528: subst).
% 3.49/0.95 thf(func_def_667, type, sK529: subst).
% 3.49/0.95 thf(func_def_668, type, sK530: term).
% 3.49/0.95 thf(func_def_669, type, sK531: term).
% 3.49/0.95 thf(func_def_670, type, sK532: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_671, type, sK533: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_672, type, sK534: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_673, type, sK535: term).
% 3.49/0.95 thf(func_def_674, type, sK536: term).
% 3.49/0.95 thf(func_def_675, type, sK537: (subst > term > term)).
% 3.49/0.95 thf(func_def_676, type, sK538: term).
% 3.49/0.95 thf(func_def_677, type, sK539: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_678, type, sK540: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_679, type, sK541: (term > subst > term > term)).
% 3.49/0.95 thf(func_def_680, type, sK542: term).
% 3.49/0.95 thf(func_def_681, type, sK543: term).
% 3.49/0.95 thf(func_def_682, type, sK544: term).
% 3.49/0.95 thf(func_def_683, type, sK545: term).
% 3.49/0.95 thf(func_def_684, type, sK546: term).
% 3.49/0.95 thf(func_def_685, type, sK547: term).
% 3.49/0.95 thf(func_def_686, type, sK548: (term > d_term)).
% 3.49/0.95 thf(func_def_687, type, sK549: term).
% 3.49/0.95 thf(func_def_688, type, sK550: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_689, type, sK551: term).
% 3.49/0.95 thf(func_def_690, type, sK552: subst).
% 3.49/0.95 thf(func_def_691, type, sK553: term).
% 3.49/0.95 thf(func_def_692, type, sK554: term).
% 3.49/0.95 thf(func_def_693, type, sK555: term).
% 3.49/0.95 thf(func_def_694, type, sK556: term).
% 3.49/0.95 thf(func_def_695, type, sK557: term).
% 3.49/0.95 thf(func_def_696, type, sK558: term).
% 3.49/0.95 thf(func_def_697, type, sK559: term).
% 3.49/0.95 thf(func_def_698, type, sK560: (term > subst > term > term)).
% 3.49/0.95 thf(func_def_699, type, sK561: (term > $o)).
% 3.49/0.95 thf(func_def_700, type, sK562: term).
% 3.49/0.95 thf(func_def_701, type, sK563: (term > $o)).
% 3.49/0.95 thf(func_def_702, type, sK564: term).
% 3.49/0.95 thf(func_def_703, type, sK565: subst).
% 3.49/0.95 thf(func_def_704, type, sK566: (term > $o)).
% 3.49/0.95 thf(func_def_705, type, sK567: term).
% 3.49/0.95 thf(func_def_706, type, sK568: subst).
% 3.49/0.95 thf(func_def_707, type, sK569: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_708, type, sK570: (subst > term > (term > $o) > term > $o)).
% 3.49/0.95 thf(func_def_709, type, sK571: term).
% 3.49/0.95 thf(func_def_710, type, sK572: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_711, type, sK573: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_712, type, sK574: ((subst > term > subst > $o) > term > $o)).
% 3.49/0.95 thf(func_def_713, type, sK575: term).
% 3.49/0.95 thf(func_def_714, type, sK576: term).
% 3.49/0.95 thf(func_def_715, type, sK577: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_716, type, sK578: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_717, type, sK579: (term > subst > term > term)).
% 3.49/0.95 thf(func_def_718, type, sK580: subst).
% 3.49/0.95 thf(func_def_719, type, sK581: term).
% 3.49/0.95 thf(func_def_720, type, sK582: term).
% 3.49/0.95 thf(func_def_721, type, sK583: term).
% 3.49/0.95 thf(func_def_722, type, sK584: term).
% 3.49/0.95 thf(func_def_723, type, sK585: term).
% 3.49/0.95 thf(func_def_724, type, sK586: subst).
% 3.49/0.95 thf(func_def_725, type, sK587: (term > subst > term > term)).
% 3.49/0.95 thf(func_def_726, type, sK588: term).
% 3.49/0.95 thf(func_def_727, type, sK589: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_728, type, sK590: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_729, type, sK591: ((subst > term > subst > $o) > term > $o)).
% 3.49/0.95 thf(func_def_730, type, sK592: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_731, type, sK593: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_732, type, sK594: term).
% 3.49/0.95 thf(func_def_733, type, sK595: (subst > term > term)).
% 3.49/0.95 thf(func_def_734, type, sK596: subst).
% 3.49/0.95 thf(func_def_735, type, sK597: term).
% 3.49/0.95 thf(func_def_736, type, sK598: (subst > term > term)).
% 3.49/0.95 thf(func_def_737, type, sK599: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_738, type, sK600: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_739, type, sK601: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_740, type, sK602: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_741, type, sK603: ((subst > term > term) > term)).
% 3.49/0.95 thf(func_def_742, type, sK604: ((subst > term > term) > subst)).
% 3.49/0.95 thf(func_def_743, type, sK605: (subst > d_subst)).
% 3.49/0.95 thf(func_def_744, type, sK606: subst).
% 3.49/0.95 thf(func_def_745, type, sK607: subst).
% 3.49/0.95 thf(func_def_746, type, sK608: term).
% 3.49/0.95 thf(func_def_747, type, sK609: term).
% 3.49/0.95 thf(func_def_748, type, sK610: term).
% 3.49/0.95 thf(func_def_749, type, sK611: term).
% 3.49/0.95 thf(func_def_750, type, sK612: term).
% 3.49/0.95 thf(func_def_751, type, sK613: (term > subst > term > term)).
% 3.49/0.95 thf(func_def_752, type, sK614: ((subst > term > subst > $o) > term > $o)).
% 3.49/0.95 thf(func_def_753, type, sK615: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_754, type, sK616: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_755, type, sK617: subst).
% 3.49/0.95 thf(func_def_756, type, sK618: ((subst > term > subst > $o) > term > $o)).
% 3.49/0.95 thf(func_def_757, type, sK619: term).
% 3.49/0.95 thf(func_def_758, type, sK620: (subst > term > subst > $o)).
% 3.49/0.95 thf(func_def_759, type, sK621: ((term > $o) > term)).
% 3.49/0.95 thf(func_def_760, type, sK622: term).
% 3.49/0.95 thf(func_def_761, type, sK623: term).
% 3.49/0.95 thf(func_def_762, type, sK624: term).
% 3.49/0.95 thf(func_def_763, type, sK625: term).
% 3.49/0.95 thf(func_def_764, type, sK626: term).
% 3.49/0.95 thf(func_def_765, type, sK627: ((term > $o) > subst > term > (term > $o) > term)).
% 3.49/0.95 thf(func_def_766, type, sK628: subst).
% 3.49/0.95 thf(func_def_767, type, sK629: term).
% 3.49/0.95 thf(func_def_768, type, sK630: (term > $o)).
% 3.49/0.95 thf(func_def_769, type, sK631: term).
% 3.49/0.95 thf(func_def_770, type, sK632: subst).
% 3.49/0.95 thf(func_def_771, type, sK633: (term > $o)).
% 3.49/0.95 thf(func_def_772, type, sK634: term).
% 3.49/0.95 thf(func_def_773, type, sK635: (term > $o)).
% 3.49/0.95 thf(func_def_774, type, sK636: (term > $o)).
% 3.49/0.95 thf(func_def_775, type, sK637: subst).
% 3.49/0.95 thf(func_def_776, type, sK638: term).
% 3.49/0.95 thf(func_def_777, type, sK639: subst).
% 3.49/0.95 thf(func_def_778, type, sK640: term).
% 3.49/0.95 thf(func_def_779, type, sK641: term).
% 3.49/0.95 thf(func_def_780, type, sK642: subst).
% 3.49/0.96 thf(func_def_781, type, sK643: (subst > term > subst > $o)).
% 3.49/0.96 thf(func_def_782, type, sK644: term).
% 3.49/0.96 thf(f1,axiom,(
% 3.49/0.96 termmset_gthm & (hoasinduction_lem2 <=> ! [X10 : (subst > term > subst > $o),X23 : term,X24 : term] : ((X10 @ id @ (ap @ X23 @ X24) @ id) | ~(X10 @ id @ X23 @ id) | ~ ! [X13 : term,X14 : subst,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~(X10 @ id @ X24 @ id))) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (hoasapinj1 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & axapp & (induction2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)))) => ! [X22 : term,X10 : (term > $o)] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | (X10 @ X22) | ~ ! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | ~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)))))) & ! [X0 : term] : ? [X1 : d_term] : (X0 = ((d2term @ X1))) & ((! [X10 : (term > $o),X22 : term] : ((X10 @ X22) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13))) => (! [X24 : term,X10 : (subst > term > subst > $o),X23 : term] : (~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~(X10 @ id @ X24 @ id)) => (! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))) => ! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))))) <=> hoasinduction_lthm) & ~ulamvar1 & pushprop_lem3v2_lthm & (! [X14 : subst,X10 : (term > $o),X13 : term] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) <=> pushprop_lem0_lthm) & hoasinduction_lem1v2 & hoaslamnotap_gthm & ! [X6 : d_subst,X7 : d_subst] : ((((d2subst @ X6)) = ((d2subst @ X7))) => (X6 = X7)) & hoasapinj1_gthm & hoasinduction_lem1 & (id = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & ((^[X8 : subst, X9 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (pushprop_lem1v2 <=> ! [X14 : subst,X13 : term,X11 : (term > $o),X10 : (term > $o)] : ((X11 @ one) | ~(X10 @ X13) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) & ! [X5 : d_subst] : (X5 = d_id) & (! [X14 : subst] : (X14 = ((comp @ id @ X14))) <=> axidl) & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => (! [X15 : term,X13 : term] : ((((lam @ X13)) != ((lam @ X15))) | (X13 = X15)) => ! [X33 : term,X31 : (subst > term > term),X32 : subst,X18 : (subst > term > term)] : (~ ! [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)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) <=> hoaslaminj_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & induction2_gthm & (! [X15 : term,X13 : term,X10 : (term > $o),X26 : (term > $o),X14 : subst] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))) <=> pushprop_lem1) & hoasinduction_lem1_lthm & ((! [X14 : subst,X13 : term] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => (! [X13 : term,X14 : subst] : (X14 = ((comp @ sh @ (push @ X13 @ X14)))) => ! [X26 : (term > $o),X14 : subst,X13 : term,X10 : (term > $o),X15 : term] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14)))))) <=> pushprop_lem1_lthm) & (pushprop_lem0 <=> ! [X10 : (term > $o),X13 : term,X14 : subst] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X42 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id)) => ! [X10 : (subst > term > subst > $o),X43 : term] : (~ ! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X10 @ id @ (lam @ X43) @ id)))) <=> hoasinduction_lem3a_lthm) & ! [X3 : d_term,X2 : d_term] : ((((d2term @ X2)) = ((d2term @ X3))) => (X2 = X3)) & (! [X13 : term] : (X13 = ((sub @ X13 @ id))) <=> axvarid) & ulamvarind & (! [X10 : (subst > term > subst > $o),X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)))) <=> hoasinduction_lem3aa) & (! [X15 : term,X13 : term] : ((((sub @ X13 @ sh)) != ((sub @ X15 @ sh))) | (X13 = X15)) <=> shinj) & axabs & substmonoid_gthm & (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))) => ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))))) & axassoc & pushprop_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_gthm & hoasinduction_lem2_gthm & (induction2lem <=> ! [X10 : (term > $o),X16 : term,X17 : subst] : ((X10 @ (sub @ X16 @ X17)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~ ! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)))) & (induction <=> ! [X10 : (term > $o),X21 : term] : ((X10 @ X21) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & (hoasinduction_lem3b_lthm <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh))))) & (termmset <=> ! [X13 : term] : (X13 = ((sub @ X13 @ id)))) & (axshiftcons <=> ! [X14 : subst,X13 : term] : (X14 = ((comp @ sh @ (push @ X13 @ X14))))) & (sh = ((d2subst @ d_id))) & ((! [X19 : term,X15 : term,X20 : term,X13 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) => ! [X20 : term,X19 : term,X15 : term,X13 : term] : ((X19 = X20) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))))) <=> hoasapinj2_lthm) & pushprop_lem2v2 & ((^[X10 : (subst > term > subst > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))))) = hoasinduction_p_and_p_prime) & hoasapnotvar_lthm & (hoasapinj2 <=> ! [X15 : term,X20 : term,X19 : term,X13 : term] : ((((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20))) | (X19 = X20))) & (hoasinduction_lem3v2_f <=> ! [X15 : term] : ~ ! [X18 : (subst > term > term)] : ~ ! [X13 : term,X14 : subst] : (((sub @ X15 @ (push @ X13 @ X14))) = ((X18 @ X14 @ X13)))) & hoasinduction_lem2_lthm & hoasinduction_gthm & pushprop_lem1v2_gthm & (! [X13 : term,X15 : term] : ((X13 = X15) | (((lam @ X13)) != ((lam @ X15)))) <=> laminj) & hoaslaminj_gthm & (! [X14 : subst] : (X14 = ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)))) <=> axscons) & (! [X27 : term,X10 : (subst > term > subst > $o)] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id)) <=> hoasinduction_lem3) & (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)] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X29 : term,X10 : (subst > term > subst > $o),X11 : (term > $o)] : ((X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X30 : term,X10 : (subst > term > subst > $o)] : (~ ! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X30 @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))))))))) & (termmset_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X13 : term] : (X13 = ((sub @ X13 @ id))))) & (! [X42 : term,X10 : (subst > term > subst > $o)] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~ ! [X18 : (subst > term > term)] : (~ ! [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 @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & hoaslamnotap_lthm & ((! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) => (! [X10 : (term > $o),X22 : term] : (~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | (X10 @ X22)) => (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X10 : (subst > term > subst > $o),X11 : (term > $o),X29 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)) | (X11 @ (lam @ X29)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) => ! [X10 : (subst > term > subst > $o),X28 : term] : ((X10 @ id @ X28 @ id) | ~ ! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id))))))) <=> hoasinduction_lthm_3) & pushprop & ((! [X14 : subst] : (X14 = ((comp @ id @ X14))) => (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) => (! [X14 : subst] : (X14 = ((comp @ id @ X14))) & ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))))) <=> substmonoid_lthm) & (axidr <=> ! [X14 : subst] : (X14 = ((comp @ X14 @ id)))) & hoaslamnotvar_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X4 : subst] : ? [X5 : d_subst] : (X4 = ((d2subst @ X5))) & (hoaslamnotap <=> ! [X18 : (subst > term > term),X47 : term,X46 : term] : ((((lam @ (X18 @ sh @ one))) != ((ap @ (sub @ X46 @ id) @ X47))) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))) & pushprop_lem0_gthm & (hoasinduction_lem0_lthm <=> ! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))) & (hoasinduction_no_psi_cond <=> ! [X10 : (subst > term > subst > $o),X30 : term] : (~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X30 @ id) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)))) & hoaslamnotvar & (! [X28 : term,X10 : (subst > term > subst > $o)] : (~ ! [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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~ ! [X26 : subst,X25 : subst,X13 : term,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 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | (X10 @ id @ X28 @ id) | ~ ! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id)))) <=> hoasinduction) & pushprop_gthm & (hoaslaminj <=> ! [X18 : (subst > term > term),X33 : term,X31 : (subst > term > term),X32 : subst] : (~ ! [X25 : subst,X13 : term,X14 : subst] : (((sub @ (X31 @ X14 @ X13) @ X25)) = ((X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((X18 @ X32 @ X33)) = ((X31 @ X32 @ X33))) | ~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (((lam @ (X18 @ sh @ one))) != ((lam @ (X31 @ sh @ one)))))) & (hoasinduction_lem3v2a <=> ! [X10 : (subst > term > subst > $o),X29 : term,X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X25 : subst,X14 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | (X11 @ (lam @ X29)) | ~ ! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15)))) & ulamvarsh & (hoasinduction_lem3v2 <=> ! [X10 : (subst > term > subst > $o),X11 : (term > $o),X48 : term] : (~ ! [X26 : subst,X14 : subst,X25 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X13 : term,X26 : subst,X25 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [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)))) & lamnotvar & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem1_gthm & (! [X20 : term,X19 : term,X13 : term,X15 : term] : ((X13 = X15) | (((ap @ X13 @ X19)) != ((ap @ X15 @ X20)))) <=> apinj1) & hoasapinj2_gthm & hoasinduction_lem3a_gthm & induction2lem_gthm & ~(var @ (d2term @ d_one)) & (induction2lem_lthm <=> (! [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))) => (! [X10 : (term > $o),X21 : term] : (~ ! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~ ! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~(X10 @ X13)) | (X10 @ X21)) => ! [X10 : (term > $o),X17 : subst,X16 : term] : (~ ! [X13 : term] : ((X10 @ (lam @ X13)) | ~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))) | ~ ! [X15 : term] : (~(var @ X15) | (X10 @ (sub @ X15 @ X17))) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | (X10 @ (sub @ X16 @ X17)))))))) & pushprop_lthm_orig & hoasinduction_lem1v2_gthm & ((! [X13 : term] : (X13 = ((sub @ X13 @ id))) => (! [X20 : term,X15 : term,X13 : term,X19 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X13 = X15)) => ! [X19 : term,X13 : term,X15 : term,X20 : term] : ((X13 = X15) | (((ap @ (sub @ X13 @ id) @ X19)) != ((ap @ (sub @ X15 @ id) @ X20)))))) <=> hoasapinj1_lthm) & axmap & (! [X10 : (subst > term > subst > $o)] : ~ ! [X11 : (term > $o)] : ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) <=> hoasinduction_lem0) & pushprop_lem3v2 & hoasinduction_lem1_gthm & (! [X15 : term] : ~ ! [X18 : (subst > term > term)] : (((X18 @ sh @ one)) != ((sub @ X15 @ (push @ one @ sh)))) <=> hoasinduction_lem3b) & (! [X10 : (subst > term > subst > $o),X34 : term] : ((X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | ~ ! [X18 : (subst > term > term),X35 : term] : (~ ! [X41 : subst,X40 : term,X39 : subst] : (((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41))) = ((sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41))))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X37 : term,X38 : subst,X36 : subst] : (((sub @ (X18 @ X36 @ X37) @ X38)) = ((sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & (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) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id))) => ! [X10 : (subst > term > subst > $o),X27 : term] : (~ ! [X18 : (subst > term > term)] : (~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~ ! [X13 : term,X25 : subst,X14 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~ ! [X25 : subst,X26 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (lam @ X27) @ id) | ~ ! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))))) & hoasinduction_lem2v2_gthm & (! [X13 : term,X19 : term,X15 : term,X20 : term] : ((((ap @ X13 @ X19)) != ((ap @ X15 @ X20))) | (X19 = X20)) <=> apinj2) & ((^[X13 : term, X14 : subst, X10 : (term > $o), X11 : (term > $o)] : (! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))))) = pushprop_p_and_p_prime) & (one = ((d2term @ d_one))) & (hoasinduction_lem3a <=> ! [X10 : (subst > term > subst > $o),X43 : term] : ((X10 @ id @ (lam @ X43) @ id) | ~ ! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)) | ~ ! [X18 : (subst > term > term)] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~ ! [X14 : subst,X13 : term,X25 : subst] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))))) & hoasapnotvar_gthm & apnotvar & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_lthm & (! [X11 : (term > $o),X10 : (subst > term > subst > $o),X44 : term,X45 : term] : (~ ! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id))) | ~ ! [X14 : subst,X26 : subst,X25 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X44) | ~ ! [X14 : subst,X26 : subst,X13 : term,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~(X11 @ X45)) <=> hoasinduction_lem2v2) & (substmonoid <=> (! [X14 : subst] : (X14 = ((comp @ X14 @ id))) & ! [X14 : subst] : (X14 = ((comp @ id @ X14))))) & axclos & hoasinduction_lem3_gthm & (induction2 <=> ! [X22 : term,X10 : (term > $o)] : ((X10 @ X22) | ~ ! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~ ! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~ ! [X13 : term] : (~ ! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))))) & hoasinduction_lem3b_gthm & axvarshift & ~lamnotap & ! [X1 : d_term] : (X1 = d_one) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : (X13 = ((sub @ X13 @ id))) => ! [X11 : (term > $o),X10 : (subst > term > subst > $o),X48 : term] : (~ ! [X25 : subst,X13 : term,X26 : subst,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~ ! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~ ! [X18 : (subst > term > term)] : (~ ! [X14 : subst,X25 : subst,X13 : term] : (((sub @ (X18 @ X14 @ X13) @ X25)) = ((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~ ! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~ ! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | (X11 @ (lam @ X48)) | ~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ id @ X12 @ id)))))) & ((! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14)))) => ! [X13 : term,X14 : subst,X10 : (term > $o),X11 : (term > $o)] : (~ ! [X12 : term] : (((X11 @ X12)) = ((X10 @ (sub @ X12 @ (push @ X13 @ X14))))) | ~(X10 @ X13) | (X11 @ one))) <=> pushprop_lem1v2_lthm) & hoasapnotvar & pushprop_lem2v2_lthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one)))),
% 3.49/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alg444_1)).
% 3.49/0.96 thf(f2,conjecture,(
% 3.49/0.96 (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X1 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X3 : subst,X4 : subst,X2 : term] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => ! [X2 : term] : ((var @ X2) => (X0 @ id @ X2 @ id))))) = hoasinduction_lem1)),
% 3.49/0.96 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1)).
% 3.49/0.96 thf(f3,negated_conjecture,(
% 3.49/0.96 ~ (! [X0 : (subst > term > subst > $o)] : (! [X3 : subst,X4 : subst,X1 : subst,X2 : term] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X1 : subst,X3 : subst,X4 : subst,X2 : term] : ((X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3) => (X0 @ X1 @ X2 @ (comp @ X4 @ X3))) => (! [X2 : term] : ((hoasvar @ id @ X2 @ id) => (X0 @ id @ X2 @ id)) => ! [X2 : term] : ((var @ X2) => (X0 @ id @ X2 @ id))))) = hoasinduction_lem1)),
% 3.49/0.96 inference(negated_conjecture,[status(cth)],[f2])).
% 3.49/0.96 thf(f4,plain,(
% 3.49/0.96 termmset_gthm & (hoasinduction_lem2 <=> ! [X0 : (subst > term > subst > $o),X1 : term,X2 : term] : ((X0 @ id @ (ap @ X1 @ X2) @ id) | ~(X0 @ id @ X1 @ id) | ~ ! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (~(X0 @ X4 @ X3 @ (comp @ X6 @ X5)) | (X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5)) | ~ ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : ((X0 @ X8 @ X10 @ (comp @ X9 @ X7)) | ~(X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) | ~ ! [X11 : term,X12 : term] : ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id) | ~(X0 @ id @ X12 @ id) | ~(X0 @ id @ X11 @ id)) | ~(X0 @ id @ X2 @ id))) & (axvarcons <=> ! [X13 : term,X14 : subst] : (X13 = ((sub @ one @ (push @ X13 @ X14))))) & (hoasapinj1 <=> ! [X15 : term,X16 : term,X17 : term,X18 : term] : ((X15 = X17) | (((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))))) & (((lam @ (d2term @ d_one))) = ((d2term @ d_one))) & axapp & (induction2_lthm <=> (! [X19 : term] : (((sub @ X19 @ id)) = X19) => (! [X20 : (term > $o),X21 : subst,X22 : term] : (~ ! [X23 : term] : ((X20 @ (sub @ X23 @ X21)) | ~(var @ X23)) | (X20 @ (sub @ X22 @ X21)) | ~ ! [X24 : term,X25 : term] : (~(X20 @ X24) | (X20 @ (ap @ X24 @ X25)) | ~(X20 @ X25)) | ~ ! [X26 : term] : ((X20 @ (lam @ X26)) | ~ ! [X27 : term] : ((X20 @ (sub @ X26 @ (push @ X27 @ id))) | ~(X20 @ X27)))) => ! [X28 : term,X29 : (term > $o)] : (~ ! [X30 : term] : ((X29 @ (lam @ X30)) | ~ ! [X31 : term] : ((X29 @ (sub @ X30 @ (push @ X31 @ id))) | ~(X29 @ X31))) | (X29 @ X28) | ~ ! [X32 : term,X33 : term] : ((X29 @ (ap @ X33 @ X32)) | ~(X29 @ X33) | ~(X29 @ X32)) | ~ ! [X34 : term] : (~(var @ X34) | (X29 @ X34)))))) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & ((! [X37 : (term > $o),X38 : term] : ((X37 @ X38) | ~ ! [X39 : term] : (~ ! [X40 : term] : (~(X37 @ X40) | (X37 @ (sub @ X39 @ (push @ X40 @ id)))) | (X37 @ (lam @ X39))) | ~ ! [X41 : term] : ((X37 @ X41) | ~(var @ X41)) | ~ ! [X42 : term,X43 : term] : ((X37 @ (ap @ X42 @ X43)) | ~(X37 @ X43) | ~(X37 @ X42))) => (! [X44 : term,X45 : (subst > term > subst > $o),X46 : term] : (~ ! [X47 : term,X48 : subst,X49 : subst,X50 : subst] : (~(X45 @ X50 @ X47 @ (comp @ X49 @ X48)) | (X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48)) | (X45 @ id @ (ap @ X46 @ X44) @ id) | ~ ! [X51 : term,X52 : term] : ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id) | ~(X45 @ id @ X51 @ id) | ~(X45 @ id @ X52 @ id)) | ~ ! [X53 : subst,X54 : subst,X55 : term,X56 : subst] : ((X45 @ X53 @ X55 @ (comp @ X56 @ X54)) | ~(X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) | ~(X45 @ id @ X46 @ id) | ~(X45 @ id @ X44 @ id)) => (! [X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : term] : (~(X57 @ id @ X59 @ id) | (X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) | ~ ! [X60 : (subst > term > term)] : ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id) | ~ ! [X61 : term] : (~(X57 @ id @ X61 @ id) | (X57 @ id @ (X60 @ id @ X61) @ id)) | ~ ! [X62 : subst,X63 : subst,X64 : term] : (((sub @ (X60 @ X62 @ X64) @ X63)) = ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))) | (X57 @ id @ (lam @ X58) @ id) | ~ ! [X65 : subst,X66 : term,X67 : subst,X68 : subst] : ((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67) | ~(X57 @ X65 @ X66 @ (comp @ X68 @ X67))) | ~ ! [X69 : subst,X70 : subst,X71 : term,X72 : subst] : (~(X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72) | (X57 @ X70 @ X71 @ (comp @ X69 @ X72)))) => ! [X73 : term,X74 : (subst > term > subst > $o)] : (~ ! [X75 : subst,X76 : term,X77 : subst,X78 : subst] : (~(X74 @ X75 @ X76 @ (comp @ X78 @ X77)) | (X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)) | ~ ! [X79 : term] : ((X74 @ id @ X79 @ id) | ~(var @ (sub @ X79 @ id))) | ~ ! [X80 : (subst > term > term)] : ((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id) | ~ ! [X81 : term] : ((X74 @ id @ (X80 @ id @ X81) @ id) | ~(X74 @ id @ X81 @ id)) | ~ ! [X82 : subst,X83 : term,X84 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82)))) | ~ ! [X85 : term,X86 : term] : (~(X74 @ id @ X85 @ id) | (X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id) | ~(X74 @ id @ X86 @ id)) | (X74 @ id @ X73 @ id) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : (~(X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88) | (X74 @ X90 @ X87 @ (comp @ X89 @ X88))))))) <=> hoasinduction_lthm) & ~ulamvar1 & pushprop_lem3v2_lthm & (! [X91 : subst,X92 : (term > $o),X93 : term] : ~ ! [X94 : (term > $o)] : ~ ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) <=> pushprop_lem0_lthm) & hoasinduction_lem1v2 & hoaslamnotap_gthm & ! [X96 : d_subst,X97 : d_subst] : ((((d2subst @ X97)) = ((d2subst @ X96))) => (X96 = X97)) & hoasapinj1_gthm & hoasinduction_lem1 & (id = ((d2subst @ d_id))) & hoasinduction_lem3v2_gthm & ((^[X98 : subst, X99 : (subst > term > term)] : ((d2term @ d_one))) = hoaslam) & (pushprop_lem1v2 <=> ! [X100 : subst,X101 : term,X102 : (term > $o),X103 : (term > $o)] : ((X102 @ one) | ~(X103 @ X101) | ~ ! [X104 : term] : (((X102 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X100))))))) & ! [X105 : d_subst] : (d_id = X105) & (! [X106 : subst] : (((comp @ id @ X106)) = X106) <=> axidl) & ((! [X107 : subst,X108 : term] : (((sub @ one @ (push @ X108 @ X107))) = X108) => (! [X109 : subst,X110 : term] : (((comp @ sh @ (push @ X110 @ X109))) = X109) => (! [X111 : term,X112 : term] : ((((lam @ X112)) != ((lam @ X111))) | (X111 = X112)) => ! [X113 : term,X114 : (subst > term > term),X115 : subst,X116 : (subst > term > term)] : (~ ! [X117 : subst,X118 : subst,X119 : term] : (((X114 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118))) = ((sub @ (X114 @ X117 @ X119) @ X118))) | (((lam @ (X114 @ sh @ one))) != ((lam @ (X116 @ sh @ one)))) | (((X114 @ X115 @ X113)) = ((X116 @ X115 @ X113))) | ~ ! [X120 : subst,X121 : term,X122 : subst] : (((X116 @ (comp @ X120 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X116 @ X120 @ X121) @ X122))))))) <=> hoaslaminj_lthm) & (hoasinduction_lem3v2_f_lthm <=> ! [X123 : term] : ~ ! [X124 : (subst > term > term)] : ~ ! [X125 : term,X126 : subst] : (((X124 @ X126 @ X125)) = ((sub @ X123 @ (push @ X125 @ X126))))) & induction2_gthm & (! [X127 : term,X128 : term,X129 : (term > $o),X130 : (term > $o),X131 : subst] : (~(X129 @ X128) | (X130 @ (sub @ X128 @ (push @ X127 @ X131)))) <=> pushprop_lem1) & hoasinduction_lem1_lthm & ((! [X132 : subst,X133 : term] : (((sub @ one @ (push @ X133 @ X132))) = X133) => (! [X134 : term,X135 : subst] : (((comp @ sh @ (push @ X134 @ X135))) = X135) => ! [X136 : (term > $o),X137 : subst,X138 : term,X139 : (term > $o),X140 : term] : (~(X139 @ X138) | (X136 @ (sub @ X138 @ (push @ X140 @ X137)))))) <=> pushprop_lem1_lthm) & (pushprop_lem0 <=> ! [X141 : (term > $o),X142 : term,X143 : subst] : ~ ! [X144 : (term > $o)] : ~ ! [X145 : term] : (((X144 @ X145)) = ((X141 @ (sub @ X145 @ (push @ X142 @ X143)))))) & ((! [X146 : term] : (((sub @ X146 @ id)) = X146) => (! [X147 : (subst > term > subst > $o),X148 : term] : (~ ! [X149 : (subst > term > term)] : (~ ! [X150 : term,X151 : subst,X152 : subst] : (((X149 @ (comp @ X152 @ X151) @ (sub @ X150 @ X151))) = ((sub @ (X149 @ X152 @ X150) @ X151))) | ~ ! [X153 : term] : ((X147 @ id @ (X149 @ id @ X153) @ id) | ~(X147 @ id @ X153 @ id)) | (X147 @ id @ (lam @ (X149 @ sh @ one)) @ id)) | ~ ! [X154 : term] : ((X147 @ id @ (sub @ X148 @ (push @ X154 @ id)) @ id) | ~(X147 @ id @ X154 @ id)) | (X147 @ id @ (lam @ (sub @ X148 @ (push @ one @ sh))) @ id)) => ! [X155 : (subst > term > subst > $o),X156 : term] : (~ ! [X157 : term] : ((X155 @ id @ (sub @ X156 @ (push @ X157 @ id)) @ id) | ~(X155 @ id @ X157 @ id)) | ~ ! [X158 : (subst > term > term)] : ((X155 @ id @ (lam @ (X158 @ sh @ one)) @ id) | ~ ! [X159 : term] : ((X155 @ id @ (X158 @ id @ X159) @ id) | ~(X155 @ id @ X159 @ id)) | ~ ! [X160 : subst,X161 : term,X162 : subst] : (((X158 @ (comp @ X162 @ X160) @ (sub @ X161 @ X160))) = ((sub @ (X158 @ X162 @ X161) @ X160)))) | (X155 @ id @ (lam @ X156) @ id)))) <=> hoasinduction_lem3a_lthm) & ! [X163 : d_term,X164 : d_term] : ((((d2term @ X163)) = ((d2term @ X164))) => (X163 = X164)) & (! [X165 : term] : (((sub @ X165 @ id)) = X165) <=> axvarid) & ulamvarind & (! [X166 : (subst > term > subst > $o),X167 : term] : ((X166 @ id @ (lam @ (sub @ X167 @ (push @ one @ sh))) @ id) | ~ ! [X168 : term] : ((X166 @ id @ (sub @ X167 @ (push @ X168 @ id)) @ id) | ~(X166 @ id @ X168 @ id)) | ~ ! [X169 : (subst > term > term)] : (~ ! [X170 : subst,X171 : term,X172 : subst] : (((sub @ (X169 @ X172 @ X171) @ X170)) = ((X169 @ (comp @ X172 @ X170) @ (sub @ X171 @ X170)))) | (X166 @ id @ (lam @ (X169 @ sh @ one)) @ id) | ~ ! [X173 : term] : (~(X166 @ id @ X173 @ id) | (X166 @ id @ (X169 @ id @ X173) @ id)))) <=> hoasinduction_lem3aa) & (! [X174 : term,X175 : term] : ((((sub @ X175 @ sh)) != ((sub @ X174 @ sh))) | (X174 = X175)) <=> shinj) & axabs & substmonoid_gthm & (hoasinduction_lem3v2a_lthm <=> (! [X176 : term] : ~ ! [X177 : (subst > term > term)] : ~ ! [X178 : term,X179 : subst] : (((sub @ X176 @ (push @ X178 @ X179))) = ((X177 @ X179 @ X178))) => (! [X180 : term] : (((sub @ X180 @ id)) = X180) => ! [X181 : (subst > term > subst > $o),X182 : term,X183 : (term > $o)] : (~ ! [X184 : term] : ((X183 @ (sub @ X182 @ (push @ X184 @ id))) | ~(X183 @ X184)) | (X183 @ (lam @ X182)) | ~ ! [X185 : (subst > term > term)] : (~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X185 @ X188 @ X187) @ X186)) = ((X185 @ (comp @ X188 @ X186) @ (sub @ X187 @ X186)))) | ~ ! [X189 : term] : (~(X181 @ id @ X189 @ id) | (X181 @ id @ (X185 @ id @ X189) @ id)) | (X181 @ id @ (lam @ (X185 @ sh @ one)) @ id)) | ~ ! [X190 : term] : (((X183 @ X190)) = ((X181 @ id @ X190 @ id))))))) & axassoc & pushprop_lthm & (((sub @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2term @ d_one))) & pushprop_lem2v2_gthm & hoasinduction_lem2_gthm & (induction2lem <=> ! [X191 : (term > $o),X192 : term,X193 : subst] : ((X191 @ (sub @ X192 @ X193)) | ~ ! [X194 : term,X195 : term] : (~(X191 @ X195) | (X191 @ (ap @ X195 @ X194)) | ~(X191 @ X194)) | ~ ! [X196 : term] : ((X191 @ (lam @ X196)) | ~ ! [X197 : term] : ((X191 @ (sub @ X196 @ (push @ X197 @ id))) | ~(X191 @ X197))) | ~ ! [X198 : term] : ((X191 @ (sub @ X198 @ X193)) | ~(var @ X198)))) & (induction <=> ! [X199 : (term > $o),X200 : term] : ((X199 @ X200) | ~ ! [X201 : term,X202 : term] : (~(X199 @ X201) | (X199 @ (ap @ X201 @ X202)) | ~(X199 @ X202)) | ~ ! [X203 : term] : ((X199 @ (lam @ X203)) | ~(X199 @ X203)) | ~ ! [X204 : term] : ((X199 @ X204) | ~(var @ X204)))) & (hoasinduction_lem3b_lthm <=> ! [X205 : term] : ~ ! [X206 : (subst > term > term)] : (((sub @ X205 @ (push @ one @ sh))) != ((X206 @ sh @ one)))) & (termmset <=> ! [X207 : term] : (((sub @ X207 @ id)) = X207)) & (axshiftcons <=> ! [X208 : subst,X209 : term] : (((comp @ sh @ (push @ X209 @ X208))) = X208)) & (sh = ((d2subst @ d_id))) & ((! [X210 : term,X211 : term,X212 : term,X213 : term] : ((((ap @ X213 @ X210)) != ((ap @ X211 @ X212))) | (X210 = X212)) => ! [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 = X215) | (((ap @ (sub @ X217 @ id) @ X215)) != ((ap @ (sub @ X216 @ id) @ X214))))) <=> hoasapinj2_lthm) & pushprop_lem2v2 & ((^[X218 : (subst > term > subst > $o), X219 : (term > $o)] : (! [X220 : term] : (((X219 @ X220)) = ((X218 @ id @ X220 @ id))))) = hoasinduction_p_and_p_prime) & hoasapnotvar_lthm & (hoasapinj2 <=> ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((((ap @ (sub @ X224 @ id) @ X223)) != ((ap @ (sub @ X221 @ id) @ X222))) | (X222 = X223))) & (hoasinduction_lem3v2_f <=> ! [X225 : term] : ~ ! [X226 : (subst > term > term)] : ~ ! [X227 : term,X228 : subst] : (((sub @ X225 @ (push @ X227 @ X228))) = ((X226 @ X228 @ X227)))) & hoasinduction_lem2_lthm & hoasinduction_gthm & pushprop_lem1v2_gthm & (! [X229 : term,X230 : term] : ((X229 = X230) | (((lam @ X229)) != ((lam @ X230)))) <=> laminj) & hoaslaminj_gthm & (! [X231 : subst] : (((push @ (sub @ one @ X231) @ (comp @ sh @ X231))) = X231) <=> axscons) & (! [X232 : term,X233 : (subst > term > subst > $o)] : (~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (~(X233 @ id @ X235 @ id) | (X233 @ id @ (X234 @ id @ X235) @ id)) | (X233 @ id @ (lam @ (X234 @ sh @ one)) @ id) | ~ ! [X236 : subst,X237 : subst,X238 : term] : (((sub @ (X234 @ X236 @ X238) @ X237)) = ((X234 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237))))) | ~ ! [X239 : term] : ((X233 @ id @ (sub @ X232 @ (push @ X239 @ id)) @ id) | ~(X233 @ id @ X239 @ id)) | ~ ! [X240 : subst,X241 : subst,X242 : term,X243 : subst] : (~(X233 @ X243 @ X242 @ (comp @ X241 @ X240)) | (X233 @ (comp @ X243 @ X241) @ (sub @ X242 @ X241) @ X240)) | ~ ! [X244 : subst,X245 : subst,X246 : subst,X247 : term] : ((X233 @ X245 @ X247 @ (comp @ X244 @ X246)) | ~(X233 @ (comp @ X245 @ X244) @ (sub @ X247 @ X244) @ X246)) | (X233 @ id @ (lam @ X232) @ id)) <=> hoasinduction_lem3) & (hoasinduction_no_psi_cond_lthm <=> (! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X248 @ id @ X250 @ id)) = ((X249 @ X250))) => (! [X251 : term,X252 : (term > $o)] : ((X252 @ X251) | ~ ! [X253 : term] : ((X252 @ X253) | ~(var @ X253)) | ~ ! [X254 : term] : ((X252 @ (lam @ X254)) | ~ ! [X255 : term] : (~(X252 @ X255) | (X252 @ (sub @ X254 @ (push @ X255 @ id))))) | ~ ! [X256 : term,X257 : term] : ((X252 @ (ap @ X256 @ X257)) | ~(X252 @ X256) | ~(X252 @ X257))) => (! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : term,X260 : (subst > term > subst > $o),X261 : (term > $o)] : ((X261 @ (lam @ X259)) | ~ ! [X262 : term] : ((X261 @ (sub @ X259 @ (push @ X262 @ id))) | ~(X261 @ X262)) | ~ ! [X263 : (subst > term > term)] : (~ ! [X264 : term,X265 : subst,X266 : subst] : (((X263 @ (comp @ X266 @ X265) @ (sub @ X264 @ X265))) = ((sub @ (X263 @ X266 @ X264) @ X265))) | ~ ! [X267 : term] : (~(X260 @ id @ X267 @ id) | (X260 @ id @ (X263 @ id @ X267) @ id)) | (X260 @ id @ (lam @ (X263 @ sh @ one)) @ id)) | ~ ! [X268 : term] : (((X261 @ X268)) = ((X260 @ id @ X268 @ id)))) => ! [X269 : term,X270 : (subst > term > subst > $o)] : (~ ! [X271 : term,X272 : term] : (~(X270 @ id @ X271 @ id) | ~(X270 @ id @ X272 @ id) | (X270 @ id @ (ap @ (sub @ X271 @ id) @ X272) @ id)) | (X270 @ id @ X269 @ id) | ~ ! [X273 : (subst > term > term)] : (~ ! [X274 : term] : ((X270 @ id @ (X273 @ id @ X274) @ id) | ~(X270 @ id @ X274 @ id)) | (X270 @ id @ (lam @ (X273 @ sh @ one)) @ id) | ~ ! [X275 : subst,X276 : subst,X277 : term] : (((X273 @ (comp @ X276 @ X275) @ (sub @ X277 @ X275))) = ((sub @ (X273 @ X276 @ X277) @ X275)))))))))) & (termmset_lthm <=> (! [X278 : term] : (((sub @ X278 @ id)) = X278) => ! [X279 : term] : (((sub @ X279 @ id)) = X279))) & (! [X280 : term,X281 : (subst > term > subst > $o)] : ((X281 @ id @ (lam @ (sub @ X280 @ (push @ one @ sh))) @ id) | ~ ! [X282 : (subst > term > term)] : (~ ! [X283 : term,X284 : subst,X285 : subst] : (((sub @ (X282 @ X284 @ X283) @ X285)) = ((X282 @ (comp @ X284 @ X285) @ (sub @ X283 @ X285)))) | (X281 @ id @ (lam @ (X282 @ sh @ one)) @ id) | ~ ! [X286 : term] : ((X281 @ id @ (X282 @ id @ X286) @ id) | ~(X281 @ id @ X286 @ id))) | ~ ! [X287 : term] : (~(X281 @ id @ X287 @ id) | (X281 @ id @ (sub @ X280 @ (push @ X287 @ id)) @ id))) <=> hoasinduction_lem3aa_lthm) & hoaslamnotap_lthm & ((! [X288 : (subst > term > subst > $o)] : ~ ! [X289 : (term > $o)] : ~ ! [X290 : term] : (((X289 @ X290)) = ((X288 @ id @ X290 @ id))) => (! [X291 : (term > $o),X292 : term] : (~ ! [X293 : term] : ((X291 @ X293) | ~(var @ X293)) | ~ ! [X294 : term] : (~ ! [X295 : term] : (~(X291 @ X295) | (X291 @ (sub @ X294 @ (push @ X295 @ id)))) | (X291 @ (lam @ X294))) | ~ ! [X296 : term,X297 : term] : (~(X291 @ X297) | (X291 @ (ap @ X297 @ X296)) | ~(X291 @ X296)) | (X291 @ X292)) => (! [X298 : term] : (((sub @ X298 @ id)) = X298) => (! [X299 : (subst > term > subst > $o),X300 : (term > $o),X301 : term] : (~ ! [X302 : (subst > term > term)] : ((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id) | ~ ! [X303 : term] : (~(X299 @ id @ X303 @ id) | (X299 @ id @ (X302 @ id @ X303) @ id)) | ~ ! [X304 : subst,X305 : term,X306 : subst] : (((sub @ (X302 @ X304 @ X305) @ X306)) = ((X302 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))))) | ~ ! [X307 : term] : ((X300 @ (sub @ X301 @ (push @ X307 @ id))) | ~(X300 @ X307)) | (X300 @ (lam @ X301)) | ~ ! [X308 : term] : (((X299 @ id @ X308 @ id)) = ((X300 @ X308)))) => ! [X309 : (subst > term > subst > $o),X310 : term] : ((X309 @ id @ X310 @ id) | ~ ! [X311 : subst,X312 : subst,X313 : subst,X314 : term] : (~(X309 @ X312 @ X314 @ (comp @ X313 @ X311)) | (X309 @ (comp @ X312 @ X313) @ (sub @ X314 @ X313) @ X311)) | ~ ! [X315 : (subst > term > term)] : (~ ! [X316 : subst,X317 : term,X318 : subst] : (((X315 @ (comp @ X316 @ X318) @ (sub @ X317 @ X318))) = ((sub @ (X315 @ X316 @ X317) @ X318))) | ~ ! [X319 : term] : (~(X309 @ id @ X319 @ id) | (X309 @ id @ (X315 @ id @ X319) @ id)) | (X309 @ id @ (lam @ (X315 @ sh @ one)) @ id)) | ~ ! [X320 : subst,X321 : subst,X322 : subst,X323 : term] : (~(X309 @ (comp @ X321 @ X320) @ (sub @ X323 @ X320) @ X322) | (X309 @ X321 @ X323 @ (comp @ X320 @ X322))) | ~ ! [X324 : term] : (~(var @ (sub @ X324 @ id)) | (X309 @ id @ X324 @ id)) | ~ ! [X325 : term,X326 : term] : (~(X309 @ id @ X325 @ id) | (X309 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id) | ~(X309 @ id @ X326 @ id))))))) <=> hoasinduction_lthm_3) & pushprop & ((! [X327 : subst] : (((comp @ id @ X327)) = X327) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) => (! [X329 : subst] : (((comp @ id @ X329)) = X329) & ! [X330 : subst] : (((comp @ X330 @ id)) = X330)))) <=> substmonoid_lthm) & (axidr <=> ! [X331 : subst] : (((comp @ X331 @ id)) = X331)) & hoaslamnotvar_gthm & (((push @ (d2term @ d_one) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & ! [X332 : subst] : ? [X333 : d_subst] : (((d2subst @ X333)) = X332) & (hoaslamnotap <=> ! [X334 : (subst > term > term),X335 : term,X336 : term] : ((((lam @ (X334 @ sh @ one))) != ((ap @ (sub @ X336 @ id) @ X335))) | ~ ! [X337 : subst,X338 : term,X339 : subst] : (((X334 @ (comp @ X337 @ X339) @ (sub @ X338 @ X339))) = ((sub @ (X334 @ X337 @ X338) @ X339))))) & pushprop_lem0_gthm & (hoasinduction_lem0_lthm <=> ! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X340 @ id @ X342 @ id)) = ((X341 @ X342)))) & (hoasinduction_no_psi_cond <=> ! [X343 : (subst > term > subst > $o),X344 : term] : (~ ! [X345 : (subst > term > term)] : ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id) | ~ ! [X346 : subst,X347 : term,X348 : subst] : (((X345 @ (comp @ X346 @ X348) @ (sub @ X347 @ X348))) = ((sub @ (X345 @ X346 @ X347) @ X348))) | ~ ! [X349 : term] : (~(X343 @ id @ X349 @ id) | (X343 @ id @ (X345 @ id @ X349) @ id))) | (X343 @ id @ X344 @ id) | ~ ! [X350 : term,X351 : term] : (~(X343 @ id @ X350 @ id) | ~(X343 @ id @ X351 @ id) | (X343 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id)))) & hoaslamnotvar & (! [X352 : term,X353 : (subst > term > subst > $o)] : (~ ! [X354 : (subst > term > term)] : (~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X354 @ X355 @ X356) @ X357)) = ((X354 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357)))) | (X353 @ id @ (lam @ (X354 @ sh @ one)) @ id) | ~ ! [X358 : term] : ((X353 @ id @ (X354 @ id @ X358) @ id) | ~(X353 @ id @ X358 @ id))) | ~ ! [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (~(X353 @ (comp @ X362 @ X359) @ (sub @ X361 @ X359) @ X360) | (X353 @ X362 @ X361 @ (comp @ X359 @ X360))) | ~ ! [X363 : subst,X364 : subst,X365 : term,X366 : subst] : ((X353 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X363) | ~(X353 @ X364 @ X365 @ (comp @ X366 @ X363))) | ~ ! [X367 : term,X368 : term] : (~(X353 @ id @ X367 @ id) | ~(X353 @ id @ X368 @ id) | (X353 @ id @ (ap @ (sub @ X368 @ id) @ X367) @ id)) | (X353 @ id @ X352 @ id) | ~ ! [X369 : term] : ((X353 @ id @ X369 @ id) | ~(var @ (sub @ X369 @ id)))) <=> hoasinduction) & pushprop_gthm & (hoaslaminj <=> ! [X370 : (subst > term > term),X371 : term,X372 : (subst > term > term),X373 : subst] : (~ ! [X374 : subst,X375 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X375) @ X374)) = ((X372 @ (comp @ X376 @ X374) @ (sub @ X375 @ X374)))) | (((X370 @ X373 @ X371)) = ((X372 @ X373 @ X371))) | ~ ! [X377 : subst,X378 : subst,X379 : term] : (((sub @ (X370 @ X377 @ X379) @ X378)) = ((X370 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378)))) | (((lam @ (X370 @ sh @ one))) != ((lam @ (X372 @ sh @ one)))))) & (hoasinduction_lem3v2a <=> ! [X380 : (subst > term > subst > $o),X381 : term,X382 : (term > $o)] : (~ ! [X383 : term] : (((X380 @ id @ X383 @ id)) = ((X382 @ X383))) | ~ ! [X384 : (subst > term > term)] : (~ ! [X385 : term] : ((X380 @ id @ (X384 @ id @ X385) @ id) | ~(X380 @ id @ X385 @ id)) | (X380 @ id @ (lam @ (X384 @ sh @ one)) @ id) | ~ ! [X386 : subst,X387 : subst,X388 : term] : (((sub @ (X384 @ X387 @ X388) @ X386)) = ((X384 @ (comp @ X387 @ X386) @ (sub @ X388 @ X386))))) | (X382 @ (lam @ X381)) | ~ ! [X389 : term] : ((X382 @ (sub @ X381 @ (push @ X389 @ id))) | ~(X382 @ X389)))) & ulamvarsh & (hoasinduction_lem3v2 <=> ! [X390 : (subst > term > subst > $o),X391 : (term > $o),X392 : term] : (~ ! [X393 : subst,X394 : subst,X395 : subst,X396 : term] : (~(X390 @ X394 @ X396 @ (comp @ X393 @ X395)) | (X390 @ (comp @ X394 @ X393) @ (sub @ X396 @ X393) @ X395)) | ~ ! [X397 : term] : (~(X391 @ X397) | (X391 @ (sub @ X392 @ (push @ X397 @ id)))) | (X391 @ (lam @ X392)) | ~ ! [X398 : term] : (((X390 @ id @ X398 @ id)) = ((X391 @ X398))) | ~ ! [X399 : term,X400 : subst,X401 : subst,X402 : subst] : ((X390 @ X402 @ X399 @ (comp @ X400 @ X401)) | ~(X390 @ (comp @ X402 @ X400) @ (sub @ X399 @ X400) @ X401)) | ~ ! [X403 : (subst > term > term)] : (~ ! [X404 : term] : ((X390 @ id @ (X403 @ id @ X404) @ id) | ~(X390 @ id @ X404 @ id)) | ~ ! [X405 : subst,X406 : term,X407 : subst] : (((sub @ (X403 @ X407 @ X406) @ X405)) = ((X403 @ (comp @ X407 @ X405) @ (sub @ X406 @ X405)))) | (X390 @ id @ (lam @ (X403 @ sh @ one)) @ id)))) & lamnotvar & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & pushprop_lem1_gthm & (! [X408 : term,X409 : term,X410 : term,X411 : term] : ((X410 = X411) | (((ap @ X411 @ X408)) != ((ap @ X410 @ X409)))) <=> apinj1) & hoasapinj2_gthm & hoasinduction_lem3a_gthm & induction2lem_gthm & ~(var @ (d2term @ d_one)) & (induction2lem_lthm <=> (! [X412 : subst,X413 : term] : (((sub @ one @ (push @ X413 @ X412))) = X413) => (! [X414 : subst,X415 : term] : (((comp @ sh @ (push @ X415 @ X414))) = X414) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) => (! [X417 : (term > $o),X418 : term] : (~ ! [X419 : term] : (~(var @ X419) | (X417 @ X419)) | ~ ! [X420 : term,X421 : term] : (~(X417 @ X420) | (X417 @ (ap @ X420 @ X421)) | ~(X417 @ X421)) | ~ ! [X422 : term] : ((X417 @ (lam @ X422)) | ~(X417 @ X422)) | (X417 @ X418)) => ! [X423 : (term > $o),X424 : subst,X425 : term] : (~ ! [X426 : term] : ((X423 @ (lam @ X426)) | ~ ! [X427 : term] : (~(X423 @ X427) | (X423 @ (sub @ X426 @ (push @ X427 @ id))))) | ~ ! [X428 : term] : (~(var @ X428) | (X423 @ (sub @ X428 @ X424))) | ~ ! [X429 : term,X430 : term] : (~(X423 @ X429) | (X423 @ (ap @ X430 @ X429)) | ~(X423 @ X430)) | (X423 @ (sub @ X425 @ X424)))))))) & pushprop_lthm_orig & hoasinduction_lem1v2_gthm & ((! [X431 : term] : (((sub @ X431 @ id)) = X431) => (! [X432 : term,X433 : term,X434 : term,X435 : term] : ((((ap @ X434 @ X435)) != ((ap @ X433 @ X432))) | (X433 = X434)) => ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X437 = X438) | (((ap @ (sub @ X438 @ id) @ X439)) != ((ap @ (sub @ X437 @ id) @ X436)))))) <=> hoasapinj1_lthm) & axmap & (! [X440 : (subst > term > subst > $o)] : ~ ! [X441 : (term > $o)] : ~ ! [X442 : term] : (((X440 @ id @ X442 @ id)) = ((X441 @ X442))) <=> hoasinduction_lem0) & pushprop_lem3v2 & hoasinduction_lem1_gthm & (! [X443 : term] : ~ ! [X444 : (subst > term > term)] : (((sub @ X443 @ (push @ one @ sh))) != ((X444 @ sh @ one))) <=> hoasinduction_lem3b) & (! [X445 : (subst > term > subst > $o),X446 : term] : ((X445 @ id @ (lam @ (sub @ X446 @ (push @ one @ sh))) @ id) | ~ ! [X447 : term] : ((X445 @ id @ (sub @ X446 @ (push @ X447 @ id)) @ id) | ~(X445 @ id @ X447 @ id)) | ~ ! [X448 : (subst > term > term),X449 : term] : (~ ! [X450 : subst,X451 : term,X452 : subst] : (((X448 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) = ((sub @ X449 @ (push @ (sub @ X451 @ X450) @ (comp @ X452 @ X450))))) | ~ ! [X453 : term] : (~(X445 @ id @ X453 @ id) | (X445 @ id @ (X448 @ id @ X453) @ id)) | ~ ! [X454 : term,X455 : subst,X456 : subst] : (((sub @ (sub @ X449 @ (push @ X454 @ X456)) @ X455)) = ((sub @ (X448 @ X456 @ X454) @ X455))) | (X445 @ id @ (lam @ (X448 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & (hoasinduction_lem3_lthm <=> (! [X457 : term] : (((sub @ X457 @ id)) = X457) => (! [X458 : term,X459 : (subst > term > subst > $o)] : ((X459 @ id @ (lam @ (sub @ X458 @ (push @ one @ sh))) @ id) | ~ ! [X460 : (subst > term > term)] : ((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id) | ~ ! [X461 : term] : ((X459 @ id @ (X460 @ id @ X461) @ id) | ~(X459 @ id @ X461 @ id)) | ~ ! [X462 : term,X463 : subst,X464 : subst] : (((X460 @ (comp @ X464 @ X463) @ (sub @ X462 @ X463))) = ((sub @ (X460 @ X464 @ X462) @ X463)))) | ~ ! [X465 : term] : (~(X459 @ id @ X465 @ id) | (X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id))) => ! [X466 : (subst > term > subst > $o),X467 : term] : (~ ! [X468 : (subst > term > term)] : (~ ! [X469 : term] : (~(X466 @ id @ X469 @ id) | (X466 @ id @ (X468 @ id @ X469) @ id)) | ~ ! [X470 : term,X471 : subst,X472 : subst] : (((X468 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) = ((sub @ (X468 @ X472 @ X470) @ X471))) | (X466 @ id @ (lam @ (X468 @ sh @ one)) @ id)) | ~ ! [X473 : term,X474 : subst,X475 : subst,X476 : subst] : (~(X466 @ X476 @ X473 @ (comp @ X475 @ X474)) | (X466 @ (comp @ X476 @ X475) @ (sub @ X473 @ X475) @ X474)) | ~ ! [X477 : subst,X478 : subst,X479 : subst,X480 : term] : ((X466 @ X479 @ X480 @ (comp @ X478 @ X477)) | ~(X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477)) | (X466 @ id @ (lam @ X467) @ id) | ~ ! [X481 : term] : ((X466 @ id @ (sub @ X467 @ (push @ X481 @ id)) @ id) | ~(X466 @ id @ X481 @ id)))))) & hoasinduction_lem2v2_gthm & (! [X482 : term,X483 : term,X484 : term,X485 : term] : ((((ap @ X484 @ X485)) != ((ap @ X482 @ X483))) | (X483 = X485)) <=> apinj2) & ((^[X486 : term, X487 : subst, X488 : (term > $o), X489 : (term > $o)] : (! [X490 : term] : (((X489 @ X490)) = ((X488 @ (sub @ X490 @ (push @ X486 @ X487))))))) = pushprop_p_and_p_prime) & (one = ((d2term @ d_one))) & (hoasinduction_lem3a <=> ! [X491 : (subst > term > subst > $o),X492 : term] : ((X491 @ id @ (lam @ X492) @ id) | ~ ! [X493 : term] : (~(X491 @ id @ X493 @ id) | (X491 @ id @ (sub @ X492 @ (push @ X493 @ id)) @ id)) | ~ ! [X494 : (subst > term > term)] : ((X491 @ id @ (lam @ (X494 @ sh @ one)) @ id) | ~ ! [X495 : subst,X496 : term,X497 : subst] : (((X494 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X494 @ X495 @ X496) @ X497))) | ~ ! [X498 : term] : ((X491 @ id @ (X494 @ id @ X498) @ id) | ~(X491 @ id @ X498 @ id))))) & hoasapnotvar_gthm & apnotvar & (((comp @ (d2subst @ d_id) @ (d2subst @ d_id))) = ((d2subst @ d_id))) & hoaslamnotvar_lthm & (! [X499 : (term > $o),X500 : (subst > term > subst > $o),X501 : term,X502 : term] : (~ ! [X503 : term,X504 : term] : ((X500 @ id @ (ap @ (sub @ X504 @ id) @ X503) @ id) | ~(X500 @ id @ X503 @ id) | ~(X500 @ id @ X504 @ id)) | ~ ! [X505 : term] : (((X499 @ X505)) = ((X500 @ id @ X505 @ id))) | ~ ! [X506 : subst,X507 : subst,X508 : subst,X509 : term] : (~(X500 @ (comp @ X506 @ X507) @ (sub @ X509 @ X507) @ X508) | (X500 @ X506 @ X509 @ (comp @ X507 @ X508))) | (X499 @ (ap @ X501 @ X502)) | ~(X499 @ X501) | ~ ! [X510 : subst,X511 : subst,X512 : term,X513 : subst] : ((X500 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511) @ X513) | ~(X500 @ X510 @ X512 @ (comp @ X511 @ X513))) | ~(X499 @ X502)) <=> hoasinduction_lem2v2) & (substmonoid <=> (! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515))) & axclos & hoasinduction_lem3_gthm & (induction2 <=> ! [X516 : term,X517 : (term > $o)] : ((X517 @ X516) | ~ ! [X518 : term] : ((X517 @ X518) | ~(var @ X518)) | ~ ! [X519 : term,X520 : term] : (~(X517 @ X519) | ~(X517 @ X520) | (X517 @ (ap @ X520 @ X519))) | ~ ! [X521 : term] : (~ ! [X522 : term] : (~(X517 @ X522) | (X517 @ (sub @ X521 @ (push @ X522 @ id)))) | (X517 @ (lam @ X521))))) & hoasinduction_lem3b_gthm & axvarshift & ~lamnotap & ! [X523 : d_term] : (d_one = X523) & (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) = ((d2term @ d_one))) & (hoasinduction_lem3v2_lthm <=> (! [X524 : term] : (((sub @ X524 @ id)) = X524) => ! [X525 : (term > $o),X526 : (subst > term > subst > $o),X527 : term] : (~ ! [X528 : subst,X529 : term,X530 : subst,X531 : subst] : (~(X526 @ (comp @ X531 @ X530) @ (sub @ X529 @ X530) @ X528) | (X526 @ X531 @ X529 @ (comp @ X530 @ X528))) | ~ ! [X532 : term] : (~(X525 @ X532) | (X525 @ (sub @ X527 @ (push @ X532 @ id)))) | ~ ! [X533 : (subst > term > term)] : (~ ! [X534 : subst,X535 : subst,X536 : term] : (((sub @ (X533 @ X534 @ X536) @ X535)) = ((X533 @ (comp @ X534 @ X535) @ (sub @ X536 @ X535)))) | ~ ! [X537 : term] : (~(X526 @ id @ X537 @ id) | (X526 @ id @ (X533 @ id @ X537) @ id)) | (X526 @ id @ (lam @ (X533 @ sh @ one)) @ id)) | ~ ! [X538 : subst,X539 : term,X540 : subst,X541 : subst] : ((X526 @ (comp @ X541 @ X538) @ (sub @ X539 @ X538) @ X540) | ~(X526 @ X541 @ X539 @ (comp @ X538 @ X540))) | (X525 @ (lam @ X527)) | ~ ! [X542 : term] : (((X525 @ X542)) = ((X526 @ id @ X542 @ id)))))) & ((! [X543 : term,X544 : subst] : (((sub @ one @ (push @ X543 @ X544))) = X543) => ! [X545 : term,X546 : subst,X547 : (term > $o),X548 : (term > $o)] : (~ ! [X549 : term] : (((X547 @ (sub @ X549 @ (push @ X545 @ X546)))) = ((X548 @ X549))) | ~(X547 @ X545) | (X548 @ one))) <=> pushprop_lem1v2_lthm) & hoasapnotvar & pushprop_lem2v2_lthm & (((ap @ (d2term @ d_one) @ (d2term @ d_one))) = ((d2term @ d_one)))),
% 3.49/0.96 inference(rectify,[],[f1])).
% 3.49/0.96 thf(f5,plain,(
% 3.49/0.96 (termmset_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X0 : (subst > term > subst > $o),X1 : term,X2 : term] : (($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ~ ($true = ((X0 @ id @ X1 @ id))) | ~ ! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (~ ($true = ((X0 @ X4 @ X3 @ (comp @ X6 @ X5)))) | ($true = ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5)))) | ~ ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : ((((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) = $true) | ~ (((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) = $true)) | ~ ! [X11 : term,X12 : term] : (($true = ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) | ~ (((X0 @ id @ X12 @ id)) = $true) | ~ ($true = ((X0 @ id @ X11 @ id)))) | ~ (((X0 @ id @ X2 @ id)) = $true))) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axapp = $true) & ((induction2_lthm = $true) <=> (! [X19 : term] : (((sub @ X19 @ id)) = X19) => (! [X20 : (term > $o),X21 : subst,X22 : term] : (~ ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ~ ($true = ((var @ X23)))) | (((X20 @ (sub @ X22 @ X21))) = $true) | ~ ! [X24 : term,X25 : term] : (~ (((X20 @ X24)) = $true) | ($true = ((X20 @ (ap @ X24 @ X25)))) | ~ ($true = ((X20 @ X25)))) | ~ ! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ~ ! [X27 : term] : ((((X20 @ (sub @ X26 @ (push @ X27 @ id)))) = $true) | ~ ($true = ((X20 @ X27)))))) => ! [X28 : term,X29 : (term > $o)] : (~ ! [X30 : term] : (($true = ((X29 @ (lam @ X30)))) | ~ ! [X31 : term] : (($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id))))) | ~ (((X29 @ X31)) = $true))) | ($true = ((X29 @ X28))) | ~ ! [X32 : term,X33 : term] : (($true = ((X29 @ (ap @ X33 @ X32)))) | ~ ($true = ((X29 @ X33))) | ~ (((X29 @ X32)) = $true)) | ~ ! [X34 : term] : (~ ($true = ((var @ X34))) | ($true = ((X29 @ X34)))))))) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & ((! [X37 : (term > $o),X38 : term] : (($true = ((X37 @ X38))) | ~ ! [X39 : term] : (~ ! [X40 : term] : (~ (((X37 @ X40)) = $true) | ($true = ((X37 @ (sub @ X39 @ (push @ X40 @ id)))))) | ($true = ((X37 @ (lam @ X39))))) | ~ ! [X41 : term] : (($true = ((X37 @ X41))) | ~ ($true = ((var @ X41)))) | ~ ! [X42 : term,X43 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | ~ (((X37 @ X43)) = $true) | ~ (((X37 @ X42)) = $true))) => (! [X44 : term,X45 : (subst > term > subst > $o),X46 : term] : (~ ! [X47 : term,X48 : subst,X49 : subst,X50 : subst] : (~ (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) = $true) | ($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48)))) | ($true = ((X45 @ id @ (ap @ X46 @ X44) @ id))) | ~ ! [X51 : term,X52 : term] : (($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id))) | ~ (((X45 @ id @ X51 @ id)) = $true) | ~ ($true = ((X45 @ id @ X52 @ id)))) | ~ ! [X53 : subst,X54 : subst,X55 : term,X56 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | ~ (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) = $true)) | ~ (((X45 @ id @ X46 @ id)) = $true) | ~ ($true = ((X45 @ id @ X44 @ id)))) => (! [X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : term] : (~ ($true = ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) | ~ ! [X60 : (subst > term > term)] : (($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ~ ! [X61 : term] : (~ ($true = ((X57 @ id @ X61 @ id))) | ($true = ((X57 @ id @ (X60 @ id @ X61) @ id)))) | ~ ! [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) = ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))) | ($true = ((X57 @ id @ (lam @ X58) @ id))) | ~ ! [X65 : subst,X66 : term,X67 : subst,X68 : subst] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ~ ($true = ((X57 @ X65 @ X66 @ (comp @ X68 @ X67))))) | ~ ! [X69 : subst,X70 : subst,X71 : term,X72 : subst] : (~ ($true = ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72)))))) => ! [X73 : term,X74 : (subst > term > subst > $o)] : (~ ! [X75 : subst,X76 : term,X77 : subst,X78 : subst] : (~ ($true = ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) | ($true = ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ~ ! [X79 : term] : ((((X74 @ id @ X79 @ id)) = $true) | ~ ($true = ((var @ (sub @ X79 @ id))))) | ~ ! [X80 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) = $true) | ~ ! [X81 : term] : (($true = ((X74 @ id @ (X80 @ id @ X81) @ id))) | ~ ($true = ((X74 @ id @ X81 @ id)))) | ~ ! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82)))) | ~ ! [X85 : term,X86 : term] : (~ ($true = ((X74 @ id @ X85 @ id))) | (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) = $true) | ~ ($true = ((X74 @ id @ X86 @ id)))) | ($true = ((X74 @ id @ X73 @ id))) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : (~ (((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) = $true) | ($true = ((X74 @ X90 @ X87 @ (comp @ X89 @ X88))))))))) <=> (hoasinduction_lthm = $true)) & ~ (ulamvar1 = $true) & (pushprop_lem3v2_lthm = $true) & (! [X92 : (term > $o),X93 : term,X91 : subst] : ~ ! [X94 : (term > $o)] : ~ ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_gthm = $true) & ! [X97 : d_subst,X96 : d_subst] : ((((d2subst @ X97)) = ((d2subst @ X96))) => (X96 = X97)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((pushprop_lem1v2 = $true) <=> ! [X100 : subst,X101 : term,X102 : (term > $o),X103 : (term > $o)] : ((((X102 @ one)) = $true) | ~ ($true = ((X103 @ X101))) | ~ ! [X104 : term] : (((X102 @ X104)) = ((X103 @ (sub @ X104 @ (push @ X101 @ X100))))))) & ! [X105 : d_subst] : (d_id = X105) & (! [X106 : subst] : (((comp @ id @ X106)) = X106) <=> (axidl = $true)) & ((! [X107 : subst,X108 : term] : (((sub @ one @ (push @ X108 @ X107))) = X108) => (! [X109 : subst,X110 : term] : (((comp @ sh @ (push @ X110 @ X109))) = X109) => (! [X111 : term,X112 : term] : ((((lam @ X112)) != ((lam @ X111))) | (X111 = X112)) => ! [X113 : term,X114 : (subst > term > term),X115 : subst,X116 : (subst > term > term)] : (~ ! [X117 : subst,X118 : subst,X119 : term] : (((X114 @ (comp @ X117 @ X118) @ (sub @ X119 @ X118))) = ((sub @ (X114 @ X117 @ X119) @ X118))) | (((lam @ (X114 @ sh @ one))) != ((lam @ (X116 @ sh @ one)))) | (((X114 @ X115 @ X113)) = ((X116 @ X115 @ X113))) | ~ ! [X120 : subst,X121 : term,X122 : subst] : (((X116 @ (comp @ X120 @ X122) @ (sub @ X121 @ X122))) = ((sub @ (X116 @ X120 @ X121) @ X122))))))) <=> (hoaslaminj_lthm = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X123 : term] : ~ ! [X124 : (subst > term > term)] : ~ ! [X125 : term,X126 : subst] : (((X124 @ X126 @ X125)) = ((sub @ X123 @ (push @ X125 @ X126))))) & (induction2_gthm = $true) & (! [X127 : term,X128 : term,X129 : (term > $o),X130 : (term > $o),X131 : subst] : (~ ($true = ((X129 @ X128))) | (((X130 @ (sub @ X128 @ (push @ X127 @ X131)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_lthm = $true) & ((! [X132 : subst,X133 : term] : (((sub @ one @ (push @ X133 @ X132))) = X133) => (! [X134 : term,X135 : subst] : (((comp @ sh @ (push @ X134 @ X135))) = X135) => ! [X136 : (term > $o),X137 : subst,X138 : term,X139 : (term > $o),X140 : term] : (~ ($true = ((X139 @ X138))) | (((X136 @ (sub @ X138 @ (push @ X140 @ X137)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & ((pushprop_lem0 = $true) <=> ! [X141 : (term > $o),X142 : term,X143 : subst] : ~ ! [X144 : (term > $o)] : ~ ! [X145 : term] : (((X144 @ X145)) = ((X141 @ (sub @ X145 @ (push @ X142 @ X143)))))) & ((! [X146 : term] : (((sub @ X146 @ id)) = X146) => (! [X147 : (subst > term > subst > $o),X148 : term] : (~ ! [X149 : (subst > term > term)] : (~ ! [X150 : term,X151 : subst,X152 : subst] : (((X149 @ (comp @ X152 @ X151) @ (sub @ X150 @ X151))) = ((sub @ (X149 @ X152 @ X150) @ X151))) | ~ ! [X153 : term] : ((((X147 @ id @ (X149 @ id @ X153) @ id)) = $true) | ~ (((X147 @ id @ X153 @ id)) = $true)) | ($true = ((X147 @ id @ (lam @ (X149 @ sh @ one)) @ id)))) | ~ ! [X154 : term] : ((((X147 @ id @ (sub @ X148 @ (push @ X154 @ id)) @ id)) = $true) | ~ (((X147 @ id @ X154 @ id)) = $true)) | ($true = ((X147 @ id @ (lam @ (sub @ X148 @ (push @ one @ sh))) @ id)))) => ! [X155 : (subst > term > subst > $o),X156 : term] : (~ ! [X157 : term] : ((((X155 @ id @ (sub @ X156 @ (push @ X157 @ id)) @ id)) = $true) | ~ ($true = ((X155 @ id @ X157 @ id)))) | ~ ! [X158 : (subst > term > term)] : (($true = ((X155 @ id @ (lam @ (X158 @ sh @ one)) @ id))) | ~ ! [X159 : term] : (($true = ((X155 @ id @ (X158 @ id @ X159) @ id))) | ~ (((X155 @ id @ X159 @ id)) = $true)) | ~ ! [X160 : subst,X161 : term,X162 : subst] : (((X158 @ (comp @ X162 @ X160) @ (sub @ X161 @ X160))) = ((sub @ (X158 @ X162 @ X161) @ X160)))) | (((X155 @ id @ (lam @ X156) @ id)) = $true)))) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X163 : d_term,X164 : d_term] : ((((d2term @ X163)) = ((d2term @ X164))) => (X163 = X164)) & (! [X165 : term] : (((sub @ X165 @ id)) = X165) <=> (axvarid = $true)) & (ulamvarind = $true) & (! [X166 : (subst > term > subst > $o),X167 : term] : ((((X166 @ id @ (lam @ (sub @ X167 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X168 : term] : (($true = ((X166 @ id @ (sub @ X167 @ (push @ X168 @ id)) @ id))) | ~ ($true = ((X166 @ id @ X168 @ id)))) | ~ ! [X169 : (subst > term > term)] : (~ ! [X170 : subst,X171 : term,X172 : subst] : (((sub @ (X169 @ X172 @ X171) @ X170)) = ((X169 @ (comp @ X172 @ X170) @ (sub @ X171 @ X170)))) | ($true = ((X166 @ id @ (lam @ (X169 @ sh @ one)) @ id))) | ~ ! [X173 : term] : (~ ($true = ((X166 @ id @ X173 @ id))) | (((X166 @ id @ (X169 @ id @ X173) @ id)) = $true)))) <=> (hoasinduction_lem3aa = $true)) & (! [X174 : term,X175 : term] : ((((sub @ X175 @ sh)) != ((sub @ X174 @ sh))) | (X174 = X175)) <=> (shinj = $true)) & (axabs = $true) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X176 : term] : ~ ! [X177 : (subst > term > term)] : ~ ! [X178 : term,X179 : subst] : (((sub @ X176 @ (push @ X178 @ X179))) = ((X177 @ X179 @ X178))) => (! [X180 : term] : (((sub @ X180 @ id)) = X180) => ! [X181 : (subst > term > subst > $o),X182 : term,X183 : (term > $o)] : (~ ! [X184 : term] : (($true = ((X183 @ (sub @ X182 @ (push @ X184 @ id))))) | ~ ($true = ((X183 @ X184)))) | ($true = ((X183 @ (lam @ X182)))) | ~ ! [X185 : (subst > term > term)] : (~ ! [X186 : subst,X187 : term,X188 : subst] : (((sub @ (X185 @ X188 @ X187) @ X186)) = ((X185 @ (comp @ X188 @ X186) @ (sub @ X187 @ X186)))) | ~ ! [X189 : term] : (~ (((X181 @ id @ X189 @ id)) = $true) | ($true = ((X181 @ id @ (X185 @ id @ X189) @ id)))) | ($true = ((X181 @ id @ (lam @ (X185 @ sh @ one)) @ id)))) | ~ ! [X190 : term] : (((X183 @ X190)) = ((X181 @ id @ X190 @ id))))))) & (axassoc = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((induction2lem = $true) <=> ! [X191 : (term > $o),X192 : term,X193 : subst] : ((((X191 @ (sub @ X192 @ X193))) = $true) | ~ ! [X194 : term,X195 : term] : (~ (((X191 @ X195)) = $true) | (((X191 @ (ap @ X195 @ X194))) = $true) | ~ ($true = ((X191 @ X194)))) | ~ ! [X196 : term] : (($true = ((X191 @ (lam @ X196)))) | ~ ! [X197 : term] : (($true = ((X191 @ (sub @ X196 @ (push @ X197 @ id))))) | ~ (((X191 @ X197)) = $true))) | ~ ! [X198 : term] : (($true = ((X191 @ (sub @ X198 @ X193)))) | ~ (((var @ X198)) = $true)))) & ((induction = $true) <=> ! [X199 : (term > $o),X200 : term] : ((((X199 @ X200)) = $true) | ~ ! [X201 : term,X202 : term] : (~ (((X199 @ X201)) = $true) | ($true = ((X199 @ (ap @ X201 @ X202)))) | ~ (((X199 @ X202)) = $true)) | ~ ! [X203 : term] : ((((X199 @ (lam @ X203))) = $true) | ~ (((X199 @ X203)) = $true)) | ~ ! [X204 : term] : (($true = ((X199 @ X204))) | ~ ($true = ((var @ X204)))))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X205 : term] : ~ ! [X206 : (subst > term > term)] : (((sub @ X205 @ (push @ one @ sh))) != ((X206 @ sh @ one)))) & ((termmset = $true) <=> ! [X207 : term] : (((sub @ X207 @ id)) = X207)) & ((axshiftcons = $true) <=> ! [X208 : subst,X209 : term] : (((comp @ sh @ (push @ X209 @ X208))) = X208)) & (((d2subst @ d_id)) = sh) & ((! [X210 : term,X211 : term,X212 : term,X213 : term] : ((((ap @ X213 @ X210)) != ((ap @ X211 @ X212))) | (X210 = X212)) => ! [X214 : term,X215 : term,X216 : term,X217 : term] : ((X214 = X215) | (((ap @ (sub @ X217 @ id) @ X215)) != ((ap @ (sub @ X216 @ id) @ X214))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X221 : term,X222 : term,X223 : term,X224 : term] : ((((ap @ (sub @ X224 @ id) @ X223)) != ((ap @ (sub @ X221 @ id) @ X222))) | (X222 = X223))) & ((hoasinduction_lem3v2_f = $true) <=> ! [X225 : term] : ~ ! [X226 : (subst > term > term)] : ~ ! [X227 : term,X228 : subst] : (((sub @ X225 @ (push @ X227 @ X228))) = ((X226 @ X228 @ X227)))) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X229 : term,X230 : term] : ((X229 = X230) | (((lam @ X229)) != ((lam @ X230)))) <=> (laminj = $true)) & (hoaslaminj_gthm = $true) & (! [X231 : subst] : (((push @ (sub @ one @ X231) @ (comp @ sh @ X231))) = X231) <=> (axscons = $true)) & (! [X232 : term,X233 : (subst > term > subst > $o)] : (~ ! [X234 : (subst > term > term)] : (~ ! [X235 : term] : (~ (((X233 @ id @ X235 @ id)) = $true) | ($true = ((X233 @ id @ (X234 @ id @ X235) @ id)))) | ($true = ((X233 @ id @ (lam @ (X234 @ sh @ one)) @ id))) | ~ ! [X236 : subst,X237 : subst,X238 : term] : (((sub @ (X234 @ X236 @ X238) @ X237)) = ((X234 @ (comp @ X236 @ X237) @ (sub @ X238 @ X237))))) | ~ ! [X239 : term] : (($true = ((X233 @ id @ (sub @ X232 @ (push @ X239 @ id)) @ id))) | ~ (((X233 @ id @ X239 @ id)) = $true)) | ~ ! [X240 : subst,X241 : subst,X242 : term,X243 : subst] : (~ ($true = ((X233 @ X243 @ X242 @ (comp @ X241 @ X240)))) | (((X233 @ (comp @ X243 @ X241) @ (sub @ X242 @ X241) @ X240)) = $true)) | ~ ! [X244 : subst,X245 : subst,X246 : subst,X247 : term] : (($true = ((X233 @ X245 @ X247 @ (comp @ X244 @ X246)))) | ~ ($true = ((X233 @ (comp @ X245 @ X244) @ (sub @ X247 @ X244) @ X246)))) | ($true = ((X233 @ id @ (lam @ X232) @ id)))) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X248 : (subst > term > subst > $o)] : ~ ! [X249 : (term > $o)] : ~ ! [X250 : term] : (((X248 @ id @ X250 @ id)) = ((X249 @ X250))) => (! [X251 : term,X252 : (term > $o)] : ((((X252 @ X251)) = $true) | ~ ! [X253 : term] : (($true = ((X252 @ X253))) | ~ ($true = ((var @ X253)))) | ~ ! [X254 : term] : ((((X252 @ (lam @ X254))) = $true) | ~ ! [X255 : term] : (~ (((X252 @ X255)) = $true) | (((X252 @ (sub @ X254 @ (push @ X255 @ id)))) = $true))) | ~ ! [X256 : term,X257 : term] : (($true = ((X252 @ (ap @ X256 @ X257)))) | ~ (((X252 @ X256)) = $true) | ~ ($true = ((X252 @ X257))))) => (! [X258 : term] : (((sub @ X258 @ id)) = X258) => (! [X259 : term,X260 : (subst > term > subst > $o),X261 : (term > $o)] : (($true = ((X261 @ (lam @ X259)))) | ~ ! [X262 : term] : ((((X261 @ (sub @ X259 @ (push @ X262 @ id)))) = $true) | ~ ($true = ((X261 @ X262)))) | ~ ! [X263 : (subst > term > term)] : (~ ! [X264 : term,X265 : subst,X266 : subst] : (((X263 @ (comp @ X266 @ X265) @ (sub @ X264 @ X265))) = ((sub @ (X263 @ X266 @ X264) @ X265))) | ~ ! [X267 : term] : (~ (((X260 @ id @ X267 @ id)) = $true) | (((X260 @ id @ (X263 @ id @ X267) @ id)) = $true)) | (((X260 @ id @ (lam @ (X263 @ sh @ one)) @ id)) = $true)) | ~ ! [X268 : term] : (((X261 @ X268)) = ((X260 @ id @ X268 @ id)))) => ! [X269 : term,X270 : (subst > term > subst > $o)] : (~ ! [X271 : term,X272 : term] : (~ ($true = ((X270 @ id @ X271 @ id))) | ~ ($true = ((X270 @ id @ X272 @ id))) | ($true = ((X270 @ id @ (ap @ (sub @ X271 @ id) @ X272) @ id)))) | (((X270 @ id @ X269 @ id)) = $true) | ~ ! [X273 : (subst > term > term)] : (~ ! [X274 : term] : (($true = ((X270 @ id @ (X273 @ id @ X274) @ id))) | ~ ($true = ((X270 @ id @ X274 @ id)))) | ($true = ((X270 @ id @ (lam @ (X273 @ sh @ one)) @ id))) | ~ ! [X275 : subst,X276 : subst,X277 : term] : (((X273 @ (comp @ X276 @ X275) @ (sub @ X277 @ X275))) = ((sub @ (X273 @ X276 @ X277) @ X275)))))))))) & ((termmset_lthm = $true) <=> (! [X278 : term] : (((sub @ X278 @ id)) = X278) => ! [X279 : term] : (((sub @ X279 @ id)) = X279))) & (! [X280 : term,X281 : (subst > term > subst > $o)] : ((((X281 @ id @ (lam @ (sub @ X280 @ (push @ one @ sh))) @ id)) = $true) | ~ ! [X282 : (subst > term > term)] : (~ ! [X283 : term,X284 : subst,X285 : subst] : (((sub @ (X282 @ X284 @ X283) @ X285)) = ((X282 @ (comp @ X284 @ X285) @ (sub @ X283 @ X285)))) | ($true = ((X281 @ id @ (lam @ (X282 @ sh @ one)) @ id))) | ~ ! [X286 : term] : (($true = ((X281 @ id @ (X282 @ id @ X286) @ id))) | ~ ($true = ((X281 @ id @ X286 @ id))))) | ~ ! [X287 : term] : (~ ($true = ((X281 @ id @ X287 @ id))) | ($true = ((X281 @ id @ (sub @ X280 @ (push @ X287 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((! [X288 : (subst > term > subst > $o)] : ~ ! [X289 : (term > $o)] : ~ ! [X290 : term] : (((X289 @ X290)) = ((X288 @ id @ X290 @ id))) => (! [X291 : (term > $o),X292 : term] : (~ ! [X293 : term] : ((((X291 @ X293)) = $true) | ~ ($true = ((var @ X293)))) | ~ ! [X294 : term] : (~ ! [X295 : term] : (~ ($true = ((X291 @ X295))) | (((X291 @ (sub @ X294 @ (push @ X295 @ id)))) = $true)) | ($true = ((X291 @ (lam @ X294))))) | ~ ! [X296 : term,X297 : term] : (~ ($true = ((X291 @ X297))) | ($true = ((X291 @ (ap @ X297 @ X296)))) | ~ (((X291 @ X296)) = $true)) | (((X291 @ X292)) = $true)) => (! [X298 : term] : (((sub @ X298 @ id)) = X298) => (! [X299 : (subst > term > subst > $o),X300 : (term > $o),X301 : term] : (~ ! [X302 : (subst > term > term)] : (($true = ((X299 @ id @ (lam @ (X302 @ sh @ one)) @ id))) | ~ ! [X303 : term] : (~ ($true = ((X299 @ id @ X303 @ id))) | ($true = ((X299 @ id @ (X302 @ id @ X303) @ id)))) | ~ ! [X304 : subst,X305 : term,X306 : subst] : (((sub @ (X302 @ X304 @ X305) @ X306)) = ((X302 @ (comp @ X304 @ X306) @ (sub @ X305 @ X306))))) | ~ ! [X307 : term] : (($true = ((X300 @ (sub @ X301 @ (push @ X307 @ id))))) | ~ (((X300 @ X307)) = $true)) | ($true = ((X300 @ (lam @ X301)))) | ~ ! [X308 : term] : (((X299 @ id @ X308 @ id)) = ((X300 @ X308)))) => ! [X309 : (subst > term > subst > $o),X310 : term] : (($true = ((X309 @ id @ X310 @ id))) | ~ ! [X311 : subst,X312 : subst,X313 : subst,X314 : term] : (~ (((X309 @ X312 @ X314 @ (comp @ X313 @ X311))) = $true) | ($true = ((X309 @ (comp @ X312 @ X313) @ (sub @ X314 @ X313) @ X311)))) | ~ ! [X315 : (subst > term > term)] : (~ ! [X316 : subst,X317 : term,X318 : subst] : (((X315 @ (comp @ X316 @ X318) @ (sub @ X317 @ X318))) = ((sub @ (X315 @ X316 @ X317) @ X318))) | ~ ! [X319 : term] : (~ (((X309 @ id @ X319 @ id)) = $true) | ($true = ((X309 @ id @ (X315 @ id @ X319) @ id)))) | ($true = ((X309 @ id @ (lam @ (X315 @ sh @ one)) @ id)))) | ~ ! [X320 : subst,X321 : subst,X322 : subst,X323 : term] : (~ ($true = ((X309 @ (comp @ X321 @ X320) @ (sub @ X323 @ X320) @ X322))) | ($true = ((X309 @ X321 @ X323 @ (comp @ X320 @ X322))))) | ~ ! [X324 : term] : (~ ($true = ((var @ (sub @ X324 @ id)))) | (((X309 @ id @ X324 @ id)) = $true)) | ~ ! [X325 : term,X326 : term] : (~ ($true = ((X309 @ id @ X325 @ id))) | ($true = ((X309 @ id @ (ap @ (sub @ X326 @ id) @ X325) @ id))) | ~ ($true = ((X309 @ id @ X326 @ id))))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop = $true) & ((! [X327 : subst] : (((comp @ id @ X327)) = X327) => (! [X328 : subst] : (((comp @ X328 @ id)) = X328) => (! [X329 : subst] : (((comp @ id @ X329)) = X329) & ! [X330 : subst] : (((comp @ X330 @ id)) = X330)))) <=> (substmonoid_lthm = $true)) & ((axidr = $true) <=> ! [X331 : subst] : (((comp @ X331 @ id)) = X331)) & (hoaslamnotvar_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X332 : subst] : ? [X333 : d_subst] : (((d2subst @ X333)) = X332) & ((hoaslamnotap = $true) <=> ! [X334 : (subst > term > term),X335 : term,X336 : term] : ((((lam @ (X334 @ sh @ one))) != ((ap @ (sub @ X336 @ id) @ X335))) | ~ ! [X337 : subst,X338 : term,X339 : subst] : (((X334 @ (comp @ X337 @ X339) @ (sub @ X338 @ X339))) = ((sub @ (X334 @ X337 @ X338) @ X339))))) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X340 : (subst > term > subst > $o)] : ~ ! [X341 : (term > $o)] : ~ ! [X342 : term] : (((X340 @ id @ X342 @ id)) = ((X341 @ X342)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X343 : (subst > term > subst > $o),X344 : term] : (~ ! [X345 : (subst > term > term)] : (($true = ((X343 @ id @ (lam @ (X345 @ sh @ one)) @ id))) | ~ ! [X346 : subst,X347 : term,X348 : subst] : (((X345 @ (comp @ X346 @ X348) @ (sub @ X347 @ X348))) = ((sub @ (X345 @ X346 @ X347) @ X348))) | ~ ! [X349 : term] : (~ ($true = ((X343 @ id @ X349 @ id))) | ($true = ((X343 @ id @ (X345 @ id @ X349) @ id))))) | (((X343 @ id @ X344 @ id)) = $true) | ~ ! [X350 : term,X351 : term] : (~ ($true = ((X343 @ id @ X350 @ id))) | ~ (((X343 @ id @ X351 @ id)) = $true) | ($true = ((X343 @ id @ (ap @ (sub @ X351 @ id) @ X350) @ id)))))) & (hoaslamnotvar = $true) & (! [X352 : term,X353 : (subst > term > subst > $o)] : (~ ! [X354 : (subst > term > term)] : (~ ! [X355 : subst,X356 : term,X357 : subst] : (((sub @ (X354 @ X355 @ X356) @ X357)) = ((X354 @ (comp @ X355 @ X357) @ (sub @ X356 @ X357)))) | ($true = ((X353 @ id @ (lam @ (X354 @ sh @ one)) @ id))) | ~ ! [X358 : term] : (($true = ((X353 @ id @ (X354 @ id @ X358) @ id))) | ~ ($true = ((X353 @ id @ X358 @ id))))) | ~ ! [X359 : subst,X360 : subst,X361 : term,X362 : subst] : (~ (((X353 @ (comp @ X362 @ X359) @ (sub @ X361 @ X359) @ X360)) = $true) | ($true = ((X353 @ X362 @ X361 @ (comp @ X359 @ X360))))) | ~ ! [X363 : subst,X364 : subst,X365 : term,X366 : subst] : (($true = ((X353 @ (comp @ X364 @ X366) @ (sub @ X365 @ X366) @ X363))) | ~ (((X353 @ X364 @ X365 @ (comp @ X366 @ X363))) = $true)) | ~ ! [X367 : term,X368 : term] : (~ (((X353 @ id @ X367 @ id)) = $true) | ~ ($true = ((X353 @ id @ X368 @ id))) | ($true = ((X353 @ id @ (ap @ (sub @ X368 @ id) @ X367) @ id)))) | (((X353 @ id @ X352 @ id)) = $true) | ~ ! [X369 : term] : ((((X353 @ id @ X369 @ id)) = $true) | ~ (((var @ (sub @ X369 @ id))) = $true))) <=> (hoasinduction = $true)) & (pushprop_gthm = $true) & ((hoaslaminj = $true) <=> ! [X370 : (subst > term > term),X371 : term,X372 : (subst > term > term),X373 : subst] : (~ ! [X374 : subst,X375 : term,X376 : subst] : (((sub @ (X372 @ X376 @ X375) @ X374)) = ((X372 @ (comp @ X376 @ X374) @ (sub @ X375 @ X374)))) | (((X370 @ X373 @ X371)) = ((X372 @ X373 @ X371))) | ~ ! [X377 : subst,X378 : subst,X379 : term] : (((sub @ (X370 @ X377 @ X379) @ X378)) = ((X370 @ (comp @ X377 @ X378) @ (sub @ X379 @ X378)))) | (((lam @ (X370 @ sh @ one))) != ((lam @ (X372 @ sh @ one)))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X380 : (subst > term > subst > $o),X381 : term,X382 : (term > $o)] : (~ ! [X383 : term] : (((X380 @ id @ X383 @ id)) = ((X382 @ X383))) | ~ ! [X384 : (subst > term > term)] : (~ ! [X385 : term] : ((((X380 @ id @ (X384 @ id @ X385) @ id)) = $true) | ~ (((X380 @ id @ X385 @ id)) = $true)) | ($true = ((X380 @ id @ (lam @ (X384 @ sh @ one)) @ id))) | ~ ! [X386 : subst,X387 : subst,X388 : term] : (((sub @ (X384 @ X387 @ X388) @ X386)) = ((X384 @ (comp @ X387 @ X386) @ (sub @ X388 @ X386))))) | ($true = ((X382 @ (lam @ X381)))) | ~ ! [X389 : term] : ((((X382 @ (sub @ X381 @ (push @ X389 @ id)))) = $true) | ~ (((X382 @ X389)) = $true)))) & (ulamvarsh = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X390 : (subst > term > subst > $o),X391 : (term > $o),X392 : term] : (~ ! [X393 : subst,X394 : subst,X395 : subst,X396 : term] : (~ ($true = ((X390 @ X394 @ X396 @ (comp @ X393 @ X395)))) | (((X390 @ (comp @ X394 @ X393) @ (sub @ X396 @ X393) @ X395)) = $true)) | ~ ! [X397 : term] : (~ ($true = ((X391 @ X397))) | ($true = ((X391 @ (sub @ X392 @ (push @ X397 @ id)))))) | ($true = ((X391 @ (lam @ X392)))) | ~ ! [X398 : term] : (((X390 @ id @ X398 @ id)) = ((X391 @ X398))) | ~ ! [X399 : term,X400 : subst,X401 : subst,X402 : subst] : (($true = ((X390 @ X402 @ X399 @ (comp @ X400 @ X401)))) | ~ (((X390 @ (comp @ X402 @ X400) @ (sub @ X399 @ X400) @ X401)) = $true)) | ~ ! [X403 : (subst > term > term)] : (~ ! [X404 : term] : (($true = ((X390 @ id @ (X403 @ id @ X404) @ id))) | ~ ($true = ((X390 @ id @ X404 @ id)))) | ~ ! [X405 : subst,X406 : term,X407 : subst] : (((sub @ (X403 @ X407 @ X406) @ X405)) = ((X403 @ (comp @ X407 @ X405) @ (sub @ X406 @ X405)))) | ($true = ((X390 @ id @ (lam @ (X403 @ sh @ one)) @ id)))))) & (lamnotvar = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem1_gthm = $true) & (! [X408 : term,X409 : term,X410 : term,X411 : term] : ((X410 = X411) | (((ap @ X411 @ X408)) != ((ap @ X410 @ X409)))) <=> (apinj1 = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((induction2lem_lthm = $true) <=> (! [X412 : subst,X413 : term] : (((sub @ one @ (push @ X413 @ X412))) = X413) => (! [X414 : subst,X415 : term] : (((comp @ sh @ (push @ X415 @ X414))) = X414) => (! [X416 : subst] : (((comp @ X416 @ id)) = X416) => (! [X417 : (term > $o),X418 : term] : (~ ! [X419 : term] : (~ ($true = ((var @ X419))) | (((X417 @ X419)) = $true)) | ~ ! [X420 : term,X421 : term] : (~ (((X417 @ X420)) = $true) | (((X417 @ (ap @ X420 @ X421))) = $true) | ~ ($true = ((X417 @ X421)))) | ~ ! [X422 : term] : (($true = ((X417 @ (lam @ X422)))) | ~ ($true = ((X417 @ X422)))) | (((X417 @ X418)) = $true)) => ! [X423 : (term > $o),X424 : subst,X425 : term] : (~ ! [X426 : term] : ((((X423 @ (lam @ X426))) = $true) | ~ ! [X427 : term] : (~ ($true = ((X423 @ X427))) | (((X423 @ (sub @ X426 @ (push @ X427 @ id)))) = $true))) | ~ ! [X428 : term] : (~ (((var @ X428)) = $true) | (((X423 @ (sub @ X428 @ X424))) = $true)) | ~ ! [X429 : term,X430 : term] : (~ ($true = ((X423 @ X429))) | (((X423 @ (ap @ X430 @ X429))) = $true) | ~ (((X423 @ X430)) = $true)) | (((X423 @ (sub @ X425 @ X424))) = $true))))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1v2_gthm = $true) & ((! [X431 : term] : (((sub @ X431 @ id)) = X431) => (! [X432 : term,X433 : term,X434 : term,X435 : term] : ((((ap @ X434 @ X435)) != ((ap @ X433 @ X432))) | (X433 = X434)) => ! [X436 : term,X437 : term,X438 : term,X439 : term] : ((X437 = X438) | (((ap @ (sub @ X438 @ id) @ X439)) != ((ap @ (sub @ X437 @ id) @ X436)))))) <=> (hoasapinj1_lthm = $true)) & (axmap = $true) & (! [X440 : (subst > term > subst > $o)] : ~ ! [X441 : (term > $o)] : ~ ! [X442 : term] : (((X440 @ id @ X442 @ id)) = ((X441 @ X442))) <=> (hoasinduction_lem0 = $true)) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X443 : term] : ~ ! [X444 : (subst > term > term)] : (((sub @ X443 @ (push @ one @ sh))) != ((X444 @ sh @ one))) <=> (hoasinduction_lem3b = $true)) & (! [X445 : (subst > term > subst > $o),X446 : term] : (($true = ((X445 @ id @ (lam @ (sub @ X446 @ (push @ one @ sh))) @ id))) | ~ ! [X447 : term] : (($true = ((X445 @ id @ (sub @ X446 @ (push @ X447 @ id)) @ id))) | ~ (((X445 @ id @ X447 @ id)) = $true)) | ~ ! [X448 : (subst > term > term),X449 : term] : (~ ! [X450 : subst,X451 : term,X452 : subst] : (((X448 @ (comp @ X452 @ X450) @ (sub @ X451 @ X450))) = ((sub @ X449 @ (push @ (sub @ X451 @ X450) @ (comp @ X452 @ X450))))) | ~ ! [X453 : term] : (~ ($true = ((X445 @ id @ X453 @ id))) | ($true = ((X445 @ id @ (X448 @ id @ X453) @ id)))) | ~ ! [X454 : term,X455 : subst,X456 : subst] : (((sub @ (sub @ X449 @ (push @ X454 @ X456)) @ X455)) = ((sub @ (X448 @ X456 @ X454) @ X455))) | (((X445 @ id @ (lam @ (X448 @ sh @ one)) @ id)) = $true))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X457 : term] : (((sub @ X457 @ id)) = X457) => (! [X458 : term,X459 : (subst > term > subst > $o)] : (($true = ((X459 @ id @ (lam @ (sub @ X458 @ (push @ one @ sh))) @ id))) | ~ ! [X460 : (subst > term > term)] : ((((X459 @ id @ (lam @ (X460 @ sh @ one)) @ id)) = $true) | ~ ! [X461 : term] : ((((X459 @ id @ (X460 @ id @ X461) @ id)) = $true) | ~ (((X459 @ id @ X461 @ id)) = $true)) | ~ ! [X462 : term,X463 : subst,X464 : subst] : (((X460 @ (comp @ X464 @ X463) @ (sub @ X462 @ X463))) = ((sub @ (X460 @ X464 @ X462) @ X463)))) | ~ ! [X465 : term] : (~ (((X459 @ id @ X465 @ id)) = $true) | ($true = ((X459 @ id @ (sub @ X458 @ (push @ X465 @ id)) @ id))))) => ! [X466 : (subst > term > subst > $o),X467 : term] : (~ ! [X468 : (subst > term > term)] : (~ ! [X469 : term] : (~ ($true = ((X466 @ id @ X469 @ id))) | (((X466 @ id @ (X468 @ id @ X469) @ id)) = $true)) | ~ ! [X470 : term,X471 : subst,X472 : subst] : (((X468 @ (comp @ X472 @ X471) @ (sub @ X470 @ X471))) = ((sub @ (X468 @ X472 @ X470) @ X471))) | (((X466 @ id @ (lam @ (X468 @ sh @ one)) @ id)) = $true)) | ~ ! [X473 : term,X474 : subst,X475 : subst,X476 : subst] : (~ ($true = ((X466 @ X476 @ X473 @ (comp @ X475 @ X474)))) | (((X466 @ (comp @ X476 @ X475) @ (sub @ X473 @ X475) @ X474)) = $true)) | ~ ! [X477 : subst,X478 : subst,X479 : subst,X480 : term] : (($true = ((X466 @ X479 @ X480 @ (comp @ X478 @ X477)))) | ~ (((X466 @ (comp @ X479 @ X478) @ (sub @ X480 @ X478) @ X477)) = $true)) | ($true = ((X466 @ id @ (lam @ X467) @ id))) | ~ ! [X481 : term] : (($true = ((X466 @ id @ (sub @ X467 @ (push @ X481 @ id)) @ id))) | ~ (((X466 @ id @ X481 @ id)) = $true)))))) & (hoasinduction_lem2v2_gthm = $true) & (! [X482 : term,X483 : term,X484 : term,X485 : term] : ((((ap @ X484 @ X485)) != ((ap @ X482 @ X483))) | (X483 = X485)) <=> (apinj2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3a = $true) <=> ! [X491 : (subst > term > subst > $o),X492 : term] : ((((X491 @ id @ (lam @ X492) @ id)) = $true) | ~ ! [X493 : term] : (~ ($true = ((X491 @ id @ X493 @ id))) | (((X491 @ id @ (sub @ X492 @ (push @ X493 @ id)) @ id)) = $true)) | ~ ! [X494 : (subst > term > term)] : (($true = ((X491 @ id @ (lam @ (X494 @ sh @ one)) @ id))) | ~ ! [X495 : subst,X496 : term,X497 : subst] : (((X494 @ (comp @ X495 @ X497) @ (sub @ X496 @ X497))) = ((sub @ (X494 @ X495 @ X496) @ X497))) | ~ ! [X498 : term] : ((((X491 @ id @ (X494 @ id @ X498) @ id)) = $true) | ~ ($true = ((X491 @ id @ X498 @ id))))))) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (! [X499 : (term > $o),X500 : (subst > term > subst > $o),X501 : term,X502 : term] : (~ ! [X503 : term,X504 : term] : (($true = ((X500 @ id @ (ap @ (sub @ X504 @ id) @ X503) @ id))) | ~ ($true = ((X500 @ id @ X503 @ id))) | ~ ($true = ((X500 @ id @ X504 @ id)))) | ~ ! [X505 : term] : (((X499 @ X505)) = ((X500 @ id @ X505 @ id))) | ~ ! [X506 : subst,X507 : subst,X508 : subst,X509 : term] : (~ ($true = ((X500 @ (comp @ X506 @ X507) @ (sub @ X509 @ X507) @ X508))) | ($true = ((X500 @ X506 @ X509 @ (comp @ X507 @ X508))))) | (((X499 @ (ap @ X501 @ X502))) = $true) | ~ ($true = ((X499 @ X501))) | ~ ! [X510 : subst,X511 : subst,X512 : term,X513 : subst] : (($true = ((X500 @ (comp @ X510 @ X511) @ (sub @ X512 @ X511) @ X513))) | ~ (((X500 @ X510 @ X512 @ (comp @ X511 @ X513))) = $true)) | ~ (((X499 @ X502)) = $true)) <=> (hoasinduction_lem2v2 = $true)) & ((substmonoid = $true) <=> (! [X514 : subst] : (((comp @ X514 @ id)) = X514) & ! [X515 : subst] : (((comp @ id @ X515)) = X515))) & (axclos = $true) & (hoasinduction_lem3_gthm = $true) & ((induction2 = $true) <=> ! [X516 : term,X517 : (term > $o)] : (($true = ((X517 @ X516))) | ~ ! [X518 : term] : (($true = ((X517 @ X518))) | ~ ($true = ((var @ X518)))) | ~ ! [X519 : term,X520 : term] : (~ ($true = ((X517 @ X519))) | ~ (((X517 @ X520)) = $true) | ($true = ((X517 @ (ap @ X520 @ X519))))) | ~ ! [X521 : term] : (~ ! [X522 : term] : (~ ($true = ((X517 @ X522))) | (((X517 @ (sub @ X521 @ (push @ X522 @ id)))) = $true)) | ($true = ((X517 @ (lam @ X521))))))) & (hoasinduction_lem3b_gthm = $true) & (axvarshift = $true) & ~ (lamnotap = $true) & ! [X523 : d_term] : (d_one = X523) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X524 : term] : (((sub @ X524 @ id)) = X524) => ! [X525 : (term > $o),X526 : (subst > term > subst > $o),X527 : term] : (~ ! [X528 : subst,X529 : term,X530 : subst,X531 : subst] : (~ (((X526 @ (comp @ X531 @ X530) @ (sub @ X529 @ X530) @ X528)) = $true) | (((X526 @ X531 @ X529 @ (comp @ X530 @ X528))) = $true)) | ~ ! [X532 : term] : (~ (((X525 @ X532)) = $true) | ($true = ((X525 @ (sub @ X527 @ (push @ X532 @ id)))))) | ~ ! [X533 : (subst > term > term)] : (~ ! [X534 : subst,X535 : subst,X536 : term] : (((sub @ (X533 @ X534 @ X536) @ X535)) = ((X533 @ (comp @ X534 @ X535) @ (sub @ X536 @ X535)))) | ~ ! [X537 : term] : (~ ($true = ((X526 @ id @ X537 @ id))) | (((X526 @ id @ (X533 @ id @ X537) @ id)) = $true)) | ($true = ((X526 @ id @ (lam @ (X533 @ sh @ one)) @ id)))) | ~ ! [X538 : subst,X539 : term,X540 : subst,X541 : subst] : ((((X526 @ (comp @ X541 @ X538) @ (sub @ X539 @ X538) @ X540)) = $true) | ~ (((X526 @ X541 @ X539 @ (comp @ X538 @ X540))) = $true)) | ($true = ((X525 @ (lam @ X527)))) | ~ ! [X542 : term] : (((X525 @ X542)) = ((X526 @ id @ X542 @ id)))))) & ((! [X543 : term,X544 : subst] : (((sub @ one @ (push @ X543 @ X544))) = X543) => ! [X545 : term,X546 : subst,X547 : (term > $o),X548 : (term > $o)] : (~ ! [X549 : term] : (((X547 @ (sub @ X549 @ (push @ X545 @ X546)))) = ((X548 @ X549))) | ~ ($true = ((X547 @ X545))) | (((X548 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasapnotvar = $true) & (pushprop_lem2v2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one))))),
% 3.49/0.96 inference(fool_elimination,[],[f4])).
% 3.49/0.96 thf(f6,plain,(
% 3.49/0.96 ~ (! [X0 : (subst > term > subst > $o)] : (! [X1 : subst,X2 : subst,X3 : subst,X4 : term] : ((X0 @ X3 @ X4 @ (comp @ X2 @ X1)) => (X0 @ (comp @ X3 @ X2) @ (sub @ X4 @ X2) @ X1)) => (! [X5 : subst,X6 : subst,X7 : subst,X8 : term] : ((X0 @ (comp @ X5 @ X7) @ (sub @ X8 @ X7) @ X6) => (X0 @ X5 @ X8 @ (comp @ X7 @ X6))) => (! [X9 : term] : ((hoasvar @ id @ X9 @ id) => (X0 @ id @ X9 @ id)) => ! [X10 : term] : ((var @ X10) => (X0 @ id @ X10 @ id))))) = hoasinduction_lem1)),
% 3.49/0.96 inference(rectify,[],[f3])).
% 3.49/0.96 thf(f7,plain,(
% 3.49/0.96 ~ (hoasinduction_lem1 = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y4 @ Y2) @ (sub @ Y1 @ Y2) @ Y3) => (Y0 @ Y4 @ Y1 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))))),
% 3.49/0.96 inference(fool_elimination,[],[f6])).
% 3.49/0.96 thf(f8,plain,(
% 3.49/0.96 (hoasinduction_lem1 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y4 @ Y2) @ (sub @ Y1 @ Y2) @ Y3) => (Y0 @ Y4 @ Y1 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))))),
% 3.49/0.96 inference(flattening,[],[f7])).
% 3.49/0.96 thf(f9,plain,(
% 3.49/0.96 (termmset_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X0 : (subst > term > subst > $o),X1 : term,X2 : term] : (($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ~ ($true = ((X0 @ id @ X1 @ id))) | ~ ! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (~ ($true = ((X0 @ X4 @ X3 @ (comp @ X6 @ X5)))) | ($true = ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5)))) | ~ ! [X7 : subst,X8 : subst,X9 : subst,X10 : term] : ((((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) = $true) | ~ (((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) = $true)) | ~ ! [X11 : term,X12 : term] : (($true = ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) | ~ (((X0 @ id @ X12 @ id)) = $true) | ~ ($true = ((X0 @ id @ X11 @ id)))) | ~ (((X0 @ id @ X2 @ id)) = $true))) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (axapp = $true) & ((induction2_lthm = $true) <=> (! [X19 : term] : (((sub @ X19 @ id)) = X19) => (! [X20 : (term > $o),X21 : subst,X22 : term] : (~ ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ~ ($true = ((var @ X23)))) | (((X20 @ (sub @ X22 @ X21))) = $true) | ~ ! [X24 : term,X25 : term] : (~ (((X20 @ X24)) = $true) | ($true = ((X20 @ (ap @ X24 @ X25)))) | ~ ($true = ((X20 @ X25)))) | ~ ! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ~ ! [X27 : term] : ((((X20 @ (sub @ X26 @ (push @ X27 @ id)))) = $true) | ~ ($true = ((X20 @ X27)))))) => ! [X28 : term,X29 : (term > $o)] : (~ ! [X30 : term] : (($true = ((X29 @ (lam @ X30)))) | ~ ! [X31 : term] : (($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id))))) | ~ (((X29 @ X31)) = $true))) | ($true = ((X29 @ X28))) | ~ ! [X32 : term,X33 : term] : (($true = ((X29 @ (ap @ X33 @ X32)))) | ~ ($true = ((X29 @ X33))) | ~ (((X29 @ X32)) = $true)) | ~ ! [X34 : term] : (~ ($true = ((var @ X34))) | ($true = ((X29 @ X34)))))))) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & ((! [X37 : (term > $o),X38 : term] : (($true = ((X37 @ X38))) | ~ ! [X39 : term] : (~ ! [X40 : term] : (~ (((X37 @ X40)) = $true) | ($true = ((X37 @ (sub @ X39 @ (push @ X40 @ id)))))) | ($true = ((X37 @ (lam @ X39))))) | ~ ! [X41 : term] : (($true = ((X37 @ X41))) | ~ ($true = ((var @ X41)))) | ~ ! [X42 : term,X43 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | ~ (((X37 @ X43)) = $true) | ~ (((X37 @ X42)) = $true))) => (! [X44 : term,X45 : (subst > term > subst > $o),X46 : term] : (~ ! [X47 : term,X48 : subst,X49 : subst,X50 : subst] : (~ (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) = $true) | ($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48)))) | ($true = ((X45 @ id @ (ap @ X46 @ X44) @ id))) | ~ ! [X51 : term,X52 : term] : (($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id))) | ~ (((X45 @ id @ X51 @ id)) = $true) | ~ ($true = ((X45 @ id @ X52 @ id)))) | ~ ! [X53 : subst,X54 : subst,X55 : term,X56 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | ~ (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) = $true)) | ~ (((X45 @ id @ X46 @ id)) = $true) | ~ ($true = ((X45 @ id @ X44 @ id)))) => (! [X57 : (subst > term > subst > $o),X58 : term] : (~ ! [X59 : term] : (~ ($true = ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) | ~ ! [X60 : (subst > term > term)] : (($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ~ ! [X61 : term] : (~ ($true = ((X57 @ id @ X61 @ id))) | ($true = ((X57 @ id @ (X60 @ id @ X61) @ id)))) | ~ ! [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) = ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))) | ($true = ((X57 @ id @ (lam @ X58) @ id))) | ~ ! [X65 : subst,X66 : term,X67 : subst,X68 : subst] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ~ ($true = ((X57 @ X65 @ X66 @ (comp @ X68 @ X67))))) | ~ ! [X69 : subst,X70 : subst,X71 : term,X72 : subst] : (~ ($true = ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72)))))) => ! [X73 : term,X74 : (subst > term > subst > $o)] : (~ ! [X75 : subst,X76 : term,X77 : subst,X78 : subst] : (~ ($true = ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) | ($true = ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ~ ! [X79 : term] : ((((X74 @ id @ X79 @ id)) = $true) | ~ ($true = ((var @ (sub @ X79 @ id))))) | ~ ! [X80 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) = $true) | ~ ! [X81 : term] : (($true = ((X74 @ id @ (X80 @ id @ X81) @ id))) | ~ ($true = ((X74 @ id @ X81 @ id)))) | ~ ! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82)))) | ~ ! [X85 : term,X86 : term] : (~ ($true = ((X74 @ id @ X85 @ id))) | (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) = $true) | ~ ($true = ((X74 @ id @ X86 @ id)))) | ($true = ((X74 @ id @ X73 @ id))) | ~ ! [X87 : term,X88 : subst,X89 : subst,X90 : subst] : (~ (((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) = $true) | ($true = ((X74 @ X90 @ X87 @ (comp @ X89 @ X88))))))))) <=> (hoasinduction_lthm = $true)) & ~ (ulamvar1 = $true) & (pushprop_lem3v2_lthm = $true) & (! [X92 : (term > $o),X93 : term,X91 : subst] : ~ ! [X94 : (term > $o)] : ~ ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslamnotap_gthm = $true) & ! [X97 : d_subst,X96 : d_subst] : ((((d2subst @ X97)) = ((d2subst @ X96))) => (X96 = X97)) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1 = $true) & (((d2subst @ d_id)) = id) & (hoasinduction_lem3v2_gthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((pushprop_lem1v2 = $true) <=> ! [X98 : subst,X99 : term,X100 : (term > $o),X101 : (term > $o)] : (($true = ((X100 @ one))) | ~ (((X101 @ X99)) = $true) | ~ ! [X102 : term] : (((X100 @ X102)) = ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))))) & ! [X103 : d_subst] : (d_id = X103) & ((axidl = $true) <=> ! [X104 : subst] : (((comp @ id @ X104)) = X104)) & ((hoaslaminj_lthm = $true) <=> (! [X106 : term,X105 : subst] : (((sub @ one @ (push @ X106 @ X105))) = X106) => (! [X108 : term,X107 : subst] : (((comp @ sh @ (push @ X108 @ X107))) = X107) => (! [X110 : term,X109 : term] : ((X109 = X110) | (((lam @ X110)) != ((lam @ X109)))) => ! [X111 : term,X113 : subst,X114 : (subst > term > term),X112 : (subst > term > term)] : ((((lam @ (X114 @ sh @ one))) != ((lam @ (X112 @ sh @ one)))) | (((X114 @ X113 @ X111)) = ((X112 @ X113 @ X111))) | ~ ! [X115 : subst,X116 : subst,X117 : term] : (((sub @ (X112 @ X115 @ X117) @ X116)) = ((X112 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116)))) | ~ ! [X119 : term,X120 : subst,X118 : subst] : (((X114 @ (comp @ X118 @ X120) @ (sub @ X119 @ X120))) = ((sub @ (X114 @ X118 @ X119) @ X120)))))))) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X121 : term] : ~ ! [X122 : (subst > term > term)] : ~ ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123)))) & (induction2_gthm = $true) & (! [X125 : term,X126 : term,X127 : (term > $o),X128 : (term > $o),X129 : subst] : (~ ($true = ((X127 @ X126))) | (((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_lthm = $true) & ((! [X131 : term,X130 : subst] : (((sub @ one @ (push @ X131 @ X130))) = X131) => (! [X133 : subst,X132 : term] : (((comp @ sh @ (push @ X132 @ X133))) = X133) => ! [X134 : (term > $o),X135 : subst,X136 : term,X137 : (term > $o),X138 : term] : (~ (((X137 @ X136)) = $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)))) <=> (pushprop_lem1_lthm = $true)) & (! [X140 : term,X141 : subst,X139 : (term > $o)] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141))))) <=> (pushprop_lem0 = $true)) & ((! [X144 : term] : (((sub @ X144 @ id)) = X144) => (! [X145 : (subst > term > subst > $o),X146 : term] : (~ ! [X147 : (subst > term > term)] : (~ ! [X149 : subst,X150 : subst,X148 : term] : (((X147 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) = ((sub @ (X147 @ X150 @ X148) @ X149))) | ~ ! [X151 : term] : (($true = ((X145 @ id @ (X147 @ id @ X151) @ id))) | ~ ($true = ((X145 @ id @ X151 @ id)))) | (((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id)) = $true)) | ~ ! [X152 : term] : ((((X145 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) = $true) | ~ ($true = ((X145 @ id @ X152 @ id)))) | ($true = ((X145 @ id @ (lam @ (sub @ X146 @ (push @ one @ sh))) @ id)))) => ! [X153 : (subst > term > subst > $o),X154 : term] : (~ ! [X155 : term] : (($true = ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id))) | ~ ($true = ((X153 @ id @ X155 @ id)))) | ~ ! [X156 : (subst > term > term)] : (($true = ((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id))) | ~ ! [X157 : term] : ((((X153 @ id @ (X156 @ id @ X157) @ id)) = $true) | ~ ($true = ((X153 @ id @ X157 @ id)))) | ~ ! [X159 : term,X160 : subst,X158 : subst] : (((sub @ (X156 @ X160 @ X159) @ X158)) = ((X156 @ (comp @ X160 @ X158) @ (sub @ X159 @ X158))))) | ($true = ((X153 @ id @ (lam @ X154) @ id)))))) <=> (hoasinduction_lem3a_lthm = $true)) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) = ((d2term @ X161))) => (X161 = X162)) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) <=> (axvarid = $true)) & (ulamvarind = $true) & (! [X164 : (subst > term > subst > $o),X165 : term] : (($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))) | ~ ! [X166 : term] : ((((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) = $true) | ~ ($true = ((X164 @ id @ X166 @ id)))) | ~ ! [X167 : (subst > term > term)] : (~ ! [X169 : term,X168 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X169) @ X168)) = ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)))) | ($true = ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id))) | ~ ! [X171 : term] : (~ (((X164 @ id @ X171 @ id)) = $true) | (((X164 @ id @ (X167 @ id @ X171) @ id)) = $true)))) <=> (hoasinduction_lem3aa = $true)) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) <=> (shinj = $true)) & (axabs = $true) & (substmonoid_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X174 : term] : ~ ! [X175 : (subst > term > term)] : ~ ! [X177 : subst,X176 : term] : (((sub @ X174 @ (push @ X176 @ X177))) = ((X175 @ X177 @ X176))) => (! [X178 : term] : (((sub @ X178 @ id)) = X178) => ! [X179 : (subst > term > subst > $o),X180 : term,X181 : (term > $o)] : (~ ! [X182 : term] : (($true = ((X181 @ (sub @ X180 @ (push @ X182 @ id))))) | ~ (((X181 @ X182)) = $true)) | (((X181 @ (lam @ X180))) = $true) | ~ ! [X183 : (subst > term > term)] : (~ ! [X186 : subst,X185 : term,X184 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) = ((sub @ (X183 @ X186 @ X185) @ X184))) | ~ ! [X187 : term] : (~ ($true = ((X179 @ id @ X187 @ id))) | (((X179 @ id @ (X183 @ id @ X187) @ id)) = $true)) | (((X179 @ id @ (lam @ (X183 @ sh @ one)) @ id)) = $true)) | ~ ! [X188 : term] : (((X181 @ X188)) = ((X179 @ id @ X188 @ id))))))) & (axassoc = $true) & (pushprop_lthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((induction2lem = $true) <=> ! [X189 : (term > $o),X190 : term,X191 : subst] : (($true = ((X189 @ (sub @ X190 @ X191)))) | ~ ! [X192 : term,X193 : term] : (~ ($true = ((X189 @ X193))) | ($true = ((X189 @ (ap @ X193 @ X192)))) | ~ ($true = ((X189 @ X192)))) | ~ ! [X194 : term] : (($true = ((X189 @ (lam @ X194)))) | ~ ! [X195 : term] : (($true = ((X189 @ (sub @ X194 @ (push @ X195 @ id))))) | ~ ($true = ((X189 @ X195))))) | ~ ! [X196 : term] : (($true = ((X189 @ (sub @ X196 @ X191)))) | ~ ($true = ((var @ X196)))))) & ((induction = $true) <=> ! [X197 : (term > $o),X198 : term] : ((((X197 @ X198)) = $true) | ~ ! [X199 : term,X200 : term] : (~ ($true = ((X197 @ X199))) | (((X197 @ (ap @ X199 @ X200))) = $true) | ~ ($true = ((X197 @ X200)))) | ~ ! [X201 : term] : (($true = ((X197 @ (lam @ X201)))) | ~ ($true = ((X197 @ X201)))) | ~ ! [X202 : term] : (($true = ((X197 @ X202))) | ~ (((var @ X202)) = $true)))) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X203 : term] : ~ ! [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) != ((X204 @ sh @ one)))) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) <=> (termmset = $true)) & (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) <=> (axshiftcons = $true)) & (((d2subst @ d_id)) = sh) & ((! [X210 : term,X208 : term,X211 : term,X209 : term] : ((X208 = X210) | (((ap @ X209 @ X210)) != ((ap @ X211 @ X208)))) => ! [X213 : term,X212 : term,X215 : term,X214 : term] : ((X212 = X213) | (((ap @ (sub @ X214 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X213))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (hoasapnotvar_lthm = $true) & ((hoasapinj2 = $true) <=> ! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218))))) & (! [X220 : term] : ~ ! [X221 : (subst > term > term)] : ~ ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223)))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_lem2_lthm = $true) & (hoasinduction_gthm = $true) & (pushprop_lem1v2_gthm = $true) & ((laminj = $true) <=> ! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224))))) & (hoaslaminj_gthm = $true) & ((axscons = $true) <=> ! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226)) & (! [X227 : term,X228 : (subst > term > subst > $o)] : (~ ! [X229 : (subst > term > term)] : (~ ! [X230 : term] : (~ ($true = ((X228 @ id @ X230 @ id))) | ($true = ((X228 @ id @ (X229 @ id @ X230) @ id)))) | ($true = ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id))) | ~ ! [X231 : subst,X233 : term,X232 : subst] : (((sub @ (X229 @ X231 @ X233) @ X232)) = ((X229 @ (comp @ X231 @ X232) @ (sub @ X233 @ X232))))) | ~ ! [X234 : term] : (($true = ((X228 @ id @ (sub @ X227 @ (push @ X234 @ id)) @ id))) | ~ ($true = ((X228 @ id @ X234 @ id)))) | ~ ! [X235 : subst,X236 : subst,X237 : term,X238 : subst] : (~ (((X228 @ X238 @ X237 @ (comp @ X236 @ X235))) = $true) | (((X228 @ (comp @ X238 @ X236) @ (sub @ X237 @ X236) @ X235)) = $true)) | ~ ! [X239 : subst,X240 : subst,X241 : subst,X242 : term] : (($true = ((X228 @ X240 @ X242 @ (comp @ X239 @ X241)))) | ~ ($true = ((X228 @ (comp @ X240 @ X239) @ (sub @ X242 @ X239) @ X241)))) | ($true = ((X228 @ id @ (lam @ X227) @ id)))) <=> (hoasinduction_lem3 = $true)) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X243 : (subst > term > subst > $o)] : ~ ! [X244 : (term > $o)] : ~ ! [X245 : term] : (((X243 @ id @ X245 @ id)) = ((X244 @ X245))) => (! [X246 : term,X247 : (term > $o)] : (($true = ((X247 @ X246))) | ~ ! [X248 : term] : (($true = ((X247 @ X248))) | ~ ($true = ((var @ X248)))) | ~ ! [X249 : term] : (($true = ((X247 @ (lam @ X249)))) | ~ ! [X250 : term] : (~ ($true = ((X247 @ X250))) | (((X247 @ (sub @ X249 @ (push @ X250 @ id)))) = $true))) | ~ ! [X251 : term,X252 : term] : (($true = ((X247 @ (ap @ X251 @ X252)))) | ~ (((X247 @ X251)) = $true) | ~ ($true = ((X247 @ X252))))) => (! [X253 : term] : (((sub @ X253 @ id)) = X253) => (! [X254 : term,X255 : (subst > term > subst > $o),X256 : (term > $o)] : ((((X256 @ (lam @ X254))) = $true) | ~ ! [X257 : term] : (($true = ((X256 @ (sub @ X254 @ (push @ X257 @ id))))) | ~ (((X256 @ X257)) = $true)) | ~ ! [X258 : (subst > term > term)] : (~ ! [X261 : subst,X259 : term,X260 : subst] : (((X258 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260))) = ((sub @ (X258 @ X261 @ X259) @ X260))) | ~ ! [X262 : term] : (~ ($true = ((X255 @ id @ X262 @ id))) | ($true = ((X255 @ id @ (X258 @ id @ X262) @ id)))) | (((X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) = $true)) | ~ ! [X263 : term] : (((X256 @ X263)) = ((X255 @ id @ X263 @ id)))) => ! [X264 : term,X265 : (subst > term > subst > $o)] : (~ ! [X266 : term,X267 : term] : (~ (((X265 @ id @ X266 @ id)) = $true) | ~ ($true = ((X265 @ id @ X267 @ id))) | (((X265 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) = $true)) | (((X265 @ id @ X264 @ id)) = $true) | ~ ! [X268 : (subst > term > term)] : (~ ! [X269 : term] : ((((X265 @ id @ (X268 @ id @ X269) @ id)) = $true) | ~ (((X265 @ id @ X269 @ id)) = $true)) | (((X265 @ id @ (lam @ (X268 @ sh @ one)) @ id)) = $true) | ~ ! [X272 : term,X271 : subst,X270 : subst] : (((sub @ (X268 @ X271 @ X272) @ X270)) = ((X268 @ (comp @ X271 @ X270) @ (sub @ X272 @ X270))))))))))) & ((termmset_lthm = $true) <=> (! [X273 : term] : (((sub @ X273 @ id)) = X273) => ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (! [X275 : term,X276 : (subst > term > subst > $o)] : (($true = ((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id))) | ~ ! [X277 : (subst > term > term)] : (~ ! [X279 : subst,X280 : subst,X278 : term] : (((sub @ (X277 @ X279 @ X278) @ X280)) = ((X277 @ (comp @ X279 @ X280) @ (sub @ X278 @ X280)))) | ($true = ((X276 @ id @ (lam @ (X277 @ sh @ one)) @ id))) | ~ ! [X281 : term] : ((((X276 @ id @ (X277 @ id @ X281) @ id)) = $true) | ~ ($true = ((X276 @ id @ X281 @ id))))) | ~ ! [X282 : term] : (~ ($true = ((X276 @ id @ X282 @ id))) | ($true = ((X276 @ id @ (sub @ X275 @ (push @ X282 @ id)) @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & (hoaslamnotap_lthm = $true) & ((! [X283 : (subst > term > subst > $o)] : ~ ! [X284 : (term > $o)] : ~ ! [X285 : term] : (((X283 @ id @ X285 @ id)) = ((X284 @ X285))) => (! [X286 : (term > $o),X287 : term] : (~ ! [X288 : term] : (($true = ((X286 @ X288))) | ~ ($true = ((var @ X288)))) | ~ ! [X289 : term] : (~ ! [X290 : term] : (~ (((X286 @ X290)) = $true) | ($true = ((X286 @ (sub @ X289 @ (push @ X290 @ id)))))) | ($true = ((X286 @ (lam @ X289))))) | ~ ! [X291 : term,X292 : term] : (~ ($true = ((X286 @ X292))) | ($true = ((X286 @ (ap @ X292 @ X291)))) | ~ (((X286 @ X291)) = $true)) | ($true = ((X286 @ X287)))) => (! [X293 : term] : (((sub @ X293 @ id)) = X293) => (! [X294 : (subst > term > subst > $o),X295 : (term > $o),X296 : term] : (~ ! [X297 : (subst > term > term)] : ((((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ~ ! [X298 : term] : (~ (((X294 @ id @ X298 @ id)) = $true) | ($true = ((X294 @ id @ (X297 @ id @ X298) @ id)))) | ~ ! [X301 : subst,X299 : subst,X300 : term] : (((sub @ (X297 @ X299 @ X300) @ X301)) = ((X297 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301))))) | ~ ! [X302 : term] : (($true = ((X295 @ (sub @ X296 @ (push @ X302 @ id))))) | ~ ($true = ((X295 @ X302)))) | (((X295 @ (lam @ X296))) = $true) | ~ ! [X303 : term] : (((X295 @ X303)) = ((X294 @ id @ X303 @ id)))) => ! [X304 : (subst > term > subst > $o),X305 : term] : (($true = ((X304 @ id @ X305 @ id))) | ~ ! [X306 : subst,X307 : subst,X308 : subst,X309 : term] : (~ (((X304 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true) | ($true = ((X304 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)))) | ~ ! [X310 : (subst > term > term)] : (~ ! [X312 : term,X313 : subst,X311 : subst] : (((X310 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))) = ((sub @ (X310 @ X311 @ X312) @ X313))) | ~ ! [X314 : term] : (~ ($true = ((X304 @ id @ X314 @ id))) | (((X304 @ id @ (X310 @ id @ X314) @ id)) = $true)) | ($true = ((X304 @ id @ (lam @ (X310 @ sh @ one)) @ id)))) | ~ ! [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (~ ($true = ((X304 @ (comp @ X316 @ X315) @ (sub @ X318 @ X315) @ X317))) | ($true = ((X304 @ X316 @ X318 @ (comp @ X315 @ X317))))) | ~ ! [X319 : term] : (~ (((var @ (sub @ X319 @ id))) = $true) | ($true = ((X304 @ id @ X319 @ id)))) | ~ ! [X320 : term,X321 : term] : (~ ($true = ((X304 @ id @ X320 @ id))) | ($true = ((X304 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id))) | ~ (((X304 @ id @ X321 @ id)) = $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (pushprop = $true) & ((substmonoid_lthm = $true) <=> (! [X322 : subst] : (((comp @ id @ X322)) = X322) => (! [X323 : subst] : (((comp @ X323 @ id)) = X323) => (! [X324 : subst] : (((comp @ id @ X324)) = X324) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))))) & (! [X326 : subst] : (((comp @ X326 @ id)) = X326) <=> (axidr = $true)) & (hoaslamnotvar_gthm = $true) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (! [X331 : term,X330 : term,X329 : (subst > term > term)] : (~ ! [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) = ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (pushprop_lem0_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X335 : (subst > term > subst > $o)] : ~ ! [X336 : (term > $o)] : ~ ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X338 : (subst > term > subst > $o),X339 : term] : (~ ! [X340 : (subst > term > term)] : (($true = ((X338 @ id @ (lam @ (X340 @ sh @ one)) @ id))) | ~ ! [X341 : subst,X343 : subst,X342 : term] : (((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343))) = ((sub @ (X340 @ X341 @ X342) @ X343))) | ~ ! [X344 : term] : (~ ($true = ((X338 @ id @ X344 @ id))) | (((X338 @ id @ (X340 @ id @ X344) @ id)) = $true))) | ($true = ((X338 @ id @ X339 @ id))) | ~ ! [X345 : term,X346 : term] : (~ (((X338 @ id @ X345 @ id)) = $true) | ~ ($true = ((X338 @ id @ X346 @ id))) | ($true = ((X338 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id)))))) & (hoaslamnotvar = $true) & (! [X347 : term,X348 : (subst > term > subst > $o)] : (~ ! [X349 : (subst > term > term)] : (~ ! [X350 : subst,X351 : term,X352 : subst] : (((X349 @ (comp @ X350 @ X352) @ (sub @ X351 @ X352))) = ((sub @ (X349 @ X350 @ X351) @ X352))) | ($true = ((X348 @ id @ (lam @ (X349 @ sh @ one)) @ id))) | ~ ! [X353 : term] : (($true = ((X348 @ id @ (X349 @ id @ X353) @ id))) | ~ (((X348 @ id @ X353 @ id)) = $true))) | ~ ! [X354 : subst,X355 : subst,X356 : term,X357 : subst] : (~ ($true = ((X348 @ (comp @ X357 @ X354) @ (sub @ X356 @ X354) @ X355))) | ($true = ((X348 @ X357 @ X356 @ (comp @ X354 @ X355))))) | ~ ! [X358 : subst,X359 : subst,X360 : term,X361 : subst] : ((((X348 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361) @ X358)) = $true) | ~ ($true = ((X348 @ X359 @ X360 @ (comp @ X361 @ X358))))) | ~ ! [X362 : term,X363 : term] : (~ (((X348 @ id @ X362 @ id)) = $true) | ~ (((X348 @ id @ X363 @ id)) = $true) | ($true = ((X348 @ id @ (ap @ (sub @ X363 @ id) @ X362) @ id)))) | ($true = ((X348 @ id @ X347 @ id))) | ~ ! [X364 : term] : (($true = ((X348 @ id @ X364 @ id))) | ~ (((var @ (sub @ X364 @ id))) = $true))) <=> (hoasinduction = $true)) & (pushprop_gthm = $true) & (! [X366 : term,X368 : subst,X367 : (subst > term > term),X365 : (subst > term > term)] : ((((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | ~ ! [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) = ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | ~ ! [X374 : term,X372 : subst,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X365 @ X372 @ X374) @ X373))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one))))) <=> (hoaslaminj = $true)) & ((hoasinduction_lem3v2a = $true) <=> ! [X375 : (subst > term > subst > $o),X376 : term,X377 : (term > $o)] : (~ ! [X378 : term] : (((X375 @ id @ X378 @ id)) = ((X377 @ X378))) | ~ ! [X379 : (subst > term > term)] : (~ ! [X380 : term] : (($true = ((X375 @ id @ (X379 @ id @ X380) @ id))) | ~ (((X375 @ id @ X380 @ id)) = $true)) | ($true = ((X375 @ id @ (lam @ (X379 @ sh @ one)) @ id))) | ~ ! [X381 : subst,X383 : term,X382 : subst] : (((X379 @ (comp @ X382 @ X381) @ (sub @ X383 @ X381))) = ((sub @ (X379 @ X382 @ X383) @ X381)))) | (((X377 @ (lam @ X376))) = $true) | ~ ! [X384 : term] : (($true = ((X377 @ (sub @ X376 @ (push @ X384 @ id))))) | ~ ($true = ((X377 @ X384)))))) & (ulamvarsh = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X385 : (subst > term > subst > $o),X386 : (term > $o),X387 : term] : (~ ! [X388 : subst,X389 : subst,X390 : subst,X391 : term] : (~ (((X385 @ X389 @ X391 @ (comp @ X388 @ X390))) = $true) | ($true = ((X385 @ (comp @ X389 @ X388) @ (sub @ X391 @ X388) @ X390)))) | ~ ! [X392 : term] : (~ ($true = ((X386 @ X392))) | (((X386 @ (sub @ X387 @ (push @ X392 @ id)))) = $true)) | (((X386 @ (lam @ X387))) = $true) | ~ ! [X393 : term] : (((X385 @ id @ X393 @ id)) = ((X386 @ X393))) | ~ ! [X394 : term,X395 : subst,X396 : subst,X397 : subst] : (($true = ((X385 @ X397 @ X394 @ (comp @ X395 @ X396)))) | ~ ($true = ((X385 @ (comp @ X397 @ X395) @ (sub @ X394 @ X395) @ X396)))) | ~ ! [X398 : (subst > term > term)] : (~ ! [X399 : term] : ((((X385 @ id @ (X398 @ id @ X399) @ id)) = $true) | ~ ($true = ((X385 @ id @ X399 @ id)))) | ~ ! [X401 : term,X402 : subst,X400 : subst] : (((sub @ (X398 @ X402 @ X401) @ X400)) = ((X398 @ (comp @ X402 @ X400) @ (sub @ X401 @ X400)))) | ($true = ((X385 @ id @ (lam @ (X398 @ sh @ one)) @ id)))))) & (lamnotvar = $true) & ~ (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) = $true) & (pushprop_lem1_gthm = $true) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) <=> (apinj1 = $true)) & (hoasapinj2_gthm = $true) & (hoasinduction_lem3a_gthm = $true) & (induction2lem_gthm = $true) & ~ (((var @ (d2term @ d_one))) = $true) & ((induction2lem_lthm = $true) <=> (! [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) = X408) => (! [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) = X409) => (! [X411 : subst] : (((comp @ X411 @ id)) = X411) => (! [X412 : (term > $o),X413 : term] : (~ ! [X414 : term] : (~ ($true = ((var @ X414))) | ($true = ((X412 @ X414)))) | ~ ! [X415 : term,X416 : term] : (~ (((X412 @ X415)) = $true) | (((X412 @ (ap @ X415 @ X416))) = $true) | ~ ($true = ((X412 @ X416)))) | ~ ! [X417 : term] : (($true = ((X412 @ (lam @ X417)))) | ~ (((X412 @ X417)) = $true)) | ($true = ((X412 @ X413)))) => ! [X418 : (term > $o),X419 : subst,X420 : term] : (~ ! [X421 : term] : ((((X418 @ (lam @ X421))) = $true) | ~ ! [X422 : term] : (~ ($true = ((X418 @ X422))) | ($true = ((X418 @ (sub @ X421 @ (push @ X422 @ id))))))) | ~ ! [X423 : term] : (~ (((var @ X423)) = $true) | ($true = ((X418 @ (sub @ X423 @ X419))))) | ~ ! [X424 : term,X425 : term] : (~ ($true = ((X418 @ X424))) | ($true = ((X418 @ (ap @ X425 @ X424)))) | ~ (((X418 @ X425)) = $true)) | ($true = ((X418 @ (sub @ X420 @ X419)))))))))) & (pushprop_lthm_orig = $true) & (hoasinduction_lem1v2_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X426 : term] : (((sub @ X426 @ id)) = X426) => (! [X428 : term,X429 : term,X427 : term,X430 : term] : ((((ap @ X429 @ X430)) != ((ap @ X428 @ X427))) | (X428 = X429)) => ! [X433 : term,X431 : term,X434 : term,X432 : term] : ((X432 = X433) | (((ap @ (sub @ X433 @ id) @ X434)) != ((ap @ (sub @ X432 @ id) @ X431))))))) & (axmap = $true) & ((hoasinduction_lem0 = $true) <=> ! [X435 : (subst > term > subst > $o)] : ~ ! [X436 : (term > $o)] : ~ ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id)))) & (pushprop_lem3v2 = $true) & (hoasinduction_lem1_gthm = $true) & (! [X438 : term] : ~ ! [X439 : (subst > term > term)] : (((X439 @ sh @ one)) != ((sub @ X438 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (! [X440 : (subst > term > subst > $o),X441 : term] : (($true = ((X440 @ id @ (lam @ (sub @ X441 @ (push @ one @ sh))) @ id))) | ~ ! [X442 : term] : (($true = ((X440 @ id @ (sub @ X441 @ (push @ X442 @ id)) @ id))) | ~ (((X440 @ id @ X442 @ id)) = $true)) | ~ ! [X443 : (subst > term > term),X444 : term] : (~ ! [X446 : term,X447 : subst,X445 : subst] : (((X443 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X444 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) | ~ ! [X448 : term] : (~ (((X440 @ id @ X448 @ id)) = $true) | ($true = ((X440 @ id @ (X443 @ id @ X448) @ id)))) | ~ ! [X451 : subst,X450 : subst,X449 : term] : (((sub @ (sub @ X444 @ (push @ X449 @ X451)) @ X450)) = ((sub @ (X443 @ X451 @ X449) @ X450))) | ($true = ((X440 @ id @ (lam @ (X443 @ sh @ one)) @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X452 : term] : (((sub @ X452 @ id)) = X452) => (! [X453 : term,X454 : (subst > term > subst > $o)] : (($true = ((X454 @ id @ (lam @ (sub @ X453 @ (push @ one @ sh))) @ id))) | ~ ! [X455 : (subst > term > term)] : (($true = ((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id))) | ~ ! [X456 : term] : ((((X454 @ id @ (X455 @ id @ X456) @ id)) = $true) | ~ (((X454 @ id @ X456 @ id)) = $true)) | ~ ! [X459 : subst,X458 : subst,X457 : term] : (((sub @ (X455 @ X459 @ X457) @ X458)) = ((X455 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458))))) | ~ ! [X460 : term] : (~ (((X454 @ id @ X460 @ id)) = $true) | ($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))))) => ! [X461 : (subst > term > subst > $o),X462 : term] : (~ ! [X463 : (subst > term > term)] : (~ ! [X464 : term] : (~ ($true = ((X461 @ id @ X464 @ id))) | ($true = ((X461 @ id @ (X463 @ id @ X464) @ id)))) | ~ ! [X467 : subst,X466 : subst,X465 : term] : (((sub @ (X463 @ X467 @ X465) @ X466)) = ((X463 @ (comp @ X467 @ X466) @ (sub @ X465 @ X466)))) | (((X461 @ id @ (lam @ (X463 @ sh @ one)) @ id)) = $true)) | ~ ! [X468 : term,X469 : subst,X470 : subst,X471 : subst] : (~ (((X461 @ X471 @ X468 @ (comp @ X470 @ X469))) = $true) | (((X461 @ (comp @ X471 @ X470) @ (sub @ X468 @ X470) @ X469)) = $true)) | ~ ! [X472 : subst,X473 : subst,X474 : subst,X475 : term] : (($true = ((X461 @ X474 @ X475 @ (comp @ X473 @ X472)))) | ~ ($true = ((X461 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473) @ X472)))) | (((X461 @ id @ (lam @ X462) @ id)) = $true) | ~ ! [X476 : term] : ((((X461 @ id @ (sub @ X462 @ (push @ X476 @ id)) @ id)) = $true) | ~ (((X461 @ id @ X476 @ id)) = $true)))))) & (hoasinduction_lem2v2_gthm = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) <=> (apinj2 = $true)) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (one = ((d2term @ d_one))) & ((hoasinduction_lem3a = $true) <=> ! [X481 : (subst > term > subst > $o),X482 : term] : (($true = ((X481 @ id @ (lam @ X482) @ id))) | ~ ! [X483 : term] : (~ ($true = ((X481 @ id @ X483 @ id))) | ($true = ((X481 @ id @ (sub @ X482 @ (push @ X483 @ id)) @ id)))) | ~ ! [X484 : (subst > term > term)] : ((((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ~ ! [X487 : subst,X485 : subst,X486 : term] : (((sub @ (X484 @ X485 @ X486) @ X487)) = ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) | ~ ! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ~ ($true = ((X481 @ id @ X488 @ id))))))) & (hoasapnotvar_gthm = $true) & (apnotvar = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (hoaslamnotvar_lthm = $true) & (! [X489 : (term > $o),X490 : (subst > term > subst > $o),X491 : term,X492 : term] : (~ ! [X493 : term,X494 : term] : ((((X490 @ id @ (ap @ (sub @ X494 @ id) @ X493) @ id)) = $true) | ~ ($true = ((X490 @ id @ X493 @ id))) | ~ (((X490 @ id @ X494 @ id)) = $true)) | ~ ! [X495 : term] : (((X489 @ X495)) = ((X490 @ id @ X495 @ id))) | ~ ! [X496 : subst,X497 : subst,X498 : subst,X499 : term] : (~ ($true = ((X490 @ (comp @ X496 @ X497) @ (sub @ X499 @ X497) @ X498))) | ($true = ((X490 @ X496 @ X499 @ (comp @ X497 @ X498))))) | (((X489 @ (ap @ X491 @ X492))) = $true) | ~ (((X489 @ X491)) = $true) | ~ ! [X500 : subst,X501 : subst,X502 : term,X503 : subst] : ((((X490 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true) | ~ ($true = ((X490 @ X500 @ X502 @ (comp @ X501 @ X503))))) | ~ ($true = ((X489 @ X492)))) <=> (hoasinduction_lem2v2 = $true)) & ((substmonoid = $true) <=> (! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504))) & (axclos = $true) & (hoasinduction_lem3_gthm = $true) & ((induction2 = $true) <=> ! [X506 : term,X507 : (term > $o)] : (($true = ((X507 @ X506))) | ~ ! [X508 : term] : (($true = ((X507 @ X508))) | ~ ($true = ((var @ X508)))) | ~ ! [X509 : term,X510 : term] : (~ ($true = ((X507 @ X509))) | ~ ($true = ((X507 @ X510))) | ($true = ((X507 @ (ap @ X510 @ X509))))) | ~ ! [X511 : term] : (~ ! [X512 : term] : (~ ($true = ((X507 @ X512))) | ($true = ((X507 @ (sub @ X511 @ (push @ X512 @ id)))))) | ($true = ((X507 @ (lam @ X511))))))) & (hoasinduction_lem3b_gthm = $true) & (axvarshift = $true) & ~ (lamnotap = $true) & ! [X513 : d_term] : (d_one = X513) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X514 : term] : (((sub @ X514 @ id)) = X514) => ! [X515 : (term > $o),X516 : (subst > term > subst > $o),X517 : term] : (~ ! [X518 : subst,X519 : term,X520 : subst,X521 : subst] : (~ ($true = ((X516 @ (comp @ X521 @ X520) @ (sub @ X519 @ X520) @ X518))) | (((X516 @ X521 @ X519 @ (comp @ X520 @ X518))) = $true)) | ~ ! [X522 : term] : (~ (((X515 @ X522)) = $true) | ($true = ((X515 @ (sub @ X517 @ (push @ X522 @ id)))))) | ~ ! [X523 : (subst > term > term)] : (~ ! [X525 : subst,X526 : term,X524 : subst] : (((X523 @ (comp @ X524 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X524 @ X526) @ X525))) | ~ ! [X527 : term] : (~ ($true = ((X516 @ id @ X527 @ id))) | ($true = ((X516 @ id @ (X523 @ id @ X527) @ id)))) | (((X516 @ id @ (lam @ (X523 @ sh @ one)) @ id)) = $true)) | ~ ! [X528 : subst,X529 : term,X530 : subst,X531 : subst] : (($true = ((X516 @ (comp @ X531 @ X528) @ (sub @ X529 @ X528) @ X530))) | ~ ($true = ((X516 @ X531 @ X529 @ (comp @ X528 @ X530))))) | (((X515 @ (lam @ X517))) = $true) | ~ ! [X532 : term] : (((X515 @ X532)) = ((X516 @ id @ X532 @ id)))))) & ((! [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) = X533) => ! [X535 : term,X536 : subst,X537 : (term > $o),X538 : (term > $o)] : (~ ! [X539 : term] : (((X538 @ X539)) = ((X537 @ (sub @ X539 @ (push @ X535 @ X536))))) | ~ ($true = ((X537 @ X535))) | (((X538 @ one)) = $true))) <=> (pushprop_lem1v2_lthm = $true)) & (hoasapnotvar = $true) & (pushprop_lem2v2_lthm = $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one))))),
% 3.49/0.96 inference(rectify,[],[f5])).
% 3.49/0.96 thf(f10,plain,(
% 3.49/0.96 (! [X326 : subst] : (((comp @ X326 @ id)) = X326) <=> (axidr = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasapnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axidl = $true) <=> ! [X104 : subst] : (((comp @ id @ X104)) = X104)) & (ulamvarsh = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X377 : (term > $o),X376 : term,X375 : (subst > term > subst > $o)] : (~ ! [X384 : term] : (($true = ((X377 @ (sub @ X376 @ (push @ X384 @ id))))) | ($true != ((X377 @ X384)))) | (((X377 @ (lam @ X376))) = $true) | ~ ! [X379 : (subst > term > term)] : (($true = ((X375 @ id @ (lam @ (X379 @ sh @ one)) @ id))) | ~ ! [X380 : term] : (($true = ((X375 @ id @ (X379 @ id @ X380) @ id))) | (((X375 @ id @ X380 @ id)) != $true)) | ~ ! [X381 : subst,X383 : term,X382 : subst] : (((X379 @ (comp @ X382 @ X381) @ (sub @ X383 @ X381))) = ((sub @ (X379 @ X382 @ X383) @ X381)))) | ~ ! [X378 : term] : (((X375 @ id @ X378 @ id)) = ((X377 @ X378)))) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem3_gthm = $true) & (! [X385 : (subst > term > subst > $o),X386 : (term > $o),X387 : term] : (~ ! [X392 : term] : (($true != ((X386 @ X392))) | (((X386 @ (sub @ X387 @ (push @ X392 @ id)))) = $true)) | ~ ! [X396 : subst,X395 : subst,X397 : subst,X394 : term] : (($true = ((X385 @ X397 @ X394 @ (comp @ X395 @ X396)))) | ($true != ((X385 @ (comp @ X397 @ X395) @ (sub @ X394 @ X395) @ X396)))) | (((X386 @ (lam @ X387))) = $true) | ~ ! [X393 : term] : (((X385 @ id @ X393 @ id)) = ((X386 @ X393))) | ~ ! [X398 : (subst > term > term)] : (($true = ((X385 @ id @ (lam @ (X398 @ sh @ one)) @ id))) | ~ ! [X401 : term,X402 : subst,X400 : subst] : (((sub @ (X398 @ X402 @ X401) @ X400)) = ((X398 @ (comp @ X402 @ X400) @ (sub @ X401 @ X400)))) | ~ ! [X399 : term] : (($true != ((X385 @ id @ X399 @ id))) | (((X385 @ id @ (X398 @ id @ X399) @ id)) = $true))) | ~ ! [X389 : subst,X391 : term,X388 : subst,X390 : subst] : ((((X385 @ X389 @ X391 @ (comp @ X388 @ X390))) != $true) | ($true = ((X385 @ (comp @ X389 @ X388) @ (sub @ X391 @ X388) @ X390))))) <=> (hoasinduction_lem3v2 = $true)) & ((induction2lem = $true) <=> ! [X189 : (term > $o),X190 : term,X191 : subst] : (~ ! [X196 : term] : (($true != ((var @ X196))) | ($true = ((X189 @ (sub @ X196 @ X191))))) | ~ ! [X194 : term] : (($true = ((X189 @ (lam @ X194)))) | ~ ! [X195 : term] : (($true != ((X189 @ X195))) | ($true = ((X189 @ (sub @ X194 @ (push @ X195 @ id))))))) | ($true = ((X189 @ (sub @ X190 @ X191)))) | ~ ! [X193 : term,X192 : term] : (($true != ((X189 @ X192))) | ($true = ((X189 @ (ap @ X193 @ X192)))) | ($true != ((X189 @ X193)))))) & ((! [X243 : (subst > term > subst > $o)] : ~ ! [X244 : (term > $o)] : ~ ! [X245 : term] : (((X243 @ id @ X245 @ id)) = ((X244 @ X245))) => (! [X246 : term,X247 : (term > $o)] : (~ ! [X248 : term] : (($true != ((var @ X248))) | ($true = ((X247 @ X248)))) | ($true = ((X247 @ X246))) | ~ ! [X249 : term] : (~ ! [X250 : term] : ((((X247 @ (sub @ X249 @ (push @ X250 @ id)))) = $true) | ($true != ((X247 @ X250)))) | ($true = ((X247 @ (lam @ X249))))) | ~ ! [X252 : term,X251 : term] : (($true != ((X247 @ X252))) | ($true = ((X247 @ (ap @ X251 @ X252)))) | (((X247 @ X251)) != $true))) => (! [X253 : term] : (((sub @ X253 @ id)) = X253) => (! [X255 : (subst > term > subst > $o),X254 : term,X256 : (term > $o)] : ((((X256 @ (lam @ X254))) = $true) | ~ ! [X258 : (subst > term > term)] : (~ ! [X261 : subst,X259 : term,X260 : subst] : (((X258 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260))) = ((sub @ (X258 @ X261 @ X259) @ X260))) | (((X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) = $true) | ~ ! [X262 : term] : (($true != ((X255 @ id @ X262 @ id))) | ($true = ((X255 @ id @ (X258 @ id @ X262) @ id))))) | ~ ! [X263 : term] : (((X256 @ X263)) = ((X255 @ id @ X263 @ id))) | ~ ! [X257 : term] : ((((X256 @ X257)) != $true) | ($true = ((X256 @ (sub @ X254 @ (push @ X257 @ id))))))) => ! [X264 : term,X265 : (subst > term > subst > $o)] : (~ ! [X268 : (subst > term > term)] : (~ ! [X272 : term,X271 : subst,X270 : subst] : (((sub @ (X268 @ X271 @ X272) @ X270)) = ((X268 @ (comp @ X271 @ X270) @ (sub @ X272 @ X270)))) | ~ ! [X269 : term] : ((((X265 @ id @ X269 @ id)) != $true) | (((X265 @ id @ (X268 @ id @ X269) @ id)) = $true)) | (((X265 @ id @ (lam @ (X268 @ sh @ one)) @ id)) = $true)) | (((X265 @ id @ X264 @ id)) = $true) | ~ ! [X267 : term,X266 : term] : ((((X265 @ id @ X266 @ id)) != $true) | (((X265 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) = $true) | ($true != ((X265 @ id @ X267 @ id))))))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (apnotvar = $true) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & (hoasinduction_lem1 = $true) & (hoasinduction_gthm = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) = ((d2term @ X161))) => (X161 = X162)) & ((axscons = $true) <=> ! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226)) & (pushprop_lem0_gthm = $true) & (induction2lem_gthm = $true) & ((laminj = $true) <=> ! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (! [X331 : term,X330 : term,X329 : (subst > term > term)] : (~ ! [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) = ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) <=> ! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126))))) & (substmonoid_gthm = $true) & ((hoasinduction_lem0_lthm = $true) <=> ! [X335 : (subst > term > subst > $o)] : ~ ! [X336 : (term > $o)] : ~ ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id)))) & ! [X97 : d_subst,X96 : d_subst] : ((((d2subst @ X97)) = ((d2subst @ X96))) => (X96 = X97)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((! [X19 : term] : (((sub @ X19 @ id)) = X19) => (! [X20 : (term > $o),X22 : term,X21 : subst] : ((((X20 @ (sub @ X22 @ X21))) = $true) | ~ ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ($true != ((var @ X23)))) | ~ ! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ~ ! [X27 : term] : (($true != ((X20 @ X27))) | (((X20 @ (sub @ X26 @ (push @ X27 @ id)))) = $true))) | ~ ! [X24 : term,X25 : term] : (($true = ((X20 @ (ap @ X24 @ X25)))) | ($true != ((X20 @ X25))) | (((X20 @ X24)) != $true))) => ! [X28 : term,X29 : (term > $o)] : (~ ! [X34 : term] : (($true != ((var @ X34))) | ($true = ((X29 @ X34)))) | ~ ! [X30 : term] : (~ ! [X31 : term] : ((((X29 @ X31)) != $true) | ($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id)))))) | ($true = ((X29 @ (lam @ X30))))) | ~ ! [X32 : term,X33 : term] : ((((X29 @ X32)) != $true) | ($true = ((X29 @ (ap @ X33 @ X32)))) | ($true != ((X29 @ X33)))) | ($true = ((X29 @ X28)))))) <=> (induction2_lthm = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X440 : (subst > term > subst > $o),X441 : term] : (~ ! [X444 : term,X443 : (subst > term > term)] : (~ ! [X451 : subst,X450 : subst,X449 : term] : (((sub @ (sub @ X444 @ (push @ X449 @ X451)) @ X450)) = ((sub @ (X443 @ X451 @ X449) @ X450))) | ~ ! [X448 : term] : ((((X440 @ id @ X448 @ id)) != $true) | ($true = ((X440 @ id @ (X443 @ id @ X448) @ id)))) | ($true = ((X440 @ id @ (lam @ (X443 @ sh @ one)) @ id))) | ~ ! [X446 : term,X447 : subst,X445 : subst] : (((X443 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X444 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445)))))) | ~ ! [X442 : term] : ((((X440 @ id @ X442 @ id)) != $true) | ($true = ((X440 @ id @ (sub @ X441 @ (push @ X442 @ id)) @ id)))) | ($true = ((X440 @ id @ (lam @ (sub @ X441 @ (push @ one @ sh))) @ id))))) & ((! [X38 : term,X37 : (term > $o)] : (($true = ((X37 @ X38))) | ~ ! [X39 : term] : (($true = ((X37 @ (lam @ X39)))) | ~ ! [X40 : term] : (($true = ((X37 @ (sub @ X39 @ (push @ X40 @ id))))) | (((X37 @ X40)) != $true))) | ~ ! [X41 : term] : (($true = ((X37 @ X41))) | ($true != ((var @ X41)))) | ~ ! [X43 : term,X42 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | (((X37 @ X43)) != $true) | (((X37 @ X42)) != $true))) => (! [X44 : term,X46 : term,X45 : (subst > term > subst > $o)] : (~ ! [X51 : term,X52 : term] : ((((X45 @ id @ X51 @ id)) != $true) | ($true != ((X45 @ id @ X52 @ id))) | ($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id)))) | (((X45 @ id @ X46 @ id)) != $true) | ~ ! [X49 : subst,X48 : subst,X47 : term,X50 : subst] : (($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48))) | (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) != $true)) | ($true = ((X45 @ id @ (ap @ X46 @ X44) @ id))) | ($true != ((X45 @ id @ X44 @ id))) | ~ ! [X53 : subst,X56 : subst,X55 : term,X54 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) != $true))) => (! [X58 : term,X57 : (subst > term > subst > $o)] : (~ ! [X60 : (subst > term > term)] : (~ ! [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) = ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63)))) | ~ ! [X61 : term] : (($true != ((X57 @ id @ X61 @ id))) | ($true = ((X57 @ id @ (X60 @ id @ X61) @ id)))) | ($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id)))) | ($true = ((X57 @ id @ (lam @ X58) @ id))) | ~ ! [X59 : term] : (($true != ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) | ~ ! [X71 : term,X72 : subst,X69 : subst,X70 : subst] : (($true != ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72))))) | ~ ! [X65 : subst,X68 : subst,X67 : subst,X66 : term] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ($true != ((X57 @ X65 @ X66 @ (comp @ X68 @ X67)))))) => ! [X74 : (subst > term > subst > $o),X73 : term] : (~ ! [X89 : subst,X88 : subst,X87 : term,X90 : subst] : ((((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) != $true) | ($true = ((X74 @ X90 @ X87 @ (comp @ X89 @ X88))))) | ~ ! [X85 : term,X86 : term] : (($true != ((X74 @ id @ X85 @ id))) | ($true != ((X74 @ id @ X86 @ id))) | (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) = $true)) | ~ ! [X78 : subst,X75 : subst,X77 : subst,X76 : term] : (($true != ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) | ($true = ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ($true = ((X74 @ id @ X73 @ id))) | ~ ! [X79 : term] : (($true != ((var @ (sub @ X79 @ id)))) | (((X74 @ id @ X79 @ id)) = $true)) | ~ ! [X80 : (subst > term > term)] : ((((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) = $true) | ~ ! [X81 : term] : (($true != ((X74 @ id @ X81 @ id))) | ($true = ((X74 @ id @ (X80 @ id @ X81) @ id)))) | ~ ! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82)))))))) <=> (hoasinduction_lthm = $true)) & (! [X220 : term] : ~ ! [X221 : (subst > term > term)] : ~ ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223)))) <=> (hoasinduction_lem3v2_f = $true)) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasapinj2_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & (hoasinduction_lem1_gthm = $true) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) <=> (apinj1 = $true)) & (termmset_gthm = $true) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & (! [X100 : (term > $o),X101 : (term > $o),X98 : subst,X99 : term] : (($true = ((X100 @ one))) | (((X101 @ X99)) != $true) | ~ ! [X102 : term] : (((X100 @ X102)) = ((X101 @ (sub @ X102 @ (push @ X99 @ X98)))))) <=> (pushprop_lem1v2 = $true)) & ((induction2 = $true) <=> ! [X507 : (term > $o),X506 : term] : (~ ! [X508 : term] : (($true != ((var @ X508))) | ($true = ((X507 @ X508)))) | ($true = ((X507 @ X506))) | ~ ! [X509 : term,X510 : term] : (($true = ((X507 @ (ap @ X510 @ X509)))) | ($true != ((X507 @ X510))) | ($true != ((X507 @ X509)))) | ~ ! [X511 : term] : (($true = ((X507 @ (lam @ X511)))) | ~ ! [X512 : term] : (($true != ((X507 @ X512))) | ($true = ((X507 @ (sub @ X511 @ (push @ X512 @ id))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X490 : (subst > term > subst > $o),X491 : term,X489 : (term > $o),X492 : term] : (($true != ((X489 @ X492))) | ~ ! [X502 : term,X500 : subst,X501 : subst,X503 : subst] : (($true != ((X490 @ X500 @ X502 @ (comp @ X501 @ X503)))) | (((X490 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) = $true)) | ~ ! [X493 : term,X494 : term] : ((((X490 @ id @ (ap @ (sub @ X494 @ id) @ X493) @ id)) = $true) | ($true != ((X490 @ id @ X493 @ id))) | (((X490 @ id @ X494 @ id)) != $true)) | ~ ! [X495 : term] : (((X489 @ X495)) = ((X490 @ id @ X495 @ id))) | (((X489 @ (ap @ X491 @ X492))) = $true) | (((X489 @ X491)) != $true) | ~ ! [X496 : subst,X499 : term,X498 : subst,X497 : subst] : (($true != ((X490 @ (comp @ X496 @ X497) @ (sub @ X499 @ X497) @ X498))) | ($true = ((X490 @ X496 @ X499 @ (comp @ X497 @ X498))))))) & ((termmset_lthm = $true) <=> (! [X273 : term] : (((sub @ X273 @ id)) = X273) => ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (! [X276 : (subst > term > subst > $o),X275 : term] : (($true = ((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id))) | ~ ! [X277 : (subst > term > term)] : (($true = ((X276 @ id @ (lam @ (X277 @ sh @ one)) @ id))) | ~ ! [X281 : term] : ((((X276 @ id @ (X277 @ id @ X281) @ id)) = $true) | ($true != ((X276 @ id @ X281 @ id)))) | ~ ! [X279 : subst,X280 : subst,X278 : term] : (((sub @ (X277 @ X279 @ X278) @ X280)) = ((X277 @ (comp @ X279 @ X280) @ (sub @ X278 @ X280))))) | ~ ! [X282 : term] : (($true = ((X276 @ id @ (sub @ X275 @ (push @ X282 @ id)) @ id))) | ($true != ((X276 @ id @ X282 @ id))))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((! [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) = X533) => ! [X536 : subst,X537 : (term > $o),X538 : (term > $o),X535 : term] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ~ ! [X539 : term] : (((X538 @ X539)) = ((X537 @ (sub @ X539 @ (push @ X535 @ X536))))))) <=> (pushprop_lem1v2_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lem3a = $true) <=> ! [X481 : (subst > term > subst > $o),X482 : term] : (~ ! [X483 : term] : (($true = ((X481 @ id @ (sub @ X482 @ (push @ X483 @ id)) @ id))) | ($true != ((X481 @ id @ X483 @ id)))) | ~ ! [X484 : (subst > term > term)] : ((((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)) = $true) | ~ ! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ($true != ((X481 @ id @ X488 @ id)))) | ~ ! [X487 : subst,X485 : subst,X486 : term] : (((sub @ (X484 @ X485 @ X486) @ X487)) = ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487))))) | ($true = ((X481 @ id @ (lam @ X482) @ id))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (lamnotap != $true) & ((pushprop_lem1_lthm = $true) <=> (! [X131 : term,X130 : subst] : (((sub @ one @ (push @ X131 @ X130))) = X131) => (! [X133 : subst,X132 : term] : (((comp @ sh @ (push @ X132 @ X133))) = X133) => ! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true))))) & (hoasapinj1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (one = ((d2term @ d_one))) & (! [X2 : term,X0 : (subst > term > subst > $o),X1 : term] : (~ ! [X11 : term,X12 : term] : (($true != ((X0 @ id @ X11 @ id))) | ($true = ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) | (((X0 @ id @ X12 @ id)) != $true)) | ($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ~ ! [X3 : term,X4 : subst,X5 : subst,X6 : subst] : (($true = ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5))) | ($true != ((X0 @ X4 @ X3 @ (comp @ X6 @ X5))))) | (((X0 @ id @ X2 @ id)) != $true) | ($true != ((X0 @ id @ X1 @ id))) | ~ ! [X10 : term,X7 : subst,X9 : subst,X8 : subst] : ((((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) != $true) | (((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) = $true))) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X121 : term] : ~ ! [X122 : (subst > term > term)] : ~ ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123)))) & ((! [X283 : (subst > term > subst > $o)] : ~ ! [X284 : (term > $o)] : ~ ! [X285 : term] : (((X283 @ id @ X285 @ id)) = ((X284 @ X285))) => (! [X287 : term,X286 : (term > $o)] : (~ ! [X292 : term,X291 : term] : ((((X286 @ X291)) != $true) | ($true != ((X286 @ X292))) | ($true = ((X286 @ (ap @ X292 @ X291))))) | ~ ! [X289 : term] : (($true = ((X286 @ (lam @ X289)))) | ~ ! [X290 : term] : ((((X286 @ X290)) != $true) | ($true = ((X286 @ (sub @ X289 @ (push @ X290 @ id))))))) | ~ ! [X288 : term] : (($true = ((X286 @ X288))) | ($true != ((var @ X288)))) | ($true = ((X286 @ X287)))) => (! [X293 : term] : (((sub @ X293 @ id)) = X293) => (! [X296 : term,X295 : (term > $o),X294 : (subst > term > subst > $o)] : (~ ! [X302 : term] : (($true = ((X295 @ (sub @ X296 @ (push @ X302 @ id))))) | ($true != ((X295 @ X302)))) | ~ ! [X297 : (subst > term > term)] : (~ ! [X298 : term] : ((((X294 @ id @ X298 @ id)) != $true) | ($true = ((X294 @ id @ (X297 @ id @ X298) @ id)))) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true) | ~ ! [X301 : subst,X299 : subst,X300 : term] : (((sub @ (X297 @ X299 @ X300) @ X301)) = ((X297 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301))))) | ~ ! [X303 : term] : (((X295 @ X303)) = ((X294 @ id @ X303 @ id))) | (((X295 @ (lam @ X296))) = $true)) => ! [X305 : term,X304 : (subst > term > subst > $o)] : (~ ! [X317 : subst,X318 : term,X316 : subst,X315 : subst] : (($true != ((X304 @ (comp @ X316 @ X315) @ (sub @ X318 @ X315) @ X317))) | ($true = ((X304 @ X316 @ X318 @ (comp @ X315 @ X317))))) | ($true = ((X304 @ id @ X305 @ id))) | ~ ! [X319 : term] : (($true = ((X304 @ id @ X319 @ id))) | (((var @ (sub @ X319 @ id))) != $true)) | ~ ! [X310 : (subst > term > term)] : (~ ! [X314 : term] : (($true != ((X304 @ id @ X314 @ id))) | (((X304 @ id @ (X310 @ id @ X314) @ id)) = $true)) | ~ ! [X312 : term,X313 : subst,X311 : subst] : (((X310 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))) = ((sub @ (X310 @ X311 @ X312) @ X313))) | ($true = ((X304 @ id @ (lam @ (X310 @ sh @ one)) @ id)))) | ~ ! [X307 : subst,X308 : subst,X306 : subst,X309 : term] : ((((X304 @ X307 @ X309 @ (comp @ X308 @ X306))) != $true) | ($true = ((X304 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306)))) | ~ ! [X320 : term,X321 : term] : (($true != ((X304 @ id @ X320 @ id))) | ($true = ((X304 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id))) | (((X304 @ id @ X321 @ id)) != $true))))))) <=> (hoasinduction_lthm_3 = $true)) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & ((! [X452 : term] : (((sub @ X452 @ id)) = X452) => (! [X453 : term,X454 : (subst > term > subst > $o)] : (($true = ((X454 @ id @ (lam @ (sub @ X453 @ (push @ one @ sh))) @ id))) | ~ ! [X455 : (subst > term > term)] : (~ ! [X456 : term] : ((((X454 @ id @ X456 @ id)) != $true) | (((X454 @ id @ (X455 @ id @ X456) @ id)) = $true)) | ($true = ((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id))) | ~ ! [X459 : subst,X458 : subst,X457 : term] : (((sub @ (X455 @ X459 @ X457) @ X458)) = ((X455 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458))))) | ~ ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | (((X454 @ id @ X460 @ id)) != $true))) => ! [X461 : (subst > term > subst > $o),X462 : term] : (~ ! [X476 : term] : ((((X461 @ id @ (sub @ X462 @ (push @ X476 @ id)) @ id)) = $true) | (((X461 @ id @ X476 @ id)) != $true)) | ~ ! [X468 : term,X471 : subst,X470 : subst,X469 : subst] : ((((X461 @ X471 @ X468 @ (comp @ X470 @ X469))) != $true) | (((X461 @ (comp @ X471 @ X470) @ (sub @ X468 @ X470) @ X469)) = $true)) | (((X461 @ id @ (lam @ X462) @ id)) = $true) | ~ ! [X475 : term,X472 : subst,X473 : subst,X474 : subst] : (($true = ((X461 @ X474 @ X475 @ (comp @ X473 @ X472)))) | ($true != ((X461 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473) @ X472)))) | ~ ! [X463 : (subst > term > term)] : (~ ! [X467 : subst,X466 : subst,X465 : term] : (((sub @ (X463 @ X467 @ X465) @ X466)) = ((X463 @ (comp @ X467 @ X466) @ (sub @ X465 @ X466)))) | (((X461 @ id @ (lam @ (X463 @ sh @ one)) @ id)) = $true) | ~ ! [X464 : term] : (($true = ((X461 @ id @ (X463 @ id @ X464) @ id))) | ($true != ((X461 @ id @ X464 @ id)))))))) <=> (hoasinduction_lem3_lthm = $true)) & (axabs = $true) & ((substmonoid_lthm = $true) <=> (! [X322 : subst] : (((comp @ id @ X322)) = X322) => (! [X323 : subst] : (((comp @ X323 @ id)) = X323) => (! [X324 : subst] : (((comp @ id @ X324)) = X324) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325))))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X144 : term] : (((sub @ X144 @ id)) = X144) => (! [X145 : (subst > term > subst > $o),X146 : term] : (~ ! [X152 : term] : ((((X145 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) = $true) | ($true != ((X145 @ id @ X152 @ id)))) | ~ ! [X147 : (subst > term > term)] : (~ ! [X151 : term] : (($true != ((X145 @ id @ X151 @ id))) | ($true = ((X145 @ id @ (X147 @ id @ X151) @ id)))) | (((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id)) = $true) | ~ ! [X149 : subst,X150 : subst,X148 : term] : (((X147 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) = ((sub @ (X147 @ X150 @ X148) @ X149)))) | ($true = ((X145 @ id @ (lam @ (sub @ X146 @ (push @ one @ sh))) @ id)))) => ! [X154 : term,X153 : (subst > term > subst > $o)] : (($true = ((X153 @ id @ (lam @ X154) @ id))) | ~ ! [X156 : (subst > term > term)] : (($true = ((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id))) | ~ ! [X159 : term,X160 : subst,X158 : subst] : (((sub @ (X156 @ X160 @ X159) @ X158)) = ((X156 @ (comp @ X160 @ X158) @ (sub @ X159 @ X158)))) | ~ ! [X157 : term] : ((((X153 @ id @ (X156 @ id @ X157) @ id)) = $true) | ($true != ((X153 @ id @ X157 @ id))))) | ~ ! [X155 : term] : (($true = ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id))) | ($true != ((X153 @ id @ X155 @ id)))))))) & ((! [X210 : term,X208 : term,X211 : term,X209 : term] : ((X208 = X210) | (((ap @ X209 @ X210)) != ((ap @ X211 @ X208)))) => ! [X213 : term,X212 : term,X215 : term,X214 : term] : ((X212 = X213) | (((ap @ (sub @ X214 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X213))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X203 : term] : ~ ! [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) != ((X204 @ sh @ one)))) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & ((hoasapinj1_lthm = $true) <=> (! [X426 : term] : (((sub @ X426 @ id)) = X426) => (! [X428 : term,X429 : term,X427 : term,X430 : term] : ((((ap @ X429 @ X430)) != ((ap @ X428 @ X427))) | (X428 = X429)) => ! [X433 : term,X431 : term,X434 : term,X432 : term] : ((X432 = X433) | (((ap @ (sub @ X433 @ id) @ X434)) != ((ap @ (sub @ X432 @ id) @ X431))))))) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & (! [X198 : term,X197 : (term > $o)] : (~ ! [X201 : term] : (($true = ((X197 @ (lam @ X201)))) | ($true != ((X197 @ X201)))) | ~ ! [X199 : term,X200 : term] : ((((X197 @ (ap @ X199 @ X200))) = $true) | ($true != ((X197 @ X199))) | ($true != ((X197 @ X200)))) | ~ ! [X202 : term] : ((((var @ X202)) != $true) | ($true = ((X197 @ X202)))) | (((X197 @ X198)) = $true)) <=> (induction = $true)) & (pushprop_gthm = $true) & (! [X339 : term,X338 : (subst > term > subst > $o)] : (~ ! [X346 : term,X345 : term] : (($true = ((X338 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id))) | ($true != ((X338 @ id @ X346 @ id))) | (((X338 @ id @ X345 @ id)) != $true)) | ($true = ((X338 @ id @ X339 @ id))) | ~ ! [X340 : (subst > term > term)] : (~ ! [X344 : term] : ((((X338 @ id @ (X340 @ id @ X344) @ id)) = $true) | ($true != ((X338 @ id @ X344 @ id)))) | ($true = ((X338 @ id @ (lam @ (X340 @ sh @ one)) @ id))) | ~ ! [X341 : subst,X343 : subst,X342 : term] : (((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343))) = ((sub @ (X340 @ X341 @ X342) @ X343))))) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (! [X366 : term,X368 : subst,X367 : (subst > term > term),X365 : (subst > term > term)] : ((((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | ~ ! [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) = ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | ~ ! [X374 : term,X372 : subst,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X365 @ X372 @ X374) @ X373))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one))))) <=> (hoaslaminj = $true)) & (! [X92 : (term > $o),X93 : term,X91 : subst] : ~ ! [X94 : (term > $o)] : ~ ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) <=> (pushprop_lem0_lthm = $true)) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (lamnotvar = $true) & (! [X438 : term] : ~ ! [X439 : (subst > term > term)] : (((X439 @ sh @ one)) != ((sub @ X438 @ (push @ one @ sh)))) <=> (hoasinduction_lem3b = $true)) & (axapp = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) <=> ! [X164 : (subst > term > subst > $o),X165 : term] : (($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))) | ~ ! [X167 : (subst > term > term)] : (($true = ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id))) | ~ ! [X169 : term,X168 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X169) @ X168)) = ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)))) | ~ ! [X171 : term] : ((((X164 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X164 @ id @ X171 @ id)) != $true))) | ~ ! [X166 : term] : ((((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) = $true) | ($true != ((X164 @ id @ X166 @ id)))))) & (pushprop_lem1v2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218))))) & (! [X140 : term,X141 : subst,X139 : (term > $o)] : ~ ! [X142 : (term > $o)] : ~ ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141))))) <=> (pushprop_lem0 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm = $true) & (axvarshift = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X174 : term] : ~ ! [X175 : (subst > term > term)] : ~ ! [X177 : subst,X176 : term] : (((sub @ X174 @ (push @ X176 @ X177))) = ((X175 @ X177 @ X176))) => (! [X178 : term] : (((sub @ X178 @ id)) = X178) => ! [X179 : (subst > term > subst > $o),X181 : (term > $o),X180 : term] : (~ ! [X183 : (subst > term > term)] : ((((X179 @ id @ (lam @ (X183 @ sh @ one)) @ id)) = $true) | ~ ! [X187 : term] : (($true != ((X179 @ id @ X187 @ id))) | (((X179 @ id @ (X183 @ id @ X187) @ id)) = $true)) | ~ ! [X186 : subst,X185 : term,X184 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) = ((sub @ (X183 @ X186 @ X185) @ X184)))) | (((X181 @ (lam @ X180))) = $true) | ~ ! [X188 : term] : (((X181 @ X188)) = ((X179 @ id @ X188 @ id))) | ~ ! [X182 : term] : (($true = ((X181 @ (sub @ X180 @ (push @ X182 @ id))))) | (((X181 @ X182)) != $true)))))) & (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) <=> (axshiftcons = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & ((hoasinduction = $true) <=> ! [X348 : (subst > term > subst > $o),X347 : term] : (~ ! [X362 : term,X363 : term] : ((((X348 @ id @ X362 @ id)) != $true) | ($true = ((X348 @ id @ (ap @ (sub @ X363 @ id) @ X362) @ id))) | (((X348 @ id @ X363 @ id)) != $true)) | ~ ! [X355 : subst,X356 : term,X357 : subst,X354 : subst] : (($true = ((X348 @ X357 @ X356 @ (comp @ X354 @ X355)))) | ($true != ((X348 @ (comp @ X357 @ X354) @ (sub @ X356 @ X354) @ X355)))) | ~ ! [X358 : subst,X359 : subst,X361 : subst,X360 : term] : (($true != ((X348 @ X359 @ X360 @ (comp @ X361 @ X358)))) | (((X348 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361) @ X358)) = $true)) | ($true = ((X348 @ id @ X347 @ id))) | ~ ! [X349 : (subst > term > term)] : (($true = ((X348 @ id @ (lam @ (X349 @ sh @ one)) @ id))) | ~ ! [X350 : subst,X351 : term,X352 : subst] : (((X349 @ (comp @ X350 @ X352) @ (sub @ X351 @ X352))) = ((sub @ (X349 @ X350 @ X351) @ X352))) | ~ ! [X353 : term] : (($true = ((X348 @ id @ (X349 @ id @ X353) @ id))) | (((X348 @ id @ X353 @ id)) != $true))) | ~ ! [X364 : term] : (($true = ((X348 @ id @ X364 @ id))) | (((var @ (sub @ X364 @ id))) != $true)))) & (hoasinduction_lem3a_gthm = $true) & (pushprop = $true) & ((hoasinduction_lem3 = $true) <=> ! [X228 : (subst > term > subst > $o),X227 : term] : (~ ! [X239 : subst,X242 : term,X241 : subst,X240 : subst] : (($true != ((X228 @ (comp @ X240 @ X239) @ (sub @ X242 @ X239) @ X241))) | ($true = ((X228 @ X240 @ X242 @ (comp @ X239 @ X241))))) | ~ ! [X234 : term] : (($true = ((X228 @ id @ (sub @ X227 @ (push @ X234 @ id)) @ id))) | ($true != ((X228 @ id @ X234 @ id)))) | ~ ! [X235 : subst,X236 : subst,X238 : subst,X237 : term] : ((((X228 @ X238 @ X237 @ (comp @ X236 @ X235))) != $true) | (((X228 @ (comp @ X238 @ X236) @ (sub @ X237 @ X236) @ X235)) = $true)) | ($true = ((X228 @ id @ (lam @ X227) @ id))) | ~ ! [X229 : (subst > term > term)] : (~ ! [X230 : term] : (($true != ((X228 @ id @ X230 @ id))) | ($true = ((X228 @ id @ (X229 @ id @ X230) @ id)))) | ~ ! [X231 : subst,X233 : term,X232 : subst] : (((sub @ (X229 @ X231 @ X233) @ X232)) = ((X229 @ (comp @ X231 @ X232) @ (sub @ X233 @ X232)))) | ($true = ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id)))))) & (((var @ (d2term @ d_one))) != $true) & ((substmonoid = $true) <=> (! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504))) & (pushprop_lem1_gthm = $true) & (axmap = $true) & ((hoaslaminj_lthm = $true) <=> (! [X106 : term,X105 : subst] : (((sub @ one @ (push @ X106 @ X105))) = X106) => (! [X108 : term,X107 : subst] : (((comp @ sh @ (push @ X108 @ X107))) = X107) => (! [X110 : term,X109 : term] : ((X109 = X110) | (((lam @ X110)) != ((lam @ X109)))) => ! [X111 : term,X113 : subst,X114 : (subst > term > term),X112 : (subst > term > term)] : ((((lam @ (X114 @ sh @ one))) != ((lam @ (X112 @ sh @ one)))) | (((X114 @ X113 @ X111)) = ((X112 @ X113 @ X111))) | ~ ! [X115 : subst,X116 : subst,X117 : term] : (((sub @ (X112 @ X115 @ X117) @ X116)) = ((X112 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116)))) | ~ ! [X119 : term,X120 : subst,X118 : subst] : (((X114 @ (comp @ X118 @ X120) @ (sub @ X119 @ X120))) = ((sub @ (X114 @ X118 @ X119) @ X120)))))))) & (axclos = $true) & (axassoc = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X514 : term] : (((sub @ X514 @ id)) = X514) => ! [X516 : (subst > term > subst > $o),X515 : (term > $o),X517 : term] : (~ ! [X530 : subst,X529 : term,X528 : subst,X531 : subst] : (($true != ((X516 @ X531 @ X529 @ (comp @ X528 @ X530)))) | ($true = ((X516 @ (comp @ X531 @ X528) @ (sub @ X529 @ X528) @ X530)))) | (((X515 @ (lam @ X517))) = $true) | ~ ! [X523 : (subst > term > term)] : (~ ! [X525 : subst,X526 : term,X524 : subst] : (((X523 @ (comp @ X524 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X524 @ X526) @ X525))) | (((X516 @ id @ (lam @ (X523 @ sh @ one)) @ id)) = $true) | ~ ! [X527 : term] : (($true = ((X516 @ id @ (X523 @ id @ X527) @ id))) | ($true != ((X516 @ id @ X527 @ id))))) | ~ ! [X532 : term] : (((X515 @ X532)) = ((X516 @ id @ X532 @ id))) | ~ ! [X518 : subst,X519 : term,X521 : subst,X520 : subst] : ((((X516 @ X521 @ X519 @ (comp @ X520 @ X518))) = $true) | ($true != ((X516 @ (comp @ X521 @ X520) @ (sub @ X519 @ X520) @ X518)))) | ~ ! [X522 : term] : (($true = ((X515 @ (sub @ X517 @ (push @ X522 @ id))))) | (((X515 @ X522)) != $true))))) & (hoaslamnotvar = $true) & ! [X103 : d_subst] : (d_id = X103) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) <=> (axvarid = $true)) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) <=> (shinj = $true)) & ((induction2lem_lthm = $true) <=> (! [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) = X408) => (! [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) = X409) => (! [X411 : subst] : (((comp @ X411 @ id)) = X411) => (! [X412 : (term > $o),X413 : term] : (~ ! [X414 : term] : (($true = ((X412 @ X414))) | ($true != ((var @ X414)))) | ($true = ((X412 @ X413))) | ~ ! [X416 : term,X415 : term] : (($true != ((X412 @ X416))) | (((X412 @ X415)) != $true) | (((X412 @ (ap @ X415 @ X416))) = $true)) | ~ ! [X417 : term] : (($true = ((X412 @ (lam @ X417)))) | (((X412 @ X417)) != $true))) => ! [X418 : (term > $o),X419 : subst,X420 : term] : (($true = ((X418 @ (sub @ X420 @ X419)))) | ~ ! [X425 : term,X424 : term] : ((((X418 @ X425)) != $true) | ($true = ((X418 @ (ap @ X425 @ X424)))) | ($true != ((X418 @ X424)))) | ~ ! [X423 : term] : (($true = ((X418 @ (sub @ X423 @ X419)))) | (((var @ X423)) != $true)) | ~ ! [X421 : term] : (~ ! [X422 : term] : (($true != ((X418 @ X422))) | ($true = ((X418 @ (sub @ X421 @ (push @ X422 @ id)))))) | (((X418 @ (lam @ X421))) = $true)))))))) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) <=> (termmset = $true)) & (((d2subst @ d_id)) = sh) & ((hoasinduction_lem0 = $true) <=> ! [X435 : (subst > term > subst > $o)] : ~ ! [X436 : (term > $o)] : ~ ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))))),
% 3.49/0.96 inference(flattening,[],[f9])).
% 3.49/0.96 thf(f11,plain,(
% 3.49/0.96 (! [X326 : subst] : (((comp @ X326 @ id)) = X326) <=> (axidr = $true)) & (hoasinduction_lem2_gthm = $true) & (hoasapnotvar = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axidl = $true) <=> ! [X104 : subst] : (((comp @ id @ X104)) = X104)) & (ulamvarsh = $true) & (hoasinduction_lem1v2_gthm = $true) & (! [X375 : (subst > term > subst > $o),X377 : (term > $o),X376 : term] : (? [X378 : term] : (((X375 @ id @ X378 @ id)) != ((X377 @ X378))) | ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true = ((X375 @ id @ (X379 @ id @ X380) @ id))) | (((X375 @ id @ X380 @ id)) != $true)) & ($true != ((X375 @ id @ (lam @ (X379 @ sh @ one)) @ id))) & ! [X381 : subst,X383 : term,X382 : subst] : (((X379 @ (comp @ X382 @ X381) @ (sub @ X383 @ X381))) = ((sub @ (X379 @ X382 @ X383) @ X381)))) | ? [X384 : term] : (($true = ((X377 @ X384))) & ($true != ((X377 @ (sub @ X376 @ (push @ X384 @ id)))))) | (((X377 @ (lam @ X376))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (hoasinduction_lem3_gthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X386 : (term > $o),X385 : (subst > term > subst > $o),X387 : term] : ((((X386 @ (lam @ X387))) = $true) | ? [X389 : subst,X391 : term,X390 : subst,X388 : subst] : ((((X385 @ X389 @ X391 @ (comp @ X388 @ X390))) = $true) & ($true != ((X385 @ (comp @ X389 @ X388) @ (sub @ X391 @ X388) @ X390)))) | ? [X392 : term] : ((((X386 @ (sub @ X387 @ (push @ X392 @ id)))) != $true) & ($true = ((X386 @ X392)))) | ? [X393 : term] : (((X385 @ id @ X393 @ id)) != ((X386 @ X393))) | ? [X397 : subst,X395 : subst,X396 : subst,X394 : term] : (($true != ((X385 @ X397 @ X394 @ (comp @ X395 @ X396)))) & ($true = ((X385 @ (comp @ X397 @ X395) @ (sub @ X394 @ X395) @ X396)))) | ? [X398 : (subst > term > term)] : (! [X399 : term] : (($true != ((X385 @ id @ X399 @ id))) | (((X385 @ id @ (X398 @ id @ X399) @ id)) = $true)) & ($true != ((X385 @ id @ (lam @ (X398 @ sh @ one)) @ id))) & ! [X401 : term,X402 : subst,X400 : subst] : (((sub @ (X398 @ X402 @ X401) @ X400)) = ((X398 @ (comp @ X402 @ X400) @ (sub @ X401 @ X400))))))) & (! [X189 : (term > $o),X190 : term,X191 : subst] : (? [X192 : term,X193 : term] : (($true = ((X189 @ X192))) & ($true = ((X189 @ X193))) & ($true != ((X189 @ (ap @ X193 @ X192))))) | ? [X194 : term] : (! [X195 : term] : (($true != ((X189 @ X195))) | ($true = ((X189 @ (sub @ X194 @ (push @ X195 @ id)))))) & ($true != ((X189 @ (lam @ X194))))) | ($true = ((X189 @ (sub @ X190 @ X191)))) | ? [X196 : term] : (($true = ((var @ X196))) & ($true != ((X189 @ (sub @ X196 @ X191)))))) <=> (induction2lem = $true)) & (((((! [X265 : (subst > term > subst > $o),X264 : term] : (? [X266 : term,X267 : term] : ((((X265 @ id @ X266 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & ($true = ((X265 @ id @ X267 @ id)))) | (((X265 @ id @ X264 @ id)) = $true) | ? [X268 : (subst > term > term)] : (! [X272 : term,X271 : subst,X270 : subst] : (((sub @ (X268 @ X271 @ X272) @ X270)) = ((X268 @ (comp @ X271 @ X270) @ (sub @ X272 @ X270)))) & ! [X269 : term] : ((((X265 @ id @ X269 @ id)) != $true) | (((X265 @ id @ (X268 @ id @ X269) @ id)) = $true)) & (((X265 @ id @ (lam @ (X268 @ sh @ one)) @ id)) != $true))) | ? [X256 : (term > $o),X254 : term,X255 : (subst > term > subst > $o)] : ((((X256 @ (lam @ X254))) != $true) & ! [X258 : (subst > term > term)] : (? [X262 : term] : (($true != ((X255 @ id @ (X258 @ id @ X262) @ id))) & ($true = ((X255 @ id @ X262 @ id)))) | ? [X261 : subst,X259 : term,X260 : subst] : (((X258 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260))) != ((sub @ (X258 @ X261 @ X259) @ X260))) | (((X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) = $true)) & ! [X263 : term] : (((X256 @ X263)) = ((X255 @ id @ X263 @ id))) & ! [X257 : term] : ((((X256 @ X257)) != $true) | ($true = ((X256 @ (sub @ X254 @ (push @ X257 @ id)))))))) | ? [X253 : term] : (((sub @ X253 @ id)) != X253)) | ? [X247 : (term > $o),X246 : term] : (! [X249 : term] : (? [X250 : term] : ((((X247 @ (sub @ X249 @ (push @ X250 @ id)))) != $true) & ($true = ((X247 @ X250)))) | ($true = ((X247 @ (lam @ X249))))) & ($true != ((X247 @ X246))) & ! [X252 : term,X251 : term] : (($true != ((X247 @ X252))) | ($true = ((X247 @ (ap @ X251 @ X252)))) | (((X247 @ X251)) != $true)) & ! [X248 : term] : (($true != ((var @ X248))) | ($true = ((X247 @ X248)))))) | ? [X243 : (subst > term > subst > $o)] : ! [X244 : (term > $o)] : ? [X245 : term] : (((X243 @ id @ X245 @ id)) != ((X244 @ X245)))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (apnotvar = $true) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & (hoasinduction_lem1 = $true) & (hoasinduction_gthm = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) != ((d2term @ X161))) | (X161 = X162)) & ((axscons = $true) <=> ! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226)) & (pushprop_lem0_gthm = $true) & (induction2lem_gthm = $true) & ((laminj = $true) <=> ! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224))))) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (! [X330 : term,X331 : term,X329 : (subst > term > term)] : (? [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) != ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) <=> (hoaslamnotap = $true)) & (pushprop_lem3v2 = $true) & ((pushprop_lem1 = $true) <=> ! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126))))) & (substmonoid_gthm = $true) & (! [X335 : (subst > term > subst > $o)] : ? [X336 : (term > $o)] : ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & ! [X96 : d_subst,X97 : d_subst] : ((X96 = X97) | (((d2subst @ X97)) != ((d2subst @ X96)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((! [X29 : (term > $o),X28 : term] : (? [X33 : term,X32 : term] : (($true != ((X29 @ (ap @ X33 @ X32)))) & (((X29 @ X32)) = $true) & ($true = ((X29 @ X33)))) | ? [X30 : term] : (($true != ((X29 @ (lam @ X30)))) & ! [X31 : term] : ((((X29 @ X31)) != $true) | ($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id))))))) | ? [X34 : term] : (($true != ((X29 @ X34))) & ($true = ((var @ X34)))) | ($true = ((X29 @ X28)))) | ? [X21 : subst,X22 : term,X20 : (term > $o)] : (! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ? [X27 : term] : ((((X20 @ (sub @ X26 @ (push @ X27 @ id)))) != $true) & ($true = ((X20 @ X27))))) & (((X20 @ (sub @ X22 @ X21))) != $true) & ! [X24 : term,X25 : term] : (($true = ((X20 @ (ap @ X24 @ X25)))) | ($true != ((X20 @ X25))) | (((X20 @ X24)) != $true)) & ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ($true != ((var @ X23)))))) | ? [X19 : term] : (((sub @ X19 @ id)) != X19)) <=> (induction2_lthm = $true)) & (! [X440 : (subst > term > subst > $o),X441 : term] : (($true = ((X440 @ id @ (lam @ (sub @ X441 @ (push @ one @ sh))) @ id))) | ? [X443 : (subst > term > term),X444 : term] : (! [X446 : term,X447 : subst,X445 : subst] : (((X443 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X444 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ! [X451 : subst,X450 : subst,X449 : term] : (((sub @ (sub @ X444 @ (push @ X449 @ X451)) @ X450)) = ((sub @ (X443 @ X451 @ X449) @ X450))) & ! [X448 : term] : ((((X440 @ id @ X448 @ id)) != $true) | ($true = ((X440 @ id @ (X443 @ id @ X448) @ id)))) & ($true != ((X440 @ id @ (lam @ (X443 @ sh @ one)) @ id)))) | ? [X442 : term] : ((((X440 @ id @ X442 @ id)) = $true) & ($true != ((X440 @ id @ (sub @ X441 @ (push @ X442 @ id)) @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((((! [X73 : term,X74 : (subst > term > subst > $o)] : (? [X86 : term,X85 : term] : (($true = ((X74 @ id @ X86 @ id))) & ($true = ((X74 @ id @ X85 @ id))) & (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) != $true)) | ? [X77 : subst,X76 : term,X75 : subst,X78 : subst] : (($true = ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) & ($true != ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ? [X80 : (subst > term > term)] : (! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82))) & ! [X81 : term] : (($true != ((X74 @ id @ X81 @ id))) | ($true = ((X74 @ id @ (X80 @ id @ X81) @ id)))) & (((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) != $true)) | ($true = ((X74 @ id @ X73 @ id))) | ? [X79 : term] : ((((X74 @ id @ X79 @ id)) != $true) & ($true = ((var @ (sub @ X79 @ id))))) | ? [X90 : subst,X88 : subst,X87 : term,X89 : subst] : (($true != ((X74 @ X90 @ X87 @ (comp @ X89 @ X88)))) & (((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) = $true))) | ? [X57 : (subst > term > subst > $o),X58 : term] : (! [X59 : term] : (($true != ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) & ($true != ((X57 @ id @ (lam @ X58) @ id))) & ! [X65 : subst,X68 : subst,X67 : subst,X66 : term] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ($true != ((X57 @ X65 @ X66 @ (comp @ X68 @ X67))))) & ! [X60 : (subst > term > term)] : (($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ? [X61 : term] : (($true != ((X57 @ id @ (X60 @ id @ X61) @ id))) & ($true = ((X57 @ id @ X61 @ id)))) | ? [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) != ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))) & ! [X71 : term,X72 : subst,X69 : subst,X70 : subst] : (($true != ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72))))))) | ? [X45 : (subst > term > subst > $o),X44 : term,X46 : term] : (($true = ((X45 @ id @ X44 @ id))) & ! [X51 : term,X52 : term] : ((((X45 @ id @ X51 @ id)) != $true) | ($true != ((X45 @ id @ X52 @ id))) | ($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id)))) & (((X45 @ id @ X46 @ id)) = $true) & ! [X49 : subst,X48 : subst,X47 : term,X50 : subst] : (($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48))) | (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) != $true)) & ! [X53 : subst,X56 : subst,X55 : term,X54 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) != $true)) & ($true != ((X45 @ id @ (ap @ X46 @ X44) @ id))))) | ? [X37 : (term > $o),X38 : term] : (! [X43 : term,X42 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | (((X37 @ X43)) != $true) | (((X37 @ X42)) != $true)) & ! [X39 : term] : (? [X40 : term] : ((((X37 @ X40)) = $true) & ($true != ((X37 @ (sub @ X39 @ (push @ X40 @ id)))))) | ($true = ((X37 @ (lam @ X39))))) & ($true != ((X37 @ X38))) & ! [X41 : term] : (($true = ((X37 @ X41))) | ($true != ((var @ X41)))))) <=> (hoasinduction_lthm = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X220 : term] : ? [X221 : (subst > term > term)] : ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223))))) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasapinj2_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & (hoasinduction_lem1_gthm = $true) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) <=> (apinj1 = $true)) & (termmset_gthm = $true) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & (! [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (? [X102 : term] : (((X100 @ X102)) != ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) | (((X101 @ X99)) != $true) | ($true = ((X100 @ one)))) <=> (pushprop_lem1v2 = $true)) & ((induction2 = $true) <=> ! [X506 : term,X507 : (term > $o)] : (($true = ((X507 @ X506))) | ? [X508 : term] : (($true != ((X507 @ X508))) & ($true = ((var @ X508)))) | ? [X510 : term,X509 : term] : (($true != ((X507 @ (ap @ X510 @ X509)))) & ($true = ((X507 @ X509))) & ($true = ((X507 @ X510)))) | ? [X511 : term] : (($true != ((X507 @ (lam @ X511)))) & ! [X512 : term] : (($true != ((X507 @ X512))) | ($true = ((X507 @ (sub @ X511 @ (push @ X512 @ id))))))))) & ((hoasinduction_lem2v2 = $true) <=> ! [X489 : (term > $o),X490 : (subst > term > subst > $o),X492 : term,X491 : term] : (? [X502 : term,X500 : subst,X501 : subst,X503 : subst] : (($true = ((X490 @ X500 @ X502 @ (comp @ X501 @ X503)))) & (((X490 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) != $true)) | (((X489 @ (ap @ X491 @ X492))) = $true) | (((X489 @ X491)) != $true) | ? [X493 : term,X494 : term] : ((((X490 @ id @ (ap @ (sub @ X494 @ id) @ X493) @ id)) != $true) & ($true = ((X490 @ id @ X493 @ id))) & (((X490 @ id @ X494 @ id)) = $true)) | ($true != ((X489 @ X492))) | ? [X495 : term] : (((X489 @ X495)) != ((X490 @ id @ X495 @ id))) | ? [X496 : subst,X498 : subst,X499 : term,X497 : subst] : (($true = ((X490 @ (comp @ X496 @ X497) @ (sub @ X499 @ X497) @ X498))) & ($true != ((X490 @ X496 @ X499 @ (comp @ X497 @ X498))))))) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X275 : term,X276 : (subst > term > subst > $o)] : (? [X277 : (subst > term > term)] : (! [X281 : term] : ((((X276 @ id @ (X277 @ id @ X281) @ id)) = $true) | ($true != ((X276 @ id @ X281 @ id)))) & ($true != ((X276 @ id @ (lam @ (X277 @ sh @ one)) @ id))) & ! [X279 : subst,X280 : subst,X278 : term] : (((sub @ (X277 @ X279 @ X278) @ X280)) = ((X277 @ (comp @ X279 @ X280) @ (sub @ X278 @ X280))))) | ($true = ((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id))) | ? [X282 : term] : (($true = ((X276 @ id @ X282 @ id))) & ($true != ((X276 @ id @ (sub @ X275 @ (push @ X282 @ id)) @ id)))))) & ((! [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ? [X539 : term] : (((X538 @ X539)) != ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) | ? [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) != X533)) <=> (pushprop_lem1v2_lthm = $true)) & (ulamvarind = $true) & ((hoasinduction_lem3a = $true) <=> ! [X481 : (subst > term > subst > $o),X482 : term] : (($true = ((X481 @ id @ (lam @ X482) @ id))) | ? [X484 : (subst > term > term)] : (! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ($true != ((X481 @ id @ X488 @ id)))) & ! [X487 : subst,X485 : subst,X486 : term] : (((sub @ (X484 @ X485 @ X486) @ X487)) = ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) & (((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)) != $true)) | ? [X483 : term] : (($true = ((X481 @ id @ X483 @ id))) & ($true != ((X481 @ id @ (sub @ X482 @ (push @ X483 @ id)) @ id)))))) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (lamnotap != $true) & ((pushprop_lem1_lthm = $true) <=> ((! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)) | ? [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) != X133)) | ? [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) != X131))) & (hoasapinj1_gthm = $true) & (hoaslamnotvar_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (one = ((d2term @ d_one))) & (! [X1 : term,X0 : (subst > term > subst > $o),X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | ? [X12 : term,X11 : term] : (($true != ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) & (((X0 @ id @ X12 @ id)) = $true) & ($true = ((X0 @ id @ X11 @ id)))) | ? [X6 : subst,X3 : term,X5 : subst,X4 : subst] : (($true != ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5))) & ($true = ((X0 @ X4 @ X3 @ (comp @ X6 @ X5))))) | ($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ($true != ((X0 @ id @ X1 @ id))) | ? [X8 : subst,X9 : subst,X10 : term,X7 : subst] : ((((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) != $true) & (((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) = $true))) <=> (hoasinduction_lem2 = $true)) & (! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (((((! [X305 : term,X304 : (subst > term > subst > $o)] : (($true = ((X304 @ id @ X305 @ id))) | ? [X319 : term] : (($true != ((X304 @ id @ X319 @ id))) & (((var @ (sub @ X319 @ id))) = $true)) | ? [X308 : subst,X309 : term,X306 : subst,X307 : subst] : (($true != ((X304 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306))) & (((X304 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true)) | ? [X317 : subst,X316 : subst,X318 : term,X315 : subst] : (($true != ((X304 @ X316 @ X318 @ (comp @ X315 @ X317)))) & ($true = ((X304 @ (comp @ X316 @ X315) @ (sub @ X318 @ X315) @ X317)))) | ? [X310 : (subst > term > term)] : (($true != ((X304 @ id @ (lam @ (X310 @ sh @ one)) @ id))) & ! [X312 : term,X313 : subst,X311 : subst] : (((X310 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))) = ((sub @ (X310 @ X311 @ X312) @ X313))) & ! [X314 : term] : (($true != ((X304 @ id @ X314 @ id))) | (((X304 @ id @ (X310 @ id @ X314) @ id)) = $true))) | ? [X320 : term,X321 : term] : ((((X304 @ id @ X321 @ id)) = $true) & ($true = ((X304 @ id @ X320 @ id))) & ($true != ((X304 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id))))) | ? [X294 : (subst > term > subst > $o),X295 : (term > $o),X296 : term] : (! [X297 : (subst > term > term)] : (? [X299 : subst,X300 : term,X301 : subst] : (((sub @ (X297 @ X299 @ X300) @ X301)) != ((X297 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301)))) | ? [X298 : term] : ((((X294 @ id @ X298 @ id)) = $true) & ($true != ((X294 @ id @ (X297 @ id @ X298) @ id)))) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)) & ! [X303 : term] : (((X295 @ X303)) = ((X294 @ id @ X303 @ id))) & ! [X302 : term] : (($true = ((X295 @ (sub @ X296 @ (push @ X302 @ id))))) | ($true != ((X295 @ X302)))) & (((X295 @ (lam @ X296))) != $true))) | ? [X293 : term] : (((sub @ X293 @ id)) != X293)) | ? [X287 : term,X286 : (term > $o)] : (! [X288 : term] : (($true = ((X286 @ X288))) | ($true != ((var @ X288)))) & ! [X292 : term,X291 : term] : ((((X286 @ X291)) != $true) | ($true != ((X286 @ X292))) | ($true = ((X286 @ (ap @ X292 @ X291))))) & ($true != ((X286 @ X287))) & ! [X289 : term] : (($true = ((X286 @ (lam @ X289)))) | ? [X290 : term] : ((((X286 @ X290)) = $true) & ($true != ((X286 @ (sub @ X289 @ (push @ X290 @ id))))))))) | ? [X283 : (subst > term > subst > $o)] : ! [X284 : (term > $o)] : ? [X285 : term] : (((X283 @ id @ X285 @ id)) != ((X284 @ X285)))) <=> (hoasinduction_lthm_3 = $true)) & (((d2subst @ d_id)) = id) & (pushprop_lem2v2 = $true) & (((! [X462 : term,X461 : (subst > term > subst > $o)] : (? [X463 : (subst > term > term)] : (! [X467 : subst,X466 : subst,X465 : term] : (((sub @ (X463 @ X467 @ X465) @ X466)) = ((X463 @ (comp @ X467 @ X466) @ (sub @ X465 @ X466)))) & ! [X464 : term] : (($true = ((X461 @ id @ (X463 @ id @ X464) @ id))) | ($true != ((X461 @ id @ X464 @ id)))) & (((X461 @ id @ (lam @ (X463 @ sh @ one)) @ id)) != $true)) | ? [X476 : term] : ((((X461 @ id @ (sub @ X462 @ (push @ X476 @ id)) @ id)) != $true) & (((X461 @ id @ X476 @ id)) = $true)) | (((X461 @ id @ (lam @ X462) @ id)) = $true) | ? [X471 : subst,X470 : subst,X469 : subst,X468 : term] : ((((X461 @ (comp @ X471 @ X470) @ (sub @ X468 @ X470) @ X469)) != $true) & (((X461 @ X471 @ X468 @ (comp @ X470 @ X469))) = $true)) | ? [X474 : subst,X472 : subst,X473 : subst,X475 : term] : (($true != ((X461 @ X474 @ X475 @ (comp @ X473 @ X472)))) & ($true = ((X461 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473) @ X472))))) | ? [X454 : (subst > term > subst > $o),X453 : term] : (! [X455 : (subst > term > term)] : (? [X458 : subst,X459 : subst,X457 : term] : (((sub @ (X455 @ X459 @ X457) @ X458)) != ((X455 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458)))) | ? [X456 : term] : ((((X454 @ id @ X456 @ id)) = $true) & (((X454 @ id @ (X455 @ id @ X456) @ id)) != $true)) | ($true = ((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)))) & ($true != ((X454 @ id @ (lam @ (sub @ X453 @ (push @ one @ sh))) @ id))) & ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | (((X454 @ id @ X460 @ id)) != $true)))) | ? [X452 : term] : (((sub @ X452 @ id)) != X452)) <=> (hoasinduction_lem3_lthm = $true)) & (axabs = $true) & ((substmonoid_lthm = $true) <=> (((! [X324 : subst] : (((comp @ id @ X324)) = X324) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325)) | ? [X323 : subst] : (((comp @ X323 @ id)) != X323)) | ? [X322 : subst] : (((comp @ id @ X322)) != X322))) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lthm_orig = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) <=> (apinj2 = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X154 : term,X153 : (subst > term > subst > $o)] : (? [X156 : (subst > term > term)] : (! [X159 : term,X160 : subst,X158 : subst] : (((sub @ (X156 @ X160 @ X159) @ X158)) = ((X156 @ (comp @ X160 @ X158) @ (sub @ X159 @ X158)))) & ($true != ((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id))) & ! [X157 : term] : ((((X153 @ id @ (X156 @ id @ X157) @ id)) = $true) | ($true != ((X153 @ id @ X157 @ id))))) | ? [X155 : term] : (($true = ((X153 @ id @ X155 @ id))) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))) | ($true = ((X153 @ id @ (lam @ X154) @ id)))) | ? [X146 : term,X145 : (subst > term > subst > $o)] : (($true != ((X145 @ id @ (lam @ (sub @ X146 @ (push @ one @ sh))) @ id))) & ! [X147 : (subst > term > term)] : (? [X151 : term] : (($true != ((X145 @ id @ (X147 @ id @ X151) @ id))) & ($true = ((X145 @ id @ X151 @ id)))) | ? [X150 : subst,X148 : term,X149 : subst] : (((X147 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) != ((sub @ (X147 @ X150 @ X148) @ X149))) | (((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id)) = $true)) & ! [X152 : term] : ((((X145 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) = $true) | ($true != ((X145 @ id @ X152 @ id)))))) | ? [X144 : term] : (((sub @ X144 @ id)) != X144))) & ((? [X208 : term,X210 : term,X209 : term,X211 : term] : ((((ap @ X209 @ X210)) = ((ap @ X211 @ X208))) & (X208 != X210)) | ! [X213 : term,X212 : term,X215 : term,X214 : term] : ((X212 = X213) | (((ap @ (sub @ X214 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X213))))) <=> (hoasapinj2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one)))) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & ((hoasapinj1_lthm = $true) <=> ((! [X433 : term,X431 : term,X434 : term,X432 : term] : ((X432 = X433) | (((ap @ (sub @ X433 @ id) @ X434)) != ((ap @ (sub @ X432 @ id) @ X431)))) | ? [X427 : term,X430 : term,X429 : term,X428 : term] : ((X428 != X429) & (((ap @ X429 @ X430)) = ((ap @ X428 @ X427))))) | ? [X426 : term] : (((sub @ X426 @ id)) != X426))) & (hoaslamnotap_gthm = $true) & (hoaslamnotvar_lthm = $true) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (induction2_gthm = $true) & ((induction = $true) <=> ! [X198 : term,X197 : (term > $o)] : (? [X202 : term] : (($true != ((X197 @ X202))) & (((var @ X202)) = $true)) | (((X197 @ X198)) = $true) | ? [X201 : term] : (($true = ((X197 @ X201))) & ($true != ((X197 @ (lam @ X201))))) | ? [X200 : term,X199 : term] : (($true = ((X197 @ X200))) & (((X197 @ (ap @ X199 @ X200))) != $true) & ($true = ((X197 @ X199)))))) & (pushprop_gthm = $true) & (! [X339 : term,X338 : (subst > term > subst > $o)] : (($true = ((X338 @ id @ X339 @ id))) | ? [X346 : term,X345 : term] : ((((X338 @ id @ X345 @ id)) = $true) & ($true != ((X338 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id))) & ($true = ((X338 @ id @ X346 @ id)))) | ? [X340 : (subst > term > term)] : (! [X344 : term] : ((((X338 @ id @ (X340 @ id @ X344) @ id)) = $true) | ($true != ((X338 @ id @ X344 @ id)))) & ! [X341 : subst,X343 : subst,X342 : term] : (((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343))) = ((sub @ (X340 @ X341 @ X342) @ X343))) & ($true != ((X338 @ id @ (lam @ (X340 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoaslaminj = $true) <=> ! [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (? [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) != ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | (((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one)))) | ? [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X365 @ X372 @ X374) @ X373))))) & ((pushprop_lem0_lthm = $true) <=> ! [X92 : (term > $o),X93 : term,X91 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91)))))) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (lamnotvar = $true) & ((hoasinduction_lem3b = $true) <=> ! [X438 : term] : ? [X439 : (subst > term > term)] : (((X439 @ sh @ one)) = ((sub @ X438 @ (push @ one @ sh))))) & (axapp = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((hoasinduction_lem3aa = $true) <=> ! [X164 : (subst > term > subst > $o),X165 : term] : (? [X166 : term] : (($true = ((X164 @ id @ X166 @ id))) & (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) != $true)) | ? [X167 : (subst > term > term)] : (! [X171 : term] : ((((X164 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X164 @ id @ X171 @ id)) != $true)) & ! [X169 : term,X168 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X169) @ X168)) = ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)))) & ($true != ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id)))) | ($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))))) & (pushprop_lem1v2_gthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (hoasinduction_lem2v2_gthm = $true) & ((hoasapinj2 = $true) <=> ! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218))))) & ((pushprop_lem0 = $true) <=> ! [X139 : (term > $o),X140 : term,X141 : subst] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141)))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (pushprop_lthm = $true) & (axvarshift = $true) & (hoasapnotvar_gthm = $true) & ((hoasinduction_lem3v2a_lthm = $true) <=> ((! [X181 : (term > $o),X180 : term,X179 : (subst > term > subst > $o)] : (? [X182 : term] : (($true != ((X181 @ (sub @ X180 @ (push @ X182 @ id))))) & (((X181 @ X182)) = $true)) | ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : term,X184 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) = ((sub @ (X183 @ X186 @ X185) @ X184))) & (((X179 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true) & ! [X187 : term] : (($true != ((X179 @ id @ X187 @ id))) | (((X179 @ id @ (X183 @ id @ X187) @ id)) = $true))) | ? [X188 : term] : (((X181 @ X188)) != ((X179 @ id @ X188 @ id))) | (((X181 @ (lam @ X180))) = $true)) | ? [X178 : term] : (((sub @ X178 @ id)) != X178)) | ? [X174 : term] : ! [X175 : (subst > term > term)] : ? [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) != ((X175 @ X177 @ X176))))) & (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) <=> (axshiftcons = $true)) & (hoasinduction_lem1v2 = $true) & (hoaslaminj_gthm = $true) & (ulamvar1 != $true) & (! [X348 : (subst > term > subst > $o),X347 : term] : (($true = ((X348 @ id @ X347 @ id))) | ? [X360 : term,X361 : subst,X359 : subst,X358 : subst] : (($true = ((X348 @ X359 @ X360 @ (comp @ X361 @ X358)))) & (((X348 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361) @ X358)) != $true)) | ? [X362 : term,X363 : term] : ((((X348 @ id @ X362 @ id)) = $true) & (((X348 @ id @ X363 @ id)) = $true) & ($true != ((X348 @ id @ (ap @ (sub @ X363 @ id) @ X362) @ id)))) | ? [X349 : (subst > term > term)] : (($true != ((X348 @ id @ (lam @ (X349 @ sh @ one)) @ id))) & ! [X350 : subst,X351 : term,X352 : subst] : (((X349 @ (comp @ X350 @ X352) @ (sub @ X351 @ X352))) = ((sub @ (X349 @ X350 @ X351) @ X352))) & ! [X353 : term] : (($true = ((X348 @ id @ (X349 @ id @ X353) @ id))) | (((X348 @ id @ X353 @ id)) != $true))) | ? [X364 : term] : (($true != ((X348 @ id @ X364 @ id))) & (((var @ (sub @ X364 @ id))) = $true)) | ? [X355 : subst,X357 : subst,X354 : subst,X356 : term] : (($true != ((X348 @ X357 @ X356 @ (comp @ X354 @ X355)))) & ($true = ((X348 @ (comp @ X357 @ X354) @ (sub @ X356 @ X354) @ X355))))) <=> (hoasinduction = $true)) & (hoasinduction_lem3a_gthm = $true) & (pushprop = $true) & (! [X228 : (subst > term > subst > $o),X227 : term] : (($true = ((X228 @ id @ (lam @ X227) @ id))) | ? [X229 : (subst > term > term)] : (! [X231 : subst,X233 : term,X232 : subst] : (((sub @ (X229 @ X231 @ X233) @ X232)) = ((X229 @ (comp @ X231 @ X232) @ (sub @ X233 @ X232)))) & ! [X230 : term] : (($true != ((X228 @ id @ X230 @ id))) | ($true = ((X228 @ id @ (X229 @ id @ X230) @ id)))) & ($true != ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id)))) | ? [X241 : subst,X242 : term,X239 : subst,X240 : subst] : (($true != ((X228 @ X240 @ X242 @ (comp @ X239 @ X241)))) & ($true = ((X228 @ (comp @ X240 @ X239) @ (sub @ X242 @ X239) @ X241)))) | ? [X234 : term] : (($true = ((X228 @ id @ X234 @ id))) & ($true != ((X228 @ id @ (sub @ X227 @ (push @ X234 @ id)) @ id)))) | ? [X238 : subst,X235 : subst,X236 : subst,X237 : term] : ((((X228 @ X238 @ X237 @ (comp @ X236 @ X235))) = $true) & (((X228 @ (comp @ X238 @ X236) @ (sub @ X237 @ X236) @ X235)) != $true))) <=> (hoasinduction_lem3 = $true)) & (((var @ (d2term @ d_one))) != $true) & ((substmonoid = $true) <=> (! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504))) & (pushprop_lem1_gthm = $true) & (axmap = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X112 : (subst > term > term),X114 : (subst > term > term),X111 : term,X113 : subst] : ((((X114 @ X113 @ X111)) = ((X112 @ X113 @ X111))) | ? [X119 : term,X120 : subst,X118 : subst] : (((X114 @ (comp @ X118 @ X120) @ (sub @ X119 @ X120))) != ((sub @ (X114 @ X118 @ X119) @ X120))) | ? [X116 : subst,X115 : subst,X117 : term] : (((sub @ (X112 @ X115 @ X117) @ X116)) != ((X112 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116)))) | (((lam @ (X114 @ sh @ one))) != ((lam @ (X112 @ sh @ one))))) | ? [X109 : term,X110 : term] : ((X109 != X110) & (((lam @ X110)) = ((lam @ X109))))) | ? [X108 : term,X107 : subst] : (((comp @ sh @ (push @ X108 @ X107))) != X107)) | ? [X105 : subst,X106 : term] : (((sub @ one @ (push @ X106 @ X105))) != X106))) & (axclos = $true) & (axassoc = $true) & (hoasapnotvar_lthm = $true) & ((! [X517 : term,X516 : (subst > term > subst > $o),X515 : (term > $o)] : (? [X532 : term] : (((X515 @ X532)) != ((X516 @ id @ X532 @ id))) | ? [X531 : subst,X528 : subst,X530 : subst,X529 : term] : (($true = ((X516 @ X531 @ X529 @ (comp @ X528 @ X530)))) & ($true != ((X516 @ (comp @ X531 @ X528) @ (sub @ X529 @ X528) @ X530)))) | ? [X521 : subst,X518 : subst,X520 : subst,X519 : term] : (($true = ((X516 @ (comp @ X521 @ X520) @ (sub @ X519 @ X520) @ X518))) & (((X516 @ X521 @ X519 @ (comp @ X520 @ X518))) != $true)) | ? [X523 : (subst > term > term)] : (! [X527 : term] : (($true = ((X516 @ id @ (X523 @ id @ X527) @ id))) | ($true != ((X516 @ id @ X527 @ id)))) & ! [X525 : subst,X526 : term,X524 : subst] : (((X523 @ (comp @ X524 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X524 @ X526) @ X525))) & (((X516 @ id @ (lam @ (X523 @ sh @ one)) @ id)) != $true)) | (((X515 @ (lam @ X517))) = $true) | ? [X522 : term] : (($true != ((X515 @ (sub @ X517 @ (push @ X522 @ id))))) & (((X515 @ X522)) = $true))) | ? [X514 : term] : (((sub @ X514 @ id)) != X514)) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoaslamnotvar = $true) & ! [X103 : d_subst] : (d_id = X103) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) <=> (axvarid = $true)) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) <=> (shinj = $true)) & ((induction2lem_lthm = $true) <=> ((((! [X419 : subst,X418 : (term > $o),X420 : term] : (? [X424 : term,X425 : term] : (($true = ((X418 @ X424))) & ($true != ((X418 @ (ap @ X425 @ X424)))) & (((X418 @ X425)) = $true)) | ($true = ((X418 @ (sub @ X420 @ X419)))) | ? [X423 : term] : (($true != ((X418 @ (sub @ X423 @ X419)))) & (((var @ X423)) = $true)) | ? [X421 : term] : (! [X422 : term] : (($true != ((X418 @ X422))) | ($true = ((X418 @ (sub @ X421 @ (push @ X422 @ id)))))) & (((X418 @ (lam @ X421))) != $true))) | ? [X412 : (term > $o),X413 : term] : (! [X414 : term] : (($true = ((X412 @ X414))) | ($true != ((var @ X414)))) & ! [X417 : term] : (($true = ((X412 @ (lam @ X417)))) | (((X412 @ X417)) != $true)) & ($true != ((X412 @ X413))) & ! [X416 : term,X415 : term] : (($true != ((X412 @ X416))) | (((X412 @ X415)) != $true) | (((X412 @ (ap @ X415 @ X416))) = $true)))) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411)) | ? [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) != X409)) | ? [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) != X408))) & (hoasinduction_lem1_lthm = $true) & (hoaslamnotap_lthm = $true) & (pushprop_lem2v2_gthm = $true) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) <=> (termmset = $true)) & (((d2subst @ d_id)) = sh) & (! [X435 : (subst > term > subst > $o)] : ? [X436 : (term > $o)] : ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))) <=> (hoasinduction_lem0 = $true))),
% 3.49/0.96 inference(ennf_transformation,[],[f10])).
% 3.49/0.96 thf(f12,plain,(
% 3.49/0.96 (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) <=> (axshiftcons = $true)) & (! [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (? [X102 : term] : (((X100 @ X102)) != ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) | (((X101 @ X99)) != $true) | ($true = ((X100 @ one)))) <=> (pushprop_lem1v2 = $true)) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X139 : (term > $o),X140 : term,X141 : subst] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141)))))) & ((induction2lem_lthm = $true) <=> (? [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) != X409) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411) | ! [X419 : subst,X418 : (term > $o),X420 : term] : (? [X424 : term,X425 : term] : (($true = ((X418 @ X424))) & ($true != ((X418 @ (ap @ X425 @ X424)))) & (((X418 @ X425)) = $true)) | ($true = ((X418 @ (sub @ X420 @ X419)))) | ? [X423 : term] : (($true != ((X418 @ (sub @ X423 @ X419)))) & (((var @ X423)) = $true)) | ? [X421 : term] : (! [X422 : term] : (($true != ((X418 @ X422))) | ($true = ((X418 @ (sub @ X421 @ (push @ X422 @ id)))))) & (((X418 @ (lam @ X421))) != $true))) | ? [X412 : (term > $o),X413 : term] : (! [X414 : term] : (($true = ((X412 @ X414))) | ($true != ((var @ X414)))) & ! [X417 : term] : (($true = ((X412 @ (lam @ X417)))) | (((X412 @ X417)) != $true)) & ($true != ((X412 @ X413))) & ! [X416 : term,X415 : term] : (($true != ((X412 @ X416))) | (((X412 @ X415)) != $true) | (((X412 @ (ap @ X415 @ X416))) = $true))) | ? [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) != X408))) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (! [X348 : (subst > term > subst > $o),X347 : term] : (($true = ((X348 @ id @ X347 @ id))) | ? [X360 : term,X361 : subst,X359 : subst,X358 : subst] : (($true = ((X348 @ X359 @ X360 @ (comp @ X361 @ X358)))) & (((X348 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361) @ X358)) != $true)) | ? [X362 : term,X363 : term] : ((((X348 @ id @ X362 @ id)) = $true) & (((X348 @ id @ X363 @ id)) = $true) & ($true != ((X348 @ id @ (ap @ (sub @ X363 @ id) @ X362) @ id)))) | ? [X349 : (subst > term > term)] : (($true != ((X348 @ id @ (lam @ (X349 @ sh @ one)) @ id))) & ! [X350 : subst,X351 : term,X352 : subst] : (((X349 @ (comp @ X350 @ X352) @ (sub @ X351 @ X352))) = ((sub @ (X349 @ X350 @ X351) @ X352))) & ! [X353 : term] : (($true = ((X348 @ id @ (X349 @ id @ X353) @ id))) | (((X348 @ id @ X353 @ id)) != $true))) | ? [X364 : term] : (($true != ((X348 @ id @ X364 @ id))) & (((var @ (sub @ X364 @ id))) = $true)) | ? [X355 : subst,X357 : subst,X354 : subst,X356 : term] : (($true != ((X348 @ X357 @ X356 @ (comp @ X354 @ X355)))) & ($true = ((X348 @ (comp @ X357 @ X354) @ (sub @ X356 @ X354) @ X355))))) <=> (hoasinduction = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (? [X454 : (subst > term > subst > $o),X453 : term] : (! [X455 : (subst > term > term)] : (? [X458 : subst,X459 : subst,X457 : term] : (((sub @ (X455 @ X459 @ X457) @ X458)) != ((X455 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458)))) | ? [X456 : term] : ((((X454 @ id @ X456 @ id)) = $true) & (((X454 @ id @ (X455 @ id @ X456) @ id)) != $true)) | ($true = ((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)))) & ($true != ((X454 @ id @ (lam @ (sub @ X453 @ (push @ one @ sh))) @ id))) & ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | (((X454 @ id @ X460 @ id)) != $true))) | ? [X452 : term] : (((sub @ X452 @ id)) != X452) | ! [X462 : term,X461 : (subst > term > subst > $o)] : (? [X463 : (subst > term > term)] : (! [X467 : subst,X466 : subst,X465 : term] : (((sub @ (X463 @ X467 @ X465) @ X466)) = ((X463 @ (comp @ X467 @ X466) @ (sub @ X465 @ X466)))) & ! [X464 : term] : (($true = ((X461 @ id @ (X463 @ id @ X464) @ id))) | ($true != ((X461 @ id @ X464 @ id)))) & (((X461 @ id @ (lam @ (X463 @ sh @ one)) @ id)) != $true)) | ? [X476 : term] : ((((X461 @ id @ (sub @ X462 @ (push @ X476 @ id)) @ id)) != $true) & (((X461 @ id @ X476 @ id)) = $true)) | (((X461 @ id @ (lam @ X462) @ id)) = $true) | ? [X471 : subst,X470 : subst,X469 : subst,X468 : term] : ((((X461 @ (comp @ X471 @ X470) @ (sub @ X468 @ X470) @ X469)) != $true) & (((X461 @ X471 @ X468 @ (comp @ X470 @ X469))) = $true)) | ? [X474 : subst,X472 : subst,X473 : subst,X475 : term] : (($true != ((X461 @ X474 @ X475 @ (comp @ X473 @ X472)))) & ($true = ((X461 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473) @ X472))))))) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X330 : term,X331 : term,X329 : (subst > term > term)] : (? [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) != ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X220 : term] : ? [X221 : (subst > term > term)] : ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223))))) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) <=> (apinj1 = $true)) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & (! [X375 : (subst > term > subst > $o),X377 : (term > $o),X376 : term] : (? [X378 : term] : (((X375 @ id @ X378 @ id)) != ((X377 @ X378))) | ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true = ((X375 @ id @ (X379 @ id @ X380) @ id))) | (((X375 @ id @ X380 @ id)) != $true)) & ($true != ((X375 @ id @ (lam @ (X379 @ sh @ one)) @ id))) & ! [X381 : subst,X383 : term,X382 : subst] : (((X379 @ (comp @ X382 @ X381) @ (sub @ X383 @ X381))) = ((sub @ (X379 @ X382 @ X383) @ X381)))) | ? [X384 : term] : (($true = ((X377 @ X384))) & ($true != ((X377 @ (sub @ X376 @ (push @ X384 @ id)))))) | (((X377 @ (lam @ X376))) = $true)) <=> (hoasinduction_lem3v2a = $true)) & (! [X339 : term,X338 : (subst > term > subst > $o)] : (($true = ((X338 @ id @ X339 @ id))) | ? [X346 : term,X345 : term] : ((((X338 @ id @ X345 @ id)) = $true) & ($true != ((X338 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id))) & ($true = ((X338 @ id @ X346 @ id)))) | ? [X340 : (subst > term > term)] : (! [X344 : term] : ((((X338 @ id @ (X340 @ id @ X344) @ id)) = $true) | ($true != ((X338 @ id @ X344 @ id)))) & ! [X341 : subst,X343 : subst,X342 : term] : (((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343))) = ((sub @ (X340 @ X341 @ X342) @ X343))) & ($true != ((X338 @ id @ (lam @ (X340 @ sh @ one)) @ id))))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & ((! [X433 : term,X431 : term,X434 : term,X432 : term] : ((X432 = X433) | (((ap @ (sub @ X433 @ id) @ X434)) != ((ap @ (sub @ X432 @ id) @ X431)))) | ? [X426 : term] : (((sub @ X426 @ id)) != X426) | ? [X427 : term,X430 : term,X429 : term,X428 : term] : ((X428 != X429) & (((ap @ X429 @ X430)) = ((ap @ X428 @ X427))))) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((? [X146 : term,X145 : (subst > term > subst > $o)] : (($true != ((X145 @ id @ (lam @ (sub @ X146 @ (push @ one @ sh))) @ id))) & ! [X147 : (subst > term > term)] : (? [X151 : term] : (($true != ((X145 @ id @ (X147 @ id @ X151) @ id))) & ($true = ((X145 @ id @ X151 @ id)))) | ? [X150 : subst,X148 : term,X149 : subst] : (((X147 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) != ((sub @ (X147 @ X150 @ X148) @ X149))) | (((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id)) = $true)) & ! [X152 : term] : ((((X145 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) = $true) | ($true != ((X145 @ id @ X152 @ id))))) | ? [X144 : term] : (((sub @ X144 @ id)) != X144) | ! [X154 : term,X153 : (subst > term > subst > $o)] : (? [X156 : (subst > term > term)] : (! [X159 : term,X160 : subst,X158 : subst] : (((sub @ (X156 @ X160 @ X159) @ X158)) = ((X156 @ (comp @ X160 @ X158) @ (sub @ X159 @ X158)))) & ($true != ((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id))) & ! [X157 : term] : ((((X153 @ id @ (X156 @ id @ X157) @ id)) = $true) | ($true != ((X153 @ id @ X157 @ id))))) | ? [X155 : term] : (($true = ((X153 @ id @ X155 @ id))) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))) | ($true = ((X153 @ id @ (lam @ X154) @ id))))) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ! [X481 : (subst > term > subst > $o),X482 : term] : (($true = ((X481 @ id @ (lam @ X482) @ id))) | ? [X484 : (subst > term > term)] : (! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ($true != ((X481 @ id @ X488 @ id)))) & ! [X487 : subst,X485 : subst,X486 : term] : (((sub @ (X484 @ X485 @ X486) @ X487)) = ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) & (((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)) != $true)) | ? [X483 : term] : (($true = ((X481 @ id @ X483 @ id))) & ($true != ((X481 @ id @ (sub @ X482 @ (push @ X483 @ id)) @ id)))))) & ((substmonoid_lthm = $true) <=> ((! [X324 : subst] : (((comp @ id @ X324)) = X324) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325)) | ? [X323 : subst] : (((comp @ X323 @ id)) != X323) | ? [X322 : subst] : (((comp @ id @ X322)) != X322))) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) <=> (axvarid = $true)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) <=> (shinj = $true)) & (termmset_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & ((laminj = $true) <=> ! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224))))) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X438 : term] : ? [X439 : (subst > term > term)] : (((X439 @ sh @ one)) = ((sub @ X438 @ (push @ one @ sh))))) & ((? [X208 : term,X210 : term,X209 : term,X211 : term] : ((((ap @ X209 @ X210)) = ((ap @ X211 @ X208))) & (X208 != X210)) | ! [X213 : term,X212 : term,X215 : term,X214 : term] : ((X212 = X213) | (((ap @ (sub @ X214 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X213))))) <=> (hoasapinj2_lthm = $true)) & ((induction2 = $true) <=> ! [X506 : term,X507 : (term > $o)] : (($true = ((X507 @ X506))) | ? [X508 : term] : (($true != ((X507 @ X508))) & ($true = ((var @ X508)))) | ? [X510 : term,X509 : term] : (($true != ((X507 @ (ap @ X510 @ X509)))) & ($true = ((X507 @ X509))) & ($true = ((X507 @ X510)))) | ? [X511 : term] : (($true != ((X507 @ (lam @ X511)))) & ! [X512 : term] : (($true != ((X507 @ X512))) | ($true = ((X507 @ (sub @ X511 @ (push @ X512 @ id))))))))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (! [X440 : (subst > term > subst > $o),X441 : term] : (($true = ((X440 @ id @ (lam @ (sub @ X441 @ (push @ one @ sh))) @ id))) | ? [X443 : (subst > term > term),X444 : term] : (! [X446 : term,X447 : subst,X445 : subst] : (((X443 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X444 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ! [X451 : subst,X450 : subst,X449 : term] : (((sub @ (sub @ X444 @ (push @ X449 @ X451)) @ X450)) = ((sub @ (X443 @ X451 @ X449) @ X450))) & ! [X448 : term] : ((((X440 @ id @ X448 @ id)) != $true) | ($true = ((X440 @ id @ (X443 @ id @ X448) @ id)))) & ($true != ((X440 @ id @ (lam @ (X443 @ sh @ one)) @ id)))) | ? [X442 : term] : ((((X440 @ id @ X442 @ id)) = $true) & ($true != ((X440 @ id @ (sub @ X441 @ (push @ X442 @ id)) @ id))))) <=> (hoasinduction_lem3aaa = $true)) & ((pushprop_lem1 = $true) <=> ! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126))))) & ((pushprop_lem0_lthm = $true) <=> ! [X92 : (term > $o),X93 : term,X91 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91)))))) & ((? [X253 : term] : (((sub @ X253 @ id)) != X253) | ? [X243 : (subst > term > subst > $o)] : ! [X244 : (term > $o)] : ? [X245 : term] : (((X243 @ id @ X245 @ id)) != ((X244 @ X245))) | ! [X265 : (subst > term > subst > $o),X264 : term] : (? [X266 : term,X267 : term] : ((((X265 @ id @ X266 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & ($true = ((X265 @ id @ X267 @ id)))) | (((X265 @ id @ X264 @ id)) = $true) | ? [X268 : (subst > term > term)] : (! [X272 : term,X271 : subst,X270 : subst] : (((sub @ (X268 @ X271 @ X272) @ X270)) = ((X268 @ (comp @ X271 @ X270) @ (sub @ X272 @ X270)))) & ! [X269 : term] : ((((X265 @ id @ X269 @ id)) != $true) | (((X265 @ id @ (X268 @ id @ X269) @ id)) = $true)) & (((X265 @ id @ (lam @ (X268 @ sh @ one)) @ id)) != $true))) | ? [X256 : (term > $o),X254 : term,X255 : (subst > term > subst > $o)] : ((((X256 @ (lam @ X254))) != $true) & ! [X258 : (subst > term > term)] : (? [X262 : term] : (($true != ((X255 @ id @ (X258 @ id @ X262) @ id))) & ($true = ((X255 @ id @ X262 @ id)))) | ? [X261 : subst,X259 : term,X260 : subst] : (((X258 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260))) != ((sub @ (X258 @ X261 @ X259) @ X260))) | (((X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) = $true)) & ! [X263 : term] : (((X256 @ X263)) = ((X255 @ id @ X263 @ id))) & ! [X257 : term] : ((((X256 @ X257)) != $true) | ($true = ((X256 @ (sub @ X254 @ (push @ X257 @ id))))))) | ? [X247 : (term > $o),X246 : term] : (! [X249 : term] : (? [X250 : term] : ((((X247 @ (sub @ X249 @ (push @ X250 @ id)))) != $true) & ($true = ((X247 @ X250)))) | ($true = ((X247 @ (lam @ X249))))) & ($true != ((X247 @ X246))) & ! [X252 : term,X251 : term] : (($true != ((X247 @ X252))) | ($true = ((X247 @ (ap @ X251 @ X252)))) | (((X247 @ X251)) != $true)) & ! [X248 : term] : (($true != ((var @ X248))) | ($true = ((X247 @ X248)))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = id) & ((! [X181 : (term > $o),X180 : term,X179 : (subst > term > subst > $o)] : (? [X182 : term] : (($true != ((X181 @ (sub @ X180 @ (push @ X182 @ id))))) & (((X181 @ X182)) = $true)) | ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : term,X184 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) = ((sub @ (X183 @ X186 @ X185) @ X184))) & (((X179 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true) & ! [X187 : term] : (($true != ((X179 @ id @ X187 @ id))) | (((X179 @ id @ (X183 @ id @ X187) @ id)) = $true))) | ? [X188 : term] : (((X181 @ X188)) != ((X179 @ id @ X188 @ id))) | (((X181 @ (lam @ X180))) = $true)) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ? [X174 : term] : ! [X175 : (subst > term > term)] : ? [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) != ((X175 @ X177 @ X176)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2subst @ d_id)) = sh) & ((? [X57 : (subst > term > subst > $o),X58 : term] : (! [X59 : term] : (($true != ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) & ($true != ((X57 @ id @ (lam @ X58) @ id))) & ! [X65 : subst,X68 : subst,X67 : subst,X66 : term] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ($true != ((X57 @ X65 @ X66 @ (comp @ X68 @ X67))))) & ! [X60 : (subst > term > term)] : (($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ? [X61 : term] : (($true != ((X57 @ id @ (X60 @ id @ X61) @ id))) & ($true = ((X57 @ id @ X61 @ id)))) | ? [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) != ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))) & ! [X71 : term,X72 : subst,X69 : subst,X70 : subst] : (($true != ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72)))))) | ! [X73 : term,X74 : (subst > term > subst > $o)] : (? [X86 : term,X85 : term] : (($true = ((X74 @ id @ X86 @ id))) & ($true = ((X74 @ id @ X85 @ id))) & (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) != $true)) | ? [X77 : subst,X76 : term,X75 : subst,X78 : subst] : (($true = ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) & ($true != ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ? [X80 : (subst > term > term)] : (! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82))) & ! [X81 : term] : (($true != ((X74 @ id @ X81 @ id))) | ($true = ((X74 @ id @ (X80 @ id @ X81) @ id)))) & (((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) != $true)) | ($true = ((X74 @ id @ X73 @ id))) | ? [X79 : term] : ((((X74 @ id @ X79 @ id)) != $true) & ($true = ((var @ (sub @ X79 @ id))))) | ? [X90 : subst,X88 : subst,X87 : term,X89 : subst] : (($true != ((X74 @ X90 @ X87 @ (comp @ X89 @ X88)))) & (((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) = $true))) | ? [X45 : (subst > term > subst > $o),X44 : term,X46 : term] : (($true = ((X45 @ id @ X44 @ id))) & ! [X51 : term,X52 : term] : ((((X45 @ id @ X51 @ id)) != $true) | ($true != ((X45 @ id @ X52 @ id))) | ($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id)))) & (((X45 @ id @ X46 @ id)) = $true) & ! [X49 : subst,X48 : subst,X47 : term,X50 : subst] : (($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48))) | (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) != $true)) & ! [X53 : subst,X56 : subst,X55 : term,X54 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) != $true)) & ($true != ((X45 @ id @ (ap @ X46 @ X44) @ id)))) | ? [X37 : (term > $o),X38 : term] : (! [X43 : term,X42 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | (((X37 @ X43)) != $true) | (((X37 @ X42)) != $true)) & ! [X39 : term] : (? [X40 : term] : ((((X37 @ X40)) = $true) & ($true != ((X37 @ (sub @ X39 @ (push @ X40 @ id)))))) | ($true = ((X37 @ (lam @ X39))))) & ($true != ((X37 @ X38))) & ! [X41 : term] : (($true = ((X37 @ X41))) | ($true != ((var @ X41)))))) <=> (hoasinduction_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((? [X109 : term,X110 : term] : ((X109 != X110) & (((lam @ X110)) = ((lam @ X109)))) | ! [X112 : (subst > term > term),X114 : (subst > term > term),X111 : term,X113 : subst] : ((((X114 @ X113 @ X111)) = ((X112 @ X113 @ X111))) | ? [X119 : term,X120 : subst,X118 : subst] : (((X114 @ (comp @ X118 @ X120) @ (sub @ X119 @ X120))) != ((sub @ (X114 @ X118 @ X119) @ X120))) | ? [X116 : subst,X115 : subst,X117 : term] : (((sub @ (X112 @ X115 @ X117) @ X116)) != ((X112 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116)))) | (((lam @ (X114 @ sh @ one))) != ((lam @ (X112 @ sh @ one))))) | ? [X108 : term,X107 : subst] : (((comp @ sh @ (push @ X108 @ X107))) != X107) | ? [X105 : subst,X106 : term] : (((sub @ one @ (push @ X106 @ X105))) != X106)) <=> (hoaslaminj_lthm = $true)) & (! [X228 : (subst > term > subst > $o),X227 : term] : (($true = ((X228 @ id @ (lam @ X227) @ id))) | ? [X229 : (subst > term > term)] : (! [X231 : subst,X233 : term,X232 : subst] : (((sub @ (X229 @ X231 @ X233) @ X232)) = ((X229 @ (comp @ X231 @ X232) @ (sub @ X233 @ X232)))) & ! [X230 : term] : (($true != ((X228 @ id @ X230 @ id))) | ($true = ((X228 @ id @ (X229 @ id @ X230) @ id)))) & ($true != ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id)))) | ? [X241 : subst,X242 : term,X239 : subst,X240 : subst] : (($true != ((X228 @ X240 @ X242 @ (comp @ X239 @ X241)))) & ($true = ((X228 @ (comp @ X240 @ X239) @ (sub @ X242 @ X239) @ X241)))) | ? [X234 : term] : (($true = ((X228 @ id @ X234 @ id))) & ($true != ((X228 @ id @ (sub @ X227 @ (push @ X234 @ id)) @ id)))) | ? [X238 : subst,X235 : subst,X236 : subst,X237 : term] : ((((X228 @ X238 @ X237 @ (comp @ X236 @ X235))) = $true) & (((X228 @ (comp @ X238 @ X236) @ (sub @ X237 @ X236) @ X235)) != $true))) <=> (hoasinduction_lem3 = $true)) & ((axidl = $true) <=> ! [X104 : subst] : (((comp @ id @ X104)) = X104)) & (axapp = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) <=> (apinj2 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((! [X517 : term,X516 : (subst > term > subst > $o),X515 : (term > $o)] : (? [X532 : term] : (((X515 @ X532)) != ((X516 @ id @ X532 @ id))) | ? [X531 : subst,X528 : subst,X530 : subst,X529 : term] : (($true = ((X516 @ X531 @ X529 @ (comp @ X528 @ X530)))) & ($true != ((X516 @ (comp @ X531 @ X528) @ (sub @ X529 @ X528) @ X530)))) | ? [X521 : subst,X518 : subst,X520 : subst,X519 : term] : (($true = ((X516 @ (comp @ X521 @ X520) @ (sub @ X519 @ X520) @ X518))) & (((X516 @ X521 @ X519 @ (comp @ X520 @ X518))) != $true)) | ? [X523 : (subst > term > term)] : (! [X527 : term] : (($true = ((X516 @ id @ (X523 @ id @ X527) @ id))) | ($true != ((X516 @ id @ X527 @ id)))) & ! [X525 : subst,X526 : term,X524 : subst] : (((X523 @ (comp @ X524 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X524 @ X526) @ X525))) & (((X516 @ id @ (lam @ (X523 @ sh @ one)) @ id)) != $true)) | (((X515 @ (lam @ X517))) = $true) | ? [X522 : term] : (($true != ((X515 @ (sub @ X517 @ (push @ X522 @ id))))) & (((X515 @ X522)) = $true))) | ? [X514 : term] : (((sub @ X514 @ id)) != X514)) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axscons = $true) <=> ! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226)) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ! [X275 : term,X276 : (subst > term > subst > $o)] : (? [X277 : (subst > term > term)] : (! [X281 : term] : ((((X276 @ id @ (X277 @ id @ X281) @ id)) = $true) | ($true != ((X276 @ id @ X281 @ id)))) & ($true != ((X276 @ id @ (lam @ (X277 @ sh @ one)) @ id))) & ! [X279 : subst,X280 : subst,X278 : term] : (((sub @ (X277 @ X279 @ X278) @ X280)) = ((X277 @ (comp @ X279 @ X280) @ (sub @ X278 @ X280))))) | ($true = ((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id))) | ? [X282 : term] : (($true = ((X276 @ id @ X282 @ id))) & ($true != ((X276 @ id @ (sub @ X275 @ (push @ X282 @ id)) @ id)))))) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (! [X189 : (term > $o),X190 : term,X191 : subst] : (? [X192 : term,X193 : term] : (($true = ((X189 @ X192))) & ($true = ((X189 @ X193))) & ($true != ((X189 @ (ap @ X193 @ X192))))) | ? [X194 : term] : (! [X195 : term] : (($true != ((X189 @ X195))) | ($true = ((X189 @ (sub @ X194 @ (push @ X195 @ id)))))) & ($true != ((X189 @ (lam @ X194))))) | ($true = ((X189 @ (sub @ X190 @ X191)))) | ? [X196 : term] : (($true = ((var @ X196))) & ($true != ((X189 @ (sub @ X196 @ X191)))))) <=> (induction2lem = $true)) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem2v2 = $true) <=> ! [X489 : (term > $o),X490 : (subst > term > subst > $o),X492 : term,X491 : term] : (? [X502 : term,X500 : subst,X501 : subst,X503 : subst] : (($true = ((X490 @ X500 @ X502 @ (comp @ X501 @ X503)))) & (((X490 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) != $true)) | (((X489 @ (ap @ X491 @ X492))) = $true) | (((X489 @ X491)) != $true) | ? [X493 : term,X494 : term] : ((((X490 @ id @ (ap @ (sub @ X494 @ id) @ X493) @ id)) != $true) & ($true = ((X490 @ id @ X493 @ id))) & (((X490 @ id @ X494 @ id)) = $true)) | ($true != ((X489 @ X492))) | ? [X495 : term] : (((X489 @ X495)) != ((X490 @ id @ X495 @ id))) | ? [X496 : subst,X498 : subst,X499 : term,X497 : subst] : (($true = ((X490 @ (comp @ X496 @ X497) @ (sub @ X499 @ X497) @ X498))) & ($true != ((X490 @ X496 @ X499 @ (comp @ X497 @ X498))))))) & (hoasapnotvar_gthm = $true) & (! [X335 : (subst > term > subst > $o)] : ? [X336 : (term > $o)] : ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem3v2 = $true) & ! [X96 : d_subst,X97 : d_subst] : ((X96 = X97) | (((d2subst @ X97)) != ((d2subst @ X96)))) & (ulamvarind = $true) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) <=> (termmset = $true)) & (axabs = $true) & ((hoaslaminj = $true) <=> ! [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (? [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) != ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | (((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one)))) | ? [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X365 @ X372 @ X374) @ X373))))) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & (! [X1 : term,X0 : (subst > term > subst > $o),X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | ? [X12 : term,X11 : term] : (($true != ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) & (((X0 @ id @ X12 @ id)) = $true) & ($true = ((X0 @ id @ X11 @ id)))) | ? [X6 : subst,X3 : term,X5 : subst,X4 : subst] : (($true != ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5))) & ($true = ((X0 @ X4 @ X3 @ (comp @ X6 @ X5))))) | ($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ($true != ((X0 @ id @ X1 @ id))) | ? [X8 : subst,X9 : subst,X10 : term,X7 : subst] : ((((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) != $true) & (((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) = $true))) <=> (hoasinduction_lem2 = $true)) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasinduction_lem1v2 = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) != ((d2term @ X161))) | (X161 = X162)) & ((substmonoid = $true) <=> (! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2 = $true) <=> ! [X386 : (term > $o),X385 : (subst > term > subst > $o),X387 : term] : ((((X386 @ (lam @ X387))) = $true) | ? [X389 : subst,X391 : term,X390 : subst,X388 : subst] : ((((X385 @ X389 @ X391 @ (comp @ X388 @ X390))) = $true) & ($true != ((X385 @ (comp @ X389 @ X388) @ (sub @ X391 @ X388) @ X390)))) | ? [X392 : term] : ((((X386 @ (sub @ X387 @ (push @ X392 @ id)))) != $true) & ($true = ((X386 @ X392)))) | ? [X393 : term] : (((X385 @ id @ X393 @ id)) != ((X386 @ X393))) | ? [X397 : subst,X395 : subst,X396 : subst,X394 : term] : (($true != ((X385 @ X397 @ X394 @ (comp @ X395 @ X396)))) & ($true = ((X385 @ (comp @ X397 @ X395) @ (sub @ X394 @ X395) @ X396)))) | ? [X398 : (subst > term > term)] : (! [X399 : term] : (($true != ((X385 @ id @ X399 @ id))) | (((X385 @ id @ (X398 @ id @ X399) @ id)) = $true)) & ($true != ((X385 @ id @ (lam @ (X398 @ sh @ one)) @ id))) & ! [X401 : term,X402 : subst,X400 : subst] : (((sub @ (X398 @ X402 @ X401) @ X400)) = ((X398 @ (comp @ X402 @ X400) @ (sub @ X401 @ X400))))))) & (axvarshift = $true) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one)))) & (! [X435 : (subst > term > subst > $o)] : ? [X436 : (term > $o)] : ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))) <=> (hoasinduction_lem0 = $true)) & (! [X326 : subst] : (((comp @ X326 @ id)) = X326) <=> (axidr = $true)) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X293 : term] : (((sub @ X293 @ id)) != X293) | ! [X305 : term,X304 : (subst > term > subst > $o)] : (($true = ((X304 @ id @ X305 @ id))) | ? [X319 : term] : (($true != ((X304 @ id @ X319 @ id))) & (((var @ (sub @ X319 @ id))) = $true)) | ? [X308 : subst,X309 : term,X306 : subst,X307 : subst] : (($true != ((X304 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306))) & (((X304 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true)) | ? [X317 : subst,X316 : subst,X318 : term,X315 : subst] : (($true != ((X304 @ X316 @ X318 @ (comp @ X315 @ X317)))) & ($true = ((X304 @ (comp @ X316 @ X315) @ (sub @ X318 @ X315) @ X317)))) | ? [X310 : (subst > term > term)] : (($true != ((X304 @ id @ (lam @ (X310 @ sh @ one)) @ id))) & ! [X312 : term,X313 : subst,X311 : subst] : (((X310 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))) = ((sub @ (X310 @ X311 @ X312) @ X313))) & ! [X314 : term] : (($true != ((X304 @ id @ X314 @ id))) | (((X304 @ id @ (X310 @ id @ X314) @ id)) = $true))) | ? [X320 : term,X321 : term] : ((((X304 @ id @ X321 @ id)) = $true) & ($true = ((X304 @ id @ X320 @ id))) & ($true != ((X304 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id))))) | ? [X283 : (subst > term > subst > $o)] : ! [X284 : (term > $o)] : ? [X285 : term] : (((X283 @ id @ X285 @ id)) != ((X284 @ X285))) | ? [X294 : (subst > term > subst > $o),X295 : (term > $o),X296 : term] : (! [X297 : (subst > term > term)] : (? [X299 : subst,X300 : term,X301 : subst] : (((sub @ (X297 @ X299 @ X300) @ X301)) != ((X297 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301)))) | ? [X298 : term] : ((((X294 @ id @ X298 @ id)) = $true) & ($true != ((X294 @ id @ (X297 @ id @ X298) @ id)))) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)) & ! [X303 : term] : (((X295 @ X303)) = ((X294 @ id @ X303 @ id))) & ! [X302 : term] : (($true = ((X295 @ (sub @ X296 @ (push @ X302 @ id))))) | ($true != ((X295 @ X302)))) & (((X295 @ (lam @ X296))) != $true)) | ? [X287 : term,X286 : (term > $o)] : (! [X288 : term] : (($true = ((X286 @ X288))) | ($true != ((var @ X288)))) & ! [X292 : term,X291 : term] : ((((X286 @ X291)) != $true) | ($true != ((X286 @ X292))) | ($true = ((X286 @ (ap @ X292 @ X291))))) & ($true != ((X286 @ X287))) & ! [X289 : term] : (($true = ((X286 @ (lam @ X289)))) | ? [X290 : term] : ((((X286 @ X290)) = $true) & ($true != ((X286 @ (sub @ X289 @ (push @ X290 @ id)))))))))) & (pushprop_lem1_gthm = $true) & (axclos = $true) & ((induction = $true) <=> ! [X198 : term,X197 : (term > $o)] : (? [X202 : term] : (($true != ((X197 @ X202))) & (((var @ X202)) = $true)) | (((X197 @ X198)) = $true) | ? [X201 : term] : (($true = ((X197 @ X201))) & ($true != ((X197 @ (lam @ X201))))) | ? [X200 : term,X199 : term] : (($true = ((X197 @ X200))) & (((X197 @ (ap @ X199 @ X200))) != $true) & ($true = ((X197 @ X199)))))) & ((hoasapinj2 = $true) <=> ! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218))))) & (hoasinduction_lem1 = $true) & ((induction2_lthm = $true) <=> (? [X19 : term] : (((sub @ X19 @ id)) != X19) | ? [X21 : subst,X22 : term,X20 : (term > $o)] : (! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ? [X27 : term] : ((((X20 @ (sub @ X26 @ (push @ X27 @ id)))) != $true) & ($true = ((X20 @ X27))))) & (((X20 @ (sub @ X22 @ X21))) != $true) & ! [X24 : term,X25 : term] : (($true = ((X20 @ (ap @ X24 @ X25)))) | ($true != ((X20 @ X25))) | (((X20 @ X24)) != $true)) & ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ($true != ((var @ X23))))) | ! [X29 : (term > $o),X28 : term] : (? [X33 : term,X32 : term] : (($true != ((X29 @ (ap @ X33 @ X32)))) & (((X29 @ X32)) = $true) & ($true = ((X29 @ X33)))) | ? [X30 : term] : (($true != ((X29 @ (lam @ X30)))) & ! [X31 : term] : ((((X29 @ X31)) != $true) | ($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id))))))) | ? [X34 : term] : (($true != ((X29 @ X34))) & ($true = ((var @ X34)))) | ($true = ((X29 @ X28)))))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & ((! [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ? [X539 : term] : (((X538 @ X539)) != ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) | ? [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) != X533)) <=> (pushprop_lem1v2_lthm = $true)) & ! [X103 : d_subst] : (d_id = X103) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) <=> ! [X164 : (subst > term > subst > $o),X165 : term] : (? [X166 : term] : (($true = ((X164 @ id @ X166 @ id))) & (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) != $true)) | ? [X167 : (subst > term > term)] : (! [X171 : term] : ((((X164 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X164 @ id @ X171 @ id)) != $true)) & ! [X169 : term,X168 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X169) @ X168)) = ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)))) & ($true != ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id)))) | ($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))))) & ((pushprop_lem1_lthm = $true) <=> (? [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) != X131) | ! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)) | ? [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) != X133))) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(flattening,[],[f11])).
% 3.49/0.96 thf(f13,definition,(
% 3.49/0.96 ! [X164 : (subst > term > subst > $o)] : (($true = ((sP0 @ X164))) <=> ? [X167 : (subst > term > term)] : (! [X171 : term] : ((((X164 @ id @ (X167 @ id @ X171) @ id)) = $true) | (((X164 @ id @ X171 @ id)) != $true)) & ! [X169 : term,X168 : subst,X170 : subst] : (((sub @ (X167 @ X170 @ X169) @ X168)) = ((X167 @ (comp @ X170 @ X168) @ (sub @ X169 @ X168)))) & ($true != ((X164 @ id @ (lam @ (X167 @ sh @ one)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f14,definition,(
% 3.49/0.96 ($true = sP1) <=> ! [X164 : (subst > term > subst > $o),X165 : term] : (? [X166 : term] : (($true = ((X164 @ id @ X166 @ id))) & (((X164 @ id @ (sub @ X165 @ (push @ X166 @ id)) @ id)) != $true)) | ($true = ((sP0 @ X164))) | ($true = ((X164 @ id @ (lam @ (sub @ X165 @ (push @ one @ sh))) @ id))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f15,definition,(
% 3.49/0.96 ! [X29 : (term > $o)] : ((((sP2 @ X29)) = $true) <=> ? [X30 : term] : (($true != ((X29 @ (lam @ X30)))) & ! [X31 : term] : ((((X29 @ X31)) != $true) | ($true = ((X29 @ (sub @ X30 @ (push @ X31 @ id))))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f16,definition,(
% 3.49/0.96 ! [X29 : (term > $o)] : (($true = ((sP3 @ X29))) <=> ? [X33 : term,X32 : term] : (($true != ((X29 @ (ap @ X33 @ X32)))) & (((X29 @ X32)) = $true) & ($true = ((X29 @ X33)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f17,definition,(
% 3.49/0.96 ! [X20 : (term > $o)] : ((((sP4 @ X20)) = $true) <=> ! [X24 : term,X25 : term] : (($true = ((X20 @ (ap @ X24 @ X25)))) | ($true != ((X20 @ X25))) | (((X20 @ X24)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f18,definition,(
% 3.49/0.96 ! [X21 : subst,X20 : (term > $o)] : ((((sP5 @ X20 @ X21)) = $true) <=> ! [X23 : term] : (($true = ((X20 @ (sub @ X23 @ X21)))) | ($true != ((var @ X23)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f19,definition,(
% 3.49/0.96 ! [X20 : (term > $o)] : (($true = ((sP6 @ X20))) <=> ! [X26 : term] : (($true = ((X20 @ (lam @ X26)))) | ? [X27 : term] : ((((X20 @ (sub @ X26 @ (push @ X27 @ id)))) != $true) & ($true = ((X20 @ X27))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f20,definition,(
% 3.49/0.96 ($true = sP7) <=> ! [X29 : (term > $o),X28 : term] : (($true = ((sP3 @ X29))) | (((sP2 @ X29)) = $true) | ? [X34 : term] : (($true != ((X29 @ X34))) & ($true = ((var @ X34)))) | ($true = ((X29 @ X28))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f21,definition,(
% 3.49/0.96 (sP8 = $true) <=> ? [X21 : subst,X22 : term,X20 : (term > $o)] : (($true = ((sP6 @ X20))) & (((X20 @ (sub @ X22 @ X21))) != $true) & (((sP4 @ X20)) = $true) & (((sP5 @ X20 @ X21)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f22,definition,(
% 3.49/0.96 ! [X197 : (term > $o)] : ((((sP9 @ X197)) = $true) <=> ? [X200 : term,X199 : term] : (($true = ((X197 @ X200))) & (((X197 @ (ap @ X199 @ X200))) != $true) & ($true = ((X197 @ X199)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f23,definition,(
% 3.49/0.96 ! [X197 : (term > $o)] : ((((sP10 @ X197)) = $true) <=> ? [X201 : term] : (($true = ((X197 @ X201))) & ($true != ((X197 @ (lam @ X201))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f24,definition,(
% 3.49/0.96 (sP11 = $true) <=> ! [X198 : term,X197 : (term > $o)] : (? [X202 : term] : (($true != ((X197 @ X202))) & (((var @ X202)) = $true)) | (((X197 @ X198)) = $true) | (((sP10 @ X197)) = $true) | (((sP9 @ X197)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f25,definition,(
% 3.49/0.96 ! [X286 : (term > $o)] : (($true = ((sP12 @ X286))) <=> ! [X292 : term,X291 : term] : ((((X286 @ X291)) != $true) | ($true != ((X286 @ X292))) | ($true = ((X286 @ (ap @ X292 @ X291))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f26,definition,(
% 3.49/0.96 ! [X286 : (term > $o)] : ((((sP13 @ X286)) = $true) <=> ! [X289 : term] : (($true = ((X286 @ (lam @ X289)))) | ? [X290 : term] : ((((X286 @ X290)) = $true) & ($true != ((X286 @ (sub @ X289 @ (push @ X290 @ id))))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f27,definition,(
% 3.49/0.96 ! [X294 : (subst > term > subst > $o)] : ((((sP14 @ X294)) = $true) <=> ! [X297 : (subst > term > term)] : (? [X299 : subst,X300 : term,X301 : subst] : (((sub @ (X297 @ X299 @ X300) @ X301)) != ((X297 @ (comp @ X299 @ X301) @ (sub @ X300 @ X301)))) | ? [X298 : term] : ((((X294 @ id @ X298 @ id)) = $true) & ($true != ((X294 @ id @ (X297 @ id @ X298) @ id)))) | (((X294 @ id @ (lam @ (X297 @ sh @ one)) @ id)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f28,definition,(
% 3.49/0.96 ! [X304 : (subst > term > subst > $o)] : ((((sP15 @ X304)) = $true) <=> ? [X310 : (subst > term > term)] : (($true != ((X304 @ id @ (lam @ (X310 @ sh @ one)) @ id))) & ! [X312 : term,X313 : subst,X311 : subst] : (((X310 @ (comp @ X311 @ X313) @ (sub @ X312 @ X313))) = ((sub @ (X310 @ X311 @ X312) @ X313))) & ! [X314 : term] : (($true != ((X304 @ id @ X314 @ id))) | (((X304 @ id @ (X310 @ id @ X314) @ id)) = $true))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f29,definition,(
% 3.49/0.96 ! [X304 : (subst > term > subst > $o)] : (($true = ((sP16 @ X304))) <=> ? [X320 : term,X321 : term] : ((((X304 @ id @ X321 @ id)) = $true) & ($true = ((X304 @ id @ X320 @ id))) & ($true != ((X304 @ id @ (ap @ (sub @ X321 @ id) @ X320) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f30,definition,(
% 3.49/0.96 ! [X304 : (subst > term > subst > $o)] : ((((sP17 @ X304)) = $true) <=> ? [X317 : subst,X316 : subst,X318 : term,X315 : subst] : (($true != ((X304 @ X316 @ X318 @ (comp @ X315 @ X317)))) & ($true = ((X304 @ (comp @ X316 @ X315) @ (sub @ X318 @ X315) @ X317)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f31,definition,(
% 3.49/0.96 ! [X304 : (subst > term > subst > $o)] : ((((sP18 @ X304)) = $true) <=> ? [X308 : subst,X309 : term,X306 : subst,X307 : subst] : (($true != ((X304 @ (comp @ X307 @ X308) @ (sub @ X309 @ X308) @ X306))) & (((X304 @ X307 @ X309 @ (comp @ X308 @ X306))) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f32,definition,(
% 3.49/0.96 (sP19 = $true) <=> ! [X305 : term,X304 : (subst > term > subst > $o)] : (($true = ((X304 @ id @ X305 @ id))) | ? [X319 : term] : (($true != ((X304 @ id @ X319 @ id))) & (((var @ (sub @ X319 @ id))) = $true)) | (((sP18 @ X304)) = $true) | (((sP17 @ X304)) = $true) | (((sP15 @ X304)) = $true) | ($true = ((sP16 @ X304))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f33,definition,(
% 3.49/0.96 ($true = sP20) <=> ? [X287 : term,X286 : (term > $o)] : (! [X288 : term] : (($true = ((X286 @ X288))) | ($true != ((var @ X288)))) & ($true = ((sP12 @ X286))) & ($true != ((X286 @ X287))) & (((sP13 @ X286)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f34,definition,(
% 3.49/0.96 (sP21 = $true) <=> ? [X294 : (subst > term > subst > $o),X295 : (term > $o),X296 : term] : ((((sP14 @ X294)) = $true) & ! [X303 : term] : (((X295 @ X303)) = ((X294 @ id @ X303 @ id))) & ! [X302 : term] : (($true = ((X295 @ (sub @ X296 @ (push @ X302 @ id))))) | ($true != ((X295 @ X302)))) & (((X295 @ (lam @ X296))) != $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f35,definition,(
% 3.49/0.96 ! [X385 : (subst > term > subst > $o)] : (($true = ((sP22 @ X385))) <=> ? [X398 : (subst > term > term)] : (! [X399 : term] : (($true != ((X385 @ id @ X399 @ id))) | (((X385 @ id @ (X398 @ id @ X399) @ id)) = $true)) & ($true != ((X385 @ id @ (lam @ (X398 @ sh @ one)) @ id))) & ! [X401 : term,X402 : subst,X400 : subst] : (((sub @ (X398 @ X402 @ X401) @ X400)) = ((X398 @ (comp @ X402 @ X400) @ (sub @ X401 @ X400))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f36,definition,(
% 3.49/0.96 ! [X385 : (subst > term > subst > $o)] : (($true = ((sP23 @ X385))) <=> ? [X397 : subst,X395 : subst,X396 : subst,X394 : term] : (($true != ((X385 @ X397 @ X394 @ (comp @ X395 @ X396)))) & ($true = ((X385 @ (comp @ X397 @ X395) @ (sub @ X394 @ X395) @ X396)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f37,definition,(
% 3.49/0.96 ! [X387 : term,X386 : (term > $o)] : (($true = ((sP24 @ X386 @ X387))) <=> ? [X392 : term] : ((((X386 @ (sub @ X387 @ (push @ X392 @ id)))) != $true) & ($true = ((X386 @ X392)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f38,definition,(
% 3.49/0.96 (sP25 = $true) <=> ! [X386 : (term > $o),X385 : (subst > term > subst > $o),X387 : term] : ((((X386 @ (lam @ X387))) = $true) | ? [X389 : subst,X391 : term,X390 : subst,X388 : subst] : ((((X385 @ X389 @ X391 @ (comp @ X388 @ X390))) = $true) & ($true != ((X385 @ (comp @ X389 @ X388) @ (sub @ X391 @ X388) @ X390)))) | ($true = ((sP24 @ X386 @ X387))) | ? [X393 : term] : (((X385 @ id @ X393 @ id)) != ((X386 @ X393))) | ($true = ((sP23 @ X385))) | ($true = ((sP22 @ X385))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f39,definition,(
% 3.49/0.96 ! [X0 : (subst > term > subst > $o)] : (($true = ((sP26 @ X0))) <=> ? [X12 : term,X11 : term] : (($true != ((X0 @ id @ (ap @ (sub @ X11 @ id) @ X12) @ id))) & (((X0 @ id @ X12 @ id)) = $true) & ($true = ((X0 @ id @ X11 @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f40,definition,(
% 3.49/0.96 ! [X0 : (subst > term > subst > $o)] : (($true = ((sP27 @ X0))) <=> ? [X8 : subst,X9 : subst,X10 : term,X7 : subst] : ((((X0 @ X8 @ X10 @ (comp @ X9 @ X7))) != $true) & (((X0 @ (comp @ X8 @ X9) @ (sub @ X10 @ X9) @ X7)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f41,definition,(
% 3.49/0.96 ($true = sP28) <=> ! [X1 : term,X0 : (subst > term > subst > $o),X2 : term] : ((((X0 @ id @ X2 @ id)) != $true) | ($true = ((sP26 @ X0))) | ? [X6 : subst,X3 : term,X5 : subst,X4 : subst] : (($true != ((X0 @ (comp @ X4 @ X6) @ (sub @ X3 @ X6) @ X5))) & ($true = ((X0 @ X4 @ X3 @ (comp @ X6 @ X5))))) | ($true = ((X0 @ id @ (ap @ X1 @ X2) @ id))) | ($true != ((X0 @ id @ X1 @ id))) | ($true = ((sP27 @ X0))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f42,definition,(
% 3.49/0.96 ! [X490 : (subst > term > subst > $o)] : (($true = ((sP29 @ X490))) <=> ? [X493 : term,X494 : term] : ((((X490 @ id @ (ap @ (sub @ X494 @ id) @ X493) @ id)) != $true) & ($true = ((X490 @ id @ X493 @ id))) & (((X490 @ id @ X494 @ id)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f43,definition,(
% 3.49/0.96 ! [X490 : (subst > term > subst > $o)] : (($true = ((sP30 @ X490))) <=> ? [X496 : subst,X498 : subst,X499 : term,X497 : subst] : (($true = ((X490 @ (comp @ X496 @ X497) @ (sub @ X499 @ X497) @ X498))) & ($true != ((X490 @ X496 @ X499 @ (comp @ X497 @ X498))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f44,definition,(
% 3.49/0.96 ($true = sP31) <=> ! [X489 : (term > $o),X490 : (subst > term > subst > $o),X492 : term,X491 : term] : (? [X502 : term,X500 : subst,X501 : subst,X503 : subst] : (($true = ((X490 @ X500 @ X502 @ (comp @ X501 @ X503)))) & (((X490 @ (comp @ X500 @ X501) @ (sub @ X502 @ X501) @ X503)) != $true)) | (((X489 @ (ap @ X491 @ X492))) = $true) | (((X489 @ X491)) != $true) | ($true = ((sP29 @ X490))) | ($true != ((X489 @ X492))) | ? [X495 : term] : (((X489 @ X495)) != ((X490 @ id @ X495 @ id))) | ($true = ((sP30 @ X490))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f45,definition,(
% 3.49/0.96 ! [X189 : (term > $o)] : (($true = ((sP32 @ X189))) <=> ? [X194 : term] : (! [X195 : term] : (($true != ((X189 @ X195))) | ($true = ((X189 @ (sub @ X194 @ (push @ X195 @ id)))))) & ($true != ((X189 @ (lam @ X194))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f46,definition,(
% 3.49/0.96 ! [X189 : (term > $o)] : (($true = ((sP33 @ X189))) <=> ? [X192 : term,X193 : term] : (($true = ((X189 @ X192))) & ($true = ((X189 @ X193))) & ($true != ((X189 @ (ap @ X193 @ X192))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f47,definition,(
% 3.49/0.96 ($true = sP34) <=> ! [X189 : (term > $o),X190 : term,X191 : subst] : (($true = ((sP33 @ X189))) | ($true = ((sP32 @ X189))) | ($true = ((X189 @ (sub @ X190 @ X191)))) | ? [X196 : term] : (($true = ((var @ X196))) & ($true != ((X189 @ (sub @ X196 @ X191))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f48,definition,(
% 3.49/0.96 ! [X276 : (subst > term > subst > $o)] : (($true = ((sP35 @ X276))) <=> ? [X277 : (subst > term > term)] : (! [X281 : term] : ((((X276 @ id @ (X277 @ id @ X281) @ id)) = $true) | ($true != ((X276 @ id @ X281 @ id)))) & ($true != ((X276 @ id @ (lam @ (X277 @ sh @ one)) @ id))) & ! [X279 : subst,X280 : subst,X278 : term] : (((sub @ (X277 @ X279 @ X278) @ X280)) = ((X277 @ (comp @ X279 @ X280) @ (sub @ X278 @ X280))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f49,definition,(
% 3.49/0.96 ($true = sP36) <=> ! [X275 : term,X276 : (subst > term > subst > $o)] : (($true = ((sP35 @ X276))) | ($true = ((X276 @ id @ (lam @ (sub @ X275 @ (push @ one @ sh))) @ id))) | ? [X282 : term] : (($true = ((X276 @ id @ X282 @ id))) & ($true != ((X276 @ id @ (sub @ X275 @ (push @ X282 @ id)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f50,definition,(
% 3.49/0.96 ! [X516 : (subst > term > subst > $o)] : (($true = ((sP37 @ X516))) <=> ? [X523 : (subst > term > term)] : (! [X527 : term] : (($true = ((X516 @ id @ (X523 @ id @ X527) @ id))) | ($true != ((X516 @ id @ X527 @ id)))) & ! [X525 : subst,X526 : term,X524 : subst] : (((X523 @ (comp @ X524 @ X525) @ (sub @ X526 @ X525))) = ((sub @ (X523 @ X524 @ X526) @ X525))) & (((X516 @ id @ (lam @ (X523 @ sh @ one)) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f51,definition,(
% 3.49/0.96 ! [X517 : term,X515 : (term > $o)] : (($true = ((sP38 @ X515 @ X517))) <=> ? [X522 : term] : (($true != ((X515 @ (sub @ X517 @ (push @ X522 @ id))))) & (((X515 @ X522)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f52,definition,(
% 3.49/0.96 ! [X516 : (subst > term > subst > $o)] : (($true = ((sP39 @ X516))) <=> ? [X521 : subst,X518 : subst,X520 : subst,X519 : term] : (($true = ((X516 @ (comp @ X521 @ X520) @ (sub @ X519 @ X520) @ X518))) & (((X516 @ X521 @ X519 @ (comp @ X520 @ X518))) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f53,definition,(
% 3.49/0.96 ($true = sP40) <=> ! [X517 : term,X516 : (subst > term > subst > $o),X515 : (term > $o)] : (? [X532 : term] : (((X515 @ X532)) != ((X516 @ id @ X532 @ id))) | ? [X531 : subst,X528 : subst,X530 : subst,X529 : term] : (($true = ((X516 @ X531 @ X529 @ (comp @ X528 @ X530)))) & ($true != ((X516 @ (comp @ X531 @ X528) @ (sub @ X529 @ X528) @ X530)))) | ($true = ((sP39 @ X516))) | ($true = ((sP37 @ X516))) | (((X515 @ (lam @ X517))) = $true) | ($true = ((sP38 @ X515 @ X517))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f54,definition,(
% 3.49/0.96 ! [X228 : (subst > term > subst > $o)] : ((((sP41 @ X228)) = $true) <=> ? [X229 : (subst > term > term)] : (! [X231 : subst,X233 : term,X232 : subst] : (((sub @ (X229 @ X231 @ X233) @ X232)) = ((X229 @ (comp @ X231 @ X232) @ (sub @ X233 @ X232)))) & ! [X230 : term] : (($true != ((X228 @ id @ X230 @ id))) | ($true = ((X228 @ id @ (X229 @ id @ X230) @ id)))) & ($true != ((X228 @ id @ (lam @ (X229 @ sh @ one)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f55,definition,(
% 3.49/0.96 ! [X228 : (subst > term > subst > $o)] : (($true = ((sP42 @ X228))) <=> ? [X238 : subst,X235 : subst,X236 : subst,X237 : term] : ((((X228 @ X238 @ X237 @ (comp @ X236 @ X235))) = $true) & (((X228 @ (comp @ X238 @ X236) @ (sub @ X237 @ X236) @ X235)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f56,definition,(
% 3.49/0.96 ! [X228 : (subst > term > subst > $o),X227 : term] : (($true = ((sP43 @ X227 @ X228))) <=> ? [X234 : term] : (($true = ((X228 @ id @ X234 @ id))) & ($true != ((X228 @ id @ (sub @ X227 @ (push @ X234 @ id)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f57,definition,(
% 3.49/0.96 ($true = sP44) <=> ! [X228 : (subst > term > subst > $o),X227 : term] : (($true = ((X228 @ id @ (lam @ X227) @ id))) | (((sP41 @ X228)) = $true) | ? [X241 : subst,X242 : term,X239 : subst,X240 : subst] : (($true != ((X228 @ X240 @ X242 @ (comp @ X239 @ X241)))) & ($true = ((X228 @ (comp @ X240 @ X239) @ (sub @ X242 @ X239) @ X241)))) | ($true = ((sP43 @ X227 @ X228))) | ($true = ((sP42 @ X228))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f58,definition,(
% 3.49/0.96 ($true = sP45) <=> ! [X112 : (subst > term > term),X114 : (subst > term > term),X111 : term,X113 : subst] : ((((X114 @ X113 @ X111)) = ((X112 @ X113 @ X111))) | ? [X119 : term,X120 : subst,X118 : subst] : (((X114 @ (comp @ X118 @ X120) @ (sub @ X119 @ X120))) != ((sub @ (X114 @ X118 @ X119) @ X120))) | ? [X116 : subst,X115 : subst,X117 : term] : (((sub @ (X112 @ X115 @ X117) @ X116)) != ((X112 @ (comp @ X115 @ X116) @ (sub @ X117 @ X116)))) | (((lam @ (X114 @ sh @ one))) != ((lam @ (X112 @ sh @ one)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f59,definition,(
% 3.49/0.96 ($true = sP46) <=> (? [X109 : term,X110 : term] : ((X109 != X110) & (((lam @ X110)) = ((lam @ X109)))) | ($true = sP45) | ? [X108 : term,X107 : subst] : (((comp @ sh @ (push @ X108 @ X107))) != X107) | ? [X105 : subst,X106 : term] : (((sub @ one @ (push @ X106 @ X105))) != X106))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f60,definition,(
% 3.49/0.96 ! [X37 : (term > $o)] : (($true = ((sP47 @ X37))) <=> ! [X43 : term,X42 : term] : (($true = ((X37 @ (ap @ X42 @ X43)))) | (((X37 @ X43)) != $true) | (((X37 @ X42)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f61,definition,(
% 3.49/0.96 ! [X37 : (term > $o)] : ((((sP48 @ X37)) = $true) <=> ! [X41 : term] : (($true = ((X37 @ X41))) | ($true != ((var @ X41)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f62,definition,(
% 3.49/0.96 ! [X37 : (term > $o)] : ((((sP49 @ X37)) = $true) <=> ! [X39 : term] : (? [X40 : term] : ((((X37 @ X40)) = $true) & ($true != ((X37 @ (sub @ X39 @ (push @ X40 @ id)))))) | ($true = ((X37 @ (lam @ X39))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f63,definition,(
% 3.49/0.96 ! [X45 : (subst > term > subst > $o)] : ((((sP50 @ X45)) = $true) <=> ! [X51 : term,X52 : term] : ((((X45 @ id @ X51 @ id)) != $true) | ($true != ((X45 @ id @ X52 @ id))) | ($true = ((X45 @ id @ (ap @ (sub @ X52 @ id) @ X51) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f64,definition,(
% 3.49/0.96 ! [X45 : (subst > term > subst > $o)] : (($true = ((sP51 @ X45))) <=> ! [X53 : subst,X56 : subst,X55 : term,X54 : subst] : ((((X45 @ X53 @ X55 @ (comp @ X56 @ X54))) = $true) | (((X45 @ (comp @ X53 @ X56) @ (sub @ X55 @ X56) @ X54)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f65,definition,(
% 3.49/0.96 ! [X74 : (subst > term > subst > $o)] : (($true = ((sP52 @ X74))) <=> ? [X80 : (subst > term > term)] : (! [X84 : subst,X83 : term,X82 : subst] : (((X80 @ (comp @ X84 @ X82) @ (sub @ X83 @ X82))) = ((sub @ (X80 @ X84 @ X83) @ X82))) & ! [X81 : term] : (($true != ((X74 @ id @ X81 @ id))) | ($true = ((X74 @ id @ (X80 @ id @ X81) @ id)))) & (((X74 @ id @ (lam @ (X80 @ sh @ one)) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f66,definition,(
% 3.49/0.96 ! [X74 : (subst > term > subst > $o)] : (($true = ((sP53 @ X74))) <=> ? [X86 : term,X85 : term] : (($true = ((X74 @ id @ X86 @ id))) & ($true = ((X74 @ id @ X85 @ id))) & (((X74 @ id @ (ap @ (sub @ X86 @ id) @ X85) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f67,definition,(
% 3.49/0.96 ! [X74 : (subst > term > subst > $o)] : ((((sP54 @ X74)) = $true) <=> ? [X90 : subst,X88 : subst,X87 : term,X89 : subst] : (($true != ((X74 @ X90 @ X87 @ (comp @ X89 @ X88)))) & (((X74 @ (comp @ X90 @ X89) @ (sub @ X87 @ X89) @ X88)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f68,definition,(
% 3.49/0.96 ! [X74 : (subst > term > subst > $o)] : ((((sP55 @ X74)) = $true) <=> ? [X79 : term] : ((((X74 @ id @ X79 @ id)) != $true) & ($true = ((var @ (sub @ X79 @ id))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f69,definition,(
% 3.49/0.96 ! [X57 : (subst > term > subst > $o)] : (($true = ((sP56 @ X57))) <=> ! [X60 : (subst > term > term)] : (($true = ((X57 @ id @ (lam @ (X60 @ sh @ one)) @ id))) | ? [X61 : term] : (($true != ((X57 @ id @ (X60 @ id @ X61) @ id))) & ($true = ((X57 @ id @ X61 @ id)))) | ? [X62 : subst,X64 : term,X63 : subst] : (((sub @ (X60 @ X62 @ X64) @ X63)) != ((X60 @ (comp @ X62 @ X63) @ (sub @ X64 @ X63))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f70,definition,(
% 3.49/0.96 ! [X57 : (subst > term > subst > $o)] : ((((sP57 @ X57)) = $true) <=> ! [X71 : term,X72 : subst,X69 : subst,X70 : subst] : (($true != ((X57 @ (comp @ X70 @ X69) @ (sub @ X71 @ X69) @ X72))) | ($true = ((X57 @ X70 @ X71 @ (comp @ X69 @ X72))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f71,definition,(
% 3.49/0.96 ! [X57 : (subst > term > subst > $o)] : (($true = ((sP58 @ X57))) <=> ! [X65 : subst,X68 : subst,X67 : subst,X66 : term] : ((((X57 @ (comp @ X65 @ X68) @ (sub @ X66 @ X68) @ X67)) = $true) | ($true != ((X57 @ X65 @ X66 @ (comp @ X68 @ X67))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f72,definition,(
% 3.49/0.96 (sP59 = $true) <=> ! [X73 : term,X74 : (subst > term > subst > $o)] : (($true = ((sP53 @ X74))) | ? [X77 : subst,X76 : term,X75 : subst,X78 : subst] : (($true = ((X74 @ X75 @ X76 @ (comp @ X78 @ X77)))) & ($true != ((X74 @ (comp @ X75 @ X78) @ (sub @ X76 @ X78) @ X77)))) | ($true = ((sP52 @ X74))) | ($true = ((X74 @ id @ X73 @ id))) | (((sP55 @ X74)) = $true) | (((sP54 @ X74)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f73,definition,(
% 3.49/0.96 ($true = sP60) <=> ? [X45 : (subst > term > subst > $o),X44 : term,X46 : term] : (($true = ((X45 @ id @ X44 @ id))) & (((sP50 @ X45)) = $true) & (((X45 @ id @ X46 @ id)) = $true) & ! [X49 : subst,X48 : subst,X47 : term,X50 : subst] : (($true = ((X45 @ (comp @ X50 @ X49) @ (sub @ X47 @ X49) @ X48))) | (((X45 @ X50 @ X47 @ (comp @ X49 @ X48))) != $true)) & ($true = ((sP51 @ X45))) & ($true != ((X45 @ id @ (ap @ X46 @ X44) @ id))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f74,definition,(
% 3.49/0.96 ($true = sP61) <=> ? [X57 : (subst > term > subst > $o),X58 : term] : (! [X59 : term] : (($true != ((X57 @ id @ X59 @ id))) | (((X57 @ id @ (sub @ X58 @ (push @ X59 @ id)) @ id)) = $true)) & ($true != ((X57 @ id @ (lam @ X58) @ id))) & ($true = ((sP58 @ X57))) & ($true = ((sP56 @ X57))) & (((sP57 @ X57)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f75,definition,(
% 3.49/0.96 ($true = sP62) <=> ? [X37 : (term > $o),X38 : term] : (($true = ((sP47 @ X37))) & (((sP49 @ X37)) = $true) & ($true != ((X37 @ X38))) & (((sP48 @ X37)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f76,definition,(
% 3.49/0.96 ! [X179 : (subst > term > subst > $o)] : ((((sP63 @ X179)) = $true) <=> ? [X183 : (subst > term > term)] : (! [X186 : subst,X185 : term,X184 : subst] : (((X183 @ (comp @ X186 @ X184) @ (sub @ X185 @ X184))) = ((sub @ (X183 @ X186 @ X185) @ X184))) & (((X179 @ id @ (lam @ (X183 @ sh @ one)) @ id)) != $true) & ! [X187 : term] : (($true != ((X179 @ id @ X187 @ id))) | (((X179 @ id @ (X183 @ id @ X187) @ id)) = $true))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f77,definition,(
% 3.49/0.96 ($true = sP64) <=> ! [X181 : (term > $o),X180 : term,X179 : (subst > term > subst > $o)] : (? [X182 : term] : (($true != ((X181 @ (sub @ X180 @ (push @ X182 @ id))))) & (((X181 @ X182)) = $true)) | (((sP63 @ X179)) = $true) | ? [X188 : term] : (((X181 @ X188)) != ((X179 @ id @ X188 @ id))) | (((X181 @ (lam @ X180))) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f78,definition,(
% 3.49/0.96 ! [X247 : (term > $o)] : (($true = ((sP65 @ X247))) <=> ! [X252 : term,X251 : term] : (($true != ((X247 @ X252))) | ($true = ((X247 @ (ap @ X251 @ X252)))) | (((X247 @ X251)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f79,definition,(
% 3.49/0.96 ! [X247 : (term > $o)] : ((((sP66 @ X247)) = $true) <=> ! [X248 : term] : (($true != ((var @ X248))) | ($true = ((X247 @ X248)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f80,definition,(
% 3.49/0.96 ! [X247 : (term > $o)] : ((((sP67 @ X247)) = $true) <=> ! [X249 : term] : (? [X250 : term] : ((((X247 @ (sub @ X249 @ (push @ X250 @ id)))) != $true) & ($true = ((X247 @ X250)))) | ($true = ((X247 @ (lam @ X249))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f81,definition,(
% 3.49/0.96 ! [X255 : (subst > term > subst > $o)] : (($true = ((sP68 @ X255))) <=> ! [X258 : (subst > term > term)] : (? [X262 : term] : (($true != ((X255 @ id @ (X258 @ id @ X262) @ id))) & ($true = ((X255 @ id @ X262 @ id)))) | ? [X261 : subst,X259 : term,X260 : subst] : (((X258 @ (comp @ X261 @ X260) @ (sub @ X259 @ X260))) != ((sub @ (X258 @ X261 @ X259) @ X260))) | (((X255 @ id @ (lam @ (X258 @ sh @ one)) @ id)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f82,definition,(
% 3.49/0.96 ! [X265 : (subst > term > subst > $o)] : ((((sP69 @ X265)) = $true) <=> ? [X268 : (subst > term > term)] : (! [X272 : term,X271 : subst,X270 : subst] : (((sub @ (X268 @ X271 @ X272) @ X270)) = ((X268 @ (comp @ X271 @ X270) @ (sub @ X272 @ X270)))) & ! [X269 : term] : ((((X265 @ id @ X269 @ id)) != $true) | (((X265 @ id @ (X268 @ id @ X269) @ id)) = $true)) & (((X265 @ id @ (lam @ (X268 @ sh @ one)) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f83,definition,(
% 3.49/0.96 ! [X265 : (subst > term > subst > $o)] : (($true = ((sP70 @ X265))) <=> ? [X266 : term,X267 : term] : ((((X265 @ id @ X266 @ id)) = $true) & (((X265 @ id @ (ap @ (sub @ X266 @ id) @ X267) @ id)) != $true) & ($true = ((X265 @ id @ X267 @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f84,definition,(
% 3.49/0.96 ($true = sP71) <=> ! [X265 : (subst > term > subst > $o),X264 : term] : (($true = ((sP70 @ X265))) | (((X265 @ id @ X264 @ id)) = $true) | (((sP69 @ X265)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f85,definition,(
% 3.49/0.96 (sP72 = $true) <=> ? [X256 : (term > $o),X254 : term,X255 : (subst > term > subst > $o)] : ((((X256 @ (lam @ X254))) != $true) & ($true = ((sP68 @ X255))) & ! [X263 : term] : (((X256 @ X263)) = ((X255 @ id @ X263 @ id))) & ! [X257 : term] : ((((X256 @ X257)) != $true) | ($true = ((X256 @ (sub @ X254 @ (push @ X257 @ id)))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f86,definition,(
% 3.49/0.96 ($true = sP73) <=> ? [X247 : (term > $o),X246 : term] : ((((sP67 @ X247)) = $true) & ($true != ((X247 @ X246))) & ($true = ((sP65 @ X247))) & (((sP66 @ X247)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f87,definition,(
% 3.49/0.96 ! [X440 : (subst > term > subst > $o)] : (($true = ((sP74 @ X440))) <=> ? [X443 : (subst > term > term),X444 : term] : (! [X446 : term,X447 : subst,X445 : subst] : (((X443 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445))) = ((sub @ X444 @ (push @ (sub @ X446 @ X445) @ (comp @ X447 @ X445))))) & ! [X451 : subst,X450 : subst,X449 : term] : (((sub @ (sub @ X444 @ (push @ X449 @ X451)) @ X450)) = ((sub @ (X443 @ X451 @ X449) @ X450))) & ! [X448 : term] : ((((X440 @ id @ X448 @ id)) != $true) | ($true = ((X440 @ id @ (X443 @ id @ X448) @ id)))) & ($true != ((X440 @ id @ (lam @ (X443 @ sh @ one)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f88,definition,(
% 3.49/0.96 ($true = sP75) <=> ! [X440 : (subst > term > subst > $o),X441 : term] : (($true = ((X440 @ id @ (lam @ (sub @ X441 @ (push @ one @ sh))) @ id))) | ($true = ((sP74 @ X440))) | ? [X442 : term] : ((((X440 @ id @ X442 @ id)) = $true) & ($true != ((X440 @ id @ (sub @ X441 @ (push @ X442 @ id)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f89,definition,(
% 3.49/0.96 ! [X507 : (term > $o)] : (($true = ((sP76 @ X507))) <=> ? [X511 : term] : (($true != ((X507 @ (lam @ X511)))) & ! [X512 : term] : (($true != ((X507 @ X512))) | ($true = ((X507 @ (sub @ X511 @ (push @ X512 @ id))))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f90,definition,(
% 3.49/0.96 ! [X507 : (term > $o)] : (($true = ((sP77 @ X507))) <=> ? [X510 : term,X509 : term] : (($true != ((X507 @ (ap @ X510 @ X509)))) & ($true = ((X507 @ X509))) & ($true = ((X507 @ X510)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f91,definition,(
% 3.49/0.96 (sP78 = $true) <=> ! [X506 : term,X507 : (term > $o)] : (($true = ((X507 @ X506))) | ? [X508 : term] : (($true != ((X507 @ X508))) & ($true = ((var @ X508)))) | ($true = ((sP77 @ X507))) | ($true = ((sP76 @ X507))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f92,definition,(
% 3.49/0.96 ($true = sP79) <=> ! [X213 : term,X212 : term,X215 : term,X214 : term] : ((X212 = X213) | (((ap @ (sub @ X214 @ id) @ X212)) != ((ap @ (sub @ X215 @ id) @ X213))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f93,definition,(
% 3.49/0.96 ($true = sP80) <=> (? [X208 : term,X210 : term,X209 : term,X211 : term] : ((((ap @ X209 @ X210)) = ((ap @ X211 @ X208))) & (X208 != X210)) | ($true = sP79))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f94,definition,(
% 3.49/0.96 (sP81 = $true) <=> ((! [X324 : subst] : (((comp @ id @ X324)) = X324) & ! [X325 : subst] : (((comp @ X325 @ id)) = X325)) | ? [X323 : subst] : (((comp @ X323 @ id)) != X323) | ? [X322 : subst] : (((comp @ id @ X322)) != X322))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f95,definition,(
% 3.49/0.96 ! [X481 : (subst > term > subst > $o)] : (($true = ((sP82 @ X481))) <=> ? [X484 : (subst > term > term)] : (! [X488 : term] : (($true = ((X481 @ id @ (X484 @ id @ X488) @ id))) | ($true != ((X481 @ id @ X488 @ id)))) & ! [X487 : subst,X485 : subst,X486 : term] : (((sub @ (X484 @ X485 @ X486) @ X487)) = ((X484 @ (comp @ X485 @ X487) @ (sub @ X486 @ X487)))) & (((X481 @ id @ (lam @ (X484 @ sh @ one)) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f96,definition,(
% 3.49/0.96 ($true = sP83) <=> ! [X481 : (subst > term > subst > $o),X482 : term] : (($true = ((X481 @ id @ (lam @ X482) @ id))) | ($true = ((sP82 @ X481))) | ? [X483 : term] : (($true = ((X481 @ id @ X483 @ id))) & ($true != ((X481 @ id @ (sub @ X482 @ (push @ X483 @ id)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f97,definition,(
% 3.49/0.96 ! [X153 : (subst > term > subst > $o)] : (($true = ((sP84 @ X153))) <=> ? [X156 : (subst > term > term)] : (! [X159 : term,X160 : subst,X158 : subst] : (((sub @ (X156 @ X160 @ X159) @ X158)) = ((X156 @ (comp @ X160 @ X158) @ (sub @ X159 @ X158)))) & ($true != ((X153 @ id @ (lam @ (X156 @ sh @ one)) @ id))) & ! [X157 : term] : ((((X153 @ id @ (X156 @ id @ X157) @ id)) = $true) | ($true != ((X153 @ id @ X157 @ id))))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f98,definition,(
% 3.49/0.96 ! [X145 : (subst > term > subst > $o)] : (($true = ((sP85 @ X145))) <=> ! [X147 : (subst > term > term)] : (? [X151 : term] : (($true != ((X145 @ id @ (X147 @ id @ X151) @ id))) & ($true = ((X145 @ id @ X151 @ id)))) | ? [X150 : subst,X148 : term,X149 : subst] : (((X147 @ (comp @ X150 @ X149) @ (sub @ X148 @ X149))) != ((sub @ (X147 @ X150 @ X148) @ X149))) | (((X145 @ id @ (lam @ (X147 @ sh @ one)) @ id)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f99,definition,(
% 3.49/0.96 ($true = sP86) <=> ! [X154 : term,X153 : (subst > term > subst > $o)] : (($true = ((sP84 @ X153))) | ? [X155 : term] : (($true = ((X153 @ id @ X155 @ id))) & ($true != ((X153 @ id @ (sub @ X154 @ (push @ X155 @ id)) @ id)))) | ($true = ((X153 @ id @ (lam @ X154) @ id))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f100,definition,(
% 3.49/0.96 ($true = sP87) <=> ? [X146 : term,X145 : (subst > term > subst > $o)] : (($true != ((X145 @ id @ (lam @ (sub @ X146 @ (push @ one @ sh))) @ id))) & ($true = ((sP85 @ X145))) & ! [X152 : term] : ((((X145 @ id @ (sub @ X146 @ (push @ X152 @ id)) @ id)) = $true) | ($true != ((X145 @ id @ X152 @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f101,definition,(
% 3.49/0.96 ($true = sP88) <=> ! [X433 : term,X431 : term,X434 : term,X432 : term] : ((X432 = X433) | (((ap @ (sub @ X433 @ id) @ X434)) != ((ap @ (sub @ X432 @ id) @ X431))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f102,definition,(
% 3.49/0.96 ($true = sP89) <=> (($true = sP88) | ? [X426 : term] : (((sub @ X426 @ id)) != X426) | ? [X427 : term,X430 : term,X429 : term,X428 : term] : ((X428 != X429) & (((ap @ X429 @ X430)) = ((ap @ X428 @ X427)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f103,definition,(
% 3.49/0.96 ! [X338 : (subst > term > subst > $o)] : (($true = ((sP90 @ X338))) <=> ? [X340 : (subst > term > term)] : (! [X344 : term] : ((((X338 @ id @ (X340 @ id @ X344) @ id)) = $true) | ($true != ((X338 @ id @ X344 @ id)))) & ! [X341 : subst,X343 : subst,X342 : term] : (((X340 @ (comp @ X341 @ X343) @ (sub @ X342 @ X343))) = ((sub @ (X340 @ X341 @ X342) @ X343))) & ($true != ((X338 @ id @ (lam @ (X340 @ sh @ one)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f104,definition,(
% 3.49/0.96 ! [X338 : (subst > term > subst > $o)] : ((((sP91 @ X338)) = $true) <=> ? [X346 : term,X345 : term] : ((((X338 @ id @ X345 @ id)) = $true) & ($true != ((X338 @ id @ (ap @ (sub @ X346 @ id) @ X345) @ id))) & ($true = ((X338 @ id @ X346 @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f105,definition,(
% 3.49/0.96 ! [X375 : (subst > term > subst > $o)] : ((((sP92 @ X375)) = $true) <=> ? [X379 : (subst > term > term)] : (! [X380 : term] : (($true = ((X375 @ id @ (X379 @ id @ X380) @ id))) | (((X375 @ id @ X380 @ id)) != $true)) & ($true != ((X375 @ id @ (lam @ (X379 @ sh @ one)) @ id))) & ! [X381 : subst,X383 : term,X382 : subst] : (((X379 @ (comp @ X382 @ X381) @ (sub @ X383 @ X381))) = ((sub @ (X379 @ X382 @ X383) @ X381)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f106,definition,(
% 3.49/0.96 ($true = sP93) <=> ! [X375 : (subst > term > subst > $o),X377 : (term > $o),X376 : term] : (? [X378 : term] : (((X375 @ id @ X378 @ id)) != ((X377 @ X378))) | (((sP92 @ X375)) = $true) | ? [X384 : term] : (($true = ((X377 @ X384))) & ($true != ((X377 @ (sub @ X376 @ (push @ X384 @ id)))))) | (((X377 @ (lam @ X376))) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f107,definition,(
% 3.49/0.96 ! [X461 : (subst > term > subst > $o)] : (($true = ((sP94 @ X461))) <=> ? [X463 : (subst > term > term)] : (! [X467 : subst,X466 : subst,X465 : term] : (((sub @ (X463 @ X467 @ X465) @ X466)) = ((X463 @ (comp @ X467 @ X466) @ (sub @ X465 @ X466)))) & ! [X464 : term] : (($true = ((X461 @ id @ (X463 @ id @ X464) @ id))) | ($true != ((X461 @ id @ X464 @ id)))) & (((X461 @ id @ (lam @ (X463 @ sh @ one)) @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f108,definition,(
% 3.49/0.96 ! [X461 : (subst > term > subst > $o)] : (($true = ((sP95 @ X461))) <=> ? [X474 : subst,X472 : subst,X473 : subst,X475 : term] : (($true != ((X461 @ X474 @ X475 @ (comp @ X473 @ X472)))) & ($true = ((X461 @ (comp @ X474 @ X473) @ (sub @ X475 @ X473) @ X472)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f109,definition,(
% 3.49/0.96 ! [X461 : (subst > term > subst > $o)] : ((((sP96 @ X461)) = $true) <=> ? [X471 : subst,X470 : subst,X469 : subst,X468 : term] : ((((X461 @ (comp @ X471 @ X470) @ (sub @ X468 @ X470) @ X469)) != $true) & (((X461 @ X471 @ X468 @ (comp @ X470 @ X469))) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f110,definition,(
% 3.49/0.96 ! [X454 : (subst > term > subst > $o)] : (($true = ((sP97 @ X454))) <=> ! [X455 : (subst > term > term)] : (? [X458 : subst,X459 : subst,X457 : term] : (((sub @ (X455 @ X459 @ X457) @ X458)) != ((X455 @ (comp @ X459 @ X458) @ (sub @ X457 @ X458)))) | ? [X456 : term] : ((((X454 @ id @ X456 @ id)) = $true) & (((X454 @ id @ (X455 @ id @ X456) @ id)) != $true)) | ($true = ((X454 @ id @ (lam @ (X455 @ sh @ one)) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f111,definition,(
% 3.49/0.96 (sP98 = $true) <=> ! [X462 : term,X461 : (subst > term > subst > $o)] : (($true = ((sP94 @ X461))) | ? [X476 : term] : ((((X461 @ id @ (sub @ X462 @ (push @ X476 @ id)) @ id)) != $true) & (((X461 @ id @ X476 @ id)) = $true)) | (((X461 @ id @ (lam @ X462) @ id)) = $true) | (((sP96 @ X461)) = $true) | ($true = ((sP95 @ X461))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f112,definition,(
% 3.49/0.96 ($true = sP99) <=> ? [X454 : (subst > term > subst > $o),X453 : term] : (($true = ((sP97 @ X454))) & ($true != ((X454 @ id @ (lam @ (sub @ X453 @ (push @ one @ sh))) @ id))) & ! [X460 : term] : (($true = ((X454 @ id @ (sub @ X453 @ (push @ X460 @ id)) @ id))) | (((X454 @ id @ X460 @ id)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f113,definition,(
% 3.49/0.96 ! [X348 : (subst > term > subst > $o)] : (($true = ((sP100 @ X348))) <=> ? [X349 : (subst > term > term)] : (($true != ((X348 @ id @ (lam @ (X349 @ sh @ one)) @ id))) & ! [X350 : subst,X351 : term,X352 : subst] : (((X349 @ (comp @ X350 @ X352) @ (sub @ X351 @ X352))) = ((sub @ (X349 @ X350 @ X351) @ X352))) & ! [X353 : term] : (($true = ((X348 @ id @ (X349 @ id @ X353) @ id))) | (((X348 @ id @ X353 @ id)) != $true))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f114,definition,(
% 3.49/0.96 ! [X348 : (subst > term > subst > $o)] : (($true = ((sP101 @ X348))) <=> ? [X362 : term,X363 : term] : ((((X348 @ id @ X362 @ id)) = $true) & (((X348 @ id @ X363 @ id)) = $true) & ($true != ((X348 @ id @ (ap @ (sub @ X363 @ id) @ X362) @ id)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f115,definition,(
% 3.49/0.96 ! [X348 : (subst > term > subst > $o)] : (($true = ((sP102 @ X348))) <=> ? [X355 : subst,X357 : subst,X354 : subst,X356 : term] : (($true != ((X348 @ X357 @ X356 @ (comp @ X354 @ X355)))) & ($true = ((X348 @ (comp @ X357 @ X354) @ (sub @ X356 @ X354) @ X355)))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f116,definition,(
% 3.49/0.96 ! [X348 : (subst > term > subst > $o)] : (($true = ((sP103 @ X348))) <=> ? [X364 : term] : (($true != ((X348 @ id @ X364 @ id))) & (((var @ (sub @ X364 @ id))) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f117,definition,(
% 3.49/0.96 ($true = sP104) <=> ! [X348 : (subst > term > subst > $o),X347 : term] : (($true = ((X348 @ id @ X347 @ id))) | ? [X360 : term,X361 : subst,X359 : subst,X358 : subst] : (($true = ((X348 @ X359 @ X360 @ (comp @ X361 @ X358)))) & (((X348 @ (comp @ X359 @ X361) @ (sub @ X360 @ X361) @ X358)) != $true)) | ($true = ((sP101 @ X348))) | ($true = ((sP100 @ X348))) | ($true = ((sP103 @ X348))) | ($true = ((sP102 @ X348))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f118,definition,(
% 3.49/0.96 ! [X412 : (term > $o)] : ((((sP105 @ X412)) = $true) <=> ! [X416 : term,X415 : term] : (($true != ((X412 @ X416))) | (((X412 @ X415)) != $true) | (((X412 @ (ap @ X415 @ X416))) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f119,definition,(
% 3.49/0.96 ! [X412 : (term > $o)] : (($true = ((sP106 @ X412))) <=> ! [X417 : term] : (($true = ((X412 @ (lam @ X417)))) | (((X412 @ X417)) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f120,definition,(
% 3.49/0.96 ! [X418 : (term > $o)] : (($true = ((sP107 @ X418))) <=> ? [X421 : term] : (! [X422 : term] : (($true != ((X418 @ X422))) | ($true = ((X418 @ (sub @ X421 @ (push @ X422 @ id)))))) & (((X418 @ (lam @ X421))) != $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f121,definition,(
% 3.49/0.96 ! [X418 : (term > $o)] : ((((sP108 @ X418)) = $true) <=> ? [X424 : term,X425 : term] : (($true = ((X418 @ X424))) & ($true != ((X418 @ (ap @ X425 @ X424)))) & (((X418 @ X425)) = $true)))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f122,definition,(
% 3.49/0.96 ($true = sP109) <=> ! [X419 : subst,X418 : (term > $o),X420 : term] : ((((sP108 @ X418)) = $true) | ($true = ((X418 @ (sub @ X420 @ X419)))) | ? [X423 : term] : (($true != ((X418 @ (sub @ X423 @ X419)))) & (((var @ X423)) = $true)) | ($true = ((sP107 @ X418))))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f123,definition,(
% 3.49/0.96 ($true = sP110) <=> ? [X412 : (term > $o),X413 : term] : (! [X414 : term] : (($true = ((X412 @ X414))) | ($true != ((var @ X414)))) & ($true = ((sP106 @ X412))) & ($true != ((X412 @ X413))) & (((sP105 @ X412)) = $true))),
% 3.49/0.96 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 3.49/0.96 thf(f124,plain,(
% 3.49/0.96 (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) <=> (axshiftcons = $true)) & (! [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (? [X102 : term] : (((X100 @ X102)) != ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) | (((X101 @ X99)) != $true) | ($true = ((X100 @ one)))) <=> (pushprop_lem1v2 = $true)) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((pushprop_lem0 = $true) <=> ! [X139 : (term > $o),X140 : term,X141 : subst] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141)))))) & ((induction2lem_lthm = $true) <=> (? [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) != X409) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411) | ($true = sP109) | ($true = sP110) | ? [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) != X408))) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (($true = sP104) <=> (hoasinduction = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (($true = sP99) | ? [X452 : term] : (((sub @ X452 @ id)) != X452) | (sP98 = $true))) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X330 : term,X331 : term,X329 : (subst > term > term)] : (? [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) != ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) <=> (hoaslamnotap = $true)) & ((hoasinduction_lem3v2_f = $true) <=> ! [X220 : term] : ? [X221 : (subst > term > term)] : ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223))))) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((termmset_lthm = $true) <=> (? [X273 : term] : (((sub @ X273 @ id)) != X273) | ! [X274 : term] : (((sub @ X274 @ id)) = X274))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) <=> (apinj1 = $true)) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & (($true = sP93) <=> (hoasinduction_lem3v2a = $true)) & (! [X339 : term,X338 : (subst > term > subst > $o)] : (($true = ((X338 @ id @ X339 @ id))) | (((sP91 @ X338)) = $true) | ($true = ((sP90 @ X338)))) <=> (hoasinduction_no_psi_cond = $true)) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) <=> ! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13)) & (($true = sP89) <=> (hoasapinj1_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & ((($true = sP87) | ? [X144 : term] : (((sub @ X144 @ id)) != X144) | ($true = sP86)) <=> (hoasinduction_lem3a_lthm = $true)) & ((hoasinduction_lem3a = $true) <=> ($true = sP83)) & ((substmonoid_lthm = $true) <=> (sP81 = $true)) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) <=> (axvarid = $true)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) <=> (shinj = $true)) & (termmset_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & ((laminj = $true) <=> ! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224))))) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3b = $true) <=> ! [X438 : term] : ? [X439 : (subst > term > term)] : (((X439 @ sh @ one)) = ((sub @ X438 @ (push @ one @ sh))))) & (($true = sP80) <=> (hoasapinj2_lthm = $true)) & ((induction2 = $true) <=> (sP78 = $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP75) <=> (hoasinduction_lem3aaa = $true)) & ((pushprop_lem1 = $true) <=> ! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126))))) & ((pushprop_lem0_lthm = $true) <=> ! [X92 : (term > $o),X93 : term,X91 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91)))))) & ((? [X253 : term] : (((sub @ X253 @ id)) != X253) | ? [X243 : (subst > term > subst > $o)] : ! [X244 : (term > $o)] : ? [X245 : term] : (((X243 @ id @ X245 @ id)) != ((X244 @ X245))) | ($true = sP71) | (sP72 = $true) | ($true = sP73)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (((d2subst @ d_id)) = id) & ((($true = sP64) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ? [X174 : term] : ! [X175 : (subst > term > term)] : ? [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) != ((X175 @ X177 @ X176)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (((d2subst @ d_id)) = sh) & ((($true = sP61) | (sP59 = $true) | ($true = sP60) | ($true = sP62)) <=> (hoasinduction_lthm = $true)) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (($true = sP46) <=> (hoaslaminj_lthm = $true)) & (($true = sP44) <=> (hoasinduction_lem3 = $true)) & ((axidl = $true) <=> ! [X104 : subst] : (((comp @ id @ X104)) = X104)) & (axapp = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) <=> (apinj2 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((($true = sP40) | ? [X514 : term] : (((sub @ X514 @ id)) != X514)) <=> (hoasinduction_lem3v2_lthm = $true)) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axscons = $true) <=> ! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226)) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa_lthm = $true) <=> ($true = sP36)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (($true = sP34) <=> (induction2lem = $true)) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem2v2 = $true) <=> ($true = sP31)) & (hoasapnotvar_gthm = $true) & (! [X335 : (subst > term > subst > $o)] : ? [X336 : (term > $o)] : ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id))) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem3v2 = $true) & ! [X96 : d_subst,X97 : d_subst] : ((X96 = X97) | (((d2subst @ X97)) != ((d2subst @ X96)))) & (ulamvarind = $true) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) <=> (termmset = $true)) & (axabs = $true) & ((hoaslaminj = $true) <=> ! [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (? [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) != ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | (((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one)))) | ? [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X365 @ X372 @ X374) @ X373))))) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & (($true = sP28) <=> (hoasinduction_lem2 = $true)) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasinduction_lem1v2 = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) != ((d2term @ X161))) | (X161 = X162)) & ((substmonoid = $true) <=> (! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2 = $true) <=> (sP25 = $true)) & (axvarshift = $true) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) <=> (hoasapinj1 = $true)) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one)))) & (! [X435 : (subst > term > subst > $o)] : ? [X436 : (term > $o)] : ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))) <=> (hoasinduction_lem0 = $true)) & (! [X326 : subst] : (((comp @ X326 @ id)) = X326) <=> (axidr = $true)) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lthm_3 = $true) <=> (? [X293 : term] : (((sub @ X293 @ id)) != X293) | (sP19 = $true) | ? [X283 : (subst > term > subst > $o)] : ! [X284 : (term > $o)] : ? [X285 : term] : (((X283 @ id @ X285 @ id)) != ((X284 @ X285))) | (sP21 = $true) | ($true = sP20))) & (pushprop_lem1_gthm = $true) & (axclos = $true) & ((induction = $true) <=> (sP11 = $true)) & ((hoasapinj2 = $true) <=> ! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218))))) & (hoasinduction_lem1 = $true) & ((induction2_lthm = $true) <=> (? [X19 : term] : (((sub @ X19 @ id)) != X19) | (sP8 = $true) | ($true = sP7))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & ((! [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ? [X539 : term] : (((X538 @ X539)) != ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) | ? [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) != X533)) <=> (pushprop_lem1v2_lthm = $true)) & ! [X103 : d_subst] : (d_id = X103) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) <=> ($true = sP1)) & ((pushprop_lem1_lthm = $true) <=> (? [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) != X131) | ! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)) | ? [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) != X133))) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(definition_folding,[],[f12,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,f72,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])).
% 3.49/0.96 thf(f462,plain,(
% 3.49/0.96 ((! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) != X206))) & ((! [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (? [X102 : term] : (((X100 @ X102)) != ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) | (((X101 @ X99)) != $true) | ($true = ((X100 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (! [X102 : term] : (((X100 @ X102)) = ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) & (((X101 @ X99)) = $true) & ($true != ((X100 @ one)))))) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & (((pushprop_lem0 = $true) | ? [X139 : (term > $o),X140 : term,X141 : subst] : ! [X142 : (term > $o)] : ? [X143 : term] : (((X142 @ X143)) != ((X139 @ (sub @ X143 @ (push @ X140 @ X141)))))) & (! [X139 : (term > $o),X140 : term,X141 : subst] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141))))) | (pushprop_lem0 != $true))) & (((induction2lem_lthm = $true) | (! [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) = X409) & ! [X411 : subst] : (((comp @ X411 @ id)) = X411) & ($true != sP109) & ($true != sP110) & ! [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) = X408))) & ((? [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) != X409) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411) | ($true = sP109) | ($true = sP110) | ? [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) != X408)) | (induction2lem_lthm != $true))) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & ((($true = sP104) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP104))) & (((hoasinduction_lem3_lthm = $true) | (($true != sP99) & ! [X452 : term] : (((sub @ X452 @ id)) = X452) & (sP98 != $true))) & ((($true = sP99) | ? [X452 : term] : (((sub @ X452 @ id)) != X452) | (sP98 = $true)) | (hoasinduction_lem3_lthm != $true))) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & ((! [X330 : term,X331 : term,X329 : (subst > term > term)] : (? [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) != ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X330 : term,X331 : term,X329 : (subst > term > term)] : (! [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) = ((sub @ (X329 @ X332 @ X333) @ X334))) & (((ap @ (sub @ X331 @ id) @ X330)) = ((lam @ (X329 @ sh @ one))))))) & (((hoasinduction_lem3v2_f = $true) | ? [X220 : term] : ! [X221 : (subst > term > term)] : ? [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) != ((sub @ X220 @ (push @ X222 @ X223))))) & (! [X220 : term] : ? [X221 : (subst > term > term)] : ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223)))) | (hoasinduction_lem3v2_f != $true))) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & (((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))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 != X406) & (((ap @ X406 @ X403)) = ((ap @ X405 @ X404)))))) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & ((($true = sP93) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP93))) & ((! [X339 : term,X338 : (subst > term > subst > $o)] : (($true = ((X338 @ id @ X339 @ id))) | (((sP91 @ X338)) = $true) | ($true = ((sP90 @ X338)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X339 : term,X338 : (subst > term > subst > $o)] : (($true != ((X338 @ id @ X339 @ id))) & (((sP91 @ X338)) != $true) & ($true != ((sP90 @ X338)))))) & (hoasinduction_lem2v2_gthm = $true) & (((axvarcons = $true) | ? [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) != X13)) & (! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13) | (axvarcons != $true))) & ((($true = sP89) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP89))) & (hoasinduction_lem1_lthm = $true) & (((($true = sP87) | ? [X144 : term] : (((sub @ X144 @ id)) != X144) | ($true = sP86)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP87) & ! [X144 : term] : (((sub @ X144 @ id)) = X144) & ($true != sP86)))) & (((hoasinduction_lem3a = $true) | ($true != sP83)) & (($true = sP83) | (hoasinduction_lem3a != $true))) & (((substmonoid_lthm = $true) | (sP81 != $true)) & ((sP81 = $true) | (substmonoid_lthm != $true))) & ((! [X163 : term] : (((sub @ X163 @ id)) = X163) | (axvarid != $true)) & ((axvarid = $true) | ? [X163 : term] : (((sub @ X163 @ id)) != X163))) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & ((! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) | (shinj != $true)) & ((shinj = $true) | ? [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) = ((sub @ X172 @ sh))) & (X172 != X173)))) & (termmset_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & (((laminj = $true) | ? [X225 : term,X224 : term] : ((X224 != X225) & (((lam @ X225)) = ((lam @ X224))))) & (! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224)))) | (laminj != $true))) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & (((hoasinduction_lem3b = $true) | ? [X438 : term] : ! [X439 : (subst > term > term)] : (((X439 @ sh @ one)) != ((sub @ X438 @ (push @ one @ sh))))) & (! [X438 : term] : ? [X439 : (subst > term > term)] : (((X439 @ sh @ one)) = ((sub @ X438 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true))) & ((($true = sP80) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP80))) & (((induction2 = $true) | (sP78 != $true)) & ((sP78 = $true) | (induction2 != $true))) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & ((($true = sP75) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP75))) & (((pushprop_lem1 = $true) | ? [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) != $true) & ($true = ((X127 @ X126))))) & (! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126)))) | (pushprop_lem1 != $true))) & (((pushprop_lem0_lthm = $true) | ? [X92 : (term > $o),X93 : term,X91 : subst] : ! [X94 : (term > $o)] : ? [X95 : term] : (((X94 @ X95)) != ((X92 @ (sub @ X95 @ (push @ X93 @ X91)))))) & (! [X92 : (term > $o),X93 : term,X91 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) | (pushprop_lem0_lthm != $true))) & (((? [X253 : term] : (((sub @ X253 @ id)) != X253) | ? [X243 : (subst > term > subst > $o)] : ! [X244 : (term > $o)] : ? [X245 : term] : (((X243 @ id @ X245 @ id)) != ((X244 @ X245))) | ($true = sP71) | (sP72 = $true) | ($true = sP73)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X253 : term] : (((sub @ X253 @ id)) = X253) & ! [X243 : (subst > term > subst > $o)] : ? [X244 : (term > $o)] : ! [X245 : term] : (((X243 @ id @ X245 @ id)) = ((X244 @ X245))) & ($true != sP71) & (sP72 != $true) & ($true != sP73)))) & (((d2subst @ d_id)) = id) & (((($true = sP64) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ? [X174 : term] : ! [X175 : (subst > term > term)] : ? [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) != ((X175 @ X177 @ X176)))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP64) & ! [X178 : term] : (((sub @ X178 @ id)) = X178) & ! [X174 : term] : ? [X175 : (subst > term > term)] : ! [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) = ((X175 @ X177 @ X176)))))) & (((d2subst @ d_id)) = sh) & (((($true = sP61) | (sP59 = $true) | ($true = sP60) | ($true = sP62)) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP61) & (sP59 != $true) & ($true != sP60) & ($true != sP62)))) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & ((($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46))) & ((($true = sP44) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP44))) & (((axidl = $true) | ? [X104 : subst] : (((comp @ id @ X104)) != X104)) & (! [X104 : subst] : (((comp @ id @ X104)) = X104) | (axidl != $true))) & (axapp = $true) & ((! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) = ((ap @ X479 @ X480))) & (X478 != X480)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((($true = sP40) | ? [X514 : term] : (((sub @ X514 @ id)) != X514)) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP40) & ! [X514 : term] : (((sub @ X514 @ id)) = X514)))) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & (((axscons = $true) | ? [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) != X226)) & (! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226) | (axscons != $true))) & (hoasapnotvar = $true) & (((hoasinduction_lem3aa_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3aa_lthm != $true))) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & ((! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X121 : term] : ! [X122 : (subst > term > term)] : ? [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) != ((X122 @ X124 @ X123))))) & ((($true = sP34) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP34))) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & (((hoasinduction_lem2v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2v2 != $true))) & (hoasapnotvar_gthm = $true) & ((! [X335 : (subst > term > subst > $o)] : ? [X336 : (term > $o)] : ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X335 : (subst > term > subst > $o)] : ! [X336 : (term > $o)] : ? [X337 : term] : (((X336 @ X337)) != ((X335 @ id @ X337 @ id))))) & (pushprop_lem3v2 = $true) & ! [X96 : d_subst,X97 : d_subst] : ((X96 = X97) | (((d2subst @ X97)) != ((d2subst @ X96)))) & (ulamvarind = $true) & ((! [X205 : term] : (((sub @ X205 @ id)) = X205) | (termmset != $true)) & ((termmset = $true) | ? [X205 : term] : (((sub @ X205 @ id)) != X205))) & (axabs = $true) & (((hoaslaminj = $true) | ? [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (! [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) = ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) & (((X367 @ X368 @ X366)) != ((X365 @ X368 @ X366))) & (((lam @ (X367 @ sh @ one))) = ((lam @ (X365 @ sh @ one)))) & ! [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X365 @ X372 @ X374) @ X373))))) & (! [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (? [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) != ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | (((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one)))) | ? [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X365 @ X372 @ X374) @ X373)))) | (hoaslaminj != $true))) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & ((($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28))) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasinduction_lem1v2 = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) != ((d2term @ X161))) | (X161 = X162)) & (((substmonoid = $true) | (? [X505 : subst] : (((comp @ id @ X505)) != X505) | ? [X504 : subst] : (((comp @ X504 @ id)) != X504))) & ((! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504)) | (substmonoid != $true))) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & (((hoasinduction_lem3v2 = $true) | (sP25 != $true)) & ((sP25 = $true) | (hoasinduction_lem3v2 != $true))) & (axvarshift = $true) & ((! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) = ((ap @ (sub @ X15 @ id) @ X18))) & (X15 != X17)))) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X203 : term] : ! [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) != ((X204 @ sh @ one)))) & (! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true))) & ((! [X435 : (subst > term > subst > $o)] : ? [X436 : (term > $o)] : ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X435 : (subst > term > subst > $o)] : ! [X436 : (term > $o)] : ? [X437 : term] : (((X436 @ X437)) != ((X435 @ id @ X437 @ id))))) & ((! [X326 : subst] : (((comp @ X326 @ id)) = X326) | (axidr != $true)) & ((axidr = $true) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326))) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & (((hoasinduction_lthm_3 = $true) | (! [X293 : term] : (((sub @ X293 @ id)) = X293) & (sP19 != $true) & ! [X283 : (subst > term > subst > $o)] : ? [X284 : (term > $o)] : ! [X285 : term] : (((X283 @ id @ X285 @ id)) = ((X284 @ X285))) & (sP21 != $true) & ($true != sP20))) & ((? [X293 : term] : (((sub @ X293 @ id)) != X293) | (sP19 = $true) | ? [X283 : (subst > term > subst > $o)] : ! [X284 : (term > $o)] : ? [X285 : term] : (((X283 @ id @ X285 @ id)) != ((X284 @ X285))) | (sP21 = $true) | ($true = sP20)) | (hoasinduction_lthm_3 != $true))) & (pushprop_lem1_gthm = $true) & (axclos = $true) & (((induction = $true) | (sP11 != $true)) & ((sP11 = $true) | (induction != $true))) & (((hoasapinj2 = $true) | ? [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 != X218) & (((ap @ (sub @ X216 @ id) @ X217)) = ((ap @ (sub @ X219 @ id) @ X218))))) & (! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218)))) | (hoasapinj2 != $true))) & (hoasinduction_lem1 = $true) & (((induction2_lthm = $true) | (! [X19 : term] : (((sub @ X19 @ id)) = X19) & (sP8 != $true) & ($true != sP7))) & ((? [X19 : term] : (((sub @ X19 @ id)) != X19) | (sP8 = $true) | ($true = sP7)) | (induction2_lthm != $true))) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & (((! [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ? [X539 : term] : (((X538 @ X539)) != ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) | ? [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) != X533)) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true = ((X537 @ X535))) & (((X538 @ one)) != $true) & ! [X539 : term] : (((X538 @ X539)) = ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) & ! [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) = X533)))) & ! [X103 : d_subst] : (d_id = X103) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & (((hoasinduction_lem3aa = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem3aa != $true))) & (((pushprop_lem1_lthm = $true) | (! [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) = X131) & ? [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) = $true) & (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) != $true)) & ! [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) = X133))) & ((? [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) != X131) | ! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)) | ? [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) != X133)) | (pushprop_lem1_lthm != $true))) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(nnf_transformation,[],[f124])).
% 3.49/0.96 thf(f463,plain,(
% 3.49/0.96 (! [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) = X206) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X207 : term,X206 : subst] : (((comp @ sh @ (push @ X207 @ X206))) != X206)) & (! [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (? [X102 : term] : (((X100 @ X102)) != ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) | (((X101 @ X99)) != $true) | ($true = ((X100 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X99 : term,X100 : (term > $o),X101 : (term > $o),X98 : subst] : (! [X102 : term] : (((X100 @ X102)) = ((X101 @ (sub @ X102 @ (push @ X99 @ X98))))) & (((X101 @ X99)) = $true) & ($true != ((X100 @ one))))) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((pushprop_lem0 = $true) | ? [X139 : (term > $o),X140 : term,X141 : subst] : ! [X142 : (term > $o)] : ? [X143 : term] : (((X142 @ X143)) != ((X139 @ (sub @ X143 @ (push @ X140 @ X141)))))) & (! [X139 : (term > $o),X140 : term,X141 : subst] : ? [X142 : (term > $o)] : ! [X143 : term] : (((X142 @ X143)) = ((X139 @ (sub @ X143 @ (push @ X140 @ X141))))) | (pushprop_lem0 != $true)) & ((induction2lem_lthm = $true) | (! [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) = X409) & ! [X411 : subst] : (((comp @ X411 @ id)) = X411) & ($true != sP109) & ($true != sP110) & ! [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) = X408))) & (? [X410 : term,X409 : subst] : (((comp @ sh @ (push @ X410 @ X409))) != X409) | ? [X411 : subst] : (((comp @ X411 @ id)) != X411) | ($true = sP109) | ($true = sP110) | ? [X407 : subst,X408 : term] : (((sub @ one @ (push @ X408 @ X407))) != X408) | (induction2lem_lthm != $true)) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (($true = sP104) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP104)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP99) & ! [X452 : term] : (((sub @ X452 @ id)) = X452) & (sP98 != $true))) & (($true = sP99) | ? [X452 : term] : (((sub @ X452 @ id)) != X452) | (sP98 = $true) | (hoasinduction_lem3_lthm != $true)) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X330 : term,X331 : term,X329 : (subst > term > term)] : (? [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) != ((sub @ (X329 @ X332 @ X333) @ X334))) | (((ap @ (sub @ X331 @ id) @ X330)) != ((lam @ (X329 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X330 : term,X331 : term,X329 : (subst > term > term)] : (! [X334 : subst,X332 : subst,X333 : term] : (((X329 @ (comp @ X332 @ X334) @ (sub @ X333 @ X334))) = ((sub @ (X329 @ X332 @ X333) @ X334))) & (((ap @ (sub @ X331 @ id) @ X330)) = ((lam @ (X329 @ sh @ one)))))) & ((hoasinduction_lem3v2_f = $true) | ? [X220 : term] : ! [X221 : (subst > term > term)] : ? [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) != ((sub @ X220 @ (push @ X222 @ X223))))) & (! [X220 : term] : ? [X221 : (subst > term > term)] : ! [X223 : subst,X222 : term] : (((X221 @ X223 @ X222)) = ((sub @ X220 @ (push @ X222 @ X223)))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((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)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 = X406) | (((ap @ X406 @ X403)) != ((ap @ X405 @ X404)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X404 : term,X403 : term,X405 : term,X406 : term] : ((X405 != X406) & (((ap @ X406 @ X403)) = ((ap @ X405 @ X404))))) & ! [X35 : term] : ? [X36 : d_term] : (((d2term @ X36)) = X35) & (($true = sP93) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP93)) & (! [X339 : term,X338 : (subst > term > subst > $o)] : (($true = ((X338 @ id @ X339 @ id))) | (((sP91 @ X338)) = $true) | ($true = ((sP90 @ X338)))) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X339 : term,X338 : (subst > term > subst > $o)] : (($true != ((X338 @ id @ X339 @ id))) & (((sP91 @ X338)) != $true) & ($true != ((sP90 @ X338))))) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) | ? [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) != X13)) & (! [X13 : term,X14 : subst] : (((sub @ one @ (push @ X13 @ X14))) = X13) | (axvarcons != $true)) & (($true = sP89) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP89)) & (hoasinduction_lem1_lthm = $true) & (($true = sP87) | ? [X144 : term] : (((sub @ X144 @ id)) != X144) | ($true = sP86) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP87) & ! [X144 : term] : (((sub @ X144 @ id)) = X144) & ($true != sP86))) & ((hoasinduction_lem3a = $true) | ($true != sP83)) & (($true = sP83) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (sP81 != $true)) & ((sP81 = $true) | (substmonoid_lthm != $true)) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) | (axvarid != $true)) & ((axvarid = $true) | ? [X163 : term] : (((sub @ X163 @ id)) != X163)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (! [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) != ((sub @ X172 @ sh))) | (X172 = X173)) | (shinj != $true)) & ((shinj = $true) | ? [X173 : term,X172 : term] : ((((sub @ X173 @ sh)) = ((sub @ X172 @ sh))) & (X172 != X173))) & (termmset_gthm = $true) & ! [X513 : d_term] : (d_one = X513) & ((laminj = $true) | ? [X225 : term,X224 : term] : ((X224 != X225) & (((lam @ X225)) = ((lam @ X224))))) & (! [X225 : term,X224 : term] : ((X224 = X225) | (((lam @ X225)) != ((lam @ X224)))) | (laminj != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X438 : term] : ! [X439 : (subst > term > term)] : (((X439 @ sh @ one)) != ((sub @ X438 @ (push @ one @ sh))))) & (! [X438 : term] : ? [X439 : (subst > term > term)] : (((X439 @ sh @ one)) = ((sub @ X438 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (($true = sP80) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP80)) & ((induction2 = $true) | (sP78 != $true)) & ((sP78 = $true) | (induction2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP75) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP75)) & ((pushprop_lem1 = $true) | ? [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) != $true) & ($true = ((X127 @ X126))))) & (! [X127 : (term > $o),X126 : term,X128 : (term > $o),X125 : term,X129 : subst] : ((((X128 @ (sub @ X126 @ (push @ X125 @ X129)))) = $true) | ($true != ((X127 @ X126)))) | (pushprop_lem1 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X92 : (term > $o),X93 : term,X91 : subst] : ! [X94 : (term > $o)] : ? [X95 : term] : (((X94 @ X95)) != ((X92 @ (sub @ X95 @ (push @ X93 @ X91)))))) & (! [X92 : (term > $o),X93 : term,X91 : subst] : ? [X94 : (term > $o)] : ! [X95 : term] : (((X94 @ X95)) = ((X92 @ (sub @ X95 @ (push @ X93 @ X91))))) | (pushprop_lem0_lthm != $true)) & (? [X253 : term] : (((sub @ X253 @ id)) != X253) | ? [X243 : (subst > term > subst > $o)] : ! [X244 : (term > $o)] : ? [X245 : term] : (((X243 @ id @ X245 @ id)) != ((X244 @ X245))) | ($true = sP71) | (sP72 = $true) | ($true = sP73) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X253 : term] : (((sub @ X253 @ id)) = X253) & ! [X243 : (subst > term > subst > $o)] : ? [X244 : (term > $o)] : ! [X245 : term] : (((X243 @ id @ X245 @ id)) = ((X244 @ X245))) & ($true != sP71) & (sP72 != $true) & ($true != sP73))) & (((d2subst @ d_id)) = id) & (($true = sP64) | ? [X178 : term] : (((sub @ X178 @ id)) != X178) | ? [X174 : term] : ! [X175 : (subst > term > term)] : ? [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) != ((X175 @ X177 @ X176))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP64) & ! [X178 : term] : (((sub @ X178 @ id)) = X178) & ! [X174 : term] : ? [X175 : (subst > term > term)] : ! [X176 : term,X177 : subst] : (((sub @ X174 @ (push @ X176 @ X177))) = ((X175 @ X177 @ X176))))) & (((d2subst @ d_id)) = sh) & (($true = sP61) | (sP59 = $true) | ($true = sP60) | ($true = sP62) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP61) & (sP59 != $true) & ($true != sP60) & ($true != sP62))) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (($true = sP44) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP44)) & ((axidl = $true) | ? [X104 : subst] : (((comp @ id @ X104)) != X104)) & (! [X104 : subst] : (((comp @ id @ X104)) = X104) | (axidl != $true)) & (axapp = $true) & (! [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) != ((ap @ X479 @ X480))) | (X478 = X480)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X479 : term,X480 : term,X477 : term,X478 : term] : ((((ap @ X477 @ X478)) = ((ap @ X479 @ X480))) & (X478 != X480))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (($true = sP40) | ? [X514 : term] : (((sub @ X514 @ id)) != X514) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP40) & ! [X514 : term] : (((sub @ X514 @ id)) = X514))) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axscons = $true) | ? [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) != X226)) & (! [X226 : subst] : (((push @ (sub @ one @ X226) @ (comp @ sh @ X226))) = X226) | (axscons != $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3aa_lthm != $true)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (! [X121 : term] : ? [X122 : (subst > term > term)] : ! [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) = ((X122 @ X124 @ X123))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X121 : term] : ! [X122 : (subst > term > term)] : ? [X123 : term,X124 : subst] : (((sub @ X121 @ (push @ X123 @ X124))) != ((X122 @ X124 @ X123)))) & (($true = sP34) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP34)) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem2v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_gthm = $true) & (! [X335 : (subst > term > subst > $o)] : ? [X336 : (term > $o)] : ! [X337 : term] : (((X336 @ X337)) = ((X335 @ id @ X337 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X335 : (subst > term > subst > $o)] : ! [X336 : (term > $o)] : ? [X337 : term] : (((X336 @ X337)) != ((X335 @ id @ X337 @ id)))) & (pushprop_lem3v2 = $true) & ! [X96 : d_subst,X97 : d_subst] : ((X96 = X97) | (((d2subst @ X97)) != ((d2subst @ X96)))) & (ulamvarind = $true) & (! [X205 : term] : (((sub @ X205 @ id)) = X205) | (termmset != $true)) & ((termmset = $true) | ? [X205 : term] : (((sub @ X205 @ id)) != X205)) & (axabs = $true) & ((hoaslaminj = $true) | ? [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (! [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) = ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) & (((X367 @ X368 @ X366)) != ((X365 @ X368 @ X366))) & (((lam @ (X367 @ sh @ one))) = ((lam @ (X365 @ sh @ one)))) & ! [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) = ((sub @ (X365 @ X372 @ X374) @ X373))))) & (! [X365 : (subst > term > term),X368 : subst,X366 : term,X367 : (subst > term > term)] : (? [X371 : subst,X370 : term,X369 : subst] : (((sub @ (X367 @ X371 @ X370) @ X369)) != ((X367 @ (comp @ X371 @ X369) @ (sub @ X370 @ X369)))) | (((X367 @ X368 @ X366)) = ((X365 @ X368 @ X366))) | (((lam @ (X367 @ sh @ one))) != ((lam @ (X365 @ sh @ one)))) | ? [X372 : subst,X374 : term,X373 : subst] : (((X365 @ (comp @ X372 @ X373) @ (sub @ X374 @ X373))) != ((sub @ (X365 @ X372 @ X374) @ X373)))) | (hoaslaminj != $true)) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & ! [X327 : subst] : ? [X328 : d_subst] : (((d2subst @ X328)) = X327) & (hoasinduction_lem1v2 = $true) & ! [X161 : d_term,X162 : d_term] : ((((d2term @ X162)) != ((d2term @ X161))) | (X161 = X162)) & ((substmonoid = $true) | ? [X505 : subst] : (((comp @ id @ X505)) != X505) | ? [X504 : subst] : (((comp @ X504 @ id)) != X504)) & ((! [X505 : subst] : (((comp @ id @ X505)) = X505) & ! [X504 : subst] : (((comp @ X504 @ id)) = X504)) | (substmonoid != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2 = $true) | (sP25 != $true)) & ((sP25 = $true) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & (! [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) != ((ap @ (sub @ X15 @ id) @ X18))) | (X15 = X17)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X18 : term,X16 : term,X15 : term,X17 : term] : ((((ap @ (sub @ X17 @ id) @ X16)) = ((ap @ (sub @ X15 @ id) @ X18))) & (X15 != X17))) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X203 : term] : ! [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) != ((X204 @ sh @ one)))) & (! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (! [X435 : (subst > term > subst > $o)] : ? [X436 : (term > $o)] : ! [X437 : term] : (((X436 @ X437)) = ((X435 @ id @ X437 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X435 : (subst > term > subst > $o)] : ! [X436 : (term > $o)] : ? [X437 : term] : (((X436 @ X437)) != ((X435 @ id @ X437 @ id)))) & (! [X326 : subst] : (((comp @ X326 @ id)) = X326) | (axidr != $true)) & ((axidr = $true) | ? [X326 : subst] : (((comp @ X326 @ id)) != X326)) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X293 : term] : (((sub @ X293 @ id)) = X293) & (sP19 != $true) & ! [X283 : (subst > term > subst > $o)] : ? [X284 : (term > $o)] : ! [X285 : term] : (((X283 @ id @ X285 @ id)) = ((X284 @ X285))) & (sP21 != $true) & ($true != sP20))) & (? [X293 : term] : (((sub @ X293 @ id)) != X293) | (sP19 = $true) | ? [X283 : (subst > term > subst > $o)] : ! [X284 : (term > $o)] : ? [X285 : term] : (((X283 @ id @ X285 @ id)) != ((X284 @ X285))) | (sP21 = $true) | ($true = sP20) | (hoasinduction_lthm_3 != $true)) & (pushprop_lem1_gthm = $true) & (axclos = $true) & ((induction = $true) | (sP11 != $true)) & ((sP11 = $true) | (induction != $true)) & ((hoasapinj2 = $true) | ? [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 != X218) & (((ap @ (sub @ X216 @ id) @ X217)) = ((ap @ (sub @ X219 @ id) @ X218))))) & (! [X219 : term,X218 : term,X216 : term,X217 : term] : ((X217 = X218) | (((ap @ (sub @ X216 @ id) @ X217)) != ((ap @ (sub @ X219 @ id) @ X218)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ((induction2_lthm = $true) | (! [X19 : term] : (((sub @ X19 @ id)) = X19) & (sP8 != $true) & ($true != sP7))) & (? [X19 : term] : (((sub @ X19 @ id)) != X19) | (sP8 = $true) | ($true = sP7) | (induction2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & (! [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true != ((X537 @ X535))) | (((X538 @ one)) = $true) | ? [X539 : term] : (((X538 @ X539)) != ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) | ? [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) != X533) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X537 : (term > $o),X535 : term,X536 : subst,X538 : (term > $o)] : (($true = ((X537 @ X535))) & (((X538 @ one)) != $true) & ! [X539 : term] : (((X538 @ X539)) = ((X537 @ (sub @ X539 @ (push @ X535 @ X536)))))) & ! [X534 : subst,X533 : term] : (((sub @ one @ (push @ X533 @ X534))) = X533))) & ! [X103 : d_subst] : (d_id = X103) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1_lthm = $true) | (! [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) = X131) & ? [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) = $true) & (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) != $true)) & ! [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) = X133))) & (? [X130 : subst,X131 : term] : (((sub @ one @ (push @ X131 @ X130))) != X131) | ! [X136 : term,X137 : (term > $o),X134 : (term > $o),X135 : subst,X138 : term] : ((((X137 @ X136)) != $true) | (((X134 @ (sub @ X136 @ (push @ X138 @ X135)))) = $true)) | ? [X132 : term,X133 : subst] : (((comp @ sh @ (push @ X132 @ X133))) != X133) | (pushprop_lem1_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(flattening,[],[f462])).
% 3.49/0.96 thf(f464,plain,(
% 3.49/0.96 (! [X0 : term,X1 : subst] : (((comp @ sh @ (push @ X0 @ X1))) = X1) | (axshiftcons != $true)) & ((axshiftcons = $true) | ? [X2 : term,X3 : subst] : (((comp @ sh @ (push @ X2 @ X3))) != X3)) & (! [X4 : term,X5 : (term > $o),X6 : (term > $o),X7 : subst] : (? [X8 : term] : (((X5 @ X8)) != ((X6 @ (sub @ X8 @ (push @ X4 @ X7))))) | ($true != ((X6 @ X4))) | ($true = ((X5 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X9 : term,X10 : (term > $o),X11 : (term > $o),X12 : subst] : (! [X13 : term] : (((X10 @ X13)) = ((X11 @ (sub @ X13 @ (push @ X9 @ X12))))) & (((X11 @ X9)) = $true) & (((X10 @ one)) != $true))) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((pushprop_lem0 = $true) | ? [X14 : (term > $o),X15 : term,X16 : subst] : ! [X17 : (term > $o)] : ? [X18 : term] : (((X14 @ (sub @ X18 @ (push @ X15 @ X16)))) != ((X17 @ X18)))) & (! [X19 : (term > $o),X20 : term,X21 : subst] : ? [X22 : (term > $o)] : ! [X23 : term] : (((X22 @ X23)) = ((X19 @ (sub @ X23 @ (push @ X20 @ X21))))) | (pushprop_lem0 != $true)) & ((induction2lem_lthm = $true) | (! [X24 : term,X25 : subst] : (((comp @ sh @ (push @ X24 @ X25))) = X25) & ! [X26 : subst] : (((comp @ X26 @ id)) = X26) & ($true != sP109) & ($true != sP110) & ! [X27 : subst,X28 : term] : (((sub @ one @ (push @ X28 @ X27))) = X28))) & (? [X29 : term,X30 : subst] : (((comp @ sh @ (push @ X29 @ X30))) != X30) | ? [X31 : subst] : (((comp @ X31 @ id)) != X31) | ($true = sP109) | ($true = sP110) | ? [X32 : subst,X33 : term] : (((sub @ one @ (push @ X33 @ X32))) != X33) | (induction2lem_lthm != $true)) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (($true = sP104) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP104)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP99) & ! [X34 : term] : (((sub @ X34 @ id)) = X34) & (sP98 != $true))) & (($true = sP99) | ? [X35 : term] : (((sub @ X35 @ id)) != X35) | (sP98 = $true) | (hoasinduction_lem3_lthm != $true)) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X36 : term,X37 : term,X38 : (subst > term > term)] : (? [X39 : subst,X40 : subst,X41 : term] : (((X38 @ (comp @ X40 @ X39) @ (sub @ X41 @ X39))) != ((sub @ (X38 @ X40 @ X41) @ X39))) | (((ap @ (sub @ X37 @ id) @ X36)) != ((lam @ (X38 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X42 : term,X43 : term,X44 : (subst > term > term)] : (! [X45 : subst,X46 : subst,X47 : term] : (((X44 @ (comp @ X46 @ X45) @ (sub @ X47 @ X45))) = ((sub @ (X44 @ X46 @ X47) @ X45))) & (((ap @ (sub @ X43 @ id) @ X42)) = ((lam @ (X44 @ sh @ one)))))) & ((hoasinduction_lem3v2_f = $true) | ? [X48 : term] : ! [X49 : (subst > term > term)] : ? [X50 : subst,X51 : term] : (((X49 @ X50 @ X51)) != ((sub @ X48 @ (push @ X51 @ X50))))) & (! [X52 : term] : ? [X53 : (subst > term > term)] : ! [X54 : subst,X55 : term] : (((X53 @ X54 @ X55)) = ((sub @ X52 @ (push @ X55 @ X54)))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((termmset_lthm = $true) | (! [X56 : term] : (((sub @ X56 @ id)) = X56) & ? [X57 : term] : (((sub @ X57 @ id)) != X57))) & (? [X58 : term] : (((sub @ X58 @ id)) != X58) | ! [X59 : term] : (((sub @ X59 @ id)) = X59) | (termmset_lthm != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X60 : term,X61 : term,X62 : term,X63 : term] : ((X62 = X63) | (((ap @ X62 @ X60)) != ((ap @ X63 @ X61)))) | (apinj1 != $true)) & ((apinj1 = $true) | ? [X64 : term,X65 : term,X66 : term,X67 : term] : ((X66 != X67) & (((ap @ X66 @ X64)) = ((ap @ X67 @ X65))))) & ! [X68 : term] : ? [X69 : d_term] : (((d2term @ X69)) = X68) & (($true = sP93) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP93)) & (! [X70 : term,X71 : (subst > term > subst > $o)] : (($true = ((X71 @ id @ X70 @ id))) | (((sP91 @ X71)) = $true) | (((sP90 @ X71)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ? [X72 : term,X73 : (subst > term > subst > $o)] : (($true != ((X73 @ id @ X72 @ id))) & ($true != ((sP91 @ X73))) & ($true != ((sP90 @ X73))))) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) | ? [X74 : term,X75 : subst] : (((sub @ one @ (push @ X74 @ X75))) != X74)) & (! [X76 : term,X77 : subst] : (((sub @ one @ (push @ X76 @ X77))) = X76) | (axvarcons != $true)) & (($true = sP89) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP89)) & (hoasinduction_lem1_lthm = $true) & (($true = sP87) | ? [X78 : term] : (((sub @ X78 @ id)) != X78) | ($true = sP86) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP87) & ! [X79 : term] : (((sub @ X79 @ id)) = X79) & ($true != sP86))) & ((hoasinduction_lem3a = $true) | ($true != sP83)) & (($true = sP83) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (sP81 != $true)) & ((sP81 = $true) | (substmonoid_lthm != $true)) & (! [X80 : term] : (((sub @ X80 @ id)) = X80) | (axvarid != $true)) & ((axvarid = $true) | ? [X81 : term] : (((sub @ X81 @ id)) != X81)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (! [X82 : term,X83 : term] : ((((sub @ X83 @ sh)) != ((sub @ X82 @ sh))) | (X82 = X83)) | (shinj != $true)) & ((shinj = $true) | ? [X84 : term,X85 : term] : ((((sub @ X84 @ sh)) = ((sub @ X85 @ sh))) & (X84 != X85))) & (termmset_gthm = $true) & ! [X86 : d_term] : (d_one = X86) & ((laminj = $true) | ? [X87 : term,X88 : term] : ((X87 != X88) & (((lam @ X87)) = ((lam @ X88))))) & (! [X89 : term,X90 : term] : ((X89 = X90) | (((lam @ X90)) != ((lam @ X89)))) | (laminj != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3b = $true) | ? [X91 : term] : ! [X92 : (subst > term > term)] : (((sub @ X91 @ (push @ one @ sh))) != ((X92 @ sh @ one)))) & (! [X93 : term] : ? [X94 : (subst > term > term)] : (((X94 @ sh @ one)) = ((sub @ X93 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (($true = sP80) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP80)) & ((induction2 = $true) | (sP78 != $true)) & ((sP78 = $true) | (induction2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP75) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP75)) & ((pushprop_lem1 = $true) | ? [X95 : (term > $o),X96 : term,X97 : (term > $o),X98 : term,X99 : subst] : ((((X97 @ (sub @ X96 @ (push @ X98 @ X99)))) != $true) & (((X95 @ X96)) = $true))) & (! [X100 : (term > $o),X101 : term,X102 : (term > $o),X103 : term,X104 : subst] : (($true = ((X102 @ (sub @ X101 @ (push @ X103 @ X104))))) | (((X100 @ X101)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem0_lthm = $true) | ? [X105 : (term > $o),X106 : term,X107 : subst] : ! [X108 : (term > $o)] : ? [X109 : term] : (((X105 @ (sub @ X109 @ (push @ X106 @ X107)))) != ((X108 @ X109)))) & (! [X110 : (term > $o),X111 : term,X112 : subst] : ? [X113 : (term > $o)] : ! [X114 : term] : (((X110 @ (sub @ X114 @ (push @ X111 @ X112)))) = ((X113 @ X114))) | (pushprop_lem0_lthm != $true)) & (? [X115 : term] : (((sub @ X115 @ id)) != X115) | ? [X116 : (subst > term > subst > $o)] : ! [X117 : (term > $o)] : ? [X118 : term] : (((X116 @ id @ X118 @ id)) != ((X117 @ X118))) | ($true = sP71) | (sP72 = $true) | ($true = sP73) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X119 : term] : (((sub @ X119 @ id)) = X119) & ! [X120 : (subst > term > subst > $o)] : ? [X121 : (term > $o)] : ! [X122 : term] : (((X120 @ id @ X122 @ id)) = ((X121 @ X122))) & ($true != sP71) & (sP72 != $true) & ($true != sP73))) & (((d2subst @ d_id)) = id) & (($true = sP64) | ? [X123 : term] : (((sub @ X123 @ id)) != X123) | ? [X124 : term] : ! [X125 : (subst > term > term)] : ? [X126 : term,X127 : subst] : (((X125 @ X127 @ X126)) != ((sub @ X124 @ (push @ X126 @ X127)))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP64) & ! [X128 : term] : (((sub @ X128 @ id)) = X128) & ! [X129 : term] : ? [X130 : (subst > term > term)] : ! [X131 : term,X132 : subst] : (((sub @ X129 @ (push @ X131 @ X132))) = ((X130 @ X132 @ X131))))) & (((d2subst @ d_id)) = sh) & (($true = sP61) | (sP59 = $true) | ($true = sP60) | ($true = sP62) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP61) & (sP59 != $true) & ($true != sP60) & ($true != sP62))) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (($true = sP44) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP44)) & ((axidl = $true) | ? [X133 : subst] : (((comp @ id @ X133)) != X133)) & (! [X134 : subst] : (((comp @ id @ X134)) = X134) | (axidl != $true)) & (axapp = $true) & (! [X135 : term,X136 : term,X137 : term,X138 : term] : ((((ap @ X137 @ X138)) != ((ap @ X135 @ X136))) | (X136 = X138)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X139 : term,X140 : term,X141 : term,X142 : term] : ((((ap @ X141 @ X142)) = ((ap @ X139 @ X140))) & (X140 != X142))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (($true = sP40) | ? [X143 : term] : (((sub @ X143 @ id)) != X143) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP40) & ! [X144 : term] : (((sub @ X144 @ id)) = X144))) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axscons = $true) | ? [X145 : subst] : (((push @ (sub @ one @ X145) @ (comp @ sh @ X145))) != X145)) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) | (axscons != $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3aa_lthm != $true)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (! [X147 : term] : ? [X148 : (subst > term > term)] : ! [X149 : term,X150 : subst] : (((X148 @ X150 @ X149)) = ((sub @ X147 @ (push @ X149 @ X150)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X151 : term] : ! [X152 : (subst > term > term)] : ? [X153 : term,X154 : subst] : (((X152 @ X154 @ X153)) != ((sub @ X151 @ (push @ X153 @ X154))))) & (($true = sP34) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP34)) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem2v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_gthm = $true) & (! [X155 : (subst > term > subst > $o)] : ? [X156 : (term > $o)] : ! [X157 : term] : (((X156 @ X157)) = ((X155 @ id @ X157 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X158 : (subst > term > subst > $o)] : ! [X159 : (term > $o)] : ? [X160 : term] : (((X159 @ X160)) != ((X158 @ id @ X160 @ id)))) & (pushprop_lem3v2 = $true) & ! [X161 : d_subst,X162 : d_subst] : ((X161 = X162) | (((d2subst @ X161)) != ((d2subst @ X162)))) & (ulamvarind = $true) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) | (termmset != $true)) & ((termmset = $true) | ? [X164 : term] : (((sub @ X164 @ id)) != X164)) & (axabs = $true) & ((hoaslaminj = $true) | ? [X165 : (subst > term > term),X166 : subst,X167 : term,X168 : (subst > term > term)] : (! [X169 : subst,X170 : term,X171 : subst] : (((X168 @ (comp @ X169 @ X171) @ (sub @ X170 @ X171))) = ((sub @ (X168 @ X169 @ X170) @ X171))) & (((X165 @ X166 @ X167)) != ((X168 @ X166 @ X167))) & (((lam @ (X165 @ sh @ one))) = ((lam @ (X168 @ sh @ one)))) & ! [X172 : subst,X173 : term,X174 : subst] : (((sub @ (X165 @ X172 @ X173) @ X174)) = ((X165 @ (comp @ X172 @ X174) @ (sub @ X173 @ X174)))))) & (! [X175 : (subst > term > term),X176 : subst,X177 : term,X178 : (subst > term > term)] : (? [X179 : subst,X180 : term,X181 : subst] : (((X178 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181))) != ((sub @ (X178 @ X179 @ X180) @ X181))) | (((X175 @ X176 @ X177)) = ((X178 @ X176 @ X177))) | (((lam @ (X175 @ sh @ one))) != ((lam @ (X178 @ sh @ one)))) | ? [X182 : subst,X183 : term,X184 : subst] : (((sub @ (X175 @ X182 @ X183) @ X184)) != ((X175 @ (comp @ X182 @ X184) @ (sub @ X183 @ X184))))) | (hoaslaminj != $true)) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & ! [X185 : subst] : ? [X186 : d_subst] : (((d2subst @ X186)) = X185) & (hoasinduction_lem1v2 = $true) & ! [X187 : d_term,X188 : d_term] : ((((d2term @ X187)) != ((d2term @ X188))) | (X187 = X188)) & ((substmonoid = $true) | ? [X189 : subst] : (((comp @ id @ X189)) != X189) | ? [X190 : subst] : (((comp @ X190 @ id)) != X190)) & ((! [X191 : subst] : (((comp @ id @ X191)) = X191) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | (substmonoid != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2 = $true) | (sP25 != $true)) & ((sP25 = $true) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & (! [X193 : term,X194 : term,X195 : term,X196 : term] : ((((ap @ (sub @ X195 @ id) @ X193)) != ((ap @ (sub @ X196 @ id) @ X194))) | (X195 = X196)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ? [X197 : term,X198 : term,X199 : term,X200 : term] : ((((ap @ (sub @ X199 @ id) @ X197)) = ((ap @ (sub @ X200 @ id) @ X198))) & (X199 != X200))) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X201 : term] : ! [X202 : (subst > term > term)] : (((X202 @ sh @ one)) != ((sub @ X201 @ (push @ one @ sh))))) & (! [X203 : term] : ? [X204 : (subst > term > term)] : (((sub @ X203 @ (push @ one @ sh))) = ((X204 @ sh @ one))) | (hoasinduction_lem3b_lthm != $true)) & (! [X205 : (subst > term > subst > $o)] : ? [X206 : (term > $o)] : ! [X207 : term] : (((X206 @ X207)) = ((X205 @ id @ X207 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ? [X208 : (subst > term > subst > $o)] : ! [X209 : (term > $o)] : ? [X210 : term] : (((X208 @ id @ X210 @ id)) != ((X209 @ X210)))) & (! [X211 : subst] : (((comp @ X211 @ id)) = X211) | (axidr != $true)) & ((axidr = $true) | ? [X212 : subst] : (((comp @ X212 @ id)) != X212)) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X213 : term] : (((sub @ X213 @ id)) = X213) & (sP19 != $true) & ! [X214 : (subst > term > subst > $o)] : ? [X215 : (term > $o)] : ! [X216 : term] : (((X214 @ id @ X216 @ id)) = ((X215 @ X216))) & (sP21 != $true) & ($true != sP20))) & (? [X217 : term] : (((sub @ X217 @ id)) != X217) | (sP19 = $true) | ? [X218 : (subst > term > subst > $o)] : ! [X219 : (term > $o)] : ? [X220 : term] : (((X219 @ X220)) != ((X218 @ id @ X220 @ id))) | (sP21 = $true) | ($true = sP20) | (hoasinduction_lthm_3 != $true)) & (pushprop_lem1_gthm = $true) & (axclos = $true) & ((induction = $true) | (sP11 != $true)) & ((sP11 = $true) | (induction != $true)) & ((hoasapinj2 = $true) | ? [X221 : term,X222 : term,X223 : term,X224 : term] : ((X222 != X224) & (((ap @ (sub @ X223 @ id) @ X224)) = ((ap @ (sub @ X221 @ id) @ X222))))) & (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X226 = X228) | (((ap @ (sub @ X225 @ id) @ X226)) != ((ap @ (sub @ X227 @ id) @ X228)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ((induction2_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & (sP8 != $true) & ($true != sP7))) & (? [X230 : term] : (((sub @ X230 @ id)) != X230) | (sP8 = $true) | ($true = sP7) | (induction2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & (! [X231 : (term > $o),X232 : term,X233 : subst,X234 : (term > $o)] : (($true != ((X231 @ X232))) | ($true = ((X234 @ one))) | ? [X235 : term] : (((X231 @ (sub @ X235 @ (push @ X232 @ X233)))) != ((X234 @ X235)))) | ? [X236 : subst,X237 : term] : (((sub @ one @ (push @ X237 @ X236))) != X237) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | (? [X238 : (term > $o),X239 : term,X240 : subst,X241 : (term > $o)] : ((((X238 @ X239)) = $true) & (((X241 @ one)) != $true) & ! [X242 : term] : (((X238 @ (sub @ X242 @ (push @ X239 @ X240)))) = ((X241 @ X242)))) & ! [X243 : subst,X244 : term] : (((sub @ one @ (push @ X244 @ X243))) = X244))) & ! [X245 : d_subst] : (d_id = X245) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1_lthm = $true) | (! [X246 : subst,X247 : term] : (((sub @ one @ (push @ X247 @ X246))) = X247) & ? [X248 : term,X249 : (term > $o),X250 : (term > $o),X251 : subst,X252 : term] : (($true = ((X249 @ X248))) & ($true != ((X250 @ (sub @ X248 @ (push @ X252 @ X251)))))) & ! [X253 : term,X254 : subst] : (((comp @ sh @ (push @ X253 @ X254))) = X254))) & (? [X255 : subst,X256 : term] : (((sub @ one @ (push @ X256 @ X255))) != X256) | ! [X257 : term,X258 : (term > $o),X259 : (term > $o),X260 : subst,X261 : term] : ((((X258 @ X257)) != $true) | (((X259 @ (sub @ X257 @ (push @ X261 @ X260)))) = $true)) | ? [X262 : term,X263 : subst] : (((comp @ sh @ (push @ X262 @ X263))) != X263) | (pushprop_lem1_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(rectify,[],[f463])).
% 3.49/0.96 thf(f465,plain,(
% 3.49/0.96 (! [X0 : term,X1 : subst] : (((comp @ sh @ (push @ X0 @ X1))) = X1) | (axshiftcons != $true)) & ((axshiftcons = $true) | (sK515 != ((comp @ sh @ (push @ sK514 @ sK515))))) & (! [X4 : term,X5 : (term > $o),X6 : (term > $o),X7 : subst] : ((((X6 @ (sub @ (sK516 @ X7 @ X6 @ X5 @ X4) @ (push @ X4 @ X7)))) != ((X5 @ (sK516 @ X7 @ X6 @ X5 @ X4)))) | ($true != ((X6 @ X4))) | ($true = ((X5 @ one)))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X13 : term] : (((sK518 @ X13)) = ((sK519 @ (sub @ X13 @ (push @ sK517 @ sK520))))) & ($true = ((sK519 @ sK517))) & ($true != ((sK518 @ one))))) & (pushprop_gthm = $true) & (((d2term @ d_one)) = ((sub @ (d2term @ d_one) @ (d2subst @ d_id)))) & (induction2lem_gthm = $true) & ((pushprop_lem0 = $true) | ! [X17 : (term > $o)] : (((X17 @ (sK524 @ X17))) != ((sK521 @ (sub @ (sK524 @ X17) @ (push @ sK522 @ sK523)))))) & (! [X19 : (term > $o),X20 : term,X21 : subst] : ! [X23 : term] : (((sK525 @ X21 @ X20 @ X19 @ X23)) = ((X19 @ (sub @ X23 @ (push @ X20 @ X21))))) | (pushprop_lem0 != $true)) & ((induction2lem_lthm = $true) | (! [X24 : term,X25 : subst] : (((comp @ sh @ (push @ X24 @ X25))) = X25) & ! [X26 : subst] : (((comp @ X26 @ id)) = X26) & ($true != sP109) & ($true != sP110) & ! [X27 : subst,X28 : term] : (((sub @ one @ (push @ X28 @ X27))) = X28))) & ((sK527 != ((comp @ sh @ (push @ sK526 @ sK527)))) | (((comp @ sK528 @ id)) != sK528) | ($true = sP109) | ($true = sP110) | (((sub @ one @ (push @ sK530 @ sK529))) != sK530) | (induction2lem_lthm != $true)) & (ulamvarsh = $true) & (hoaslamnotvar = $true) & (hoasinduction_lem1_gthm = $true) & (($true = sP104) | (hoasinduction != $true)) & ((hoasinduction = $true) | ($true != sP104)) & ((hoasinduction_lem3_lthm = $true) | (($true != sP99) & ! [X34 : term] : (((sub @ X34 @ id)) = X34) & (sP98 != $true))) & (($true = sP99) | (sK531 != ((sub @ sK531 @ id))) | (sP98 = $true) | (hoasinduction_lem3_lthm != $true)) & (pushprop = $true) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3_gthm = $true) & (pushprop_lthm_orig = $true) & (axassoc = $true) & (! [X36 : term,X37 : term,X38 : (subst > term > term)] : ((((X38 @ (comp @ (sK533 @ X38) @ (sK532 @ X38)) @ (sub @ (sK534 @ X38) @ (sK532 @ X38)))) != ((sub @ (X38 @ (sK533 @ X38) @ (sK534 @ X38)) @ (sK532 @ X38)))) | (((ap @ (sub @ X37 @ id) @ X36)) != ((lam @ (X38 @ sh @ one))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (! [X45 : subst,X46 : subst,X47 : term] : (((sub @ (sK537 @ X46 @ X47) @ X45)) = ((sK537 @ (comp @ X46 @ X45) @ (sub @ X47 @ X45)))) & (((lam @ (sK537 @ sh @ one))) = ((ap @ (sub @ sK536 @ id) @ sK535))))) & ((hoasinduction_lem3v2_f = $true) | ! [X49 : (subst > term > term)] : (((sub @ sK538 @ (push @ (sK540 @ X49) @ (sK539 @ X49)))) != ((X49 @ (sK539 @ X49) @ (sK540 @ X49))))) & (! [X52 : term] : ! [X54 : subst,X55 : term] : (((sK541 @ X52 @ X54 @ X55)) = ((sub @ X52 @ (push @ X55 @ X54)))) | (hoasinduction_lem3v2_f != $true)) & (hoasinduction_lem3v2_gthm = $true) & (hoaslamnotvar_gthm = $true) & ((termmset_lthm = $true) | (! [X56 : term] : (((sub @ X56 @ id)) = X56) & (((sub @ sK542 @ id)) != sK542))) & ((sK543 != ((sub @ sK543 @ id))) | ! [X59 : term] : (((sub @ X59 @ id)) = X59) | (termmset_lthm != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (! [X60 : term,X61 : term,X62 : term,X63 : term] : ((X62 = X63) | (((ap @ X62 @ X60)) != ((ap @ X63 @ X61)))) | (apinj1 != $true)) & ((apinj1 = $true) | ((sK547 != sK546) & (((ap @ sK546 @ sK544)) = ((ap @ sK547 @ sK545))))) & ! [X68 : term] : (((d2term @ (sK548 @ X68))) = X68) & (($true = sP93) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | ($true != sP93)) & (! [X70 : term,X71 : (subst > term > subst > $o)] : (($true = ((X71 @ id @ X70 @ id))) | (((sP91 @ X71)) = $true) | (((sP90 @ X71)) = $true)) | (hoasinduction_no_psi_cond != $true)) & ((hoasinduction_no_psi_cond = $true) | ((((sK550 @ id @ sK549 @ id)) != $true) & (((sP91 @ sK550)) != $true) & ($true != ((sP90 @ sK550))))) & (hoasinduction_lem2v2_gthm = $true) & ((axvarcons = $true) | (sK551 != ((sub @ one @ (push @ sK551 @ sK552))))) & (! [X76 : term,X77 : subst] : (((sub @ one @ (push @ X76 @ X77))) = X76) | (axvarcons != $true)) & (($true = sP89) | (hoasapinj1_lthm != $true)) & ((hoasapinj1_lthm = $true) | ($true != sP89)) & (hoasinduction_lem1_lthm = $true) & (($true = sP87) | (sK553 != ((sub @ sK553 @ id))) | ($true = sP86) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP87) & ! [X79 : term] : (((sub @ X79 @ id)) = X79) & ($true != sP86))) & ((hoasinduction_lem3a = $true) | ($true != sP83)) & (($true = sP83) | (hoasinduction_lem3a != $true)) & ((substmonoid_lthm = $true) | (sP81 != $true)) & ((sP81 = $true) | (substmonoid_lthm != $true)) & (! [X80 : term] : (((sub @ X80 @ id)) = X80) | (axvarid != $true)) & ((axvarid = $true) | (((sub @ sK554 @ id)) != sK554)) & (ulamvar1 != $true) & (pushprop_lem2v2_gthm = $true) & (! [X82 : term,X83 : term] : ((((sub @ X83 @ sh)) != ((sub @ X82 @ sh))) | (X82 = X83)) | (shinj != $true)) & ((shinj = $true) | ((((sub @ sK555 @ sh)) = ((sub @ sK556 @ sh))) & (sK556 != sK555))) & (termmset_gthm = $true) & ! [X86 : d_term] : (d_one = X86) & ((laminj = $true) | ((sK558 != sK557) & (((lam @ sK557)) = ((lam @ sK558))))) & (! [X89 : term,X90 : term] : ((X89 = X90) | (((lam @ X90)) != ((lam @ X89)))) | (laminj != $true)) & (substmonoid_gthm = $true) & (hoasinduction_lem2_gthm = $true) & ((hoasinduction_lem3b = $true) | ! [X92 : (subst > term > term)] : (((X92 @ sh @ one)) != ((sub @ sK559 @ (push @ one @ sh))))) & (! [X93 : term] : (((sK560 @ X93 @ sh @ one)) = ((sub @ X93 @ (push @ one @ sh)))) | (hoasinduction_lem3b != $true)) & (($true = sP80) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | ($true != sP80)) & ((induction2 = $true) | (sP78 != $true)) & ((sP78 = $true) | (induction2 != $true)) & (((d2subst @ d_id)) = ((push @ (d2term @ d_one) @ (d2subst @ d_id)))) & (($true = sP75) | (hoasinduction_lem3aaa != $true)) & ((hoasinduction_lem3aaa = $true) | ($true != sP75)) & ((pushprop_lem1 = $true) | (($true != ((sK563 @ (sub @ sK562 @ (push @ sK564 @ sK565))))) & ($true = ((sK561 @ sK562))))) & (! [X100 : (term > $o),X101 : term,X102 : (term > $o),X103 : term,X104 : subst] : (($true = ((X102 @ (sub @ X101 @ (push @ X103 @ X104))))) | (((X100 @ X101)) != $true)) | (pushprop_lem1 != $true)) & ((pushprop_lem0_lthm = $true) | ! [X108 : (term > $o)] : (((X108 @ (sK569 @ X108))) != ((sK566 @ (sub @ (sK569 @ X108) @ (push @ sK567 @ sK568)))))) & (! [X110 : (term > $o),X111 : term,X112 : subst] : ! [X114 : term] : (((sK570 @ X112 @ X111 @ X110 @ X114)) = ((X110 @ (sub @ X114 @ (push @ X111 @ X112))))) | (pushprop_lem0_lthm != $true)) & ((((sub @ sK571 @ id)) != sK571) | ! [X117 : (term > $o)] : (((sK572 @ id @ (sK573 @ X117) @ id)) != ((X117 @ (sK573 @ X117)))) | ($true = sP71) | (sP72 = $true) | ($true = sP73) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | (! [X119 : term] : (((sub @ X119 @ id)) = X119) & ! [X120 : (subst > term > subst > $o)] : ! [X122 : term] : (((X120 @ id @ X122 @ id)) = ((sK574 @ X120 @ X122))) & ($true != sP71) & (sP72 != $true) & ($true != sP73))) & (((d2subst @ d_id)) = id) & (($true = sP64) | (((sub @ sK575 @ id)) != sK575) | ! [X125 : (subst > term > term)] : (((X125 @ (sK578 @ X125) @ (sK577 @ X125))) != ((sub @ sK576 @ (push @ (sK577 @ X125) @ (sK578 @ X125))))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP64) & ! [X128 : term] : (((sub @ X128 @ id)) = X128) & ! [X129 : term] : ! [X131 : term,X132 : subst] : (((sK579 @ X129 @ X132 @ X131)) = ((sub @ X129 @ (push @ X131 @ X132)))))) & (((d2subst @ d_id)) = sh) & (($true = sP61) | (sP59 = $true) | ($true = sP60) | ($true = sP62) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | (($true != sP61) & (sP59 != $true) & ($true != sP60) & ($true != sP62))) & (hoaslamnotvar_lthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (($true = sP46) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | ($true != sP46)) & (($true = sP44) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | ($true != sP44)) & ((axidl = $true) | (((comp @ id @ sK580)) != sK580)) & (! [X134 : subst] : (((comp @ id @ X134)) = X134) | (axidl != $true)) & (axapp = $true) & (! [X135 : term,X136 : term,X137 : term,X138 : term] : ((((ap @ X137 @ X138)) != ((ap @ X135 @ X136))) | (X136 = X138)) | (apinj2 != $true)) & ((apinj2 = $true) | ((((ap @ sK581 @ sK582)) = ((ap @ sK583 @ sK584))) & (sK582 != sK584))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (($true = sP40) | (((sub @ sK585 @ id)) != sK585) | (hoasinduction_lem3v2_lthm != $true)) & ((hoasinduction_lem3v2_lthm = $true) | (($true != sP40) & ! [X144 : term] : (((sub @ X144 @ id)) = X144))) & (pushprop_lem2v2_lthm = $true) & (((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) != $true) & (pushprop_lem1v2_gthm = $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y3 @ Y4) = (Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))))) & ((axscons = $true) | (sK586 != ((push @ (sub @ one @ sK586) @ (comp @ sh @ sK586))))) & (! [X146 : subst] : (((push @ (sub @ one @ X146) @ (comp @ sh @ X146))) = X146) | (axscons != $true)) & (hoasapnotvar = $true) & ((hoasinduction_lem3aa_lthm = $true) | ($true != sP36)) & (($true = sP36) | (hoasinduction_lem3aa_lthm != $true)) & (hoasapnotvar_lthm = $true) & (((d2term @ d_one)) = ((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one)))) & (one = ((d2term @ d_one))) & (! [X147 : term] : ! [X149 : term,X150 : subst] : (((sK587 @ X147 @ X150 @ X149)) = ((sub @ X147 @ (push @ X149 @ X150)))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X152 : (subst > term > term)] : (((X152 @ (sK590 @ X152) @ (sK589 @ X152))) != ((sub @ sK588 @ (push @ (sK589 @ X152) @ (sK590 @ X152)))))) & (($true = sP34) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP34)) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((d2subst @ d_id)) = ((comp @ (d2subst @ d_id) @ (d2subst @ d_id)))) & ((hoasinduction_lem2v2 = $true) | ($true != sP31)) & (($true = sP31) | (hoasinduction_lem2v2 != $true)) & (hoasapnotvar_gthm = $true) & (! [X155 : (subst > term > subst > $o)] : ! [X157 : term] : (((sK591 @ X155 @ X157)) = ((X155 @ id @ X157 @ id))) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X159 : (term > $o)] : (((X159 @ (sK593 @ X159))) != ((sK592 @ id @ (sK593 @ X159) @ id)))) & (pushprop_lem3v2 = $true) & ! [X161 : d_subst,X162 : d_subst] : ((X161 = X162) | (((d2subst @ X161)) != ((d2subst @ X162)))) & (ulamvarind = $true) & (! [X163 : term] : (((sub @ X163 @ id)) = X163) | (termmset != $true)) & ((termmset = $true) | (sK594 != ((sub @ sK594 @ id)))) & (axabs = $true) & ((hoaslaminj = $true) | (! [X169 : subst,X170 : term,X171 : subst] : (((sK598 @ (comp @ X169 @ X171) @ (sub @ X170 @ X171))) = ((sub @ (sK598 @ X169 @ X170) @ X171))) & (((sK595 @ sK596 @ sK597)) != ((sK598 @ sK596 @ sK597))) & (((lam @ (sK595 @ sh @ one))) = ((lam @ (sK598 @ sh @ one)))) & ! [X172 : subst,X173 : term,X174 : subst] : (((sK595 @ (comp @ X172 @ X174) @ (sub @ X173 @ X174))) = ((sub @ (sK595 @ X172 @ X173) @ X174))))) & (! [X175 : (subst > term > term),X176 : subst,X177 : term,X178 : (subst > term > term)] : ((((sub @ (X178 @ (sK599 @ X178) @ (sK600 @ X178)) @ (sK601 @ X178))) != ((X178 @ (comp @ (sK599 @ X178) @ (sK601 @ X178)) @ (sub @ (sK600 @ X178) @ (sK601 @ X178))))) | (((X175 @ X176 @ X177)) = ((X178 @ X176 @ X177))) | (((lam @ (X175 @ sh @ one))) != ((lam @ (X178 @ sh @ one)))) | (((sub @ (X175 @ (sK602 @ X175) @ (sK603 @ X175)) @ (sK604 @ X175))) != ((X175 @ (comp @ (sK602 @ X175) @ (sK604 @ X175)) @ (sub @ (sK603 @ X175) @ (sK604 @ X175)))))) | (hoaslaminj != $true)) & (induction2_gthm = $true) & (hoasinduction_lem3b_gthm = $true) & (lamnotvar = $true) & (($true = sP28) | (hoasinduction_lem2 != $true)) & ((hoasinduction_lem2 = $true) | ($true != sP28)) & ! [X185 : subst] : (((d2subst @ (sK605 @ X185))) = X185) & (hoasinduction_lem1v2 = $true) & ! [X187 : d_term,X188 : d_term] : ((((d2term @ X187)) != ((d2term @ X188))) | (X187 = X188)) & ((substmonoid = $true) | (sK606 != ((comp @ id @ sK606))) | (((comp @ sK607 @ id)) != sK607)) & ((! [X191 : subst] : (((comp @ id @ X191)) = X191) & ! [X192 : subst] : (((comp @ X192 @ id)) = X192)) | (substmonoid != $true)) & (((d2term @ d_one)) = ((lam @ (d2term @ d_one)))) & ((hoasinduction_lem3v2 = $true) | (sP25 != $true)) & ((sP25 = $true) | (hoasinduction_lem3v2 != $true)) & (axvarshift = $true) & (! [X193 : term,X194 : term,X195 : term,X196 : term] : ((((ap @ (sub @ X195 @ id) @ X193)) != ((ap @ (sub @ X196 @ id) @ X194))) | (X195 = X196)) | (hoasapinj1 != $true)) & ((hoasapinj1 = $true) | ((((ap @ (sub @ sK611 @ id) @ sK609)) = ((ap @ (sub @ sK610 @ id) @ sK608))) & (sK610 != sK611))) & (hoasinduction_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (((var @ (d2term @ d_one))) != $true) & (apnotvar = $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X202 : (subst > term > term)] : (((sub @ sK612 @ (push @ one @ sh))) != ((X202 @ sh @ one)))) & (! [X203 : term] : (((sK613 @ X203 @ sh @ one)) = ((sub @ X203 @ (push @ one @ sh)))) | (hoasinduction_lem3b_lthm != $true)) & (! [X205 : (subst > term > subst > $o)] : ! [X207 : term] : (((sK614 @ X205 @ X207)) = ((X205 @ id @ X207 @ id))) | (hoasinduction_lem0 != $true)) & ((hoasinduction_lem0 = $true) | ! [X209 : (term > $o)] : (((sK615 @ id @ (sK616 @ X209) @ id)) != ((X209 @ (sK616 @ X209))))) & (! [X211 : subst] : (((comp @ X211 @ id)) = X211) | (axidr != $true)) & ((axidr = $true) | (((comp @ sK617 @ id)) != sK617)) & (hoaslamnotap_gthm = $true) & (pushprop_lthm = $true) & ((hoasinduction_lthm_3 = $true) | (! [X213 : term] : (((sub @ X213 @ id)) = X213) & (sP19 != $true) & ! [X214 : (subst > term > subst > $o)] : ! [X216 : term] : (((sK618 @ X214 @ X216)) = ((X214 @ id @ X216 @ id))) & (sP21 != $true) & ($true != sP20))) & ((sK619 != ((sub @ sK619 @ id))) | (sP19 = $true) | ! [X219 : (term > $o)] : (((X219 @ (sK621 @ X219))) != ((sK620 @ id @ (sK621 @ X219) @ id))) | (sP21 = $true) | ($true = sP20) | (hoasinduction_lthm_3 != $true)) & (pushprop_lem1_gthm = $true) & (axclos = $true) & ((induction = $true) | (sP11 != $true)) & ((sP11 = $true) | (induction != $true)) & ((hoasapinj2 = $true) | ((sK623 != sK625) & (((ap @ (sub @ sK624 @ id) @ sK625)) = ((ap @ (sub @ sK622 @ id) @ sK623))))) & (! [X225 : term,X226 : term,X227 : term,X228 : term] : ((X226 = X228) | (((ap @ (sub @ X225 @ id) @ X226)) != ((ap @ (sub @ X227 @ id) @ X228)))) | (hoasapinj2 != $true)) & (hoasinduction_lem1 = $true) & ((induction2_lthm = $true) | (! [X229 : term] : (((sub @ X229 @ id)) = X229) & (sP8 != $true) & ($true != sP7))) & ((((sub @ sK626 @ id)) != sK626) | (sP8 = $true) | ($true = sP7) | (induction2_lthm != $true)) & (pushprop_lem2v2 = $true) & (hoasinduction_lem2_lthm = $true) & (hoasapinj1_gthm = $true) & (! [X231 : (term > $o),X232 : term,X233 : subst,X234 : (term > $o)] : (($true != ((X231 @ X232))) | ($true = ((X234 @ one))) | (((X231 @ (sub @ (sK627 @ X234 @ X233 @ X232 @ X231) @ (push @ X232 @ X233)))) != ((X234 @ (sK627 @ X234 @ X233 @ X232 @ X231))))) | (sK629 != ((sub @ one @ (push @ sK629 @ sK628)))) | (pushprop_lem1v2_lthm != $true)) & ((pushprop_lem1v2_lthm = $true) | ((($true = ((sK630 @ sK631))) & ($true != ((sK633 @ one))) & ! [X242 : term] : (((sK630 @ (sub @ X242 @ (push @ sK631 @ sK632)))) = ((sK633 @ X242)))) & ! [X243 : subst,X244 : term] : (((sub @ one @ (push @ X244 @ X243))) = X244))) & ! [X245 : d_subst] : (d_id = X245) & (hoaslaminj_gthm = $true) & (lamnotap != $true) & (((d2term @ d_one)) = ((ap @ (d2term @ d_one) @ (d2term @ d_one)))) & ((hoasinduction_lem3aa = $true) | ($true != sP1)) & (($true = sP1) | (hoasinduction_lem3aa != $true)) & ((pushprop_lem1_lthm = $true) | (! [X246 : subst,X247 : term] : (((sub @ one @ (push @ X247 @ X246))) = X247) & ((((sK635 @ sK634)) = $true) & ($true != ((sK636 @ (sub @ sK634 @ (push @ sK638 @ sK637)))))) & ! [X253 : term,X254 : subst] : (((comp @ sh @ (push @ X253 @ X254))) = X254))) & ((sK640 != ((sub @ one @ (push @ sK640 @ sK639)))) | ! [X257 : term,X258 : (term > $o),X259 : (term > $o),X260 : subst,X261 : term] : ((((X258 @ X257)) != $true) | (((X259 @ (sub @ X257 @ (push @ X261 @ X260)))) = $true)) | (sK642 != ((comp @ sh @ (push @ sK641 @ sK642)))) | (pushprop_lem1_lthm != $true)) & (pushprop_lem0_gthm = $true) & (hoaslamnotap_lthm = $true)),
% 3.49/0.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK514,sK515,vAPP,sK517,sK518,sK519,sK520,sK521,sK522,sK523,vAPP,vAPP,sK526,sK527,sK528,sK529,sK530,sK531,vAPP,vAPP,vAPP,sK535,sK536,sK537,sK538,vAPP,vAPP,vAPP,sK542,sK543,sK544,sK545,sK546,sK547,vAPP,sK549,sK550,sK551,sK552,sK553,sK554,sK555,sK556,sK557,sK558,sK559,vAPP,sK561,sK562,sK563,sK564,sK565,sK566,sK567,sK568,vAPP,vAPP,sK571,sK572,vAPP,vAPP,sK575,sK576,vAPP,vAPP,vAPP,sK580,sK581,sK582,sK583,sK584,sK585,sK586,vAPP,sK588,vAPP,vAPP,vAPP,sK592,vAPP,sK594,sK595,sK596,sK597,sK598,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP,sK606,sK607,sK608,sK609,sK610,sK611,sK612,vAPP,vAPP,sK615,vAPP,sK617,vAPP,sK619,sK620,vAPP,sK622,sK623,sK624,sK625,sK626,vAPP,sK628,sK629,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,sK640,sK641,sK642]),skolemize(X2,sK514),skolemize(X3,sK515),skolemize(X2,sK111 @ X0),skolemize(X9,sK517),skolemize(X10,sK518),skolemize(X11,sK519),skolemize(X12,sK520),skolemize(X14,sK521),skolemize(X15,sK522),skolemize(X16,sK523),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X29,sK526),skolemize(X30,sK527),skolemize(X31,sK528),skolemize(X32,sK529),skolemize(X33,sK530),skolemize(X35,sK531),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X42,sK535),skolemize(X43,sK536),skolemize(X44,sK537),skolemize(X48,sK538),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X57,sK542),skolemize(X58,sK543),skolemize(X64,sK544),skolemize(X65,sK545),skolemize(X66,sK546),skolemize(X67,sK547),skolemize(X2,sK111 @ X0),skolemize(X72,sK549),skolemize(X73,sK550),skolemize(X74,sK551),skolemize(X75,sK552),skolemize(X78,sK553),skolemize(X81,sK554),skolemize(X84,sK555),skolemize(X85,sK556),skolemize(X87,sK557),skolemize(X88,sK558),skolemize(X91,sK559),skolemize(X2,sK111 @ X0),skolemize(X95,sK561),skolemize(X96,sK562),skolemize(X97,sK563),skolemize(X98,sK564),skolemize(X99,sK565),skolemize(X105,sK566),skolemize(X106,sK567),skolemize(X107,sK568),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X115,sK571),skolemize(X116,sK572),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X123,sK575),skolemize(X124,sK576),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X133,sK580),skolemize(X139,sK581),skolemize(X140,sK582),skolemize(X141,sK583),skolemize(X142,sK584),skolemize(X143,sK585),skolemize(X145,sK586),skolemize(X2,sK111 @ X0),skolemize(X151,sK588),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X158,sK592),skolemize(X2,sK111 @ X0),skolemize(X164,sK594),skolemize(X165,sK595),skolemize(X166,sK596),skolemize(X167,sK597),skolemize(X168,sK598),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X189,sK606),skolemize(X190,sK607),skolemize(X197,sK608),skolemize(X198,sK609),skolemize(X199,sK610),skolemize(X200,sK611),skolemize(X201,sK612),skolemize(X2,sK111 @ X0),skolemize(X2,sK111 @ X0),skolemize(X208,sK615),skolemize(X2,sK111 @ X0),skolemize(X212,sK617),skolemize(X2,sK111 @ X0),skolemize(X217,sK619),skolemize(X218,sK620),skolemize(X2,sK111 @ X0),skolemize(X221,sK622),skolemize(X222,sK623),skolemize(X223,sK624),skolemize(X224,sK625),skolemize(X230,sK626),skolemize(X2,sK111 @ X0),skolemize(X236,sK628),skolemize(X237,sK629),skolemize(X238,sK630),skolemize(X239,sK631),skolemize(X240,sK632),skolemize(X241,sK633),skolemize(X248,sK634),skolemize(X249,sK635),skolemize(X250,sK636),skolemize(X251,sK637),skolemize(X252,sK638),skolemize(X255,sK639),skolemize(X256,sK640),skolemize(X262,sK641),skolemize(X263,sK642)],[f464])).
% 3.49/0.96 thf(f1010,plain,(
% 3.49/0.96 (hoasinduction_lem1 = $true)),
% 3.49/0.96 inference(cnf_transformation,[],[f465])).
% 3.49/0.96 thf(f1033,plain,(
% 3.49/0.96 (((var @ (d2term @ d_one))) != $true)),
% 3.49/0.96 inference(cnf_transformation,[],[f465])).
% 3.49/0.96 thf(f1077,plain,(
% 3.49/0.96 (one = ((d2term @ d_one)))),
% 3.49/0.96 inference(cnf_transformation,[],[f465])).
% 3.49/0.96 thf(f1141,plain,(
% 3.49/0.96 ( ! [X86 : d_term] : ((d_one = X86)) )),
% 3.49/0.96 inference(cnf_transformation,[],[f465])).
% 3.49/0.96 thf(f1170,plain,(
% 3.49/0.96 ( ! [X68 : term] : ((((d2term @ (sK548 @ X68))) = X68)) )),
% 3.49/0.96 inference(cnf_transformation,[],[f465])).
% 3.49/0.96 thf(f1216,plain,(
% 3.49/0.96 (hoasinduction_lem1 != ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y4 @ Y2) @ (sub @ Y1 @ Y2) @ Y3) => (Y0 @ Y4 @ Y1 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))))),
% 3.49/0.96 inference(cnf_transformation,[],[f8])).
% 3.49/0.96 thf(f1219,plain,(
% 3.49/0.96 (((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y4 @ Y2) @ (sub @ Y1 @ Y2) @ Y3) => (Y0 @ Y4 @ Y1 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))) != $true)),
% 3.49/0.96 inference(definition_unfolding,[],[f1216,f1010])).
% 3.49/0.96 thf(f1244,plain,(
% 3.49/0.96 ($false = (((^[Y0 : subst > term > subst > $o]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4)) => (Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y4 @ Y2) @ (sub @ Y1 @ Y2) @ Y3) => (Y0 @ Y4 @ Y1 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ term @ (^[Y1 : term]: ((hoasvar @ id @ Y1 @ id) => (Y0 @ id @ Y1 @ id)))) => (!! @ term @ (^[Y1 : term]: ((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))) @ sK643)))),
% 3.49/0.96 inference(sigma_proxy_clausification,[],[f1219])).
% 3.49/0.96 thf(f1245,plain,(
% 3.49/0.96 ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK643 @ Y1 @ Y0 @ (comp @ Y2 @ Y3)) => (sK643 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3)))))))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK643 @ (comp @ Y3 @ Y1) @ (sub @ Y0 @ Y1) @ Y2) => (sK643 @ Y3 @ Y0 @ (comp @ Y1 @ Y2))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK643 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK643 @ id @ Y0 @ id)))))))) = $false)),
% 3.49/0.96 inference(beta-eta_normalization,[],[f1244])).
% 3.49/0.96 thf(f1246,plain,(
% 3.49/0.96 ($false = (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK643 @ (comp @ Y3 @ Y1) @ (sub @ Y0 @ Y1) @ Y2) => (sK643 @ Y3 @ Y0 @ (comp @ Y1 @ Y2))))))))))) => ((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK643 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK643 @ id @ Y0 @ id))))))))),
% 3.49/0.96 inference(imp_proxy_clausification,[],[f1245])).
% 3.49/0.96 thf(f1257,plain,(
% 3.49/0.96 ((((!! @ term @ (^[Y0 : term]: ((hoasvar @ id @ Y0 @ id) => (sK643 @ id @ Y0 @ id)))) => (!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK643 @ id @ Y0 @ id)))))) = $false)),
% 3.49/0.96 inference(imp_proxy_clausification,[],[f1246])).
% 3.49/0.96 thf(f1268,plain,(
% 3.49/0.96 ($false = ((!! @ term @ (^[Y0 : term]: ((var @ Y0) => (sK643 @ id @ Y0 @ id))))))),
% 3.49/0.96 inference(imp_proxy_clausification,[],[f1257])).
% 3.49/0.96 thf(f1273,plain,(
% 3.49/0.96 ($false = (((^[Y0 : term]: ((var @ Y0) => (sK643 @ id @ Y0 @ id))) @ sK644)))),
% 3.49/0.96 inference(sigma_proxy_clausification,[],[f1268])).
% 3.49/0.96 thf(f1274,plain,(
% 3.49/0.96 ($false = (((var @ sK644) => (sK643 @ id @ sK644 @ id))))),
% 3.49/0.96 inference(beta-eta_normalization,[],[f1273])).
% 3.49/0.96 thf(f1276,plain,(
% 3.49/0.96 (((var @ sK644)) = $true)),
% 3.49/0.96 inference(imp_proxy_clausification,[],[f1274])).
% 3.49/0.96 thf(f3448,plain,(
% 3.49/0.96 ( ! [X0 : d_term] : ((one = ((d2term @ X0)))) )),
% 3.49/0.96 inference(constrained_superposition,[],[f1077,f1141])).
% 3.49/0.96 thf(f3494,plain,(
% 3.49/0.96 ($true != ((var @ one)))),
% 3.49/0.96 inference(forward_demodulation,[],[f1033,f1077])).
% 3.49/0.96 thf(f3514,plain,(
% 3.49/0.96 ( ! [X68 : term] : ((one = X68)) )),
% 3.49/0.96 inference(forward_demodulation,[],[f1170,f3448])).
% 3.49/0.96 thf(f3566,plain,(
% 3.49/0.96 ($true = ((var @ one)))),
% 3.49/0.96 inference(constrained_superposition,[],[f1276,f3514])).
% 3.49/0.96 thf(f3567,plain,(
% 3.49/0.96 $false),
% 3.49/0.96 inference(forward_subsumption_resolution,[],[f3566,f3494])).
% 3.49/0.96 % SZS output end Proof for theBenchmark
% 3.49/0.96 % (538996)------------------------------
% 3.49/0.96 % (538996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.49/0.96 % (538996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/0.96 % (538996)CaDiCaL version: 2.1.3
% 3.49/0.96 % (538996)Termination reason: Refutation
% 3.49/0.96 % (538996)Time elapsed: 0.135 s
% 3.49/0.96 % (538996)Peak memory usage: 17 MB
% 3.49/0.96 % (538996)Instructions burned: 379 (million)
% 3.49/0.96 % (538752)Success in time 0.666 s
% 3.49/0.96 % Vampire exiting
%------------------------------------------------------------------------------